Impact of Multivariate Background Error Covariance on the WRF-3DVAR Assimilation for the Yellow Sea Fog Modeling
Impact of Multivariate Background Error Covariance on the WRF-3DVAR Assimilation for the Yellow...
Gao, Xiaoyu;Gao, Shanhong
2020-11-10 00:00:00
Hindawi Advances in Meteorology Volume 2020, Article ID 8816185, 19 pages https://doi.org/10.1155/2020/8816185 Research Article Impact of Multivariate Background Error Covariance on the WRF-3DVAR Assimilation for the Yellow Sea Fog Modeling 1,2 1 Xiaoyu Gao and Shanhong Gao Key Laboratory of Physical Oceanography, College of Oceanic and Atmospheric Sciences, Ocean University of China, Qingdao 266100, China Ministry of Education Key Laboratory for Earth System Modeling, Department of Earth System Science and Joint Center for Global Change Studies, Tsinghua University, Beijing 10084, China Correspondence should be addressed to Shanhong Gao; gaosh@ouc.edu.cn Received 9 July 2020; Revised 30 September 2020; Accepted 23 October 2020; Published 10 November 2020 Academic Editor: Haydee Salmun Copyright © 2020 Xiaoyu Gao and Shanhong Gao. 'is 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. Numerical modeling of sea fog is highly sensitive to initial conditions, especially to moisture in the marine atmospheric boundary layer (MABL). Data assimilation plays a vital role in the improvement of initial MABL moisture for sea fog modeling over the Yellow Sea. In this study, the weather research and forecasting (WRF) model and its three-dimensional variational (3DVAR) data assimilation module are employed for sea fog simulations. Two kinds of background error (BE) covariances with different control variables (CV) used in WRF-3DVAR, that is, CV5 and multivariate BE (CV6), are compared in detail by explorative case studies and a series of application experiments. Statistical verification metrics including probability of detection (POD) and equitable threat scores (ETS) of forecasted sea fog area are computed and compared for simulations with the implementations of CV5 and CV6 in the WRF-3DVAR system. 'e following is found: (1) there exists a dominant negative correlation between temperature and moisture in CV6 near the sea surface, which makes it possible to improve the initial moisture condition in the MABL by assimilation of observed temperature; (2) in general, the performance of the WRF-3DVAR assimilation with CV6 is distinctly better, and the results of 10 additional sea fog cases clearly suggest that CV6 is more suitable than CV5 for sea fog modeling. Compared to those with CV5, the average POD and ETS of forecasted sea fog area using 3DVAR with CV6 can be improved by 27.6% and 21.0%, respectively. Sea, leading to the formation of advection sea fog in the 1. Introduction inversion layer [3]. 'erefore, the sensitivity of sea fog Sea fog occurs within the marine atmospheric boundary modeling to the initial condition is actually largely related to layer (MABL). It is a type of fog that forms over an ocean temperature and moisture in the MABL [6–12]. surface and spreads over coastal areas. It can seriously affect After the textbook Sea Fog published in 1985 by Wang many maritime activities (e.g., transport, navigation, fishery, [4], Koracin and Dorman [2] published a book in 2017, in and rescue) due to its low horizontal visibility [1, 2]. 'e which they summarize the challenges and advancements in Yellow Sea has the largest number of foggy days among the observations, modeling, and forecasting of marine fog over four seas of China [3–5], with a long fog season starting from the world. Modeling and forecasting have become an im- March and ending in September. 'e Yellow Sea is located to portant research content of sea fog. In order to mitigate the north of the Kuroshio Current and under influences of socioeconomic impacts of sea fog over the Yellow Sea and warm-moist air mass that is transported northward as the meet increasing practical demands, it is urgent to improve East Asia summer monsoon gradually intensifies. Due to the the forecast skill of sea fog. Undoubtedly, a high-quality cold sea surface temperature (SST), an atmospheric inver- initial condition is very beneficial to the numerical fore- sion layer can easily develop in the MABL over the Yellow casting for sea fog. A vital way to improve the initial 2 Advances in Meteorology caused by monsoon depressions and tropical cyclones can be condition in numerical modeling is data assimilation [13–19]. For the assimilation of given observations, different improved by applying data assimilation with CV6, which is better than CV5. However, among existing research work on data assimilation methods yield different assimilation effects. In general, better effect can be obtained when using more sea fog over the Yellow Sea involving numerical modeling advanced data assimilation method. For instance, in their [24, 36–40], quite a few studies, especially those works with modeling study of sea fog using the weather research and focus on the mechanism of sea fog evolution, have little or no forecasting (WRF) model, Gao et al. [20] demonstrated that mention of data assimilation. Even if data assimilation is ensemble Kalman filter (EnKF) performs better than three- employed in the numerical simulations for sea fog, CV5 is dimensional variational (3DVAR) assimilation, which is generally used [22, 23, 41–43]. 'e reason might be that CV5 is the default option except CV3 in the WRF-3DVAR, which attributed to the flow-dependent background error (BE) covariance used in the EnKF. However, the EnKF requires results in the fact that little attention has been paid to CV6 in the application of data assimilation for sea fog modeling. much more computing resources compared to the 3DVAR, which is an issue that has to be considered for real-time As stated previously, a successful sea fog modeling definitely requires the assimilation of observations over the forecast of sea fog. 'e WRF-3DVAR [18] has been widely used for sea fog modeling over the Yellow Sea due to its low sea [22]. Unfortunately, in spite of a large amount of sat- computational cost [21–24]. ellite-retrieved data available over the sea, the accuracy of the 3DVAR minimizes the analysis error variance by min- retrieved water vapor profiles is unsatisfactory. Divakarla imizing the cost function, which is defined by the weighted et al. [44] performed an evaluation of satellite-retrieved data sum of analysis increment and observation innovation [25], using global radiosonde observations and found that the respectively, with BE and observational error (OE) covari- root mean square difference is larger than 15% for relative humidity at 1000hPa. Such big observational errors lead to a ance. A better estimate of BE can definitely lead to a better assimilation analysis. 'us, how to conduct reasonable malfunction of the retrieved humidity in data assimilation. 'e approach to correct errors in the observed humidity field statistics of BE is an important issue, which has spawned a lot of related research works [26–31]. Currently, the National and make it more realistic by increments of other control variables is probably an efficient way to modify the MBL Meteorology Center (NMC; now called the National Centers for Environmental Prediction, NCEP) method [32] is the moisture structure. Hence, the purpose of the present study most commonly used to generate BE for the 3DVAR. It first is to investigate the impact of multivariate background error conducts transformation of model variables to a set of covariance on the WRF-3DVAR assimilation for fog control variables and then estimates the relationships be- modeling over the Yellow Sea. 