A multi-objective calibration approach using in-situ soil moisture data for improved hydrological simulation of the Prairies

ABSTRACT

Traditionally, hydrological models are only calibrated to reproduce streamflow regime without considering other hydrological state variables, such as soil moisture and evapotranspiration. Limited studies have been performed on constraining the model parameters, despite the fact that the presence of a large number of parameters may provide large degree of freedom, resulting in equifinality and poor model performance. In this study, a multi-objective optimization approach is adopted, and both streamflow and soil moisture data are calibrated simultaneously for an experimental study basin in the Saskatchewan Prairies in western Canada. The results of this study show that the multi-objective calibration improves model fidelity compared to the single objective calibration. Moreover, the study demonstrates that single objective calibration performed against only streamflow can fairly mimic the streamflow hydrograph but does not yield realistic estimation of other fluxes such as evapotranspiration and soil moisture (especially in deeper soil layers).     

Error distribution modelling of satellite soil moisture measurements for hydrological applications

Satellite‐based soil moisture data accuracies are of important concerns by hydrologists because they could significantly influence hydrological modelling uncertainty. Without proper quantification of their uncertainties, it is difficult to optimize the hydrological modelling system and make robust decisions. Currently, the satellite soil moisture data uncertainty has been limited to summary statistics with the validations mainly from the in situ measurements. This study attempts to build the first error distribution model with additional higher‐order uncertainty modelling for satellite soil moisture observations. The methodology is demonstrated by a case study using the Soil Moisture and Ocean Salinity satellite soil moisture observations. The validation is based on soil moisture estimates from hydrological modelling, which is more relevant to the intended data use than the in situ measurements. Four probability distributions have been explored to find suitable error distribution curves using the statistical tests and bootstrapping resampling technique. General extreme value is identified as the most suitable one among all the curves. The error distribution model is still in its infant stage, which ignores spatial and temporal correlations, and nonstationarity. Further improvements should be carried out by the hydrological community by expanding the methodology to a wide range of satellite soil moisture data using different hydrological models. Copyright © 2016 John Wiley & Sons, Ltd.     

Could operational hydrological models be made compatible with satellite soil moisture observations?

Soil moisture is a significant state variable in flood forecasting. Nowadays more and more satellite soil moisture products are available, yet their usage in the operational hydrology is still limited. This is because the soil moisture state variables in most operational hydrological models (mostly conceptual models) are over‐simplified—resulting in poor compatibility with the satellite soil moisture observations. A case study is provided to discuss this in more detail, with the adoption of the XAJ model and the Soil Moisture and Ocean Salinity (SMOS) level‐3 soil moisture observation to illustrate the relevant issues. It is found that there are three distinct deficiencies existed in the XAJ model that could cause the mismatch issues with the SMOS soil moisture observation: (i) it is based on runoff generation via the field capacity excess mechanism (interestingly, such a runoff mechanism is called the saturation excess in XAJ while in fact it is clearly a misnomer); (ii) evaporation occurs at the potential rate in its upper soil layer until the water storage in the upper layer is exhausted, and then the evapotranspiration process from the lower layers will commence – leading to an abrupt soil water depletion in the upper soil layer; (iii) it uses the multi‐bucket concept at each soil layer – hence the model has varied soil layers. Therefore, it is a huge challenge to make an operational hydrological model compatible with the satellite soil moisture data. The paper argues that this is possible and some new ideas have been explored and discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

Configuration of hydrological processes in a steep hillslope through causality analysis of soil moisture measurements

The vertical and lateral profiles of temporal variations in soil moisture are important for understanding the hydrological process along hillside transects. In this study, relationships among measured soil moistures were explored to configure the hydrological contributions of different flowpaths. All the measured soil moistures included a common stochastic structure because rainfall, the hydrometeological driver, is the main factor that determines the soil moisture response feature, and the infiltration process through the topsoil at a shallow depth is also common in all measured soil moisture histories. Therefore, the relationships between the measured series are also affected by both rainfall and topsoil infiltration. The common stochastic structure of the soil moisture series was removed via a prewhitening procedure. A systematic analysis procedure is presented to delineate the exclusive causal relationships among multiple soil moisture measurements. A monitoring system based on multiplexed time domain reflectometry was used to obtain soil moisture time series along two transects on a steep hillslope during the rainy season. The application of the proposed method for monitoring points in two adjacent locations provided 8, 12, 14, and 13, 16, 22 causal relationships for vertical, lateral in parallel, and diagonal directions, respectively, along the two transects. The point‐based contributions of the internal flowpath can be evaluated as the correlation is normalized in the context of inflow and outflow. The hydrological processes in the soil layer, vertical flow, lateral flow, downslope recharge, and return flow were quantified, and the relative importance of each hydrological component was determined to improve our understanding of the hydrological processes along the two transects of the study area. Copyright © 2011 John Wiley & Sons, Ltd.     

