Evaluation criteria play a key role in assessing the performances of hydrological models. Most previous criteria are based on the standard least square method, which assumes model residuals to be homoscedastic and is, therefore, not suitable for assessing cases with heteroscedastic residuals. Here, we compared a heteroscedastic and symmetric efficiency (HSE) criterion with the Nash–Sutcliffe efficiency (NSE) and the heteroscedastic maximum-likelihood estimator (HMLE) by running a monthly water balance model with four parameters (i.e., the abcd model) in 138 basins located in the continental United States derived from the Model Parameter Estimation Experiment dataset. The results show that compared to the NSE, the HSE and HMLE are both more effective for stabilizing variance and producing more uniform performances with flow magnitude, and the latter is slightly more effective than the former on stabilizing the residual heteroscedasticity, with the aid of an additional parameter.

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