Neural network approach to stream-aquifer modeling for improved river basin management

Journal of Hydrology 391 (2010) 235–247

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Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol

Neural network approach to stream-aquifer modeling for improved river basin management Enrique Triana a, John W. Labadie b,*, Timothy K. Gates b, Charles W. Anderson c a

AECOM USA Inc., 215 Union Blvd. Suite 500, Lakewood, CO 80228, USA Dept. of Civil and Environmental Engineering, Colorado State Univ., Fort Collins, CO 80523, USA c Dept. of Computer Science, Colorado State Univ., Fort Collins, CO 80523, USA b

a r t i c l e

i n f o

Article history: Received 15 August 2009 Received in revised form 13 July 2010 Accepted 20 July 2010 This manuscript was handled by A. Bardossy, Editor-n-Chief, with the assistance of P.C. Nayak, Associate Editor Keywords: Artificial neural network Geographic information system Numerical groundwater modeling River basin management Salinity Stream-aquifer modeling

s u m m a r y Artificial neural networks (ANNs) are applied to efficient modeling of stream-aquifer responses in an intensively irrigated river basin under a variety of water management alternatives for improving irrigation efficiency, reducing soil water salinity, increasing crop yields, controlling nonbeneficial consumptive use, and decreasing salt loadings to the river. Two ANNs for the main stem river and the tributary regime are trained and tested using solution datasets from a high resolution, finite difference MODFLOW– MT3DMS groundwater flow and contaminant transport model of a representative subregion within the river basin. Stream-aquifer modeling in the subregion is supported by a dense field data collection network with the ultimate goal of extending knowledge gained from the subregion modeling to the sparsely monitored remainder of the river basin where data insufficiency precludes application of MODFLOW– MT3DMS at the desired spatial resolution. The trained and tested ANNs capture the MODFLOW–MT3DMS modeled subregion stream-aquifer responses to system stresses using geographic information system (GIS) processed explanatory variables correlated with irrigation return flow quantity and quality for basin-wide application. The methodology is applied to the Lower Arkansas River basin in Colorado by training and testing ANNs derived from a MODFLOW–MT3DMS modeled subregion of the Lower Arkansas River basin in Colorado, which includes detailed unsaturated and saturated zone modeling and calibration to the extensive field data monitoring network in the subregion. Testing and validation of the trained ANNs shows good performance in predicting return flow quantities and salinity concentrations. The ANNs are linked with the GeoMODSIM river basin network flow model for basin-wide evaluation of water management alternatives. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction Stream-aquifer interaction is a fundamental modeling component required for addressing issues of conjunctive management of surface water and groundwater in river systems hydraulically connected to phreatic aquifers. Commonly, river basin models include simplified stream-aquifer response models, such as the stream depletion factor (sdf) method (Jenkins, 1968), the Glover model (Glover, 1977), segmented and segregated modeling approaches (Frevert, 1983), or the interconnected lumped-parameter groundwater basin approach adopted by the California Department of Water Resources in the CalSim model (Draper et al., 2004). Although the sdf method is capable of aggregating complex boundary conditions and aquifer heterogeneity into the stream depletion factors, Fredericks et al. (1998) show that methods of this type fail

* Corresponding author. Tel.: +1 970 491 6898; fax: +1 970 491 7707. E-mail address: [email protected] (J.W. Labadie). 0022-1694/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2010.07.024

to adequately capture the complex dynamic and spatial characteristics of stream-aquifer systems. Another approach to modeling stream-aquifer interactions at the basin scale is the use of response functions that describe the relative impacts on return flows and stream depletions of unit changes in aquifer stresses (i.e., recharge/pumping) at locations adjacent to the river. Analytically derived response functions were called surrogate parameters by Labadie (1972), algebraic technologic functions by Maddock (1972), discrete kernels by Morel-Seytoux and Daly (1975), influence coefficients by Illangasekare and Morel-Seytoux (1982), and response matrices by Gorelick (1983). MODRSP (Maddock and Lacher, 1991), a modified version of the USGS Modular Three-Dimensional Groundwater Flow Model (MODFLOW) (McDonald and Harbaugh, 1988), automatically applies unit stresses to all individual grid cells, with MODFLOW calculating the resultant steady state and transient unit responses at the river cells. Once developed, response functions can be incorporated into river basin management models for optimal conjunctive use of surface water and groundwater resources. Response