Modelling spatio-temporal soil moisture dynamics in mountain tundra

Soil moisture has a fundamental influence on the processes and functions of tundra ecosystems. Yet, the local dynamics of soil moisture are often ignored, due to the lack of fine resolution, spatially extensive data. In this study, we modelled soil moisture with two mechanistic models, SpaFHy (a catchment-scale hydrological model) and JSBACH (a global land surface model), and examined the results in comparison with extensive growing-season field measurements over a mountain tundra area in northwestern Finland. Our results show that soil moisture varies considerably in the study area and this variation creates a mosaic of moisture conditions, ranging from dry ridges (growing season average 12 VWC%, Volumetric Water Content) to water-logged mires (65 VWC%). The models, particularly SpaFHy, simulated temporal soil moisture dynamics reasonably well in parts of the landscape, but both underestimated the range of variation spatially and temporally. Soil properties and topography were important drivers of spatial variation in soil moisture dynamics. By testing the applicability of two mechanistic models to predict fine-scale spatial and temporal variability in soil moisture, this study paves the way towards understanding the functioning of tundra ecosystems under climate change.     

Deriving hydrological signatures from soil moisture data

Soil moisture is an important variable in hydrological studies, but has been little used for model evaluation due to its high sensitivity to local conditions. We explore the possibility to derive hydrological signatures from soil moisture data that could overcome this limitation and be helpful for model evaluation. A set of eight hydrological signatures was built, encompassing long-term to short-term time scales. These signatures were tested according to robustness, representativeness and discriminatory power, using in situ data sets from New Zealand, including national network and experimental watershed data. Field capacity, type of soil moisture distribution, and starting dates of seasonal transitions typically meet the criteria, subject to uniform sensor depths and homogeneous land uses. Durations of seasonal transitions and event-based signatures showed higher variability and lower discriminatory power. In general, long-term signatures are more robust, more representative of large areas, and have a high discriminatory power, thus showing a good potential for use in diagnostic evaluation of regional models.     

Perspectives in using a remotely sensed dryness index in distributed hydrological models at the river‐basin scale

In a previous study a spatially distributed hydrological model, based on the MIKE SHE code, was constructed and validated for the 375 000 km² Senegal River basin in West Africa. The model was constructed using spatial data on topography, soil types and vegetation characteristics together with time‐series of precipitation from 112 stations in the basin. The model was calibrated and validated based on river discharge data from nine stations in the basin for 11 years. Calibration and validation results suggested that the spatial resolution of the input data in parts of the area was not sufficient for a satisfactory evaluation of the modelling performance. The study further examined the spatial patterns in the model input and output, and it was found that particularly the spatial resolution of the precipitation input had a major impact on the model response. In an attempt to improve the model performance, this study examines a remotely sensed dryness index for its relationship to simulated soil moisture and evaporation for six days in the wet season 1990. The index is derived from observations of surface temperature and vegetation index as measured by the NOAA Advanced Very High Resolution Radiometer (AVHRR) sensor. The correlation results between the index and the simulation results are of mixed quality. A sensitivity analysis, conducted on both estimates, reveals significant uncertainties in both. The study suggests that the remotely sensed dryness index with its current use of NOAA AVHRR data does not offer information that leads to a better calibration or validation of the simulation model in a spatial sense. The method potentially may become more suitable with the use of the upcoming high‐resolution temporal Meteosat Second Generation data. Copyright © 2002 John Wiley & Sons, Ltd.     