'e assimilation effects with tween different variables by linear regression. 'e NMC CV5 and CV6 are examined. method is implemented in the WRF-3DVAR [18]. 'ere are 'e remaining content is arranged as follows. Section 2 briefly describes the multivariate BE of the WRF-3DVAR two types of BE with different control variables (CV): one defines the control variables in the physical space (CV3), and and the data assimilation scheme, and Section 3 outlines numerical experiments, including data, sea fog cases, model the other defines the control variables in eigenvector space (CV5, CV6, and CV7). CV3 uses a vertical recursive filter to configurations, and numerical experiments. Results, analy- model the vertical covariance, while the others use an sis, and evaluation are presented in detail in Section 4. Fi- empirical orthogonal function (EOF) to represent the ver- nally, summary and conclusions are provided in Section 5. tical covariance. CV3 is a global BE and can be used for any regional domain, while CV5, CV6, and CV7 are domain- 2. Methodology dependent and therefore must be generated based on forecast or ensemble data over the same domain. Due to the 2.1. Multivariate BE. 'e cost function for 3DVAR poor performance of CV3, it is not suitable for sea fog is defined by modeling. In CV5, the moisture control variable is not related to any other variables. In CV6, the moisture control 1 T b −1 b T −1 J(x) � J + J � x–x B x–x + (y–Hx) R (y–Hx) , b o variable is the unbalanced portion of the pseudo-relative humidity, and six additional correlation coefficients in the (1) definition of the balanced part of analysis control variables where x and x are, respectively, the model state and the are introduced. Namely, CV6 is a multivariate background background field, y is the observation, and H is the ob- error covariance, especially for the moisture. CV7 is similar servation operator matrix that transforms data from model to CV5, but it uses a different set of control variables and space to observation space. In equation (1), analysis incre- there exist no correlations between the moisture and other ment (x–x ) and observation innovation (y–Hx) are, re- control variables. spectively, weighed by BE (B) and OE (R). OE is determined 'e issue on the strengths and shortcomings of CV5 and by instrument errors and representation errors caused by the CV6 has been discussed. Based on the work to use multiple transformation of data from model space to observation linear regressions to estimate multivariate analysis of hu- space; BE is determined by model forecast errors. 'e midity in a limited-area model, Berre [33] pointed that the analysis x represents a posterior maximum likelihood es- relationships between forecast errors of humidity and those timate of the true state of the atmosphere, and it can be of mass and wind fields cannot be negligible. Dhanya and obtained if the cost function J(x) is minimized. 'e WRF- Chandrasekar [34, 35] found that the forecasts of rainfall Advances in Meteorology 3 3DVAR system uses Quasi-Newton method [45] to realize χ(i, j, k) � χ (i, j, k) + α (k) ψ(i, j, k), (3a) u ψχ the minimization process. Assuming that the model has m degrees of freedom and the assimilated observation number is p, x and x are T(i, j, k) � T (i, j, k) + α (k, l)ψ(i, j, l), (3b) ψT m-dimensional vectors, y is an p-dimensional vector, H is l�1 a p × m-dimensional matrix, B is a m × m-dimensional matrix, and R is a p × p-dimensional matrix that is di- P (i, j) � P (i, j) + α (l) ψ(i, j, l), (3c) s su ψP agonal because observational errors are usually supposed s l�1 to be uncorrelated. In practice, the amount of calculation of J is much larger than that of J , since R is diagonal and where i and j denote the horizontal dimension index, k and l b o p is far less than m. indicate the vertical levels, n is the total number of vertical Usually, a numerical model has m degrees of freedom levels, and the regression coefficients are usually supposed to with a typical value of 10 ; thus it is almost impossible to be horizontally homogeneous. explicitly solve J , which requires ∼O(m ) calculations. Compared to CV5, the multivariate BE (CV6) contains six However, in the model space, the correlations between extra coefficients, that is, α , α , α , α , χ T χ P ψRH χ RH u u s s u s different variables or between the same variables at dif- α and α .RH alsoconsistsofbalancedandunbalanced T RH P RH s u s su s ferent grid points are available only within a limited range, components. 'e control variable transform can be expressed by and thus BE is a sparse matrix. As a result, by decom- χ(i, j, k) � χ (i, j, k) + α (k)ψ(i, j, k), (4a) u ψχ posing BE, a lot of computational cost can be greatly reduced. 'is process is known as control variable transform; that is, the model variables x are transformed T(i, j, k) � T (i, j, k) + α (k, l)ψ(i, j, l) u ψT to control variables v, and J can then be calculated by v l�1 b b (4b) ′ ′ ′ instead of by x. Let x � x–x , x � Uv, y � y–Hx , so b b y–Hx � (y–Hx )–H(x–x ) � y –HUv. Note that U is the + α (k, l)χ (i, j, l), χ T transform matrix defined in a way that satisfies B � UU . l�1 Using the increment formulation [46], equation (1) can be rewritten as P (i, j) � P (i, j) + α (i, j, l)ψ(i, j, l) s su ψP l�1 T –1 (4c) ′ ′ n J(v) � J + J � v v + y –HUv R y –HUv . b o + α (l)χ (i, j, l), χ P u u s (2) l�1 'e WRF-3DVAR system takes three steps to complete the control variable transform: the horizontal transform U , RH (i, j, k) � RH (i, j, k) + α (k, l)ψ(i, j, l) s su ψRH the vertical transform U , and the physical transform U . l�1 v p 'erefore, U � U U U . U uses recursive filter [47, 48] to p v h h + α (k, l)χ (i, j, l) calculate the correlations between data on different grid χ RH u u s (4d) l�1 points at the same level, U implements empirical orthog- onal function (EOF) decomposition to obtain the correla- + α (k, l)T (i, j, l) T RH u tions between data at different model levels, and U does u s l�1 linear regression to get the correlations between different + α (k)P (i, j). P RH su variables. su s In the physical transform x � U v , the increments of p p Formula (4d) indicates that an increment of four other model variables, that is, zonal wind u, meridional wind v, variables can lead to an increment of RH in CV6. As temperature T, pressure P, and mixing ratio Q, are first mentioned in Introduction, moisture information in the converted to a new set of variables, that is, stream function ψ, initial condition is vital for sea fog modeling. Note that the velocity potential χ, temperature T, surface pressure P , and analysis of moisture is retrieved from the analysis of RH , pseudo-relative humidity RH . 'ese new variables are then background temperature, and pressure together. 'e divided into balanced and unbalanced components: moisture increment is directly proportional to RH incre- φ � φ + φ , where φ can be any variable. 'e balanced part b u ment because background data are recognized as constant. φ is related to other control variables μ by linear regression α ; that is, φ � α μ. 'e unbalanced part φ is inde- μφ b μφ u pendent and serves as input to the vertical transform. By the 2.2. Data Assimilation Scheme. A cycling-3DVAR scheme above procedures, the correlated model variables are [21] is employed to do data assimilation (DA) in this study. transformed into uncorrelated variables. 