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functions developed from MODFLOW have been successfully applied to conjunctive management in the Lower Nile River basin (El-Beshri and Labadie, 1994), the Upper Snake River basin (Cosgrove and Johnson, 2005), and the Upper San Pedro River basin (Leake and Reeves, 2008). The development of steady state and transient response functions from systematic excitation of numerical groundwater flow models such as MODFLOW and MODRSP represents a significant improvement over simplified stream-aquifer models and analytically derived response functions. Disadvantages of this approach include (i) application of linear superposition to combine the responses that approximates the nonlinear behavior of the streamaquifer system; (ii) difficulty in applying the response functions to return flow water quality; and (iii) restriction of the response functions to those areas specifically included in the numerical groundwater modeling since they are difficult to extrapolate and extend to regions outside of the modeled areas. Most often, lack of sufficient data for model calibration and extreme computational requirements inhibit the application of spatially-distributed, numerical groundwater models over an entire river basin, particularly when finely discretized grid cells or dense triangulated irregular networks are required for accurate solutions. ANNs have been demonstrated as powerful tools for modeling complex, highly nonlinear relationships between sets of explanatory variables and observed data in groundwater basins by Rogers and Dowla (1994) and Maskey et al. (2000), and more generally in the field of hydrology by Govindaraju and Ramachandra (2000). Parkin et al. (2007) trained an ANN based on numerical simulations using the SHETRAN integrated watershed modeling system (Ewen et al., 2000) for application to various hydrologic/geologic/geomorphological conditions in the United Kingdom, with primary focus on river depletions due to pumping. As originally proposed by Triana et al. (2005), a machine-learning approach is presented for modeling stream-aquifer interactions at the river basin scale that trains artificial neural networks (ANNs) to datasets generated by a three-dimensional numerical groundwater quantity/quality model applied to a representative subregion of the river basin. Inputs to the ANNs include georeferenced explanatory variables describing landscape, hydrologic, and geologic features correlated to the quantity and quality of spatially distributed irrigation return flows and easily processed by a geographic information system (GIS). The advantages of this methodology include: (i) capturing the stream-aquifer behavior of the finite difference groundwater modeling system by training the stream-aquifer ANN with a well-calibrated, subregional-scale MODFLOW–MT3DMS groundwater model (Harbaugh et al., 2000; Zheng and Wang, 1999) that includes conservative contaminant transport for estimating total dissolved solid concentrations in irrigation return flows; (ii) creates a set of GIS-processed, spatially distributed explanatory variables as inputs to the stream-aquifer ANN, allowing extrapolation of return flow quantity and quality predictions beyond the subregion to areas of the river basin with insufficient data for calibrating a high resolution MODFLOW/MT3DMS model; and (iii) provides efficient computational mechanisms for embedding the stream-aquifer ANN into comprehensive river basin management models such as GeoMODSIM (Triana and Labadie, 2007). The ANN/GIS-based methodology for basin-wide stream-aquifer interaction modeling is presented, along with description of the explanatory variables used for extending return flow water quantity and quality predictions from the modeled subregion to non-modeled areas within the river basin. The methodology is demonstrated by implementation in the Lower Arkansas River Valley of Colorado where detailed subregional-scale groundwater modeling is available for both the historical baseline case as well as for evaluation of improved river basin water management alternatives.

2. Artificial neural networks According to Kohonen (1988), artificial neural networks (ANN) are ‘‘massively parallel interconnected networks of simple elements and their hierarchical organizations which are intended to interact with the objects of the real world in the same way as biological nervous systems do.” As illustrated in Fig. 1, feedforward neural networks are a widely used ANN architecture in water resources and hydrological applications (Wang et al., 2008) consisting of an input layer, hidden layer and output layer, with each layer including a number of nodes or neurons. Input nodes receive data from sources external to the network and are scaled and transmitted over synapses as weighted signals with a connection strength to nodes in the hidden layer. A combiner sums the total weighted signals at each node in the hidden layer, along with a constant bias term, and applies an activation function to the weighted sum which is then transmitted to each node in the output layer with an assigned weight. An activation function is applied to the weighted sum inputs to each node in the output layer, resulting in the final outputs. The output from each layer of the ANN is computed as follows:

v hj ðtÞ ¼

I X

whij xi ðtÞ þ hhj

ð1Þ

i¼1

zj ðtÞ ¼ hj ðv hj ðtÞÞ;

v ok ðtÞ ¼

J X

j ¼ 1; . . . ; J

wojk zj ðtÞ þ hok

ð2Þ ð3Þ

j¼1

yk ðtÞ ¼ ok ðv 0k ðtÞÞ;

k ¼ 1; . . . ; K

ð4Þ

where I is the total number of external inputs applied to neurons in the input layer; J is the total number of neurons in the hidden layer; whij is the synaptic weight of connection of neuron i in the input layer to neuron j in the hidden layer; wojk is the synaptic weight of connection of neuron j in the hidden layer to neuron k in the output

Fig. 1. Schematic diagram of multilayer feedforward neural network example.

