Analysis of the different influence between initial/boundary and physical perturbation during ensemble forecast of fog

To explore the different effects of initial/boundary condition (ICBC) and physical perturbation during fog ensemble forecast, ensemble forecast experiments are done for a heavy fog episode from December 31, 2016 to January 2, 2017. Three ensemble schemes [ICBC, multi-physics (MPY), and a combination of ICBC and MPY (COM)] were compared. Their forecast performances are analyzed in detail and compared with the reference deterministic forecast. The results show that all ensemble schemes, especially the COM, are able to noticeably improve fog prediction. The TS score of ensemble-based fog forecast with 50% probability threshold is higher than that of the control deterministic prediction by ~ 26%. Compared with the ICBC scheme, the MPY scheme can produce a larger ensemble spread and has more skill in fog and the near-surface variables forecast. When ICBC and MPY are combined (the COM scheme), the ensemble spread is enhanced and the prediction performance is also further improved. The sensitivity experiments of different physical parameterization schemes are also analyzed among microphysics, planetary boundary layer, and land surface. The fog forecast is found to be most sensitive to the land surface scheme, followed by planetary boundary layer scheme, and the least sensitive to microphysics.


Introduction
Fog is a condition in which water droplets or ice crystals in the air near the ground reduce horizontal visibility to less than 1000 m. Foggy weather threatens the safety of land, sea, and air transportation, and the effects of fog are becoming increasingly serious with the development of society and economy. The physical process of fog formation and maintenance is very complex. Therefore, fog has also received extensive attention from scholars at home and abroad.
With the improvement of computing power, numerical simulation has become an important tool for studying the mechanism of fog development and making fog forecasts. Many researchers have used high-resolution numerical weather prediction models to study the phenomenon of fog and to forecast fog (Ballard et al. 1991;Gao et al. 2007).
They found that the numerical prediction performance of fog depends on many factors such as initial and boundary conditions and physical parameterizations.
Previous studies have shown that fog numerical prediction is very sensitive to the initial fields (Koračin et al. 2005;Gao et al. 2010). The initial fields of the model can be improved by using data assimilation, which can effectively improve the numerical simulation effect of fog. Based on the WRF model and its three-dimensional variational assimilation system, Liang et al. (2007) assimilated meteorological data to study a dense fog event and found that the assimilation of different kinds of data to different extents improved fog forecasting. Further analysis found that the data assimilation could provide better humidity and temperature structure in the lower layer, and the degree of improvement varied among different data. Some studies of sea fog numerical simulations have also found that assimilation of non-conventional information (e.g., radar and satellites) can improve the temperature stratification and water vapor distribution in the maritime atmospheric boundary layer Liu et al. 2011), thus having a positive impact on sea fog forecasting.
The formation, development, and dissipation of fog are influenced by various physical processes, so the choice of physical parameterization schemes is also important for the fog simulation (Lin et al. 2017;Chen et al. 2020;Zhang et al. 44 Page 2 of 16 2020). Studies have shown that fog is sensitive to planetary boundary layer (PBL) scheme, cloud microphysics scheme, and land surface model (LSM) (Gultepe et al. 2006;Wan et al. 2010;Huang et al. 2016). Lu et al. (2014) used WRF to study the sensitivity of PBL scheme and microphysics scheme for 10 sea fog events over the Yellow Sea, and found that the microphysics scheme mainly affects the density and depth of simulated sea fog, while the PBL scheme plays a decisive role in the simulation of fog area, and the best PBL scheme varies with the sea fog cases. The research results of Steeneveld et al. (2015) showed that the fog simulated by WDM6 microphysics scheme dissipates earlier than that by WSM6 scheme, and the fog area simulated by YSU PBL scheme is larger than MYNN. Jiang and Gao (2021) found that the performance of different LSM schemes differed for a land fog (offshore fog) event and a sea fog event.
The above studies also found that the accurate simulation of near-surface humidity, temperature distribution, and wind field is closely related to the successful prediction of fog, so the uncertainty of near-surface temperature, humidity, and wind field will affect the prediction of fog. However, most of the fog forecasts were deterministic and did not consider uncertainty. Due to the chaotic nature of the atmosphere, errors of initial/boundary conditions (ICBCs), and model itself, there are always some uncertainties in a single model forecast (Lorenz 1965;Leith 1974;Anderson 1996;Van der Velde et al. 2010). Therefore, the use of ensemble methods for fog forecasting is reasonable and necessary (Lewis et al. 2004;Du and Zhou 2016;Gultepe et al. 2019). Gao et al. (2014) used a mesoscale ensemble system (based on WRF model with initial perturbation and SST perturbation) to predict a heavy sea fog over the Yellow Sea and showed that using the ensemble-based forecast can improve the ETS by 29%. Pahlavan et al. (2021) simulated several airport fog events using an ensemble prediction system and found the ensemble prediction system outperformed the single deterministic fog forecast when the probability thresholds of the ensemble forecasts were 37.5%, 50%, and 62.5%.
In this study, we design three ensemble schemes (ICBC, MPY, as well as COM) to forecast a heavy fog event and compare the results with a reference deterministic forecast. We document and evaluate the performance of ensemble forecasts in both the deterministic and probabilistic sense. By comparing the verification statistics for the three ensemble experiments with different perturbations, we investigate the effect of the ICBC and model physics on fog forecast.

