A New Observation Operator for the Assimilation of Satellite-derived Relative Humidity: Methodology and Experiments with Three Sea Fog Cases over the Yellow Sea

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  • Corresponding author: Yongming WANG, yongming.w@hotmail.com
  • Funds:

    Supported by the National Natural Science Foundation of China (42075069), and the Key Research and Development Program of Shandong Province (2019GSF111066).

  • doi: 10.1007/s13351-021-1084-0
  • Note: This paper will appear in the forthcoming issue. It is not the finalized version yet. Please use with caution.

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  • Assimilation of satellite-derived relative humidity (Satellite-RH) is capable of improving sea fog forecasts by saturating the background in the observed foggy areas. Previous studies have achieved saturation by increasing the moisture only (Method-q). However, this method can lead to large wetting and warming biases within the marine atmospheric boundary layer (MABL). A new method using an RH observation operator (Method-RH) is designed to alleviate these biases by simultaneously adjusting the moisture and the temperature. For comparison, saturation is also achieved by decreasing the temperature only (Method-t). The three Satellite-RH assimilation methods are implemented within the Gridpoint Statistical Interpolation-based three-dimensional variational system and examined for three sea fog cases over the Yellow Sea. The three cases on 28 April 2007, 9 April 2009, and 29 March 2015 fail to be predicted without the Satellite-RH assimilation as their MABLs have both warming and drying, drying, and warming biases, respectively. Intercomparisons and evaluations show that Method-RH has the best overall performance of the three methods in terms of the forecast of sea fog and MABL structures as only Method-RH can fully or partially address all the bias scenarios in forecasting sea fog. Compared with Method-q, Method-RH produces more well-defined sea fog areas by adding a smaller amount of moisture as well as decreasing the temperature. Compared with Method-t, Method-RH enlarges the sea fog areas by increasing the amount of moisture in addition to the cooling.
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  • Fig. 1.  Geographic map of the Yellow Sea overlaid with sea surface temperature (shaded; °C) and 10 m wind field (vectors; m s−1) from the Final (FNL) Operational Global Analysis data at (a) 1900 UTC 28 April 2007, (b) 1200 UTC 9 May 2009, and (c) 0100 UTC 29 March 2015. The distribution of 2 m temperature (shaded; °C) over land is also shown in (c). The locations of the sounding stations are marked with black dots. QD, Qingdao; CS, Chengshantou; SH, Shanghai; RC, Rongcheng; DD, Dandong; OS, Osan.

    Fig. 2.  WRF domain and the locations of surface observations (in-situ stations, ships, and buoys; black dots) and sounding stations (red triangles) in Case07 as an example.

    Fig. 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.

    Fig. 4.  Evolution of the MTSAT-derived 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 cross-section in Fig. 6.

    Fig. 5.  Schematics of the DA configuration for (a) Case07, (b) Case09, and (c) Case15. The conventional (Satellite-RH) data assimilation used a 3 h (1 h) frequency.

    Fig. 6.  Vertical cross-sections of (a) RH first guess and RH analyses (shaded) from a single DA cycle (b) using Method-q, (c) Method-t, and (d) Method-RH, 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).

    Fig. 7.  The predicted fog area initialized at 2100 UTC 28 April 2007 for (a–f) Exp-noMT, (g–l) Exp-q, (m–r) Exp-t, and (s–x) Exp-RH. 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.

    Fig. 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 Exp-noMT (black lines), Exp-q (red lines), Exp-t (blue lines), and Exp-RH (purple lines).

    Fig. 9.  Comparison between 3 h forecast vertical profiles from Exp-noMT (black lines), Exp-q (red lines), Exp-t (blue lines), Exp-RH (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.

    Fig. 10.  As in Fig. 7, but for the forecasts initialized at (a–x) 1200 UTC and (y–ar) 1800 UTC 9 April 2009.

    Fig. 11.  As in Fig. 9, but for the (a, b) 12 h, (c, d) 9 h, and (e, f) 6 h forecasts valid at 0000 UTC 10 April 2009 at SH station. SH, Shanghai.

