Use of Double Channel Differences for Reducing the Surface Emissivity Dependence of Microwave Atmospheric Temperature and Humidity Retrievals

Surface emissivity has a significant impact on atmospheric parameter retrievals from microwave sounding instruments. To reduce the dependence of retrievals on surface emissivity, a double channel differences equation is deduced, and a corresponding retrieval scheme is constructed. Retrieval experiments are performed using Advanced Microwave Sounding Unit‐A (AMSU‐A) and Microwave Humidity Sounder (MHS) simulations and global measurements. Simulation experiments show that the double channel differences scheme can reduce the root mean square errors (RMSE) of the temperature and humidity profiles in the middle and lower atmosphere. Retrieval experiments based on AMSU‐A and MHS global measurements show that the proposed scheme can significantly reduce the RMSE of temperature profiles in the lower atmosphere and humidity profiles in the middle and lower atmosphere for cloudy and cloudless conditions, different surface types, and different scan angles, with maximum reduction values of 0.64 K and 9.03%, respectively. Regarding RMSE improvement, that of the cloudy condition is greater than that of the cloudless condition, that of the land is greater than that of the coast and the sea, and there is no significant dependence on the scan angles. The double channel differences scheme is very sensitive to initial near‐surface temperatures. Reducing the initial near‐surface temperature error can significantly improve the temperature retrieval accuracy below 900 hPa, with maximum reduction value of 3.25 K.


Introduction
Microwave sounding instruments have been widely used in atmospheric parameter retrieval and data assimilation (Aumann et al., 2003;He et al., 2011;He et al., 2018;Li et al., 2000;Milstein & Blackwell, 2016;Yao et al., 2005), but the results of retrieval and assimilation in the lower atmosphere are generally poor (He et al., 2011;Karbou, Aires, et al., 2005;Zou et al., 2013). The reason is mainly due to the impact of surface emissivity. For the lower atmosphere channel, it is difficult to extract the atmospheric temperature and humidity information from the measurements due to the surface emissivity dependence. To reduce the impact of surface emissivity, non-lower atmosphere channels are usually given priority in atmospheric parameter retrieval or assimilation applications (He et al., 2011;Weng, 2007;Zou et al., 2013).
When the lower atmosphere channels are used for the atmospheric parameters retrieval and assimilation, surface emissivity is commonly used as known input parameters (Karbou, Aires, et al., 2005;Weng et al., 2012;Zou et al., 2013). For example, Karbou, Aires, et al. (2005) used satellite measurements to precalculate the surface emissivity for use in atmospheric parameter retrieval. He et al. (2011) calculated surface emissivity using the Community Radiative Transfer Model (CRTM) and analyzed the effects of the 4 th and 5 th channels of AMSU-A on assimilation performance. He et al. (2018) and Aires (2018) corrected the observed brightness temperature based on the precalculated surface emissivity to reduce the retrieval errors of the temperature and humidity profiles. Although the precalculated surface emissivity is favorable for the improvement of retrieval and assimilation accuracy, the surface emissivity, which changes significantly over time and space, is difficult to accurately obtain over the global . Moreover, most of the existing emissivity studies are focusing on clear-sky cases (Tian et al., 2015). Thus, reducing the surface emissivity dependence of microwave atmospheric parameter retrievals is urgent.
To reduce the dependence of the atmospheric parameter retrievals on surface emissivity, this paper proposes a microwave temperature and humidity profiles retrieval scheme based on double channel differences, and validates the scheme by using AMSU-A/MHS simulations and global measurements. The second chapter of this paper deduces the double channel differences equation. The third chapter introduces the data and methods. The fourth chapter presents the simulation experiment. The fifth chapter presents the retrieval application experiment. The sixth chapter is the summary and discussion.