'e scheme is shown in Figure 1. CV5/6 presents CV5 or In the WRF-3DVAR, the correlations are available only CV6, and “obs” stands for observations. Individual assim- within a subset of the variables. CV5 has three basic coef- ilation cycles are connected by the WRF integration (i.e., ficients: α , α , and α , and these coefficients link χ, T, ψχ ψT ψP wrf.exe), and the final analysis x is taken as the initial and P to ψ: s condition for the WRF simulation. In this study, all WRF 4 Advances in Meteorology (MTSAT), including albedo, infrared, and visible cloud CV5/6 wrf.exe CV5/6 wrf.exe CV5/6 imageries. 'e NCEP ship observations in PrepBUFR for- 3DVAR 3DVAR 3DVAR mat, which can be downloaded from the NCAR Compu- tational and Information Systems Laboratory (CISL) b b b a wrf.exe x x x x Research Data Archive, were used to evaluate model results. obs obs obs 3.2. Sea Fog Cases. Two typical sea fog cases over the Yellow 1st update 2nd update 3rd update Sea, one spreading narrowly over the eastern Yellow Sea Figure 1: Flowchart of the 3DVAR data assimilation scheme. See along the Korean Peninsula coast (Figure 2(b)) and the other details in the text. occupying a broad area over the southern Yellow Sea (Figure 3(b)), were selected for case studies. Additionally, simulations are designed with two domains in two-way extra 10 sea fog cases were chosen for quantitative evaluation nesting. on sea fog area forecast with the application of multivariate As shown in Figure 1, the cycling-3DVAR scheme in- background error covariance. cludes three 3DVAR updates. Each update is only performed 'e two typical sea fog cases occurred on 31 March 2011 on the outer WRF model domain with its BE, and initial and 10 April 2009 (hereafter referred to as Case-A and Case- condition of the inner domain is obtained by interpolation B), respectively. Looking at the correspondence between of analysis field for the outer domain after its 3rd update. In spatial distributions of weather system and fog patches the case study, the data assimilation period is 6 hours with a shown in Figures 2 and 3 (cf. Figure 2(a) with Figure 2(b); cf. DA interval of 3 hours. Figure 3(a) with Figure 3(a)), both cases formed over the 'e NMC method [32] is used to generate CV5 and CV6, areas controlled by a high-pressure system. However, the assuming that the BEs are well approximated by the averaged SST conditions are different for the two cases. Case-A oc- differences between 12-hour forecasts and 24-hour forecasts, curred along the west coast of the Korean Peninsula, where which are expressed by the SST was about 5 C (Figure 2(c)). 'e fog area was under the control of a weak high-pressure system with the center 12 24 12 24 (5) B ≈ x –x x –x , located at the Korean Peninsula (Figure 2(a)). Warm-moist air mass was transported from the central Yellow Sea to the 12 24 where x and x are 12-hour and 24-hour forecasts, re- cold SST area near the coast by the southwesterly wind spectively. 'ese forecasts can be obtained from a period of (Figure 2(c)). Case-B occurred over an ocean area, where a time (e.g., 15−30 days) or can be got from an ensemble warm SST tongue and a cold SST tongue (Figure 3(c)) prediction system. 'e former way is adopted here, and thus coexisted with large SSTgradients. Such an SSTdistribution equation (5) is rewritten as is usually favorable for the formation of sea fog [49]. In addition, easterly winds developed over the southern Yellow 24h 12h 24h 12h B ≈ x − x x − x , (6) Sea (Figure 3(c)) due to the influence of the high pressure t t t t T − 1 t�1 (Figure 3(a)), transporting huge amounts of warm-moist air mass to the fog area. where T is the time period for statistics. Here, the forecasts are collected within 15 days centered at the initial day of the case simulation. 3.3. Model and Its Configuration. 'e Advanced Research core of the WRF (ARW, version 3.8.1) and its corresponding 3. Numerical Experiments WRF-3DVAR were employed in the present study for nu- merical simulations and data assimilations. Based on the 3.1. Data. Initial and lateral boundary conditions for nu- previous work related to sea fog simulation over the Yellow merical modeling were derived from the NCEP Final Sea fog [22–24, 42], the Yonsei University (YSU) planetary ° ° Analysis (FNL) Data (1 ×1 ; 6 hourly). Bottom boundary boundary layer (PBL) scheme and the Lin microphysics conditions were extracted from the daily SST dataset scheme (LIN) were selected for the present study. Appro- ° ° (0.25 ×0.25 ) of the North-East Asian Regional Global priate, vertical levels were specified as well. Detailed model Ocean Observing System (NEAR-GOOS). Observational configurations are listed in Table 1. Due to the distinctly data for the 3DVAR data assimilation include conventional different occurrence locations and areas between the two sea surface and upper air measurements from the Global fog cases, the model domains and resolutions were sepa- Telecommunication System (GTS), buoy and island mea- rately designed for the two cases (Figure 4). Two-way nesting surements, and AIRS (Atmospheric Infrared Sounder) re- was implemented in the simulations. trieved temperature and humidity profiles. Surface synoptic maps were downloaded from the Korea Meteorological Administration (KMA) to show weather 3.4. Experimental Design. 'e experiments in this study situations of the sea fog cases in the present study. 'e were divided into 3 categories: single-observation experi- observed fog areas were empirically retrieved following the ments, case study experiments, and evaluation experiments. approach of Wang et al. [22], which uses the multichannel 'e single-observation experiments were conducted based data of Japanese Multifunctional Transport Satellite on Case-A, with a focus on RHs in CV6. 'e case study Advances in Meteorology 5 (a) (b) (c) 22 40N °C 35N 30N 10m/s 120E 125E 130E Figure 2: Korea Meteorological Administration (KMA) surface synoptic chart (a), Multifunctional Transport Satellite (MTSAT) visible image (b), and 10m wind vectors over the sea and SST (c) at 00UTC, 31 March 2011. (a) (b) (c) 22 40N 35N °C 30N 8 25N 10m/s 115E 120E 125E 130E Figure 3: Korea Meteorological Administration (KMA) surface synoptic chart (a), Multifunctional Transport Satellite (MTSAT) visible image (b), and 10m wind vectors over the sea and SST (c) at 00UTC, 10 April 2009. experiments include six experiments, which were conducted observations assimilated include the GTS routine observa- tions, buoy and ship observations and island measurements, to explore the impacts of CV6 on the 3DVAR assimilation. 'e evaluation experiments were conducted for the purpose and AIRS retrieved data. As with the BEs of those experi- of evaluating the effect of CV6 application. ments listed in Table 2, CV5 and CV6 were generated in Table 2 lists the case study experiments for Case-A and advance separately for each case using the method described Case-B. 'e initial times of these simulations are presented in in Section 2.2. 'e model configurations are the same as Table 1, and all the simulations ran out to 24 hours. 'e as- those used for the widespread sea fog case (see the de- similation of observations collected at different platforms may scription for Case-B in Table 1 and the domains in have complicated superposition effects, which is not favorable (Figure 4(b)). 'e experiments consist of two groups: for clear analysis on the assimilation impact. 