    Fig. 12.  As in Fig. 7, but for the forecasts initialized at (a−p) 0000 UTC and (q−af) 0600 UTC 9 March 2015.

    Fig. 13.  As in Fig. 9, but for the analyses valid at (a−d) 0000 UTC 29 March 2015 at the (a, b) RC and (c, d) DD stations, and (e, f) 0600 UTC 29 March at the OS station. OS, Oscan.

    Table 1.  List of experiments

    ExperimentSpecification
    Exp-noMTWithout assimilation of Satellite-RH
    Exp-qAssimilating Satellite-RH using Method-q
    Exp-tAssimilating Satellite-RH using Method-t
    Exp-RHAssimilating Satellite-RH using Method-RH
    Download: Download as CSV

    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 Exp-q, Exp-t, and Exp-RH. For Case07, only forecasts until 0600 UTC 29 April are used. The 0–18 h forecasts are used in Case09 and Case15

    CaseScoreExp-noMTExp-qExp-tExp-RH
    Case07ETS0.00.213 (0.197)0.0 (0.0)0.226 (0.238)
    FBIAS0.03.264 (3.625)0.0 (0.0)2.105 (2.633)
    Case09ETS0.2030.387 (0.390)0.299 (0.313)0.356 (0.361)
    FBIAS0.2941.400 (1.414)0.804 (0.848)1.253 (1.282)
    Case15ETS0.1960.446 (0.455)0.469 (0.483)0.468 (0.478)
    FBIAS0.6611.570 (1.615)1.454 (1.499)1.520 (1.567)
    Download: Download as CSV

    Table 3.  Overall evaluation of the three Satellite-RH 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.

    CaseMethod-RHMethod-qMethod-t
    Case07210
    Case09120
    Case15102
    Total432
    Download: Download as CSV
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A New Observation Operator for the Assimilation of Satellite-derived Relative Humidity: Methodology and Experiments with Three Sea Fog Cases over the Yellow Sea

    Corresponding author: Yongming WANG, yongming.w@hotmail.com
  • 1. Key Laboratory of Physical Oceanography, College of Oceanic and Atmospheric Sciences, Ocean University of China, Qingdao 266100, China
  • 2. School of Meteorology, University of Oklahoma, Norman, OK 73072, USA
  • 3. Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
Funds: Supported by the National Natural Science Foundation of China (42075069), and the Key Research and Development Program of Shandong Province (2019GSF111066).

Abstract: Assimilation of satellite-derived relative humidity (Satellite-RH) is capable of improving sea fog forecasts by saturating the background in the observed foggy areas. Previous studies have achieved saturation by increasing the moisture only (Method-q). However, this method can lead to large wetting and warming biases within the marine atmospheric boundary layer (MABL). A new method using an RH observation operator (Method-RH) is designed to alleviate these biases by simultaneously adjusting the moisture and the temperature. For comparison, saturation is also achieved by decreasing the temperature only (Method-t). The three Satellite-RH assimilation methods are implemented within the Gridpoint Statistical Interpolation-based three-dimensional variational system and examined for three sea fog cases over the Yellow Sea. The three cases on 28 April 2007, 9 April 2009, and 29 March 2015 fail to be predicted without the Satellite-RH assimilation as their MABLs have both warming and drying, drying, and warming biases, respectively. Intercomparisons and evaluations show that Method-RH has the best overall performance of the three methods in terms of the forecast of sea fog and MABL structures as only Method-RH can fully or partially address all the bias scenarios in forecasting sea fog. Compared with Method-q, Method-RH produces more well-defined sea fog areas by adding a smaller amount of moisture as well as decreasing the temperature. Compared with Method-t, Method-RH enlarges the sea fog areas by increasing the amount of moisture in addition to the cooling.

