Quantifying the probabilistic divergences related to time-space scales for inferences in water resource management

Studies focusing on time-space scaling issues have not yet established guidelines for choosing a time-space scale for water resources management. This study attempts to develop a methodology to understand the deviations induced by the scaling framework on water resource variables. The study addresses eight variables: streamflow, groundwater level, precipitation, air temperature, soil moisture, solar radiation, wind speed, and relative humidity. For each variable, a 10-year (2001 to 2010) daily time-series data were retrieved from weather and hydrologic stations selected across Oklahoma. The methodology entailed three phases, including a variable rescaling, a probability analysis, and a divergence quantification. Hence, daily time-series of the selected variables were rescaled to weekly, biweekly, monthly, bimonthly, and trimonthly scales. To derive the probability density function of each variable, a kernel density estimator was applied to the rescaled time-series. The Kullback–Leibler divergence was used to evaluate the deviations pertaining to the time-space scaling. Results showed meaningful divergences that were a consequence of time-space scale variations. However, the sensitivity of variables to the scaling framework differed. For instance, air temperature was less sensitive to time-space scaling, while wind speed, soil moisture, and precipitation were highly sensitive. Correlation analysis showed that correlations tended to gradually increase with the increase in scale, even though the strength of the relation varied, depending on the variable involved. The methodology was tested via a case study where data obtained from a location outside of the study region were used to address the scaling effect on the Normalized Difference Vegetation Index’s response to precipitation and soil moisture. It was concluded that understanding the divergences associated with time-space scales was critical for interpreting results in water resource studies.