Impact of model development,calibration and validation decisions on hydrological simulations in West Lake Erie Basin

Watershed simulation models are used extensively to investigate hydrologic processes, landuse and climate change impacts, pollutant load assessments and best management practices (BMPs). Developing, calibrating and validating these models require a number of critical decisions that will influence the ability of the model to represent real world conditions. Understanding how these decisions influence model performance is crucial, especially when making science‐based policy decisions. This study used the Soil and Water Assessment Tool (SWAT) model in West Lake Erie Basin (WLEB) to examine the influence of several of these decisions on hydrological processes and streamflow simulations. Specifically, this study addressed the following objectives (1) demonstrate the importance of considering intra‐watershed processes during model development, (2) compare and evaluated spatial calibration versus calibration at outlet and (3) evaluate parameter transfers across temporal and spatial scales. A coarser resolution (HUC‐12) model and a finer resolution model (NHDPlus model) were used to support the objectives. Results showed that knowledge of watershed characteristics and intra‐watershed processes are critical to produced accurate and realistic hydrologic simulations. The spatial calibration strategy produced better results compared to outlet calibration strategy and provided more confidence. Transferring parameter values across spatial scales (i.e. from coarser resolution model to finer resolution model) needs additional fine tuning to produce realistic results. Transferring parameters across temporal scales (i.e. from monthly to yearly and daily time‐steps) performed well with a similar spatial resolution model. Furthermore, this study shows that relying solely on quantitative statistics without considering additional information can produce good but unrealistic simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

On characterizing the temporal dominance patterns of model parameters and processes

Diagnostic analyses of hydrological models intend to improve the understanding of how processes and their dynamics are represented in models. Temporal patterns of parameter dominance could be precisely characterized with a temporally resolved parameter sensitivity analysis. In this way, the discharge conditions are characterized, that lead to a parameter dominance in the model. To achieve this, the analysis of temporal dynamics in parameter sensitivity is enhanced by including additional information in a three‐tiered framework on different aggregation levels. Firstly, temporal dynamics of parameter sensitivity provide daily time series of their sensitivities to detect variations in the dominance of model parameters. Secondly, the daily sensitivities are related to the flow duration curve (FDC) to emphasize high sensitivities of model parameters in relation to specific discharge magnitudes. Thirdly, parameter sensitivities are monthly averaged separately for five segments of the FDC to detect typical patterns of parameter dominances for different discharge magnitudes. The three methodical steps are applied on two contrasting catchments (upland and lowland catchment) to demonstrate how the temporal patterns of parameter dynamics represent different hydrological regimes. The discharge dynamic in the lowland catchment is controlled by groundwater parameters for all discharge magnitudes. In contrast, different processes are relevant in the upland catchment, because the dominances of parameters from fast and slow runoff components in the upland catchment are changing over the year for the different discharge magnitudes. The joined interpretation of these three diagnostic steps provides deeper insights of how model parameters represent hydrological dynamics in models for different discharge magnitudes. Thus, this diagnostic framework leads to a better characterization of model parameters and their temporal dynamics and helps to understand the process behaviour in hydrological models. Copyright © 2015 John Wiley & Sons, Ltd.     

Automated calibration applied to watershed‐scale flow simulations

Complexity in simulating the hydrological response in large watersheds over long times has prompted a significant need for procedures for automatic calibration. Such a procedure is implemented in the basin‐scale hydrological model (BSHM), a physically based distributed parameter watershed model. BSHM simulates the most important basin‐scale hydrological processes, such as overland flow, groundwater flow and stream–aquifer interaction in watersheds. Here, the emphasis is on estimating the groundwater parameters with water levels in wells and groundwater baseflows selected as the calibration targets. The best set of parameters is selected from within plausible ranges of parameters by adjusting the values of hydraulic conductivity, storativity, groundwater recharge and stream bed permeability. The baseflow is determined from stream flow hydrographs by using an empirical scheme validated using a chemical approach to hydrograph separation. Field studies determined that the specific conductance for components of the composite hydrograph were sufficiently unique to make the chemical approach feasible. The method was applied to the Big Darby Creek Watershed, Ohio. The parameter set selected for the groundwater system provides a good fit with the estimated baseflow and observed water well data. Copyright © 1999 John Wiley & Sons, Ltd.     

