Scale Analysis of Blocking Events from 2002 to 2004: A Case Study of an Unusually Persistent Blocking Event Leading to a Heat Wave in the Gulf of Alaska during August 2004

H. Athar; Anthony R. Lupo

doi:10.1155/2010/610263

Scale Analysis of Blocking Events from 2002 to 2004: A Case Study of an Unusually Persistent Blocking Event Leading to a Heat Wave in the Gulf of Alaska during August 2004

Athar, H.;Lupo, Anthony R. 2010-08-25 00:00:00 Hindawi Publishing Corporation Advances in Meteorology Volume 2010, Article ID 610263, 15 pages doi:10.1155/2010/610263 Research Article Scale Analysis of Blocking Events from 2002 to 2004: A Case Study of an Unusually Persistent Blocking Event Leading to a Heat Wave in the Gulf of Alaska during August 2004 1 2 H. Athar and Anthony R. Lupo Center of Excellence for Climate Change Research, King Abdulaziz University, P.O. Box 80208, Jeddah 21589, Saudi Arabia Department of Soil, Environmental and Atmospheric Sciences, 302 ABNR Building, University of Missouri, Columbia, MO 65211, USA Correspondence should be addressed to H. Athar, ahussain1@kau.edu.sa Received 19 February 2010; Revised 14 May 2010; Accepted 28 June 2010 Academic Editor: Luis Gimeno Copyright © 2010 H. Athar and A. R. Lupo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The climatology of northern hemisphere blocking events is presented assessing the relative contributions of the planetary and synoptic scales to 500 hPa heights in order to determine the proportion of blocks dominated by a single-scale. The heights were averaged over a region encompassing the block, and then compared with corresponding monthly mean values. If planetary- scale or synoptic-scale heights are greater than the monthly mean, the block is called single-scale dominant. In the study, 79% of blocks were single-scale dominant, whereas the remaining 21% of events were alternating-scale prominent. This proportion varied by season with winter (summer) events being synoptic (planetary) scale dominant. The stability of blocks is also examined to determine if two stability indicators were useful in the assessment of the character of planetary and synoptic-scale ﬂows. These quantities are area integrated enstrophy, and the maximum value of stream function gradients within the block region. The analysis of a prolonged block occurring in the Gulf of Alaska during August 2004 shows the planetary-scale is unstable during block onset and then stabilizes during the mature stage. The synoptic-scale played a dominant role in destabilizing the planetary-scale during the mature stage of the block initiating decay. 1. Introduction incorporate the high-frequency (synoptic-scale) dynamics into the quasigeostropic barotropic vorticity equation to The development of a predominantly mid-tropospheric, obtain the blocking events for prescribed forcings [6]. Both meridional circulation pattern within a sector of the north- models oﬀer numerical solutions of the nonlinear barotropic ern or southern hemisphere is commonly referred to as vorticity equation. Other studies include both scales in their blocking (e.g., [1, 2]). This stagnation of the zonal ﬂow gives modeled analysis of the blocking events [7, 8]. rise to diﬃculties in operational weather forecasts for regions From a synoptic-dynamic point of view, and making within and near the blocked region (e.g., [3, 4]). Developing use of surface and upper air data provided by reanalyses, an understanding of the processes that leads to the formation numerous case studies have been carried out leading to of such circulation patterns is thus of signiﬁcant interest. valuable insight into the forcing mechanisms that may be TheCharney andDeVoremodel provides aframe- important during various stages of the blocking (e.g., [9– work for incorporating the low frequency (planetary-scale) 17]). In several of these case studies, the question of the role dynamics into the quasigeostrophic barotropic vorticity of planetary-scale versus synoptic-scale processes during the equation in order to obtain the blocking patterns for the various stages of the blocking life-cycle is addressed. given forcings using the concept of stable equilibria [5]. The In recent years, several studies also have examined the Shutts model, on the other hand, provides a framework to relative role of each scale and their interactions as well as the 2 Advances in Meteorology nature of the interactions themselves (e.g., [9, 18, 19], and study, the details of the synoptic and the stability analyses references cited therein). In addition to these studies, and of a selected blocking event are presented in Section 4.The those of earlier pioneers (e.g., [20–23]), a consistent picture emphasis in this case study is on the relative role of the emerges that the synoptic-scale plays an important role in the planetary- and synoptic-scales to quantify the ﬂow stability. life-cycle of the blocking events. These studies show that the A summary of the three-year study and the results for the magnitude of the synoptic-scale forcing is generally large as case study are presented in Section 5. compared to the planetary-scale forcing. While the studies referenced in the above paragraph 2. Data and Methods do not downplay the role of the planetary-scale, they do focus more on the role of the synoptic-scale contributions. 2.1. Data Set. The data set used here was the National Center However, others have shown that the planetary-scale is very for Environmental Prediction (NCEP) and National Center inﬂuential in the life-cycle of the blocking events (e.g., [24– for Atmospheric Research (NCAR) gridded reanalyses data ◦ ◦ 27]). For instance, in their model study, [24]suggested [31, 32]. These data were provided on the 2.5 by 2.5 that the blocking regimes will break down when there is a latitude-longitude grids available on 17 mandatory levels substantial change in the planetary-scale ﬂow regime. Then, from 1000 hPa to 10 hPa at 6-h intervals on daily basis. [25] focus on the role of the planetary-scale deformation A three-year period leading up to the year the case study in a preconditioned environment during the formation occurred was examined. of the blocking events (see also [28]). These two studies together support the notion that while the planetary-scale 2.2. Blocking Deﬁnition. The blocking criterion of [33]will may not itself lead to the block formation and maintenance, be used to determine the onset and termination times for the nevertheless this scale may provide a favorable environment blocking events studied. The blocking events may be sub- in the interaction with the synoptic-scale environment. Thus, divided into onset, intensiﬁcation, maintenance, and decay a substantial change in the planetary-scale ﬂow regime may stages (e.g., [12, 14, 15]). Onset is the period before the not support blocking and these events would decay fairly block formation, while intensiﬁcation (decay) is represented quickly. by a general increase (decrease) in center point heights. In this paper, the scale characteristics of all the midlati- Maintenance is generally represented by periods where the tude blocking events occurring in the northern hemisphere center point time evolution is close to zero. In brief, these (NH) during the three-year period 2002–2004 are examined studies employ a combined and extended set of conditions in order to assess the relative role of the synoptic- and set forth earlier by the subjective deﬁnition of [1, 2], and the planetary-scales. We present a detailed characterization of objective criterion of Lejenas and Okland [34]. the blocking events during the above three-year period The 500 hPa height at 1200 UTC is used as a diagnostic based on the relative role of planetary-scale and/or synoptic- atmospheric variable. Brieﬂy, the blocking detection crite- scale contributions. The aim is to provide a reference rion includes: (i) satisfying the Rex [1, 2] criteria for the document that may be used to select suitable blocking events blocking with the minimum duration of the blocking as 5 as examples for the three classes of the quasigeostrophic days; (ii) a negative or small positive LO 83 index [34], must barotropic vorticity equation solutions mentioned earlier in be present on a time-longitude or Hovmol ¨ ler diagram; (iii) this section. conditions (i) and (ii) satisﬁed for 24 h after onset to 24 h It is further pointed out that abrupt changes in the before termination; (iv) the blocking should be pole ward planetary-scale environment can lead to the onset or decay of 35 N, and the ridge should have an amplitude of greater of the blocking. In order to accomplish this, we will look than 5 latitude; and (v) blocking onset is described to occur at the area integrated regional enstrophy and maximum of when condition (iv) and either conditions (i) or (ii) are the absolute value of geostrophic stream function gradient, satisﬁed, (v) termination is designated at the time the event as diagnostic tools in a selected blocking case study. These fails condition (v) for a 24 h period or longer. This procedure are then calculated using both the planetary- and synoptic- is used to detect the blocking events at 500 hPa and deﬁnes scale components of the ﬂow. These indicators of stability the blocking duration with start and end dates. were originally developed by [29, 30], and will be applied, The blocking intensity (BI) is deﬁned as [33] to our knowledge, for the ﬁrst time, to a NH case study. Also, the time evolution of the planetary/synoptic-scale height and BI = 100[(Z max /Z ) − 1]. (1) of the stability indicators will be studied. In contrast to many previous studies mentioned in this section, we concentrate In (1), Z max is the maximum 500 hPa height in the closed on examining the relative role of both the planetary- and anticyclone region or on a line associated with the ridge, synoptic- scales (and determining the ﬂow stability). and Z is the subjectively chosen 500 hPa height contour The paper outline is as follows. In Section 2,wepresent encompassing the upstream and downstream troughs. The the details of the data set used and describe the method- BI measures the amplitude of the ﬂow around the block. For ologies, including the stability indicators. In Section 3,we further details and examples, the reader is referred to [33]. elaborate the results of the predominance of synoptic- versus As mentioned before, this study will point out that planetary-scale contributions analysis performed for all the changes in the planetary-scale and synoptic-scale ﬂow midlatitude blocking events occurring during the three-year regimes can be related to the onset and the decay of the period (2002–2004) in the NH. As a representative case blocking events. The techniques used to extract planetary- Advances in Meteorology 3 and synoptic-scale heights have been used in many of Table 1: Assessment of the blocking domain size variation, for the 500 hPa monthly average planetary-scale height, during August the previous studies [11, 12, 14], and will be only brieﬂy 2004, for the selected blocking event. presented. A second-order, two-dimensional ﬁlter was used on the Monthly planetary-scale reanalysis heights in order to separate the planetary-scale D (latitude × longitude) height averaged over the heights (Z ) from the observed 500 hPa height value (Z ) blocking domain D (m) [35]. The ﬁlter performs a center weighted symmetric ﬁnite ◦ ◦ 40 × 60 element calculation in spatial dimensions. The ﬁltered data ◦ ◦ 50 × 70 retain 2%, 44%, and 80% of the original signal at wavelengths ◦ ◦ ◦ 60 × 80 of 3000 km, 4500 km, and 6000 km at 45 N. The synoptic- ◦ ◦ 70 × 90 scale heights (Z ) were obtained using Z = Z − Z . More s s p ◦ ◦ 80 × 100 details regarding the use of the ﬁltering procedure can be 5728 found in [11]. Then, the planetary-scale height ﬁelds were averaged ◦ ◦ over 40 latitude by 60 longitude box within the blocking sector to produce one number for each block detection. where f = 2Ω sin(φ) is the Coriolis parameter with latitude This process is analogous to the procedure used by [36]in denoted by φ. The variable Ω is the rotation speed of earth deriving the wave amplitude index, with the exception that −5 −1 (Ω is taken as 7.292 × 10 rad s ), and the acceleration we ﬁltered the ﬁelds ﬁrst and then averaged them within a due to the gravity is g.The ψ is the total stream function, so box. They averaged the entire midlatitude height ﬁeld into a the quantity represented by max|∇ψ| may also be referred band and then ﬁltered to obtain a single number for the time as maximum geosptrophic wind speed. The maximum value period for the NH. of this quantity is taken within the blocking domain D and is meant to reﬂect the meridional variations in the 2.3. Blocking Area Integrated Regional Enstrophy. In [29], ﬂow. The behavior of this indicator of stability may have a blocking was deﬁned as a meridional perturbation that simple physical meaning. In the case of vanishing zonal ﬂow, destabilizes the zonal ﬂow. Starting from the barotropic meridional variations will have the dominant contribution. vorticity equation, the blocking area integrated enstrophy is It may thus acquire a relative maximum positive value during suggested as a measure for the change in the zonal ﬂow that the blocking state. For more details, see [30]. may lead to the blocking. Here, we make use of the conjecture in [29] which suggests a relationship between the sum of the positive eigenvalues of the linearization operator of the 2.5. The Eﬀect of Domain Size Variation. The domain D used barotropic ﬂow and the blocking domain integrated regional ◦ ◦ in (2) is deﬁned as the 40 latitude by 60 longitude box as enstrophy, that is, mentioned in Section 2.3. The latitude span is 40 which + encompasses the latitudinal extent of the blocking event in λ ≈ σ y dx dy,(2) the midlatitudes. The longitude is centered at the blocking onset center and depends on the longitude extent of the where σ =−∂u/∂y and D is the blocking domain. A brief selected blocking event. ◦ ◦ discussion of how to obtain (2)isprovidedin Appendix A, Enlarging the blocking area domain D from 40 × 60 following [29]. The blocking domain D is deﬁned as a does not lead to any sizable deviation in the planetary- latitude and longitude box as mentioned above. We will call scale height when averaged over it. A representative example the right hand side of (2) as the blocking area integrated is displayed in Table 1, where the impact of enlarging the regional enstrophy (IRE) here. We can regard the IRE as a blocking area domain D is assessed for the 500 hPa monthly stability indicator. This has not been used in the literature average planetary-scale height for a selected blocking event, before as a blocking diagnostic for observed case studies, and our case study. The blocking event occurred during 05– ◦ ◦ ◦ ◦ (2) will be used to determine the relative stability of the ﬂow 28 August 2004 over 40 N–80 N and 160 E–260 E. The in region D. Higher positive values of the IRE correspond to Table 1 indicates that the maximum variation in the monthly more unstable ﬂow and vice versa. For a discussion of time average planetary-scale height value is less than 1% relative to ◦ ◦ evolution of the eigenmodes of the barotropic ﬂow including 40 ×60 box averaging value. Similar magnitude of variation ◦ ◦ the eﬀect of β,see [37]. relative to 40 × 60 box averaging value was found when we varied the latitude only, the longitude only, and the selected 2.4. Maximum of the Absolute Value of the Stream Function blocking event, over the blocking domain D. Gradient. We have calculated numerically another indicator It is thus concluded that the blocking domain averaged of ﬂow regime stability following [30], that is, the maximum results for planetary-scale height presented in this study are of absolute value of the gradient of the geosptrophic stream not sensitive to the choice of the size of the blocking domain function (max|∇ψ|). Here D within the range of latitude and longitude values speciﬁed in Table 1. The synoptic scale height, being a small-scale gZ length is somewhat sensitive to the variations of the blocking ψ =,(3) domain D (of the order of 15%–20%). 