3.3. Data combining method of spatially- and temporally-extensive soil moisture
In this study, we found that the first EOF can predict the general patterns of soil moisture, for example at the 20-cm soil depth with 85% of the variance explained. Although the relative importance of the first EOF on daily patterns of soil moisture waxes and wanes during cycles of wetting and drying, the spatial pattern of the EOF is invariant in time. Therefore, we considered it is an efficient way to integrate the spatially extensive (but temporally limited) manual measurement sites with other field long-term automatic monitoring datasets that are temporally extensive (but spatially limited). Conceivably, based on the EOFs for all spatially extensive sites, it was possible to predict the spatially-distributed soil moisture for all those sites based on the derived regressive equation between the EOFs of the temporally-extensive sites and its automated monitoring datasets. For instance, the first EOF of soil moisture at 20-cm soil depth was derived from a manual dataset with the higher explained variations, but there also was a strong-correlated regression coefficient between the soil moisture automated monitoring sites (e.g., five sites 15, 51, 55, 61, and 74) and their corresponding EOFs values. Based on the derived equations, all manual measurement values could be predicted by either the manual measurements or the monitored values at those five monitoring sites. To validate this assumption, we selected three wetness conditions on the same dates as used in Figure 3 (i.e. wet: ; moist: ; dry: ). Remarkably, the predicted values via the manually-measured data (Fig. 6) have a strong linear correlation to the measurements with high confidence levels (95%). These results mean that the suggested method is practical to combine the manually-measured datasets with the automated- monitored datasets.
Note that the results showed a relatively large scatter when the automated- monitored values were used to predicate soil moisture values at the spatially extensive sites (Fig. 7). Whether this approach is accurate is also dependent on how well the manually-measured data and the automated-monitored data closely match for the same soil depths at the same sites. Due to the differences in the measured thickness and horizonation, spatial dimensions and scales for the two methods (Gu et al., 2018), the values between manually-measured and automated-monitored datasets may not necessarily match well with one another. As indicated in Figure 8, except for site 55, there were large differences between manually-measured and automated-monitored soil moisture values. For instance, the manually-measured moisture contents are consistently higher than the automated- monitored values for the site 51 during the entire measurement period. Even worse, the trends between both datasets for sites 15 and 74 are somewhat irregular. These results challenged the suitability of this approach when the automated-monitored data, instead of the manually-measured data were used at the temporally-limited site. As shown in Figure 9, we found that the fit between manual-measured and auto-recorded soil moisture datasets were significant, but relatively weak. Therefore, to apply this method reasonably, it is important for the predicted data accuracy accounting the manually-measured and automated monitored data to be somewhat in agreement. It is expected that the EOF method could be a practical and efficient data merging method if the primary EOF explains >60% of the variation. Nevertheless, taking into account those differences, the EOF method as applied in this study could be quite valuable, and therefore provide an essential way to assimilate data from multiple sources.
Furthermore, we explored the EOF method to breakdown a more dynamic time series of soil moisture in to a lesser number of orthogonal spatial EOF patterns (that are invariant in time) and the corresponding EC components (that are invariant in space). This modification greatly simplifies our task as we can just deal with only a few spatial EOF structures instead of the whole data set. The higher-order EOFs are usually taken into account depending on the amount of the total variance explained by them. The associated EC components show the variation in the influence of the EOFs during the wetting/drying phases, which could be reasonably associated with the automated monitoring moisture dynamics and theoretically provided the basic for the data fusion. To determine the dominant physical controls, the EOF patterns were correlated to the geophysical characteristics of the region. From our analyses, we inferred that some of the variability of the soil moisture EOF patterns is related to both topography and soil texture. We assessed that, using the EOF analysis, it is particularly applicable to combine the manual datasets with the automatic datasets in terms of different resolutions for different data sources. The soil moisture dataset is currently providing either better spatial coverage or better temporal coverage. Our data assimilation approach provides an important way to combine both datasets together which certainly improved the explanations for the variation and data use.