'erefore, only Group-CV5 running with CV5 and Group-CV6 running with CV6, respectively. the GTS routine observations were used for assimilation. For the coastal sea fog case, only observations over the southern Korean Peninsula (Figure 4(a)) were assimilated and the data 4. Results collected at other far away observational sites were excluded. For the widespread sea fog case, all the GTS observations in D1 4.1. Single-Observation Experiments were assimilated (Figure 4(b)). A suite of experiments were conducted for 10 additional 4.1.1. Relationship between RH and T . As mentioned in s u sea fog cases that occurred over the Yellow Sea during Introduction, there is no relationship between moisture 2007–2014. In order to produce better initial conditions for control variable and any other variable in CV5. However, the WRF model, the assimilation window was extended from such relationships exist in CV6. Equation (4a) shows that, in 6 hours for the case study to 12 hours for these cases, and the CV6, RH is related to four other variables, and the s 6 Advances in Meteorology Table 1: Configurations of the weather research and forecasting (WRF). Specification Model setting and option Case-A Case-B Map projection Lambert ° ° ° ° Central point (37.0 N, 125.0 E) (34.2 N, 124.1 E) Domain Grid number 80 ×80 for D1, 151 ×151 for D2 166 ×190 for D1, 120 ×120 for D2 Horizontal resolution 30km for D1, 6km for D2 30km for D1, 10km for D2 Vertical grid 44 η with a pressure top at 50hPa Initial time 00UTC, 31 March 10 2011 12UTC, 9 April 2009 Time step Adaptive time step (60–120s for D1) PBL scheme YSU scheme [50] Cumulus parameterization Kain-Fritsch scheme [51, 52] Microphysics Lin (Perdue) scheme [53] Long-shortwave radiation RRTMG scheme [54] Land surface model Noah [55] η �1.0000, 0.9975, 0.9925, 0.9850, 0.9775, 0.9700, 0.9540, 0.9340, 0.9090, 0.8800, 0.8506, 0.8212, 0.7918, 0.7625, 0.7084, 0.6573, 0.6090, 0.5634, 0.5204, 0.4798, 0.4415, 0.4055, 0.3716, 0.3397, 0.3097, 0.2815, 0.2551, 0.2303, 0.2071, 0.1854, 0.1651, 0.1461, 0.1284, 0.1118, 0.0965, 0.0822, 0.0689, 0.0566, 0.0452, 0.0346, 0.0249, 0.0159, 0.0076, and 0.0000. 110°E 120°E 130°E 140°E 100°E 120°E 140°E D1 D1 40°N D2 40°N 40°N 40°N D2 30°N AB 30°N 30°N 30°N 20°N 20°N 115°E 125°E 135°E 110°E 120°E 130°E (a) (b) Figure 4: Geographic map of the two nesting domains of the weather research and forecasting (WRF) simulations for Case-A (a) and Case- B (b). Sites of surface (small dots) and upper-air (large dots) observations are indicated. 'e red dot in (a) is the observation location for single-observation experiments in Section 4.1, and the red dots in (b) are locations of upper-air observations for verification of Case-B. Table 2: Design of experiments. Experiment Fog case BE type Assimilated observations Exp-A_CV5 CV5 Case-A Radiosonde and surface measurements over the southern Korean Peninsula Exp-A_CV6 CV6 Exp-B_CV5 CV5 Radiosonde and surface measurements Exp-B_CV6 CV6 Case-B Exp-B_CV5e CV5 Same as Exp-B_CV5/6 but excluding the observations over the southern Korean Peninsula Exp-B_CV6e CV6 relationships between them are decided by the regression Figure 5(a). At low levels of the model, the balanced coefficients. In order to investigate how close these variables component accounts for 30–40% of the total RH , among are related, contribution rates of other control variables to which the term T contributes up to 20%–30% of the total. RH were calculated from CV6 generated in advance via the Other individual terms can only make a contribution of less NMC method for Case-A. 'e results are shown in than 5%. As a result, the term T accounts for more than u 0 Advances in Meteorology 7 (a) (b) 0.03 0.02 0.01 –0.01 20 –0.02 –0.03 –0.04 –0.05 –0.06 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1246 8 101214161820 Contribution rate Model level of unbalanced T Blance chi_u ps_u psi t_u Figure 5: Contribution rates of individual terms to RH at different model levels (a) and regression coefficients of T (b) at vertical model s u level (horizontal axis) for RH calculation (vertical axis). 'ick-dashed line in (b) indicates the regression coefficients at the same level. ∼70% of the balanced component of RH , indicating that the same level, though there exist some slight influences from temperature increment is much more important for the neighboring levels. Compared with CV6, although similar humidity increment than the wind and pressure increments. patterns and a little bit weaker intensities of temperature Similar results are also found for Case-B (figure not shown). assimilation result are obtained for CV5 (cf. Figure 6(e) with Figure 5(b) presents the distribution of regression co- Figure 6(f) and Figure 6(a) with Figure 6(b), respectively), efficient α (k1, k2) of T at level k2 to calculate RH at there is not obviously any gain for mixing ratio (Figures 6(g) T RH u s u s level k1 (see equation (4a)). 'e horizontal/vertical axis and 6(h)) due to the fact that there is no relationship between stands for k2/k1. 'e coefficients along the diagonal of moisture control variable and any other variable. Figure 5(b) are all negative, and their absolute values are Overall, for CV6, regression coefficients α of the T RH u s much larger than other data on the same row. As a result, the same level are all negative and their absolute values are humidity increment at any specific point is basically decided usually much larger than those of neighboring levels, leading by temperature increment at the same point, and a negative to an increase of mixing ratio when a lower temperature increment of T always causes a positive increment of RH . observation is assimilated. For 3DVAR with CV5, assimi- u s lation of temperature observations cannot change humidity analysis, since RH is an independent variable in CV5. 4.1.2. Contribution Rate of T to RH . A series of single- u s observation experiments were designed based on Case-A with CV5/CV6, and the single observation is marked by the 4.2. Case Study 1: ?e Coastal Sea Fog red dot shown in Figure 4(a). Each experiment was con- 4.2.1. Verification. Simulated sea fog is defined to those ducted at different vertical model level with a temperature areas where the following criteria are met [22]: cloud liquid observation of 1K lower than the background. 'ese ex- water (CLW) at the model’s lowest level is ≥0.016g/kg or periments are denoted by Exp-Sk, where k (from 1 to 20) cloud top is ≤400m. CLW ≥016g/kg is equivalent to a stands for the vertical level number. visibility ≤1km. 'e cloud top is calculated based on the Since α (1,1) is negative, decrease of temperature T RH u s threshold of CLW ≥0.016g/kg; and observations indicate with a maximum value of about −0.3K (Figure 6(a)) pro- that advection sea fogs are deeper than other types of fog but duces an increase of mixing ratio with a maximum value of rarely exceed 400m [56]. about 0.06g/kg (Figure 6(c)). 'e maximum values of 'e fog occurred over a narrow ocean area along the temperature and mixing ratio increments at levels 1–20 from western coast of the Korean Peninsula (Figures 7(a)–7(e)). Exp-S1–20 are illustrated in Figures 6(b) and 6(d). 'rough As mentioned in Section 3.4, only observations over the vertical transform, the negative temperature increment southern Korean Peninsula Figure 4(a) were assimilated, spreads to several vertical levels and causes increases of because we want to explore the impact of assimilating ob- mixing ratio there. Figure 6(d) has a very similar pattern to servations that are close to the fog area. 