Overview of the fog event
From the evening of December 31, 2016 to the morning of January 2, 2017, a heavy fog event occurred over a large area (including Beijing, Tianjin, Hebei, Shandong, and Jiangsu), with visibility reaching below 50 m in some areas. The fog covered a wide area and lasted for a long time, greatly impacting transportation.
The fog formed in some areas of Tianjin and southern Hebei in the evening of December 31, 2016, spreading gradually across Jiangsu and Shandong. During the morning of January 1, 2017, fog developed over southern North China and most areas of Shandong and Jiangsu (Fig. 1a), with relative humidity above 90%. Then the fog in Shandong and Jiangsu dissipated rapidly, and visibility rose to more than 1 km by noon; visibility in Tianjin and southern Hebei increased slightly, but remained below 1 km (Fig. 1b). After nightfall, the fog began to expand in scope and intensity (Fig. 1c) and reached the maximum fog coverage at 0000UTC 2 January (visibility reached below 50 m at some stations) (Fig. 1d). Influenced by weak cold air, visibility improved during the daytime on 2 January, and the fogging process gradually ended.

Data and methodology
The WRF model (WRF4.1) dynamic core is used in this study. Two model domains are configured with a horizontal grid spacing of 9 km and 3 km (Fig. 2). There are 51 Sigma layers in the vertical direction. The results of the inner domain are used to predict the fog events in this study. Forecasts were initialized beginning at 1200 UTC on 31 December 2016.
The initial and lateral boundary conditions are from the Global Ensemble Forecast System (GEFS) (Wei et al. 2008) of the National Centers for Environmental Prediction (NCEP). Observations of horizontal visibility, temperature, and relative humidity at 2 m above ground, and wind at 10 m above ground at stations inside the 3 km domain were used to verify the corresponding variables by predicted.