Comparison of two rainfall–runoff models: effects of conceptualization on water budget components

Rainfall–runoff models with different conceptual structures for the hydrological processes can be calibrated to effectively reproduce the hydrographs of the total runoff, while resulting in water budget components that are essentially different. This finding poses an open question on the reliability of rainfall–runoff models in reproducing hydrological components other than those used for calibration. In an effort to address this question, we use data from the Glafkos catchment in western Greece to calibrate and compare the ENNS model, a research-oriented lumped model developed for the river Enns in Austria developed for the river Enns in Austria, with the operational MIKE SHE model. Model performance is assessed in the light of the conceptual/structural differences of the modelled hydrological processes, using indices calculated independently for each year, rather than for the whole calibration period, since the former are stricter. We show that even small differences in the representation of hydrological processes may impact considerably on the water budget components that are not measured (i.e. not used for model calibration). From all water budget components, direct runoff exhibits the highest sensitivity to structural differences and related model parameters.

EDITOR M.C. Acreman

ASSOCIATE EDITOR S. Huang     

Implementation of an automatic calibration procedure for HYDROTEL based on prior OAT sensitivity and complementary identifiability analysis

Efficiency of hydrological models mostly depends on the quality of the calibration performed prior to use. In this paper, an automatic calibration framework for the distributed hydrological model HYDROTEL is proposed. The calibration procedure was performed for three watersheds characterized with different hydroclimatological conditions: the Sassandra located in Ivory Coast, Africa, and the Montmorency and Beaurivage watersheds located in Quebec (Canada). Results of one‐a‐time (OAT) sensitivity analysis showed that the order of the most sensitive parameters differs for each watershed. Thus, the sensitivity depends on the hydroclimatic and physiographic characteristics of the watersheds. Co‐linearity indices showed that all model parameters were identifiable, that is, none of the studied parameters could be explained by a combination of the other parameters. Following these findings, an automatic calibration was run. Results indicated there was good agreement between simulated and measured streamflows at the outlet of each watershed; Nash–Sutcliffe efficiency (NSE) ranging between 0.77 and 0.92 and R² ranging from 0.87 to 0.97. When comparing NSE and R² values obtained using a process‐oriented, multiple‐objective, manual calibration strategy, a slight increase in model efficiency was reached with the automatic calibration procedure (4.15% for NSE and 2.95% for R²) improving predictions of peak flows for the Montmorency and Beaurivage watersheds (temperate climate conditions) and flows beyond the rainfall season in the Sassandra watershed. The proposed automatic calibration procedure introduced in this paper may be applied to other distributed hydrological model. Copyright © 2013 John Wiley & Sons, Ltd.     

Assessing parameter identifiability for multiple performance criteria to constrain model parameters

ABSTRACT

Reliable simulations of hydrological models require that model parameters are precisely identified. In constraining model parameters to small ranges, high parameter identifiability is achieved. In this study, it is investigated how precisely model parameters can be constrained in relation to a set of contrasting performance criteria. For this, model simulations with identical parameter samplings are carried out with a hydrological model (SWAT) applied to three contrasting catchments in Germany (lowland, mid-range mountains, alpine regions). Ten performance criteria including statistical metrics and signature measures are calculated for each model simulation. Based on the parameter identifiability that is computed separately for each performance criterion, model parameters are constrained to smaller ranges individually for each catchment. An iterative repetition of model simulations with successively constrained parameter ranges leads to more precise parameter identifiability and improves model performance. Based on these results, a more consistent handling of model parameters is achieved for model calibration.     

Multi‐site calibration using a grid‐based event rainfall–runoff model: a case study of the upstream areas of the Nakdong River basin in Korea

Most runoff analyses using a grid‐based distributed model use one parameter group calibrated at the outlet of a watershed, instead of dividing the watershed into subwatersheds. Significant differences between the observed value and the simulation result of the subwatersheds can occur if just one parameter group is used in all subwatersheds that have different hydrological characteristics from each other. Therefore, to improve the simulation results of the subwatersheds within a watershed, a model calibrated at every subwatershed needs to be used to reflect the characteristics of each subwatershed. In this study, different parameter groups were set up for one or two sites using a distributed model, the GRM (Grid based Rainfall‐runoff Model), and the evaluations were based on the results of rainfall–runoff analysis, which uses a multi‐site calibration (MSC) technique to calibrate the model at the outlet of each site. The Hyangseok watershed in Naeseong River, which is a tributary of Nakdong River in Korea, was chosen as the study area. The watershed was divided into five subwatersheds each with a subwatershed outlet that was applied to the calibration sites . The MSC was applied for five cases. When a site was added for calibration in a watershed, the runoff simulation showed better results than the calibration of only one site at the most downstream area of the watershed. The MSC approach could improve the simulation results on the calibrated sites and even on the non‐calibrated sites, and the effect of MSC was improved when the calibrated site was closer to the runoff site. Copyright © 2014 John Wiley & Sons, Ltd.     