'e fog areas that of Figure 6(b), which again shows that the humidity forecasted by Exp-A_CV5 and Exp-A_CV6 are shown in change mainly results from the change of temperature at the Model level Model level of pseudo-RH 0 8 Advances in Meteorology 20 20 45 N 45 N (a) (b) (c) (d) 18 18 16 16 14 14 40 N 40 N 12 12 10 10 35 N 35 N 8 8 6 6 4 4 30 N 30 N 2 2 1 1 20 20 45 N 45 N (e) (f ) (g) (h) 18 18 16 16 14 14 40 N 40 N 12 12 10 10 35 N 35 N 8 8 6 6 4 4 30 N 30 N 2 2 1 1 120E 125E 130E 1 2 4 6 8 101214161820 120E 125E 130E 1 2468 10 12 14 16 18 20 Level of observed T Level of observed T –0.3 –0.25 –0.2 –0.15 –0.1 –0.05 –0.05 0.1 0.15 0.2 0.25 0.3 –0.1 –0.08 –0.06 –0.04 –0.02 –0.01 0.01 0.02 0.04 0.06 0.08 0.1 °C g/kg Figure 6: Analysis increments in the single-observation experiments for CV6 (upper row) and CV5 (lower row): horizontal distribution of analysis increments of temperature (a, e) and mixing ratio (c, g) at the bottom model level when the single observation is at the same level; analysis increments of temperature (b, f) and mixing ratio (d, h) at individual levels (vertical axis) when the single observation is specified at each level (horizontal axis). Figure 7. It is apparent that Exp-A_CV6 performs better Korean Peninsula. Compared to Exp-A_CV5, the im- than Exp-A_CV5, because the former can well capture the provements at these three sites in Exp-A_CV6 are, re- sea fog evolution, while the latter completely fails to re- spectively, 48.7%, 76.7%, and 100%, and the corresponding produce the sea fog (cf. Figures 7(f)–7(j) and 7(k)–7(o) with biases are reduced by 0.39, 0.23, and 0.47g/kg, respectively. 7(a)–7(e), respectively). Note that the difference of 925hPa wind speeds between these two experiments is less than 1m/ s (figure not shown), which indicates that CV6 makes a 4.2.2. Analysis Increments. Exp-A_CV5 performs poorly. As shown in Figures 7(f)–7(j), it produces almost no sea fog trivial change for wind field. during the whole forecast period. In contrast, Exp-A_CV6 'e agreement between the initial conditions and the successfully simulates the sea fog event (Figures 7(k)–7(o)). radiosonde observations (see the big dots in Figure 4(a) for From Figure 9, it is found that the initial condition of Exp- their locations) over the Korean Peninsula was examined. Figure 8 shows the average vertical profiles of bias and root A_CV5 is quite dry. For example, the moisture bias at the site of S6 is about −0.8g/kg. Note that this dry bias is mean square error (RMSE) of temperature and mixing ratio for Exp-A_CV5 and Exp-A_CV6. Below the height of 600m, corrected in Exp-A_CV6 and the bias is reduced to 0.4g/kg. 'e reason why Exp-A_CV6 can gain such a significant the initial temperatures of both experiments are higher than observations (Figure 8(a)), while most of the initial mixing moisture improvement is discussed below. During the analysis update of the WRF-3DVAR, the ratios are smaller than observations (Figure 8(b)). Never- theless, the mixing ratio bias of Exp-A_CV6 is much smaller minimization of the cost function (equation (1)) produces a a the analysis field x . x is determined by the balance of than that of Exp-A_CV5. 'e same is true for the RMSE. It means that the initial moisture condition of Exp-A_CV6 is analysis increment (x–x ) and observation innovation much wetter than that of Exp-A_CV5, which results in the (y–Hx) under the joint constraint of OE and BE. Because better forecasted sea fog area by Exp-A_CV6. OE is usually prescribed regardless of a specific sea fog case, In addition, ship measurements (not assimilated; see BE plays the key role. 'ere are three updates for x in the designed data assimilation scheme (Figure 1), and the 3rd their sites in Figure 9(a) were used to verify the moisture condition near the sea surface. Biases between model output update yields the initial condition for the experiments. Figure 10 demonstrates analysis fields of temperature, wind, and the measurements were calculated and results are shown in Figure 9(b). It is obvious that the initial moisture con- and mixing ratio at the lowest model level for three DA updates in Exp-A_CV5 (upper row) and Exp-A_CV6 (lower ditions of both Exp-A_CV5 and Exp-A_CV6 are drier than the observed ones. However, the dry condition is signifi- row). It is clearly seen that the analysis fields of both temperature and wind are almost the same between Exp- cantly improved in Exp-A_CV6 compared to that in Exp- A_CV5. Note that the sites S6, S7, and S8 are close to the A_CV5 and Exp-A_CV6. 'e analysis fields of mixing ratio Level of analysis Level of analysis Level of analysis Level of analysis Advances in Meteorology 9 0200UTC 31 Mar 0400UTC 31 Mar 0600UTC 31 Mar 0800UTC 31 Mar 0100UTC 31 Mar (a) (b) (c) (d) (e) (f ) (g) (h) (i) (j) 39 N 36 N (k) (l) (m) (n) (o) 39 N 36 N 123E126E123E126E123E 126E123E126E123E126 E –1 10 ms 0 100 150 200 250 300 350 400 m Figure 7: Comparison between the forecasted and observed sea fog areas (upper row; MTSATvisible imageries) for Case-A. 'e middle and lower rows show the results of Exp-A_CV5 and Exp-A_CV6, respectively. Fog depth is shown by shadings, and surface winds are displayed by vectors. are obviously different, especially at the 3rd update (cf. dashed frame (Figure 11(f)) is a little bit larger in Exp- Figure 10(c) with Figure 10(f); see bold lines with the value A_CV6 than in Exp-A_CV5 (Figure 11(b)). However, of 5.5g/kg). Water vapor is much less near surface over sea Exp-A_CV6 obtains much more moisture increment than area west of Korean Peninsula in Exp-A_CV5 than that in Exp-A_CV5 (cf. Figure 11(c) with Figure 11(g)). Does this Exp-A_CV6, which leads to its failure. Analysis fields at moisture increment still result from temperature inno- upper levels are also checked and significant difference of vation through the way revealed in the single-observation mixing ratio between Exp-A_CV5 and Exp-A_CV6 exists experiments of Section 4.1? To answer this question, two extra experiments were conducted, and the value of T below ∼600m (not shown). Next, we try to investigate in detail the difference between the observation innovations of (see equations (3a)–(3c) and (4a)–(4d)) is set to 0 in the Exp-A_CV5 and Exp-A_CV6 at the 3rd update, as well as 3rd cycle of the WRF-3DVAR; namely, the temperature the consequence of the difference on analysis increment. information is not used in the assimilation process. Re- Figure 11 illustrates the observation innovations and sults of the two extra experiments show that the difference analysis increments at the lowest model level for Exp- in moisture increment between Exp-A_CV6 and Exp- A_CV5 and Exp-A_CV6. For the temperature innovation, A_CV5 is very small (cf. Figure 11(d) with Figure 11(h)), there is nearly no difference between Exp-A_CV5 and which confirms that the larger moisture increment shown Exp-A_CV6 (cf. Figure 11(a) with Figure 11(e)). Mean- in Figure 11(g) is due to the negative temperature in- while, the difference in moisture innovation is very small, novation shown in Figure 11(e) by the function of CV6 in and the moisture innovation in the area denoted by a red- Exp-A_CV6. Note that the area of positive moisture 10 Advances in Meteorology (a) (b) 1.1 1.1 900 900 925 925 950 0.6 950 0.6 975 975 0.2 0.2 1000 1000 0.0 1.0 2.0 3.0 –0.9 –0.6 –0.3 0 0.3 0.6 0.9 Temperature (K) Mixing ratio (g/kg) Exp-A_CV5 RMSE Exp-A_CV5 bias Exp-A_CV5 RMSE Exp-A_CV5 bias Exp-A_CV6 RMSE Exp-A_CV6 bias Exp-A_CV6 RMSE Exp-A_CV6 bias Figure 8: Vertical profiles of root mean square errors (RMSEs) (solid lines) and biases (dashed lines) between the initial analysis and the radiosonde observations of temperature (a) and mixing ratio (b) for Exp-A_CV5 and Exp-A_CV6. 