4 Advances in Meteorology 3. Details of the Three-Year Study with the NH climatological track movement of the blocking events [41]. The results presented in Appendix B are sensitive In this section, we ﬁrst present the main characteristics and to variations in domain size D (see Section 2.5). synoptic description of the blocking events for the three-year The ﬁltered planetary-scale height was averaged over this duration 2002–2004 and then the scale contribution charac- latitude and longitude box. Next, the synoptic-scale height teristics of these events using the methodology presented in for each grid point of the domain was calculated following Section 2. the procedure outlined in Section 2, and then averaged over the box. In the Appendix B, the entry labeled positive in the planetary-scale height column occurs if, at least, 3.1. The Blocking Events during 2002–2004. The number of this height averaged over the mature stage of the blocking NH blocking events lasting 5 days or more during the three- event is larger than the corresponding monthly mean height year period (2002–2004) under study are as follows: 2002 value. A similar deﬁnition was used for a positive entry in (41), 2003 (48), and 2004 (37). During this three-year period, synoptic-scale column. If the blocking event fell within two the total number of blocking events is 126. The highest months such as from 25 July through 15 August, the scale number of blocking events occurred during the year 2003 contribution dominance was determined by comparing the (38%). The detected blocking events during the above three- behavior of the averaged heights relative to the two month year period are in line with the ﬁndings in [38]. mean value. The synoptic details of the blocking events during The monthly mean was chosen simply to provide a the three-year period in tabular form are presented in zero reference point from which to assess which scale was Appendix B. The blocking events’ details include the start prominent during the life-cycle of the event. There is no date, the end date, the duration, the BI as well as the reason to assume apriori that the size or sign of the monthly geographic location. Table 2 summarizes the characteristics value for each scale would be related to whether or not a of the blocking events during the three-year period. blocking event formed since the monthly mean would vary Table 2 indicates that, in general, the overall character of annually and would depend on where the box is located and blocking events taken from this three-year period is similar to the size of the box used. The block formation mechanisms the climatologies of [33, 39] in that there were more winter also depend on the inter basin diﬀerences [41, 42]. season (Jan–Mar) events and more Atlantic region (290 E– Based on our above subjectively chosen criterion for 30 E) events than in the other regions. Also, winter season comparison of heights, the blocking events are categorized events were, in general, stronger than those of summer into the following three types: season (Jul–Sep) events and oceanic region events were stronger than those found over the continents. Additionally, (i) planetary-scale height dominant events, the events from this three-year period were more numerous, (ii) synoptic-scale height dominant events, slightly weaker, and more persistent than those found in [39] (iii) alternating-scale height dominant events. which is consistent with the results of [38, 40]. During the three-year period (2002–2004), the longest In Section 4, a representative example of a blocking event duration (35 days) blocking event occurred over the conti- ◦ ◦ ◦ ◦ with planetary-scale height dominant behavior (category (i)) nental area (100 W–80 Wand 40 E–140 E) during 4 June is discussed in detail. Representative examples of category (ii) through 9 July, 2002, with BI = 1.99 (weak event). It is event synoptic-scale height dominance, and (iii) alternating-scale number 24 in Table 4. During the same three-year period, height dominance, in which both the height scales dominate the strongest blocking event occurred over the Paciﬁc area in a time series fashion, are described next in some detail in ◦ ◦ (140 E–100 W), with BI = 5.39 with a duration of 6 days this section. (19 March through 25 March 2003). It is event number 11 in Figure 1 displays a single-scale contribution behavior Table 5. case for a selected blocking event, corresponding to event The synoptic description of the blocking events displayed number 8 in Table 6. This event occurred over the Atlantic in Appendix B is used subsequently in this section to assess with BI = 4.62, indicating that it is a strong event [39]. The the behavior of the scale contributions and to perform the event lasted for 5 days (15th March 2004 through 20th March detailed stability analysis of a selected blocking event in the 2004). The block longitude center at the onset was located next section and this event is identiﬁed in italics. at 0 E. A single (synoptic)-scale dominance can be noted, during the mature stage, as the monthly mean value for 3.2. Scale Contribution Comparison for the Blocking Events synoptic-scale is 0.03361 m, whereas the monthly mean value during 2002–2004. The longitude at block onset was for the planetary-scale is 5633 m (compare with Figure 4). obtained from the blocking event archive ([38], Appendix B). Figure 2 displays an alternating-scale contribution Then the blocking event box was formed relative to the behavior for a selected blocking event, corresponding to blocking onset center location by adding 30 in the east event number 3 in Table 4. This event occurred over the and the west directions. The latitude span was taken as 40 Paciﬁc with BI = 4.50, which is a strong event [39]. The centered at the midlatitude in accordance with discussion in event lasted for 21 days (07th January 2002 through 28th ◦ ◦ Section 2. The stationary 40 × 60 latitude longitude box January 2002). The block longitude center at the onset size selection is in line with the climatological NH spatial was located at 250 E. We note thatincontrastto Figure 4, distribution of the blocking events [34]. It is also in line there is no single height dominance during the mature Advances in Meteorology 5 Table 2: A summary of the occurrence and character of the blocking events for the calendar years 2002–2004. Blocking parameters in each cell are blocking events/durations (days)/BI. Summer Fall Winter Spring Total Atlantic 9/12.7/2.30 17/10.7/3.27 16/11.1/3.52 16/10.0/2.78 58/10.9/3.03 Paciﬁc 10/9.4/2.28 7/10.6/3.36 16/8.0/3.52 9/11.6/2.65 42/9.5/3.01 Continental 10/12.9/2.18 6/5.7/2.64 4/8.4/2.88 6/15.5/2.44 26/11.1/2.46 Total 29/11.6/2.25 30/9.7/3.16 36/9.3/3.44 31/11.5/2.67 126/10.5/2.90 Average planetary-scale height (m) Average planetary-scale height (m) versus time (days) for 500 hPa versus time (days) for 500 hPa 1 6 11 16 21 26 31 1 6 11 16 21 26 31 Time (days for March 2004) Time (days for January 2002) (a) (a) Average synoptic-scale height (m) Average synoptic-scale height (m) versus time (days) for 500 hPa versus time (days) for 500 hPa 0.6 0.4 0.4 0.2 0.2 −0.2 −0.2 −0.4 −0.4 −0.6 −0.6 −0.8 −0.8 1 6 11 16 21 26 31 1 6 11 16 21 26 31 Time (days for March 2004) Time (days for January 2002) (b) (b) Figure 1: (a) The blocking area averaged planetary-scale 500 hPa Figure 2: (a) The blocking area averaged planetary-scale 500 hPa ◦ ◦ ◦ ◦ height (m) versus time (days), for a stationary box (20 Nto60 N height (m) versus time (days), for a stationary box (20 Nto60 N ◦ ◦ ◦ ◦ and 330 Eto30 E), in the midlatitude northern hemispheric ﬂow. and 290 E to 230 E), in the midlatitude northern hemispheric ﬂow. The dashed dotted horizontal line deﬁnes the monthly mean value The dashed dotted horizontal line deﬁnes the monthly mean value for the planetary-scale height. The left vertical line marks the for the planetary-scale height. The left vertical upward arrow marks beginning, whereas the right vertical line marks the end of the the beginning, whereas the right vertical upward arrow marks the selected blocking event; (b) same as Figure 1(a) except for the end of the selected blocking event; (b) same as Figure 2(a) except synoptic-scale height. for the synoptic-scale height. Average synoptic-scale height (m) Average planetary-scale height (m) Average planetary-scale height (m) Average synoptic-scale height (m) 6 Advances in Meteorology 90N Average planetary-scale height (m) 5400 5400 5500 versus time (days) for 500 hPa 80N 70N 60N 5700 5650 5750 5600 5800 5650 50N 40N 5750 30N 150E 160E 170E 180 170W 160W 150W 140W 130W 120W 110W 100W 90W (a) 05 August 2004 90N Onset Mature stage Decay 80N 1 6 11 16 21 26 31 70N Time (days for August 2004) (a) 60N Average synoptic-scale height (m) 50N versus time (days) for 500 hPa 5650 5900 0.5 40N 0.4 30N 150E 160E 170E 180 170W 160W 150W 140W 130W 120W 110W 100W 90W 0.3 (b) 13 August 2004 0.2 90N 0.1 80N 70N −0.1 −0.2 60N 5600 −0.3 50N 1 6 11 16 21 26 31 40N Time (days for August 2004) 30N (b) 150E 160E 170E 180 170W 160W 150W 140W 130W 120W 110W 100W 90W (c) 27 August 2004 Figure 4: (a) The blocking area averaged planetary-scale 500 hPa ◦ ◦ height (m) versus time (days), for a stationary box (40 Nto80 N Figure 3: (a) The 500 hPa mean daily height. The cross indicates the ◦ ◦ and 160 E to 260 E), in the midlatitude northern hemispheric center of blocking at the onset. The blocking domain boundary is ﬂow. The dashed dotted horizontal line deﬁnes the monthly mean marked around the center by thick solid black line. The continuous value for the planetary-scale height. The left vertical line marks curves represent height contours at 50 m interval, for 05 August the beginning, whereas the right vertical line marks the end of 2004. Note the meridional (split)-ﬂow character of the block; (b) the selected blocking event; (b) same as Figure 4aexceptfor the for 13 August 2004; (c) for 27 August 2004. synoptic-scale height. 3.3. Analysis Summary. Table 3 summarizes our ﬁndings stage of the selected blocking event. Both the planetary- and for the blocking events with single and alternating-scale synoptic-scale heights rise and fall occur during the life-cycle dominance for the three-year period over the entire NH. of the blocking event relative to their respective monthly The maximum (minimum) number of blocking event having mean values. The blocking events displaying this type of planetary-scale dominance occurs during 2003 (2002) in height-time evolution are categorized as the alternating-scale NH. The minimum (maximum) number of blocking events height dominance behavior blocking events. However, this having synoptic-scale dominance occurs during 2003 (2002). category of the blocking events consists of only 21% of the The seasonal results show that the winter and spring season total detected blocking events during the three-year period events are more synoptic-scale dominant, while summer under study. and fall events are strongly planetary-scale dominant. The Average synoptic-scale height (m) Average planetary-scale height (m) Advances in Meteorology 7 −1 Planetary-scale IRE Planetary-scale max|∇ψ|(ms ) −10 versus time (days) for 500 hPa ×10 versus time (days) for 500 hPa 2.2 10.89 10.88 1.8 10.87 1.6 1.4 10.86 1.2 10.85 10.84 0.8 1 6 11 16 21 26 31 1 6 11 16 21 26 31 Time (days for August 2004) Time (days for August 2004) (a) (a) Synoptic-scale IRE −1 −11 Synoptic-scale max|∇ψ|(ms ) ×10 versus time (days) for 500 hPa versus time (days) for 500 hPa 1 6 11 16 21 26 31 1 6 11 16 21 26 31 Time (days for August 2004) Time (days for August 2004) (b) (b) Figure 5: (a) The blocking area averaged enstrophy using (2)for Figure 6: (a) The 500 hPa planetary-scale max|∇ψ| versus time the blocking event displayed in Figure 3 which occurred during 05– ◦ ◦ ◦ ◦ (days) for a stationary box (40 Nto80 N and 160 E to 260 E) in 28 August 2004. The relative stability level changes at onset (02– the midlatitude northern hemispheric ﬂow. The dash dotted line 05 August) and at decay (20–28 August) stages. The dash dotted deﬁnes the mean monthly value for max|∇ψ|. The left vertical line horizontal line deﬁnes the monthly mean value. The left vertical line marks the beginning, whereas the right vertical line marks the end marks the beginning, whereas the right vertical line marks the end of the selected blocking event; (b) same as Figure 6(a) except that of the selected blocking event; (b) same as Figure 5(a) except for the now the synoptic-scale eﬀect is taken into account. synoptic-scale height. events occurring during the three-year study period. We thus seasonal variation of synoptic dominance is consistent with perform next a detailed case study for the single-scale height the seasonal variations in the number and strength of midlatitude cyclones (e.g., [43]). Table 3 is valid only for the dominance as a representative case study. blocking detection method, and scale categorization used in this study. 4. Case Study A prominent feature of our study is the ﬁnding that the scale contributions of a vast majority of the blocking In this section, detailed discussions of the synoptic aspects as events are governed by the dominance of the single-scale well as the scale and the stability analysis of the ﬂow for an height scale. This category of blocking events thus constitutes unusually persistent blocking event that led to a heat wave a representative category of all the midlatitude blocking in the Gulf of Alaska during August 2004 are presented [44]. 2 −2 2 −2 Blocking area IRE (m s ) Blocking area IRE (m s ) −1 max|∇ψ|(ms ) −1 max|∇ψ|(ms ) 8 Advances in Meteorology Table 3: Planetary-, synoptic-, and alternating-scale dominance split-ﬂow block deepened as the blocking intensiﬁed, as did results for the three-year period (2002–2004) analysis and for each the ridge (Figure 3(b)). The last several days of the period season performed in this study, over the entire NH. The number showed this feature propagating over the Alaskan Peninsula and percentage for each year or season and the total is displayed. as the new ridge ampliﬁed over the Bering Sea upstream of the dying event. The block became fully suppressed by 27 (a) August as the mean 500 hPa height ﬁeld became nearly zonal Year Planetary Synoptic Alternating in character (Figure 3(c)). 2002 15/37% 17/41% 9/22% 2003 22/46% 11/23% 15/31% 4.2. Scale Analysis. Figure 4(a) displays the 500 hPa blocking 2004 18/49% 16/43% 3/8% area averaged planetary-scale height for the entire life-cycle Total 55/44% 44/35% 27/21% of the block. During the mature stage of the block life-cycle, the height attains its relative maximum value (5778 m). Note (b) the occurrence of a positive height during the mature stage Season Planetary Synoptic Alternating (05–20 August 2004) of the blocking as the monthly mean Winter 12/33% 17/48% 7/19% value for the entire month of August lies at 5748 m only. The Spring 12/39% 14/45% 5/16% average heights within the box start falling until just before Summer 16/55% 6/21% 7/24% the block decay (day number 21). This suggests changes in the behavior of the planetary-scale ﬂow regime. Fall 15/50% 7/23% 8/27% Figure 4(b) displays the 500 hPa synoptic-scale height for the entire life-cycle of the selected blocking event. During the decay stage (20–28 August), the temporal activity of the migratory synoptic-scale heights is greater than during the The synoptic analysis is performed ﬁrst, and then a scale and onset and mature stages since during the decay stage, the stability analysis of the NH ﬂow region where the selected synoptic-scale environment becomes unstable. The oscilla- blocking event occurred. tory behavior is indicative of area averaged synoptic-scale For the case study presented in the next section, a ridge-trough dominance for the advection of the heat wave diﬀerent latitude-longitude window is used to accommodate at the given isobaric level. A positive diﬀerence corresponds the unusually large spatial extent of the selected blocking to the high pressure system/ridge, whereas the negative event. diﬀerence corresponds to the formation of a trough. This blocking event is the second longest blocking event 4.1. Synoptic Analysis. The selected blocking event occurred in the east Paciﬁc region for the calendar year 2004. This during 02 August through 28 August 2004. Following [33], ﬁnding is in agreement with the estimates of longevity by the block onset and intensiﬁcation stage was during 02–05 [45]. This unusually prolonged blocking event impacted August, its mature stage was during 05–20 August and its the downstream regional weather over the continental US decay stage was during 20–28 August. The blocking ridge as well. The west cost of the mainland continental US lasted for 23.5 days. The blocking ﬂow was located in the experienced mild summer during August 2004 [46]. This is ◦ ◦ ◦ ◦ region encompassing 40 Nto80 N and 160 E to 260 E, with yet another example of the occurrence of mid-tropospheric block longitude at the onset was located at 210 E. This is level blocking aﬀecting the regional weather upstream and/or eventnumber26in Table 6 in Appendix B.Above normal downstream of the event (e.g., [47]). For details of clima- surface temperatures and below normal precipitation was tological aspects of downstream weather impacts associated reported during August over the entire Alaska region [44]. with the blockings, see also [48]. The height variations (taken at 500 hPa) that lead to identiﬁcation of the blocking on an upper air chart can conveniently be quantiﬁed in terms of BI. According to the 4.3. Stability Analysis. Figure 5(a) displays the time evolu- deﬁnition of BI [33], the BI for the considered blocking event tion of the blocking area integrated regional enstrophy (IRE) averaged over its entire life-cycle is 2.44, implying that it is a for the 500 hPa planetary-scale height. Comparing this with moderate strength blocking event. Figure 4(a) that gives the time evolution of the planetary- Figure 3 indicates that during the block onset, a merid- scale height, it is noted that between 21 and 23 August, ional (split)-ﬂow pattern became prevalent in the 500 hPa the IRE increases considerably (peaking on 22 August), mean height ﬁeld around the position marked with cross. indicating the rise in the instability in the planetary-scale In the Gulf of Alaska, a lower height value on the order of ﬂow which corresponds well in time with the fall in the 5600 m was located directly east of the main higher height amplitude of the planetary-scale height during the same value. Of particular interest, however, is to note that this period. trough remained quasistationary over the Gulf of Alaska Calculation of the IRE following (2) for entire life-cycle while the ridge ampliﬁed (see Figure 3(b)—the 5750 m of the blocking event under study indicates a relationship contour was located over Alaska