Basic Principles
The microwave radiation transfer equation can be expressed as where I represents the radiation measured by the sensor. I s ,I ↓ and I ↑ are the skin and atmospheric downwelling and upwelling radiation, respectively. ε is the surface emissivity. B Ts and B are the surface and each layer Planck radiation, respectively. p ∞ and p s are space and surface pressure, respectively. τ p s , τ s and τ are surface to space, pressure layer to surface, and pressure layer to space atmospheric transmittance, respectively.
The weight function (K) of equation (1) is: The surface emissivity of a single channel varies significantly with time and space , whether there is a certain correlation between the surface emissivity of adjacent channels; thereby equation (1) can simplify the surface emissivity item and facilitate temperature and humidity profiles retrieval to become the key. For various surface types,  showed that the most difference between the mean surface emissivity of adjacent channels is less than 0.02 in 23.8 GHz, 31.4 GHz and 50.3 GHz, 50.3 GHz and 89 GHz, and 89 GHz and 150 GHz. Moncet et al. (2011) analyzed the surface emissivity change between 6.925 GHz,10.65 GHz,18.7 GHz,23.8 GHz,36.5 GHz and 89 GHz for horizontal and vertical polarization, and the difference is approximately 0.01. Yan and Weng (2011) showed that the difference between the mean surface emissivity of different desert types between 23.8 GHz, 31.4 GHz, 50.3 GHz and 89 GHz was basically less than 0.01. Although the current study does not fully explain the surface emissivity changes of adjacent channels on all surface types, the above studies show that there is a certain correlation between the surface emissivity change trend of adjacent channels. In addition, compared with the surface emissivity of each channel (land:~0.9; sea:~0.5), the difference of adjacent channels is small, which provides the condition for reducing the impact of surface emissivity. The surface emissivity of each channel can be expressed as where ε i and ε j are the surface emissivity of adjacent channels, respectively. δε is the difference of surface emissivity of adjacent channels as a function of time and space.
The microwave radiation transfer equation (1) of different channels can be expressed as The subscripts i and j represent different channels. The equation of channels i and j are multiplied by I s of the other channel as follows: Simplify the equations 5: Equation 6 is the double channel differences equation. It can be seen that the radiation on the left side of equation 6 (recorded asI d ) is composed of the sensor measurement radiation (I i I j ) and the skin radiation (I s,i I s,j ). In the actual retrieval application, I s,i and I s,j are first calculated and combined with I i and I j to calculate I d , and I d is used to retrieve the temperature and humidity profiles.
The weight function of equation 6 is: 3. Data and Methods

The Data
At present, the on-orbit operation microwave atmospheric sounding instruments mainly includes Advanced Microwave Sounding Unit-A (AMSU-A), Microwave Humidity Sounder (MHS), Advanced Technology Microwave Sounder (ATMS), Microwave Temperature Sounder (MWTS) and Microwave Humidity Sounder (MWHS). AMSU-A and MHS loaded on NOAA and METOP satellites have been widely used. This paper carries out retrieval research with the AMSU-A and MHS loaded on METOP-B. Channel characteristics for both AMSU-A and MHS radiometers are given in Table 1. Figure 1 shows the weighting function

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Earth and Space Science distributions for all AMSU-A and MHS channels calculated for a >51-level reference profile of Radiation Transfer for TOVS (RTTOV) at nadir.
The simulation experiment used the sampled databases of 60-level atmospheric profiles (60 L-SD) issued by the European Centre for Medium-Range Weather Forecasts (ECMWF) (Chevallier, 2001). The profiles in the 60 L-SD are selected from the ECMWF 40-year re-analysis (ERA-40). The database has a total of 13495 profiles, and gathers profiles corresponding to various sea conditions as well as to land conditions, including high elevated grounds. The 6790 profiles with surface pressure greater than 1000 hPa in 60 L-SD are used in this paper (recorded as 60 L-SD choose). Figure 2 shows the statistics and distribution of the 60 L-SD choose database and 60 L-SD database.
The retrieval application experiment uses the global AMSU-A and MHS L1B products of the METOP-B satellite obtained from European Meteorological Satellite (EUMETSAT). The Infrared Atmospheric Sounding Interferometer (IASI) on the METOP-B satellite is synchronized with AMSU-A and MHS, and the IASI Atmospheric Temperature Water Vapor and Surface Skin Temperature product (IASI L2) is used to identify areas for cloudy and cloudless conditions. The target profiles are reanalysis data (ERA-Interim) issued by ECMWF at 0.5°× 0.5°, four times per day, and 37 layers in the vertical direction.