0.2 40N 0.0 –0.2 S6 S7 –0.4 35N S8 S3 S2 –0.6 S4 S1 S9 S5 –0.8 30N –1.0 S1 S2 S3 S4 S5 S6 S7 S8 S9 120E125E130E (80) (19.2) (45.2) (16.1) (40.8) (48.7) (76.7) (100) (13.2) Ship no. CV5 CV6 (a) (b) Figure 9: Locations of ship measurements (a) and biases of forecasted mixing ratio compared with observation (b) for Case-A. 'e improvements (%) of Exp-A_CV6 compared to Exp-A_CV5 are presented below the S# (identified mark of ship sites) along horizontal coordinates. increments in Figure 11(g) only covers the fog area (see fields of the two experiments are almost the same (cf. Figure 7). 'erefore, the success of Exp-A_CV6 is un- Figures 12(f)–12(j) with 12(k)–12(o), respectively). Al- doubtedly the consequence of the moisture improvement though the two experiments both underestimate the sea in its initial condition, and CV6 is vital to guarantee this fog areas, it is clear that Exp-B_CV6 still performs better improvement. than Exp-B_CV5. Compared with that produced by Exp- B_CV5, the fog area produced by Exp-B_CV6 is much closer to the observed one (cf. Figures 12(f)–12(j) and 4.3. Case Study 2: ?e Widespread Sea Fog 12(k)–12(o) with 12(a)–12(e), respectively). Similar to the coastal sea fog, the difference in winds between the 4.3.1. Verification. 'e results of forecasted sea fog area two experiments in the MABL is quite small (figure not for Exp-B_CV5 and Exp-B_CV6 are shown in Figure 12. shown). Similar to the results of Case-A, the sea surface wind Pressure (hPa) Mixing ratio bias (g/kg) Height (km) Pressure (hPa) Height (km) Advances in Meteorology 11 1st update 2nd update 3rd update 40 N (a) (b) (c) CV5 35 N 30 N 40 N (c) (d) (e) 35 N CV6 30 N 125 E 130 E 125 E 130 E 125 E 130 E 10 m/s –2 0 2 4 6 8 1012141618 Figure 10: Analysis fields of temperature (color shades), wind (vectors), and mixing ratio (contours) at the lowest model level after three DA updates: (a)–(c) for CV5 and (d)–(f) for CV6. 'e bold lines indicate mixing ratio of 5.5g/kg. 'e temperature and moisture structures of the MABL their initial conditions. Figure 15 shows the differences in in the initial conditions of Exp-B_CV5 and Exp-B_CV6 initial condition near the surface between the two experi- were compared with six radiosonde soundings (red dots in ments (Exp-B_CV6 minus Exp-B_CV5). 'e differences in Figure 4(b). Vertical profiles of RMSE and bias of tem- pressure and wind are not presented because they are very perature and mixing ratio for Exp-A_CV5 and Exp-A_CV6 small. 'e difference in moisture is relatively larger than that are presented in Figure 13. Similar to Figure 8, the initial in temperature. 'e differences in moisture and temperature temperatures of both experiments are higher than obser- over the sea fog area (see the sea fog in Figures 12(a), 12(f), vations (Figure 13(a)). However, the initial mixing ratios are and 12(k)) are quite small. For example, the difference in smaller than observations below 300m see the biases in temperature is within the range of about −0.2–+0.2 C, and (Figure 13(b)). Compared to Exp-B_CV5, the drier condi- the differences in mixing ratio and relative humidity are tion is alleviated by 0.2g/kg in Exp-B_CV6, which results in within the ranges of about −0.2–+0.2g/kg and 0–5%, re- better performance. Ship measurements (not assimilated; see spectively. Note that there are two areas with large positive their sites in (Figure 14(a)) were also employed to check the and negative differences in mixing ratio, respectively moisture condition near the sea surface. 'e biases between (Figure 15(b)). 'e area of positive difference is located over model outputs and the measurements are displayed in the northwestern Yellow Sea (see the red shading around (Figure 14(b)), which shows clearly that Exp-B_CV6 out- Shandong Peninsula marked in Figure 2(b)), and the area of performs Exp-B_CV5 at six out of eight sites and the negative difference is located over the southern Korea maximum improvement is up to 36.7%. Peninsula. 'e area of positive mixing ratio difference stretches to the southeast, while positive difference in rel- ative humidity occurs over almost the entire Yellow Sea 4.3.2. Differences in Initial Condition. Since Exp-B_CV5 and (Figure 15(c)). Different from the positive analysis incre- Exp-B_CV6 share the same model configuration, their ment of mixing ratio over the Yellow Sea in Exp-B_CV6, different performances are attributed to differences between 12 Advances in Meteorology Temperature Moisture With temperature Without temperature (a) (b) (c) (d) 38 N 40 N 36 N 35 N 34 N 32 N 30 N 40 N (e) (f ) (g) (h) 38 N 36 N 35 N 34 N 32 N 30 N 124 E 126 E 128 E 130 E 24 E 126 E 128 E 130 E 120 E 125 E 130 E 120 E 125 E 130 E –3 –2.5 –2 –1.5 –1 –0.5 0.5 1 1.5 2 2.5 3 °C –1 –0.8 –0.6 –0.4 –0.2 –0.1 0 0.1 0.2 0.4 0.6 0.8 1 g/kg –2 –1.6 –1.2 –0.8 –0.4 –0.2 0.2 0.4 0.8 1.2 1.6 2 g/kg Analysis increments Observation innovations Figure 11: Observation innovations and analysis increments of the 3rd update at the lowest model level for CV5 (upper row) and CV6 (lower row): innovations of temperature (a, e) and mixing ratio (b, f); increments of mixing ratio with (c, g) and without (d, h) assimilation of temperature. 'e dots indicate the observational sites. there is almost no positive gain of mixing ratio in Exp- Yellow Sea due to the assimilation of other observations B_CV5 (cf. Figures 16(a) and 16(b)). 'e above results beyond Area-K. demonstrate that the initial condition of Exp-B_CV6 is Forced by the sea surface wind field (see the vectors in wetter than that of Exp-B_CV5 in the MABL, which leads to Figure12),thesouthwesterlyadvectionpullsdrierairmassfrom better performance. Area-K to the southern Yellow Sea, which is not conducive to For Case-A described in Section 4.2, the assimilation the formation and development of sea fog there. Despite this of the observations over the Korea Peninsula (see their unfavorable situation, Exp-B_CV6 still performs better than sites in Figure 4(a) can noticeably improve the modeling Exp-B_CV5, which is attributed to the fact that its initial result of Exp-A_CV6, because positive analysis increment condition contains positive moisture increment over the Yellow of moisture is produced by negative temperature ob- Sea caused by the correlation between moisture and other servation innovation (see Figure 11). On the contrary, for control variables in CV6. To further explore the impact of CV6, Case-B, both Exp-B_CV5 and Exp-B_CV6 get negative two sensitivity experiments—Exp-B_CV5e and Exp- analysis increments of moisture over Area-K (shown in B_CV6e—were, respectively, conducted based on Exp-B_CV5 Figure 16), and the increment for Exp-B_CV6 is larger and Exp-B_CV6 but without assimilation of the observations than that for Exp-B_CV5. 'is can be explained by the over the southern Korea Peninsula (the domain framed by observation innovations of moisture and temperature dashed line in Figure 4(b). Figure 17 compares the analysis over Area-K. 