Parameter estimation and uncertainty analysis of SWAT model in upper reaches of the Heihe river basin

Heihe river basin, the second largest inland river basin in China, has attracted more attention in China due to the ever increasing water resources and eco‐environmental problems. In this article, SWAT (Soil and Water Assessment Tool; http://www.brc.tamus.edu/swat/ ) model was applied to upper reaches of the basin for better understanding of the hydrological process over the watershed. Parameter uncertainty and its contribution on model simulation are the main foci. In model calibration, the aggregate parameters instead of the original parameters in SWAT model were used to reduce the computing effort. The Bayesian approach was employed for parameter estimation and uncertainty analysis because its posterior distribution provides not only parameter estimation but also uncertainty analysis without normality assumption. The results indicated that: (1) SWAT model performs satisfactorily in this watershed as a whole, although some low and high flows were under‐ or overestimated, particularly in dry (e.g. 1991) and wet (e.g. 1996) years; (2) all calibrated parameters were not normally distributed (essentially positively or negatively skewed) and the parameter uncertainties were relatively small; and (3) the contributions of parameter uncertainty on model simulation uncertainty were relatively small. Copyright © 2009 John Wiley & Sons, Ltd.     

An approach to measure parameter sensitivity in watershed hydrological modelling

Hydrological responses vary spatially and temporally according to watershed characteristics. In this study, the hydrological models that we developed earlier for the Little Miami River (LMR) and Las Vegas Wash (LVW) watersheds in the USA were used for detailed sensitivity analyses. To compare the relative sensitivities of the hydrological parameters of these two models, we used normalized root mean square error (NRMSE). By combining the NRMSE index with the flow duration curve analysis, we derived an approach to measure parameter sensitivities under different flow regimes. Results show that the parameters related to groundwater are highly sensitive in the LMR watershed, whereas the LVW watershed is primarily sensitive to near-surface and impervious parameters. The high and medium flows are more impacted by most of the parameters. The low flow regime was highly sensitive to groundwater-related parameters. Moreover, our approach is found to be useful in facilitating model development and calibration.

EDITOR D. Koutsoyiannis

ASSOCIATE EDITOR S. Huang     

Impact of the numbers of observations and calibration parameters on equifinality,model performance,and output and parameter uncertainty

The level of model complexity that can be effectively supported by available information has long been a subject of many studies in hydrologic modelling. In particular, distributed parameter models tend to be regarded as overparameterized because of numerous parameters used to describe spatially heterogeneous hydrologic processes. However, it is not clear how parameters and observations influence the degree of overparameterization, equifinality of parameter values, and uncertainty. This study investigated the impact of the numbers of observations and parameters on calibration quality including equifinality among calibrated parameter values, model performance, and output/parameter uncertainty using the Soil and Water Assessment Tool model. In the experiments, the number of observations was increased by expanding the calibration period or by including measurements made at inner points of a watershed. Similarly, additional calibration parameters were included in the order of their sensitivity. Then, unique sets of parameters were calibrated with the same objective function, optimization algorithm, and stopping criteria but different numbers of observations. The calibration quality was quantified with statistics calculated based on the ‘behavioural’ parameter sets, identified using 1% and 5% cut‐off thresholds in a generalized likelihood uncertainty estimation framework. The study demonstrated that equifinality, model performance, and output/parameter uncertainty were responsive to the numbers of observations and calibration parameters; however, the relationship between the numbers, equifinality, and uncertainty was not always conclusive. Model performance improved with increased numbers of calibration parameters and observations, and substantial equifinality did neither necessarily mean bad model performance nor large uncertainty in the model outputs and parameters. Copyright © 2015 John Wiley & Sons, Ltd.     

Choosing an arbitrary calibration period for hydrologic models: How much does it influence water balance simulations?