    • Sea fog is hazardous for many human activities (for example, fishing, aviation, and transportation) in marine and coastal areas (Wang, 1983; Lewis et al., 2004; Koračin and Dorman, 2017) because the atmospheric horizontal visibility is severely reduced to less than 1 km (WMO, 1996). In China, sea fog frequently occurs over the Yellow Sea (its location is shown in Fig. 1), especially from March to July every year (Zhang et al., 2012; Wang et al., 2014). For example, it has been recorded that sea fog occurs more than 50 days per year on the northwest coast of the Yellow Sea (Zhang et al., 2009). The maximum number of foggy days of 83 and 89 were observed at Chengshantou (CS in Fig. 1a; Zhang et al., 2009) between 1971 and 2000 and at Qingdao (QD in Fig. 1a; Zhang and Bao, 2008; Fu et al., 2012) in 2006, respectively. To alleviate the negative impacts of sea fog over the Yellow Sea, numerous studies have been dedicated to improving its numerical prediction (e.g., Gao et al., 2010, 2014, 2018; Wang et al., 2014).

      Figure 1.  Geographic map of the Yellow Sea overlaid with sea surface temperature (shaded; °C) and 10 m wind field (vectors; m s−1) from the Final (FNL) Operational Global Analysis data at (a) 1900 UTC 28 April 2007, (b) 1200 UTC 9 May 2009, and (c) 0100 UTC 29 March 2015. The distribution of 2 m temperature (shaded; °C) over land is also shown in (c). The locations of the sounding stations are marked with black dots. QD, Qingdao; CS, Chengshantou; SH, Shanghai; RC, Rongcheng; DD, Dandong; OS, Osan.

      Sea fog events over the Yellow Sea are dominated by advection fog, which occurs when warm, moist air masses flow over the cold sea surface under appropriate synoptic systems (Wang, 1983; Yang and Gao, 2015). Therefore, the structure of the marine atmospheric boundary layer (MABL) has a critical role in the formation and development of advection fog. As the measurements from coastal in-situ stations, buoys, ships, and aircraft are unable to fully capture the spatiotemporal evolution of sea fog and its environment owing to their sparsity over the ocean (Fig. 2), the accuracy of the MABL structure during the sea fog period determined through data assimilation (DA) is limited and remains to be improved. To address the lack of observations over the ocean, several studies have been devoted to assimilating satellite data or its retrievals to initialize sea fog forecasting because of the high-spatiotemporal-resolution information provided by satellites (e.g., Li et al., 2012; Wang et al., 2014). For instance, geostationary-orbit satellite imagery data with a spatial resolution of 1–5 km and a frequency of about 30 min are preferred for the continuous monitoring of sea fog evolution over the Yellow Sea (e.g., Gao et al., 2009; Li et al., 2012; Wang et al., 2014; Shin and Kim, 2018; Yang J. H. et al., 2019; Kim et al., 2020). However, it is challenging to properly assimilate the satellite data or its retrievals for initialization of the sea fog forecasting.

      Figure 2.  WRF domain and the locations of surface observations (in-situ stations, ships, and buoys; black dots) and sounding stations (red triangles) in Case07 as an example.

      Li et al. (2012) directly assimilated satellite radiances to examine their impact on sea fog forecasting and the associated MABL structure. They found that such direct assimilation has a large positive impact on the inversion thermal structure of the MABL, which favors sea fog formation and evolution. However, the MABL humidity structure barely changes. Note that the direct assimilation of satellite radiances is still in an experimental phase (e.g., Chevallier et al., 2004; Martinet et al., 2013) and may face many difficulties in the implementation, such as the specification of the bias correction and the forward modeling (Schomburg et al., 2015). Alternatively, assimilating information derived from satellite retrievals has been employed in several studies to improve sea fog predictions. Wang et al. (2014) derived three-dimensional (3D) distributions of sea fog from the infrared and albedo products of the Multi-functional Transportation Satellite (MTSAT). Like many studies that assimilate satellite-derived cloud information (e.g., Macpherson et al., 1996; Renshaw and Francis, 2011; Schomburg et al., 2015; Ladwig et al., 2021), they converted the spatial information of sea fog to pseudo relative humidity (RH) profiles using the assumption that the air inside sea fog reaches saturation (RH 100%). By testing with 12 cases, their results showed that assimilating this satellite-derived RH (Satellite-RH) can significantly improve the forecasting of sea fog and the moisture structure of the MABL. It is noted that Wang et al. (2014) assimilated the Satellite-RH without changing the background temperature. In other words, saturation within the sea fog is achieved by increasing the moisture only when assimilating the Satellite-RH. Therefore, warm and wet biases within the MABL were also yielded in these studies for some sea fog events, despite the remarkable improvements in sea fog forecasting. In addition, Ladwig et al. (2021) adopted a similar strategy to assimilate the satellite-derived cloud information and also found large moisture and temperature biases. Therefore, the approach of increasing the accuracy of the MABL structure associated with sea fog forecasting through assimilating the Satellite-RH needs to be further improved.