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layer; xi ðtÞ is the external input signal entering neuron i in the input layer at time t; yk ðtÞ is the output from neuron k in the output layer; hhj is the threshold or bias unit applied to neuron j in the hidden layer; hok is the threshold or bias unit applied to neuron k in the output layer; v hj ðtÞ is the net internal activity level of neuron j in the hidden layer; v ok ðtÞ is the net internal activity level of neuron k in the output layer; zj ðtÞ is the output from neuron j in the hidden layer produced from operation of activation function hj ðv hj ðtÞÞ on net internal activity v hj ðtÞ for neuron j; and ok ðv ok ðtÞÞ is the activation function operating on net internal activity v ok ðtÞ for neuron k in the output layer. The linear activation function is most commonly applied to the output layer, whereas the logistic sigmoid function is often used in the hidden layer:

zj ðtÞ ¼ hj ðv hj ðtÞÞ ¼

1 v hj ðtÞ

1þe

ð5Þ

where 0 6 zj ðtÞ 6 1 (Haykin, 1999). Other commonly used activation or transfer functions include the hyperbolic tangent sigmoid function, the log-sigmoid function, and the radial basis function. A popular radial basis function (RBF) is the Gaussian kernel: 2

zj ðxÞ ¼ ekxcj k

=2rj

ð6Þ

where the kernel centers cj and spread rj parameters must be estimated. The RBF is directly applied to the input vector x rather than the weighted sum of inputs, implying that weights on the synapses connecting the input layer to the hidden layer are assigned nominal values of 1. Generalized regression networks are a special type of RBF ANN introduced by Specht (1991) that include a second hidden layer using linear activation functions. Feedforward networks are often called backpropagation networks, referring to the methodology employed in calibrating or training the ANNs. Training is a gradient-based process known as the Widrow-Hoff learning rule (Rumelhart et al., 1986) for adjusting the synaptic weights and bias terms until a performance function representing the sum-of-squares deviation between the measured output from exemplars, or input–output training datasets, and the ANN output is minimized. For RBF ANNs, the reduced number of weights requiring estimation provides for a more efficient training process, where methods such as K-means clustering are used for determining the kernel center and spread parameters. In this way, each RBF only evaluates the response for a certain range of the input data. As part of the training process, experiments may be conducted to identify the optimum number of nodes in the hidden layer, or even the number of hidden layers required. The goal is to develop a parsimonious network structure providing good performance while avoiding over-training. ANN verification or testing involves using a separate set of exemplars not included in the training dataset to evaluate performance of the ANN. Other popular ANN architectures include the class of dynamic or recurrent neural networks that add a feedback loop for learning both spatial and temporal patterns or trends in the given datasets. The Elman neural network (Elman, 1990) provides feedback of the hidden layer output to the input layer according to a specified time delay, which supplies input information to the hidden layer from previous time steps. The Jordan neural network (Jordan, 1986) differs from the Elman network in that feedback occurs from the output layer back to the input layer. Generally, the training of recurrent neural networks is more challenging than for standard feedforward ANNs due to the high degree of nonlinearity of the optimal estimation problem and the attendant danger of premature convergence to local minima of the performance function.

