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Using Enstrophy-Based Diagnostics in an Ensemble for Two Blocking Events

Using Enstrophy-Based Diagnostics in an Ensemble for Two Blocking Events Hindawi Publishing Corporation Advances in Meteorology Volume 2013, Article ID 693859, 7 pages http://dx.doi.org/10.1155/2013/693859 Research Article Using Enstrophy-Based Diagnostics in an Ensemble for Two Blocking Events Andrew D. Jensen and Anthony R. Lupo Department of Soil, Environmental, and Atmospheric Science, University of Missouri, 302 Anheuser Busch Natural Resources Building, Columbia, MO 65211, USA Correspondence should be addressed to Andrew D. Jensen; jensenad@missouri.edu Received 10 September 2013; Revised 4 November 2013; Accepted 8 November 2013 Academic Editor: Yafei Wang Copyright © 2013 A. D. Jensen 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. Recent research has used enstrophy-based diagnostics to identify the development and dissipation stages of blocking events. These previous studies made use of reanalysis data sets in the calculations of the enstrophy-based diagnostics, such as the NCEP-NCAR ∘ ∘ reanalysis (2.5 × 2.5 ) of geopotential height and horizontal winds. However, none of these studies has explored the use of the enstrophy-based diagnostics in weather or climate models with higher horizontal resolution. In this paper, the enstrophy-based ∘ ∘ diagnostics are used to analyze two blocking events, using data from the ERA-Interim reanalysis data set (0.75 × 0.75 )and also the ∘ ∘ Global Ensemble Forecast System (GEFS) (1 × 1 ). eTh results of this work indicate that using an ensemble may be more effective than a single dynamical control forecast in evaluating the enstrophy-based diagnostic quantities, and that the results are similar to those obtained with coarser resolution. 1. Introduction blocking onset was better predicted than block decay overall. In [9], it was found that ensemble forecasts which were calib- Many studies have noted an upscale cascade of enstrophy rated to correct for the under prediction of blocking were upstream of blocking events (see, e.g., [1, 2]). Moreover, in [3], more accurate than uncalibrated ensemble forecasts. [11] enstrophy and large-scale instability are compared by means found the ensemble mean to perform better than the control of finite-time Lyapunov exponents. Using these ideas and the group for forecast times longer than 3-4 days in two atmo- instability at block onset and decay [4], in a series of recent spheric models. Errors were found to be largest at block onset articles (see [5–8]), enstrophy-based diagnostics have been and decay (see also [4]). used to study large-scale stability changes during the develop- The purpose of this study is to use the enstrophy-based ment and termination of blocking events. es Th e studies used diagnostics (explained below and introduced in [6, 7]) to ana- reanalysis data sets such as the NCEP-NCAR reanalysis of lyze two blocking events, using data from the ERA-Interim geopotential heights and winds to calculate the enstrophy- reanalysis and also the Global Ensemble Forecast System based diagnostics. However, no work has yet explored the use (GEFS), both of which have higher horizontal resolution than of thesediagnostics in weatherorclimate models or in an the NCEP-NCAR reanalysis data set. The previous results ensemble. ∘ ∘ in this area used relatively low-resolution (2.5 × 2.5 )data The utility of using ensemble-based forecasting to better in the calculations. u Th s, a primary objective of this study predict blocking is well known (e.g., [9–11]). Several studies is to determine if the results are sensitive to the resolution note the increased skill of forecasts of blocking episodes used in the calculations by employing model data with over solely dynamical prediction methods. For example, [10] higher horizontal resolution and thus to assess the extension showed that ECMWF ensemble prediction system forecasts of the overall usefulness of the diagnostics. eTh outcomes of blocking are more skilful than the deterministic and cli- matology forecasts of Euro-Atlantic sector blocking, although suggest that the use of an ensemble is preferable over a single 2 Advances in Meteorology dynamical control forecast to the use of the enstrophy-based inner product (⋅, ⋅) by (𝐴 x, y)=(x,𝐴 y).Tomodel blocked diagnostics in a weather model. flow, suppose that eTh outlineofthe paperisasfollows. In Section 2,the (5) 𝜓 (𝑥, 𝑦) = 𝜓 (𝑦) 𝑒 . data sets and the enstrophy-based diagnostics and their use are explained. In Section 3, two blocking episodes are studied When by means of these diagnostics using ERA-Interim reanalysis 𝜕 𝜕 ∗ 2 2 𝑆=𝐴 + 𝐴 = 𝑢 ∇ −∇ ( 𝑢 ), (6) data and GEFS. In Section 4,wediscuss andsummarize our conclusions. it canbeshown that 𝑆 = −𝑖𝑘𝐾 ,where 𝐾 is a skew-symmetric operator. Because the eigenvalues 𝑆 are symmetric about zero, 2. Data and Methods the eigenvalues of the operator 𝐾 are studied instead. Using finite differencing to project onto ni fi te space, the sum of 2.1. Preliminaries. In order to explain the enstrophy diag- the positive local Lyapunov exponents can be shown to be nostics to be used, the local Lyapunov exponents for the determined by the integral of enstrophy, where the integral barotropic vorticity equation must rfi st be considered. Local is over a ni fi te and bounded region. Lyapunov exponents for the barotropic vorticity equation, where 𝜁 is relative vorticity, are dene fi d by 𝜆 (𝜁 ,𝑇) = 𝑖 0 (1/2𝑛) log ] for initial 𝜁 and time 𝑇=𝑛Δ𝑡 .The ] are the 2.2. Enstrophy Advection and Its Integral. As sketched above, 𝑖 0 𝑖 𝑘=𝑛 eigenvalues of 𝑀 𝑀 ,where 𝑀= ∏ 𝐴(𝑘Δ𝑡) and 𝐴(𝑡) is 𝑛 𝑛 𝑘=−𝑛 ∑ 𝜆 ≈ ∫ 𝜁 d𝐴, the linearization operator of the barotropic vorticity equation. (7) 𝜆 >0 u Th s, the local Lyapunov exponents provide a measure of n fi ite-time instability. In [ 12], n fi ite-time instability is where the integral is taken over the Northern Hemisphere estimatedbymeans of thelargest singular