Experimental design
There are 4 ensemble forecasting experiments in this study. The first three ensemble forecasting experiments are performed to assess the impact on the heavy fog forecast to the initial and boundary conditions (ICBCs) versus the model physics. The fourth ensemble experiment is applied to further analyze the sensitivity of the fog forecast to different physics schemes.
Experiment 1 uses 21 members of the GEFS as the ICBCs and is referred to as ICBC ensemble. All the members use the same combinations of physics schemes: Kian-Fritsch scheme (Kain and Fritsch 1990) for cumulus cloud (for the 9-km grids only); the Yonsei University PBL scheme (YSU; Hong et al. 2006) and MM5 surface layer scheme (Jiménez et al. 2012); the thermal diffusion (Dudhia 1996) LSM; the Lin microphysics scheme (Lin et al. 2017); and the RRTMG shortwave and longwave radiation scheme (Iacono et al. 2008).
Experiment 2 has the same members as Experiment 1, which is created by varying the physics schemes in the WRF model as presented in Table 1. The ICBCs are derived from the control member of the GEFS. The experiment is referred to as the multi-physics ensemble (MPY). In order to eliminate the impact of different surface layer schemes, the same surface layer scheme should be chosen (Yang et al. 2019;Wu et al. 2023). Except for MYJ, all other PBL schemes are coupled with MM5 surface layer scheme; MYJ PBL coupled MM5 would lead to WRF collapse, so MYJ PBL is coupled with Eta surface layer scheme (Janjic 1996). The two Experiment 3 is referred to as the combined perturbation ensemble (COM), in which the ICBCs are from the 21 members of the GEFS, and the physics configuration is the same as the MPY ensemble. In this study, a single deterministic forecast (ensemble member 1 in Table 1) is used as the reference control forecast (CTL).
Experiment 4 is performed to further investigate the relative sensitivity of the fog forecast to different physics schemes in Experiment 2, which is referred to as MPY2. The members in MPY2 are conducted using different combinations of parameterization schemes. The combinations consist of four PBL schemes (ACM2, MYJ, MYNN2.5, and YSU), four LSM schemes (Noah, RUC, P-X, and thermal), and four microphysics schemes (Thompson, WDM6, WSM6, and Lin). Therefore, MPY2 includes 64 members, which are combined into 12 ensemble-based cases and divided into three groups for sensitivity analysis ( Table 2). Each group contains all 64 members. Taking Group-LSM as an example, each case has 16 members. Each member has different combinations of PBL and microphysics schemes with the same LSM scheme. Therefore, each case in Group-LSM only contains uncertainty from PBL and microphysics parameterization perturbations. The differences among the four cases in Group-LSM come from different LSM schemes used in each case.

Fog diagnosis
NWP models do not forecast horizontal visibility directly, and the visibility is calculated by the formula (Stoelinga and Warner 1999).

Threat score (TS)
Binary verification scores were used to verify a deterministic forecast against its corresponding verifying observation for the fog event (Zhou and Du 2010;Wang et al. 2014), including the threat score (TS), false alarm ratio (FAR), bias, and missing rate (MR). The best value for the bias is 1, while values less (greater) than 1 indicate under-forecast (overforecast). TS is a positively oriented score, that is, the larger the TS, the better a forecast will be.
where H, M, F, and C refer to the numbers of correctly forecast points (hits), incorrect forecasts of occurrence, incorrect forecasts of non-occurrence, and correct forecasts of nonoccurrence, respectively.

Brier skill score (BSS)
The BS gives a sense of the magnitude of the probability forecast errors, while the Brier skill score (BSS) measures the relative skill of the probabilistic forecast over that of persistence (Zhou and Du 2010), in terms of predicting whether or not an event occurred.
where n denotes the forecast number (out of the total number of forecasts); N is the total number of forecast observation pairs for all forecasts; P n (n) is the ith forecast (observed) probability, where the forecast probability ranges in from 0 to 1 but the observed probability is either 1 (yes event) or 0 (no event); and f n is the ith forecast of reference forecast with a value that either ranges from 0 to 1 (if a probabilistic forecast is used) or is 1 or 0 (if a single deterministic forecast used). In this study, a single deterministic (control) forecast will be used as a reference forecast. The perfect BS is 0 and the perfect BSS is 1. The smaller the BS or the larger the BSS, the better a probabilistic forecast will be. A positive BSS indicates a skillful probabilistic forecast with respect to its reference forecast; otherwise, the probabilistic forecast has no skill.

Root mean square error (RMSE) and ensemble spread
For a better ensemble forecast, its members should show the possible true state of the future atmosphere as much as possible. Ensemble forecast systems are conventionally evaluated in terms of the relationship between the root mean square error (RMSE) of the mean forecast compared with observations and the standard deviation (spread) of the ensemble members (Eckel and Mass 2005). In an ideal ensemble, the RMSE and spread match throughout the forecast.
where A fi is the forecast value, A oi is the observation value, and N is the total number of stations in the test area; where f i is the ith member forecast value, f is the ensemble average forecast value, and M is the number of ensemble members.

