Temporal covariance of spatial soil moisture variations: A mechanistic error modeling approach

Abstract

When estimating field-scale average soil moisture from sensors measuring at fixed positions, spatial variability in soil moisture leads to “measurement errors” of the spatial mean, which may persist over time due to persistent soil moisture patterns resulting in autocorrelated measurement errors. The uncertainty of parameters that are derived from such measurements may be underestimated when they are assumed to be independent. Temporal autocorrelation models assume stationary random errors, but such error models are not necessarily applicable to soil moisture measurements. As an alternative, we propose a mechanistic error model that is based on the spatial variability of the water retention curve and assumes a uniform water potential. We tested whether spatial soil moisture variability and its temporal covariance could be predicted based on (1) mean soil moisture, (2) water retention variability, and (3) (co)variances of the van Genuchten parameters using a first-order expansion of the retention curve. The proposed models were tested in a numerical and a field experiment. For the field experiment, in situ sensor measurements and water retention curves were obtained in a field plot. Both experiments showed that water retention variability under a uniform water potential is a good predictor for spatial soil moisture variability, and that soil moisture errors are strongly correlated in time and neglecting them would be an incorrect assumption. The temporal error covariance could be predicted as a function of the mean moisture contents at two observation times. Further research is required to assess the impact of these temporal correlations on soil moisture predictions.