following the period from between these values and the trend displayed in Figure 4(a), Figure 3(a)). This feature appeared to be the central focus where blocking area averaged planetary-scale height is for action in the blocking region. The four days beginning displayed. From Figure 5(a), it is noted that the area averaged on 10 August 2004 show the lower height responsible for the enstrophy reaches a minimum shortly after block onset (after Advances in Meteorology 9 Table 4: Planetary-scale and synoptic-scale dominance results for all the blocking events during the year 2002. The italic entries are the selected case studies. See text for details. Event no. Start date End date Duration (days) Planetary-scale dominance Synoptic-scale dominance 1 02Jan. 11Jan. 9.5 Positive Negative 2 03Jan. 08Jan. 5 Positive Negative 3 07 Jan. 28 Jan. 21 Alternating Alternating 4 13 Jan. 27 Jan. 14 Negative Positive 5 25Jan. 30Jan. 5 Negative Positive 6 30Jan. 05Feb. 6 Negative Positive 7 31Jan. 06Feb. 5.5 Negative Positive 8 06 Feb. 11 Feb. 5 Alternating Alternating 9 02 Feb. 12 Feb. 10 Negative Positive 10 12 Feb. 17 Feb. 5 Negative Positive 11 11 Feb. 28 Feb. 17 Alternating Alternating 12 01 Mar. 07 Mar. 6 Positive Negative 13 04 Mar. 21 Mar. 17 Negative Positive 14 06 Mar. 21 Mar. 15 Positive Negative 15 09 Mar. 28 Mar. 19 Negative Positive 16 01 Apr. 18 Apr. 17 Positive Negative 17 02 Apr. 07 Apr. 5 Negative Positive 18 15 Apr. 24 Apr. 9 Positive Negative 19 19 Apr. 04 May 13.5 Negative Positive 20 23 Apr. 03 May 8.5 Negative Positive 21 10 May 19 May 9 Positive Negative 22 09 May 29 May 20 Positive Negative 23 01 Jun. 10 Jun. 9 Alternating Alternating 24 04 Jun. 09 Jul. 35 Alternating Alternating 25 22 Jun. 30 Jun. 8 Negative Positive 26 30 Jun. 08 Jul. 9 Positive Negative 27 06 Jul. 17 Jul. 9 Negative Positive 28 30 Jul. 07 Aug. 8 Positive Negative 29 01 Aug. 11 Aug. 10 Positive Negative 30 15 Aug. 28 Aug. 13 Negative Positive 31 07 Sep. 18 Sep. 11 Alternating Alternating 32 23 Sep. 28 Sep. 5 Positive Negative 33 20 Sep. 02 Oct. 12 Positive Negative 34 06 Oct. 15 Oct. 9 Positive Negative 35 13 Oct. 18 Oct. 5 Alternating Alternating 36 22 Oct. 03 Nov. 12 Negative Positive 37 25 Oct. 30 Oct. 5 Negative Positive 38 01 Nov. 06 Nov. 5.5 Alternating Alternating 39 18 Nov. 25 Nov. 7 Positive Negative 40 20 Nov. 11 Dec. 21 Negative Positive 41 26 Nov. 28 Dec. 32.5 Alternating Alternating 2 August) and is at a relative minimum during the mature supports this observation. This is also consistent with the stage of this blocking event. The appearance of relatively view that, in a quasibarotropic ﬂow, the planetary-scale ﬂow small peaks on 5 and 15 August indicate the decreasing should be strongly barotropic [49]. Figure 5(a) indicates that role played by the planetary-scale heights in advection of after the onset of the blocking state, the block IRE attains the (quasi stationary) ridge in terms of its location and relatively lower positive values. orientation. Inspection of series of 500 hPa height plots (such The calculation for the IRE was also performed by as those displayed in Figure 3) for the chosen blocking event taking into account the eﬀects of synoptic-scale eddies and 10 Advances in Meteorology Table 5: Same as Table 4 except for the year 2003. Event no. Start date End date Duration (days) Planetary-scale dominance Synoptic-scale dominance 1 02Jan. 10Jan. 8 Negative Positive 2 12Jan. 18Jan. 6 Positive Negative 3 14Jan. 20Jan. 6 Positive Negative 4 23 Jan. 06 Feb. 14.5 Alternating Alternating 5 25Jan. 01Feb. 7 Positive Negative 6 09 Feb. 15 Feb. 6 Alternating Alternating 7 09 Feb. 22 Feb. 13 Positive Negative 8 20Feb. 02Mar. 11 Negative Positive 9 20 Feb. 26 Feb. 6 Negative Positive 10 07 Mar. 18 Mar. 10.5 Positive Negative 11 19 Mar. 25 Mar. 6 Negative Positive 12 29 Mar. 08 Apr. 9.5 Negative Positive 13 04 Apr. 13 Apr. 9 Negative Positive 14 14 Apr. 22 Apr. 8.5 Positive Negative 15 26 Apr. 06 May 10 Negative Positive 16 01 May 22 May 21 Alternating Alternating 17 12 May 23 May 11 Positive Negative 18 13 May 28 May 15 Alternating Alternating 19 25 May 12 Jun. 17 Positive Negative 20 03 Jun. 12 Jun. 9 Negative Positive 21 04 Jun. 22 Jun. 18.5 Negative Positive 22 13 Jun. 24 Jun. 11 Positive Negative 23 24 Jun. 05 Jul. 11 Positive Negative 24 28 Jun. 07 Jul. 9 Alternating Alternating 25 09 Jul. 10 Aug. 32 Positive Negative 26 11 Jul. 19 Jul. 7.5 Alternating Alternating 27 18 Jul. 05 Aug. 18 Positive Negative 28 06 Aug. 13 Aug. 7 Alternating Alternating 29 12 Aug. 26 Aug. 14 Alternating Alternating 30 24 Aug. 13 Sep. 21.5 Alternating Alternating 31 01 Sep. 10 Sep. 9 Positive Negative 32 10 Sep. 20 Sep. 10 Positive Negative 33 11 Sep. 20 Sep. 9 Positive Negative 34 13 Sep. 25 Sep. 12 Negative Positive 35 24 Sep. 10 Oct. 16 Alternating Alternating 36 25 Aug. 07 Sep. 12 Alternating Alternating 37 28 Sep. 05 Oct. 7 Positive Negative 38 28 Sep. 05 Oct. 7 Alternating Alternating 39 13 Oct. 24 Oct. 11 Negative Positive 40 29 Oct. 08 Nov. 9.5 Positive Negative 41 01 Nov. 06 Nov. 5 Positive Negative 42 05 Nov. 16 Nov. 11 Positive Negative 43 27 Oct. 04 Nov. 7 Alternating Alternating 44 04 Dec. 10 Dec. 6.5 Alternating Alternating 45 16 Dec. 21 Dec. 5 Positive Negative 46 19 Dec. 26 Dec. 7 Positive Negative 47 28 Nov. 05 Dec. 8 Positive Negative 48 29 Nov. 04 Dec. 6 Alternating Alternating Advances in Meteorology 11 Table 6: Same as Table 5 except for the year 2004. Event no. Start date End date Duration (days) Planetary-scale dominance Synoptic-scale dominance 1 27Dec. 09Jan. 13 Positive Negative 2 02Jan. 11Jan. 9.5 Negative Positive 3 23Jan. 05Feb. 13 Negative Positive 4 18Jan. 18Feb. 31 Positive Negative 5 10 Feb. 14 Mar. 31.5 Alternating Alternating 6 14 Feb. 28 Feb. 14 Negative Positive 7 28 Feb. 05 Mar. 5 Alternating Alternating 8 15Mar. 20Mar. 5 Negative Positive 9 17Mar. 22Mar. 5 Negative Positive 10 22 Mar. 29 Mar. 7.5 Negative Positive 11 26 Mar. 12 Apr. 17 Negative Positive 12 11 Apr. 16 Apr. 5 Negative Positive 13 14 Apr. 22 Apr. 7.5 Positive Negative 14 16 Apr. 26 Apr. 10 Positive Negative 15 20 Apr. 13 May 23 Alternating Alternating 16 06 May 13 May 7.5 Negative Positive 17 10 May 25 May 15.5 Positive Negative 18 12 May 01 Jun. 20 Negative Positive 19 05 Jun. 10 Jun. 5 Negative Positive 20 26 Jun. 10 Jul. 14 Positive Negative 21 02 Jul. 13 Jul. 10.5 Negative Positive 22 06 Jul. 11 Jul. 5 Negative Positive 23 12 Jul. 24 Jul. 11.5 Positive Negative 24 27 Jul. 01 Aug. 5 Positive Negative 25 27 Jul. 15 Aug. 18.5 Positive Negative 26 05 Aug. 28 Aug. 23.5 Positive Negative 27 09 Aug. 15 Aug. 6.5 Positive Negative 28 06 Sep. 11 Sep. 5 Negative Positive 29 08 Oct. 15 Oct. 7 Positive Negative 30 12 Oct. 26 Oct. 14 Negative Positive 31 18 Oct. 28 Oct. 10 Negative Positive 32 02 Nov. 13 Nov. 11 Positive Negative 33 04 Nov. 26 Nov. 22 Positive Negative 34 21 Nov. 26 Nov. 5 Positive Negative 35 09 Dec. 14 Dec. 5 Positive Negative 36 19 Dec. 25 Dec. 6 Positive Negative 37 19 Dec. 26 Dec. 7 Negative Positive is displayed in Figure 5(b). At mid tropospheric level, the to the time evolution of the average planetary-scale height synoptic-scale IRE does not exhibit a clear trend in any of displayed in Figure 4(a). Following [30], it may be concluded the three stages of blocking. The only trend that is obvious is that if max|∇ψ| depicts relatively positive changes, then that near the onset (after day 5), the IRE attains a relatively the height variation is becoming increasingly unstable. lower value, thus characterizing the relative stability of the Figure 6(a) indicates that the planetary-scale ﬂow remains ﬂow at the synoptic-scale. The IRE gives a relative change largely stable during the blocking since the relative positive only andisthusalone notsuﬃcient to identify the blocking variation implied by max|∇ψ| is less than 0.2%, when event unambiguously. averaged over the blocking life-cycle. The temporal behavior of another stability indicator Figure 6(b) is similar to Figure 6(a) except that now is displayed in Figure 6(a) for the blocking area averaged we make use of the synoptic-scale height to calculate the planetary-scale height. As mentioned in Section 2.4, ψ max|∇ψ|. The appearance of the relatively sharp rise during acquires a relative maximum value, above the corresponding the decay stage, above the corresponding monthly mean monthly mean, during the blocking state and is similar value, is consistently explainable in our picture of the relative 12 Advances in Meteorology role of the two scales. The planetary-scale ﬂow is more stable dominance whereas 35% have synoptic-scale domi- during the blocking; the synoptic-scale ridge formation nance in scale contributions. The remaining 21% of destabilizes it thus causing the ﬂow to revert back to the zonal the blocking events are categorized as alternating- conﬁguration. This implies that once the blocking event height scale dominance blocking events. Blocking established itself, the planetary-scale ﬂow is relatively more events from December to May (June–November) predictable in the present case study. were more synoptic (planetary) scale dominant. (ii) The sensitivity of our results to the blocking domain size variation was studied. When the blocking 4.4. Discussion. Changes in the nature of the planetary- ◦ ◦ ◦ domain size was varied from 40 × 60 to 80 × scale ﬂow may be related with the block onset and decay 100 , the deviation of the planetary-scale height that [15, 24, 25, 50]. The planetary-scale provides a favorable is averaged over it was found to be less than 1%. environment for the blocking event to occur, in spite of This indicates that our conclusions are relatively the large contributions by the synoptic-scale ﬂow and the insensitive to the blocking domain size variation for interaction components of the forcing. the planetary-scale height within the above latitude The supporting evidence for the change in planetary- and longitude range. scale ﬂow regimes comes from examining the IRE (ﬂow stability) calculations. The IRE values (Figure 5(a))fallto Next, summary of the synoptic analysis as well as the scale a relative minimum during the mature stage of the block and the stability analysis of an unusually prolonged and a in the blocked region in agreement with what would be moderately strong blocking event occurring in the Gulf of expected for the selected blocking event (with planetary-scale Alaska during August 2004, is presented. This blocking event dominance) implying that the planetary-scale ﬂow became persisted in Gulf of Alaska for the entire month of August unstable around the time of the block onset and decay. resulting in a heat wave (up to 5 C higher than normal 1971– Further, the prominence of the synoptic-scale in winter 2000 mean temperatures in Alaska region). Our analyzed events versus the planetary-scale prominence in the summer results are as follows. events follows from the annual variation in the number and strength of midlatitude cyclones. It also follows that most (i) A synoptic study of this event was performed of the studies referenced above [9, 11, 12], studied winter through visual inspection of a series of NCEP-NCAR season events, and as such focused on the contribution of reanalysis data generated plots of observed 500 hPa the synoptic-scale in the blocking events. On the other hand, heights and was concluded that the blocking is a even though summer season events were dominated by the ◦ ◦ positive height anomaly encompassing 40 N–80 N planetary-scale, the forcing itself may still be dominated by ◦ ◦ and 160 E–260 E. The detailed scale contribution the synoptic-scale as was found by [14], or it is possible analyses, performed using explicit calculations, for that this study chose an event represented by the minority the speciﬁc case study, conﬁrm this. This positive of warm season types. This fact points to the need for more comparison lends conﬁdence in our diagnostic anal- case studies of the blocking events. ysis procedure outlined in Section 2. (ii) Synoptically, a gradual ampliﬁcation of positive 5. Summary and Conclusions height value during the ﬁrst half of the blocking event life-cycle (5–15 August 2004) and then later a de- In this section, the ﬁndings for the three-year scale contri- ampliﬁcation during later half of the blocking event butions study are summarized ﬁrst, and then results for the life-cycle (15–28 August 2004) based on same obser- case study are presented. The scale analysis is performed by vational procedure, was noticed. Our Figure 4(a) decomposing the observed 500 hPa height into the blocking conﬁrms this ﬁnding. area averaged planetary-scale and the synoptic-scale heights (iii) Subtracting the planetary mean from the total pres- and then the time evolution of both the contributions is sure plots indicates that the synoptic-scale eddies analyzed during the life-cycle for the entire set of the blocking did not play leading role in this event. Furthermore, events. through the same analysis, it is noted that planetary- Using the NCEP-NCAR gridded reanalyzed data for ◦ ◦ scale is more stable. The relative stability role of 2002–2004, and averaging over the 40 × 60 latitude the two scales under the working assumption of the longitude box encompassing the blocking event and based Dymnikov conjecture (see Appendix A) was analyzed on our criterion of scale dominance as a height value above that conﬁrms this ﬁnding. This was the ﬁrst time this the monthly mean value for that height during the month in conjecture has been used for an observational case which the blocking occurs, the ﬁndings may be summarized study. as follows. (iv) It is noted that meridional gradient of the planetary- (i) A total of 126 events were analyzed to determine the scale height ﬁeld exists at mid-tropospheric level scale contribution dominance of the planetary- and through visual inspection. Our results displayed synoptic-scales during the blocking of the zonal ﬂow. in Figure 6(a) conﬁrm this ﬁnding. This in turn 79% of the total analyzed events have single height provides support for using simple variable such as dominance. Out of these, 44% have planetary-scale max|∇ψ| as a possible stability indicator of the ﬂow. Advances in Meteorology 13 (v) These two diagnostic tools show that the planetary- The perturbation energy equation in terms of scalar scale environment becomes unstable during the onset product (Lψ , ψ )is and then stabilizes during the mature stage of the ∂E blocking whereas the synoptic-scale heights play a = Lψ , ψ . (A.3) ∂t dominant role in destabilizing the planetary-scale ﬂow during the mature stage of the blocking life-cycle Since L = S + K,where K is the skew-symmetric part of the initiating the blocking decay. The interplay of both operator L and S is the symmetric part of the operator L, the the contributions is found to be the case during the perturbation energy equation may be rewritten with L → S three stages of the blocking, when their relative role is in (A.3), that is assessed in terms of the IRE and the maximum of the gradient of the ﬂow stream function. ∂E = Sψ , ψ . (A.4) ∂t It can be pointed out, that this study also conﬁrms the tentative conclusions of earlier studies that both the Note that the stationary solution ψ will be stable if all planetary- and synoptic-scales are equally important in the the eigenvalues of the operator S with respect to stationary life-cycle of the blockings in the midlatitude NH zonal ﬂow solution are negative. We shall thus take the sum of positive in general (see Section 1 for references). Based on the three- eigenvalues of the operator S as the characteristics of the year study, the above observations are true irrespective of instability of the stationary point. whether the blocking event occurs entirely over the land, over Assuming that ψ = ψ (y); that is, the stationary solution the ocean, or partially over the land and partially over the does not depend on zonal coordinate to mimic meridionally ocean. This may indicate more dominating role played by directed perturbation (namely, the blocking) in the mainly the diﬀerent scales and their interactions in the ﬂow once the zonal ﬂow and using the periodic conditions for x and blocking sets in instead of orographic forcings. y and passing to ﬁnite dimensions, after some algebraic As exempliﬁed by the selected case study, the IRE may manipulation, the eigenvalue problem for the operator S characterize the stability of the planetary/synoptic-scale ﬂow (where 2S = L + L ) has the form in the barotropic circulation. A simultaneous knowledge of the two diagnostic tools, however, seems to provide a ∂ ∂ϕ u Δϕ − Δ u = λϕ. (A.5) more reliable scenario for the occurrence, sustenance as well ∂x ∂x as decay of a blocking event. The IRE of the Dymnikov conjecture gives only the relative stability of the ﬂow. Height Here, λ’s are the eigenvalues of the eigenoperator ϕ.The λ’s variations alone however do not provide any underlying play the role of the characteristic exponents. We shall look insight into the scale contributions and the ﬂow stability for the general solution of (A.5) in the form that depends ikx during the blocking period. A simultaneous estimate of both on x and y: ϕ(x, y) = ϕ(y)e . With this transformation, we may establish the presence and the stability behavior of the obtain the following eigenvalue equation from (A.5) ﬂow. The above observations made in this study ﬁnd some ∂σϕ ∂ϕ λ justiﬁcation in light of the previous studies mentioned in + σ = ϕ, Section 1, where it was concluded that both the planetary- ∂y ∂y ik scale as well as the synoptic-scale heights seems to play some (A.6) ∂u role in essentially all stages of the blocking life-cycle. Though σ =− . ∂y depending upon the speciﬁc case study, the relative strength of the role seems to vary. In principle, one should solve this equation to obtain the spectrum of eigenvalues λ, which depends upon σ. Note Appendices σ is the vertical component of the relative vorticity for the stationary component of the stream function. Here, we A. Area Integrated Regional Enstrophy make use of the Dymnikov et al. [29]conjecturewhich suggests a strong correlation between the sum of the positive The dynamic equation of viscous incompressible barotropic characteristic exponents (eigenvalues of the linearization ﬂuid for the stream function ψ is given by operator of barotropic ﬂow) and the (blocked) domain integrated enstrophy, that is ∂Δψ + J ψ , Δψ = 0. (A.1) ∂t λ ≈ σ y dx dy. (A.7) The Δ is the Laplacian operator. The J is the Jacobian incorporating the nonlinear interactions. Expanding ψ in terms of time-dependent and time-independent compo- Equation (A7) can be obtained from (A.6) by ﬁrst writing nents, respectively, such that ψ = ψ + ψ,where ψ = (A.6) in ﬁnite diﬀerence form and then using a known ψ (t)and ψ = ψ (t). The equation of motion for linearization algebraic relation. This is the same as (2)in Section 2.3 of the operator L is ∂Δψ /∂t + Lψ = 0, where text, with σ → σ. Let us add that a numerical implementation of equation for L via Crank-Nicholson scheme in [29] using Lψ = J ψ , Δψ + J ψ , Δψ . (A.2) data for a three-year period after applying a 15-day ﬁlter 14 Advances in Meteorology (planetary-scale) on domains D over the north Atlantic and [10] H. Nakamura and J. M. Wallace, “Observed changes in baroclinic wave activity during the life cycles of low-frequency western Europe establishes the validity of (A.7). circulation anomalies,” Journal of the Atmospheric Sciences, vol. Summarizing, to the extent that the average time for σ- 47, no. 9, pp. 1100–1116, 1990. trajectories to diverge decreases as the sum of the positive [11] A. R. Lupo and P. J. Smith, “Planetary and synoptic-scale characteristic exponent’s increases, we get a preliminary interactions during the life cycle of a midlatitude blocking indication of how physical quantities, such as enstrophy, anticyclone over the North Atlantic,” Tellus,vol. 47, no.1,pp. may be viewed as forecasting indicators. The time evolution 575–596, 1995. of right hand side of (A.7) may thus represent the relative [12] A. R. Lupo, “A diagnosis of two blocking events that occurred stability of the barotropic ﬂow. Development of a mainly simultaneously in the midlatitude Northern Hemisphere,” meridional perturbation (y dependence only of ψ ) signiﬁes Monthly Weather Review, vol. 125, no. 8, pp. 1801–1823, 1997. relative stability of the ﬂow which we interpret as the [13] H. Nakamura, M. Nakamura, and J. L. Anderson, “The role blocking under the working assumption of Dymnikov et al. of high- and low-frequency dynamics in blocking formation,” Monthly Weather Review, vol. 125, no. 9, pp. 2074–2093, 1997. conjecture [29]. Note that right hand side of (A.7)refers [14] A. R. Lupo andP.J.Smith,“Theinteractionsbetween a to area averaged (relative) vorticity squared as mentioned midlatitude blocking anticyclone and synoptic-scale cyclones earlier. that occurred during the summer season,” Monthly Weather Review, vol. 126, no. 2, pp. 503–515, 1998. B. The Blocking Height-Scale Contribution [15] J. P. Burkhardt and A. R. Lupo, “The planetary- and synoptic- scale interactions in a southeast Paciﬁc blocking episode using Analysis for 2002–2004 PV diagnostics,” Journal of the Atmospheric Sciences, vol. 62, See Tables 4, 5, and 6. no. 6, pp. 1901–1916, 2005. [16] L. Dong and S. J. Colucci, “The role of deformation and potential vorticity in Southern Hemisphere blocking onsets,” Acknowledgments Journal of the Atmospheric Sciences, vol. 62, no. 11, pp. 4043– 4056, 2005. The authors thank Dr. Courtenay Strong for helpful discus- [17] L. Dong and S. J. Colucci, “Interpreting the opposition sions during the early stages of this work. The authors also between two block-onset forcing mechanisms,” Journal of the thank Dr. Mansour Almazroui for his continuous support Atmospheric Sciences, vol. 64, no. 6, pp. 2091–2104, 2007. and cooperation. [18] R. F. C. Marques and V. B. Rao, “A diagnosis of a long-lasting blocking event over the southeast Paciﬁc Ocean,” Monthly Weather Review, vol. 127, no. 8, pp. 1761–1776, 1999. References [19] A. R. Lupo,I.I.Mokhov, S. Dostoglou,A.R.Kunz,and J. P. [1] D. Rex, “Blocking action in the middle troposphere and its Burkhardt, “Assessment of the impact of the planetary scale on the decay of blocking and the use of phase diagrams and eﬀect upon regional climate I. An aerological study of blocking action,” Tellus, vol. 2, pp. 196–211, 1950. enstrophy as a diagnostic,” Izvestiya. Atmospheric and Oceanic Physics, vol. 43, no. 1, pp. 45–51, 2007. [2] D. Rex, “Blocking action in the middle troposphere and its eﬀect upon regional climate II. The climatology of blocking [20] E. Kalnay-Rivas and L.-O. Merkine, “A simple mechanism for action,” Tellus, vol. 2, pp. 275–301, 1950. blocking,” Journal of the Atmospheric Sciences, vol. 38, no. 10, pp. 2077–2091, 1981. [3] R. Benzi, B. Saltzman, and A. C. Wiin-Nielsen, Anomalous Atmospheric Flows and Blocking, vol. 29 of Advances in [21] J. S. Frederiksen, “A uniﬁed three-dimensional instability theory of the onset of blocking and cyclogenesis,” Journal of Geophysics, Academic Press, Boston, Mass, USA, 1986. [4] J. S. Watson and S. J. Colucci, “Evaluation of ensemble the Atmospheric Sciences, vol. 39, no. 5, pp. 969–982, 1982. [22] S. L. Mullen, “The local balances of vorticity and heat for predictions of blocking in the NCEP global spectral model,” Monthly Weather Review, vol. 130, no. 12, pp. 3008–3021, blocking anticyclones in a spectral general circulation model,” Journal of the Atmospheric Sciences, vol. 43, no. 13, pp. 1406– [5] J. G. Charney and J. G. Devore, “Multiple ﬂow equilibria in the 1441, 1986. [23] S. L. Mullen, “Transient eddy forcing of blocking ﬂows,” atmosphere and blocking,” Journal of the Atmospheric Sciences, vol. 36, no. 7, pp. 1205–1216, 1979. Journal of the Atmospheric Sciences, vol. 44, no. 1, pp. 3–22, [6] G. J. Shutts, “The propagation of eddies in diﬄuent jetstreams: eddy vorticity forcing of ’ blocking’ ﬂow ﬁelds,” Quarterly [24] K. Haines and A. J. Holland, “Vacillation cycles and blocking Journalofthe RoyalMeteorologicalSociety, vol. 109, no. 462, in a channel,” Quarterly Journal of the Royal Meteorological Society, vol. 124, no. 547, pp. 873–895, 1998. pp. 737–761, 1983. [7] D. Luo, A. R. Lupo, and H. Wan, “Dynamics of eddy-driven [25] S. J. Colucci and D. P. Baumhefner, “Numerical prediction of the onset of blocking: a case study with forecast ensembles,” low-frequency dipole modes. Part I: a simple model of North Atlantic Oscillations,” Journal of the Atmospheric Sciences, vol. Monthly Weather Review, vol. 126, no. 3, pp. 773–784, 1998. [26] D. E. Tilly, A. R. Lupo,C.J.Melick, andP.S.Market, 64, no. 1, pp. 3–28, 2007. [8] D.Luo,T.T.Gong, andA.R.Lupo, “Dynamicsofeddy-driven “Calculated height tendencies in two southern hemisphere blocking and cyclone events: the contribution of diabatic low-frequency dipole modes. Part II: free mode characteristics of NAO and diagnostic study,” Journal of the Atmospheric heating to block intensiﬁcation,” Monthly Weather Review, vol. 136, no. 9, pp. 3568–3578, 2008. Sciences, vol. 64, no. 1, pp. 29–51, 2007. [9] M. S. Tracton, “Predictability and its relationship to scale [27] P. J. Roebber, “Planetary waves, cyclogenesis, and the irregular breakdown of zonal motion over the North Atlantic,” Monthly interaction processes in blocking,” Monthly Weather Review, vol. 118, no. 8, pp. 1666–1695, 1990. Weather Review, vol. 137, pp. 3907–3917, 2009. Advances in Meteorology 15 [28] S. J. Colucci, “Planetary-scale preconditioning for the onset of Soil, Environmental and Atmospheric Sciences, University of blocking,” Journal of the Atmospheric Sciences, vol. 58, no. 8, Missouri, Columbia, 2007. pp. 933–942, 2001. [47] R. S. Quiroz, “The climate of the 1983-84 winter—a season of [29] V. P. Dymnikov, Y. V. Kazantsev, and V. V. Kharin, “Infor- strong blocking and severe cold in North America,” Monthly mation entropy and local Lyapunov exponents of barotropic Weather Review, vol. 112, no. 9, pp. 1894–1912, 1984. atmospheric circulation,” Izvestiya. Atmospheric and Oceanic [48] M. L. Carrera, R. W. Higgins, and V. E. Kousky, “Downstream Physics, vol. 28, no. 6, pp. 425–432, 1993. weather impacts associated with atmospheric blocking over [30] Y. N. Skiba, “On the spectral problem in the linear stability the Northeast Paciﬁc,” Journal of Climate, vol. 17, no. 24, pp. study of ﬂows on a sphere,” Journal of Mathematical Analysis 4823–4839, 2004. and Applications, vol. 270, no. 1, pp. 165–180, 2002. [49] M. Ghil and S. Childress, Topics in Geophysical Fluid Dynamics: [31] E. Kalnay, M. Kanamitsu, R. Kistler et al., “The NCEP/NCAR Atmospheric Dynamics, Dynamo Theory, and Climate Dynam- 40-year reanalysis project,” Bulletin of the American Meteoro- ics, Springer, Berlin, Germany, 1987. logical Society, vol. 77, no. 3, pp. 437–471, 1996. [50] C. H. Tsou and P. J. Smith, “The role of synoptic/planetary- [32] R. Kistler, E. Kalnay, W. Collins et al., “The NCEP-NCAR 50- scale interactions during the development of a blocking year reanalysis: monthly means CD-ROM and documenta- anticyclone,” Tellus. Series A, vol. 42, no. 1, pp. 174–193, 1990. tion,” Bulletin of the American Meteorological Society, vol. 82, no. 2, pp. 247–267, 2001. [33] A. R. Lupo and P. J. Smith, “Climatological features of blocking anticyclones in the Northern Hemisphere,” Tellus. Series A, vol. 47, no. 4, pp. 439–456, 1995. [34] H. Lejenas and H. Okland, “Characteristics of Northern Hemisphere blocking as determined from a long time series of observational data,” Tellus. Series A, vol. 35, no. 5, pp. 350– 362, 1983. [35] R. Shapiro, “Smoothing, ﬁltering, and boundary eﬀects,” Reviews of Geophysics and Space Physics, vol. 8, no. 2, pp. 359– 387, 1970. [36] A. R. Hansen, “Observational characteristics of atmospheric planetary waves with bimodal amplitude distributions,” Advances in Geophysics, vol. 29, pp. 101–133, 1986. [37] B. Farrell, “Developing disturbances in shear,” Journal of the Atmospheric Sciences, vol. 44, no. 16, pp. 2191–2199, 1987. [38] A. R. Lupo, J. V. Clark, A. M. Hendin, et al., “The global increase in blocking occurrences,” in Proceedings of the 20th Conference on Global Climate Change, American Meteorologi- cal Society, New Orleans, La, USA, 2008. [39] J. M. Wiedenmann, A. R. Lupo, I. I. Mokhov, and E. A. Tikhonova, “The climatology of blocking anticyclones for the Northern and Southern Hemispheres: block intensity as a diagnostic,” Journal of Climate, vol. 15, no. 23, pp. 3459–3473, [40] T. C. Peterson,M.O.Baringer,H.J.Diamond et al., “State of the climate in 2008,” Bulletin of the American Meteorological Society, vol. 90, no. 8, pp. S1–S196, 2009. [41] M. Croci-Maspoli,C.Schwierz, andH.C.Davies, “A mul- tifaceted climatology of atmospheric blocking and its recent linear trend,” Journal of Climate, vol. 20, no. 4, pp. 633–649, [42] D. Luo and H. Wan, “Decadal variability of wintertime North Atlantic and Paciﬁc blockings: a possible cause,” Geophysical Research Letters, vol. 32, no. 23, Article ID L23810, 5 pages, [43] J. R. Key and A. C. K. Chan, “Multidecadal global and regional trends in 1000 mb and 500 mb cyclone frequencies,” Geophysical Research Letters, vol. 26, no. 14, pp. 2053–2056, [44] Alaskan Climate Record Center, “Record breaking summer of 2004,” http://climate.gi.alaska.edu/News/summer04.html. [45] D. Barriopedro, R. Garcıa-Herrera, A. R. Lupo, and E. Hernandez, ´ “A climatology of Northern Hemisphere block- ing,” Journal of Climate, vol. 19, no. 6, pp. 1042–1063, 2006. [46] J. M. Glisan, Two extreme cases of atmospheric blocking over Europe and North America, M.S. thesis, Department of International Journal of Journal of Ecology Mining The Scientific Journal of Geochemistry Scientifica World Journal Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Journal of Earthquakes Paleontology Journal Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Journal of Petroleum Engineering Submit your manuscripts at http://www.hindawi.com International Journal of Geophysics Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Advances in Advances in Journal of Advances in International Journal of Meteorology ClimatologyGeology Oceanography Oceanography Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Applied & Journal of Environmental International Journal of Journal of International Journal of Computational Soil Science Mineralogy Geological Research Atmospheric Sciences Environmental Sciences Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Volume 2014 Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com http://www.hindawi.com Volume 2014 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Meteorology Hindawi Publishing Corporation http://www.deepdyve.com/lp/hindawi-publishing-corporation/scale-analysis-of-blocking-events-from-2002-to-2004-a-case-study-of-an-PEI3bpCSTo

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References (51)

Record breaking summer of 2004
J. Watson, S. Colucci (2002)
Evaluation of Ensemble Predictions of Blocking in the NCEP Global Spectral Model
Monthly Weather Review, 130
K. Haines, A. Holland (1998)
Vacillation cycles and blocking in a channel
Quarterly Journal of the Royal Meteorological Society, 124
T. Peterson, M. Baringer (2009)
State of the Climate in 2008
Bulletin of the American Meteorological Society, 90
M. Kanamitsu E. Kalnay (1996)
The NCEP/NCAR 40-year reanalysis project,
Bulletin of the American Meteorological Society, 77
Jason Wiedenmann, A. Lupo, I. Mokhov, E. Tikhonova (2002)
The Climatology of Blocking Anticyclones for the Northern and Southern Hemispheres: Block Intensity as a Diagnostic.
Journal of Climate, 15
D. Rex (1950)
Blocking Action in the Middle Troposphere and its Effect upon Regional Climate I. An Aerological Study of Blocking Action.
Tellus A, 2
John Burkhardt, A. Lupo (2005)
The Planetary- and Synoptic-Scale Interactions in a Southeast Pacific Blocking Episode Using PV Diagnostics
Journal of the Atmospheric Sciences, 62
D. Luo, T. Gong, A. Lupo (2007)
Dynamics of Eddy-Driven Low-Frequency Dipole Modes. Part II: Free Mode Characteristics of NAO and Diagnostic Study
Journal of the Atmospheric Sciences, 64
A. Lupo (1997)
A Diagnosis of Two Blocking Events That Occurred Simultaneously in the Midlatitude Northern Hemisphere
Monthly Weather Review, 125
B. Farrell (1987)
Developing disturbances in shear
Journal of the Atmospheric Sciences, 44
R. Marques, V. Rao (1999)
A Diagnosis of a Long-Lasting Blocking Event over the Southeast Pacific Ocean
Monthly Weather Review, 127
S. Mullen (1987)
Transient Eddy Forcing of Blocking Flows.
Journal of the Atmospheric Sciences, 44
D. Barriopedro, R. Garcia-Herrera, A. Lupo, E. Hernández (2006)
A Climatology of Northern Hemisphere Blocking
Journal of Climate, 19
J. Charney, John DeVore (1979)
Multiple Flow Equilibria in the Atmosphere and Blocking
Journal of the Atmospheric Sciences, 36
M. Croci‐Maspoli, C. Schwierz, H. Davies (2007)
A Multifaceted Climatology of Atmospheric Blocking and Its Recent Linear Trend
Journal of Climate, 20
R. Shapiro (1970)
Smoothing, filtering, and boundary effects
Reviews of Geophysics, 8
S. Colucci (2001)
Planetary-Scale Preconditioning for the Onset of Blocking
Journal of the Atmospheric Sciences, 58
S. Colucci, D. Baumhefner (1998)
Numerical prediction of the onset of blocking : A case study with forecast ensembles
Monthly Weather Review, 126
H. Nakamura, Mototaka Nakamura, Jeffrey Anderson (1997)
The Role of High- and Low-Frequency Dynamics in Blocking Formation
Monthly Weather Review, 125
J. Glisan (2007)
Two extreme cases of atmospheric blocking over Europe and North America
M. Tracton (1990)
Predictability and Its Relationship to Scale Interaction Processes in Blocking
Monthly Weather Review, 118
M. Carrera, R. Higgins, V. Kousky (2004)
Downstream Weather Impacts Associated with Atmospheric Blocking over the Northeast Pacific
Journal of Climate, 17
Douglas Tilly, A. Lupo, C. Melick, P. Market (2008)
Calculated Height Tendencies in Two Southern Hemisphere Blocking and Cyclone Events: The Contribution of Diabatic Heating to Block Intensification
Monthly Weather Review, 136
(1986)
Wiin-Nielsen, Anomalous Atmospheric Flows and Blocking, vol. 29 of Advances in Geophysics
C. Tsou, Phillip Smith (1990)
The role of synoptic/planetary scale interactions during the development of a blocking anticyclone
Tellus A, 42
Li Dong, S. Colucci (2005)
The Role of Deformation and Potential Vorticity in Southern Hemisphere Blocking Onsets
Journal of the Atmospheric Sciences, 62
A. Hansen (1986)
Observational Characteristics of Atmospheric Planetary Waves with Bimodal Amplitude Distributions
Advances in Geophysics, 29
H. Lejenäs, H. Økland (1983)
Characteristics of northern hemisphere blocking as determined from a long time series of observational data
Tellus A, 35
A. Lupo, Phillip Smith (1995)
Climatological features of blocking anticyclones in the Northern Hemisphere
Tellus A, 47
M. Ghil, S. Childress (1987)
Topics in geophysical fluid dynamics. Atmospheric dynamics, dynamo theory, and climate dynamics.
