
The mathematical details of the GSIbased 3DVar formulations have been reported in Wang (2010). This study mirrors its description of the formula. Briefly, the analysis increment
$ {\mathbf{x'}} $ is obtained by minimizing the cost function J, which can be written as$$ J = 0.5{({\mathbf{x'}})^{\mathbf{T}}}{{\mathbf{B}}^{  1}}({\mathbf{x'}}) + 0.5{({{\mathbf{y}}^{{\mathbf{o'}}}}  {\mathbf{Hx'}})^{\mathbf{T}}}{{\mathbf{R}}^{{\mathbf{  1}}}}({{\mathbf{y}}^{{\mathbf{o'}}}}  {\mathbf{Hx'}}) . $$ (1) The first term of Eq. (1) on the righthand side is the cost function for the background term, where B represents the static backgrounderror covariances. The second term is the observation term, where R is the observation error covariance,
$ {{\mathbf{y}}^{{\mathbf{o'}}}} $ denotes the innovation vector, and H is the linearization of the observation operator. The gradient of the cost function J with respect to$ {\mathbf{x'}} $ is given as$$ {\nabla _{{\mathbf{x'}}}}J = {{\mathbf{B}}^{{\mathbf{  1}}}}{\mathbf{x'}} + {{\mathbf{H}}^{\mathbf{T}}}{{\mathbf{R}}^{{\mathbf{  1}}}}({\mathbf{Hx'}}  {{\mathbf{y}}^{{\mathbf{o'}}}}) . $$ (2) Then the iterative minimizations are followed to obtain the final analysis.

Previous studies have developed various methods to detect the spatial distribution of sea fog over the Yellow Sea using geostationaryorbit satellite imagery data, such as the products of MTSAT (2005–2015) and its replacement Himawari8 of Japan (since 2016), Fengyun4 of China (since 2018), and the Communication, Ocean, and Meteorological Satellite (COMS) of Korea (since 2010) (e.g., Gao et al., 2009; Wang et al., 2014; Yi et al., 2016; Shin and Kim, 2018; Kim et al., 2019, 2020; Yang J. H. et al., 2019). In this study, the MTSAT products from the Center for Environmental Remote Sensing of Chiba University are used to detect the 3D spatial distribution of sea fog during both nighttime and daytime following Wang et al. (2014). A series of calibration techniques have been applied to quality control these products (Takahashi, 2017). The derivation of the 3D sea fog distributions is described briefly as follows.
During the nighttime, the brightness temperature difference (BTD) between the shortwave (IR4 from MTSAT) and longwave (IR1 from MTSAT) infrared channels is used to detect sea fog (Gao et al., 2009). A BTD value ranging from −5.5°C to −2.5°C indicates the existence of sea fog. The top height of sea fog H in units of m is calculated based on the BTD value through the empirical equation
$ H =  212 + 191{\text{ }}\left {{\text{ BTD}} \times 0.5{\text{ }}} \right $ from Ellrod (1995). A daytime sea fog area is detected when the following two criteria are satisfied. First, the difference between the IR4 brightness temperature and the sea surface temperature (SST) exceeds 4°C. The daily SST is retrieved from the NorthEast Asian RegionalGlobal Ocean Observing System (NEARGOOS). The BTD value within a certain range is used as the second criterion to determine sea fog based on the solar zenith angle. When the solar zenith angle varies between 10° and 80°, the BTD ranges from 3°C to 45°C, otherwise, the BTD is within −2°C to 3°C. The daytime fogtop height is calculated by H = 45000δ^{2/3} based on the optical thickness δ, which is related to the satellite visible albedo and the solar zenith angle (Kästner et al., 1993; Fitzpatrick et al., 2004).On the basis of the 3D detected sea fog (hereafter the observed fog), the SatelliteRH is obtained with the assumption that the air within the observed fog is saturated. Although the RH values range from 95% to 100% in saturated conditions (Sorli et al., 2002; Yang and Gao, 2020), Wang et al. (2014) have demonstrated that varying the RH value between 95% and 100% makes little difference to SatelliteRH assimilation experiments. Therefore, RH = 100% is set for the observed fog. Before the assimilation, a preprocessing procedure is applied: the 100% RH within the observed fog area is allocated with a grid spacing of 5 km; each grid point has an RH profile, which contains the RH and elevation information every 20 m from the surface to the fog top. Therefore, the 3D SatelliteRH data within the observed fog consist of large numbers of RH profiles constrained by the fog top.
The purpose of assimilating the SatelliteRH is to achieve saturation in the observed foggy areas so that sea fog can be diagnosed in the subsequent forecasts. The saturation can be reached through three approaches, i.e., the increase of moisture only, the decrease of temperature only, and changes in both moisture and temperature. In this study, the three SatelliteRH assimilation methods corresponding to the three approaches are implemented within the GSIbased 3DVar system.