      Advection fog forms when the air temperature near the sea surface approaches the dewpoint temperature through cooling the air or adding moisture (Wang, 1983). Therefore, the failure of sea fog formation in numerical models may be due to three scenarios: (1) insufficient moisture, (2) the temperature is not sufficiently low, and (3) both (1) and (2). Increasing the moisture only as in Wang et al. (2014) can resolve the issue in scenario (1), but large wet and warm biases may be produced for the sea fog events under scenarios (2) and (3) because these sea fog formations also require cooling in the MABL. To properly adjust the MABL structure for sea fog forecasting through assimilating the Satellite-RH, this study proposes a new method to achieve both increasing moisture and decreasing temperature within the Gridpoint Statistical Interpolation (GSI)-based 3D variational (3DVar) DA system (Wang, 2010). Here, an RH observation operator is utilized to link both specific humidity and temperature, and therefore both moisture and temperature fields can be adjusted simultaneously. This study is the first to implement the RH observation operator and directly assimilate RH in the GSI framework. In this study, the new method of using an RH observation operator is compared with the methods that use either an increase in moisture only or a decrease in temperature only for forecasts of sea fog and the MABL structure. The overall intercomparisons and evaluations for the three methods are performed for three typical sea fog cases over the Yellow Sea that occurred on 28 April 2007, 9 April 2009, and 29 March 2015. The failures of the sea fog predictions when the Satellite-RH is unassimilated correspond to the specific scenarios of too warm air with insufficient moisture, too dry air with a sufficiently cold temperature, and too warm air with sufficient moisture, respectively.

      The remainder of this paper is structured as follows. The GSI-based 3DVar algorithm, the development of assimilating the Satellite-RH with the three methods, especially the new method to adjust moisture and temperature simultaneously, and the physical rationality of the linearized RH observation operator with respect to the background temperature and specific humidity are introduced in Section 2. Overviews of the three sea fog events and the design of the experiments are presented in Section 3. Section 4 first describes the impact of the three methods of assimilating the Satellite-RH on the moisture and temperature structures, and then intercomparison and evaluations of these methods are performed for the selected three cases, in terms of the sea fog distribution and the MABL structure. The conclusions and discussion are provided in Section 5.

    2.   Methodology
    • The mathematical details of the GSI-based 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 right-hand side is the cost function for the background term, where B represents the static background-error 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 geostationary-orbit satellite imagery data, such as the products of MTSAT (2005–2015) and its replacement Himawari-8 of Japan (since 2016), Fengyun-4 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 North-East Asian Regional-Global Ocean Observing System (NEAR-GOOS). 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 fog-top height is calculated by H = 45000δ2/3 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 Satellite-RH 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 Satellite-RH 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 Satellite-RH data within the observed fog consist of large numbers of RH profiles constrained by the fog top.

      The purpose of assimilating the Satellite-RH 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 Satellite-RH assimilation methods corresponding to the three approaches are implemented within the GSI-based 3DVar system.

    • Method-q 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 Satellite-RH profiles in the foggy areas. The GSI-based 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.

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

    • Method-q and Method-t 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 Method-RH is introduced here to simultaneously adjust the moisture and temperature fields. Method-RH 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 Satellite-RH 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 Hq and Ht, the tangent linear of the RH operator with respect to q and t, respectively. The value of Hq approximates the inverse of the saturation q, which is dominated by the background temperature. Therefore, Hq 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 Ht, 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 Method-q and Method-t, the corresponding observation errors and gross error checks are provided by the GSI package. For Method-RH, 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 Satellite-RH assimilation methods (not shown). Therefore, we leave the optimization of these configurations to future studies.

