Estimation of spatial soil moisture averages in a large gully of the Loess Plateau of China through statistical and modeling solutions

► Three-year root zone soil water datasets in a large gully were used for analysis. ► Considerable soil moisture time stability existed in the large gully. ► Time-stale locations were showed temporally robust by cross validation. ► Spatial averages were reliably estimated by only a few randomly selected locations. ► A simple model was developed and well reproduced soil moisture time series. Characterizing root-zone soil moisture patterns in large gullies is challenging as relevant datasets are scarce and difficult to collect. Therefore, we explored several statistical and modeling approaches, mainly focusing on time stability analysis, for estimating spatial soil moisture averages from point observations and precipitation time series, using 3-year root-zone (0–20, 20–40, 40–60 and 60–80cm) soil moisture datasets for a large gully in the Loess Plateau, China. We also developed a new metric, the root mean square error (RMSE) of estimated mean soil moisture, to identify time-stable locations. The time stability analysis revealed that different time-stable locations were identified at various depths. These locations were shown to be temporally robust, by cross-validation, and more likely to be located in ridges than in pipes or plane surfaces. However, we found that MRD (mean relative difference) operators, used to predict spatial soil moisture averages by applying a constant offset, could not be transferred across root zone layers for most time-stable locations. Random combination analysis revealed that at most four randomly selected locations were needed for accurate estimation of mean soil moisture time series. Finally, a simple empirical model was developed to predict root-zone soil moisture dynamics in large gullies from precipitation time series. The results showed that the model reproduced root-zone soil moisture well in dry seasons, whereas relatively large estimation error was observed during wet seasons. This implies that only precipitation observations might be not enough to accurately predict root-zone soil moisture dynamics in large gullies, and time series of soil moisture loss coefficient should be modeled and included.