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A long-standing research issue, in the hydrological sciences and beyond, is that of developing methods to evaluate the predictive/forecasting skill, errors and uncertainties of a model (or model ensembles). Various methods have been proposed for characterising time series residuals, i.e. the differences between observed (or target) and modelled (or estimate) time series. Most notably, the Taylor Diagram summarises model performance via a single plot based on three related metrics: the (linear Pearson) correlation, standard deviation, and root mean squared differences of one or multiple pairs of target and estimate time series. Despite its theoretical elegance and widespread use, the Taylor diagram does not account for bias errors, which is an important summary statistic for evaluating model performance. Further, it is very common to evaluate, compare, and report on model “skill” by use of a single aggregate metric value, even when a vector of metrics is used to calibrate/train the model; most commonly this is a dimensionless efficiency metric such as Nash-Sutcliffe Efficiency (NSE) or Kling-Gupta Efficiency (KGE). Such “efficiency” metrics typically aggregate over multiple types of residual behaviours: for example the most commonly used version of KGE is based on correlation, bias, and variability errors, although the authors recommended that it should be applied in a context-dependent fashion based on which model behaviours are deemed to be important to a given situation. Nevertheless, the use of a single summary value fails to account for the interactions among the error component terms, which can be quite informative for the evaluation and benchmarking of models. In this study, we propose a new diagram that is as easy to use and interpret as the Taylor Diagram, while also accounting for bias. We further suggest a new convention for reporting model skill that is based on foundational error terms. Our vision is that this new diagram and convention will enable resea

Ecologically relevant streamflow characteristics (SFCs) of ungauged catchments are often estimated from simulated runoff of hydrologic models that were originally calibrated on gauged catchments. However, SFC estimates of the gauged donor catchments and subsequently the ungauged catchments can be substantially uncertain when models are calibrated using traditional approaches based on optimization of statistical performance metrics (e.g., Nash-Sutcliffe model efficiency). An improved calibration strategy for gauged catchments is therefore crucial to help reduce the uncertainties of estimated SFCs for ungauged catchments. The aim of this study was to improve SFC estimates from modeled runoff time series in gauged catchments by explicitly including one or several SFCs in the calibration process. Different types of objective functions were defined consisting of the Nash-Sutcliffe model efficiency, single SFCs, or combinations thereof. We calibrated a bucket-type runoff model (HBV-Hydrologiska Byrans Vattenavdelning-model) for 25 catchments in the Tennessee River basin and evaluated the proposed calibration approach on 13 ecologically relevant SFCs representing major flow regime components and different flow conditions. While the model generally tended to underestimate the tested SFCs related to mean and high-flow conditions, SFCs related to low flow were generally overestimated. The highest estimation accuracies were achieved by a SFC-specific model calibration. Estimates of SFCs not included in the calibration process were of similar quality when comparing a multi-SFC calibration approach to a traditional model efficiency calibration. For practical applications, this implies that SFCs should preferably be estimated from targeted runoff model calibration, and modeled estimates need to be carefully interpreted.

Applications of runoff models usually rely on long and continuous runoff time series for model calibration. However, many catchments around the world are ungauged and estimating runoff for these catchments is challenging. One approach is to perform a few runoff measurements in a previously fully ungauged catchment and to constrain a runoff model by these measurements. In this study we investigated the value of such individual runoff measurements when taken at strategic points in time for applying a bucket-type runoff model (HBV) in ungauged catchments. Based on the assumption that a limited number of runoff measurements can be taken, we sought the optimal sampling strategy (i.e. when to measure the streamflow) to obtain the most informative data for constraining the runoff model. We used twenty gauged catchments across the eastern US, made the assumption that these catchments were ungauged, and applied different runoff sampling strategies. All tested strategies consisted of twelve runoff measurements within one year and ranged from simply using monthly flow maxima to a more complex selection of observation times. In each case the twelve runoff measurements were used to select 100 best parameter sets using a Monte Carlo calibration approach. Runoff simulations using these 'informed' parameter sets were then evaluated for an independent validation period in terms of the Nash-Sutcliffe efficiency of the hydrograph and the mean absolute relative error of the flow-duration curve. Model performance measures were normalized by relating them to an upper and a lower benchmark representing a well-informed and an uninformed model calibration. The hydrographs were best simulated with strategies including high runoff magnitudes as opposed to the flow-duration curves that were generally better estimated with strategies that captured low and mean flows. The choice of a sampling strategy covering the full range of runoff magnitudes enabled hydrograph and flow-duration curve simulat