value(eigenvalues here. Since the 𝜆 change with time, (7)may be dieff rentiated of 𝑀 𝑀 ) in magnitude in a kinetic energy norm. Here, the to obtain approximation introduced in [3]isusedasameasureofthe 𝜕( ∑ 𝜆 ) 𝑖 𝜕 𝜆 >0 𝑖 2 2 n fi ite-time stability. (8) ≈ ∫ 𝜁 d𝐴=− ∫ k ⋅∇𝜁 d𝐴, 𝜕𝑡 𝜕𝑡 The argument given in [ 3] proceeds as follows. A fric- tionless, nondivergent barotropic flow is assumed. As shown where nondivergent, frictionless barotropic flow on an 𝑓 - in [3], the results to be described are not fundamentally plane has been assumed. aeff cted by orography. The barotropic vorticity equation can To get a more accurate derivative, it is possible to proceed be written in terms of a stream function 𝜓 : as in [13] and consider the barotropic vorticity equation in the form 𝜕∇ 𝜓 2 𝜕 𝜕 2 2 (1) +𝐽(𝜓,∇ 𝜓) = 0, ( +𝑢 )(∇ 𝜓 − 𝐹𝜓) + 𝐽 (𝜓, ∇ 𝜓+ℎ) 𝜕𝑡 𝜕𝑡 (9) 2 2 where ∇ 𝜓=𝜁 and ∇ is the Laplacian operator. Now, (1)can 𝜕𝜓 𝜕ℎ 󸀠 2 󸀠 +(𝛽+𝐹𝑢 ) +𝑢 = −𝐽(𝜓 ,∇ 𝜓 ) , 0 0 be linearized as follows: 󸀠 where 𝑢 represents the basic state westerly wind, 𝜓 and 𝜓 𝜕𝜁 (2) +𝐴𝜁 =0, represent planetary and synoptic scales of the stream func- 𝜕𝑡 tion, respectively; ℎ is a nondimensional topography term, 𝐹 = (𝐿/𝑅 ) where 𝑅 is the Rossby deformation radius, and where 𝐴 is the linearization operator, 𝜓= 𝜓+𝜓 ,and 𝑑 𝑑 2 󸀠 󸀠 the subscript “𝑃 ” represents the planetary scale component. ∇ 𝜓 =𝜁 . Using the Crank-Nicholson scheme, the following However, in [3], the topography and friction were omitted to equation may be obtained: obtain (7), as described above. Hence, here we do not retain 󸀠 󸀠 󸀠 󸀠 such terms in the derivative, while realizing that other terms 𝜁 (𝑡+𝛿𝑡 ) −𝜁 (𝑡 ) 𝜁 (𝑡+𝛿𝑡 ) +𝜁 (𝑡 ) +𝐴 ( 𝜓( 𝑡+ )) =0. can be included to make the result more accurate. Another 2 2 reason for not retaining such terms is a practical one: con- (3) tours of enstrophy advection are easy to interpret and are explained in detail in [6]. To estimate the Lyapunov exponents, (3) can be rearranged, where 𝐼 is the identity operator: 2.3. Methodology. The enstrophy-based diagnostics (describ- −1 ed in detailabove)tobeusedinthe analysis of thetwo block- 𝜁 (𝑡+𝛿𝑡 ) =[𝐼 + 𝐴( 𝜓(𝑡 + ))] ing events considered below were introduced in [6, 7], and 2 2 they are as follows: (4) ×[𝐼− 𝐴( 𝜓(𝑡 + ))] 𝜁 𝑡 . ( ) IRE ≡ ∫ 𝜁 d𝐴, (10) 2 2 The operator in brackets in ( 4)isestimated by 𝑆=𝐴 + 𝐴 , DIRE ≡− ∫ k ⋅∇𝜁 d𝐴, (11) where 𝐴 is the adjoint operator den fi ed for vectors x, y and 𝛿𝑡 𝛿𝑡 𝛿𝑡 𝛿𝑡 𝜕𝑥 𝜕𝑥 𝜕𝑥 𝜕𝑥 𝜕𝑥 𝑖𝑘𝑥 Advances in Meteorology 3 where the integral is evaluated over some n fi ite area on an 85N isobaric surface. The integrated enstrophy (IRE), or ( 10), has 80N been showntoberelated to nfi ite-time instabilitybymeans 75N of the ni fi te-time Lyapunov exponents as described above. 5300 70N Peaks in (10) are therefore a measure of local maximum flow instability, in particular, planetary scale flow. In [ 7], it was 65N observed that the IRE increased sharply at block onset, indi- 60N cating an increase in planetary flow instability. eTh IRE was 55N then observed to decrease to a local minimum and to increase 50N againatblock decaytoalocalmaximum value. On theother 45N hand,the DIRE,or(11), is the derivative of (10) assum- 5550 5600 5650 ing barotropic, inviscid flow, and increasing (decreasing) 40N instability is indicated when (11) is positive (negative), while 35N 5750 5800 maxima in the IRE field can oeft n be found (see [ 6]) when (11) 30N crosses the time-axis from positive to negative. The diagnostics ( 10)and (11)werecalculatedinaspher- ical coordinate system for the Northern Hemisphere using Figure 1: ERA-Interim reanalysis time-averaged geopotential ECMWF ERA-Interim data, obtained from the ECMWF heightsfor October11–19,2012. data server. eTh quantities used in this study are the zonal and meridional wind components, geopotential height, and ∘ ∘ relative vorticity with a 0.75 × 0.75 horizontal resolution at 500hPa.Thesamequantitieswerealsousedfromthe Global 85N Ensemble Forecast System (GEFS), which has 20 members 80N plus the ensemble mean and control with a horizontal resolu- 75N ∘ ∘ tion of 1 × 1 ,inorder to calculate(10)and (11). We chose 70N representative ensemble members from the 20, besides the 65N ensemble mean and control, which are shown in the plots below. 60N eTh blocking denfi ition used in this studyisthatofLupo 55N and Smith [14], which can be described as a synthesis of the 50N subjective Rex criteria (see [15, 16]) and the objective Lejenas- 45N Okland criteria (see [17]), but in which a blocking event is 40N 5600 dene fi d to persist for at least five days. More specicfi ally, the 5700 5700 blocking criteria used here (i) must satisfy the Rex [15, 16]cri- 35N teria for at least vfi e days and (ii) must have a negative or small 30N positive zonal index that can be identified on a time-long- itude or Hovmol ¨ ler diagram. (iii) Conditions (i) and (ii) must be satisefi d for 24 hours aeft r (before) onset (termination); Figure 2: GEFS ensemble mean time-averaged geopotential heights (iv) the blocking event should be poleward of 35N during its for October 11–19, 2012. lifetime, and the ridge should have an amplitude of greater than 5 latitude; and (v) blocking onset is defined to occur when condition (iv) and and one of the conditions (i) or (ii) is satisfied, while (vi) termination or decay is designated at the IRE time series, corresponding to block onset and decay, the time the event fails to satisfy condition (v) for a 24-hour respectively.Aclearupwardtrend canbeseeninthe IRE efi ld period or longer. This definition was used to detect the block- during the block development stage. During the maintenance ing onset and decay times for the events considered below. stage of the event, the IRE dips to a minimum value and again achieves a local maximum during the dissipation stage of the blocking event. On the other hand, the DIRE crosses the time- 3. Dynamic Analysis axis from positive to negative at block onset, reflecting the 3.1. Event 1: October 11–19, 2012. The first blocking