D. Rex (1950)
Blocking Action in the Middle Troposphere and its Effect upon Regional Climate II. The Climatology of Blocking Action
Tellus A
H. Nakamura, J. Wallace (1990)
Observed Changes in Baroclinic Wave Activity during the Life Cycles of Low-Frequency Circulation Anomalies
Journal of the Atmospheric Sciences, 47
D. Luo, A. Lupo, H. Wan (2007)
Dynamics of Eddy-Driven Low-Frequency Dipole Modes. Part I: A Simple Model of North Atlantic Oscillations
Journal of the Atmospheric Sciences, 64
(1993)
Information entropy and local Lyapunov exponents of barotropic atmospheric circulation
E. Kálnay-Rivas, L. Merkine (1981)
A Simple Mechanism for Blocking
Journal of the Atmospheric Sciences, 38
A. Lupo, Phillip Smith (1998)
The Interactions between a Midlatitude Blocking Anticyclone and Synoptic-Scale Cyclones That Occurred during the Summer Season
Monthly Weather Review, 126
S. Mullen (1986)
The Local Balances of Vorticity and Heat for Blocking Anticyclones in a Spectral General Circulation Model
Journal of the Atmospheric Sciences, 43
A. Lupo, Phillip Smith (1995)
Planetary and synoptic-scale interactions during the life cycle of a mid-latitude blocking anticyclone over the North Atlantic
Tellus A, 47
G. Shutts (1983)
The propagation of eddies in diffluent jetstreams: Eddy vorticity forcing of ‘blocking’ flow fields
Quarterly Journal of the Royal Meteorological Society, 109
B. Saltzman, R. Benzi, A. Wiin-nielsen (1986)
Anomalous atmospheric flows and blocking
A. Lupo, I. Mokhov, S. Dostoglou, A. Kunz, John Burkhardt (2007)
Assessment of the impact of the planetary scale on the decay of blocking and the use of phase diagrams and enstrophy as a diagnostic
Izvestiya, Atmospheric and Oceanic Physics, 43
Li Dong, S. Colucci (2007)
Interpreting the Opposition between Two Block-Onset Forcing Mechanisms
Journal of the Atmospheric Sciences, 64
D. Luo, H. Wan (2005)
Decadal variability of wintertime North Atlantic and Pacific blockings: A possible cause
Geophysical Research Letters, 32
Y. Skiba (2002)
On the spectral problem in the linear stability study of flows on a sphere
Journal of Mathematical Analysis and Applications, 270
J. Key, Alan Chan (1999)
Multidecadal global and regional trends in 1000 mb and 500 mb cyclone frequencies
Geophysical Research Letters, 26
Paul Roebber (2009)
Planetary Waves, Cyclogenesis, and the Irregular Breakdown of Zonal Motion over the North Atlantic
Monthly Weather Review, 137
R. Kistler, E. Kalnay, W. Collins, S. Saha, G. White, J. Woollen, M. Chelliah, W. Ebisuzaki, M. Kanamitsu, V. Kousky, H. Dool, R. Jenne, M. Fiorino (2001)
The NCEP–NCAR 50-Year Reanalysis: Monthly Means CD-ROM and Documentation
Bulletin of the American Meteorological Society, 82
R. Quiroz (1984)
The Climate of the 1983–84 Winter—A Season of Strong Blocking and Severe Cold in North America
Monthly Weather Review, 112
A. Lupo, J. Clark, A. Hendin, A. Kelly, K. Mihalka, B. Perrin, K. Puricelli (2008)
THE GLOBAL INCREASE IN BLOCKING OCCURRENCES
J. Frederiksen (1982)
A Unified Three-Dimensional Instability Theory of the Onset of Blocking and Cyclogenesis
Journal of the Atmospheric Sciences, 39

Publisher: Hindawi Publishing Corporation
Copyright: Copyright © 2010 H. Athar and Anthony R. Lupo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ISSN: 1687-9309
eISSN: 1687-9317
DOI: 10.1155/2010/610263
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Abstract

Hindawi Publishing Corporation Advances in Meteorology Volume 2010, Article ID 610263, 15 pages doi:10.1155/2010/610263 Research Article Scale Analysis of Blocking Events from 2002 to 2004: A Case Study of an Unusually Persistent Blocking Event Leading to a Heat Wave in the Gulf of Alaska during August 2004 1 2 H. Athar and Anthony R. Lupo Center of Excellence for Climate Change Research, King Abdulaziz University, P.O. Box 80208, Jeddah 21589, Saudi Arabia Department of Soil, Environmental and Atmospheric Sciences, 302 ABNR Building, University of Missouri, Columbia, MO 65211, USA Correspondence should be addressed to H. Athar, ahussain1@kau.edu.sa Received 19 February 2010; Revised 14 May 2010; Accepted 28 June 2010 Academic Editor: Luis Gimeno Copyright © 2010 H. Athar and A. R. Lupo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The climatology of northern hemisphere blocking events is presented assessing the relative contributions of the planetary and synoptic scales to 500 hPa heights in order to determine the proportion of blocks dominated by a single-scale. The heights were averaged over a region encompassing the block, and then compared with corresponding monthly mean values. If planetary- scale or synoptic-scale heights are greater than the monthly mean, the block is called single-scale dominant. In the study, 79% of blocks were single-scale dominant, whereas the remaining 21% of events were alternating-scale prominent. This proportion varied by season with winter (summer) events being synoptic (planetary) scale dominant. The stability of blocks is also examined to determine if two stability indicators were useful in the assessment of the character of planetary and synoptic-scale ﬂows. These quantities are area integrated enstrophy, and the maximum value of stream function gradients within the block region. The analysis of a prolonged block occurring in the Gulf of Alaska during August 2004 shows the planetary-scale is unstable during block onset and then stabilizes during the mature stage. The synoptic-scale played a dominant role in destabilizing the planetary-scale during the mature stage of the block initiating decay. 1. Introduction incorporate the high-frequency (synoptic-scale) dynamics into the quasigeostropic barotropic vorticity equation to The development of a predominantly mid-tropospheric, obtain the blocking events for prescribed forcings [6]. Both meridional circulation pattern within a sector of the north- models oﬀer numerical solutions of the nonlinear barotropic ern or southern hemisphere is commonly referred to as vorticity equation. Other studies include both scales in their blocking (e.g., [1, 2]). This stagnation of the zonal ﬂow gives modeled analysis of the blocking events [7, 8]. rise to diﬃculties in operational weather forecasts for regions From a synoptic-dynamic point of view, and making within and near the blocked region (e.g., [3, 4]). Developing use of surface and upper air data provided by reanalyses, an understanding of the processes that leads to the formation numerous case studies have been carried out leading to of such circulation patterns is thus of signiﬁcant interest. valuable insight into the forcing mechanisms that may be TheCharney andDeVoremodel provides aframe- important during various stages of the blocking (e.g., [9– work for incorporating the low frequency (planetary-scale) 17]). In several of these case studies, the question of the role dynamics into the quasigeostrophic barotropic vorticity of planetary-scale versus synoptic-scale processes during the equation in order to obtain the blocking patterns for the various stages of the blocking life-cycle is addressed. given forcings using the concept of stable equilibria [5]. The In recent years, several studies also have examined the Shutts model, on the other hand, provides a framework to relative role of each scale and their interactions as well as the 2 Advances in Meteorology nature of the interactions themselves (e.g., [9, 18, 19], and study, the details of the synoptic and the stability analyses references cited therein). In addition to these studies, and of a selected blocking event are presented in Section 4.The those of earlier pioneers (e.g., [20–23]), a consistent picture emphasis in this case study is on the relative role of the emerges that the synoptic-scale plays an important role in the planetary- and synoptic-scales to quantify the ﬂow stability. life-cycle of the blocking events. These studies show that the A summary of the three-year study and the results for the magnitude of the synoptic-scale forcing is generally large as case study are presented in Section 5. compared to the planetary-scale forcing. While the studies referenced in the above paragraph 2. Data and Methods do not downplay the role of the planetary-scale, they do focus more on the role of the synoptic-scale contributions. 2.1. Data Set. The data set used here was the National Center However, others have shown that the planetary-scale is very for Environmental Prediction (NCEP) and National Center inﬂuential in the life-cycle of the blocking events (e.g., [24– for Atmospheric Research (NCAR) gridded reanalyses data ◦ ◦ 27]). For instance, in their model study, [24]suggested [31, 32]. These data were provided on the 2.5 by 2.5 that the blocking regimes will break down when there is a latitude-longitude grids available on 17 mandatory levels substantial change in the planetary-scale ﬂow regime. Then, from 1000 hPa to 10 hPa at 6-h intervals on daily basis. [25] focus on the role of the planetary-scale deformation A three-year period leading up to the year the case study in a preconditioned environment during the formation occurred was examined. of the blocking events (see also [28]). These two studies together support the notion that while the planetary-scale 2.2. Blocking Deﬁnition. The blocking criterion of [33]will may not itself lead to the block formation and maintenance, be used to determine the onset and termination times for the nevertheless this scale may provide a favorable environment blocking events studied. The blocking events may be sub- in the interaction with the synoptic-scale environment. Thus, divided into onset, intensiﬁcation, maintenance, and decay a substantial change in the planetary-scale ﬂow regime may stages (e.g., [12, 14, 15]). Onset is the period before the not support blocking and these events would decay fairly block formation, while intensiﬁcation (decay) is represented quickly. by a general increase (decrease) in center point heights. In this paper, the scale characteristics of all the midlati- Maintenance is generally represented by periods where the tude blocking events occurring in the northern hemisphere center point time evolution is close to zero. In brief, these (NH) during the three-year period 2002–2004 are examined studies employ a combined and extended set of conditions in order to assess the relative role of the synoptic- and set forth earlier by the subjective deﬁnition of [1, 2], and the planetary-scales. We present a detailed characterization of objective criterion of Lejenas and Okland [34]. the blocking events during the above three-year period The 500 hPa height at 1200 UTC is used as a diagnostic based on the relative role of planetary-scale and/or synoptic- atmospheric variable. Brieﬂy, the blocking detection crite- scale contributions. The aim is to provide a reference rion includes: (i) satisfying the Rex [1, 2] criteria for the document that may be used to select suitable blocking events blocking with the minimum duration of the blocking as 5 as examples for the three classes of the quasigeostrophic days; (ii) a negative or small positive LO 83 index [34], must barotropic vorticity equation solutions mentioned earlier in be present on a time-longitude or Hovmol ¨ ler diagram; (iii) this section. conditions (i) and (ii) satisﬁed for 24 h after onset to 24 h It is further pointed out that abrupt changes in the before termination; (iv) the blocking should be pole ward planetary-scale environment can lead to the onset or decay of 35 N, and the ridge should have an amplitude of greater of the blocking. In order to accomplish this, we will look than 5 latitude; and (v) blocking onset is described to occur at the area integrated regional enstrophy and maximum of when condition (iv) and either conditions (i) or (ii) are the absolute value of geostrophic stream function gradient, satisﬁed, (v) termination is designated at the time the event as diagnostic tools in a selected blocking case study. These fails condition (v) for a 24 h period or longer. This procedure are then calculated using both the planetary- and synoptic- is used to detect the blocking events at 500 hPa and deﬁnes scale components of the ﬂow. These indicators of stability the blocking duration with start and end dates. were originally developed by [29, 30], and will be applied, The blocking intensity (BI) is deﬁned as [33] to our knowledge, for the ﬁrst time, to a NH case study. Also, the time evolution of the planetary/synoptic-scale height and BI = 100[(Z max /Z ) − 1]. (1) of the stability indicators will be studied. In contrast to many previous studies mentioned in this section, we concentrate In (1), Z max is the maximum 500 hPa height in the closed on examining the relative role of both the planetary- and anticyclone region or on a line associated with the ridge, synoptic- scales (and determining the ﬂow stability). and Z is the subjectively chosen 500 hPa height contour The paper outline is as follows. In Section 2,wepresent encompassing the upstream and downstream troughs. The the details of the data set used and describe the method- BI measures the amplitude of the ﬂow around the block. For ologies, including the stability indicators. In Section 3,we further details and examples, the reader is referred to [33]. elaborate the results of the predominance of synoptic- versus As mentioned before, this study will point out that planetary-scale contributions analysis performed for all the changes in the planetary-scale and synoptic-scale ﬂow midlatitude blocking events occurring during the three-year regimes can be related to the onset and the decay of the period (2002–2004) in the NH. As a representative case blocking events. The techniques used to extract planetary- Advances in Meteorology 3 and synoptic-scale heights have been used in many of Table 1: Assessment of the blocking domain size variation, for the 500 hPa monthly average planetary-scale height, during August the previous studies [11, 12, 14], and will be only brieﬂy 2004, for the selected blocking event. presented. A second-order, two-dimensional ﬁlter was used on the Monthly planetary-scale reanalysis heights in order to separate the planetary-scale D (latitude × longitude) height averaged over the heights (Z ) from the observed 500 hPa height value (Z ) blocking domain D (m) [35]. The ﬁlter performs a center weighted symmetric ﬁnite ◦ ◦ 40 × 60 element calculation in spatial dimensions. The ﬁltered data ◦ ◦ 50 × 70 retain 2%, 44%, and 80% of the original signal at wavelengths ◦ ◦ ◦ 60 × 80 of 3000 km, 4500 km, and 6000 km at 45 N. The synoptic- ◦ ◦ 70 × 90 scale heights (Z ) were obtained using Z = Z − Z . More s s p ◦ ◦ 80 × 100 details regarding the use of the ﬁltering procedure can be 5728 found in [11]. Then, the planetary-scale height ﬁelds were averaged ◦ ◦ over 40 latitude by 60 longitude box within the blocking sector to produce one number for each block detection. where f = 2Ω sin(φ) is the Coriolis parameter with latitude This process is analogous to the procedure used by [36]in denoted by φ. The variable Ω is the rotation speed of earth deriving the wave amplitude index, with the exception that −5 −1 (Ω is taken as 7.292 × 10 rad s ), and the acceleration we ﬁltered the ﬁelds ﬁrst and then averaged them within a due to the gravity is g.The ψ is the total stream function, so box. They averaged the entire midlatitude height ﬁeld into a the quantity represented by max|∇ψ| may also be referred band and then ﬁltered to obtain a single number for the time as maximum geosptrophic wind speed. The maximum value period for the NH. of this quantity is taken within the blocking domain D and is meant to reﬂect the meridional variations in the 2.3. Blocking Area Integrated Regional Enstrophy. In [29], ﬂow. The behavior of this indicator of stability may have a blocking was deﬁned as a meridional perturbation that simple physical meaning. In the case of vanishing zonal ﬂow, destabilizes the zonal ﬂow. Starting from the barotropic meridional variations will have the dominant contribution. vorticity equation, the blocking area integrated enstrophy is It may thus acquire a relative maximum positive value during suggested as a measure for the change in the zonal ﬂow that the blocking state. For more details, see [30]. may lead to the blocking. Here, we make use of the conjecture in [29] which suggests a relationship between the sum of the positive eigenvalues of the linearization operator of the 2.5. The Eﬀect of Domain Size Variation. The domain D used barotropic ﬂow and the blocking domain integrated regional ◦ ◦ in (2) is deﬁned as the 40 latitude by 60 longitude box as enstrophy, that is, mentioned in Section 2.3. The latitude span is 40 which + encompasses the latitudinal extent of the blocking event in λ ≈ σ y dx dy,(2) the midlatitudes. The longitude is centered at the blocking onset center and depends on the longitude extent of the where σ =−∂u/∂y and D is the blocking domain. A brief selected blocking event. ◦ ◦ discussion of how to obtain (2)isprovidedin Appendix A, Enlarging the blocking area domain D from 40 × 60 following [29]. The blocking domain D is deﬁned as a does not lead to any sizable deviation in the planetary- latitude and longitude box as mentioned above. We will call scale height when averaged over it. A representative example the right hand side of (2) as the blocking area integrated is displayed in Table 1, where the impact of enlarging the regional enstrophy (IRE) here. We can regard the IRE as a blocking area domain D is assessed for the 500 hPa monthly stability indicator. This has not been used in the literature average planetary-scale height for a selected blocking event, before as a blocking diagnostic for observed case studies, and our case study. The blocking event occurred during 05– ◦ ◦ ◦ ◦ (2) will be used to determine the relative stability of the ﬂow 28 August 2004 over 40 N–80 N and 160 E–260 E. The in region D. Higher positive values of the IRE correspond to Table 1 indicates that the maximum variation in the monthly more unstable ﬂow and vice versa. For a discussion of time average planetary-scale height value is less than 1% relative to ◦ ◦ evolution of the eigenmodes of the barotropic ﬂow including 40 ×60 box averaging value. Similar magnitude of variation ◦ ◦ the eﬀect of β,see [37]. relative to 40 × 60 box averaging value was found when we varied the latitude only, the longitude only, and the selected 2.4. Maximum of the Absolute Value of the Stream Function blocking event, over the blocking domain D. Gradient. We have calculated numerically another indicator It is thus concluded that the blocking domain averaged of ﬂow regime stability following [30], that is, the maximum results for planetary-scale height presented in this study are of absolute value of the gradient of the geosptrophic stream not sensitive to the choice of the size of the blocking domain function (max|∇ψ|). Here D within the range of latitude and longitude values speciﬁed in Table 1. The synoptic scale height, being a small-scale gZ length is somewhat sensitive to the variations of the blocking ψ =,(3) domain D (of the order of 15%–20%). 