To test the applicability of every DLR model over the Tibetan Plateau, we use different models to estimate DLR and then validate the DLR estimate against the ground measurements. In the validation, the root mean squared error (RMSE), mean bias error (MBE) and coefficient of determination (R2) of the estimates of the different models are calculated as validation indices. Then, the optimal model(s) will be used to estimate DLR of the entire Tibetan Plateau.
4.2. Estimated DLR for the Entire Tibetan Plateau, Based on the CLDAS Dataset
After comparing the models for estimating DLR under clear-sky and cloudy conditions, the DO-CK model is found to be suitable for clear-sky conditions, and the LH-CL model can be used to estimate DLRc based on DO-CK for cloudy conditions. e in the DO-CK model can be calculated from p, SH, and Ta derived from the CLDAS dataset according to Equation (4). Therefore, we can estimate the all-weather DLR over the entire Tibetan Plateau.
As mentioned previously, the time span of the CLDAS is from 2008 to 2016, and certain ground sites (i.e., AN, TD, BJ, and GZ) had no ground measurements during this period. Therefore, only five ground sites, including HB, NQ, AL, DX, and MQ, are used to evaluate the estimated all-weather DLR based on the CLDAS dataset. The evaluation results of the five sites are presented in
Figure 5; MBE, RMSE, and R
2 are also provided. To quantitatively evaluate the model that uses the ratio of DSR provided by the CLDAS to DSR
0 to determine the cloud fraction, the all-weather DLR estimated directly by the DO-CK model is evaluated before considering the cloud coverage.
Before considering the cloud coverage, the MBE and RMSE values of the DO-CK model range from −38.6 to 1.3 W/m
2 and 36.2 to 48.3 W/m
2, respectively. For HB, NQ, ALS, and MQ sites, the estimates of DLR yield large negative deviations. The main reason is that the presence of clouds increases the atmospheric moisture content and then increases DLR. However, the DO-CK model can only be applied under clear-sky conditions and does not take the contribution of clouds to DLR into account. For the DX site, although there is no significant negative deviation, a large error is still observed. The main reason is that DO-CK has a certain overestimation of DLR under clear-sky conditions for the DX site (as displayed in
Figure 2e), which offset the underestimation under cloudy conditions and lead to no significant positive or negative deviation.
After considering the cloud coverage, the MBE and RMSE values range from −22.5 to 19.5 W/m2 and 24.9 to 34.8 W/m2, respectively. Compared with the results obtained without considering clouds, the LH-CL model can significantly reduce the underestimation of DLR by DO-CK. Specifically, for the HB, NQ, AL, and MQ sites, the negative deviations are decreased by approximately 20 W/m2. The RMSE of all five sites is smaller than before considering the cloud coverage. The reduction in the RMSE ranges from 1.4 to 16.7 W/m2. Therefore, the results demonstrate that the method based on the CLDAS dataset to account for clouds in the DSR determination is effective, and the estimated all-weather DLR of the Tibetan Plateau based on the CLDAS dataset has an acceptable accuracy.
To evaluate the contribution of the input parameters to the all-weather DLR estimation error, we calculate the error of
Ta provided by CLDAS and
e estimated based on CLDAS (
Table 7). DLR estimation errors caused by
Ta and
e are also presented in
Table 7. Note that the DLR estimation error mentioned here refers to the error in the all-weather DLR estimated by the DO-CK model before considering the influence of the cloud on DLR. From
Table 7, it is clear that
Ta and
e have large estimation errors for the AL site, and their estimation errors caused a DLR estimation error of approximately 20 W/m
2. The influence of the cloud on instantaneous
Ta and
e is also very significant. Thus, cloud will increase the estimation error of
Ta and
e, and then the error of the estimated DLR becomes larger. After considering the influence of cloud on DLR, the estimation error of DLR is reduced by 22.4 W/m
2 (
Figure 5). The correction of DLR
c by the cloudy estimation model is actually to correct the DLR estimation error caused by the estimation error of
Ta and
e.