Methodq that increases moisture only was adopted in Wang et al. (2014) and Ladwig et al. (2021). On the basis of the background temperature (t), the saturation specific humidity (q) is derived from the SatelliteRH profiles in the foggy areas. The GSIbased 3DVar is then employed to assimilate the derived q. The moisture fields are updated in the corresponding foggy areas. Refer to Wang et al. (2014) for more details of this method.

Methodt uses a similar procedure to Methodq except for the derivation of t. Given the background q, the saturation t is obtained from the SatelliteRH profiles where the sea fog is observed. Using the derived t as the observations, the 3DVar is used to adjust the temperature fields.

Methodq and Methodt derive the assimilated observations by assuming that the background t and q are constant, respectively. As discussed in Section 1, such an assumption may not be always appropriate for all sea fog events and for accurately analyzing the MABL structures. Therefore, a new method named MethodRH is introduced here to simultaneously adjust the moisture and temperature fields. MethodRH uses an RH observation operator to link both q and t:
$$ {\text{RH}} = \frac{q}{{1  q}} \cdot \frac{{p  {e_{\text{s}}}(t)}}{{0.622{e_{\text{s}}}(t)}} , $$ (3) where
$ {e_{\text{s}}}(t) = 6.112{e^{\frac{{17.67t}}{{t + 243.5}}}} $ is the saturation vapor pressure that only depends on t, and p represents the air pressure. Therefore, the observed SatelliteRH profiles can be directly assimilated using this method. To implement Eq. (3) in 3DVar, the tangent linear of the observation operator is derived by adding a small perturbation to q (t) and by keeping only the linear term of the Taylor expansion. Note that the relationship between the changes in RH and the variation of p is ignored in this study, as sea fog usually forms and evolves in a stable MABL with rare changes in pressure (Wang, 1983; Yang and Gao, 2015). The tangent linear of the RH operator with respect to q and t is given as$$ {{\mathbf{H}}_{\mathbf{q}}} = \frac{{{\text{RH}}}}{{q \cdot (1.0  q)}} \text{ , and} $$ (4) $$ {{\mathbf{H}}_{\mathbf{t}}} =  ({\text{RH}} + \frac{q}{{0.622(1.0  q)}}) \cdot (\frac{{17.67}}{{t + 243.5}}  \frac{{17.67t}}{{{{(t + 243.5)}^2}}}) . $$ (5) Figure 3 shows H_{q} and H_{t}, the tangent linear of the RH operator with respect to q and t, respectively. The value of H_{q} approximates the inverse of the saturation q, which is dominated by the background temperature. Therefore, H_{q} increases with the decrease in temperature. This result is physically consistent with the fact that warmer air requires more q than colder air to reach saturation. For example, an increase of RH from 80% to 90% requires an increase in q of 0.43 g kg^{−1} when t is 4 °C and an increase of 1 g kg^{−1} when t is 14.29 °C. For H_{t}, its value is jointly affected by the background moisture and temperature. It reflects that a warmer and drier background requires a larger decrease in temperature to reach saturation, like the location where t is 14.29 °C and q is 4 g kg^{−1}. In other words, a smaller decrease in temperature is required when the background is closer to saturation.
Figure 3. Derivative of RH (contours) with respect to (a) q and (b) t. The shading shows the corresponding RH. The figure uses water vapor mixing ratios ranging from 4 to 10 g kg^{−1} with an interval of 0.4 g kg^{−1} and temperatures ranging from 4 to 16 °C with an interval of 0.8 °C for the calculation.
In Methodq and Methodt, the corresponding observation errors and gross error checks are provided by the GSI package. For MethodRH, the observation error for RH is defined as 0.1 in this study. Further estimation of this observation error following Ha and Snyder (2014) is left for the future. Additional gross error checks for RH are also performed within GSI. The RH observations are rejected if the difference from the background value exceeds 0.5. Although the sea fog forecasts are somewhat sensitive to the observation errors and the errors in the derivation of 3D observed fog (Wang et al., 2014), tuning tests show that the sensitivity of the overall results to these errors is much less than the sensitivity to the SatelliteRH assimilation methods (not shown). Therefore, we leave the optimization of these configurations to future studies.