Analysis of incorporating groundwater exchanges in hydrological models

In many catchments, the geographical demarcation does not coincide with the limits of the aquifers, so groundwater may be exchanged beyond their topographic boundaries. By studying groundwater exchanges, the natural resources of a catchment can be better assessed, and the divergences between hydrological models and measurements can be explained. The aim of this work is to reveal the importance of including groundwater exchanges in the hydrological modelling of some catchments, using a water balance model. For this purpose, a simple example is conducted. The so‐called parent model scheme is modified to only allow groundwater exchanges, and it is applied to the headwater of the Segura River Basin District, located in the southeast of Spain. This area is selected because groundwater plays an important role in surface hydrology. The results reveal that groundwater exchanges cannot be neglected in some catchments when assessing water resources because their integration in the hydrological model corrects errors in the water balance. Moreover, this paper proves that water balance models are a useful tool for estimating groundwater exchanges between catchments, which can be contrasted with more complex distributed models or isotopic tracers if there is enough information available. Copyright © 2015 John Wiley & Sons, Ltd.     

Improving the representation of soil moisture by using a semi‐analytical infiltration model

Soil moisture is widely recognized as a fundamental variable governing the mass and energy fluxes between the land surface and the atmosphere. In this study, the soil moisture modelling at sub‐daily timescale is addressed by using an accurate representation of the infiltration component. For that, the semi‐analytical infiltration model proposed by Corradini et al. (1997) has been incorporated into a soil water balance model to simulate the evolution in time of surface and profile soil moisture. The performances of this new soil moisture model [soil water balance module‐semi‐analytical (SWBM‐SA)] are compared with those of a precedent version [SWBM‐Green–Ampt (GA)] where the GA approach was employed. Their capability to reproduce in situ soil moisture observations at three sites in Italy, Spain and France is analysed. Hourly observations of quality‐checked rainfall, temperature and soil moisture data for a 2‐year period are used for testing the modelling approaches. Specifically, different configurations for the calibration and validation of the models are adopted by varying a single parameter, that is, the saturated hydraulic conductivity. Results indicate that both SWBMs are able to reproduce satisfactorily the hourly soil moisture temporal pattern for the three sites with root mean square errors lower than 0.024 m³/m³ both in the calibration and validation periods. For all sites, the SWBM‐SA model outperforms the SWBM‐GA with an average reduction of the root mean square error of ~20%. Specifically, the higher improvement is observed for the French site for which in situ observations are measured at 30 cm depth, and this is attributed to the capability of the SA infiltration model to simulate the time evolution of the whole soil moisture profile. The reasonable models performance coupled with the need to calibrate only a single parameter makes them useful tools for soil moisture simulation in different regions worldwide, also in scarcely gauged areas. Copyright © 2013 John Wiley & Sons, Ltd.     

Year‐round estimation of soil moisture content using temporally variable soil hydraulic parameters

Soil moisture plays a key role in the hydrological cycle as it controls the flux of water between soil, vegetation, and atmosphere. This study is focused on a year‐round estimation of soil moisture in a forested mountain area using the bucket model approach. For this purpose, three different soil moisture models are utilised. The procedure is based on splitting the whole year into two complement periods (dormant and vegetation). Model parameters are allowed to vary between the two periods and also from year to year in the calibration procedure. Consequently, two sets of average model parameters corresponding to dormant and vegetation seasons are proposed. The process of splitting is strongly supported by the experimental data, and it enables us to variate saturated hydraulic conductivity and pore‐size characterisation. The use of the two different parameter sets significantly enhances the simulation of two (Teuling and Troch model and soil water balance model‐green–ampt [SWBM‐GA]) out of three models in the 6‐year period from 2009 to 2014. For these two models, the overall Nash‐Sutcliffe coefficient increased from 0.64 to 0.79 and from 0.55 to 0.80. The third model (the Laio approach) proved to be insensitive to parameter changes due to its insufficient drainage prediction. The variability of the warm and cold parameter sets between particular years is more pronounced in the warm periods. The cold periods exhibited approximately similar character during all 6 years.     