Talagrand
For a good ensemble forecasting system, when there are enough members, the members of the ensemble forecasting should be able to include the real state of the atmosphere in most cases, and the probability of occurrence of each forecast member should be equal statistically, so the real situation (truth value) may be any one of the members of the ensemble. The test method of Talagrand distribution (also called hierarchical histogram) is usually adopted (Talagrand et al. 1997). An ideal ensemble prediction system has the same probability of actually falling in each prediction interval, and the Talagrand diagram should be straight. If the distribution is "U" type, it means that the spread of the ensemble prediction system is not large enough, or the ensemble prediction has positive errors in some areas and negative errors in other areas. If the distribution is "L" type, the actual situation mostly falls in the small value area of the ensemble prediction, which indicates that the ensemble prediction system has a positive deviation, otherwise has a negative deviation.

The deterministic reference forecast
Examination of the visibility fields shows that the reference forecast simulated the fog evolution well, capturing the main areas of fog in Shandong and Jiangsu (Fig. 3). Compared with the observation, the predicted fog is smaller and denser. Overall, the reference forecast gave the general characteristics of the fog case, but there are still some differences in the fog area and fog density. We see a small peak around 0000UTC 1 January, 2017 and a larger peak around 0000UTC 2 January, 2017. This larger peak time is the time when fog develops strongest. Figure 5 also shows that the differences among the three ensemble schemes and the advantages of the ensemble-based forecasts over the single deterministic forecast. Compared to the deterministic reference forecast, the three ensemble forecasts show an increase in the number of foggy points for some ensemble members and a decrease in the number of foggy points for others. This indicates that the ensemble forecasts do not increase the systematic bias of the model in describing the uncertainty of the model forecasts. The MPY scheme has a greater variation in foggy points compared to the ICBC scheme, while the COM scheme performs similarly to the MPY scheme, but with a more balanced distribution of foggy points among different members. Examination of the visibility fields of all members of the three ensemble forecasts (plots not shown) shows that the increase and decrease of foggy points are related to the location and intensity of the fog. It is also found that some members show a decrease of fog in some areas and an increase in others, while other members maintain fog in some areas and miss fog elsewhere. These spatial variations also reflect the uncertainties in the numerical fog prediction. The effect of these changes on visibility can be seen by comparing single deterministic reference forecast (Fig. 3), ensemble-based forecasts and the observations (Fig. 1). Figure 5 shows the fog probabilities predicted by the three ensemble schemes at 0000UTC on January 2, 2017 (the fog probabilities are calculated simply by taking the proportion of members with visibility below 1 km at each grid point). The three ensemble schemes all give good forecasts, capturing the main areas of fog in Shandong and Jiangsu (Fig. 3d). Compared with the reference deterministic forecast, the ensemble schemes capture the fog in southern Hebei and central Shandong. The ICBC scheme gives very high probabilities of fog for most areas, corresponding to the areas of dense fog in the reference control forecast. These probabilities of the MPY scheme considerably reduce in Shandong. Additionally, the MPY scheme increases the probabilities of fog in southern of Hebei and Tianjin, by capturing the observed fog in these regions. The COM scheme has similar probabilities of fog but increases probabilities of fog in central Shandong, where the observed fog is under-forecasted.