Three advection fog cases on 28 April 2007, 9 April 2009, and 29 March 2015 (hereafter Case07, Case09, and Case15, respectively) are selected for detailed study. Figure 1 shows the SST and 10 m wind for the three cases, which are favorable for the formation of sea fog. The three cases have a similar SST distribution with a decreasing tendency from south to north, and they are all dominated by a typical synoptic system of a highpressure system over the sea (e.g., Gao et al., 2007; Yang and Gao, 2015). Under such an appropriate synoptic system, the prevailing flow that transports the warm moist air masses over the cold sea surface determines the formation of sea fog. Figure 4 shows the observed fog area derived from the MTSAT data (Wang et al., 2014).
Figure 4. Evolution of the MTSATderived sea fog distributions for (a–j) Case07, (k–t) Case09, and (u–ad) Case15. The corresponding valid time is indicated in each panel. The light blue shading in (u–ad) shows high clouds. The black line in (k) indicates the position of the vertical crosssection in Fig. 6.

As shown in Fig. 4a–j, Case07 is characterized by a narrow area of sea fog along the southern coast of the Shandong Peninsula. It is a shortlived sea fog event that persisted only from 1900 UTC 28 April to 0600 UTC 29 April 2007. This sea fog event initially formed over the sea adjacent to QD at the rear of the highpressure system (Fig. 1a). The south and southwest winds transported warm, moist air masses from the relatively lower latitudes over the cold sea surface, leading to the formation of sea fog. As the warm, moist air masses accumulated, sea fog patches gradually spread northeastward and moved slowly along the coast.

The sea fog of Case09 (Fig. 4k–t) initially formed in the south of the highpressure system. The warm, moist air advected by the southeasterly and easterly flows significantly cooled and condensed over the area with a sharp SST gradient between the Yellow Sea and the East China Sea (Fig. 1b). Subsequently, sea fog patches increasingly enlarged and extended toward the northeast. Owing to the movement of the high pressure after 0000 UTC 10 April 2009, the northeast and east winds constrained the extension of sea fog and allowed it to maintain closely along the coastal region near Shanghai (SH in Fig. 1b).

Case15 is a longlived sea fog event that initially formed over the marginal sea of East China to the north of SH on 27 March 2015 and lasted for more than 4 days. Starting from 0800 UTC 28 March, the sea fog patches moved northeast and maintained over the central Yellow Sea around Rongcheng (RC in Fig. 1c), the northern Yellow Sea, and its neighboring land area near Dandong (DD in Fig. 1c). Case15 refers to the sea fog evolution from 0100 UTC 29 March that occupied nearly half of the Yellow Sea to 0000 UTC 30 March (Fig. 4u–ad). At 0100 UTC 29 March, the weak northerly flow near the center of the highpressure system carried the warm air from the land with a 2 m temperature of 9–11°C to the cold sea surface with an SST below 6°C (Fig. 1c). The warm air from the land dissipated the fog over the land, resulting in a sea fog distribution with a smooth edge along the coast of the northern Yellow Sea. The cold SST was critical for the maintenance of this sea fog event during the selected period. As the high moved eastward after 1500 UTC, the sea fog patches persisted and further extended northward due to the moisture advected by the south winds from the rear of the highpressure system.

The Weather Research and Forecasting (WRF; Skamarock et al., 2008) version 3.9.1.1 with the dynamic core of the Advanced Research WRF is used in this study. A single domain (Fig. 2) with a grid spacing of 15 km (240
$ \times $ 240 grid points) is centered at 34.2°N, 124.1°W. A total of 50 fullη levels (η_{n} ranges between 1.0 and 0.0) with 16 fullη levels below the lowest 1 km (Yang and Gao, 2016, 2020) extend vertically up to the model top of 100 hPa. As the lowest model level (between η_{1} = 1.0 and η_{2}) has a critical role in resolving the MABL processes during the sea fog, its corresponding height is set to ~8 m based on Yang et al. (2019 本条文献指代信息不明确).The physical parameterizations used in this study are the Yonsei University (YSU) planetary boundary layer (Hong et al., 2006; Hong, 2010), the Lin microphysics scheme (Lin et al., 1983), the Rapid Radiative Transfer Model for General circulation models (RRTMG) longwave and shortwave radiation schemes (Iacono et al., 2008), the Kain–Fritsch cumulus scheme (Kain and Fritsch, 1990; Kain, 2004), the fifthgeneration Mesoscale Model (MM5) Monin–Obukhov surface layer scheme (Zhang and Anthes, 1982; Jiménez et al., 2012), and the unified Noah land surface model (Tewari et al., 2004).