Evaluation of satellite-based rainfall products for hydrological modelling in Morocco

ABSTRACT

Several satellite-based precipitation estimates are becoming available at a global scale, providing new possibilities for water resources modelling, particularly in data-sparse regions and developing countries. This work provides a first validation of five different satellite-based precipitation products (TRMM-3B42 v6 and v7, RFE 2.0, PERSIANN-CDR, CMORPH1.0 version 0.x) in the 1785 km² Makhazine catchment (Morocco). Precipitation products are first compared against ground observations. Ten raingauges and four different interpolation methods (inverse distance, nearest neighbour, ordinary kriging and residual kriging with altitude) were used to compute a set of interpolated precipitation reference fields. Second, a parsimonious conceptual hydrological model is considered, with a simulation approach based on the random generation of model parameters drawn from existing parameter set libraries, to compare the different precipitation inputs. The results indicate that (1) all four interpolation methods, except the nearest neighbour approach, give similar and valid precipitation estimates at the catchment scale; (2) among the different satellite-based precipitation estimates verified, the TRMM-3B42 v7 product is the closest to observed precipitation, and (3) despite poor performance at the daily time step when used in the hydrological model, TRMM-3B42 v7 estimates are found adequate to reproduce monthly dynamics of discharge in the catchment. The results provide valuable perspectives for water resources modelling of data-scarce catchments with satellite-based rainfall data in this region.

Editor M.C. Acreman; Associate editor N. Verhoest     

Determining hydrological regimes in an agriculturally used tropical inland valley wetland in Central Uganda using soil moisture,groundwater, and digital elevation data

Inadequate knowledge exists on the distribution of soil moisture and shallow groundwater in intensively cultivated inland valley wetlands in tropical environments, which are required for determining the hydrological regime. This study investigated the spatial and temporal variability of soil moisture along 4 hydrological positions segmented as riparian zone, valley bottom, fringe, and valley slope in an agriculturally used inland valley wetland in Central Uganda. The determined hydrological regimes of the defined hydrological positions are based on soil moisture deficit calculated from the depth to the groundwater table. For that, the accuracy and reliability of satellite‐derived surface models, SRTM‐30m and TanDEM‐X‐12m, for mapping microscale topography and hydrological regimes are evaluated against a 5‐m digital elevation model (DEM) derived from field measurements. Soil moisture and depth to groundwater table were measured using frequency domain reflectometry sensors and piezometers installed along the hydrological positions, respectively. Results showed that spatial and temporal variability in soil moisture increased significantly (p < .05) towards the riparian zone; however, no significant difference was observed between the valley bottom and riparian zone. The distribution of soil hydrological regimes, saturated, near‐saturated, and nonsaturated regimes does not correlate with the hydrological positions. This is due to high spatial and temporal variability in depth to groundwater and soil moisture content across the valley. Precipitation strongly controlled the temporal variability, whereas microscale topography, soil properties, distance from the stream, anthropogenic factors, and land use controlled the spatial variability in the inland valley. TanDEM‐X DEM reasonably mapped the microscale topography and thus soil hydrological regimes relative to the Shuttle Radar Topography Mission DEM. The findings of the study contribute to improved understanding of the distribution of hydrological regimes in an inland valley wetland, which is required for a better agricultural water management planning.     

A watershed rainfall data recovery approach with application to distributed hydrological models

Watershed areal rainfall estimation, which is one of the most important and fundamental aspects in hydrological forecasting and various kinds of catchment‐scale hydrological models, is widely used in the analysis of hydrological regime change, and its precision has a direct influence on the accuracy of hydrological forecasting and hydrological simulation. In China, it is difficult to obtain the watershed areal rainfall estimate with reliable precision and avoid the phenomenon of ‘the same effect of different parameters’ because of the low density of the rain gauge network. Therefore, a watershed rainfall data recovery approach of improving the precision of watershed areal rainfall estimation is proposed here. This approach is to build new observatories, establish the time–space relations of rainfall between newly built observatories and previously built observatories in a relatively short interval and then recover the rainfall data of newly built observatories prior to their construction through simulating the relations over a longer time. As a result, watershed rainfall information could be elaborated to improve the precision of watershed areal rainfall estimate and avoid the phenomenon of ‘the same effect of different parameters’ to a certain degree in the process of hydrological simulation. The approach is used in the hydrological simulation of Hali River catchment. In combination with the Soil Water Assessment Tool model, a better result can be obtained in the hydrological simulation. Therefore, the approach can be used in other similar catchments. Copyright © 2011 John Wiley & Sons, Ltd.     