The ensemble forecasts
A probabilistic forecast can be evaluated both probabilistically and deterministically (Zhou and Du 2010). For a given specific percentage threshold (such as 50%), a probabilistic forecast can be viewed as a deterministic forecast, in the way that an event is expected to occur when the forecast probability is greater than or equal to the selected threshold. Figure 6 shows the fog forecasting skill verified with deterministic measures (TS, bias, FAR, and MR) of the three ensemble schemes probabilistic forecasts and the control single forecast at 0000UTC on January 2, 2017. The TS and bias for probabilistic forecast are higher when the forecast probability is smaller and decrease as the probability threshold increases. The MR also decreases with increasing probability threshold, and the FAR does not change much. Combining the four scores, it can be seen that the scores of reference control forecast are comparable to those of the ensemble-based forecasts at 60% probability threshold. By comparing the single control forecast and ensemble-based forecasts, the probabilistic forecasts have better performance than single deterministic forecast in fog prediction.
Comparing the three ensemble schemes, the TS of the ICBC scheme decreases significantly less with increasing  forecast probability than that of the MPY ensemble scheme. The TS of the MPY scheme is higher than that of ICBC at lower probabilistic thresholds, while the TS of the MPY scheme is lower when the probabilistic thresholds rise above 50%. Examination of the visibility fields shows that all members of the ICBC scheme give good forecasts, capturing similar areas of fog (plots not shown). Comparing Fig. 4 and the predicted visibility fields, the MPY scheme clearly has the ability to make some members foggier or less foggy. That is, some members give very good fog prediction (e.g., member 2) and some members (e.g., member 15) lost fog for many areas. The COM scheme has similar scores to the MPY scheme, while has more skill in fog forecasting than the MPY scheme.
Theoretically, the ensemble mean or median (the 50% probability) forecast should have the most skill on average (Leith 1974), so we verify the median forecasts. Figure 7 shows the verifying scores for deterministic forecasts of the control forecast and the probabilistic forecasts with 50% probability for three horizontal visibility thresholds (Vis ≤ 1 km, Vis ≤ 500 m, Vis ≤ 200 m). By comparing the single control forecast and ensemble-based forecasts, it is found that the skill of ensemble system in fog forecasting is more than deterministic forecasting. The TS (MR) for probabilistic forecasts at 50% threshold is higher (lower) than that of the control forecast: except for the ICBC and the MPY schemes with horizontal visibility threshold of 200 m, the TS values of them are close to that of the reference control forecast. Figure 7 also shows that with the decrease of horizontal visibility, MR increases slightly and FAR increases significantly, which indicates that the visibility was underpredicted by the numerical forecasts for the fog case in this study.
Combining the verifying scores and visibility fields of all members, the control forecast and probabilistic forecasts underestimate the area of fog, but probabilistic forecasts show less bias (is close value to 1) than the deterministic control forecast. It is shown the better efficiency of the probabilistic forecasts in comparison with deterministic forecasts in the fog event considered here.
To further demonstrate the value of probabilistic forecasts over a deterministic forecast, Fig. 8 shows the BSS for visibility. Obviously, the ensemble-based forecasts have more skill compared with the control prediction in this study (except for the ICBC scheme below 200 m). The ICBC scheme has the lowest BSS, followed by MPY, and the highest COM. This means that the MPY scheme performs better than the ICBC ensemble, and the COM scheme performs best. Fig. 6 The scores of TS, bias, MR, and FAR of single control forecast and probabilistic forecasts (each over 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%) from the ICBC, the MPY, and the COM scheme at 0000UTC on January 2, 2017

Near-surface variables
The fog numerical forecasting performance is closely related to the accuracy of the forecast of near-surface humidity, temperature, and wind fields. The root mean square error (RMSE) of the forecasts (the ensemble mean forecasts in ICBC, MPY, and COM, and the control forecast) was verified against observations for 2 m temperature (T 2m ), 2 m relative humidity (RH 2m ), 10 m U-wind (U 10m ), and 10 m V-wind (V 10m ) (Fig. 9). Figure 9 shows that the ensemble-based forecasts had smaller RMSE than the control forecast for the three variables. The RMSE of the MPY scheme was smaller than that of the ICBC scheme, and that of the COM scheme was the smallest. The differences in errors indicate that the ensemble-based forecasts outperform the single control forecast for near-surface temperature, humidity, and wind fields prediction, which lead to improved fog forecasting.
To illustrate why the probabilistic forecasts of fog work better than the single deterministic forecast, the differences in cloud liquid water (q c ) and ground surface temperature predicted by the ensemble-based forecasts (ensemble mean) and the reference control forecast are shown in Fig. 10. It is found that compared with the control forecast, the q c of the ensemble-based forecasts around the fog area where the control forecast fails to report has increased, leading to fog generation. And for areas where the visibilities were predicted much lower by the control forecast, the q c of the ensemble-based forecasts is significantly reduced, making visibility higher and fog density lower (Fig. 10a-c). The ground temperature of the ensemble forecasts decreases in the regions where the control forecast loses fog, while the ground temperature of the ensemble forecasts increases in the areas where the fog is overestimated by the control forecast ( Fig. 10d-f). The lower (higher) ground temperature makes it easier (more difficult) for water vapor condensation, which in turn leads to fog development or dissipation (lower fog density). The difference between q c and surface temperature is an important reason for the better fog forecast of ensemble-based forecasts compared with the single control forecast.