4 Advances in Meteorology 3. Details of the Three-Year Study with the NH climatological track movement of the blocking events [41]. The results presented in Appendix B are sensitive In this section, we ﬁrst present the main characteristics and to variations in domain size D (see Section 2.5). synoptic description of the blocking events for the three-year The ﬁltered planetary-scale height was averaged over this duration 2002–2004 and then the scale contribution charac- latitude and longitude box. Next, the synoptic-scale height teristics of these events using the methodology presented in for each grid point of the domain was calculated following Section 2. the procedure outlined in Section 2, and then averaged over the box. In the Appendix B, the entry labeled positive in the planetary-scale height column occurs if, at least, 3.1. The Blocking Events during 2002–2004. The number of this height averaged over the mature stage of the blocking NH blocking events lasting 5 days or more during the three- event is larger than the corresponding monthly mean height year period (2002–2004) under study are as follows: 2002 value. A similar deﬁnition was used for a positive entry in (41), 2003 (48), and 2004 (37). During this three-year period, synoptic-scale column. If the blocking event fell within two the total number of blocking events is 126. The highest months such as from 25 July through 15 August, the scale number of blocking events occurred during the year 2003 contribution dominance was determined by comparing the (38%). The detected blocking events during the above three- behavior of the averaged heights relative to the two month year period are in line with the ﬁndings in [38]. mean value. The synoptic details of the blocking events during The monthly mean was chosen simply to provide a the three-year period in tabular form are presented in zero reference point from which to assess which scale was Appendix B. The blocking events’ details include the start prominent during the life-cycle of the event. There is no date, the end date, the duration, the BI as well as the reason to assume apriori that the size or sign of the monthly geographic location. Table 2 summarizes the characteristics value for each scale would be related to whether or not a of the blocking events during the three-year period. blocking event formed since the monthly mean would vary Table 2 indicates that, in general, the overall character of annually and would depend on where the box is located and blocking events taken from this three-year period is similar to the size of the box used. The block formation mechanisms the climatologies of [33, 39] in that there were more winter also depend on the inter basin diﬀerences [41, 42]. season (Jan–Mar) events and more Atlantic region (290 E– Based on our above subjectively chosen criterion for 30 E) events than in the other regions. Also, winter season comparison of heights, the blocking events are categorized events were, in general, stronger than those of summer into the following three types: season (Jul–Sep) events and oceanic region events were stronger than those found over the continents. Additionally, (i) planetary-scale height dominant events, the events from this three-year period were more numerous, (ii) synoptic-scale height dominant events, slightly weaker, and more persistent than those found in [39] (iii) alternating-scale height dominant events. which is consistent with the results of [38, 40]. During the three-year period (2002–2004), the longest In Section 4, a representative example of a blocking event duration (35 days) blocking event occurred over the conti- ◦ ◦ ◦ ◦ with planetary-scale height dominant behavior (category (i)) nental area (100 W–80 Wand 40 E–140 E) during 4 June is discussed in detail. Representative examples of category (ii) through 9 July, 2002, with BI = 1.99 (weak event). It is event synoptic-scale height dominance, and (iii) alternating-scale number 24 in Table 4. During the same three-year period, height dominance, in which both the height scales dominate the strongest blocking event occurred over the Paciﬁc area in a time series fashion, are described next in some detail in ◦ ◦ (140 E–100 W), with BI = 5.39 with a duration of 6 days this section. (19 March through 25 March 2003). It is event number 11 in Figure 1 displays a single-scale contribution behavior Table 5. case for a selected blocking event, corresponding to event The synoptic description of the blocking events displayed number 8 in Table 6. This event occurred over the Atlantic in Appendix B is used subsequently in this section to assess with BI = 4.62, indicating that it is a strong event [39]. The the behavior of the scale contributions and to perform the event lasted for 5 days (15th March 2004 through 20th March detailed stability analysis of a selected blocking event in the 2004). The block longitude center at the onset was located next section and this event is identiﬁed in italics. at 0 E. A single (synoptic)-scale dominance can be noted, during the mature stage, as the monthly mean value for 3.2. Scale Contribution Comparison for the Blocking Events synoptic-scale is 0.03361 m, whereas the monthly mean value during 2002–2004. The longitude at block onset was for the planetary-scale is 5633 m (compare with Figure 4). obtained from the blocking event archive ([38], Appendix B). Figure 2 displays an alternating-scale contribution Then the blocking event box was formed relative to the behavior for a selected blocking event, corresponding to blocking onset center location by adding 30 in the east event number 3 in Table 4. This event occurred over the and the west directions. The latitude span was taken as 40 Paciﬁc with BI = 4.50, which is a strong event [39]. The centered at the midlatitude in accordance with discussion in event lasted for 21 days (07th January 2002 through 28th ◦ ◦ Section 2. The stationary 40 × 60 latitude longitude box January 2002). The block longitude center at the onset size selection is in line with the climatological NH spatial was located at 250 E. We note thatincontrastto Figure 4, distribution of the blocking events [34]. It is also in line there is no single height dominance during the mature Advances in Meteorology 5 Table 2: A summary of the occurrence and character of the blocking events for the calendar years 2002–2004. Blocking parameters in each cell are blocking events/durations (days)/BI. Summer Fall Winter Spring Total Atlantic 9/12.7/2.30 17/10.7/3.27 16/11.1/3.52 16/10.0/2.78 58/10.9/3.03 Paciﬁc 10/9.4/2.28 7/10.6/3.36 16/8.0/3.52 9/11.6/2.65 42/9.5/3.01 Continental 10/12.9/2.18 6/5.7/2.64 4/8.4/2.88 6/15.5/2.44 26/11.1/2.46 Total 29/11.6/2.25 30/9.7/3.16 36/9.3/3.44 31/11.5/2.67 126/10.5/2.90 Average planetary-scale height (m) Average planetary-scale height (m) versus time (days) for 500 hPa versus time (days) for 500 hPa 1 6 11 16 21 26 31 1 6 11 16 21 26 31 Time (days for March 2004) Time (days for January 2002) (a) (a) Average synoptic-scale height (m) Average synoptic-scale height (m) versus time (days) for 500 hPa versus time (days) for 500 hPa 0.6 0.4 0.4 0.2 0.2 −0.2 −0.2 −0.4 −0.4 −0.6 −0.6 −0.8 −0.8 1 6 11 16 21 26 31 1 6 11 16 21 26 31 Time (days for March 2004) Time (days for January 2002) (b) (b) Figure 1: (a) The blocking area averaged planetary-scale 500 hPa Figure 2: (a) The blocking area averaged planetary-scale 500 hPa ◦ ◦ ◦ ◦ height (m) versus time (days), for a stationary box (20 Nto60 N height (m) versus time (days), for a stationary box (20 Nto60 N ◦ ◦ ◦ ◦ and 330 Eto30 E), in the midlatitude northern hemispheric ﬂow. and 290 E to 230 E), in the midlatitude northern hemispheric ﬂow. The dashed dotted horizontal line deﬁnes the monthly mean value The dashed dotted horizontal line deﬁnes the monthly mean value for the planetary-scale height. The left vertical line marks the for the planetary-scale height. The left vertical upward arrow marks beginning, whereas the right vertical line marks the end of the the beginning, whereas the right vertical upward arrow marks the selected blocking event; (b) same as Figure 1(a) except for the end of the selected blocking event; (b) same as Figure 2(a) except synoptic-scale height. for the synoptic-scale height. Average synoptic-scale height (m) Average planetary-scale height (m) Average planetary-scale height (m) Average synoptic-scale height (m) 6 Advances in Meteorology 90N Average planetary-scale height (m) 5400 5400 5500 versus time (days) for 500 hPa 80N 70N 60N 5700 5650 5750 5600 5800 5650 50N 40N 5750 30N 150E 160E 170E 180 170W 160W 150W 140W 130W 120W 110W 100W 90W (a) 05 August 2004 90N Onset Mature stage Decay 80N 1 6 11 16 21 26 31 70N Time (days for August 2004) (a) 60N Average synoptic-scale height (m) 50N versus time (days) for 500 hPa 5650 5900 0.5 40N 0.4 30N 150E 160E 170E 180 170W 160W 150W 140W 130W 120W 110W 100W 90W 0.3 (b) 13 August 2004 0.2 90N 0.1 80N 70N −0.1 −0.2 60N 5600 −0.3 50N 1 6 11 16 21 26 31 40N Time (days for August 2004) 30N (b) 150E 160E 170E 180 170W 160W 150W 140W 130W 120W 110W 100W 90W (c) 27 August 2004 Figure 4: (a) The blocking area averaged planetary-scale 500 hPa ◦ ◦ height (m) versus time (days), for a stationary box (40 Nto80 N Figure 3: (a) The 500 hPa mean daily height. The cross indicates the ◦ ◦ and 160 E to 260 E), in the midlatitude northern hemispheric center of blocking at the onset. The blocking domain boundary is ﬂow. The dashed dotted horizontal line deﬁnes the monthly mean marked around the center by thick solid black line. The continuous value for the planetary-scale height. The left vertical line marks curves represent height contours at 50 m interval, for 05 August the beginning, whereas the right vertical line marks the end of 2004. Note the meridional (split)-ﬂow character of the block; (b) the selected blocking event; (b) same as Figure 4aexceptfor the for 13 August 2004; (c) for 27 August 2004. synoptic-scale height. 3.3. Analysis Summary. Table 3 summarizes our ﬁndings stage of the selected blocking event. Both the planetary- and for the blocking events with single and alternating-scale synoptic-scale heights rise and fall occur during the life-cycle dominance for the three-year period over the entire NH. of the blocking event relative to their respective monthly The maximum (minimum) number of blocking event having mean values. The blocking events displaying this type of planetary-scale dominance occurs during 2003 (2002) in height-time evolution are categorized as the alternating-scale NH. The minimum (maximum) number of blocking events height dominance behavior blocking events. However, this having synoptic-scale dominance occurs during 2003 (2002). category of the blocking events consists of only 21% of the The seasonal results show that the winter and spring season total detected blocking events during the three-year period events are more synoptic-scale dominant, while summer under study. and fall events are strongly planetary-scale dominant. The Average synoptic-scale height (m) Average planetary-scale height (m) Advances in Meteorology 7 −1 Planetary-scale IRE Planetary-scale max|∇ψ|(ms ) −10 versus time (days) for 500 hPa ×10 versus time (days) for 500 hPa 2.2 10.89 10.88 1.8 10.87 1.6 1.4 10.86 1.2 10.85 10.84 0.8 1 6 11 16 21 26 31 1 6 11 16 21 26 31 Time (days for August 2004) Time (days for August 2004) (a) (a) Synoptic-scale IRE −1 −11 Synoptic-scale max|∇ψ|(ms ) ×10 versus time (days) for 500 hPa versus time (days) for 500 hPa 1 6 11 16 21 26 31 1 6 11 16 21 26 31 Time (days for August 2004) Time (days for August 2004) (b) (b) Figure 5: (a) The blocking area averaged enstrophy using (2)for Figure 6: (a) The 500 hPa planetary-scale max|∇ψ| versus time the blocking event displayed in Figure 3 which occurred during 05– ◦ ◦ ◦ ◦ (days) for a stationary box (40 Nto80 N and 160 E to 260 E) in 28 August 2004. The relative stability level changes at onset (02– the midlatitude northern hemispheric ﬂow. The dash dotted line 05 August) and at decay (20–28 August) stages. The dash dotted deﬁnes the mean monthly value for max|∇ψ|. The left vertical line horizontal line deﬁnes the monthly mean value. The left vertical line marks the beginning, whereas the right vertical line marks the end marks the beginning, whereas the right vertical line marks the end of the selected blocking event; (b) same as Figure 6(a) except that of the selected blocking event; (b) same as Figure 5(a) except for the now the synoptic-scale eﬀect is taken into account. synoptic-scale height. events occurring during the three-year study period. We thus seasonal variation of synoptic dominance is consistent with perform next a detailed case study for the single-scale height the seasonal variations in the number and strength of midlatitude cyclones (e.g., [43]). Table 3 is valid only for the dominance as a representative case study. blocking detection method, and scale categorization used in this study. 4. Case Study A prominent feature of our study is the ﬁnding that the scale contributions of a vast majority of the blocking In this section, detailed discussions of the synoptic aspects as events are governed by the dominance of the single-scale well as the scale and the stability analysis of the ﬂow for an height scale. This category of blocking events thus constitutes unusually persistent blocking event that led to a heat wave a representative category of all the midlatitude blocking in the Gulf of Alaska during August 2004 are presented [44]. 2 −2 2 −2 Blocking area IRE (m s ) Blocking area IRE (m s ) −1 max|∇ψ|(ms ) −1 max|∇ψ|(ms ) 8 Advances in Meteorology Table 3: Planetary-, synoptic-, and alternating-scale dominance split-ﬂow block deepened as the blocking intensiﬁed, as did results for the three-year period (2002–2004) analysis and for each the ridge (Figure 3(b)). The last several days of the period season performed in this study, over the entire NH. The number showed this feature propagating over the Alaskan Peninsula and percentage for each year or season and the total is displayed. as the new ridge ampliﬁed over the Bering Sea upstream of the dying event. The block became fully suppressed by 27 (a) August as the mean 500 hPa height ﬁeld became nearly zonal Year Planetary Synoptic Alternating in character (Figure 3(c)). 