Model calibration using hydropedological insights to improve the simulation of internal hydrological processes using SWAT+

Soils affect the distribution of hydrological processes by partitioning precipitation into different components of the water balance. Therefore, understanding soil-water dynamics at a catchment scale remains imperative to future water resource management. In this study, the value of hydropedological insights was examined to calibrate a processes-based model. Soil morphology was used as soft data to assist in the calibration of the Soil Water Assessment Tool (SWAT+) model at five different catchment scales (48, 56, 174, 674, and 2421 km²) in the Sabie River catchment, South Africa. The aim of this study was to calibrate the SWAT+ model to accurately simulate long-term monthly streamflow predictions as well as to reflect internal soil hydrological processes using a procedure focusing on hydropedology as a calibration tool in a multigauge system. Results indicated that calibration improved streamflow predictions where R² improved by 2%–8%. Nash-Sutcliffe Efficiency (NSE) improved from negative correlations to values exceeding 0.5 at four of the five catchment scales compared to the uncalibrated model. Results confirm that soil mapping units can be calibrated individually within SWAT+ to improve the representation of hydrological processes. Particularly, the spatial linkage between hydropedology and hydrological processes, which is captured within the soil map of the catchment, can be adequately reflected within the model simulations after calibration. This research will lead to an improved understanding of hydropedology as soft data to improve hydrological modelling accuracy.     

Sensitivity analysis of EUROSEM using Monte Carlo simulation I: hydrological,soil and vegetation parameters

Knowledge about model uncertainty is essential for erosion modelling and provides important information when it comes to parameterizing models. In this paper a sensitivity analysis of the European soil erosion model (EUROSEM) is carried out using Monte Carlo simulation, suitable for complex non‐linear models, using time‐dependent driving variables. The analysis revealed some important characteristics of the model. The variability of the static output parameters was generally high, with the hydrologic parameters being the most important ones, especially saturated hydraulic conductivity and net capillary drive followed by the percentage basal area for the hydrological and vegetation parameters and detachability and cohesion for the soil erosion parameters. Overall, sensitivity to vegetation parameters was insignificant. The coefficient of variation for the sedigraph was higher than for the hydrograph, especially from the beginning of the rainstorm and up to the peak, and may explain difficulties encountered when trying to match simulated hydrographs and sedigraphs with observed ones. The findings from this Monte Carlo simulation calls for improved within‐storm modelling of erosion processes in EUROSEM. Information about model uncertainty will be incorporated in a new EUROSEM user interface. Copyright © 2000 John Wiley & Sons, Ltd.     

Assessment of the MODIS global evapotranspiration algorithm using eddy covariance measurements and hydrological modelling in the Rio Grande basin

Abstract

Remote sensing is considered the most effective tool for estimating evapotranspiration (ET) over large spatial scales. Global terrestrial ET estimates over vegetated land surfaces are now operationally produced at 1-km spatial resolution using data from the Moderate Resolution Imaging Spectroradiometer (MODIS) and the MOD16 algorithm. To evaluate the accuracy of this product, ground-based measurements of energy fluxes obtained from eddy covariance sites installed in tropical biomes and from a hydrological model (MGB-IPH) were used to validate MOD16 products at local and regional scales. We examined the accuracy of the MOD16 algorithm at two sites in the Rio Grande basin, Brazil, one characterized by a sugar-cane plantation (USE), the other covered by natural savannah vegetation (PDG) for the year 2001. Inter-comparison between 8-day average MOD16 ET estimates and flux tower measurements yielded correlations of 0.78 to 0.81, with root mean square errors (RMSE) of 0.78 and 0.46 mm d^-1, at PDG and USE, respectively. At the PDG site, the annual ET estimate derived by the MOD16 algorithm was 19% higher than the measured amount. For the average annual ET at the basin-wide scale (over an area of 145 000 km²), MOD16 estimates were 21% lower than those from the hydrological model MGB-IPH. Misclassification of land use and land cover was identified as the largest contributor to the error from the MOD16 algorithm. These estimates improve significantly when results are integrated into monthly or annual time intervals, suggesting that the algorithm has a potential for spatial and temporal monitoring of the ET process, continuously and systematically, through the use of remote sensing data.

Editor D. Koutsoyiannis; Associate editor T. Wagener

Citation Ruhoff, A.L., Paz, A.R., Aragao, L.E.O.C., Mu, Q., Malhi, Y., Collischonn, W., Rocha, H.R., and Running, S.W., 2013. Assessment of the MODIS global evapotranspiration algorithm using eddy covariance measurements and hydrological modelling in the Rio Grande basin. Hydrological Sciences Journal, 58 (8), 1658–1676.     