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3. Stream-aquifer ANN A stream-aquifer ANN for modeling complex stream-aquifer interactions in alluvial river basins is incorporated into the RiverGeoDSS spatial decision support system for river basin water management (Triana et al., 2010a). River GeoDSS is registered as a custom extension in the ArcMap interface to the ArcGIS 9.x geographic information system software package (ESRI, Inc.), allowing full deployment of the powerful spatial processing capabilities of GIS in river basin management. The generalized user support tools and interfaces comprising the ANN Module within River GeoDSS are developed using ESRI ArcObjects, the Microsoft .NET Framework library and virtual machine, and the MATLABÒ Neural Network Toolbox libraries. As depicted in Fig. 2, the ANN Module automates the creation of spatially processed ANN training datasets by extracting relationships between current and previous measurable system states and the MODFLOW–MT3DMS modeled stream-aquifer interactions processed using the GeoMODFLOW Module. The ANN Module then performs the ANN training and testing exercises, allowing users to select options including input variable scaling methods, size and structure of the training dataset, training/testing/validation groups to be extracted from the dataset, neural network architecture and structure; and training parameters. The validated stream-aquifer ANN is then seamlessly incorporated into GeoMODSIM, a fully functional implementation of the MODSIM Generalized River Basin Management Model (Labadie, 2006) within the ArcMap interface to ArcGISTM. 3.1. Buffered grouping areas for ANN training In developing the stream-aquifer ANN training dataset, it is important to capture the types and locations of stresses used to explain the stream-aquifer responses since distance to the adjacent stream is a critical factor in the timing and magnitude of net return flows. The spatially distributed stream-aquifer responses, as well as system stresses, characteristics, and factors correlated with these responses, are spatially aggregated into discrete grouping areas, which are further subdivided into buffer-areas defined at lateral user-specified distances from the main stem river and its tributaries. As illustrated in Fig. 3, the grouping areas represent

Fig. 2. Integration of ANN Module for stream-aquifer interaction with the River GeoDSS spatial decision support system.

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Fig. 3. ArcMapTM (ESRI, Inc.) display showing buffered grouping areas, surface water features, irrigated fields, and MODFLOW river cells.

subsurface areas draining into specified river and tributary segments, and are delineated from a 1:24,000 digital elevation map (DEM) using ArcHydro Tools, available as an extension in the ArcMap interface to ArcGIS 9.x. It is assumed that the delineated surface drainage areas approximately correspond to the subsurface flow patterns in an alluvial river valley, although these boundaries can be adjusted based on flow direction patterns calculated by MODFLOW in the modeled area. The grouping areas are clipped to the aquifer extent included in the MODFLOW–MTD3MS modeled area, with Fig. 3 showing the MODFLOW river cells overlain on the main stem river and tributary hydrographic features for two buffer areas in each grouping area. Activation of River GeoDSS as a custom extension in ArcMap allows selection of the ANN Data Manager (Fig. 4) for defining the desired numbers and distances of the buffer-areas, specifying the feature classes to be clipped to the buffer-areas, and generating the Spatial Input Buffer Database. Spatially distributed explanatory variables serving as inputs to the stream-aquifer ANN are extracted from the Spatial Input Buffer Database for each buffered grouping area. Stream-aquifer interaction is represented using net return flows to the streams (i.e., net of stream depletions due to combined aquifer stresses) and corresponding salinity concentrations per grouping area as modeled using MODFLOW–MT3DMS. For this study, evaluation of water quality impacts is limited to total dissolved solids (TDS) based on electrical conductivity measurements (EC) (lS/cm) which are converted to TDS (mg/L) using a calibrated formula that considers temperature and soil moisture level influences on EC. The GeoMODFLOW Module is applied to spatially processing

the MODFLOW–MT3DMS simulation results and summarizes the predicted variables for the dataset. Net return flow amounts and TDS concentrations are calculated per unit length of the modeled stream section. Since the ANN training characteristics and relevant explanatory variables for modeling stream-aquifer interactions in the main stem river may differ significantly from stream-aquifer interactions in the tributaries, an ANN for each type of training is implemented to accurately model stream-aquifer interactions over the entire basin. Although both the main stem and the tributary ANNs rely on essentially the same set of explanatory variables, the separate stream-aquifer ANNs give the ability to better filter the dataset and improve performance by training and predicting over more homogeneous input/output cases. 3.2. ANN input explanatory variables The ANN stream-aquifer modeling methodology is based on development of dynamic, spatially dependent relationships between basin scale measurable system characteristics, which directly or indirectly impact stream-aquifer response, and the subregional-scale MODFLOW–MT3DMS model calibrated from extensive data sets collected in the representative subregion. Use of basin scale measurable characteristics, or explanatory variables, enables the application of learned relationships in the modeled subregion to estimate stream-aquifer responses in the river basin outside of the subregion. The explanatory variables are designed to provide the ANN with pertinent information believed to be highly correlated with the spatial and temporal distribution of aquifer return flows, streamflow depletions due to pumping, and

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Fig. 4. River GeoDSS graphical user interface within ArcGIS Desktop displaying the ANN Data Manager for creating the Spatial Input Buffer Database.