Channel Selection
To reduce the dependence of retrievals on surface emissivity, it is preferred to select observation channels that are significantly affected by the surface emissivity. It can be seen from Figure 1 that Channel No 1-6 and 15 in AMSU-A are significantly affected by the surface emissivity. For the MHS detection channels, since the number of channels is small, all channels are selected. Based on equation 6, this paper selects Channel No 1-6 and 15 in AMSU-A and 1-5 in MHS to construct new channels and the large numbers of new channels are constructed. To simplify the retrieval algorithm and neural network, the equation 7 is used to select the new channels with the peak of the weight function at different heights and the maximum peak value at the same height as the channels that are used for double channel differences scheme temperature and humidity profiles retrieval. To further reduce the lower atmospheric temperature retrieval error, the three channels with the weight function peak at 1000 hPa (New Channel No 2, 3 and 4 in Table 2) are used as the new channels for retrieval. Tables 2 and 3 show the new channels constructed by the AMSU-A and MHS channels, respectively. Figure 3 shows the new channel weighting functions in Tables 2 and 3.

Forward Calculation Method
The radiative transfer model used in this paper is RTTOV 10.2 (Hocking et al., 2011), which is officially released by the EUMETSAT Satellite Application Facility on Numerical Weather Prediction (NWP SAF) and contains coefficient files suitable for the AMSU-A and MHS channels.
To analyze the impact of different precision I s on the retrieval performance, the initial temperature and humidity profiles and the near-surface temperature and humidity with different precision are used as the double channel differences scheme inputs by the calculation of I s . Inputs for schemes 2, 3 and 4 are shown in Table 4.

Retrieval Method
I s is calculated from the temperature and humidity profiles, the near-surface temperature and humidity, and the surface temperature, but these factors except the surface temperature are the quantities to be retrieved. Therefore, to calculateI s , the initial temperature and humidity profiles and the initial near-surface temperature and humidity are first retrieved by the AMSU-A and MHS channels (scheme 1).
For different temperature and humidity profiles retrieval methods, Yao et al. (2005) showed that the retrieval accuracy of neural network (NN) is comparable to traditional physical iterative methods. To facilitate verification of the retrieval performance of the double channel differences scheme, this paper uses NN to retrieve temperature and humidity profiles.
For temperature retrieval, scheme 1 uses 15 channels of AMSU-A as inputs; schemes 2, 3 and 4 use 15 channels of AMSU-A and 9 channels of Table 2 as inputs. For humidity retrieval, scheme 1 uses 15 channels of AMSU-A and 5 channels of MHS as inputs; schemes 2, 3 and 4 use 15 channels of AMSU-A, 5 channels of MHS, 9 channels of Tables 2 and 4 channels of Table 3 as inputs. To facilitate calculation of I s , the outputs of NN are 51 levels that are the same as the 51-level reference profile of RTTOV. The NN contains a single hidden layer. Table 5 shows the NN structures corresponding to different schemes.
The flowchart figure of retrieval scheme is illustrated in Figure 4. The retrieval is divided into three steps. First, based on the AMSU-A and MHS radiances, NN (scheme 1) is used to retrieve the initial temperature and humidity profiles and the near-surface temperature and humidity. Second, the initial retrievals and the AMSU-A and MHS radiances are used to calculate the radiations of equation 6. Finally, the AMSU-A and MHS radiances and the radiations of equation 6 are used as NN (schemes 2/3/4) inputs to retrieve the temperature and humidity profiles.    Table 2 new channels, and the right figure shows Table 3 new channels.