Ecologically relevant streamflow characteristics (SFCs) of ungauged catchments are often estimated from simulated runoff of hydrologic models that were originally calibrated on gauged catchments. However, SFC estimates of the gauged donor catchments and subsequently the ungauged catchments can be substantially uncertain when models are calibrated using traditional approaches based on optimization of statistical performance metrics (e.g., Nash-Sutcliffe model efficiency). An improved calibration strategy for gauged catchments is therefore crucial to help reduce the uncertainties of estimated SFCs for ungauged catchments. The aim of this study was to improve SFC estimates from modeled runoff time series in gauged catchments by explicitly including one or several SFCs in the calibration process. Different types of objective functions were defined consisting of the Nash-Sutcliffe model efficiency, single SFCs, or combinations thereof. We calibrated a bucket-type runoff model (HBV-Hydrologiska Byrans Vattenavdelning-model) for 25 catchments in the Tennessee River basin and evaluated the proposed calibration approach on 13 ecologically relevant SFCs representing major flow regime components and different flow conditions. While the model generally tended to underestimate the tested SFCs related to mean and high-flow conditions, SFCs related to low flow were generally overestimated. The highest estimation accuracies were achieved by a SFC-specific model calibration. Estimates of SFCs not included in the calibration process were of similar quality when comparing a multi-SFC calibration approach to a traditional model efficiency calibration. For practical applications, this implies that SFCs should preferably be estimated from targeted runoff model calibration, and modeled estimates need to be carefully interpreted.

Ecologically relevant streamflow characteristics (SFCs) of ungauged catchments are often estimated from simulated runoff of hydrologic models that were originally calibrated on gauged catchments. However, SFC estimates of the gauged donor catchments and subsequently the ungauged catchments can be substantially uncertain when models are calibrated using traditional approaches based on optimization of statistical performance metrics (e.g., Nash-Sutcliffe model efficiency). An improved calibration strategy for gauged catchments is therefore crucial to help reduce the uncertainties of estimated SFCs for ungauged catchments. The aim of this study was to improve SFC estimates from modeled runoff time series in gauged catchments by explicitly including one or several SFCs in the calibration process. Different types of objective functions were defined consisting of the Nash-Sutcliffe model efficiency, single SFCs, or combinations thereof. We calibrated a bucket-type runoff model (HBV-Hydrologiska Byrans Vattenavdelning-model) for 25 catchments in the Tennessee River basin and evaluated the proposed calibration approach on 13 ecologically relevant SFCs representing major flow regime components and different flow conditions. While the model generally tended to underestimate the tested SFCs related to mean and high-flow conditions, SFCs related to low flow were generally overestimated. The highest estimation accuracies were achieved by a SFC-specific model calibration. Estimates of SFCs not included in the calibration process were of similar quality when comparing a multi-SFC calibration approach to a traditional model efficiency calibration. For practical applications, this implies that SFCs should preferably be estimated from targeted runoff model calibration, and modeled estimates need to be carefully interpreted.

Ecologically relevant streamflow characteristics (SFCs) of ungauged catchments are often estimated from simulated runoff of hydrologic models that were originally calibrated on gauged catchments. However, SFC estimates of the gauged donor catchments and subsequently the ungauged catchments can be substantially uncertain when models are calibrated using traditional approaches based on optimization of statistical performance metrics (e.g., Nash-Sutcliffe model efficiency). An improved calibration strategy for gauged catchments is therefore crucial to help reduce the uncertainties of estimated SFCs for ungauged catchments. The aim of this study was to improve SFC estimates from modeled runoff time series in gauged catchments by explicitly including one or several SFCs in the calibration process. Different types of objective functions were defined consisting of the Nash-Sutcliffe model efficiency, single SFCs, or combinations thereof. We calibrated a bucket-type runoff model (HBV-Hydrologiska Byrans Vattenavdelning-model) for 25 catchments in the Tennessee River basin and evaluated the proposed calibration approach on 13 ecologically relevant SFCs representing major flow regime components and different flow conditions. While the model generally tended to underestimate the tested SFCs related to mean and high-flow conditions, SFCs related to low flow were generally overestimated. The highest estimation accuracies were achieved by a SFC-specific model calibration. Estimates of SFCs not included in the calibration process were of similar quality when comparing a multi-SFC calibration approach to a traditional model efficiency calibration. For practical applications, this implies that SFCs should preferably be estimated from targeted runoff model calibration, and modeled estimates need to be carefully interpreted.

