Since the performance of the MWRI L2 VSM products compared with other satellite VSM products is rarely presented in the past, an intuitive comparison is presented first in Fig. 2 between MWRI L2 and four daily gridded VSM products derived from SMAP, SMOS, AMSR2 on GCOM-W1, and GPM Microwave Imager (GMI), respectively, for the focused land covers from 1 August 2017 to 31 May 2019. The number of daily available VSM estimates from each satellite is different but with a similar trend across time.
Figure 2. (a) Number of daily available global VSM estimates, (b) daily R2, and (c) daily ubRMSD from MWRI L2 VSM compared with AMSR2 VSM (green line), GMI VSM (blue line), SMOS VSM (red line), and SMAP VSM (black line), respectively, from 1 August 2017 to 31 May 2019.
The daily coefficient of determination (R2) scores between MWRI L2 and SMAP are much higher than the scores by comparing MWRI L2 with the other satellite products. This is positive to use MWRI observations to estimate VSM. But it is noticed that the range of the R2 scores between MWRI L2 and SMAP is large from 0.1 to 0.6, and the average value of the R2 scores is 0.44 over the whole time period. Moreover, the average values of the R2 scores are only 0.25, 0.09, and 0.09 for MWRI L2 compared with SMOS, GMI, and AMSR2, respectively. On the other hand, the unbiased root mean square difference (ubRMSD) scores are relatively large. During the whole time period, the smallest average value of ubRMSD is 0.10 m3 m−3 from the comparison between MWRI L2 VSM and SMAP, while the average ubRMSD values are all around 0.13 m3 m−3 for MWRI L2 VSM compared with the other three satellite VSM products. Therefore, we need to increase the stability of the MWRI VSM retrieval and reduce the values of the ubRMSD scores.
The training dataset used in this work is simply selected from four random days to represent the four seasons in a year, but it includes the variations in global soil texture and land cover using a high-density spatial sampling (0.25 degree). Figure 3 presents the statistical distributions of three variables in the training dataset, including land cover type, SMOPS product (learning objective), and TB observation from the 10.65 GHz horizontal channel (TB10H) typically used for VSM retrieval [e.g., National Snow and Ice Data Center (NSIDC) AMSR-E/-2 VSM product]. In Fig. 3, 91% of the VSM values range between 0.10 and 0.35 m3 m−3, and 89% of the TB10H values range from 220 to 280 K; while the proportion of extreme values is small in both SMOPS and TB10H. It should be noted that the variation of the land cover types significantly affects the VSM estimation. The maximum percentage (30%) is from open shrublands. Hence, the retrieval accuracy from open shrublands contributes a lot to the global average value of the retrieval accuracy. The proportions from woody savannas, grasslands, croplands, and barrens are similar, from 13% to 16%, while the percentages of savannas and croplands/natural vegetation mosaic lands are small (9% and 4%). Although the statistical distributions in Fig. 3 are only from 4-day observations, it approximately represents the annual distributions for a global scale.
Figure 3. Statistical distributions of (a) land cover type, (b) SMOPS, and (c) TB10H for the samples in the training dataset constructed by 4-day observations: 31 January, 30 April, 31 July, and 31 October 2018. The percent value is the ratio of the count of each bin to the total count of the samples in the training data. Bin widths are 0.05 m3 m−3 and 10 K for (b) and (c).
Based on the above training dataset, EXP1 and EXP2 models are trained by using the RF method with different input parameters. The contribution of each input in each model is evaluated by two factors: the percentage for increasing the MSE and the node impurity. The higher percentage for increasing MSE or the larger node purity value (meaning impurity), the larger contribution of the input parameter on VSM retrieval. Although DEM and soil porosity are ancillary data, not observed by MWRI, both of them are very important for increasing MSE and node impurity shown in Fig. 4. In EXP1 with all available input parameters, soil porosity is the most important parameter for increasing node impurity and the second important parameter for increasing MSE, while DEM is the top one for increasing MSE and the sixth for increasing node impurity. The following are vegetation and temperature from ECMWF and low frequency TBs and PRs from MWRI. It is similar in EXP2, without the contributions from ECMWF reanalysis data, DEM rises to the third one for increasing node impurity. From both EXP1 and EXP2 models, we consider that PRs from 36.5 and 89.0 GHz are the two least important input parameters in increasing both MSE and node impurity and can be removed from the input parameters. This is similar to that only low frequency PRs (from 6.9, 10.6, and 18.9 GHz of AMSR-E) are used in Njoku et al. (2003). Here, PR at 18.7 GHz is less important than that at 23.8 GHz in both EXP1 and EXP2 models.