The initial and lateral boundary conditions are provided by the National Centers for Environmental Prediction (NCEP) FNL Operational Global Analysis data (1° × 1°, 6 hourly). Within the GSIbased 3DVar DA system, the featuredependent B in Eq. (1) is used with q as the moisture control variable (Ménétrier and Montmerle, 2011). The conventional observations, including radiosonde and surface measurements, are assimilated every three hours, and the SatelliteRH is assimilated every hour. Figure 5 illustrates the DA procedure for the three cases. Owing to the shortlived sea fog in Case07, the DA window is from 1900 UTC to 2100 UTC 28 April 2007, and forecasts from each DA cycle until 0600 UTC 29 April are used for comparisons (Fig. 5a). The DA window for Case09 starts from 1200 UTC 9 April 2009 (Fig. 5b) and for Case15 from 0000 UTC 29 March 2015 (Fig. 5c). Then an 18 h free forecast is run for each analysis of Case09 and Case15. Hourly archived model outputs are used for assessments.
Figure 5. Schematics of the DA configuration for (a) Case07, (b) Case09, and (c) Case15. The conventional (SatelliteRH) data assimilation used a 3 h (1 h) frequency.
The four experiments listed in Table 1 are performed for each of the selected cases. ExpnoMT assimilates conventional observations only and serves as a benchmark to evaluate the effects of the SatelliteRH assimilation when compared with the other three experiments. The other three experiments Expq, Expt, and ExpRH use Methodq, Methodt, and MethodRH introduced in Section 2.2, respectively, to assimilate the SatelliteRH. The intercomparisons among these three experiments provide a comprehensive assessment of the methods for assimilating the SatelliteRH.
Experiment Specification ExpnoMT Without assimilation of SatelliteRH Expq Assimilating SatelliteRH using Methodq Expt Assimilating SatelliteRH using Methodt ExpRH Assimilating SatelliteRH using MethodRH Table 1. List of experiments

A threshold of 0.016 g kg^{−1} for the liquid water content at the lowest model level height with a fogtop height below 400 m is generally adopted to diagnose the predicted sea fog (hereafter predicted fog) area (e.g., Zhou and Du, 2010; Wang et al., 2014; Gao et al., 2018, Yang and Gao, 2020). Subjectively, for each of the three selected cases, the predicted fog distributions from ExpnoMT, Expq, Expt, and ExpRH initialized at different analysis cycles are first compared with the observed fog (Fig. 4). To quantitatively verify the sea fog area forecast, both the observed and predicted fog areas are regarded as binary events (fog or clear air, 1 or 0). Statistical scores, including the equitable threat score (
$ {\text{ETS}} = \dfrac{{H  R}}{{F + O  H  R}} $ ) and frequency bias ($ {\text{FBIAS}} = \dfrac{F}{O} $ ) are used for the evaluation (e.g., Zhou and Du, 2010; Wang et al., 2014; Gao et al., 2018; Yang et al., 2019 本条文献指代信息不明确). Here H, F, and O represent the number of correctly forecasted, forecasted, and observed foggy points, respectively;$ R = \dfrac{{F \times O}}{N} $ is a random hit penalty, and N is the number of the grid points of the verification domain. In practice, ETS is treated as a comprehensive verification score that can measure how well the forecast corresponds to the observations, i.e., the forecast skill (Zhou et al., 2012). FBIAS measures only relative frequencies, indicating that the forecast system tends to underpredict (FBIAS < 1.0) or overpredict (FBIAS > 1.0) the fog areal coverage.As discussed in the earlier studies, sea fog predictions are strongly affected by the quality of the initial conditions, especially the moisture and temperature structures within the MABL, which are critical to the formation and evolution of sea fog (e.g., Nicholls, 1984; Findlater et al., 1989; Ballard et al., 1991; Koračin et al., 2001; Lewis et al., 2003; Gao et al., 2007). To determine the causes of the differences in sea fog forecasts, the forecasted moisture and temperature structures within the MABL are directly compared against the coastal soundings near the sea fog area.

