Abstract
Abstract. The degree of belief we have in predictions from hydrologic models will normally depend on how well they can reproduce observations. Calibrations with traditional performance measures, such as the Nash-Sutcliffe model efficiency, are challenged by problems including: (1) uncertain discharge data, (2) variable sensitivity of different performance measures to different flow magnitudes, (3) influence of unknown input/output errors and (4) inability to evaluate model performance when observation time periods for discharge and model input data do not overlap. This paper explores a calibration method using flow-duration curves (FDCs) to address these problems. The method focuses on reproducing the observed discharge frequency distribution rather than the exact hydrograph. It consists of applying limits of acceptability for selected evaluation points (EPs) on the observed uncertain FDC in the extended GLUE approach. Two ways of selecting the EPs were tested – based on equal intervals of discharge and of volume of water. The method was tested and compared to a calibration using the traditional model efficiency for the daily four-parameter WASMOD model in the Paso La Ceiba catchment in Honduras and for Dynamic TOPMODEL evaluated at an hourly time scale for the Brue catchment in Great Britain. The volume method of selecting EPs gave the best results in both catchments with better calibrated slow flow, recession and evaporation than the other criteria. Observed and simulated time series of uncertain discharges agreed better for this method both in calibration and prediction in both catchments. An advantage with the method is that the rejection criterion is based on an estimation of the uncertainty in discharge data and that the EPs of the FDC can be chosen to reflect the aims of the modelling application, e.g. using more/less EPs at high/low flows. While the method appears less sensitive to epistemic input/output errors than previous use of limits of acceptability applied directly to the time series of discharge, it still requires a reasonable representation of the distribution of inputs. Additional constraints might therefore be required in catchments subject to snow and where peak-flow timing at sub-daily time scales is of high importance. The results suggest that the calibration method can be useful when observation time periods for discharge and model input data do not overlap. The method could also be suitable for calibration to regional FDCs while taking uncertainties in the hydrological model and data into account.
Highlights
Hydrologic models are used as a basis for decision making about management of water resources with important consequences for sectors such as agriculture, land planning, hydropower and water supply
The evaluation points (EPs) of the flow-duration curves (FDCs) ranged from a fraction of flow equalled or exceeded of 0.004 to 0.70 for RFDC−V and from 0.0002 to 0.30 for RFDC−Q for the two periods in the Brue and from 0.003 to 0.69 for RFDC−V and from 0.0003 to
This paper has explored a calibration method that addresses four particular problems that arise in calibration with traditional performance measures: (1) uncertain discharge data, (2) variable sensitivity of different performance measures to different flow magnitudes, (3) influence of input/output errors of an epistemic nature and (4) inability to evaluate model performance when observation time periods for discharge and model input data do not overlap
Summary
Hydrologic models are used as a basis for decision making about management of water resources with important consequences for sectors such as agriculture, land planning, hydropower and water supply. It is calculated as 1.0 minus the normalisation of the mean squared error by the variance of the observed data and varies between minus infinity to 1.0 (Nash and Sutcliffe, 1970) How appropriate this criterion is for measuring goodness of fit, as well as what is an acceptable Reff-value, has been much debated in the literature (Krause et al, 2005; Legates and McCabe, 1999; Seibert, 2001; Criss and Winston, 2008; Smith et al, 2008; Gupta et al, 2009). In a related approach, Freer et al (2003) used several performance measures for a multicriteria calibration in a Generalised Likelihood Uncertainty
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