The spread and RMSE
The time series of the ratio of the spread to RMSE for T 2m , RH 2m , U 10m , and V 10m prediction from the three ensemblebased forecasts is shown in Fig. 11. It can be seen that the spread/RMSE values of the COM scheme are closer to the ideal value (1.0) than those of the other two schemes. The spread/RMSE values of the MPY scheme are significantly higher than those of the ICBC scheme in T 2m and RH 2m , while the spread/RMSE values of the MPY scheme are slightly smaller than those of the ICBC scheme in U 10m and V 10m . The results imply that physics perturbation could create greater uncertainty in temperature and humidity, while the ICBCs mainly affect wind fields. The influence of mixed perturbation is greater than that of single perturbation in the near-surface variables forecasting. The spread/RMSE values increase significantly with the increase of forecast time, indicating that the ensemble schemes are more reliable over time. Figure 12 shows the Talagrand distribution of 2 m temperature, relative humidity, 10 m U-wind, and V-wind. It can be seen that the Talagrand distribution of the three schemes is generally "U" shaped, indicating that the spread is not large enough. The Talagrand shapes of the MPY and the COM schemes are flatter than that of the ICBC scheme, indicating that the ensemble spread of the MPY and the COM schemes are larger, and the ensemble spread of the COM scheme is the best. The "L" type of Talagrand distribution of RH2m in the ICBC implies obviously positive deviation was induced in the ICBC scheme. The MPY scheme significantly eliminated the positive bias (Talagrand distribution changed from "L" shape to "U" shape), which may be offset by different physical parameterization schemes due to different prediction bias during integration. In general, compared with the ICBC scheme, the MPY scheme has significant advantages in temperature and humidity prediction, and it can eliminate the systematic deviation of the model to a certain extent and improve the performance of ensemble-based forecasts. The COM scheme reasonably increases the ensemble spread and reduces the forecast errors, resulting in better forecasting performance.  Table 2 aims to examine the relative sensitivity of fog prediction to different physics schemes. Figure 13 shows the verification scores (TS, bias, FAR, and MR) of fog forecast for all ensemblebased cases in three groups. Compared to the other two groups, the cases of Group-LSM are generally more skillful in fog forecasting with high probability thresholds (except for the Case-Noah), and Case-Thermal has the best scores with all probability thresholds. The TS (bias) of cases in Group-PBL and Group-microphysics decreases rapidly with the increase of probability threshold, while the MR of them rises. For Group-PBL, the scores of all cases are similar in general (except for Case-ACM2). For Group-microphysics, Case-Lin and Case-Thompson have better performance for fog prediction. Figure 13 shows that the FAR of Case-WDM6 increases rapidly following the probability thresholds above 60%. To explore this error source, we compare q c at the bottom of the model and find that Case-WDM6 has much more q c than other cases (plots not shown). This may result in a higher FAR than other cases.