To examine the effects of Methodq, Methodt, and MethodRH on the adjustment of the moisture and temperature fields, analyses from a single DA cycle with only SatelliteRH assimilated are compared in Fig. 6. The first guess is provided by the FNL data valid at 1200 UTC 09 April 2009. The corresponding SatelliteRH data are retrieved as introduced in Section 2.2.
Figure 6. Vertical crosssections of (a) RH first guess and RH analyses (shaded) from a single DA cycle (b) using Methodq, (c) Methodt, and (d) MethodRH, respectively, at 1200 UTC 09 April 2009 along the black line marked in Fig. 4k. Panel (a) also shows the first guess of temperature (red contours; °C) and water vapor mixing ratio (green contours; g kg^{−1}). Panels (b–d) show the analysis increments of temperature (red contours; °C) and water vapor mixing ratio (green contours; g kg^{−1}).
Relative to the first guess (Fig. 6a), the three methods produce similar saturations (RH 100%) below 150 m. As expected, Methodq reaches saturation through an increase in moisture only over 3.5 g kg^{−1} (Fig. 6b); a decrease in temperature only up to 7°C is found to obtain saturation in Methodt (Fig. 6c); for MethodRH, the air becomes saturated by increasing the moisture by less than 3 g kg^{−1} and decreasing the temperature by less than 5 °C (Fig. 6d). These results indicate that although a similar saturation can be achieved using the three SatelliteRH assimilation methods, their adjustments to the moisture and temperature fields are significantly different.

The three selected cases are investigated as follows. For each case, we first subjectively and objectively evaluate the predicted fog distributions against the observed fog. Subsequently, the forecasted MABL moisture and temperature structures are compared with the coastal soundings.

Compared with the observed fog (Fig. 4a–j), the forecasts initialized at 2100 UTC 28 April 2007 from ExpRH perform the best among the four experiments in Table 1 (Fig. 7). ExpnoMT fails to reproduce the evolution of sea fog (Fig. 7a–f), which supports the results from Wang et al. (2014) that assimilation of SatelliteRH is essential for the successful prediction of sea fog. In addition, the decreasing temperature in Expt is also invalid for the formation of sea fog (Fig. 7m–r). Conversely, Expq overpredicts the size of the sea fog coverage, especially over 123°E after 0200 UTC 29 April (Fig. 7g–l). In comparison, the smaller sea fog area in ExpRH (Fig. 7s–x) agrees better with the observations.
Figure 7. The predicted fog area initialized at 2100 UTC 28 April 2007 for (a–f) ExpnoMT, (g–l) Expq, (m–r) Expt, and (s–x) ExpRH. The first to sixth columns are for the forecast time valid at 2200 UTC 28 April, 0000, 0100, 0200, 0400, and 0600 UTC 29 April 2007, respectively.
Subsequently, Fig. 8a,b shows the time series of ETS and FBIAS, respectively, for the four experiments aggregated over forecasts initialized from different DA cycles. The scores of ExpnoMT are the forecasts initialized at 2100 UTC 28 April, and the others are obtained by aggregating the forecasts initialized at 1900, 2000, and 2100 UTC. Owing to the failure in sea fog prediction, ExpnoMT and Expt are regarded as having the worst performance. ExpRH has up to 0.1 higher ETSs than Expq. Both ExpRH and Expq have increasing FBIAS scores with increasing lead time. The FBIAS of ExpRH is consistently smaller than that of Expq during the entire forecast period, which coincides with the subjective evaluation. In particular, the advantage of ExpRH is most remarkable during the first 4 h of lead time. The timeaveraged aggregated scores also support the highest forecast skill for sea fog area in ExpRH with the highest ETS (0.238) and an FBIAS (2.633) relatively close to 1.0 (Table 2). Expq has the second highest forecast skill with an ETS of 0.197 and an FBIAS of 3.625. With an ETS of zero, Expt and ExpnoMT have no skill in forecasting Case07. To fairly compare ExpnoMT with the other experiments, the aggregated scores over the forecasts initialized every 3 h for all experiments are calculated and they show the same conclusion that ExpnoMT and Expt have the lowest forecast skill.
Figure 8. The statistical scores of (a, c, and e) ETS and (b, d, and f) FBIAS for the predicted fog distributions aggregated over (a, b) forecasts until 0600 UTC 29 April for Case07, and 18 h forecasts for (c, d) Case09 and (e, f) Case15 from ExpnoMT (black lines), Expq (red lines), Expt (blue lines), and ExpRH (purple lines).
Case Score ExpnoMT Expq Expt ExpRH Case07 ETS 0.0 0.213 (0.197) 0.0 (0.0) 0.226 (0.238) FBIAS 0.0 3.264 (3.625) 0.0 (0.0) 2.105 (2.633) Case09 ETS 0.203 0.387 (0.390) 0.299 (0.313) 0.356 (0.361) FBIAS 0.294 1.400 (1.414) 0.804 (0.848) 1.253 (1.282) Case15 ETS 0.196 0.446 (0.455) 0.469 (0.483) 0.468 (0.478) FBIAS 0.661 1.570 (1.615) 1.454 (1.499) 1.520 (1.567) Table 2. The aggregated statistical scores over forecasts initialized every 3 h from the experiments for each case. The values shown in parentheses are the aggregated scores over forecasts initialized every hour for Expq, Expt, and ExpRH. For Case07, only forecasts until 0600 UTC 29 April are used. The 0–18 h forecasts are used in Case09 and Case15

