A framework for upscaling short-term process-level understanding to longer time scales

<jats:p>Abstract. General experience in hydrologic modelling suggests that the parameterisation of a model could change over different time scales. As a result, hydrologists often re-parameterise their models whenever different temporal resolutions are required. Here, we investigate theoretical aspects of this issue in a search for the cause(s) of the need for re-parameterisations. Based on Taylor series expansion, we present a mathematical framework for temporal upscaling and evaluate it using a simple experimental system. For that, we use a unique database of half-hourly pan evaporation measurements (comprising 237 days) and examine how the model parameters change for daily and monthly integration periods. We show that the model parameters change over different integration periods with changes in the covariance between the model variables. The theory presented here is general and can be used as a basis for temporal upscaling. </jats:p>