salinity loadings to the surface water system. Final selection of the ANN explanatory variables is based on trial and error processes that evaluate ANN prediction performance over several training cycles. The ANN input explanatory variables are categorized as spatially-dependent, time-dependent, scenario-dependent, or combinations of these, as illustrated in Fig. 5. For spatially-dependent variables, GIS processing tools are used to clip and summarize the system features and their associated time series data within the grouping and buffer-areas (Fig. 3). Geo-spatial processing tools are also applied to NEXRAD Doppler radar measurements and rain gauge data for developing spatially-distributed precipitation estimates grouped by buffer-areas (Fulton et al., 1998). Those explanatory variables aggregated per grouping area include: stream length in the grouping area (StreamLengthRiver) and tributary stream length in the grouping area (StreamLengthTrib). Explanatory variables summarized per buffer-area within the grouping areas include: total buffer-area on both sides of the river (BufArea); lengths of the canals (Canals); canal average elevations with respect to the average main stream elevation (CanalsElev); average terrain elevation with respect to the main stream elevation (AveElev); areal extent of irrigated fields (IrrgArea); surface areas of water bodies in the buffer-areas (WBArea); average elevation of the water bodies with respect to the average main stream elevation (WBElev); total precipitation over each buffer-area (Precip); groundwater volume pumped from the aquifer per modeled time step (AvePumped); and the number of active pumping wells (NoPumps).

Scenario-dependent explanatory variables are based on water management strategies modeled at the subregional-scale to improve irrigation application efficiency, reduce canal seepage losses, and expand subsurface drainage facilities for mitigating salinity and waterlogging problems. Burkhalter and Gates (2006) applied MODFLOW–MT3DMS to modeling these strategies for the Lower Arkansas River basin, Colorado, with inclusion of an improved drainage module and unsaturated-zone quantity and quality modeling. Scenario-dependent variables consist of factors capturing changes with respect to the historical baseline, including: subsurface drainage intensity improvements by grouping area (DrainSpc); percentage of increased groundwater pumping (from the baseline) by grouping area (PercPumped); percent of baseline seepage reduced by improvements in canal conveyance efficiency by bufferarea (PercSeep); and percent recharge reduction by buffer-area due to conversion to more efficient irrigation methods such as sprinkler irrigation (PercRech). Additional scenario-dependent explanatory variables are extracted from GeoMODSIM within the River GeoDSS, which provides surface water model-derived variables. These scenariodependent explanatory variables include average river flow in the grouping area (RiverFlow), average diversion by buffer-area (AveDiversion), average canal conveyance loss volume (AveVolSeep), and average estimated aquifer recharge volume (AveVolRech). The conveyance and recharge variables reflect relative changes from the historical baseline as a function of GeoMODSIM computed river diversions. The explanatory variables reflecting canal seepage reduction from the baseline and percentage of areal aquifer

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Fig. 5. Explanatory input and output variables for the main stem river and tributary stream-aquifer ANNs.

recharge reduction from improved irrigation efficiency over the baseline are calculated for each buffer-area as an average over the corresponding canal command areas and irrigated fields in the buffer-areas. The explanatory variables dataset is enhanced, at the option of the user, with previous time step river flows, modeled net return flows and corresponding TDS concentrations, to endow the explanatory variable datasets with transitional pattern memory during the training process. 3.3. ANN training output data The desired outputs for training the stream-aquifer ANNs are developed by execution of MODFLOW–MTD3MS models over each simulation time step for all combinations of the modeled management alternatives. For training the main stem river stream-aquifer ANN, net return flows to the river (NetRetFlow_River) and associated TDS concentrations (OutputConcRiver) per unit length of the stream are extracted from the MODFLOW–MT3DMS results for river segments along the main stem river associated with each grouping area (Fig. 3) within the modeled subregion. Similarly, training the stream-aquifer ANN for the tributary regime utilizes essentially

the same explanatory variable dataset, except they are defined for all buffer areas and not just the buffer-area intersecting the main stem river. The desired outputs for training the stream-aquifer ANN for the tributaries are the net return flows (NetRetFlow_Trib) and associated TDS concentrations (OutputConcTrib) per unit length of tributary. The custom Export MATLAB Input Files menu item, under ANN I/O Preparation tab in the River GeoDSS toolbar, activates the Generate MATLAB Input Files for Training form, which is used to extract user-selected explanatory variables from the Spatial Input Buffer Database. The explanatory variables are processed using zonal statistics operations performed using the Spatial Analyst extension in ArcMap. Structured Query Language (SQL) commands can also be entered by the user to filter the spatial datasets as desired. This interface allows selection of the grouping areas for training and testing, as well as selection of explanatory variables and ANN outputs to be included as time-lagged inputs to the ANN. With this selection, recurrent effects allowing the ANN to capture time-varying patterns can be simulated, although the feedback will not change during training based on the actual outputs as would occur with a recurrent Jordan ANN architecture.