The selection of calibration and validation time periods in hydrologic modelling is often done arbitrarily. Nonstationarity can lead to an optimal parameter set for one period which may not accurately simulate another. However, there is still much to be learned about the responses of hydrologic models to nonstationary conditions. We investigated how the selection of calibration and validation periods can influence water balance simulations. We calibrated Soil and Water Assessment Tool hydrologic models with observed streamflow for three United States watersheds (St. Joseph River of Indiana/Michigan, Escambia River of Florida/Alabama, and Cottonwood Creek of California), using time period splits for calibration/validation. We found that the choice of calibration period (with different patterns of observed streamflow, precipitation, and air temperature) influenced the parameter sets, leading to dissimilar simulations of water balance components. In the Cottonwood Creek watershed, simulations of 50-year mean January streamflow varied by 32%, because of lower winter precipitation and air temperature in earlier calibration periods on calibrated parameters, which impaired the ability for models calibrated to earlier periods to simulate later periods. Peaks of actual evapotranspiration for this watershed also shifted from April to May due to different parameter values depending on the calibration period's winter air temperatures. In the St. Joseph and Escambia River watersheds, adjustments of the runoff curve number parameter could vary by 10.7% and 20.8%, respectively, while 50-year mean monthly surface runoff simulations could vary by 23%–37% and 169%–209%, depending on the observed streamflow and precipitation of the chosen calibration period. It is imperative that calibration and validation time periods are chosen selectively instead of arbitrarily, for instance using change point detection methods, and that the calibration periods are appropriate for the goals of the study, considering possible broad effects of nonstationary time series on water balance simulations. It is also crucial that the hydrologic modelling community improves existing calibration and validation practices to better include nonstationary processes.     

Données isotopiques (8786/Sr) et changements hydrologiques depuis 15 000 ans sur l'Altiplano andin

Abstract

In catchments characterized by spatially varying hydrological processes and responses, the optimal parameter values or regions of attraction in parameter space may differ with location-specific characteristics and dominating processes. This paper evaluates the value of semi-distributed calibration parameters for large-scale streamflow simulation using the spatially distributed LISFLOOD model. We employ the Shuffled Complex Evolution Metropolis (SCEM-UA) global optimization algorithm to infer the calibration parameters using daily discharge observations. The resulting posterior parameter distribution reflects the uncertainty about the model parameters and forms the basis for making probabilistic flow predictions. We assess the value of semi-distributing the calibration parameters by comparing three different calibration strategies. In the first calibration strategy uniform values over the entire area of interest are adopted for the unknown parameters, which are calibrated against discharge observations at the downstream outlet of the catchment. In the second calibration strategy the parameters are also uniformly distributed, but they are calibrated against observed discharges at the catchment outlet and at internal stations. In the third strategy a semi-distributed approach is adopted. Starting from upstream, parameters in each subcatchment are calibrated against the observed discharges at the outlet of the subcatchment. In order not to propagate upstream errors in the calibration process, observed discharges at upstream catchment outlets are used as inflow when calibrating downstream subcatchments. As an illustrative example, we demonstrate the methodology for a part of the Morava catchment, covering an area of approximately 10 000 km². The calibration results reveal that the additional value of the internal discharge stations is limited when applying a lumped parameter approach. Moving from a lumped to a semi-distributed parameter approach: (i) improves the accuracy of the flow predictions, especially in the upstream subcatchments; and (ii) results in a more correct representation of flow prediction uncertainty. The results show the clear need to distribute the calibration parameters, especially in large catchments characterized by spatially varying hydrological processes and responses.     

Sensitivity-guided reduction of parametric dimensionality for multi-objective calibration of watershed models