Figure 4. Importance of each input parameter in the RF training models derived by (a, b) EXP1 and (c, d) EXP2, for (a, c) increased percentage in MSE (%IncMSE) and (b, d) increased node purity values (IncNodePurity). The higher the value, the more important the input parameter. Black crosses mean the unimportant input parameters.
Figure 5 displays an example of the estimated VSM from the independent EXP4 using the least input parameters on 15 March 2018, which is compared with SMOPS and MWRI L2 VSM products. The retrievals from other experiments are similar and not shown here. Clearly, the VSM retrievals from EXP4 are closer to SMOPS products than MWRI L2 products. Due to the MWRI data gap and the limited land covers for estimating MWRI VSM, the number of the available EXP4 estimates is smaller than that of SMOPS, but the number of the public MWRI L2 VSM products is even less, especially over the Tibetan Plateau and Northern Hemisphere high latitudes. The spatial distribution of MWRI soil moisture estimates is much improved in EXP4.
Figure 5. Surface VSM distributions from (a) SMOPS products, (b) EXP4 VSM estimates, and (c) MWRI L2 VSM products on 15 March 2018.
For an intercomparison, SMOPS and ECMWF ERA5 are used as the benchmark, respectively, for the whole time period from 1 August 2017 to 31 May 2019. Daily global scores of the MWRI VSM retrievals from EXP1, EXP2, EXP3, EXP4, and MWRI L2 are calculated only using the data where the VSM estimates from all data sources are available. Hence, the data size is the same for the four experiments and MWRI L2 product. Because of the missing data in SMOPS, the amount of SMOPS data is slightly smaller than that of ECMWF ERA5 data. We can see the dynamic change of the available data size in Fig. 6. The amount of data is much larger in summer and smaller in winter. Due to the soil freezing and snow/ice cover problems in MWRI L2 VSM products, missing data are much more common in winter.
Figure 6. Time series of the number of daily global VSM estimates used in this study, from SMOPS (red line) and ECMWF ERA5 (green line) from 1 August 2017 to 31 May 2019.
From the daily mean bias scores between various MWRI VSM and SMOPS in Fig. 7, all of the four experiments are close and around zero, while for MWRI L2 the daily mean bias ranges between −0.025 and 0.025 m3 m−3. Since SMOPS is the learning objective in the RF models, the bias between SMOPS and the model derived value is very small. But note that only 4-day SMOPS data are used in the training data, and most of the model estimates (656 of 660 days) are independent. This means that our multivariable method can produce MWRI VSM estimates with a really small bias related to SMOPS. However, based on the independent data source, ECMWF ERA5, the mean bias values of our four experiments are all below zero, displaying a negative bias, as low as −0.025 m3 m−3. The mean bias scores of the MWRI L2 products are also worse, with a larger variation from −0.050 to 0.025 m3 m−3.
Figure 7. Daily mean bias scores of the soil moisture estimates from MWRI EXP1 (red line), EXP2 (blue line), EXP3 (orange line), EXP4 (black line), and L2 (green line) based on the validations from (a) SMOPS and (b) ECMWF ERA5, respectively, from 1 August 2017 to 31 May 2019.
In Fig. 8, the VSM retrievals from all four experiments generally present a good agreement with SMOPS: R2 is not lower than 0.55, ubRMSD does not exceed 0.05 m3 m−3, and p-values are all smaller than 0.01. A significant improvement is found in the retrievals derived from our proposed multivariable method, compared with the MWRI L2 VSM products (R2 below 0.45 and ubRMSD around 0.11 m3 m−3). Among the four experiments, with the help of the ancillary LAI and temperature data, R2 scores in EXP1 and EXP3 are relatively higher than those in EXP2 and EXP4: the average value of R2 scores is 0.66 (0.65) in EXP1 (EXP3) and 0.63 in both EXP2 and EXP4. It presents the enhancement in estimating MWRI VSM with vegetation and temperature information. Moreover, the difference between EXP2 and EXP4 is neglected and thus this proves the 15 input parameters in EXP4 enough for training the independent RF model. For dependent experiments, EXP1 is slightly better than EXP3. There is no doubt that the best R2 and ubRMSD scores are from the four random days (31 January, 30 April, 31 July, and 31 October 2018) used for constructing the training dataset.