At the QD and CS stations, ExpnoMT has drying and warming biases near the surface (Fig. 9), which explains its failure to forecast sea fog formation in Fig. 7a–f. Specifically, the simulated MABL in ExpnoMT is 1.4–2.4 g kg^{−1} drier and ~2.7°C warmer than the observations below 1000 hPa at the QD station. Similarly, the forecasts at the CS station near the surface in ExpnoMT are 0.75 g kg^{−1} drier and 2.25 °C warmer than the observed soundings.
Figure 9. Comparison between 3 h forecast vertical profiles from ExpnoMT (black lines), Expq (red lines), Expt (blue lines), ExpRH (purple lines), and the soundings (gray) at (a, b) the QD station and (c, d) the CS station for (a, c) water vapor mixing ratio (Qvapor; g kg^{−1}) and (b, d) temperature (°C) valid at 0000 UTC 29 April 2007. QD, Qingdao; CS, Chengshantou.
To promote sea fog formation, it is required to increase moisture and decrease temperature simultaneously starting from ExpnoMT. Through additionally assimilating the SatelliteRH, the adjustment of moisture and temperature structures in the MABL for Expq, Expt, and ExpRH follow the discussions in Section 4.1. ExpRH adjusts the MABL structures at the QD station by increasing the water vapor mixing ratio (Qvapor) by 1–1.6 g kg^{−1} and decreasing the temperature by 1–3.5 °C compared with the ExpnoMT (Figs. 9a,b). With the smaller temperature decrease in Expq compared with ExpRH, the larger increase in Qvapor corresponds to the overestimated sea fog area. Although Expt can correct the warm bias at the QD station, the unchanged drying bias still leads to the failure of sea fog formation. Similar to the QD station, ExpRH has moderate corrections for both moisture and temperature at the CS station (Figs. 9c,d). However, Expq excessively predicts Qvapor up to 2.5 g kg^{−1} and slightly improves the temperature. Despite a significant temperature reduction of 1°C in Expt, Qvapor shows little variation. Thus, the best moisture and temperature structures in the MABL of ExpRH lead to the sea fog distributions that fit best to the observations.

Figure 10a–x presents the sea fog forecasts initialized at 1200 UTC 9 April 2009 from the four experiments in Table 1. Similar to Case07, both ExpnoMT and Expt are not able to capture the evolution of the observed fog (Figs. 4k–t), and Expq has a larger areal coverage of sea fog than ExpRH. Before 0000 UTC 10 April, the largest sea fog areal coverages in Expq show the best agreement with the observations, but the delayed formation of the southern sea fog patches at 1300 UTC 9 April in ExpRH degrades its forecast skill. After 0000 UTC 10 April, however, ExpRH performs better than Expq with more welldefined fog patches over the southern offshore area of the Korean Peninsula.
Figure 10. As in Fig. 7, but for the forecasts initialized at (a–x) 1200 UTC and (y–ar) 1800 UTC 9 April 2009.
As the DA cycles extend to 1800 UTC 9 April, the accumulated effects of the hourly SatelliteRH DA lead to the further enlarged sea fog area (Figs. 10y–ar). However, ExpnoMT still fails to capture the sea fog evolution, and Expt heavily underestimates the sea fog distribution before 2000 UTC. Compared with Expq, ExpRH restricts the extension of the sea fog area via a smaller moisture increase during the DA process, although both experiments overpredict the sea fog patches over the southern offshore area of the Korean Peninsula after 0000 UTC 10 April. In the meantime, Expt becomes more skillful than Expq and ExpRH due to more welldefined sea fog.
The time series of ETS and FBIAS of ExpnoMT (Expq, Expt, and ExpRH) are obtained by aggregating the scores from the 18 h forecasts initialized at 1200, 1500, and 1800 (1200, 1300, …, 1700, and 1800) UTC 9 April (Fig. 8c,d). For the first 9 h of lead time, Expq has the highest ETS (approaching 0.6) and the largest FBIAS (above 1.2) among the four experiments. ExpRH produces a similar trend of ETS to Expq but has slightly lower values. FBIAS in ExpRH is closer to 1.0 than Expq, especially for the forecasted sea fog area during the first 4 h of lead time. The failure or delay of sea fog formation in ExpnoMT and Expt result in the relatively low ETS and FBIAS values in the earlier stage of the forecast. However, the forecast skills of Expq and ExpRH gradually decrease and become poorer than those of ExpnoMT and Expt after 12 h of lead time. The highest ETS of Expt in the later forecast stage can be attributed to the appropriate size of sea fog coverage with an FBIAS close to 1.0. Although the forecast skill of ExpnoMT after 13 h of lead time is similar to that of Expt, the sea fog area is heavily underpredicted as its FBIAS is below 0.7. Owing to the overprediction of sea fog in the later forecast stage, Expq and ExpRH have the lowest ETSs of ~0.25. As listed in Table 2, the overall forecast skill from hourly cycles of Expq is mildly better than that of ExpRH (0.390 versus 0.361), and both experiments are more skillful than Expt (0.313). The overall FBIAS of ExpRH is much closer to 1.0 than that of Expq (1.282 versus 1.414). In contrast, the sea fog distributions are underpredicted in Expt with its overall FBIAS below 0.85. Compared with the other experiments, ExpnoMT has the lowest forecast skill with the lowest ETS and an FBIAS below 0.3.