event con- local instability maximum. During the maintenance stage, sidered here occurred October 11–19, 2012 and was centered the DIRE is negative until the 16th of October, reflecting at 160E (see Figures 1, 2,and 3). The ERA-Interim reanalysis decreasing instability. The DIRE then assumes positive values overall appeared to have tighter gradients than GEFS. The until it again crosses the time-axis from positive to negative mean height contours of theGEFSensemblemeanand con- which reflects the local instability maximum at block decay. trol appear to be similar, while differences with the ERA cal- The IRE for the GEFS mean, control, and two repre- culatedmeanheights areborne outinthe calculations below. sentative ensemble members are plotted alongside the ERA- The IRE (integrated enstrophy) and DIRE (derivative of Interim IRE for comparison (see Figure 5). The IRE for the IRE) for the ERA-Interim data were rescaled and are shown GEFS mean is strictly decreasing, and the GEFS control together in Figure 4. Two distinct maxima can be seen on appears to behave similarly. eTh ensemble member 11 is an 110E 110E 120E 120E 130E 130E 140E 140E 150E 150E 160E 160E 170E 170E 170W 170W 160W 160W 150W 150W 4 Advances in Meteorology IRE October 11–19, 2012 85N 80N 75N 70N 65N 60N 55N 50N 45N 40N 5600 35N 30N Figure 3: GEFS control time averaged geopotential heights for 11 12 13 14 15 16 17 18 19 October 11–19, 2012. Days ERA M1 IRE and DIRE October 11–19, 2012 M2 AVG 9 9 CTRL Figure 5: ERA and GEFS values of IRE for October 11–19, 2012. Shown are ERA reanalysis (black), GEFS ensemble mean (red), GEFS control (green), and two other ensemble members (dark and 8 8 light blue). reflected by their crossing the time-axis from positive to negative. Similar to the behavior of the IRE as calculated from 0 0 GEFS, M1 and M2 from the ensemble show results that are similar to the ERA-Interim DIRE with the DIRE crossing the time-axis from positive to negative values for block onset and −4 −4 decay periods. −8 −8 11 12 13 14 15 16 17 18 19 3.2. Event 2: March 9–14, 2013. The second event occurred Days March 9–14, 2013 and was centered at 170 W (see Figures 7, 8,and 9). In this case,ERA-Interim,GEFSmean, andGEFS IRE control appear more similar to each other compared to the DIRE first case. However, the contours over Alaska and gradients Figure 4: IRE and DIRE from ERA-Interim reanalysis for October over the Pacicfi are different for the reanalysis compared to 11–19, 2012. GEFS. Again, the IRE and DIRE for the ERA-Interim data were rescaled and are shown together in Figure 10.There, the extreme outlier and likely aeff cted the poor performance of IRE field is at a local maximum value during the block the ensemble mean. However, M1 and M2, which are mem- development stage. eTh IRE decreases to a minimum value bers 5 and 15 of the ensemble and are representatives of other around the 13th of March during the maintenance stage of the members of the ensemble, appear closer to the ERA-Interim event. Finally, the IRE increases to a local maximum by the IRE in that they reach maxima in the IRE field, if somewhat end of the event. Now, the DIRE crosses the time-axis from lagging in time. M2 also appears to reach a local maximum at positive to negative values on the 9th of March, reflecting block decay. the local instability maximum at block onset. eTh instability Now, the DIRE for the GEFS mean, control, and two decreases (DIRE is negative) during the maintenance stage ensemble members are plotted alongside the ERA-Interim until the 11th of March. eTh DIRE then takes on positive DIRE for comparison (see Figure 6). In contradistinction to values until again crossing the time-axis from positive to the GEFS IRE, all of the GEFS members plotted achieve negative values, which reflects the local instability maximum a distinct local maximum in instability at block onset as during the dissipation stage of the block, as expected. −5 2 −2 −11 −3 IRE ×10 m s and DIRE ×10 s 110E 120E 130E 140E 150E 160E 170E 170W 160W 150W −5 2 −2 IRE ×10 m s Advances in Meteorology 5 DIRE October 11–19, 2012 85N 80N 75N 70N 65N 60N 55N 50N −2 45N 40N −4 35N 30N −6 −8 Figure 8: GEFS ensemble mean time-averaged geopotential heights 11 12 13 14 15 16 17 18 19 for March 9–14, 2013. Days ERA M1 85N AVG M2 80N CTRL 75N Figure 6: ERA and GEFS values of DIRE for October 11–19, 2012. 70N Shown are ERA reanalysis (black), GEFS ensemble mean (red), GEFS control (green), and two other ensemble members (dark and 65N light blue). 60N 55N 50N 85N 5400 5100 45N 5200 80N 40N 75N 70N 35N 65N 30N 60N 55N 5400 Figure 9: GEFS control time-averaged geopotential heights for 50N March 9–14, 2013. 45N 40N 5400 35N at onset and rise to local maxima by the end of the blocking 30N event. Now, the DIRE for the GEFS mean, control, and two other ensemble members are plotted alongside the ERA-Interim Figure 7: ERA-Interim reanalysis time-averaged geopotential DIRE for comparison (see Figure 12). For this case, all of heights for March 9–14, 2013. the GEFS members plotted show a distinct maximum in instability at block onset as reflected by their crossing the time-axis from positive to negative (M1 crossed before), but none of them crosses at block decay. They all assume positive Again, The IRE for the GEFS mean, control, and two values indicating increasing instability, but not necessarily a ensemble members are plotted alongside the ERA-Interim maximum. IRE (see Figure 11). The IRE for the GEFS mean and control does not appear to reflect a realistic tendency in the IRE as seen in previous work [5–8]. The ensemble members 10 and 17 4. Discussion and Conclusions are extreme outliers and contributed to the poor performance oftheensemblemean.Again,M1andM2,whicharemembers For the two blocking events considered here, the higher 5 and 15 of the ensemble and are representatives of the other resolution ERA-Interim reanalysis behaved as expected (and members, appear closer to the ERA-Interim IRE in that they perhaps