2002 15/37% 17/41% 9/22% 2003 22/46% 11/23% 15/31% 4.2. Scale Analysis. Figure 4(a) displays the 500 hPa blocking 2004 18/49% 16/43% 3/8% area averaged planetary-scale height for the entire life-cycle Total 55/44% 44/35% 27/21% of the block. During the mature stage of the block life-cycle, the height attains its relative maximum value (5778 m). Note (b) the occurrence of a positive height during the mature stage Season Planetary Synoptic Alternating (05–20 August 2004) of the blocking as the monthly mean Winter 12/33% 17/48% 7/19% value for the entire month of August lies at 5748 m only. The Spring 12/39% 14/45% 5/16% average heights within the box start falling until just before Summer 16/55% 6/21% 7/24% the block decay (day number 21). This suggests changes in the behavior of the planetary-scale ﬂow regime. Fall 15/50% 7/23% 8/27% Figure 4(b) displays the 500 hPa synoptic-scale height for the entire life-cycle of the selected blocking event. During the decay stage (20–28 August), the temporal activity of the migratory synoptic-scale heights is greater than during the The synoptic analysis is performed ﬁrst, and then a scale and onset and mature stages since during the decay stage, the stability analysis of the NH ﬂow region where the selected synoptic-scale environment becomes unstable. The oscilla- blocking event occurred. tory behavior is indicative of area averaged synoptic-scale For the case study presented in the next section, a ridge-trough dominance for the advection of the heat wave diﬀerent latitude-longitude window is used to accommodate at the given isobaric level. A positive diﬀerence corresponds the unusually large spatial extent of the selected blocking to the high pressure system/ridge, whereas the negative event. diﬀerence corresponds to the formation of a trough. This blocking event is the second longest blocking event 4.1. Synoptic Analysis. The selected blocking event occurred in the east Paciﬁc region for the calendar year 2004. This during 02 August through 28 August 2004. Following [33], ﬁnding is in agreement with the estimates of longevity by the block onset and intensiﬁcation stage was during 02–05 [45]. This unusually prolonged blocking event impacted August, its mature stage was during 05–20 August and its the downstream regional weather over the continental US decay stage was during 20–28 August. The blocking ridge as well. The west cost of the mainland continental US lasted for 23.5 days. The blocking ﬂow was located in the experienced mild summer during August 2004 [46]. This is ◦ ◦ ◦ ◦ region encompassing 40 Nto80 N and 160 E to 260 E, with yet another example of the occurrence of mid-tropospheric block longitude at the onset was located at 210 E. This is level blocking aﬀecting the regional weather upstream and/or eventnumber26in Table 6 in Appendix B.Above normal downstream of the event (e.g., [47]). For details of clima- surface temperatures and below normal precipitation was tological aspects of downstream weather impacts associated reported during August over the entire Alaska region [44]. with the blockings, see also [48]. The height variations (taken at 500 hPa) that lead to identiﬁcation of the blocking on an upper air chart can conveniently be quantiﬁed in terms of BI. According to the 4.3. Stability Analysis. Figure 5(a) displays the time evolu- deﬁnition of BI [33], the BI for the considered blocking event tion of the blocking area integrated regional enstrophy (IRE) averaged over its entire life-cycle is 2.44, implying that it is a for the 500 hPa planetary-scale height. Comparing this with moderate strength blocking event. Figure 4(a) that gives the time evolution of the planetary- Figure 3 indicates that during the block onset, a merid- scale height, it is noted that between 21 and 23 August, ional (split)-ﬂow pattern became prevalent in the 500 hPa the IRE increases considerably (peaking on 22 August), mean height ﬁeld around the position marked with cross. indicating the rise in the instability in the planetary-scale In the Gulf of Alaska, a lower height value on the order of ﬂow which corresponds well in time with the fall in the 5600 m was located directly east of the main higher height amplitude of the planetary-scale height during the same value. Of particular interest, however, is to note that this period. trough remained quasistationary over the Gulf of Alaska Calculation of the IRE following (2) for entire life-cycle while the ridge ampliﬁed (see Figure 3(b)—the 5750 m of the blocking event under study indicates a relationship contour was located over Alaska following the period from between these values and the trend displayed in Figure 4(a), Figure 3(a)). This feature appeared to be the central focus where blocking area averaged planetary-scale height is for action in the blocking region. The four days beginning displayed. From Figure 5(a), it is noted that the area averaged on 10 August 2004 show the lower height responsible for the enstrophy reaches a minimum shortly after block onset (after Advances in Meteorology 9 Table 4: Planetary-scale and synoptic-scale dominance results for all the blocking events during the year 2002. The italic entries are the selected case studies. See text for details. Event no. Start date End date Duration (days) Planetary-scale dominance Synoptic-scale dominance 1 02Jan. 11Jan. 9.5 Positive Negative 2 03Jan. 08Jan. 5 Positive Negative 3 07 Jan. 28 Jan. 21 Alternating Alternating 4 13 Jan. 27 Jan. 14 Negative Positive 5 25Jan. 30Jan. 5 Negative Positive 6 30Jan. 05Feb. 6 Negative Positive 7 31Jan. 06Feb. 5.5 Negative Positive 8 06 Feb. 11 Feb. 5 Alternating Alternating 9 02 Feb. 12 Feb. 10 Negative Positive 10 12 Feb. 17 Feb. 5 Negative Positive 11 11 Feb. 28 Feb. 17 Alternating Alternating 12 01 Mar. 07 Mar. 6 Positive Negative 13 04 Mar. 21 Mar. 17 Negative Positive 14 06 Mar. 21 Mar. 15 Positive Negative 15 09 Mar. 28 Mar. 19 Negative Positive 16 01 Apr. 18 Apr. 17 Positive Negative 17 02 Apr. 07 Apr. 5 Negative Positive 18 15 Apr. 24 Apr. 9 Positive Negative 19 19 Apr. 04 May 13.5 Negative Positive 20 23 Apr. 03 May 8.5 Negative Positive 21 10 May 19 May 9 Positive Negative 22 09 May 29 May 20 Positive Negative 23 01 Jun. 10 Jun. 9 Alternating Alternating 24 04 Jun. 09 Jul. 35 Alternating Alternating 25 22 Jun. 30 Jun. 8 Negative Positive 26 30 Jun. 08 Jul. 9 Positive Negative 27 06 Jul. 17 Jul. 9 Negative Positive 28 30 Jul. 07 Aug. 8 Positive Negative 29 01 Aug. 11 Aug. 10 Positive Negative 30 15 Aug. 28 Aug. 13 Negative Positive 31 07 Sep. 18 Sep. 11 Alternating Alternating 32 23 Sep. 28 Sep. 5 Positive Negative 33 20 Sep. 02 Oct. 12 Positive Negative 34 06 Oct. 15 Oct. 9 Positive Negative 35 13 Oct. 18 Oct. 5 Alternating Alternating 36 22 Oct. 03 Nov. 12 Negative Positive 37 25 Oct. 30 Oct. 5 Negative Positive 38 01 Nov. 06 Nov. 5.5 Alternating Alternating 39 18 Nov. 25 Nov. 7 Positive Negative 40 20 Nov. 11 Dec. 21 Negative Positive 41 26 Nov. 28 Dec. 32.5 Alternating Alternating 2 August) and is at a relative minimum during the mature supports this observation. This is also consistent with the stage of this blocking event. The appearance of relatively view that, in a quasibarotropic ﬂow, the planetary-scale ﬂow small peaks on 5 and 15 August indicate the decreasing should be strongly barotropic [49]. Figure 5(a) indicates that role played by the planetary-scale heights in advection of after the onset of the blocking state, the block IRE attains the (quasi stationary) ridge in terms of its location and relatively lower positive values. orientation. Inspection of series of 500 hPa height plots (such The calculation for the IRE was also performed by as those displayed in Figure 3) for the chosen blocking event taking into account the eﬀects of synoptic-scale eddies and 10 Advances in Meteorology Table 5: Same as Table 4 except for the year 2003. Event no. Start date End date Duration (days) Planetary-scale dominance Synoptic-scale dominance 1 02Jan. 10Jan. 8 Negative Positive 2 12Jan. 18Jan. 6 Positive Negative 3 14Jan. 20Jan. 6 Positive Negative 4 23 Jan. 06 Feb. 14.5 Alternating Alternating 5 25Jan. 01Feb. 7 Positive Negative 6 09 Feb. 15 Feb. 6 Alternating Alternating 7 09 Feb. 22 Feb. 13 Positive Negative 8 20Feb. 02Mar. 11 Negative Positive 9 20 Feb. 26 Feb. 6 Negative Positive 10 07 Mar. 18 Mar. 10.5 Positive Negative 11 19 Mar. 25 Mar. 6 Negative Positive 12 29 Mar. 08 Apr. 9.5 Negative Positive 13 04 Apr. 13 Apr. 9 Negative Positive 14 14 Apr. 22 Apr. 8.5 Positive Negative 15 26 Apr. 06 May 10 Negative Positive 16 01 May 22 May 21 Alternating Alternating 17 12 May 23 May 11 Positive Negative 18 13 May 28 May 15 Alternating Alternating 19 25 May 12 Jun. 17 Positive Negative 20 03 Jun. 12 Jun. 9 Negative Positive 21 04 Jun. 22 Jun. 18.5 Negative Positive 22 13 Jun. 24 Jun. 11 Positive Negative 23 24 Jun. 05 Jul. 11 Positive Negative 24 28 Jun. 07 Jul. 9 Alternating Alternating 25 09 Jul. 10 Aug. 32 Positive Negative 26 11 Jul. 19 Jul. 7.5 Alternating Alternating 27 18 Jul. 05 Aug. 18 Positive Negative 28 06 Aug. 13 Aug. 7 Alternating Alternating 29 12 Aug. 26 Aug. 14 Alternating Alternating 30 24 Aug. 13 Sep. 21.5 Alternating Alternating 31 01 Sep. 10 Sep. 9 Positive Negative 32 10 Sep. 20 Sep. 10 Positive Negative 33 11 Sep. 20 Sep. 9 Positive Negative 34 13 Sep. 25 Sep. 12 Negative Positive 35 24 Sep. 10 Oct. 16 Alternating Alternating 36 25 Aug. 07 Sep. 12 Alternating Alternating 37 28 Sep. 05 Oct. 7 Positive Negative 38 28 Sep. 05 Oct. 7 Alternating Alternating 39 13 Oct. 24 Oct. 11 Negative Positive 40 29 Oct. 08 Nov. 9.5 Positive Negative 41 01 Nov. 06 Nov. 5 Positive Negative 42 05 Nov. 16 Nov. 11 Positive Negative 43 27 Oct. 04 Nov. 7 Alternating Alternating 44 04 Dec. 10 Dec. 6.5 Alternating Alternating 45 16 Dec. 21 Dec. 5 Positive Negative 46 19 Dec. 26 Dec. 7 Positive Negative 47 28 Nov. 05 Dec. 8 Positive Negative 48 29 Nov. 04 Dec. 6 Alternating Alternating Advances in Meteorology 11 Table 6: Same as Table 5 except for the year 2004. Event no. Start date End date Duration (days) Planetary-scale dominance Synoptic-scale dominance 1 27Dec. 09Jan. 13 Positive Negative 2 02Jan. 11Jan. 9.5 Negative Positive 3 23Jan. 05Feb. 13 Negative Positive 4 18Jan. 18Feb. 31 Positive Negative 5 10 Feb. 14 Mar. 31.5 Alternating Alternating 6 14 Feb. 28 Feb. 14 Negative Positive 7 28 Feb. 05 Mar. 5 Alternating Alternating 8 15Mar. 20Mar. 5 Negative Positive 9 17Mar. 22Mar. 5 Negative Positive 10 22 Mar. 29 Mar. 7.5 Negative Positive 11 26 Mar. 12 Apr. 17 Negative Positive 12 11 Apr. 16 Apr. 5 Negative Positive 13 14 Apr. 22 Apr. 7.5 Positive Negative 14 16 Apr. 26 Apr. 10 Positive Negative 15 20 Apr. 13 May 23 Alternating Alternating 16 06 May 13 May 7.5 Negative Positive 17 10 May 25 May 15.5 Positive Negative 18 12 May 01 Jun. 20 Negative Positive 19 05 Jun. 10 Jun. 5 Negative Positive 20 26 Jun. 10 Jul. 14 Positive Negative 21 02 Jul. 13 Jul. 10.5 Negative Positive 22 06 Jul. 11 Jul. 5 Negative Positive 23 12 Jul. 24 Jul. 11.5 Positive Negative 24 27 Jul. 01 Aug. 5 Positive Negative 25 27 Jul. 15 Aug. 18.5 Positive Negative 26 05 Aug. 28 Aug. 23.5 Positive Negative 27 09 Aug. 15 Aug. 6.5 Positive Negative 28 06 Sep. 11 Sep. 5 Negative Positive 29 08 Oct. 15 Oct. 7 Positive Negative 30 12 Oct. 26 Oct. 14 Negative Positive 31 18 Oct. 28 Oct. 10 Negative Positive 32 02 Nov. 13 Nov. 11 Positive Negative 33 04 Nov. 26 Nov. 22 Positive Negative 34 21 Nov. 26 Nov. 5 Positive Negative 35 09 Dec. 14 Dec. 5 Positive Negative 36 19 Dec. 25 Dec. 6 Positive Negative 37 19 Dec. 26 Dec. 7 Negative Positive is displayed in Figure 5(b). At mid tropospheric level, the to the time evolution of the average planetary-scale height synoptic-scale IRE does not exhibit a clear trend in any of displayed in Figure 4(a). Following [30], it may be concluded the three stages of blocking. The only trend that is obvious is that if max|∇ψ| depicts relatively positive changes, then that near the onset (after day 5), the IRE attains a relatively the height variation is becoming increasingly unstable. lower value, thus characterizing the relative stability of the Figure 6(a) indicates that the planetary-scale ﬂow remains ﬂow at the synoptic-scale. The IRE gives a relative change largely stable during the blocking since the relative positive only andisthusalone notsuﬃcient to identify the blocking variation implied by max|∇ψ| is less than 0.2%, when event unambiguously. averaged over the blocking life-cycle. The temporal behavior of another stability indicator Figure 6(b) is similar to Figure 6(a) except that now is displayed in Figure 6(a) for the blocking area averaged we make use of the synoptic-scale height to calculate the planetary-scale height. As mentioned in Section 2.4, ψ max|∇ψ|. The appearance of the relatively sharp rise during acquires a relative maximum value, above the corresponding the decay stage, above the corresponding monthly mean monthly mean, during the blocking state and is similar value, is consistently explainable in our picture of the relative 12 Advances in Meteorology role of the two scales. The planetary-scale ﬂow is more stable dominance whereas 35% have synoptic-scale domi- during the blocking; the synoptic-scale ridge formation nance in scale contributions. The remaining 21% of destabilizes it thus causing the ﬂow to revert back to the zonal the blocking events are categorized as alternating- conﬁguration. This implies that once the blocking event height scale dominance blocking events. Blocking established itself, the planetary-scale ﬂow is relatively more events from December to May (June–November) predictable in the present case study. were more synoptic (planetary) scale dominant. (ii) The sensitivity of our results to the blocking domain size variation was studied. When the blocking 4.4. Discussion. Changes in the nature of the planetary- ◦ ◦ ◦ domain size was varied from 40 × 60 to 80 × scale ﬂow may be related with the block onset and decay 100 , the deviation of the planetary-scale height that [15, 24, 25, 50]. The planetary-scale provides a favorable is averaged over it was found to be less than 1%. environment for the blocking event to occur, in spite of This indicates that our conclusions are relatively the large contributions by the synoptic-scale ﬂow and the insensitive to the blocking domain size variation for interaction components of the forcing. the planetary-scale height within the above latitude The supporting evidence for the change in planetary- and longitude range. scale ﬂow regimes comes from examining the IRE (ﬂow stability) calculations. The IRE values (Figure 5(a))fallto Next, summary of the synoptic analysis as well as the scale a relative minimum during the mature stage of the block and the stability analysis of an unusually prolonged and a in the blocked region in agreement with what would be moderately strong blocking event occurring in the Gulf of expected for the selected blocking event (with planetary-scale Alaska during August 2004, is presented. This blocking event dominance) implying that the planetary-scale ﬂow became persisted in Gulf of Alaska for the entire month of August unstable around the time of the block onset and decay. resulting in a heat wave (up to 5 C higher than normal 1971– Further, the prominence of the synoptic-scale in winter 2000 mean temperatures in Alaska region). Our analyzed events versus the planetary-scale prominence in the summer results are as follows. events follows from the annual variation in the number and strength of midlatitude cyclones. It also follows that most (i) A synoptic study of this event was performed of the studies referenced above [9, 11, 12], studied winter through visual inspection of a series of NCEP-NCAR season events, and as such focused on the contribution of reanalysis data generated plots of observed 500 hPa the synoptic-scale in the blocking events. On the other hand, heights and was concluded that the blocking is a even though summer season events were dominated by the ◦ ◦ positive height anomaly encompassing 40 N–80 N planetary-scale, the forcing itself may still be dominated by ◦ ◦ and 160 E–260 E. The detailed scale contribution the synoptic-scale as was found by [14], or it is possible analyses, performed using explicit calculations, for that this study chose an event represented by the minority the speciﬁc case study, conﬁrm this. This positive of warm season types. This fact points to the need for more comparison lends conﬁdence in our diagnostic anal- case studies of the blocking events. ysis procedure outlined in Section 2. (ii) Synoptically, a gradual ampliﬁcation of positive 5. Summary and Conclusions height value during the ﬁrst half of the blocking event life-cycle (5–15 August 2004) and then later a de- In this section, the ﬁndings for the three-year scale contri- ampliﬁcation during later half of the blocking event butions study are summarized ﬁrst, and then results for the life-cycle (15–28 August 2004) based on same obser- case study are presented. The scale analysis is performed by vational procedure, was noticed. Our Figure 4(a) decomposing the observed 500 hPa height into the blocking conﬁrms this ﬁnding. area averaged planetary-scale and the synoptic-scale heights (iii) Subtracting the planetary mean from the total pres- and then the time evolution of both the contributions is sure plots indicates that the synoptic-scale eddies analyzed during the life-cycle for the entire set of the blocking did not play leading role in this event. Furthermore, events. through the same analysis, it is noted that planetary- Using the NCEP-NCAR gridded reanalyzed data for ◦ ◦ scale is more stable. The relative stability role of 2002–2004, and averaging over the 40 × 60 latitude the two scales under the working assumption of the longitude box encompassing the blocking event and based Dymnikov conjecture (see Appendix A) was analyzed on our criterion of scale dominance as a height value above that conﬁrms this ﬁnding. This was the ﬁrst time this the monthly mean value for that height during the month in conjecture has been used for an observational case which the blocking occurs, the ﬁndings may be summarized study. as follows. (iv) It is noted that meridional gradient of the planetary- (i) A total of 126 events were analyzed to determine the scale height ﬁeld exists at mid-tropospheric level scale contribution dominance of the planetary- and through visual inspection. Our results displayed synoptic-scales during the blocking of the zonal ﬂow. in Figure 6(a) conﬁrm this ﬁnding. This in turn 79% of the total analyzed events have single height provides support for using simple variable such as dominance. Out of these, 