Ecologically relevant streamflow characteristics (SFCs) of ungauged catchments are often estimated from simulated runoff of hydrologic models that were originally calibrated on gauged catchments. However, SFC estimates of the gauged donor catchments and subsequently the ungauged catchments can be substantially uncertain when models are calibrated using traditional approaches based on optimization of statistical performance metrics (e.g., Nash-Sutcliffe model efficiency). An improved calibration strategy for gauged catchments is therefore crucial to help reduce the uncertainties of estimated SFCs for ungauged catchments. The aim of this study was to improve SFC estimates from modeled runoff time series in gauged catchments by explicitly including one or several SFCs in the calibration process. Different types of objective functions were defined consisting of the Nash-Sutcliffe model efficiency, single SFCs, or combinations thereof. We calibrated a bucket-type runoff model (HBV-Hydrologiska Byrans Vattenavdelning-model) for 25 catchments in the Tennessee River basin and evaluated the proposed calibration approach on 13 ecologically relevant SFCs representing major flow regime components and different flow conditions. While the model generally tended to underestimate the tested SFCs related to mean and high-flow conditions, SFCs related to low flow were generally overestimated. The highest estimation accuracies were achieved by a SFC-specific model calibration. Estimates of SFCs not included in the calibration process were of similar quality when comparing a multi-SFC calibration approach to a traditional model efficiency calibration. For practical applications, this implies that SFCs should preferably be estimated from targeted runoff model calibration, and modeled estimates need to be carefully interpreted.

Quantification of streamflow characteristics in ungauged catchments remains a challenge. Hydrological modeling is often used to derive flow time series and to calculate streamflow characteristics for subsequent applications that may differ from those envisioned by the modelers. While the estimation of model parameters for ungauged catchments is a challenging research task in itself, it is important to evaluate whether simulated time series preserve critical aspects of the streamflow hydrograph. To address this question, seven calibration objective functions were evaluated for their ability to preserve ecologically relevant streamflow characteristics of the average annual hydrograph using a runoff model, HBV-light, at 27 catchments in the southeastern United States. Calibration trials were repeated 100 times to reduce parameter uncertainty effects on the results, and 12 ecological flow characteristics were computed for comparison. Our results showed that the most suitable calibration strategy varied according to streamflow characteristic. Combined objective functions generally gave the best results, though a clear underprediction bias was observed. The occurrence of low prediction errors for certain combinations of objective function and flow characteristic suggests that (1) incorporating multiple ecological flow characteristics into a single objective function would increase model accuracy, potentially benefitting decision-making processes; and (2) there may be a need to have different objective functions available to address specific applications of the predicted time series.

Quantification of streamflow characteristics in ungauged catchments remains a challenge. Hydrological modeling is often used to derive flow time series and to calculate streamflow characteristics for subsequent applications that may differ from those envisioned by the modelers. While the estimation of model parameters for ungauged catchments is a challenging research task in itself, it is important to evaluate whether simulated time series preserve critical aspects of the streamflow hydrograph. To address this question, seven calibration objective functions were evaluated for their ability to preserve ecologically relevant streamflow characteristics of the average annual hydrograph using a runoff model, HBV-light, at 27 catchments in the southeastern United States. Calibration trials were repeated 100 times to reduce parameter uncertainty effects on the results, and 12 ecological flow characteristics were computed for comparison. Our results showed that the most suitable calibration strategy varied according to streamflow characteristic. Combined objective functions generally gave the best results, though a clear underprediction bias was observed. The occurrence of low prediction errors for certain combinations of objective function and flow characteristic suggests that (1) incorporating multiple ecological flow characteristics into a single objective function would increase model accuracy, potentially benefitting decision-making processes; and (2) there may be a need to have different objective functions available to address specific applications of the predicted time series.