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3.4. ANN training for dynamic conjunctive use modeling As shown in Fig. 5, a subset of the ANN explanatory variables are derived from simulation of the GeoMODSIM surface water allocation model within the River GeoDSS: RiverFlow, AveDiversion (canal diversions), AveVolSeep (canal seepage), and AveVolRech (deep percolation from irrigation). The complication is that execution of GeoMODSIM requires estimates of spatially distributed net return flows and associated concentrations from the trained ANNs, and the ANN training requires the GeoMODSIM explanatory variables. To overcome this problem, all scenarios to be included in the training are executed by GeoMODSIM within River GeoDSS prior to the initial training as an approximation in order to mimic all important model conditions such as scenario demands, seepage, and reservoir storage. Since the trained stream-aquifer ANN is not available as yet, the spatially distributed net return flows are initialized as zero (GWRetFlow = 0), although calibration links are included in the GeoMODSIM network that provide an approximate accounting of stream segment gains and losses. Execution of GeoMODSIM results in calculation of explanatory variables RiverFlow, AveDiversion, AveSeep and AveRech for all grouping areas and all combinations of management alternatives, which are then added to the explanatory variables input dataset for training the stream-aquifer ANNs. The initially trained stream-aquifer ANNs are used by the ANN Module in the River GeoDSS to produce estimates of net return flows (GWRetFlow) that replace initial estimates of net return flows to the GeoMODSIM surface water network. Explanatory variables calculated by GeoMODSIM then serve to update the ANN training dataset, followed by re-training of the stream-aquifer ANNs and GeoMODSIM execution. This procedure is repeated until successive calculations of net return flows converge. 3.5. MATLAB ANN training A set of customized tools were developed using the MATLABÒ Neural Network Toolbox libraries for importing the training datasets, selecting the desired neural network architecture, specifying the training parameters, scaling the data, and training and testing the ANNs (Triana, 2008). The imported training dataset is divided into training, testing and validation groups according to user preferences, with the testing dataset used later for performance evaluation. Since the combination of several grouping areas, many simulation time steps, and all combinations of management alternatives can produce an extremely large dataset that is computationally intractable for training, a custom ANN training tool allows random selection of a specified number of cases for training. The remaining training cases are added to the performance testing dataset. A custom dialog allows selection of one of the aforementioned neural network types: (1) feed-forward backpropagation, (2) Elman backpropagation, (3) generalized regression neural network (GRNN), and (4) radial basis function neural network (RBFNN). The backpropagation type networks use a training method that relies on sequential improvement of weights and biases to minimize errors between the predicted and observed values. Since a backpropagation training event is difficult to reproduce due to the initial training parameters being randomly selected, a sequential training process is implemented in which many training events in several sessions are performed, with the best performance training selected per session. For the feedforward neural networks, additional options are available to the user such as: stopping methods for training and types of network structure. The Elman neural network training follows the backpropagation training, but is significantly more difficult and time consuming than the other backpropagation networks. Therefore, training is restricted to a smaller number of sessions in this case.

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For ANN training, the explanatory variables are scaled between 1 and 1 and then post-processed to obtain predictions in the original units. The pre-processing algorithm automatically selects between two scaling methods: (1) min/max scaling (MnMx) and (2) standard deviation (Std) scaling. In MnMx scaling, the explanatory variables are scaled between 1 and 1 using the following transformation equation:

pni ¼ 2 

ðpi  minp Þ 1 ðmaxp  minp Þ

ð7Þ

where pni = the transformed value; pi = the explanatory variable value; minp = the minimum of explanatory variable p and maxp = the maximum value for explanatory variable p. The Std scaling normalizes the data to a mean of 0 and standard deviation of 1 using the following equation:

pni ¼

ðpi  meanp Þ stdp

ð8Þ

where meanp = the mean of the explanatory variable p, and stdp = the standard deviation of explanatory variable p. In general, MnMx scaling is used for explanatory variables when the mean of MnMx transformed data lies between 0.25 and 0.25; otherwise, Std scaling is used. This rule attempts to maintain a symmetrical spread of the scaled data around the 0 value. In an attempt to reduce the effect of errors due to numerical dispersion in explanatory variables from previous time steps during simulation, a more restrictive rule with an interval of 0.1 to 0.1 is used for assigning MnMx scaling to these variables, resulting in Std scaling in most cases. Output variables for training are always scaled using the MnMx method. During the ANN training, selection of representative ANN explanatory variables was based on the ANN prediction performance over several training cycles, with emphasis on ANN improved prediction over individual MODFLOW-modeled neighboring areas not included in the training. The optimization of ANN parameters (i.e., weights and biases) during the training process automatically selects the explanatory variables that are more important to predict the stream-aquifer interaction by assigning them larger weights. Future improvements could potentially be obtained by removing the less important variables from the training datasets. 4. Application to the Lower Arkansas River Basin, Colorado 4.1. Description of study area The Lower Arkansas River basin is located in the southeastern portion of Colorado, extending 300 km from Pueblo Reservoir downstream to the Kansas border (Fig. 6). The region is semi-arid, with an average annual precipitation of around 280 mm. Flows in the Arkansas River originate primarily from snow melt from the mountainous Upper Arkansas River drainage during spring and early summer, as well as contributions from transbasin diversions from the Colorado River Basin. Water usage in the Lower Arkansas River basin is dominated by irrigated agriculture (over 95%). Unfortunately, inefficient irrigation practice and inadequate drainage have contributed to salinization of soils in the Lower Arkansas River valley from waterlogging and high groundwater tables, resulting in reduced crop yields and loss of prime agricultural lands. The river ecology is also adversely impacted by saline return flows in the stream-aquifer system due to recharge of excess irrigation applications and seepage from unlined canals, with resultant dissolution of salts in ancient marine shale formations underlying much of the valley. Saline high water tables have also contributed to substantial water loss from nonbeneficial consumptive use on both

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Fig. 6. Location of the MODFLOW–MTD3MS modeled subregion within the Lower Arkansas River basin.

irrigated lands during the fallow season, as well adjacent fallow areas. Further aggravating these problems has been the purchase of agricultural water rights in the Arkansas River basin by municipalities along the front range of Colorado in order to augment water supplies for their growing populations. This has resulted in the ‘‘drying up” of productive irrigated lands and undermining of the social and economic framework of rural communities in the Arkansas River valley. Political and legal conflicts between the states of Colorado and Kansas over apportionment of flows in the Arkansas River have further harmed irrigated agriculture in the valley, since recent court rulings resulted in the curtailment of groundwater pumping in downstream portions of the Lower Arkansas River basin in Colorado due to violation by Colorado of the interstate compact with Kansas. 4.2. MODFLOW–MT3DMS modeling Burkhalter and Gates (2005) report on development, calibration, and testing of MODFLOW–MT3DMS in a representative modeled subregion comprising 20–25% of the Lower Arkansas River basin (Fig. 6). Of the 50,600 ha areal extent of the subregion, irrigated lands extend over 26,400 ha and drain to a 62 km length seg-

ment of the Arkansas River. The study subregion includes six major irrigation canals, eight tributary drainages, three major reservoirs, and 280 active pumping wells. Cultivated crops include alfalfa, corn, grass, wheat, sorghum, cantaloupe, watermelon, and onions. Furrow and border surface irrigation methods dominate, with only 5% of the irrigated lands under more efficient sprinkler or drip irrigation methods. The river valley alluvium consists of porous sand and gravels overlain by silty–clay loam to sandy loam covering widths between 2.4 and 18.4 km and thicknesses from 1 m to 30 m. Hydraulic conductivity values vary from 0.001 m/day in the upper layers of the alluvium to 530 m/day in the lower layers. Extensive field data collected in the study area since 1998 include shallow aquifer hydraulic conductivity, water table depth, water table salinity, soil salinity and water content, ground surface elevations, bedrock elevations, georeferenced hydrography, soil texture and storage properties, canal seepage, and surface water levels. Over 110 shallow groundwater monitoring wells were installed in the study subregion for this project, with locations based on a stratified random sampling approach, but adjusted according to fields belonging to growers and ranchers willing to cooperate in the study. Monitoring wells are 6.35 cm diameter PVC pipe ranging in depth from 3 to 8 m. Water table depth and EC is measured weekly during the irrigation season and biweekly/monthly