44% have planetary-scale max|∇ψ| as a possible stability indicator of the ﬂow. Advances in Meteorology 13 (v) These two diagnostic tools show that the planetary- The perturbation energy equation in terms of scalar scale environment becomes unstable during the onset product (Lψ , ψ )is and then stabilizes during the mature stage of the ∂E blocking whereas the synoptic-scale heights play a = Lψ , ψ . (A.3) ∂t dominant role in destabilizing the planetary-scale ﬂow during the mature stage of the blocking life-cycle Since L = S + K,where K is the skew-symmetric part of the initiating the blocking decay. The interplay of both operator L and S is the symmetric part of the operator L, the the contributions is found to be the case during the perturbation energy equation may be rewritten with L → S three stages of the blocking, when their relative role is in (A.3), that is assessed in terms of the IRE and the maximum of the gradient of the ﬂow stream function. ∂E = Sψ , ψ . (A.4) ∂t It can be pointed out, that this study also conﬁrms the tentative conclusions of earlier studies that both the Note that the stationary solution ψ will be stable if all planetary- and synoptic-scales are equally important in the the eigenvalues of the operator S with respect to stationary life-cycle of the blockings in the midlatitude NH zonal ﬂow solution are negative. We shall thus take the sum of positive in general (see Section 1 for references). Based on the three- eigenvalues of the operator S as the characteristics of the year study, the above observations are true irrespective of instability of the stationary point. whether the blocking event occurs entirely over the land, over Assuming that ψ = ψ (y); that is, the stationary solution the ocean, or partially over the land and partially over the does not depend on zonal coordinate to mimic meridionally ocean. This may indicate more dominating role played by directed perturbation (namely, the blocking) in the mainly the diﬀerent scales and their interactions in the ﬂow once the zonal ﬂow and using the periodic conditions for x and blocking sets in instead of orographic forcings. y and passing to ﬁnite dimensions, after some algebraic As exempliﬁed by the selected case study, the IRE may manipulation, the eigenvalue problem for the operator S characterize the stability of the planetary/synoptic-scale ﬂow (where 2S = L + L ) has the form in the barotropic circulation. A simultaneous knowledge of the two diagnostic tools, however, seems to provide a ∂ ∂ϕ u Δϕ − Δ u = λϕ. (A.5) more reliable scenario for the occurrence, sustenance as well ∂x ∂x as decay of a blocking event. The IRE of the Dymnikov conjecture gives only the relative stability of the ﬂow. Height Here, λ’s are the eigenvalues of the eigenoperator ϕ.The λ’s variations alone however do not provide any underlying play the role of the characteristic exponents. We shall look insight into the scale contributions and the ﬂow stability for the general solution of (A.5) in the form that depends ikx during the blocking period. A simultaneous estimate of both on x and y: ϕ(x, y) = ϕ(y)e . With this transformation, we may establish the presence and the stability behavior of the obtain the following eigenvalue equation from (A.5) ﬂow. The above observations made in this study ﬁnd some ∂σϕ ∂ϕ λ justiﬁcation in light of the previous studies mentioned in + σ = ϕ, Section 1, where it was concluded that both the planetary- ∂y ∂y ik scale as well as the synoptic-scale heights seems to play some (A.6) ∂u role in essentially all stages of the blocking life-cycle. Though σ =− . ∂y depending upon the speciﬁc case study, the relative strength of the role seems to vary. In principle, one should solve this equation to obtain the spectrum of eigenvalues λ, which depends upon σ. Note Appendices σ is the vertical component of the relative vorticity for the stationary component of the stream function. Here, we A. Area Integrated Regional Enstrophy make use of the Dymnikov et al. [29]conjecturewhich suggests a strong correlation between the sum of the positive The dynamic equation of viscous incompressible barotropic characteristic exponents (eigenvalues of the linearization ﬂuid for the stream function ψ is given by operator of barotropic ﬂow) and the (blocked) domain integrated enstrophy, that is ∂Δψ + J ψ , Δψ = 0. (A.1) ∂t λ ≈ σ y dx dy. (A.7) The Δ is the Laplacian operator. The J is the Jacobian incorporating the nonlinear interactions. Expanding ψ in terms of time-dependent and time-independent compo- Equation (A7) can be obtained from (A.6) by ﬁrst writing nents, respectively, such that ψ = ψ + ψ,where ψ = (A.6) in ﬁnite diﬀerence form and then using a known ψ (t)and ψ = ψ (t). The equation of motion for linearization algebraic relation. This is the same as (2)in Section 2.3 of the operator L is ∂Δψ /∂t + Lψ = 0, where text, with σ → σ. Let us add that a numerical implementation of equation for L via Crank-Nicholson scheme in [29] using Lψ = J ψ , Δψ + J ψ , Δψ . (A.2) data for a three-year period after applying a 15-day ﬁlter 14 Advances in Meteorology (planetary-scale) on domains D over the north Atlantic and [10] H. Nakamura and J. M. Wallace, “Observed changes in baroclinic wave activity during the life cycles of low-frequency western Europe establishes the validity of (A.7). circulation anomalies,” Journal of the Atmospheric Sciences, vol. Summarizing, to the extent that the average time for σ- 47, no. 9, pp. 1100–1116, 1990. trajectories to diverge decreases as the sum of the positive [11] A. R. Lupo and P. J. Smith, “Planetary and synoptic-scale characteristic exponent’s increases, we get a preliminary interactions during the life cycle of a midlatitude blocking indication of how physical quantities, such as enstrophy, anticyclone over the North Atlantic,” Tellus,vol. 47, no.1,pp. may be viewed as forecasting indicators. The time evolution 575–596, 1995. of right hand side of (A.7) may thus represent the relative [12] A. R. Lupo, “A diagnosis of two blocking events that occurred stability of the barotropic ﬂow. Development of a mainly simultaneously in the midlatitude Northern Hemisphere,” meridional perturbation (y dependence only of ψ ) signiﬁes Monthly Weather Review, vol. 125, no. 8, pp. 1801–1823, 1997. relative stability of the ﬂow which we interpret as the [13] H. Nakamura, M. Nakamura, and J. L. Anderson, “The role blocking under the working assumption of Dymnikov et al. of high- and low-frequency dynamics in blocking formation,” Monthly Weather Review, vol. 125, no. 9, pp. 2074–2093, 1997. conjecture [29]. Note that right hand side of (A.7)refers [14] A. R. Lupo andP.J.Smith,“Theinteractionsbetween a to area averaged (relative) vorticity squared as mentioned midlatitude blocking anticyclone and synoptic-scale cyclones earlier. that occurred during the summer season,” Monthly Weather Review, vol. 126, no. 2, pp. 503–515, 1998. B. The Blocking Height-Scale Contribution [15] J. P. Burkhardt and A. R. Lupo, “The planetary- and synoptic- scale interactions in a southeast Paciﬁc blocking episode using Analysis for 2002–2004 PV diagnostics,” Journal of the Atmospheric Sciences, vol. 62, See Tables 4, 5, and 6. no. 6, pp. 1901–1916, 2005. [16] L. Dong and S. J. Colucci, “The role of deformation and potential vorticity in Southern Hemisphere blocking onsets,” Acknowledgments Journal of the Atmospheric Sciences, vol. 62, no. 11, pp. 4043– 4056, 2005. The authors thank Dr. Courtenay Strong for helpful discus- [17] L. Dong and S. J. Colucci, “Interpreting the opposition sions during the early stages of this work. The authors also between two block-onset forcing mechanisms,” Journal of the thank Dr. Mansour Almazroui for his continuous support Atmospheric Sciences, vol. 64, no. 6, pp. 2091–2104, 2007. and cooperation. [18] R. F. C. Marques and V. B. Rao, “A diagnosis of a long-lasting blocking event over the southeast Paciﬁc Ocean,” Monthly Weather Review, vol. 127, no. 8, pp. 1761–1776, 1999. References [19] A. R. Lupo,I.I.Mokhov, S. Dostoglou,A.R.Kunz,and J. P. [1] D. Rex, “Blocking action in the middle troposphere and its Burkhardt, “Assessment of the impact of the planetary scale on the decay of blocking and the use of phase diagrams and eﬀect upon regional climate I. An aerological study of blocking action,” Tellus, vol. 2, pp. 196–211, 1950. enstrophy as a diagnostic,” Izvestiya. Atmospheric and Oceanic Physics, vol. 43, no. 1, pp. 45–51, 2007. [2] D. Rex, “Blocking action in the middle troposphere and its eﬀect upon regional climate II. The climatology of blocking [20] E. Kalnay-Rivas and L.-O. Merkine, “A simple mechanism for action,” Tellus, vol. 2, pp. 275–301, 1950. blocking,” Journal of the Atmospheric Sciences, vol. 38, no. 10, pp. 2077–2091, 1981. [3] R. Benzi, B. Saltzman, and A. C. Wiin-Nielsen, Anomalous Atmospheric Flows and Blocking, vol. 29 of Advances in [21] J. S. Frederiksen, “A uniﬁed three-dimensional instability theory of the onset of blocking and cyclogenesis,” Journal of Geophysics, Academic Press, Boston, Mass, USA, 1986. [4] J. S. Watson and S. J. Colucci, “Evaluation of ensemble the Atmospheric Sciences, vol. 39, no. 5, pp. 969–982, 1982. [22] S. L. Mullen, “The local balances of vorticity and heat for predictions of blocking in the NCEP global spectral model,” Monthly Weather Review, vol. 130, no. 12, pp. 3008–3021, blocking anticyclones in a spectral general circulation model,” Journal of the Atmospheric Sciences, vol. 43, no. 13, pp. 1406– [5] J. G. Charney and J. G. Devore, “Multiple ﬂow equilibria in the 1441, 1986. [23] S. L. Mullen, “Transient eddy forcing of blocking ﬂows,” atmosphere and blocking,” Journal of the Atmospheric Sciences, vol. 36, no. 7, pp. 1205–1216, 1979. Journal of the Atmospheric Sciences, vol. 44, no. 1, pp. 3–22, [6] G. J. Shutts, “The propagation of eddies in diﬄuent jetstreams: eddy vorticity forcing of ’ blocking’ ﬂow ﬁelds,” Quarterly [24] K. Haines and A. J. Holland, “Vacillation cycles and blocking Journalofthe RoyalMeteorologicalSociety, vol. 109, no. 462, in a channel,” Quarterly Journal of the Royal Meteorological Society, vol. 124, no. 547, pp. 873–895, 1998. pp. 737–761, 1983. [7] D. Luo, A. R. Lupo, and H. Wan, “Dynamics of eddy-driven [25] S. J. Colucci and D. P. Baumhefner, “Numerical prediction of the onset of blocking: a case study with forecast ensembles,” low-frequency dipole modes. Part I: a simple model of North Atlantic Oscillations,” Journal of the Atmospheric Sciences, vol. Monthly Weather Review, vol. 126, no. 3, pp. 773–784, 1998. [26] D. E. Tilly, A. R. Lupo,C.J.Melick, andP.S.Market, 64, no. 1, pp. 3–28, 2007. [8] D.Luo,T.T.Gong, andA.R.Lupo, “Dynamicsofeddy-driven “Calculated height tendencies in two southern hemisphere blocking and cyclone events: the contribution of diabatic low-frequency dipole modes. Part II: free mode characteristics of NAO and diagnostic study,” Journal of the Atmospheric heating to block intensiﬁcation,” Monthly Weather Review, vol. 136, no. 9, pp. 3568–3578, 2008. Sciences, vol. 64, no. 1, pp. 29–51, 2007. [9] M. S. Tracton, “Predictability and its relationship to scale [27] P. J. Roebber, “Planetary waves, cyclogenesis, and the irregular breakdown of zonal motion over the North Atlantic,” Monthly interaction processes in blocking,” Monthly Weather Review, vol. 118, no. 8, pp. 1666–1695, 1990. Weather Review, vol. 137, pp. 3907–3917, 2009. Advances in Meteorology 15 [28] S. J. Colucci, “Planetary-scale preconditioning for the onset of Soil, Environmental and Atmospheric Sciences, University of blocking,” Journal of the Atmospheric Sciences, vol. 58, no. 8, Missouri, Columbia, 2007. pp. 933–942, 2001. [47] R. S. Quiroz, “The climate of the 1983-84 winter—a season of [29] V. P. Dymnikov, Y. V. Kazantsev, and V. V. Kharin, “Infor- strong blocking and severe cold in North America,” Monthly mation entropy and local Lyapunov exponents of barotropic Weather Review, vol. 112, no. 9, pp. 1894–1912, 1984. atmospheric circulation,” Izvestiya. Atmospheric and Oceanic [48] M. L. Carrera, R. W. Higgins, and V. E. Kousky, “Downstream Physics, vol. 28, no. 6, pp. 425–432, 1993. weather impacts associated with atmospheric blocking over [30] Y. N. Skiba, “On the spectral problem in the linear stability the Northeast Paciﬁc,” Journal of Climate, vol. 17, no. 24, pp. study of ﬂows on a sphere,” Journal of Mathematical Analysis 4823–4839, 2004. and Applications, vol. 270, no. 1, pp. 165–180, 2002. [49] M. Ghil and S. Childress, Topics in Geophysical Fluid Dynamics: [31] E. Kalnay, M. Kanamitsu, R. Kistler et al., “The NCEP/NCAR Atmospheric Dynamics, Dynamo Theory, and Climate Dynam- 40-year reanalysis project,” Bulletin of the American Meteoro- ics, Springer, Berlin, Germany, 1987. logical Society, vol. 77, no. 3, pp. 437–471, 1996. [50] C. H. Tsou and P. J. Smith, “The role of synoptic/planetary- [32] R. Kistler, E. Kalnay, W. Collins et al., “The NCEP-NCAR 50- scale interactions during the development of a blocking year reanalysis: monthly means CD-ROM and documenta- anticyclone,” Tellus. Series A, vol. 42, no. 1, pp. 174–193, 1990. tion,” Bulletin of the American Meteorological Society, vol. 82, no. 2, pp. 247–267, 2001. [33] A. R. Lupo and P. J. Smith, “Climatological features of blocking anticyclones in the Northern Hemisphere,” Tellus. Series A, vol. 47, no. 4, pp. 439–456, 1995. [34] H. Lejenas and H. Okland, “Characteristics of Northern Hemisphere blocking as determined from a long time series of observational data,” Tellus. Series A, vol. 35, no. 5, pp. 350– 362, 1983. [35] R. Shapiro, “Smoothing, ﬁltering, and boundary eﬀects,” Reviews of Geophysics and Space Physics, vol. 8, no. 2, pp. 359– 387, 1970. [36] A. R. Hansen, “Observational characteristics of atmospheric planetary waves with bimodal amplitude distributions,” Advances in Geophysics, vol. 29, pp. 101–133, 1986. [37] B. Farrell, “Developing disturbances in shear,” Journal of the Atmospheric Sciences, vol. 44, no. 16, pp. 2191–2199, 1987. [38] A. R. Lupo, J. V. Clark, A. M. Hendin, et al., “The global increase in blocking occurrences,” in Proceedings of the 20th Conference on Global Climate Change, American Meteorologi- cal Society, New Orleans, La, USA, 2008. [39] J. M. Wiedenmann, A. R. Lupo, I. I. Mokhov, and E. A. Tikhonova, “The climatology of blocking anticyclones for the Northern and Southern Hemispheres: block intensity as a diagnostic,” Journal of Climate, vol. 15, no. 23, pp. 3459–3473, [40] T. C. Peterson,M.O.Baringer,H.J.Diamond et al., “State of the climate in 2008,” Bulletin of the American Meteorological Society, vol. 90, no. 8, pp. S1–S196, 2009. [41] M. Croci-Maspoli,C.Schwierz, andH.C.Davies, “A mul- tifaceted climatology of atmospheric blocking and its recent linear trend,” Journal of Climate, vol. 20, no. 4, pp. 633–649, [42] D. Luo and H. Wan, “Decadal variability of wintertime North Atlantic and Paciﬁc blockings: a possible cause,” Geophysical Research Letters, vol. 32, no. 23, Article ID L23810, 5 pages, [43] J. R. Key and A. C. K. Chan, “Multidecadal global and regional trends in 1000 mb and 500 mb cyclone frequencies,” Geophysical Research Letters, vol. 26, no. 14, pp. 2053–2056, [44] Alaskan Climate Record Center, “Record breaking summer of 2004,” http://climate.gi.alaska.edu/News/summer04.html. [45] D. Barriopedro, R. Garcıa-Herrera, A. R. Lupo, and E. Hernandez, ´ “A climatology of Northern Hemisphere block- ing,” Journal of Climate, vol. 19, no. 6, pp. 1042–1063, 2006. [46] J. M. Glisan, Two extreme cases of atmospheric blocking over Europe and North America, M.S. thesis, Department of International Journal of Journal of Ecology Mining The Scientific Journal of Geochemistry Scientifica World Journal Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Journal of Earthquakes Paleontology Journal Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Journal of Petroleum Engineering Submit your manuscripts at http://www.hindawi.com International Journal of Geophysics Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Advances in Advances in Journal of Advances in International Journal of Meteorology ClimatologyGeology Oceanography Oceanography Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Applied & Journal of Environmental International Journal of Journal of International Journal of Computational Soil Science Mineralogy Geological Research Atmospheric Sciences Environmental Sciences Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Volume 2014 Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com http://www.hindawi.com Volume 2014

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Scale Analysis of Blocking Events from 2002 to 2004: A Case Study of an Unusually Persistent Blocking Event Leading to a Heat Wave in the Gulf of Alaska during August 2004

Scale Analysis of Blocking Events from 2002 to 2004: A Case Study of an Unusually Persistent Blocking Event Leading to a Heat Wave in the Gulf of Alaska during August 2004

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Scale Analysis of Blocking Events from 2002 to 2004: A Case Study of an Unusually Persistent Blocking Event Leading to a Heat Wave in the Gulf of Alaska during August 2004

Scale Analysis of Blocking Events from 2002 to 2004: A Case Study of an Unusually Persistent Blocking Event Leading to a Heat Wave in the Gulf of Alaska during August 2004

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