    3.   DA experiments
    • 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 high-pressure 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 MTSAT-derived 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 cross-section 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 short-lived 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 high-pressure 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 high-pressure 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 long-lived 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 high-pressure 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 high-pressure 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 full-η levels (ηn ranges between 1.0 and 0.0) with 16 full-η 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 η1 = 1.0 and η2) 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 fifth-generation 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 GSI-based 3DVar DA system, the feature-dependent 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 Satellite-RH is assimilated every hour. Figure 5 illustrates the DA procedure for the three cases. Owing to the short-lived 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 (Satellite-RH) data assimilation used a 3 h (1 h) frequency.

      The four experiments listed in Table 1 are performed for each of the selected cases. Exp-noMT assimilates conventional observations only and serves as a benchmark to evaluate the effects of the Satellite-RH assimilation when compared with the other three experiments. The other three experiments Exp-q, Exp-t, and Exp-RH use Method-q, Method-t, and Method-RH introduced in Section 2.2, respectively, to assimilate the Satellite-RH. The intercomparisons among these three experiments provide a comprehensive assessment of the methods for assimilating the Satellite-RH.

      ExperimentSpecification
      Exp-noMTWithout assimilation of Satellite-RH
      Exp-qAssimilating Satellite-RH using Method-q
      Exp-tAssimilating Satellite-RH using Method-t
      Exp-RHAssimilating Satellite-RH using Method-RH

      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 fog-top 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 Exp-noMT, Exp-q, Exp-t, and Exp-RH 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.

    4.   Results
    • To examine the effects of Method-q, Method-t, and Method-RH on the adjustment of the moisture and temperature fields, analyses from a single DA cycle with only Satellite-RH assimilated are compared in Fig. 6. The first guess is provided by the FNL data valid at 1200 UTC 09 April 2009. The corresponding Satellite-RH data are retrieved as introduced in Section 2.2.

      Figure 6.  Vertical cross-sections of (a) RH first guess and RH analyses (shaded) from a single DA cycle (b) using Method-q, (c) Method-t, and (d) Method-RH, 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, Method-q reaches saturation through an increase in moisture only over 3.5 g kg1 (Fig. 6b); a decrease in temperature only up to 7°C is found to obtain saturation in Method-t (Fig. 6c); for Method-RH, the air becomes saturated by increasing the moisture by less than 3 g kg1 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 Satellite-RH 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 Exp-RH perform the best among the four experiments in Table 1 (Fig. 7). Exp-noMT fails to reproduce the evolution of sea fog (Fig. 7a–f), which supports the results from Wang et al. (2014) that assimilation of Satellite-RH is essential for the successful prediction of sea fog. In addition, the decreasing temperature in Exp-t is also invalid for the formation of sea fog (Fig. 7m–r). Conversely, Exp-q 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 Exp-RH (Fig. 7s–x) agrees better with the observations.

      Figure 7.  The predicted fog area initialized at 2100 UTC 28 April 2007 for (a–f) Exp-noMT, (g–l) Exp-q, (m–r) Exp-t, and (s–x) Exp-RH. 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 Exp-noMT 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, Exp-noMT and Exp-t are regarded as having the worst performance. Exp-RH has up to 0.1 higher ETSs than Exp-q. Both Exp-RH and Exp-q have increasing FBIAS scores with increasing lead time. The FBIAS of Exp-RH is consistently smaller than that of Exp-q during the entire forecast period, which coincides with the subjective evaluation. In particular, the advantage of Exp-RH is most remarkable during the first 4 h of lead time. The time-averaged aggregated scores also support the highest forecast skill for sea fog area in Exp-RH with the highest ETS (0.238) and an FBIAS (2.633) relatively close to 1.0 (Table 2). Exp-q has the second highest forecast skill with an ETS of 0.197 and an FBIAS of 3.625. With an ETS of zero, Exp-t and Exp-noMT have no skill in forecasting Case07. To fairly compare Exp-noMT 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 Exp-noMT and Exp-t 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 Exp-noMT (black lines), Exp-q (red lines), Exp-t (blue lines), and Exp-RH (purple lines).