Figure 8. Daily scores of (a, b) R2 and (c, d) the ubRMSD of the soil moisture estimates from MWRI EXP1 (red line), EXP2 (blue line), EXP3 (orange line), EXP4 (black line), and L2 (green line) based on the validations from (a, c) SMOPS and (b, d) ECMWF ERA5, respectively, during the time period from 1 August 2017 to 31 May 2019.
We also compare the MWRI retrievals in this study and the MWRI L2 products with the independent ECMWF ERA5 reanalysis. An improvement for estimating MWRI VSM using our method is also found in R2 scores but not significant in ubRMSD scores. The average value of R2 scores during the whole time period from 1 August 2017 to 31 May 2019 is 0.68 (0.64) in EXP1 (EXP3) and 0.62 in both EXP2 and EXP4, while for MWRI L2, it is only 0.42. Moreover, the difference between EXP1 and EXP2/EXP4 is obvious. But note that the ancillary data used in EXP1 are also from ECMWF ERA5, which are not independent and might increase the effects of vegetation and temperature on VSM retrieval. On the other hand, the average value of ubRMSD scores is around 0.11 m3 m−3 for all MWRI experiments and around 0.12 m3 m−3 for the MWRI L2 products, which is very close and much larger than that based on SMOPS. Figure 8 shows a slight improvement in MWRI experiments in spring and summer.
The detail scores for various land covers are shown in Tables 1 and 2 using SMOPS and ECMWF ERA5 as the benchmark, respectively. The largest percentage of land covers is from open shrublands (IGBP 7). Moreover, all scores (R2, bias, and ubRMSD) are good in open shrublands (Table 1). Besides, R2 scores in grasslands (IGBP 10) and ubRMSD scores in barrens (IGBP 16) are the best in all land covers. While the lowest R2 values and the largest bias values are both from croplands/natural vegetation mosaic lands (IGBP 14), and the largest ubRMSD values are from woody savannas (IGBP 8). But note the number of the daily estimates in croplands/natural vegetation mosaic lands (IGBP 14) is relatively small due to the limited global coverage. In Table 2, taking ECMWF ERA5 as the benchmark, R2 and bias scores in woody savannas (IGBP 8), croplands/natural vegetation mosaic lands (IGBP 14), and barrens (IGBP 16) are relatively low in all land covers, but ubRMSD scores in barrens (IGBP 16) are the best (around 0.05 m3 m−3) and much better than others (from 0.08 to 0.11 m3 m−3 in our experiments). From the above results, we conclude the retrieval accuracies for croplands/natural vegetation mosaic lands and woody savannas are the worst, and the results for the savannas and croplands are in the middle, while those for barrens, grasslands, and open shrublands are relatively better for estimating MWRI VSM.