Radiation Ratio
For the lower atmosphere microwave channels, the ratio of the surface emissivity item (εI s ) to the sensor measurement radiation (I) is large, and the ratio of the other items to I is small; thus, the change in I caused by the temperature and humidity profiles is small, which is disadvantageous for temperature and humidity profiles retrieval. Therefore, reducing the ratio of the surface emissivity item is beneficial to temperature and humidity profiles retrieval.
In equations (1) and 6, the ratio of the surface emissivity item is To study the impact of different surface emissivity values, 6790 group normally distributed surface emissivity values with a mean value of 0.9 and a standard deviation of 0.02 are used as inputs of the RTTOV to calculate D and D δ , and there are no correlation between the surface emissivity of each channel. The input profile is a 51-level reference profile of RTTOV.
Figures 5-8 show the ratio of the corresponding channels in AMSU-A, MHS, Tables 2 and 3. Comparing the channels of the weight function peaks at the same height in Figures 1 and 3, D δ is significantly smaller than D for the surface emissivity with a mean value of 0.9. In addition, D δ is significantly smaller than D for the same surface emissivity deviation. Thus, the double channel differences equation 6 can reduce the ratio of the surface emissivity item and then increase the ratio of temperature and humidity information item, which makes equation 6 more sensitive for the radiation change caused by the temperature and humidity profiles and more beneficial to the temperature and humidity profiles retrieval.

Simulation Retrieval Experiment
The profiles in 60 L-SD choose database are used as RTTOV 10.2 inputs. The corresponding surface emissivity values are the same as section 4.1. The scan angles are set to 0°. Noise equivalent temperature sensitivity (NEDT) is applied to each channel radiation of AMSU-A and MHS. During retrieval, the first 5000 profiles are trained in the NN, and the remaining 1790 profiles are used for retrieval verification.
In Figures 9 and 10, the overall root mean square error (RMSE) of scheme 2 is smaller than that of scheme 1 both without and with NEDT, and the bias of scheme 2 is basically the same as that of scheme 1 both without and with NEDT. For temperature retrieval, the RMSE of scheme 2 is significantly reduced below 600 hPa,

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Earth and Space Science and the maximum RMSE reductions are 0.55 K and 0.35 K without and with NEDT, respectively. For relative humidity retrieval, the RMSE of scheme 2 is significantly reduced below 500 hPa, and the maximum RMSE reductions are 4.3% and 5.3% without and with NEDT, respectively. Figure 11 shows statistics and distribution of data used for retrieval in the 60 L-SD choose database. Figures 12 and 13 show statistics and distribution of retrievals of scheme 1 and scheme 2 without and with NEDT, respectively. The statistics of the retrieval profiles in scheme 2 is closer to the target profiles than that of scheme 1 without and with NEDT, especially for the relative humidity profiles. In addition, compared with scheme 1, scheme 2 significantly modified the data distribution of lower atmospheric temperature and relative humidity retrievals, and could more accurately reflect the data change of the target profiles as a whole.

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Retrieval Application Experiment
To further analyze the retrieval performance of the double channel differences scheme, the AMSU-A and MHS L1B products between 1 February 2015 and 28 February 2015 are used to retrieve temperature and humidity profiles for cloudy and cloudless conditions, different surface types, different scan angles, and different initial values. This paper uses whether there are retrieval profiles in the IASI L2 products as the cloudy/cloudless flag, satellite_zenith of the AMSU-A L1B products as the scan angle flag and flag_landsea of the IASI L2 products as the land/coast/sea flag. To reduce the impact of surface altitude, only data with an altitude of less than 500 m are selected. The corresponding ERA-Interim 0.5°× 0.5°reanalysis data are selected as the target profiles. After data matching and screening, a total of 6,694,539 profiles are obtained for the temperature and relative humidity retrieval. Of these data, 85% are selected for training, and 15% are used for verification. Figure 14 shows the statistics and distribution of the selected ERA-Interim database.   Figures 15 and 16 show the temperature RMSE and bias of schemes 1 and 2 for land, coast and sea under cloudless and cloudy conditions. The RMSE of scheme 2 is obviously smaller than that of scheme 1 in the Figure 10. Relative humidity RMSE and bias profiles without and with NEDT. Figure 11. As shown in figure 2, but statistics and distribution of data used for retrieval in the 60 L-SD choose database.