'e moisture innovation is negative and the increments of mixing ratio near the surface between Exp- B_CV5 and Exp-B_CV5e and initial difference inmixing ratio temperature innovation is positive over Area-K for both Exp-B_CV5 and Exp-B_CV6 (figures not shown). For between them. It can be seen clearly that the assimilation of the Exp-B_CV5, the negative increment of moisture is pro- observations over the southern Korea Peninsula results in an duced because RH is an independent variable in CV5. obvious decrease of mixing ratio in the MABL in the initial For Exp-B_CV6, however, since there exist correlations condition. Comparative results of the forecasted sea fog area between RH and other variables, especially temperature between Exp-B_CV5/6 and Exp-B_CV5/6e are shown in Fig- (equation (4a)), negative moisture increment and posi- ure 18. Compared to Exp-B_CV5, the fog area simulated by tive temperature increment jointly produce a large Exp-B_CV5e is significantly improved by 29.0–45.4%. How- negative increment of moisture over Area-K. In contrast, ever, the difference between results of Exp-B_CV6e and Exp- Exp-B_CV6 gets positive moisture increment (see the B_CV6 is no more than∼5%. 'e above results indicate that the yellow shading in Figure 16(b)) over other areas of the assimilation effect of CV6 is more reliable than CV5. CV6 CV5 Advances in Meteorology 13 0000UTC 10 Apr 0200UTC 10 Apr 0400UTC 10 Apr 0600UTC 10 Apr 0800UTC 10 Apr (a) (b) (c) (d) (e) (f ) (g) (h) (i) (j) 36 N 30 N (k) (l) (m) (n) (o) 36 N 30 N 120 E 126 E 120 E 126 E 120 E 126 E 120 E 126 E 120 E 126 E –1 10 ms 0 100 150 200 250 300 350 400 m Figure 12: Comparison between the forecasted and observed sea fog areas (upper row; MTSAT visible imageries) for Case-B. 'e middle and lower rows show the results of Exp-B_CV5 and Exp-B_CV6, respectively. Fog depth is shown by shadings, and surface winds are displayed by vectors. 4.4. Discussion on the Impact of CV6. 'e results of the However, degree of improvement (i.e., development of sea fog above case studies show that CV6 outstrips CV5 in the area) is primarily dominated by the localization scales in BE, both cases. It seems that the performance of CV6 is much which limits the spatial spread of observational information. 'e better in Case-A than in Case-B (see Figures 7 and 12). In case studies indicate that the impact of CV6 depends on weather Case-A, the sea fog patch is small and very near the and real-time condition. Actually, this is directly due to the western coast of the Korean Peninsula. 'e assimilation of individual localization scales in BEs for Case-A and Case-B. temperature observations over the Korean Peninsula can 'e localization scales are calculated when BE is generated affect the area where the sea fog occurred (Figure 11(g)), by the NMC method. As mentioned in Section 2.2, forecast differences during 15 days are used to produce BE in the NMC which leads to relatively great improvement in Case-A. In contrast, the sea fog patch in Case-B is much larger than method. 'us, BE comes from the temporal average of forecast differences, which means that BE does not vary with time and that in Case-A, and most of the sea fog patch in Case-B is far away from the coast; the assimilation information of sometimes the localization scales are not suitable for a specific observations over land is difficult to spread over the area real-time condition, especially that the weather system changes where sea fog occurred. 'is results in a relatively poor rapidly. If ensemble forecast members are available from an performance in Case-B. ensembleforecastsystem,ensemble-basedperturbationscanbe Due to the negative correlation between temperature and used instead of using forecast differences to generate CV6 in moisture in CV6, assimilation of negative observational inno- the NMC method. Perhaps this kind of CV6 becomes more vations of temperature can definitely get positive moisture in- effective, because some flow-dependent information could be crements, which leads to improvement of sea fog simulation. introduced into the BE. 14 Advances in Meteorology 1.1 1.1 900 900 925 925 0.7 0.7 950 950 975 975 0.2 0.2 1000 1000 0.4 0.8 1.2 1.6 2.0 2.4 –1.0 –0.5 0.0 0.5 1.0 1.5 Temperature (K) Mixing ratio (g/kg) Exp-B_CV5 RMSE Exp-B_CV5 bias Exp-B_CV5 RMSE Exp-B_CV5 bias Exp-B_CV6 RMSE Exp-B_CV6 bias Exp-B_CV6 RMSE Exp-B_CV6 bias (a) (b) Figure 13: Vertical profiles of root mean square errors (RMSEs) (solid lines) and biases (dashed lines) between the initial analysis and the radiosonde observations of temperature (a) and mixing ratio (b) for Exp-B_CV5 and Exp-B_CV6. 1.2 40N 0.8 0.4 35N S1 S8 S3 0.0 S2 S5 S6 –0.4 S4 S7 30N 120E 125E 130E S1 S2 S3 S4 S5 S6 S7 S8 (9.3) (15.8) (1.4) (–5) (2.4) (–4) (36.7) (25.8) Ship no. CV5 CV6 (a) (b) Figure 14: Locations of ship measurements (a) and biases of forecasted mixing ratio compared with observation (b) for Case-B. 'e improvements (%) of Exp-B_CV6 compared to Exp-B_CV5 are presented below the S# (identified mark of ship sites) along horizontal coordinates. 4.5. Quantitative Evaluation. 'e evaluation method of the be regarded as a binary event (yes or no; 1 or 0). Statistical simulated sea fog area in case study is a so-called eyeball scores, including the probability of detection (POD), false method, which visually compares forecasted fog and satellite alarm ratio (FAR), bias, and equitable threat score (ETS), are observed fog. 'is is a qualitative and subjective method, which used for evaluation. 'ey are defined as follows: cannot provide a quantitative statistical result for multiple (7a) cases. According to Zhou and Du [56], a more objective and POD � , comprehensive method is to remap both the observed and forecasted fog areas onto the same grids, in which point-to- F–H (7b) FAR � , point comparisons can be conducted. Fog area prediction can Pressure (hPa) Mixing ratio bias (g/kg) Height (km) Pressure (hPa) Height (km) Advances in Meteorology 15 (a) (b) 0.5 (c) 0.6 5 40N 40N 40N 0.4 0.5 4 0.3 0.4 3 0.2 0.3 2 35N 35N 0.1 35N 0.2 1 –0.2 –1 –0.1 –0.3 –2 –0.2 30N 30N 30N –0.4 –3 –0.3 –0.5 –4 –0.4 –0.6 –5 –0.5 25N 25N 25N 115E 120E 125E 130E 115E 120E 125E 130E 115E 120E 125E 130E Figure 15: Initial differences of temperature (a), mixing ratio (b), and relative humidity (c) near the surface between Exp-B_CV6 and Exp- B_CV5 (the former minus the latter). 1 1 (a) (b) 40N 40N 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 35N 35N 0.1 0.1 0 0 –0.1 –0.1 –0.2 –0.2 30N 30N –0.4 –0.4 –0.6 –0.6 –0.8 –0.8 –1 –1 25N 25N 115E 120E 125E 130E 115E 120E 125E 130E Figure 16: Analysis increments of mixing ratio in Exp-B_CV5 (a) and Exp-B_CV6 (b) near the surface. 'e area framed by a red-dashed line box is named Area-K. 1 1 (a) (b) (c) 0.6 40N 40N 40N 0.8 0.8 0.5 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.3 35N 35N 35N 0.1 0.1 0.2 0 0 –0.2 –0.1 –0.1 –0.3 –0.2 –0.2 30N –0.4 30N –0.4 30N –0.4 –0.6 –0.6 –0.5 –0.8 –0.8 –0.6 –1 –1 25N 25N 25N 115E 120E 125E 130E 115E 120E 125E 130E 115E 120E 125E 130E Figure 17: (a) Analysis increments of mixing ratio near the surface for Exp-B_CV5 (a) and Exp-B_CV5e (b) and differences in the initial mixing ratio between them (Exp-B_CV5e minus Exp-B_CV5) (c). from the MTSATusing the method designed by [22], and D2 (7c) bias � –1, is taken as the verification domain with a mesh resolution of 0.1 . Grids covered by high-altitude clouds are excluded over both the land and the sea areas. Verification was carried out H–R (7d) ETS � . for all model outputs at 1-hour intervals. Quantitative F + O–H–R evaluation was conducted using the statistical scores defined Here, H, F, and O refer to the numbers of correctly above for each case, and the scores were then temporally forecast points (hits), forecast points, and observed points; averaged. 