IGBP type N R2 between SMOPS and Bias (m3 m−3) between SMOPS and ubRMSD (m3 m−3) between SMOPS and EXP1 EXP2 EXP3 EXP4 L2 EXP1 EXP2 EXP3 EXP4 L2 EXP1 EXP2 EXP3 EXP4 L2 All 72645 0.66 0.63 0.65 0.63 0.31 0.0013 0.0021 0.0015 0.0020 0.0032 0.0423 0.0442 0.0429 0.0440 0.1079 IGBP 7 14849 0.57 0.53 0.55 0.53 0.26 0.0008 0.0019 0.0014 0.0018 −0.0250 0.0386 0.0403 0.0392 0.0402 0.0801 IGBP 8 10876 0.51 0.45 0.48 0.46 0.10 0.0012 0.0033 0.0019 0.0030 0.0521 0.0478 0.0505 0.0490 0.0501 0.1283 IGBP 9 9689 0.53 0.46 0.50 0.47 0.21 0.0014 0.0017 0.0014 0.0016 0.0410 0.0452 0.0480 0.0465 0.0477 0.1173 IGBP 10 10616 0.58 0.56 0.57 0.56 0.26 0.0030 0.0025 0.0027 0.0023 −0.0125 0.0425 0.0437 0.0430 0.0435 0.1013 IGBP 12 10425 0.49 0.46 0.49 0.46 0.09 0.0042 0.0047 0.0046 0.0046 0.0139 0.0465 0.0478 0.0466 0.0476 0.1155 IGBP 14 2776 0.43 0.39 0.42 0.39 0.07 −0.0085 −0.0086 −0.0070 −0.0084 0.0478 0.0456 0.0472 0.0461 0.0469 0.1240 IGBP 16 12406 0.48 0.42 0.48 0.42 0.10 0.0025 0.0036 0.0021 0.0035 −0.0419 0.0305 0.0326 0.0306 0.0326 0.0472
Table 1. Comparisons of VSM between MWRI estimates (from EXP1, EXP2, EXP3, EXP4, and L2) and SMOPS products at a depth of 5 cm from 1 August 2017 to 31 May 2019. Mean R2, bias, and ubRMSD scores are given for each land cover type. IGBP numbers 7, 8, 9, 10, 12, 14, and 16 are related with open shrublands, woody savannas, savannas, grasslands, croplands, croplands/natural vegetation mosaic lands, and barrens, respectively; N is the number of the samples
IGBP type N R2 between ECMWF and Bias (m3 m−3) between ECMWF and ubRMSD (m3 m−3) between ECMWF and EXP1 EXP2 EXP3 EXP4 L2 EXP1 EXP2 EXP3 EXP4 L2 EXP1 EXP2 EXP3 EXP4 L2 All 74028 0.68 0.62 0.64 0.62 0.42 −0.0151 −0.0143 −0.0149 −0.0144 −0.0130 0.1111 0.1137 0.1128 0.1138 0.1206 IGBP 7 15073 0.56 0.50 0.53 0.49 0.35 0.0313 0.0324 0.0320 0.0323 0.0057 0.0952 0.0974 0.0967 0.0976 0.1041 IGBP 8 11040 0.39 0.30 0.30 0.29 0.15 −0.0850 −0.0829 −0.0843 −0.0831 −0.0338 0.1025 0.1068 0.1064 0.1069 0.1420 IGBP 9 9864 0.55 0.46 0.48 0.45 0.31 −0.0649 −0.0646 −0.0649 −0.0648 −0.0250 0.1041 0.1081 0.1070 0.1081 0.1247 IGBP 10 10753 0.53 0.47 0.49 0.46 0.31 −0.0320 −0.0326 −0.0324 −0.0328 −0.0475 0.0960 0.0984 0.0976 0.0986 0.1147 IGBP 12 10550 0.41 0.36 0.37 0.36 0.11 −0.0528 −0.0524 −0.0524 −0.0524 −0.0423 0.0815 0.0839 0.0832 0.0840 0.1274 IGBP 14 2823 0.28 0.21 0.22 0.21 0.06 −0.0961 −0.0962 −0.0946 −0.0961 −0.0392 0.0875 0.0906 0.0900 0.0906 0.1404 IGBP 16 12895 0.41 0.34 0.38 0.34 0.26 0.0942 0.0954 0.0938 0.0952 0.0500 0.0505 0.0527 0.0514 0.0529 0.0555
Table 2. As in Table 1, but for comparisons of VSM between MWRI estimates and the top 7-cm VSM reanalysis from ECMWF ERA5
Since the scores between MWRI L2 VSM and other satellites VSM are shown in Fig. 2, we also present the scores between EXP4 VSM (the independent estimates) and the same benchmarks in Fig. 9. The average ubRMSD score between MWRI VSM and AMSR2 is significantly improved from 0.13 (L2) to 0.07 m3 m−3 (EXP4), while for comparing with SMAP, GMI, and SMOS, the average ubRMSD values are also reduced to 0.08, 0.10, and 0.11 m3 m−3, respectively. An improvement is also found in the R2 scores. The highest one (0.51) is from the comparison between EXP4 and SMAP, the second one (0.29) is from the comparison with SMOS, while for comparing with AMSR2 and GMI, R2 scores are 0.17 and 0.14.