Ta and
e at the other four sites have different estimation errors, and DLR estimation errors induced by
Ta and
e are 18.7 W/m
2 for MQ, 13.4 W/m
2 for HB, 11.5 W/m
2 for NQ, and 93 W/m
2 for DX, respectively. After considering the influence of cloud on DLR through the LH-CL model, there is a significant positive correlation between the decrease of DLR estimation error at four sites and the estimation error caused by
Ta and
e. It can be observed that the error of the all-weather DLR estimation result is largely due to the uncertainty of the input parameters; the rest of the error is from the error of the model itself.
To further understand the contribution of
c estimated by the CLDAS to the estimation of the all-weather DLR, DOY 062 in 2012 is selected as an example, as many clouds appeared on this day. The spatial distributions of the values of
c over the entire Tibetan Plateau during the daytime are provided in
Figure 6. It can be observed that the cloud fraction over the Tibetan Plateau was low around sunrise (i.e., between 01:00 and 02:00 UTC) and sunset (i.e., at 09:00 UTC), whereas almost all the plateau was obscured by clouds at approximately noon (i.e., between 03:00–08:00 UTC). The value of
c is larger in the southeastern part of the Tibetan Plateau but lower in the northwestern part. The main reason for this phenomenon is that the air humidity in the southwestern part is more likely to form thick clouds; in contrast, the air humidity in the northwest part is lower, which is more likely to produce broken clouds [
43,
44].
The influences of the estimated
c on the estimated DLR, based on the CLDAS data for the five ground sites, are further investigated (
Figure 7). When the clouds are present, the estimated DLR would be significantly lower than the ground-measured DLR if the contribution of the clouds to DLR is not addressed. In contrast, after considering the contribution of the clouds, the estimated DLR has a much better agreement with the ground-measured DLR. In addition, the varying trend of the estimated DLR is basically consistent with the varying trend of the
c values. The latter is especially true at the NQ and AL sites.
Based on the aforementioned all-weather DLR models, we generate a DLR dataset with a 0.0625° spatial resolution and a 1-h temporal resolution for the entire Tibetan Plateau. The all-weather DLR at 06:00 UTC on DOY 001, 061, 122, 183, 245, and 305 in 2012 are presented in
Figure 8 as examples. As displayed in
Figure 1, the elevation of the southeastern Tibetan Plateau is low (approximately 60 to 4000 m); thus, the atmosphere in this region is humid and thick. In contrast, the average elevation is higher than 4000 m in the northwestern plateau, and the atmosphere is dry and thin. The difference in the atmosphere caused by the variation in elevation directly affected DLR. Therefore, we can clearly observe that DLR is higher in the southeast region of the Tibetan Plateau than in the northwest region. The temporal variations in DLR over the Tibetan Plateau are also very clear. DLR values displayed on DOY 122, 183, and 245 are significantly higher than DLR values on DOY 001, 061, and 305. The main reason for this phenomenon is the variance in
Ta in different seasons, as
Ta is one of the main input parameters of the DRL model.
We further compare the all-weather DLR estimated based on CLDAS and the GLASS Longwave Radiation Product (GLASS-LRP) from the National Earth System Science Data Center, National Science & Technology Infrastructure of China (
http://www.geodata.cn, accessed on 28 December 2020) [
45]. Since GLASS-LRP is estimated based on MODIS observation data, its temporal resolution is daily, and its spatial resolution is 1 km. Its observation time is the MODIS overpassing time. In contrast, the temporal and spatial resolutions of the all-weather DLR are 1 h and 0.0625°, respectively. Therefore, it is difficult to accurately match these two data in the temporal and spatial dimensions. Here, these two DLR data are compared based on the RMSE obtained from this study and the developer of GLASS-LRP [
45]. For GLASS-LRP, the average RMSE is 26.9 W/m
2; for the all-weather DLR, the average RMSE is approximately 26.4 W/m
2 [
45]. It is evident that the estimated all-weather DLR has a very similar accuracy to GLASS-LRP. On the one hand, the all-weather DLR estimated based on the CLDAS dataset has a higher temporal resolution and all-weather properties; on the other hand, GLASS-LRP has a much better spatial resolution.