Problem complexity for watershed model calibration is heavily dependent on the number of parameters that can be identified during model calibration. This study investigates the use of global sensitivity analysis as a screening tool to reduce the parametric dimensionality of multi-objective hydrological model calibration problems while maximizing the information extracted from hydrological response data. This study shows that by expanding calibration problem formulations beyond traditional, statistical error metrics to also include metrics that capture indices or signatures of hydrological function, it is possible to reduce the complexity of calibration while maintaining high quality model predictions. The sensitivity-guided calibration is demonstrated using the Sacramento Soil Moisture Accounting (SAC-SMA) conceptual rainfall–runoff model of moderate complexity (i.e., up to 14 freely varying parameters). Using both statistical and hydrological metrics, optimization results demonstrate that parameters controlling at least 20% of the model output variance (through individual effects and interactions) should be included in the calibration process. This threshold generally yields 30–40% reductions in the number of SAC-SMA parameters requiring calibration – setting the others to a priori values – while maintaining high quality predictions. Two parameters are recommended to be calibrated in all cases (percent impervious area and lower zone tension water storage), three parameters are needed in drier watersheds (additional impervious area, riparian zone vegetation, and percent of percolation going to tension storage), and the lower zone parameters are crucial unless the watershed is very dry. Overall, this study demonstrates that a coupled, multi-objective sensitivity and calibration analysis better captures differences between watersheds during model calibration and serves to maximize the value of available watershed response time series. These contributions are particularly important given the ongoing development of more complex integrated models, which will require new tools to address the growing discrepancy between the information content of hydrological data and the number of model parameters that have to be estimated.     

Application of a land surface model for simulating rainfall streamflow hydrograph: 2. Comparison with hydrological models

Rainfall runoff hydrographs for 12 river basins ∼10³ km² in area, simulated using land surface model SWAP, are compared with analogous hydrographs obtained using hydrological models that took part in the International Model Parameter Estimation Experiment project and demonstrated the best results. All models were calibrated against data on daily river runoff from each basin over a 20-year period (1960–1979). Optimized model parameters were used to simulate runoff hydrographs for the following 19 years (1980–1998). The comparison of the modeled hydrographs for 12 basins in different calculational periods demonstrated that the SWAP model can simulate river runoff with an accuracy comparable with that of hydrological models.     

A probabilistic framework for floodplain mapping using hydrological modeling and unsteady hydraulic modeling

ABSTRACT

Prediction of design hydrographs is key in floodplain mapping using hydraulic models, which are either steady state or unsteady. The former, which require only an input peak, substantially overestimate the volume of water entering the floodplain compared to the more realistic dynamic case simulated by the unsteady models that require the full hydrograph. Past efforts to account for the uncertainty of boundary conditions using unsteady hydraulic modeling have been based largely on a joint flood frequency–shape analysis, with only a very limited number of studies using hydrological modeling to produce the design hydrographs. This study therefore presents a generic probabilistic framework that couples a hydrological model with an unsteady hydraulic model to estimate the uncertainty of flood characteristics. The framework is demonstrated on the Swannanoa River watershed in North Carolina, USA. Given its flexibility, the framework can be applied to study other sources of uncertainty in other hydrological models and watersheds.     

SCE-UA方法在新安江模型参数优化中的应用

以前在使用新安江模型时人们遇到的最大困难可归因于缺乏有效的参数全局优化的数学方法,事实上对于一个缺乏经验的人来说,模型参数的人工试错计算的过程是一个相当不容易的过程,并且耗时颇多,为此,近些年来研究者们正在探索把概念性水文模型中的专家经验与自动优化计算相结合的方法或者数学优化中的全局优化方法,如SEC-UA方法,本文首先简述新安江模型,而后采用3个大小和气候条件各不相同的流域对SCE-UA算法就在新安江模型计算的参数优化进行了研究,研究结果表明,SCE-UA算法用来进行新安江模型的参数优化所取得的效果是好的,从率定和检验的结果来看,SCE-UA算法可以使得率定的新安江模型的参数达到全局最优并且从概念上也合理。     

Parameter identification and uncertainty analysis for simulating streamflow in a river basin of Eastern India