Figure 9. Daily scores of (a) R2 and (b) ubRMSD from EXP4 VSM compared with AMSR2 VSM (green line), GMI VSM (blue line), SMOS VSM (red line), and SMAP VSM (black line), respectively, during the time period from 1 August 2017 to 31 May 2019.
In situ VSM observations (daily mean values) at 5 cm from the NRCS–SCAN are used to further evaluate the performance of the EXP4 VSM estimates derived by our RF model and the improvement compared with the MWRI L2 VSM products. Since the VSM estimates are made at a 0.25-degree grid resolution, not all in situ stations are suitable for validating. The VSM observations from 12 stations from 1 August 2017 to 31 May 2019 are selected to assess the correlations with the SMOPS products, MWRI L2 VSM products, and EXP4 estimates, respectively. The scores from the 12 stations are shown in Table 3. The correlation coefficient (R) scores between scaled EXP4 estimates and scaled in situ observations range from 0.4 to 0.7, which are significantly better than the R scores (from −0.2 to 0.5) of scaled MWRI L2 VSM products, and slightly worse than the R scores (from 0.5 to 0.8) of scaled SMOPS products. The mean values of the ubRMSD scores from the 12 stations are 0.87, 0.98, and 1.35 m3 m−3 for scaled SMOPS products, scaled EXP4 estimates, and scaled MWRI L2 VSM products, respectively. Similar to R scores, the performance of ubRMSD scores of EXP4 estimates is much better than that of MWRI L2 products but slightly worse than that of SMOPS products.
SCAN station SMOPS vs. in situ EXP4 vs. in situ MWRI L2 vs. in situ N R ubRMSD (m3 m−3) N R ubRMSD (m3 m−3) N R ubRMSD (m3 m−3) Tok 637 0.62 0.870 637 0.74 0.712 163 −0.22 1.690 Ku-Nesa 618 0.46 1.051 618 0.36 1.132 190 −0.19 1.459 Conrad Ag Rc 642 0.69 0.790 642 0.43 1.064 362 0.48 1.072 Fort Assiniboine 653 0.48 1.020 653 0.53 0.964 346 −0.18 1.587 Moccasin 635 0.57 0.929 635 0.47 1.030 355 0.42 1.150 Violett 654 0.76 0.699 654 0.51 0.994 345 0.27 1.301 Sheldo 648 0.53 0.963 648 0.38 1.110 363 0.20 1.207 Chicken 621 0.58 0.906 621 0.53 0.966 − − − Enterprise 630 0.53 0.973 630 0.45 1.049 455 0.06 1.341 Ephraim 642 0.71 0.762 642 0.63 0.862 361 0.14 1.227 Grouse 655 0.77 0.685 655 0.59 0.910 4 0.47 1.287 Park 653 0.70 0.770 653 0.55 0.945 212 −0.19 1.546
Table 3. Comparisons of VSM between scaled in situ VSM observations at 5 cm from 12 stations in NRCS–SCAN and three scaled VSM time series (EXP4 VSM estimates, MWRI L2 VSM products, and SMOPS products) during the same time period from 1 August 2017 to 31 May 2019. The number of samples (N), correlation coefficient (R), and ubRMSD scores are given
Scaled EXP4 VSM estimates from three typical stations in Table 3 are compared in Fig. 10 with three scaled VSM time series: in situ VSM observations at a depth of 5 cm, MWRI L2 VSM products, and SMOPS products. EXP4 estimates are significantly closer to the in situ observations than the MWRI L2 VSM products. Moreover, the available MWRI L2 VSM products (N values in Table 3) are obviously less than the EXP4 estimates. Most of the missing data in MWRI L2 VSM are much more common in winter, shown in Fig. 10. It proves that more MWRI VSM estimates can be obtained and better performance of MWRI VSM can be reached by using our RF model.
|IGBP type||N||R2 between SMOPS and||Bias (m3 m−3) between SMOPS and||ubRMSD (m3 m−3) between SMOPS and|