Forensic Analysis of Accumulation of Rainfall Error in Hydrologic Models

Abstract

We performed an error budget (i.e., error breakdown) analysis of hydrologic models to understand how error in rainfall accumulated as it propagated from input (rainfall) to various outputs. The analysis was performed with a “forensic” mindset in order to trace the error in each output variable to the error in the input source. Towards that end, we hypothesized that error in rainfall input is a conservable quantity for hydrologic models that honor the principle of conservation of mass. We focused on two types of errors—systematic error and random error—and four hydrologic models of varying levels of complexity. Systematic error and random error in input were found to be insensitive to the relative accumulation of error in the simulation of stream flow and evapotranspiration (ET) for the simplest statistical model. As systematic error increased in rainfall, error accumulated relatively more in stream flow for a linear storage-discharge model, while the proportion of error in ET decreased. This increase was observed to be linear. In contrast, a linear increase in random error in rainfall appeared to induce a non-linear (exponential-type) increase in error in stream flow. Additive random error penalized more than the multiplicative random error in the simulation of outputs. Hence, the assumption of error variance being dependent of the mean is an important criterion in our understanding of the progression of error from input to output. Overall, our forensic-type analysis indicated that rainfall error had a natural affinity to accumulate more in stream flow simulation as the complexity in model structure increased. Identification of the relative level of accumulation of input error among various simulated variables should facilitate the choice of models based on satellite rainfall over ungauged regions where both systematic and random errors are known to persist in the data.