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Earth and Space Science lower atmosphere, and the RMSE improvement of land is greater than those of coast and sea. In addition, the RMSE improvement has no significant dependence on the scan angle. Under the cloudless condition, the maximum RMSE improvements in the lower atmosphere for the land, coast and sea are 0.64 K, 0.42 K and 0.37 K, respectively; under the cloudy condition, the maximum improvements in RMSE are 0.62 K, 0.48 K and 0.52 K, respectively. Except for the land under cloudy condition, the temperature bias of scheme 2 is smaller than that of scheme 1 in the lower atmosphere.  Figures 17 and 18 show the relative humidity RMSE and bias of schemes 1 and 2 for the land, coast and sea under cloudless and cloudy conditions. The RMSE of scheme 2 is significantly smaller than that of scheme 1 from 300-1050 hPa, and the RMSE improvement of land is greater than that of coast and sea. The relative humidity RMSE profiles have the largest improvement from 600-800 hPa and the RMSE improvement has no obvious dependence on the scan angle. Under the cloudless condition, the maximum RMSE

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Earth and Space Science improvements at 702.7 hPa for land, coast and sea are 5.15%, 5.88% and 3.56%, respectively; under the cloudy condition, the maximum improvements in RMSE are 9.03%, 8.19% and 7.32%, respectively. In summary, the double channel differences scheme can significantly reduce the RMSE of temperature profiles in the lower atmosphere and humidity profiles in the middle and lower atmosphere, and the retrieval results are basically the same as those of simulation experiment. The relative humidity bias of scheme 2 is basically the same as that of scheme 1. Figure 19 shows statistics and distribution of data used for retrieval in the selected ERA-Interim database. Figure 20 shows statistics and distribution of retrievals of scheme 1 and scheme 2. For the temperature, the statistics of the retrieval profiles in scheme 2 is basically the same as that of scheme 1. However, compared with the lower atmospheric temperature distribution of the target profiles (Figure 19), scheme 2 can better describe the characteristics of temperature changes in different intervals. For relative humidity, scheme 2 improves the statistics of the retrieval profiles, and reduces the number of profiles in the lower atmospheric relative humidity distribution large value area, thereby closer to the target profiles. Figures 21 and 22 show the temperature RMSE and bias of schemes 2, 3 and 4 for land, coast and sea under cloudless and cloudy conditions, respectively. Compared with scheme 2, scheme 3 has a significantly reduced RMSE (below 900 hPa), and the RMSE improvement has no significant dependence on scan angle. Under the cloudless condition, the maximum RMSE improvements in the lower atmosphere for land, coast and sea are 3.25 K, 2.2 K and 1.56 K, respectively; under the cloudy condition, the maximum RMSE improvements are 3.03 K, 2.12 K and 1.94 K, respectively. Thus, the initial near-surface temperature has a very important impact on the double channel differences scheme regarding the reduction RMSE in the lower atmosphere. The temperature bias of scheme 3 is smaller than that of scheme 2 in the lower atmosphere, especially for land and coast.

Impact of Initial Value
Compared with scheme 3, scheme 4 shows a small improvement of 0.2 K from 600-900 hPa. Since the RMSE profiles of scheme 1 is the RMSE improvement of scheme 4 compared with scheme 3 and significantly

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Earth and Space Science greater than 0.2 K, the double channel differences scheme is relatively insensitive to the initial temperature profiles. The bias of scheme 4 is basically the same as that of scheme 3.
Figures 23 and 24 show the relative humidity retrieval RMSE and bias of schemes 2, 3 and 4 for land, coast and sea under cloudless and cloudy conditions, respectively. Scheme 3 can reduce the relative humidity RMSE below 900 hPa compared with scheme 2. Under the cloudless condition, the maximum RMSE improvements for land, coast and sea are 3.04%, 3.1% and 2.34%, respectively; under the cloudy condition, the maximum RMSE improvements are 3.35%, 2% and 2.01%, respectively. For the initial near-surface relative humidity of 10% RMSE improvement (Figures 14 and 15), the RMSE improvement of scheme 3 compared with scheme 2 is less than that of the initial near-surface relative humidity. In addition, compared with scheme 3, scheme 4 has a slight improvement of 1%-3% from 700-900 hPa. Compared with the initial relative humidity RMSE profiles (Figures 14 and 15), the double channel differences scheme is relatively insensitive to the initial relative humidity profiles. The bias of scheme 3 and scheme 4 are basically the same as that of scheme 2. Figure 25 shows statistics and distribution of retrievals of scheme 3 and scheme 4. The statistics of the retrieval profiles in scheme 3 is basically the same as that of scheme 4. Compared with scheme 2, scheme 3 and scheme 4 further improve the statistics of the retrieval profiles and reduce the number of profiles in the large value area of the lower atmospheric temperature and relative humidity distribution, thereby closer to the target profiles. Figure 16. As shown in Figure 15, but under cloudy condition.