At the SH station, the forecasts of ExpnoMT at 0000 UTC 10 April from all DA cycles are consistently drier and colder than the observations by 1–1.5 g kg^{−1} and ~5 °C below 100 m, respectively (Fig. 11). Therefore, adding moisture via the assimilation of SatelliteRH is an effective approach for sea fog formation. As a result, the forecasts initialized at 1200 UTC 9 April from Expq and ExpRH have similar thermal structures, which are the closest to the observed soundings below 100 m at 0000 UTC 10 April among all the experiments (Figs. 11a,b). As the number of DA cycles increases, the forecasted MABL structures at 0000 UTC 10 April in Expq gradually become closer to the observed soundings than those in ExpRH (Fig. 11c–f). We notice that the air in the MABL becomes warmer, and the inversion layer deepens with increasing of moisture owing to the accumulated DA cycling effects in Expq and ExpRH. These results can be attributed to the entrainment atop the sea fog, which gradually warms the fog layer and raises the fog top by submerging quiescent and warm air above the fog top into the sea fog layer (Yang and Gao, 2020). The cooling of Expt allows the forecasted MABL at 0000 UTC 10 April to reach saturation by further reducing the relatively small Qvapor through the condensation process (Fig. 11). Similarly, the entrainment process also warms the MABL and deepens the inversion layer in Expt as the DA cycle increases (Fig. 11f). Therefore, sea fog in Expt at 0000 UTC 10 April forms with a warmer temperature but a much smaller Qvapor than ExpnoMT (Figs. 11e,f).

In ExpnoMT (Figs. 12a–d), the forecasts initialized at 0000 UTC 29 March 2015 produce limited and severely underpredicted fog distributions over the northern Yellow Sea compared with the observed fog (Figs. 4u–ad). Expq, Expt, and ExpRH all have a similar sea fog evolution process, and they primarily differ in the forecasts before 1100 UTC (Figs. 12e–g,i–k,m–o). Expq has slightly larger sea fog areal coverage than ExpRH. Expt underpredicts the sea fog distribution with the smallest sea fog area. For the forecasts initialized at 0600 UTC, ExpnoMT still underpredicts the sea fog in the earlier forecast stage (Fig. 12q–t), and the difference among the other experiments becomes negligible (Fig. 12u–af).
Figure 12. As in Fig. 7, but for the forecasts initialized at (a−p) 0000 UTC and (q−af) 0600 UTC 9 March 2015.
To quantitatively evaluate the forecast skills of four experiments in Table 1 for Case15, the statistical scores of ETS and FBIAS are calculated. Note that both the observed and predicted fog areas covered by the observed high clouds are excluded from the verification domain (Wang et al., 2014). In Fig. 8e,f, the time series of scores for ExpnoMT are obtained by aggregating the scores from the 18 h forecasts initialized at 0000, 0300, and 0600 UTC 29 March, and for the other experiments from forecasts initialized at 0000, 0100, …, 0500, and 0600 UTC. The underpredicted sea fog in ExpnoMT indicated by an FBIAS below 1.0 corresponds to the lowest ETS. Consistent with the subjective verification in Expt, the underpredicted sea fog area in the earlier forecast stage lowers the ETS. After 4 h of lead time, Expt is the most skillful with an ETS up to 0.65 and an FBIAS closer to 1.0. For the first 3 h of lead time, ExpRH has a higher ETS than Expt. However, after that, ExpRH becomes less skillful or comparable to Expt. Expq has a lower ETS than ExpRH after the 2 h lead time mainly due to the overestimation of sea fog area. The overall scores from the forecasts initialized every hour listed in Table 2 further suggest a similar sea fog forecast skill for Expt and ExpRH (0.483 versus 0.478), and both experiments are better than Expq (0.455). ExpnoMT still has the worst forecast skill when comparisons are carried out.

