Calibration of hydrological models using flow-duration curves

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 WAS-MOD 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 Correspondence to: I. K. Westerberg (ida.westerberg@hyd.uu.se) 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.

Hydrological model calibration for derived flood frequency analysis using stochastic rainfall and probability distributions of peak flows

“…Alternatives to using only continuous hydrographs for model calibration are the utilization of statistical flow data such as flow duration curves (Westerberg et al, 2011) or flow information in the spectral domain (Schaefli and Zehe, 2009). When flood frequency estimation is the main goal, special consideration should be given to the annual or partial peak flow series in addition to the hydrographs in the calibration process (Cameron et al, 1999;Lamb, 1999).…”

On the colour and spin of epistemic error (and what we might do about it)

“…Such an assumption can be tested in a similar way. Departures from the range of model predictions (in both calibration and prediction periods) might be useful in identifying consistent model structural error or non-stationary epistemic error (see, for example, Westerberg et al, 2011b).…”

Predicting streamflows in snowmelt-driven watersheds using the flow duration curve method

“…Smakhtin and Masse (2000) developed a variation of the FDC method to generate streamflow using rainfall observations as the donor variable instead of streamflow data. Recently, the FDC was used not only for generating streamflow directly, but also for calibrating conceptual models (Westerberg et al, 2011). Westerberg et al (2011) used the FDC as a performance measure to circumvent uncertainty in discharge data and other drawbacks in model calibration with traditional methods.…”

“…Recently, the FDC was used not only for generating streamflow directly, but also for calibrating conceptual models (Westerberg et al, 2011). Westerberg et al (2011) used the FDC as a performance measure to circumvent uncertainty in discharge data and other drawbacks in model calibration with traditional methods. Despite the numerous applications with the FDC, there is still no good approach using the FDC method to generate daily streamflow from point snow observations.…”