3.1 Spatial-temporal patterns of soil moisture
The variogram analysis and histogram of soil moisture storage indicated that interpolated soil moisture maps exhibited seasonal alignments of soil moisture storage along topographic convergent areas (Fig. 3). We found the sample variograms with a clear sill and nugget and observed that the geostatistical structure of soil moisture was seasonally evolved. During the wet winter period, high sills (15-25 (%)2) and low correlation lengths (20-30 m) were observed, whereas during the dry summer periods, sills were smaller (10-15 (%)2) and correlation lengths were longer (30-40 m). Regardless of the wetness conditions, the wettest soil was always located within the swales and the valley floor (i.e., near-stream zone). These wet-up and dry-down patterns were consistent with the overall distribution of the soil types and the topographic wetness index within the catchment. There was an exponential increase in the catchment-wide soil moisture variability with increased averaged-catchment moisture contents (Zhao et al., 2012). These conditions were obvious due to the well-drained and steep-sloped soils within the catchment that confined saturated areas to the swales and the valley floor.
The soil moisture variability was explained by using only the first few EOF patterns within the Shale Hills (Table 1). At the soil depths, the first four EOFs together explained approximately 87% of the total variability, whereas only the first EOF (or EOF1) explained about 76% of the total soil moisture variance, indicating that a single spatial structure may explain much of the overall soil moisture pattern. With increased soil depths, the total variations explained by the derived EOFs also increased. These results indicated that the seemingly complex patterns of soil moisture within the Shale Hills may largely be explained by a very small number of the underlying spatial EOFs. In the EOF analysis of spatial patterns, the impacts of temporally variable factors, which do not affect the whole area uniformly, also resulted in noise and would also be expected to have decreased the amount of the variance explained by the significant EOFs.
A close examination of the EOF patterns associated with soil land units in Figure 4 reveals that the EOF1 displayed high values within the valley floor, and low values within the hillslopes, respectively. Obviously, the high EOF values indicated the clustered site with the above average soil moistures, and conversely low EOF values is equivalent to the sites of below average soil moisture values (Fig. 4). From the weighted EC series (Fig. 5), the variance explained by the EOF1 values closely followed the increased field mean moisture contents, e.g., the variance is sharply increased with increased moisture contents following rainfall recharge. Therefore, the EOF analyses seem to represent a very powerful set of tools that helped explain the patterns in the variance associated with the general spatial patterns, the indications of positional characteristics, and the temporal dynamics. Perry and Niemann (2007) applied an EOF analysis for a 10.5 ha Tarrawarra grassland catchment, and the first EOF in their study explained 55% of the soil moisture spatial variability. The explained variances found at the Shale Hills are higher than the previously mentioned studies that were about 55% to 70% of surface soil moisture variability that may be explained by the stable spatial patterns associated with the soil parameters and topography at their study sites (Perry and Niemann, 2007; Korres et al., 2010). Because of the strong combined soil-topographic effects, the observed soil moisture patterns in the Shale Hills was high, and can largely be explained by only a few underlying spatial structures or EOF patterns that are obviously correlated to the various geophysical characteristics.