better than the NCEP-NCAR reanalysis) from pre- both reach maxima (lagging in time again) in the IRE field vious research (see [6, 7]).However,the relatively higher −11 2 −3 DIRE ×10 m s 140E 150E 160E 170E 170W 160W 150W 140W 130W 120W 110W 140E 140E 150E 150E 160E 160E 170E 170E 180 180 170W 170W 160W 160W 150W 150W 140W 140W 130W 130W 120W 120W 6 Advances in Meteorology IRE and DIRE March 9–14, 2013 IRE March 9–14, 2013 −2 −4 −6 9 1011121314 9 1011121314 Days Days IRE ERA M1 DIRE AVG M2 CTRL Figure 10: IRE and DIRE from ERA-Interim reanalysis for March 9–14, 2013. Figure 11: ERA and GEFS values of IRE for March 9–14, 2013. Shown are ERA reanalysis (black), GEFS ensemble mean (red), GEFS control (green), and two other ensemble members (dark and light blue). resolution than NCEP-NCAR reanalysis, in both cases the GEFS ensemble mean and GEFS control, failed to reproduce the expected behavior of the IRE as in the ERA reanalysis. However, as mentioned above, the outliers in both cases contributed to the poor performance of the ensemble mean in GEFS. eTh two representative ensemble members behaved DIRE March 9–14, 2013 much closer to the ERA renalysis and as expected based on previous research. eTh DIRE, on the other hand, seemed to behave more as expectedinGEFSatblock onset, butthe two representative ensemble members M1 and M2 still appeared to behave more realistically overall than the ensemble mean and control, especially, in October blocking event. Hence, it appears that the behavior of the enstrophy-based diagnostics IRE and DIRE in these two cases is better handled in an ensemble than with a single dynamical control forecast. The ensemble mean in both cases considered here is a rather poor indicator of the behavior of the diagnostics. Here, 0 an ensemble is essential for obtaining the expected results in a weather model. The use of the diagnostics in these −2 cases is considerably improved with an ensemble, since the control does not perform as well as expected. It is likely −4 that plots of several of the members of an ensemble would make the diagnostics more useful for studying blocking 910 11 12 13 14 events in a weather model. u Th s, even though the relatively Days high resolution in the ERA reanalysis (compared to NCEP- ERA NCAR reanalysis) demonstrates the expected behavior of the M1 AVG diagnostics, an ensemble was essential for weather model. It M2 CTRL is worth pointing out that using the IRE and DIRE together provides the best estimate of the instability associated with Figure 12: ERA and GEFS values of DIRE for March 9–14, 2013. block onset and decay. eTh DIRE behaved overall in a better Shown are ERA reanalysis (black), GEFS ensemble mean (red), way at block onset than decay. It appears that block decay may GEFS control (green), and two other ensemble members (dark and still be underpredicted as explained in [9, 10]. light blue). −5 2 −2 −11 2 −3 IRE ×10 m s and DIRE ×10 m s −11 2 −3 −5 2 −2 DIRE ×10 m s IRE ×10 m s Advances in Meteorology 7 In this paper, the two enstrophy-based diagnostics, the [13] D. Luo, “A barotropic envelope Rossby soliton model for block- eddy interaction. Part I: effect of topography,” Journal of the integrated enstrophy (IRE) and its derivative (DIRE) assum- Atmospheric Sciences,vol.62, no.1,pp. 5–21,2005. inginviscidbarotropicflow,havebeenusedtostudy two [14] A. R. Lupo and P. J. 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Okland, “Characteristics of northern Hemi- their insightful and helpful comments, which have consider- sphere blocking as determined from a long time series of obser- ably improved the clarity and strength of this paper. vational data,” Tellus A,vol.35, no.5,pp. 350–362, 1983. References [1] A. Fournier, “Atmospheric energetics in the wavelet domain. Part II: time-averaged observed atmospheric blocking,” Journal of the Atmospheric Sciences, vol. 60, no. 2, pp. 319–338, 2003. [2] A.R.Hansenand A. Sutera,“Acomparisonofthe spectral energy and enstrophy budgets of blocking versus nonblocking periods,” Tellus A,vol.36, no.1,pp. 52–63, 1984. [3] V. P. Dymnikov, Y. V. Kazantsev, and V. V. Kharin, “Information entropy and local Lyapunov exponents of barotropic atmo- spheric circulation,” Izvestiya, Atmospheric and Oceanic Physics, vol. 28, no. 6, pp. 425–432, 1993. [4] S. Tibaldi and F. Molteni, “On the operational predictability of blocking,” Tellus A,vol.42, no.3,pp. 343–365, 1990. [5] H. Athar and A. R. Lupo, “Scale and stability 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,” Advances in Meteorology,vol.2010,Article ID 610263, 15 pages, 2010. [6] A.D.Jensenand A. R. Lupo,“Usingenstrophy as adiagnostic to identify blocking regime transition,” Quarterly Journal of the Royal Meteorological Society,2013. [7] A.R.Lupo, I. I. Mokhov,S.Dostoglou,A.R.Kunz,and J. P. Burkhardt, “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,vol.43, no.1,pp. 45–51, 2007. [8] A.R.Lupo, I. I. Mokhov,M.G.Akperov,A.V.Cherokulsky, and H. Athar, “A dynamic analysis of the role of the planetary and synoptic scale in the summer of 2010 blocking episodes over theEuropeanpartofRussia,” Advances in Meteorology,vol.2012, Article ID 584257, 11 pages, 2012. 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Using Enstrophy-Based Diagnostics in an Ensemble for Two Blocking Events

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Copyright © 2013 Andrew D. Jensen 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.