Uncertainty is inherent in modelling studies. However, the quantification of uncertainties associated with a model is a challenging task, and hence, such studies are somewhat limited. As distributed or semi‐distributed hydrological models are being increasingly used these days to simulate hydrological processes, it is vital that these models should be equipped with robust calibration and uncertainty analysis techniques. The goal of the present study was to calibrate and validate the Soil and Water Assessment Tool (SWAT) model for simulating streamflow in a river basin of Eastern India, and to evaluate the performance of salient optimization techniques in quantifying uncertainties. The SWAT model for the study basin was developed and calibrated using Parameter Solution (ParaSol), Sequential Uncertainty Fitting Algorithm (SUFI‐2) and Generalized Likelihood Uncertainty Estimation (GLUE) optimization techniques. The daily observed streamflow data from 1998 to 2003 were used for model calibration, and those for 2004–2005 were used for model validation. Modelling results indicated that all the three techniques invariably yield better results for the monthly time step than for the daily time step during both calibration and validation. The model performances for the daily streamflow simulation using ParaSol and SUFI‐2 during calibration are reasonably good with a Nash–Sutcliffe efficiency and mean absolute error (MAE) of 0.88 and 9.70 m³/s for ParaSol, and 0.86 and 10.07 m³/s for SUFI‐2, respectively. The simulation results of GLUE revealed that the model simulates daily streamflow during calibration with the highest accuracy in the case of GLUE (R² = 0.88, MAE = 9.56 m³/s and root mean square error = 19.70 m³/s). The results of uncertainty analyses by SUFI‐2 and GLUE were compared in terms of parameter uncertainty. It was found that SUFI‐2 is capable of estimating uncertainties in complex hydrological models like SWAT, but it warrants sound knowledge of the parameters and their effects on the model output. On the other hand, GLUE predicts more reliable uncertainty ranges (R‐factor = 0.52 for daily calibration and 0.48 for validation) compared to SUFI‐2 (R‐factor = 0.59 for daily calibration and 0.55 for validation), though it is computationally demanding. Although both SUFI‐2 and GLUE appear to be promising techniques for the uncertainty analysis of modelling results, more and more studies in this direction are required under varying agro‐climatic conditions for assessing their generic capability. Copyright © 2015 John Wiley & Sons, Ltd.     

Catchment properties,function, and conceptual model representation: is there a correspondence?

This study investigates the possible correspondence between catchment structure, as represented by perceptual hydrological models developed from fieldwork investigations, and mathematical model structures, selected on the basis of reproducing observed catchment hydrographs. Three Luxembourgish headwater catchments are considered, where previous fieldwork suggested distinct flow‐generating mechanisms and hydrological dynamics. A set of lumped conceptual model structures are hypothesized and implemented using the SUPERFLEX framework. Following parameter calibration, the model performance is examined in terms of predictive accuracy, quantification of uncertainty, and the ability to reproduce the flow–duration curve signature. Our key research question is whether differences in the performance of the conceptual model structures can be interpreted based on the dominant catchment processes suggested from fieldwork investigations. For example, we propose that the permeable bedrock and the presence of multiple aquifers in the Huewelerbach catchment may explain the superior performance of model structures with storage elements connected in parallel. Conversely, model structures with serial connections perform better in the Weierbach and Wollefsbach catchments, which are characterized by impermeable bedrock and dominated by lateral flow. The presence of threshold dynamics in the Weierbach and Wollefsbach catchments may favour nonlinear models, while the smoother dynamics of the larger Huewelerbach catchment were suitably reproduced by linear models. It is also shown how hydrologically distinct processes can be effectively described by the same mathematical model components. Major research questions are reviewed, including the correspondence between hydrological processes at different levels of scale and how best to synthesize the experimentalist's and modeller's perspectives. Copyright © 2013 John Wiley & Sons, Ltd.     

Assessing effects of model complexity and structure on predictions of hydrological responses using serial and parallel model design

By utilizing functional relationships based on observations at plot or field scales, water quality models first compute surface runoff and then use it as the primary governing variable to estimate sediment and nutrient transport. When these models are applied at watershed scales, this serial model structure, coupling a surface runoff sub-model with a water quality sub-model, may be inappropriate because dominant hydrological processes differ among scales. A parallel modeling approach is proposed to evaluate how best to combine dominant hydrological processes for predicting water quality at watershed scales. In the parallel scheme, dominant variables of water quality models are identified based entirely on their statistical significance using time series analysis. Four surface runoff models of different model complexity were assessed using both the serial and parallel approaches to quantify the uncertainty on forcing variables used to predict water quality. The eight alternative model structures were tested against a 25-year high-resolution data set of streamflow, suspended sediment discharge, and phosphorous discharge at weekly time steps. Models using the parallel approach consistently performed better than serial-based models, by having less error in predictions of watershed scale streamflow, sediment and phosphorus, which suggests model structures of water quantity and quality models at watershed scales should be reformulated by incorporating the dominant variables. The implication is that hydrological models should be constructed in a way that avoids stacking one sub-model with one set of scale assumptions onto the front end of another sub-model with a different set of scale assumptions.