Quantification of streamflow characteristics in ungauged catchments remains a challenge. Hydrological modeling is often used to derive flow time series and to calculate streamflow characteristics for subsequent applications that may differ from those envisioned by the modelers. While the estimation of model parameters for ungauged catchments is a challenging research task in itself, it is important to evaluate whether simulated time series preserve critical aspects of the streamflow hydrograph. To address this question, seven calibration objective functions were evaluated for their ability to preserve ecologically relevant streamflow characteristics of the average annual hydrograph using a runoff model, HBV-light, at 27 catchments in the southeastern United States. Calibration trials were repeated 100 times to reduce parameter uncertainty effects on the results, and 12 ecological flow characteristics were computed for comparison. Our results showed that the most suitable calibration strategy varied according to streamflow characteristic. Combined objective functions generally gave the best results, though a clear underprediction bias was observed. The occurrence of low prediction errors for certain combinations of objective function and flow characteristic suggests that (1) incorporating multiple ecological flow characteristics into a single objective function would increase model accuracy, potentially benefitting decision-making processes; and (2) there may be a need to have different objective functions available to address specific applications of the predicted time series.

Quantification of streamflow characteristics in ungauged catchments remains a challenge. Hydrological modeling is often used to derive flow time series and to calculate streamflow characteristics for subsequent applications that may differ from those envisioned by the modelers. While the estimation of model parameters for ungauged catchments is a challenging research task in itself, it is important to evaluate whether simulated time series preserve critical aspects of the streamflow hydrograph. To address this question, seven calibration objective functions were evaluated for their ability to preserve ecologically relevant streamflow characteristics of the average annual hydrograph using a runoff model, HBV-light, at 27 catchments in the southeastern United States. Calibration trials were repeated 100 times to reduce parameter uncertainty effects on the results, and 12 ecological flow characteristics were computed for comparison. Our results showed that the most suitable calibration strategy varied according to streamflow characteristic. Combined objective functions generally gave the best results, though a clear underprediction bias was observed. The occurrence of low prediction errors for certain combinations of objective function and flow characteristic suggests that (1) incorporating multiple ecological flow characteristics into a single objective function would increase model accuracy, potentially benefitting decision-making processes; and (2) there may be a need to have different objective functions available to address specific applications of the predicted time series.

Quantification of streamflow characteristics in ungauged catchments remains a challenge. Hydrological modeling is often used to derive flow time series and to calculate streamflow characteristics for subsequent applications that may differ from those envisioned by the modelers. While the estimation of model parameters for ungauged catchments is a challenging research task in itself, it is important to evaluate whether simulated time series preserve critical aspects of the streamflow hydrograph. To address this question, seven calibration objective functions were evaluated for their ability to preserve ecologically relevant streamflow characteristics of the average annual hydrograph using a runoff model, HBV-light, at 27 catchments in the southeastern United States. Calibration trials were repeated 100 times to reduce parameter uncertainty effects on the results, and 12 ecological flow characteristics were computed for comparison. Our results showed that the most suitable calibration strategy varied according to streamflow characteristic. Combined objective functions generally gave the best results, though a clear underprediction bias was observed. The occurrence of low prediction errors for certain combinations of objective function and flow characteristic suggests that (1) incorporating multiple ecological flow characteristics into a single objective function would increase model accuracy, potentially benefitting decision-making processes; and (2) there may be a need to have different objective functions available to address specific applications of the predicted time series.

Quantification of streamflow characteristics in ungauged catchments remains a challenge. Hydrological modeling is often used to derive flow time series and to calculate streamflow characteristics for subsequent applications that may differ from those envisioned by the modelers. While the estimation of model parameters for ungauged catchments is a challenging research task in itself, it is important to evaluate whether simulated time series preserve critical aspects of the streamflow hydrograph. To address this question, seven calibration objective functions were evaluated for their ability to preserve ecologically relevant streamflow characteristics of the average annual hydrograph using a runoff model, HBV-light, at 27 catchments in the southeastern United States. Calibration trials were repeated 100 times to reduce parameter uncertainty effects on the results, and 12 ecological flow characteristics were computed for comparison. Our results showed that the most suitable calibration strategy varied according to streamflow characteristic. Combined objective functions generally gave the best results, though a clear underprediction bias was observed. The occurrence of low prediction errors for certain combinations of objective function and flow characteristic suggests that (1) incorporating multiple ecological flow characteristics into a single objective function would increase model accuracy, potentially benefitting decision-making processes; and (2) there may be a need to have different objective functions available to address specific applications of the predicted time series.