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Hindawi Publishing Corporation Advances in Meteorology Volume 2013, Article ID 693859, 7 pages http://dx.doi.org/10.1155/2013/693859 Research Article Using Enstrophy-Based Diagnostics in an Ensemble for Two Blocking Events Andrew D. Jensen and Anthony R. Lupo Department of Soil, Environmental, and Atmospheric Science, University of Missouri, 302 Anheuser Busch Natural Resources Building, Columbia, MO 65211, USA Correspondence should be addressed to Andrew D. Jensen; jensenad@missouri.edu Received 10 September 2013; Revised 4 November 2013; Accepted 8 November 2013 Academic Editor: Yafei Wang Copyright © 2013 A. D. Jensen 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. Recent research has used enstrophy-based diagnostics to identify the development and dissipation stages of blocking events. These previous studies made use of reanalysis data sets in the calculations of the enstrophy-based diagnostics, such as the NCEP-NCAR ∘ ∘ reanalysis (2.5 × 2.5 ) of geopotential height and horizontal winds. However, none of these studies has explored the use of the enstrophy-based diagnostics in weather or climate models with higher horizontal resolution. In this paper, the enstrophy-based ∘ ∘ diagnostics are used to analyze two blocking events, using data from the ERA-Interim reanalysis data set (0.75 × 0.75 )and also the ∘ ∘ Global Ensemble Forecast System (GEFS) (1 × 1 ). eTh results of this work indicate that using an ensemble may be more effective than a single dynamical control forecast in evaluating the enstrophy-based diagnostic quantities, and that the results are similar to those obtained with coarser resolution. 1. Introduction blocking onset was better predicted than block decay overall. In [9], it was found that ensemble forecasts which were calib- Many studies have noted an upscale cascade of enstrophy rated to correct for the under prediction of blocking were upstream of blocking events (see, e.g., [1, 2]). Moreover, in [3], more accurate than uncalibrated ensemble forecasts. [11] enstrophy and large-scale instability are compared by means found the ensemble mean to perform better than the control of finite-time Lyapunov exponents. Using these ideas and the group for forecast times longer than 3-4 days in two atmo- instability at block onset and decay [4], in a series of recent spheric models. Errors were found to be largest at block onset articles (see [5–8]), enstrophy-based diagnostics have been and decay (see also [4]). used to study large-scale stability changes during the develop- The purpose of this study is to use the enstrophy-based ment and termination of blocking events. es Th e studies used diagnostics (explained below and introduced in [6, 7]) to ana- reanalysis data sets such as the NCEP-NCAR reanalysis of lyze two blocking events, using data from the ERA-Interim geopotential heights and winds to calculate the enstrophy- reanalysis and also the Global Ensemble Forecast System based diagnostics. However, no work has yet explored the use (GEFS), both of which have higher horizontal resolution than of thesediagnostics in weatherorclimate models or in an the NCEP-NCAR reanalysis data set. The previous results ensemble. ∘ ∘ in this area used relatively low-resolution (2.5 × 2.5 )data The utility of using ensemble-based forecasting to better in the calculations. u Th s, a primary objective of this study predict blocking is well known (e.g., [9–11]). Several studies is to determine if the results are sensitive to the resolution note the increased skill of forecasts of blocking episodes used in the calculations by employing model data with over solely dynamical prediction methods. For example, [10] higher horizontal resolution and thus to assess the extension showed that ECMWF ensemble prediction system forecasts of the overall usefulness of the diagnostics. eTh outcomes of blocking are more skilful than the deterministic and cli- matology forecasts of Euro-Atlantic sector blocking, although suggest that the use of an ensemble is preferable over a single 2 Advances in Meteorology dynamical control forecast to the use of the enstrophy-based inner product (⋅, ⋅) by (𝐴 x, y)=(x,𝐴 y).Tomodel blocked diagnostics in a weather model. flow, suppose that eTh outlineofthe paperisasfollows. In Section 2,the (5) 𝜓 (𝑥, 𝑦) = 𝜓 (𝑦) 𝑒 . data sets and the enstrophy-based diagnostics and their use are explained. In Section 3, two blocking episodes are studied When by means of these diagnostics using ERA-Interim reanalysis 𝜕 𝜕 ∗ 2 2 𝑆=𝐴 + 𝐴 = 𝑢 ∇ −∇ ( 𝑢 ), (6) data and GEFS. In Section 4,wediscuss andsummarize our conclusions. it canbeshown that 𝑆 = −𝑖𝑘𝐾 ,where 𝐾 is a skew-symmetric operator. Because the eigenvalues 𝑆 are symmetric about zero, 2. Data and Methods the eigenvalues of the operator 𝐾 are studied instead. Using finite differencing to project onto ni fi te space, the sum of 2.1. Preliminaries. In order to explain the enstrophy diag- the positive local Lyapunov exponents can be shown to be nostics to be used, the local Lyapunov exponents for the determined by the integral of enstrophy, where the integral barotropic vorticity equation must rfi st be considered. Local is over a ni fi te and bounded region. Lyapunov exponents for the barotropic vorticity equation, where 𝜁 is relative vorticity, are dene fi d by 𝜆 (𝜁 ,𝑇) = 𝑖 0 (1/2𝑛) log ] for initial 𝜁 and time 𝑇=𝑛Δ𝑡 .The ] are the 2.2. Enstrophy Advection and Its Integral. As sketched above, 𝑖 0 𝑖 𝑘=𝑛 eigenvalues of 𝑀 𝑀 ,where 𝑀= ∏ 𝐴(𝑘Δ𝑡) and 𝐴(𝑡) is 𝑛 𝑛 𝑘=−𝑛 ∑ 𝜆 ≈ ∫ 𝜁 d𝐴, the linearization operator of the barotropic vorticity equation. (7) 𝜆 >0 u Th s, the local Lyapunov exponents provide a measure of n fi ite-time instability. In [ 12], n fi ite-time instability is where the integral is taken over the Northern Hemisphere estimatedbymeans of thelargest singular value(eigenvalues here. Since the 𝜆 change with time, (7)may be dieff rentiated of 𝑀 𝑀 ) in magnitude in a kinetic energy norm. Here, the to obtain approximation introduced in [3]isusedasameasureofthe 𝜕( ∑ 𝜆 ) 𝑖 𝜕 𝜆 >0 𝑖 2 2 n fi ite-time stability. (8) ≈ ∫ 𝜁 d𝐴=− ∫ k ⋅∇𝜁 d𝐴, 𝜕𝑡 𝜕𝑡 The argument given in [ 3] proceeds as follows. A fric- tionless, nondivergent barotropic flow is assumed. As shown where nondivergent, frictionless barotropic flow on an 𝑓 - in [3], the results to be described are not fundamentally plane has been assumed. aeff cted by orography. The barotropic vorticity equation can To get a more accurate derivative, it is possible to proceed be written in terms of a stream function 𝜓 : as in [13] and consider the barotropic vorticity equation in the form 𝜕∇ 𝜓 2 𝜕 𝜕 2 2 (1) +𝐽(𝜓,∇ 𝜓) = 0, ( +𝑢 )(∇ 𝜓 − 𝐹𝜓) + 𝐽 (𝜓, ∇ 𝜓+ℎ) 𝜕𝑡 𝜕𝑡 (9) 2 2 where ∇ 𝜓=𝜁 and ∇ is the Laplacian operator. Now, (1)can 𝜕𝜓 𝜕ℎ 󸀠 2 󸀠 +(𝛽+𝐹𝑢 ) +𝑢 = −𝐽(𝜓 ,∇ 𝜓 ) , 0 0 be linearized as follows: 󸀠 where 𝑢 represents the basic state westerly wind, 𝜓 and 𝜓 𝜕𝜁 (2) +𝐴𝜁 =0, represent planetary and synoptic scales of the stream func- 𝜕𝑡 tion, respectively; ℎ is a nondimensional topography term, 𝐹 = (𝐿/𝑅 ) where 𝑅 is the Rossby deformation radius, and where 𝐴 is the linearization operator, 𝜓= 𝜓+𝜓 ,and 𝑑 𝑑 2 󸀠 󸀠 the subscript “𝑃 ” represents the planetary scale component. ∇ 𝜓 =𝜁 . Using the Crank-Nicholson scheme, the following However, in [3], the topography and friction were omitted to equation may be obtained: obtain (7), as described above. Hence, here we do not retain 󸀠 󸀠 󸀠 󸀠 such terms in the derivative, while realizing that other terms 𝜁 (𝑡+𝛿𝑡 ) −𝜁 (𝑡 ) 𝜁 (𝑡+𝛿𝑡 ) +𝜁 (𝑡 ) +𝐴 ( 𝜓( 𝑡+ )) =0. can be included to make the result more accurate. Another 2 2 reason for not retaining such terms is a practical one: con- (3) tours of enstrophy advection are easy to interpret and are explained in detail in [6]. To estimate the Lyapunov exponents, (3) can be rearranged, where 𝐼 is the identity operator: 2.3. Methodology. The enstrophy-based diagnostics (describ- −1 ed in detailabove)tobeusedinthe analysis of thetwo block- 𝜁 (𝑡+𝛿𝑡 ) =[𝐼 + 𝐴( 𝜓(𝑡 + ))] ing events considered below were introduced in [6, 7], and 2 2 they are as follows: (4) ×[𝐼− 𝐴( 𝜓(𝑡 + ))] 𝜁 𝑡 . ( ) IRE ≡ ∫ 𝜁 d𝐴, (10) 2 2 The operator in brackets in ( 4)isestimated by 𝑆=𝐴 + 𝐴 , DIRE ≡− ∫ k ⋅∇𝜁 d𝐴, (11) where 𝐴 is the adjoint operator den fi ed for vectors x, y and 𝛿𝑡 𝛿𝑡 𝛿𝑡 𝛿𝑡 𝜕𝑥 𝜕𝑥 𝜕𝑥 𝜕𝑥 𝜕𝑥 𝑖𝑘𝑥 Advances in Meteorology 3 where the integral is evaluated over some n fi ite area on an 85N isobaric surface. The integrated enstrophy (IRE), or ( 10), has 80N been showntoberelated to nfi ite-time instabilitybymeans 75N of the ni fi te-time Lyapunov exponents as described above. 5300 70N Peaks in (10) are therefore a measure of local maximum flow instability, in particular, planetary scale flow. In [ 7], it was 65N observed that the IRE increased sharply at block onset, indi- 60N cating an increase in planetary flow instability. eTh IRE was 55N then observed to decrease to a local minimum and to increase 50N againatblock decaytoalocalmaximum value. On theother 45N hand,the DIRE,or(11), is the derivative of (10) assum- 5550 5600 5650 ing barotropic, inviscid flow, and increasing (decreasing) 40N instability is indicated when (11) is positive (negative), while 35N 5750 5800 maxima in the IRE field can oeft n be found (see [ 6]) when (11) 30N crosses the time-axis from positive to negative. The diagnostics ( 10)and (11)werecalculatedinaspher- ical coordinate system for the Northern Hemisphere using Figure 1: ERA-Interim reanalysis time-averaged geopotential ECMWF ERA-Interim data, obtained from the ECMWF heightsfor October11–19,2012. data server. eTh quantities used in this study are the zonal and meridional wind components, geopotential height, and ∘ ∘ relative vorticity with a 0.75 × 0.75 horizontal resolution at 500hPa.Thesamequantitieswerealsousedfromthe Global 85N Ensemble Forecast System (GEFS), which has 20 members 80N plus the ensemble mean and control with a horizontal resolu- 75N ∘ ∘ tion of 1 × 1 ,inorder to calculate(10)and (11). We chose 70N representative ensemble members from the 20, besides the 65N ensemble mean and control, which are shown in the plots below. 60N eTh blocking denfi ition used in this studyisthatofLupo 55N and Smith [14], which can be described as a synthesis of the 50N subjective Rex criteria (see [15, 16]) and the objective Lejenas- 45N Okland criteria (see [17]), but in which a blocking event is 40N 5600 dene fi d to persist for at least five days. More specicfi ally, the 5700 5700 blocking criteria used here (i) must satisfy the Rex [15, 16]cri- 35N teria for at least vfi e days and (ii) must have a negative or small 30N positive zonal index that can be identified on a time-long- itude or Hovmol ¨ ler diagram. (iii) Conditions (i) and (ii) must be satisefi d for 24 hours aeft r (before) onset (termination); Figure 2: GEFS ensemble mean time-averaged geopotential heights (iv) the blocking event should be poleward of 35N during its for October 11–19, 2012. lifetime, and the ridge should have an amplitude of greater than 5 latitude; and (v) blocking onset is defined to occur when condition (iv) and and one of the conditions (i) or (ii) is satisfied, while (vi) termination or decay is designated at the IRE time series, corresponding to block onset and decay, the time the event fails to satisfy condition (v) for a 24-hour respectively.Aclearupwardtrend canbeseeninthe IRE efi ld period or longer. This definition was used to detect the block- during the block development stage. During the maintenance ing onset and decay times for the events considered below. stage of the event, the IRE dips to a minimum value and again achieves a local maximum during the dissipation stage of the blocking event. On the other hand, the DIRE crosses the time- 3. Dynamic Analysis axis from positive to negative at block onset, reflecting the 3.1. Event 1: October 11–19, 2012. The first blocking event con- local instability maximum. During the maintenance stage, sidered here occurred October 11–19, 2012 and was centered the DIRE is negative until the 16th of October, reflecting at 160E (see Figures 1, 2,and 3). The ERA-Interim reanalysis decreasing instability. The DIRE then assumes positive values overall appeared to have tighter gradients than GEFS. The until it again crosses the time-axis from positive to negative mean height contours of theGEFSensemblemeanand con- which reflects the local instability maximum at block decay. trol appear to be similar, while differences with the ERA cal- The IRE for the GEFS mean, control, and two repre- culatedmeanheights areborne outinthe calculations