At the RC and DD stations, the analyses of ExpnoMT at 0000 UTC 29 March show a wetting bias of ~0.5 g kg^{−1} and a warming bias of 2–4 °C within the MABL (Figs. 13a–d). The addition of decreasing temperature is necessary for this case to mitigate the warming bias. Just like in Expt, the temperature within the MABL is reduced by 0.2–2°C, and Qvapor is unchanged, consistent with Fig. 6. Although ExpRH decreases the temperature comparable to Expt, Qvapor is increased by ~0.2–0.6 g kg^{−1}. These adjustments lead to the overestimated sea fog areas compared with Expt (e.g., Figs. 12i, m). Without changing the temperature, Expq further increases the moisture by ~0.4–1.0 g kg^{−1} compared with ExpnoMT. Expq therefore has the largest sea fog coverage size. At 0600 UTC, the analysis of ExpnoMT at the Oscan station (OS in Fig. 1c) is 0.5 g kg^{−1} drier and 1 °C warmer than the observations (Figs. 13e, f). After the cycled assimilation of the SatelliteRH, Expt produces a slightly wetter and 2–4 °C colder analysis than the observed soundings. Compared with Expt, ExpRH produces a warmer structure but excessively adds moisture below 100 m. Expq consistently adds excessive moisture.

For the three selected cases, the experiments with the assimilation of SatelliteRH perform consistently better than ExpnoMT for the sea fog forecast. The performance of the three methods in assimilating the SatelliteRH, i.e., Methodq, Methodt, and MethodRH, is case dependent in the sea fog forecast, as different factors are responsible for the failures of the sea fog forecast in ExpnoMT. We grade their performance for each case in Table 3. Specifically, ExpRH has the highest forecast skill for Case07 because it can increase moisture and decrease temperature simultaneously to correct the drying and warming biases in ExpnoMT. Therefore, MethodRH is given a score of two for this case. For Case09, ExpnoMT has the lowest forecast skill due to the insufficient amount of moisture in the MABL. As a result, Expq performs the best through increasing moisture, and the corresponding Methodq RH is given a score of two for Case09. For Case15, Expt generally performs better than the other experiments via decreasing the temperature as ExpnoMT has a sufficient amount of moisture but a warming bias. Therefore, Methodt RH is given a score of two. It is noted that the forecast skill of ExpRH is slightly lower than that of Expq for Case09 and similar to Expt for Case15 (Table 2). Hence, a score of one is given to MethodRH for Case09 and Case15 as the performance is only mildly worse than the best for each case. Expt (Expq) has the worst performance for Case07 and Case09 (Case15) in the overall evaluation. Thus, they are graded as the worst with a score of zero.
Case MethodRH Methodq Methodt Case07 2 1 0 Case09 1 2 0 Case15 1 0 2 Total 4 3 2 Table 3. Overall evaluation of the three SatelliteRH assimilation methods. The method with the best performance is awarded a score of two, followed by a score of one, with the worst having a score of zero for each case.
As failures of most sea fog predictions may be attributed to the drying, the warming, or both biases in the MABL, of the three SatelliteRH assimilation methods only MethodRH can partially or fully account for all these bias scenarios by simultaneously cooling and humidifying. Therefore, although the skill of ExpRH for sea fog and associated MABL forecasts is not always the highest, it is not the lowest for the three cases. Overall, MethodRH with the highest total score of four is the best choice to adjust the MABL moisture and temperature structures and improve the sea fog forecast from a practical forecast perspective.
Experiment  Specification 
ExpnoMT  Without assimilation of SatelliteRH 
Expq  Assimilating SatelliteRH using Methodq 
Expt  Assimilating SatelliteRH using Methodt 
ExpRH  Assimilating SatelliteRH using MethodRH 