Talagrand
Further analysis of the difference among the score curves for different cases in each group reveals that there are significant differences among the score curves of different cases in Group-LSM, which come from different LSM schemes. The standard deviation (SD) among the score curves of the four cases in Group-LSM (solid lines in Fig. 13) is 0.457, Fig. 10 The difference between the bottom q c (the upper; g kg) and the surface temperature (the lower; ℃) predicted by the ensemble-based forecasts (a, d the ICBC scheme; b, e the MPY scheme; c, f the COM scheme) and the single control forecast  Fig. 11 The ratio of spread to RMSE for RH 2m , T 2m , U 10m and V 10m of the three scheme ensemble forecasts  Fig. 13) and 0.077 for the cases in Group-microphysics (long dashed lines in Fig. 13). The results indicate that fog forecasting is much more sensitive to LSM schemes and less sensitive to microphysics schemes. The RMSE of the ensemble mean forecasts for T 2m and RH 2m is listed in Table 3. The RMSE differences of the 12 cases are basically consistent with the conclusion in Fig. 13. For T 2m and RH 2 , different cases in Group-LSM produce a high diversity of RMSE. The maximum difference of the RMSE among different cases in Group-LSM is up to 0.66℃ for T 2m , and up to 12.26% for RH 2m . Table 3 also shows that the RMSE differences among different cases in Group-PBL and Group-microphysics are much smaller. These demonstrate the same conclusion as previously shown in Fig. 13 that fog prediction is more sensitive to LSM schemes.
The ensemble spread for T 2m and RH 2 of all the 12 cases in three groups is given in Fig. 14. There is a much smaller ensemble spread for each case in Group-LSM, which indicates that the differences among the members in the cases of Group-LSM are small. Taking Case-Noah as an example, the ensemble spread is the smallest in all 12 cases, which indicates that the difference among Case-Noah members is the smallest. For Case-Noah, the LSM is fixed as Noah and the sample difference comes from the uncertainty introduced by different PBL and microphysics schemes. All ensemble forecasting cases in Group-LSM are given fixed LSM and have low ensemble spread. Compared to Group-LSM, there are high values of the ensemble spread with the cases in Group-PBL and Group-microphysics. In these two groups, LSM schemes are always perturbated. It means that perturbation with different LSM schemes in physics schemes can  This also confirms the conclusion mentioned earlier that fog forecasting is the most sensitive to LSM scheme. The above results show that significant difference in fog prediction among LSM schemes due to the large difference in near-surface humidity and temperature prediction. Thus, we can conclude that fog prediction is the most sensitive to LSM schemes, followed by PBL, and the least sensitive to microphysics for the fog event in this study. In addition, comparing the visibility fields and skills of fog forecast for all members in MPY2 (plots not shown), it is found that the combination of thermal LSM, YSU PBL, and Lin microphysics schemes is the best on fog forecast for this fog event in this study.

Summary
In this work, using a heavy fog event as an example, the three schemes were compared in the following aspects of fog and related variables: the performance of deterministic forecasts, ensemble probabilities with respect to the control forecast, and spread-RMSE forecast error relations. The ensemble performance of different perturbation schemes is analyzed. And the advantages of ensemble probabilistic fog forecasts are shown by comparing with the control reference forecast.
To consider a probabilistic fog forecast as a deterministic forecast, the ensemble systems outperformed the control deterministic forecast with the probability thresholds below 60% (the TS was higher than the TS for the deterministic reference forecast). With 50% probability threshold, the TS of the COM scheme was 26% better than that of the control forecast. Near-surface temperature and humidity forecast errors affect fog forecasting. The ensemble-based forecasts significantly improve the near-surface temperature and humidity prediction compared with the single deterministic forecast, and the COM scheme has the most significant improvement. Meanwhile, the MPY scheme can reduce the model system bias.
The ensemble spread and BSS of the MPY scheme are much larger than that of the ICBC scheme, and the COM scheme has the largest spread and BSS. These demonstrate that The COM can not only widen the spread but also improve the accuracy of the ensemble forecast.
Overall, by comparing forecasts of the three ensemble schemes, it is shown that the MPY scheme outperformed the ICBC scheme and the performance of ensemble-based forecasts could be further improved by combining ICBC perturbation and physics perturbation. And the improvement is more significant as the visibility decreases. These results also indicate a strong sensitivity of fog forecasting for this event to model physics.
The relative sensitivity of the predicted fog to physics schemes is investigated by running another set of 64 forecasts with different LSM, PBL, and microphysics schemes. The fog forecast is found to be most sensitive to the LSM scheme used, followed by PBL scheme, and the least sensitive to microphysics.
In general, it is concluded that the ensemble-based method can significantly improve fog forecasting when compared with single deterministic forecast. The ensemble method can not only improve the accuracy of single deterministic prediction but also provide more useful information for different users to make scientific decisions. In this work, the fog forecast is relatively more sensitive to model physics than to the ICBCs, and the sensitivity has obvious difference among different physics schemes.  Fig. 14 The spread of the ensemble forecasts for RH 2m and T 2m from the 12 cases of the three groups. The same group used the same color