The importance of the one dimensional assumption in soil moisture – rainfall depth correlation at varying spatial scales.

Inferring local land‐atmosphere coupling through correlation of colocated soil moisture and future rainfall inherently assumes a one‐dimensional (1‐D) framing of the coupling mechanism. For the first time we demonstrate the importance of upholding this assumption by examining the statistical relationship between daily soil moisture and rainfall depths over Australia, specifying spatial scales (0.05°, 0.5°, 1°, and 2.5°) to constrain the relationship to local‐only physical processes. At small scales, without consideration of the 1‐D assumption, strong land‐atmosphere coupling is suggested across much of the country. However, when adhering to a 1‐D framework, small sample sizes make correlation unsuitable for assessing local coupling at these small scales. When adhering to a 1‐D framework, at scales of 0.5° and above, we find positive correlations in northern Australia in the wet and transition seasons and negative correlations in southern Australia in austral winter. The correlation is scale dependent, suggesting that as spatial resolutions increase in the future and land‐atmosphere coupling heterogeneity is resolved, spatial distributions of local coupling may differ from larger‐scale estimates characteristic of current coarse resolution climate models.

Figure 4. Correlation between soil moisture and next‐day rainfall, 1979–2015. Only grid cells with p < 0.05 (two tailed) are colored. Maximum sample size N is 590; N < 15 are hatched. Only the first day of consecutive rainfall days was considered. Correlations are shown for local conditions (1‐D assumption upheld) at (a–d) 0.05° (wind speeds ≤0.25 m/s), (e–h) 0.5° (wind speeds ≤2 m/s), (i–l) 1° (wind speeds ≤4 m/s), and (m–p) 2.5° (wind speeds ≤10 m/s). DJF = December, January, February; JJA = June, July, August; MAM = March, April, May; SON = September, October, November.