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Summary and Discussion
To reduce the dependence of temperature and relative humidity profile retrievals on surface emissivity, a double channel differences scheme is proposed in this paper. By analyzing the weight function, the channel selection and the ratio of the surface emissivity item, this paper preliminarily illustrates the feasibility of improving retrieval accuracy of the double channel differences scheme. The retrieval performance of the double channel differences scheme is simulated both with and without NEDT and further analyzed by using one month of global AMSU-A and MHS measurements. In addition, the sensitivity of the double channel differences scheme to the initial values is analyzed. The above studies show that the double channel differences scheme can reduce retrieval RMSE of temperature and relative humidity profiles. The results are encouraging: the double channel differences scheme can significantly reduce the RMSE of temperature profiles in the lower atmosphere and humidity profiles in the middle and lower atmosphere for cloudy and cloudless conditions, different surface types, and different scan angles. The distribution of retrievals is closer to the target profiles. In addition, the RMSE improvement has no significant dependence on the scan angle. For temperature retrieval, under the cloudless condition, the maximum RMSE improvements for land, coast and sea are 0.64 K, 0.42 K and 0.37 K, respectively; under the cloudy condition, the maximum RMSE improvements are 0.62 K and 0.48 K and 0.52 K, respectively. For relative humidity retrieval, under the cloudless condition, the maximum RMSE improvements at 702.7 hPa for the land, coast and sea are 5.15%, 5.88% and 3.56%, respectively; under the cloudy condition, the maximum RMSE improvements are 9.03%, 8.19%, and 7.32%, respectively. Initial temperature and humidity profiles and near-surface temperature and humidity with less error can reduce the temperature and relative humidity retrieval RMSE of double channel differences scheme.
Reducing the initial near-surface temperature error has an important impact on lower atmospheric temperature retrieval; under the cloudless condition, the maximum RMSE improvements for the land, coast and sea are 3.25 K, 2.2 K and 1.56 K, respectively; under the cloudy condition, the maximum RMSE improvements are 3.03 K, 2.12 K and 1.94 K, respectively. Compared with the initial temperature and relative humidity profiles and the near-surface temperature and relative humidity RMSE reduction, the temperature retrieval results of the double channel differences scheme are not sensitive to the initial temperature profiles, and the relative humidity retrieval results of the double channel differences scheme are not sensitive to the initial temperature and relative humidity profiles and the near-surface temperature and relative humidity. Reducing the initial temperature and humidity profiles and near-surface temperature and humidity error can further improve thestatistics of the retrieval profiles and reduce the number of profiles in the large value area of the lower atmospheric temperature and relative humidity distribution, thereby closer to the target profiles.
In this paper, the double channel differences equation is constructed by using the relationship between the surface emissivity of adjacent channels. The simulation experiment results show that the scheme can significantly reduce the temperature and humidity RMSE. Further study using satellite measurements yield similar results. However, whether the scheme is consistent with the improvement for various surface types need to be investigated, and which channel combination is more beneficial to reducing the retrieval error remains a problem. Further analysis is needed to determine the characteristics of the double channel differences equation. In addition, for the neural network, the representativeness of the training profiles database will affect the retrieval results, and needs to be studied in detail in subsequent studies. Although the double channel differences method in this paper is only used for microwave channels, it can be extended to hyperspectral infrared temperature retrieval. For satellite data assimilation, the double channel differences scheme can be considered as new constraints to improve the application of the microwave data. Figure 19. As shown in figure 2, but statistics and distribution of data used for retrieval in the selected ERA-interim database.

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Earth and Space Science Figure 21. As shown in Figure 15, but different schemes.

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Earth and Space Science Figure 22. As shown in Figure 15, but different schemes under cloudy condition.

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Earth and Space Science Figure 23. As shown in Figure 15, but for relative humidity RMSE and bias of different schemes under cloudless condition. Figure 24. As shown in Figure 15, but for relative humidity RMSE and bias of different schemes under cloudy condition.

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