'e evaluation results are presented in Table 3, in R � F(O/N) is a random hit penalty, and N is the total which the cases are arranged chronologically according to number of grid points. 'e observed fog areas are retrieved initial time. °C g/kg g/kg g/kg g/kg g/kg g/kg % 16 Advances in Meteorology 0000UTC 10 APR 0200UTC 10 APR 0400UTC 10 APR 0600UTC 10 APR 0800UTC 10 APR 36 N (a) (b) (c) (d) (e) 30 N 29.0 31.5 29.6 45.4 33.6 (f ) (g) (h) (i) (j) 36 N 30 N 5.1 4.1 –1.1 –2.0 –3.9 120 E 126 E 120 E 126 E 120 E 126 E 120 E 126 E 120 E 126 E Figure 18: Boundaries of the forecasted sea fog area for Exp-B_CV5 (red lines) and Exp-B_CV5e (blue lines) (upper row) and for Exp- B_CV6 (red lines) and Exp-B_CV6e (blue lines) (lower row). 'e number in each panel is the enlargement rate (%) of sea fog area produced by Exp-B_CV#e compared to that by Exp-B_CV#. Table 3: Statistical verification result of the experiments of the 10 sea fog cases. 'e improvements (%) in Group-CV6 relative to Group- CV5 are in parentheses. Case and initial time Group-CV5 Group-CV6 no., yyyy-mm-dd_hh POD FAR Bias ETS POD FAR Bias ETS 1 2007-02-05_12 0.833 0.506 0.702 0.329 0.840 (0.8) 0.491 (3.0) 0.665 (3.7) 0.343 (4.3) 2 2008-04-28_12 0.510 0.281 –0.292 0.289 0.781 (53.1) 0.302 (–2.9) 0.128 ( 16.4) 0.432 (49.5) 3 2009-05-02_12 0.935 0.290 0.317 0.528 0.933 (–0.2) 0.287 (0.4) 0.309 (0.8) 0.532 (0.8) 4 2010-02-22_12 0.733 0.307 0.057 0.340 0.827 (12.8) 0.328 (–3.0) 0.232 (–17.5) 0.362 (6.5) 5 2011-03-12_12 0.674 0.481 0.299 0.212 0.681 (1.0) 0.523 (–8.1) 0.429 (–13.0) 0.172 (–18.9) 6 2011-05-17_00 0.439 0.094 –0.516 0.344 0.823 (87.5) 0.243 (–16.4) 0.087 (42.9) 0.556 (1.6 6 ) 7 2012-03-27_12 0.578 0.487 0.126 0.302 0.892 (54.3) 0.546 (–11.5) 0.968 (–84.2) 0.343 ( 13.6) 8 2012-04-13_18 0.408 0.412 –0.305 0.113 0.489 (19.9) 0.402 ( 1.7) –0.180 (12.5) 0.142 (25.7) 9 2012-05-09_12 0.245 0.384 –0.603 0.114 0.528 (115.5) 0.391 (–1.1) –0.134 (46.9) 0.236 ( 107.0) 10 2014-05-22_02 0.471 0.368 –0.199 0.242 0.644 (36.7) 0.446 (–12.3) 0.197 (0.2) 0.284 ( 17.4) Average 0.583 0.361 –0.041 0.281 0.744 (27.6) 0.396 (–5.5) 0.270 (–22.9) 0.340 (1.0 2 ) Because ETS is a comprehensive scoring indicator, the and hence promotes sea fog development and larger fog area result of ETS is analyzed first. It is clearly seen from Table 3 (see POD improvements in Table 3). Although the results of that the average ETS of Group-CV6 is much higher than that FAR and bias show that the sea fog areas are a bit over- of Croup-CV5 with an improvement of 21%, and only one forecasted in Group-CV6, this is acceptable because the case (Case-5 in Table 3) gets a worse ETS among the ten average deterioration of FAR is only 5.5%. cases. It demonstrates that implementing CV-6 BE in the WRF-3DVAR can obviously improve sea fog modeling. 5. Summary Further case-by-case analyses of POD, FAR, bias, and ETS indicate that the improvement of ETS is mainly attributed to Data assimilation is absolutely necessary for numerical the increase of POD. Compared to that for Group-CV5, modeling of sea fog, because modeling result is highly POD for Group-CV6 improved by 27.6% on average. sensitive to initial condition, especially to initial moisture Meanwhile, the average decreases in FAR and bias were status. 'e WRF-ARW model and WRF-3DVAR module −5.5% and −22.9%, respectively. Similar to the cases studied have been widely employed for sea fog modeling, and the in the present study, CV6 results in more water vapor in the WRF-3DVAR has already been proven to be able to effec- initial condition compared to CV5 for almost every case here tively improve the initial conditions for sea fog simulations Advances in Meteorology 17 monthly basis and may also have a feature of rapid variation over the Yellow Sea. However, the default domain-depen- dent BE of the WRF-3DVAR is CV5, which does not in the low-level atmosphere due to transient weather sys- tems. 'us, when ensemble forecast members are available, consider the relationship between moisture and other control variables. As a result, the improvement of moisture it is better to use ensemble-based perturbations instead of in the initial condition has to be only dependent on the using forecast differences in the NMC method. 'is is be- direct assimilation of moisture information. 'is approach cause some flow-dependent information might be intro- causes some disadvantageous issues; for example, other duced into the BE. In addition, the localizations of control variables like temperature can hardly contribute to horizontal and vertical correlation in CV6 represent an issue the improvement of moisture status. that needs to be addressed. By theoretically comparing CV5 with CV6 (multivariate BE), it is found that CV6 includes the correlation between Data Availability moisture and temperature, which is absent in CV5. In order to explore the impact of multivariate BE on the 3DVAR FNL data can be downloaded at https://rda.ucar.edu/ assimilation effect over the Yellow Sea fog modeling, two sea datasets/ds083.2. NEAR-GOOS SST data are available at fog cases that differ greatly were selected for case study. 'e http://ds.data.jma.go.jp/gmd/goos/data. AIRS-retrieved tem advantage of CV6 compared to CV5 has been primarily perature and humidity profiles can be accessed at https://rda. explained by single-observation experiments and further ucar.edu/datasets/ds735.0. MTSAT data are available at revealed in detail based on analysis of the modeling results http://weather.is.kochi-u.ac.jp/sat/GAME, including albedo, from the cases study. In addition, the impact of CV6 ap- infrared, and visible cloud imageries. 'e NCEP ship ob- plication in the WRF-3DVAR has been evaluated by a series servations are from https://rda.ucar.edu/datasets/ds337.0. of experiments of extra ten sea fog events over the Yellow Other data for this study are available from the corre- Sea. 'e major conclusions are as follows: sponding author upon request. (1) 'e performance of the WRF-3DVAR assimilation with CV6 is obviously better than that with CV5. 'e Conflicts of Interest assimilation with CV6 can significantly improve the 'e authors declare that there are no conflicts of interest forecasted sea fog area, which is clearly demonstrated regarding the publication of this paper. in the study of the selected cases. Particularly, for the case of spreading narrowly along the coast, the sea fog evolution is successfully reproduced when the Acknowledgments assimilation with CV6 is implemented. In contrast, 'is research was funded by the National Key Research and the model completely fails to capture this fog event Development Program of China (2017YFC1404200 and when using the assimilation with CV5. 2017YFC1404100), the Key Research and Development (2) 'ere exists a dominant negative correlation be- Program of Shandong Province (2019GSF111066), and the tween temperature and moisture in CV6 near the sea National Natural Science Foundation of China (42075069). surface, which makes it possible to improve initial 'e authors acknowledge UCAR/NCAR/CISL/TDD for moisture condition in the marine atmospheric providing the powerful graphic tool NCL (https://doi.org/ boundary layer by assimilating temperature obser- 10.5065/D6WD3XH5). vations near the sea surface. However, the primary way to improve moisture in the WRF-3DVAR with CV5 is to assimilate moisture observations. References (3) Experimental results of the 10 additional sea fog [1] I. Gultepe, R. Tardif, S. C. 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