      CaseScoreExp-noMTExp-qExp-tExp-RH
      Case07ETS0.00.213 (0.197)0.0 (0.0)0.226 (0.238)
      FBIAS0.03.264 (3.625)0.0 (0.0)2.105 (2.633)
      Case09ETS0.2030.387 (0.390)0.299 (0.313)0.356 (0.361)
      FBIAS0.2941.400 (1.414)0.804 (0.848)1.253 (1.282)
      Case15ETS0.1960.446 (0.455)0.469 (0.483)0.468 (0.478)
      FBIAS0.6611.570 (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 Exp-q, Exp-t, and Exp-RH. 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, Exp-noMT 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 Exp-noMT 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 Exp-noMT 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 Exp-noMT (black lines), Exp-q (red lines), Exp-t (blue lines), Exp-RH (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 Exp-noMT. Through additionally assimilating the Satellite-RH, the adjustment of moisture and temperature structures in the MABL for Exp-q, Exp-t, and Exp-RH follow the discussions in Section 4.1. Exp-RH 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 Exp-noMT (Figs. 9a,b). With the smaller temperature decrease in Exp-q compared with Exp-RH, the larger increase in Qvapor corresponds to the overestimated sea fog area. Although Exp-t 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, Exp-RH has moderate corrections for both moisture and temperature at the CS station (Figs. 9c,d). However, Exp-q excessively predicts Qvapor up to 2.5 g kg−1 and slightly improves the temperature. Despite a significant temperature reduction of 1°C in Exp-t, Qvapor shows little variation. Thus, the best moisture and temperature structures in the MABL of Exp-RH 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 Exp-noMT and Exp-t are not able to capture the evolution of the observed fog (Figs. 4k–t), and Exp-q has a larger areal coverage of sea fog than Exp-RH. Before 0000 UTC 10 April, the largest sea fog areal coverages in Exp-q show the best agreement with the observations, but the delayed formation of the southern sea fog patches at 1300 UTC 9 April in Exp-RH degrades its forecast skill. After 0000 UTC 10 April, however, Exp-RH performs better than Exp-q with more well-defined 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 Satellite-RH DA lead to the further enlarged sea fog area (Figs. 10y–ar). However, Exp-noMT still fails to capture the sea fog evolution, and Exp-t heavily underestimates the sea fog distribution before 2000 UTC. Compared with Exp-q, Exp-RH 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, Exp-t becomes more skillful than Exp-q and Exp-RH due to more well-defined sea fog.

      The time series of ETS and FBIAS of Exp-noMT (Exp-q, Exp-t, and Exp-RH) 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, Exp-q has the highest ETS (approaching 0.6) and the largest FBIAS (above 1.2) among the four experiments. Exp-RH produces a similar trend of ETS to Exp-q but has slightly lower values. FBIAS in Exp-RH is closer to 1.0 than Exp-q, especially for the forecasted sea fog area during the first 4 h of lead time. The failure or delay of sea fog formation in Exp-noMT and Exp-t result in the relatively low ETS and FBIAS values in the earlier stage of the forecast. However, the forecast skills of Exp-q and Exp-RH gradually decrease and become poorer than those of Exp-noMT and Exp-t after 12 h of lead time. The highest ETS of Exp-t 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 Exp-noMT after 13 h of lead time is similar to that of Exp-t, 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, Exp-q and Exp-RH have the lowest ETSs of ~0.25. As listed in Table 2, the overall forecast skill from hourly cycles of Exp-q is mildly better than that of Exp-RH (0.390 versus 0.361), and both experiments are more skillful than Exp-t (0.313). The overall FBIAS of Exp-RH is much closer to 1.0 than that of Exp-q (1.282 versus 1.414). In contrast, the sea fog distributions are underpredicted in Exp-t with its overall FBIAS below 0.85. Compared with the other experiments, Exp-noMT has the lowest forecast skill with the lowest ETS and an FBIAS below 0.3.

