Abstract
Abstract. General experience in hydrologic modelling suggests that the parameterisation of a model changes over different time and space scales. As a result, hydrologists often re-parameterise their models whenever different temporal or spatial 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 approach for temporal up-scaling that involves covariance-based corrections. We apply the theory using a unique database of half-hourly pan evaporation measurements (comprising 237 days) and examine how the model parameters change when integrating from half-hour to daily and then monthly integration periods. We show that the model parameters change over different integration periods because of changes in the covariance between the model variables. In our model system, we find that the covariance-based correction is highly variable from day to day but settles down to a reasonably constant value over periods longer than about 15 days. The 15 days timescale is likely to be specific to our model system, nonetheless the underlying principle that there is a characteristic timescale for the covariance-based scaling correction of a particular hydrologic process might be general. If that proved true it would open up the possibility of systematically searching for characteristic integration periods for the key covariance-based scaling terms in other key hydrologic processes. That would in turn enable the development of more generalised hydrologic closure scheme(s).
Highlights
Thirty years ago, hydrologists had a reasonable empirical knowledge of the typical rates of many basic processes like rainfall, evaporation, infiltration, etc
Our results suggest that the mean diurnal cycle of longer integration period might be sufficient to estimate a “representative” total correction factor (i.e. 1 + χAll; where χAll is the sum of all scaling corrections) that is multiplied with the product of the means (i.e. Ep∗an, fv∗)
We find that short-term measurements from an evaporation pan can be accurately up-scaled to longer integration periods by directly accounting for the covariance using covariance-based corrections per Eq (8)
Summary
Hydrologists had a reasonable empirical knowledge of the typical rates of many basic processes like rainfall, evaporation, infiltration, etc. Further extension of their work (Viglione et al, 2010a) enabled assessment of the dependence of the catchment flood response to the space-time interactions between rainfall, runoff generation and routing mechanisms followed by its application to characterise the type of flood events based on different precipitation patterns (see details in Viglione et al, 2010b) These works focused on single event flood response, a more general idea of explicitly incorporating covariance terms into the theory may assist (i) the description of the scale bias and (ii) development of a more generalised approach in hydrologic modelling. To do that we examine how the parameters of a previously formulated and tested evaporation model change when integrating from half-hourly to daily and monthly time periods We use those results to develop a covariance-based approach to up-scale evaporation
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