Operational performance of current synthetic aperture radar sensors in mapping soil surface characteristics in agricultural environments: application to hydrological and erosion modelling

Synthetic aperture radar (SAR) sensors are often used to characterize the surface of bare soils in agricultural environments. They enable the soil moisture and roughness to be estimated with constraints linked to the configurations of the sensors (polarization, incidence angle and radar wavelength). These key soil characteristics are necessary for different applications, such as hydrology and risk prediction. This article reviews the potential of currently operational SAR sensors and those planned for the near future to characterize soil surface as a function of users' needs. It details what it is possible to achieve in terms of mapping soil moisture and roughness by specifying optimal radar configurations and the precision associated with the estimation of soil surface characteristics. The summary carried out for the present article shows that mapping soil moisture is optimal with SAR sensors at low incidence angles (<35 ). This configuration, which enables an estimated moisture accuracy greater than 6% is possible several times a month taking into account all the current and future sensors. Concerning soil roughness, it is best mapped using three classes (smooth, moderately rough, and rough). Such mapping requires high‐incidence data, which is possible with certain current sensors (RADARSAT‐1 and ASAR both in band C). When L‐band sensors (ALOS) become available, this mapping accuracy should improve because the sensitivity of the radar signal to Soil Surface Characteristics (SSC) increases with wavelength. Finally, the polarimetric mode of certain imminent sensors (ALOS, RADARSAT‐2, TerraSAR‐X, etc.), and the possibility of acquiring data at very high spatial resolution (metre scale), offer great potential in terms of improving the quality of SSC mapping. Copyright © 2007 John Wiley & Sons, Ltd.     

Uncertainty assessment in river flow projections for Ethiopia’s Upper Awash Basin using multiple GCMs and hydrological models

ABSTRACT

Uncertainty in climate change impacts on river discharge in the Upper Awash Basin, Ethiopia, is assessed using five MIKE SHE hydrological models, six CMIP5 general circulation models (GCMs) and two representative concentration pathways (RCP) scenarios for the period 2071–2100. Hydrological models vary in their spatial distribution and process representations of unsaturated and saturated zones. Very good performance is achieved for 1975–1999 (NSE: 0.65–0.8; r: 0.79–0.93). GCM-related uncertainty dominates variability in projections of high and mean discharges (mean: –34% to +55% for RCP4.5, – 2% to +195% for RCP8.5). Although GCMs dominate uncertainty in projected low flows, inter-hydrological model uncertainty is considerable (RCP4.5: –60% to +228%, RCP8.5: –86% to +337%). Analysis of variance uncertainty attribution reveals that GCM-related uncertainty occupies, on average, 68% of total uncertainty for median and high flows and hydrological models no more than 1%. For low flows, hydrological model uncertainty occupies, on average, 18% of total uncertainty; GCM-related uncertainty remains substantial (average: 28%).     

Simulating the water budget of a Prairie Potholes complex from LiDAR and hydrological models in North Dakota,USA

Abstract

Hydrological processes of the wetland complex in the Prairie Pothole Region (PPR) are difficult to model, partly due to a lack of wetland morphology data. We used Light Detection And Ranging (LiDAR) data sets to derive wetland features; we then modelled rainfall, snowfall, snowmelt, runoff, evaporation, the “fill-and-spill” mechanism, shallow groundwater loss, and the effect of wet and dry conditions. For large wetlands with a volume greater than thousands of cubic metres (e.g. about 3000 m³), the modelled water volume agreed fairly well with observations; however, it did not succeed for small wetlands (e.g. volume less than 450 m³). Despite the failure for small wetlands, the modelled water area of the wetland complex coincided well with interpretation of aerial photographs, showing a linear regression with R² of around 0.80 and a mean average error of around 0.55 km². The next step is to improve the water budget modelling for small wetlands.

Editor Z.W. Kundzewicz; Associate editor X. Chen

Citation Huang, S.L., Young, C., Abdul-Aziz, O.I., Dahal, D., Feng, M., and Liu, S.G., 2013. Simulating the water budget of a Prairie Potholes complex from LiDAR and hydrological models in North Dakota, USA. Hydrological Sciences Journal, 58 (7), 1434–1444.