    • At the SH station, the forecasts of Exp-noMT 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 Satellite-RH is an effective approach for sea fog formation. As a result, the forecasts initialized at 1200 UTC 9 April from Exp-q and Exp-RH 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 Exp-q gradually become closer to the observed soundings than those in Exp-RH (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 Exp-q and Exp-RH. 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 Exp-t 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 Exp-t as the DA cycle increases (Fig. 11f). Therefore, sea fog in Exp-t at 0000 UTC 10 April forms with a warmer temperature but a much smaller Qvapor than Exp-noMT (Figs. 11e,f).

      Figure 11.  As in Fig. 9, but for the (a, b) 12 h, (c, d) 9 h, and (e, f) 6 h forecasts valid at 0000 UTC 10 April 2009 at SH station. SH, Shanghai.

    • In Exp-noMT (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). Exp-q, Exp-t, and Exp-RH 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). Exp-q has slightly larger sea fog areal coverage than Exp-RH. Exp-t underpredicts the sea fog distribution with the smallest sea fog area. For the forecasts initialized at 0600 UTC, Exp-noMT 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 Exp-noMT 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 Exp-noMT indicated by an FBIAS below 1.0 corresponds to the lowest ETS. Consistent with the subjective verification in Exp-t, the underpredicted sea fog area in the earlier forecast stage lowers the ETS. After 4 h of lead time, Exp-t 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, Exp-RH has a higher ETS than Exp-t. However, after that, Exp-RH becomes less skillful or comparable to Exp-t. Exp-q has a lower ETS than Exp-RH 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 Exp-t and Exp-RH (0.483 versus 0.478), and both experiments are better than Exp-q (0.455). Exp-noMT still has the worst forecast skill when comparisons are carried out.

    • At the RC and DD stations, the analyses of Exp-noMT 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 Exp-t, the temperature within the MABL is reduced by 0.2–2°C, and Qvapor is unchanged, consistent with Fig. 6. Although Exp-RH decreases the temperature comparable to Exp-t, Qvapor is increased by ~0.2–0.6 g kg−1. These adjustments lead to the overestimated sea fog areas compared with Exp-t (e.g., Figs. 12i, m). Without changing the temperature, Exp-q further increases the moisture by ~0.4–1.0 g kg−1 compared with Exp-noMT. Exp-q therefore has the largest sea fog coverage size. At 0600 UTC, the analysis of Exp-noMT 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 Satellite-RH, Exp-t produces a slightly wetter and 2–4 °C colder analysis than the observed soundings. Compared with Exp-t, Exp-RH produces a warmer structure but excessively adds moisture below 100 m. Exp-q consistently adds excessive moisture.

      Figure 13.  As in Fig. 9, but for the analyses valid at (a−d) 0000 UTC 29 March 2015 at the (a, b) RC and (c, d) DD stations, and (e, f) 0600 UTC 29 March at the OS station. OS, Oscan.

    • For the three selected cases, the experiments with the assimilation of Satellite-RH perform consistently better than Exp-noMT for the sea fog forecast. The performance of the three methods in assimilating the Satellite-RH, i.e., Method-q, Method-t, and Method-RH, is case dependent in the sea fog forecast, as different factors are responsible for the failures of the sea fog forecast in Exp-noMT. We grade their performance for each case in Table 3. Specifically, Exp-RH has the highest forecast skill for Case07 because it can increase moisture and decrease temperature simultaneously to correct the drying and warming biases in Exp-noMT. Therefore, Method-RH is given a score of two for this case. For Case09, Exp-noMT has the lowest forecast skill due to the insufficient amount of moisture in the MABL. As a result, Exp-q performs the best through increasing moisture, and the corresponding Method-q RH is given a score of two for Case09. For Case15, Exp-t generally performs better than the other experiments via decreasing the temperature as Exp-noMT has a sufficient amount of moisture but a warming bias. Therefore, Method-t RH is given a score of two. It is noted that the forecast skill of Exp-RH is slightly lower than that of Exp-q for Case09 and similar to Exp-t for Case15 (Table 2). Hence, a score of one is given to Method-RH for Case09 and Case15 as the performance is only mildly worse than the best for each case. Exp-t (Exp-q) 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.