below. sentative ensemble members are plotted alongside the ERA- The IRE (integrated enstrophy) and DIRE (derivative of Interim IRE for comparison (see Figure 5). The IRE for the IRE) for the ERA-Interim data were rescaled and are shown GEFS mean is strictly decreasing, and the GEFS control together in Figure 4. Two distinct maxima can be seen on appears to behave similarly. eTh ensemble member 11 is an 110E 110E 120E 120E 130E 130E 140E 140E 150E 150E 160E 160E 170E 170E 170W 170W 160W 160W 150W 150W 4 Advances in Meteorology IRE October 11–19, 2012 85N 80N 75N 70N 65N 60N 55N 50N 45N 40N 5600 35N 30N Figure 3: GEFS control time averaged geopotential heights for 11 12 13 14 15 16 17 18 19 October 11–19, 2012. Days ERA M1 IRE and DIRE October 11–19, 2012 M2 AVG 9 9 CTRL Figure 5: ERA and GEFS values of IRE for October 11–19, 2012. Shown are ERA reanalysis (black), GEFS ensemble mean (red), GEFS control (green), and two other ensemble members (dark and 8 8 light blue). reflected by their crossing the time-axis from positive to negative. Similar to the behavior of the IRE as calculated from 0 0 GEFS, M1 and M2 from the ensemble show results that are similar to the ERA-Interim DIRE with the DIRE crossing the time-axis from positive to negative values for block onset and −4 −4 decay periods. −8 −8 11 12 13 14 15 16 17 18 19 3.2. Event 2: March 9–14, 2013. The second event occurred Days March 9–14, 2013 and was centered at 170 W (see Figures 7, 8,and 9). In this case,ERA-Interim,GEFSmean, andGEFS IRE control appear more similar to each other compared to the DIRE first case. However, the contours over Alaska and gradients Figure 4: IRE and DIRE from ERA-Interim reanalysis for October over the Pacicfi are different for the reanalysis compared to 11–19, 2012. GEFS. Again, the IRE and DIRE for the ERA-Interim data were rescaled and are shown together in Figure 10.There, the extreme outlier and likely aeff cted the poor performance of IRE field is at a local maximum value during the block the ensemble mean. However, M1 and M2, which are mem- development stage. eTh IRE decreases to a minimum value bers 5 and 15 of the ensemble and are representatives of other around the 13th of March during the maintenance stage of the members of the ensemble, appear closer to the ERA-Interim event. Finally, the IRE increases to a local maximum by the IRE in that they reach maxima in the IRE field, if somewhat end of the event. Now, the DIRE crosses the time-axis from lagging in time. M2 also appears to reach a local maximum at positive to negative values on the 9th of March, reflecting block decay. the local instability maximum at block onset. eTh instability Now, the DIRE for the GEFS mean, control, and two decreases (DIRE is negative) during the maintenance stage ensemble members are plotted alongside the ERA-Interim until the 11th of March. eTh DIRE then takes on positive DIRE for comparison (see Figure 6). In contradistinction to values until again crossing the time-axis from positive to the GEFS IRE, all of the GEFS members plotted achieve negative values, which reflects the local instability maximum a distinct local maximum in instability at block onset as during the dissipation stage of the block, as expected. −5 2 −2 −11 −3 IRE ×10 m s and DIRE ×10 s 110E 120E 130E 140E 150E 160E 170E 170W 160W 150W −5 2 −2 IRE ×10 m s Advances in Meteorology 5 DIRE October 11–19, 2012 85N 80N 75N 70N 65N 60N 55N 50N −2 45N 40N −4 35N 30N −6 −8 Figure 8: GEFS ensemble mean time-averaged geopotential heights 11 12 13 14 15 16 17 18 19 for March 9–14, 2013. Days ERA M1 85N AVG M2 80N CTRL 75N Figure 6: ERA and GEFS values of DIRE for October 11–19, 2012. 70N Shown are ERA reanalysis (black), GEFS ensemble mean (red), GEFS control (green), and two other ensemble members (dark and 65N light blue). 60N 55N 50N 85N 5400 5100 45N 5200 80N 40N 75N 70N 35N 65N 30N 60N 55N 5400 Figure 9: GEFS control time-averaged geopotential heights for 50N March 9–14, 2013. 45N 40N 5400 35N at onset and rise to local maxima by the end of the blocking 30N event. Now, the DIRE for the GEFS mean, control, and two other ensemble members are plotted alongside the ERA-Interim Figure 7: ERA-Interim reanalysis time-averaged geopotential DIRE for comparison (see Figure 12). For this case, all of heights for March 9–14, 2013. the GEFS members plotted show a distinct maximum in instability at block onset as reflected by their crossing the time-axis from positive to negative (M1 crossed before), but none of them crosses at block decay. They all assume positive Again, The IRE for the GEFS mean, control, and two values indicating increasing instability, but not necessarily a ensemble members are plotted alongside the ERA-Interim maximum. IRE (see Figure 11). The IRE for the GEFS mean and control does not appear to reflect a realistic tendency in the IRE as seen in previous work [5–8]. The ensemble members 10 and 17 4. Discussion and Conclusions are extreme outliers and contributed to the poor performance oftheensemblemean.Again,M1andM2,whicharemembers For the two blocking events considered here, the higher 5 and 15 of the ensemble and are representatives of the other resolution ERA-Interim reanalysis behaved as expected (and members, appear closer to the ERA-Interim IRE in that they perhaps better than the NCEP-NCAR reanalysis) from pre- both reach maxima (lagging in time again) in the IRE field vious research (see [6, 7]).However,the relatively higher −11 2 −3 DIRE ×10 m s 140E 150E 160E 170E 170W 160W 150W 140W 130W 120W 110W 140E 140E 150E 150E 160E 160E 170E 170E 180 180 170W 170W 160W 160W 150W 150W 140W 140W 130W 130W 120W 120W 6 Advances in Meteorology IRE and DIRE March 9–14, 2013 IRE March 9–14, 2013 −2 −4 −6 9 1011121314 9 1011121314 Days Days IRE ERA M1 DIRE AVG M2 CTRL Figure 10: IRE and DIRE from ERA-Interim reanalysis for March 9–14, 2013. Figure 11: ERA and GEFS values of IRE for March 9–14, 2013. Shown are ERA reanalysis (black), GEFS ensemble mean (red), GEFS control (green), and two other ensemble members (dark and light blue). resolution than NCEP-NCAR reanalysis, in both cases the GEFS ensemble mean and GEFS control, failed to reproduce the expected behavior of the IRE as in the ERA reanalysis. However, as mentioned above, the outliers in both cases contributed to the poor performance of the ensemble mean in GEFS. eTh two representative ensemble members behaved DIRE March 9–14, 2013 much closer to the ERA renalysis and as expected based on previous research. eTh DIRE, on the other hand, seemed to behave more as expectedinGEFSatblock onset, butthe two representative ensemble members M1 and M2 still appeared to behave more realistically overall than the ensemble mean and control, especially, in October blocking event. Hence, it appears that the behavior of the enstrophy-based diagnostics IRE and DIRE in these two cases is better handled in an ensemble than with a single dynamical control forecast. The ensemble mean in both cases considered here is a rather poor indicator of the behavior of the diagnostics. Here, 0 an ensemble is essential for obtaining the expected results in a weather model. The use of the diagnostics in these −2 cases is considerably improved with an ensemble, since the control does not perform as well as expected. It is likely −4 that plots of several of the members of an ensemble would make the diagnostics more useful for studying blocking 910 11 12 13 14 events in a weather model. u Th s, even though the relatively Days high resolution in the ERA reanalysis (compared to NCEP- ERA NCAR reanalysis) demonstrates the expected behavior of the M1 AVG diagnostics, an ensemble was essential for weather model. It M2 CTRL is worth pointing out that using the IRE and DIRE together provides the best estimate of the instability associated with Figure 12: ERA and GEFS values of DIRE for March 9–14, 2013. block onset and decay. eTh DIRE behaved overall in a better Shown are ERA reanalysis (black), GEFS ensemble mean (red), way at block onset than decay. It appears that block decay may GEFS control (green), and two other ensemble members (dark and still be underpredicted as explained in [9, 10]. light blue). −5 2 −2 −11 2 −3 IRE ×10 m s and DIRE ×10 m s −11 2 −3 −5 2 −2 DIRE ×10 m s IRE ×10 m s Advances in Meteorology 7 In this paper, the two enstrophy-based diagnostics, the [13] D. Luo, “A barotropic envelope Rossby soliton model for block- eddy interaction. Part I: effect of topography,” Journal of the integrated enstrophy (IRE) and its derivative (DIRE) assum- Atmospheric Sciences,vol.62, no.1,pp. 5–21,2005. inginviscidbarotropicflow,havebeenusedtostudy two [14] A. R. Lupo and P. J. Smith, “Climatological features of blocking blocking events.TheERA-Interim reanalysis andthe Global anticyclones in the northern Hemisphere,” Tellus A,vol.47, no. Ensemble Forecast System (GEFS) have been used in the 4, pp. 439–456, 1995. study of these two blocking events. The enstrophy-based [15] D. F. Rex, “Blocking action in the middle troposphere and its diagnostics were found to behave as expected in the ERA effect on regional climate I: the climatology of blocking action,” reanalysis and required a more subtle analysis in GEFS. Tellus,vol.2,no. 3, pp.196–211, 1950. [16] F. Rex, “Blocking action in the middle troposphere and its Acknowledgments effect on regional climate II: the climatology of blocking action,” Tellus,vol.3,pp. 275–301, 1950. eTh authors wish to thank the two anonymous reviewers for [17] H. Lejenas and H. Okland, “Characteristics of northern Hemi- their insightful and helpful comments, which have consider- sphere blocking as determined from a long time series of obser- ably improved the clarity and strength of this paper. vational data,” Tellus A,vol.35, no.5,pp. 350–362, 1983. References [1] A. Fournier, “Atmospheric energetics in the wavelet domain. Part II: time-averaged observed atmospheric blocking,” Journal of the Atmospheric Sciences, vol. 60, no. 2, pp. 319–338, 2003. [2] A.R.Hansenand A. Sutera,“Acomparisonofthe spectral energy and enstrophy budgets of blocking versus nonblocking periods,” Tellus A,vol.36, no.1,pp. 52–63, 1984. [3] V. P. Dymnikov, Y. V. Kazantsev, and V. V. Kharin, “Information entropy and local Lyapunov exponents of barotropic atmo- spheric circulation,” Izvestiya, Atmospheric and Oceanic Physics, vol. 28, no. 6, pp. 425–432, 1993. [4] S. Tibaldi and F. Molteni, “On the operational predictability of blocking,” Tellus A,vol.42, no.3,pp. 343–365, 1990. [5] H. Athar and A. R. Lupo, “Scale and stability 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,” Advances in Meteorology,vol.2010,Article ID 610263, 15 pages, 2010. [6] A.D.Jensenand A. R. Lupo,“Usingenstrophy as adiagnostic to identify blocking regime transition,” Quarterly Journal of the Royal Meteorological Society,2013. [7] A.R.Lupo, I. I. Mokhov,S.Dostoglou,A.R.Kunz,and J. P. Burkhardt, “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,vol.43, no.1,pp. 45–51, 2007. [8] A.R.Lupo, I. I. Mokhov,M.G.Akperov,A.V.Cherokulsky, and H. Athar, “A dynamic analysis of the role of the planetary and synoptic scale in the summer of 2010 blocking episodes over theEuropeanpartofRussia,” Advances in Meteorology,vol.2012, Article ID 584257, 11 pages, 2012. [9] J. S. Watson and S. J. Colucci, “Evaluation of ensemble predic- tions of blocking in the NCEP global spectral model,” Monthly Weather Review,vol.130,no. 12,pp. 3008–3021, 2002. [10] J. L. Pelly and B. J. Hoskins, “How well does the ECMWF ensem- ble prediction system predict blocking?” Quarterly Journal of the Royal Meteorological Society,vol.129,no. 590, pp.1683–1702, [11] J. S. Frederiksen, M. A. Collier, and A. B. Watkins, “Ensemble prediction of blocking regime transitions,” Tellus A,vol.56, no. 5, pp. 485–500, 2004. [12] F. Molteni and T. N. Palmer, “Predictability and finite-time instability of the northern winter circulation,” Quarterly Jour- nal, vol. 119, no. 510, pp. 269–298, 1993. 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