      CaseMethod-RHMethod-qMethod-t
      Case07210
      Case09120
      Case15102
      Total432

      Table 3.  Overall evaluation of the three Satellite-RH 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 Satellite-RH assimilation methods only Method-RH can partially or fully account for all these bias scenarios by simultaneously cooling and humidifying. Therefore, although the skill of Exp-RH for sea fog and associated MABL forecasts is not always the highest, it is not the lowest for the three cases. Overall, Method-RH 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.

    5.   Conclusions and discussion
    • The assimilation of satellite-derived relative humidity (Satellite-RH) is capable of effectively improving the sea fog forecast (Wang et al., 2014). The purpose of assimilating Satellite-RH is to reach saturation in the analysis to correspond to the observed sea fog, and therefore the model can diagnose fog in the subsequent forecasts. However, earlier studies have suffered wetting and warming biases for some sea fog cases because they achieve saturation by increasing moisture only (Method-q). In this study, a new method using an observation operator for RH is proposed to alleviate these biases by jointly adjusting the moisture and temperature structures for saturation (Method-RH). Here, the RH operator is formulated with the specific humidity and temperature. An alternative method of achieving saturation through decreasing the temperature only (Method-t) is also used for comparison. The three methods are implemented in the GSI-based 3DVar DA system to improve the initial conditions for sea fog forecasts. Three experiments Exp-q, Exp-t, and Exp-RH using Method-q, Method-t, and Method-RH, respectively to assimilate the Satellite-RH are compared for three sea fog events over the Yellow Sea on 28 April 2007, 9 April 2009, and 29 March 2015 (Case07, Case09, and Case15, respectively). The main conclusions of this work are summarized as follows:

      1) A similar saturation can be reached by Method-q by increasing the moisture only, by Method-t by decreasing the temperature only, and by Method-RH by simultaneously increasing the moisture and decreasing the temperature.

      2) Experiments with the Satellite-RH assimilation are more skillful in sea fog forecasts than those without such assimilation.

      3) For the three Satellite-RH assimilation methods, their improved forecast skill is case dependent due to the different factors responsible for the failures in the sea fog prediction without the Satellite-RH assimilation. The failures of Case 07, Case09, and Case15 result from their MABLs have both warming and drying, drying, and warming biases, respectively. The skill of Exp-RH for forecasting sea fog and the associated MABL is not the worst for the three cases, as only Method-RH can partially or fully address all the temperature and moisture bias scenarios. However, Exp-t (Exp-q) is the least skillful for Case09 (Case15) among three experiments.

      4) Overall, Exp-RH is the best choice for the sea fog forecast from a practical forecast perspective. Exp-RH predicts more well-defined sea fog relative to Exp-q by reducing the increase in humidity and enhancing the cooling. Compared with Exp-t, Exp-RH enlarges the sea fog area via increasing the amount of moisture.

      In addition to improving the thermodynamic fields by assimilating the Satellite-RH, Wang and Gao (2016) emphasized the necessity of improving the wind field for the sea fog forecast. They improved the kinematic fields by assimilating radial velocity from the coastal radar sites for two coastal sea fog events. However, it still suffers from the lack of observations for the sea fog far away from land. In addition, surface winds derived from the polar-orbital satellite may be insufficient to satisfy the requirements of continuously monitoring the sea fog environment. Alternatively, it is possible to adjust the dynamic fields based on the background error correlations between the dynamical and thermodynamical fields when assimilating the Satellite-RH. This can be achieved by building multivariate background-error covariances in 3DVar or by using the flow-dependent background-error covariances in ensemble-based DA methods. It is also noted that the areal coverage of sea fog is commonly overpredicted in this study. Approaches that assimilate the retrievals of clear-sky information (Renshaw and Francis, 2011; Ladwig et al., 2021) are promising to alleviate this issue. These studies remain for the future.

      Acknowledgments. The computation for data assimilation, free forecast, and evaluations in this study were conducted at the High-Performance Computing center in the Ocean University of China.

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