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otherwise. Surface water flows, levels, and EC in canals, rivers and reservoirs in the subregion are measured weekly at up to 173 sites during the irrigation season. Soil salinity data are collected biannually on fields containing the groundwater monitoring wells using calibrated Geonics EM-38 electro-magnetic induction meters (average of 62 points collected over an average field size of 6.3 ha). A multi-layer finite difference grid of 16,188 cells at 250 m resolution was created, with the upper layer representing the low permeability zone between 0 and 3.5 m depth, and the high permeability zone at depths greater than 3.5 m. The high resolution finite difference grid is necessary for modeling field scale interventions for improved water management, where the 250 m  250 m cell size is approximately one-half of the average area of irrigated fields in the valley. According to Zheng and Bennett (2002), for the governing aquifer salt mass transport equations in MT3DMS, only advective transport is necessary for salinity (TDS) modeling in the groundwater system, although contributions from salt dissolution were considered. The primary calibration target values for MODFLOW–MT3DMS were measured water table elevations and salinity at the monitoring well locations, although other target values were used such as estimated canal seepage and return flow volumes based on flow measurements in the streams and canals. Transient simulation was conducted over 133 weekly time steps, with the first 67 time steps used for calibration and the remainder for model testing and validation. Calibration results reported by Burkhalter and Gates (2005) give the mean absolutevalue error between simulated and observed water table elevations of 1 m, with model verification results giving a mean absolute error of 1.26 m. Mean errors between simulated and observed groundwater salinity values were 48 mg/L. Using the calibrated MODFLOW–MT3DMS models, Burkhalter and Gates (2006) modeled improved water management alternatives at the subregional-scale for mitigating salinity and waterlogging problems and sustaining agriculture in the Lower Arkansas River basin. The modeled water management alternatives included (1) irrigation induced aquifer recharge reduction ranging from 10% to 90%, (2) canal seepage reduction levels of 50%, 70% and 90%; (3) 90% canal seepage reduction over 20% of the irrigation canal lengths, (4) canal lining scenarios of 90% seepage reduction in selected canals, (5) drainage improvement scenarios with subsurface tile drains installed in selected fields at spacings of 50 m to 150 m, (6) groundwater pumping increases ranging from 25% to 200% for simulation of vertical drainage, (7) combined recharge–canal seepage reduction measures of 30–50%, 50–90%, and 80–90%, respectively; (8) combinations of recharge reduction-drainage improvement of 30%–100 m (drain spacing), 50%–50 m, and 80%–50 m, respectively; (9) canal seepage reduction-drainage improvements of 50%–100 m and 90%–50 m, respectively; and (10) combinations of recharge reduction–canal seepage reduction-drainage improvement of 30– 50%–100 m, 50–90%–50 m, and 80–90%–50 m. For the purposes of aggregating the stream-aquifer ANN explanatory variables, buffered grouping areas were defined in roughly 15 km segments along the Lower Arkansas River Valley. A total of 20 grouping areas are numbered sequentially from upstream (east of Pueblo Reservoir) to downstream (Colorado–Kansas State Line). Lateral buffer-areas surrounding the river are created using incremental buffer zones along the main stream segment, with the first buffer-area extending 3 km east and west of the stream and the second buffer-area extending 6 km east and west of the first buffer-area external boundary (Fig. 3).

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ing based on prediction performance and generalization capabilities. Evaluation of numerous combinations of parameters and training error goals resulted in an RBFNN able to model the process with the least number of neurons in the hidden layer and produce predictions with the smallest errors. Automated tools were created for conducting multiple trainings of the RBFNN by changing the spread parameter within a user-specified range to achieve the user-specified sum-of-squares error (SSE) goal. Use of various network spreads resulted in different separations of the neurons and consequently required varying numbers of neurons to minimize the error goal. Parsimony in the number of neurons required resulted in better generalization capabilities of the ANN and avoided over-training. The combination of about 130 weekly time steps for the historical baseline case and 36 management scenarios produces a large dataset for training. Since training a radial basis neural network with a sizable dataset becomes impractical or impossible due to computing limitations, the custom ANN training tool was used to randomly select a specified number of examplars for training, with the remaining training cases used for performance testing. Training of the ANNs for the Arkansas River and its tributary regime was performed with 2500 cases (approximately 10–15% of the available cases). Several training events were performed in order to select the most representative training cases based on the ANN prediction performance. For both the Arkansas River and tributary ANNs, the explanatory variables are spatially grouped using the same buffer-areas. For the Arkansas River stream-aquifer interaction modeling, the ANN training dataset was prepared using river flow, return flow and corresponding TDS concentration variables from four chronological previous time steps (weeks) with explanatory variables restricted to the buffer-areas bordering the Arkansas River. For stream-aquifer interaction modeling in the tributary regime, the dataset includes return flows and concentration variables from the previous two weeks, along with explanatory variables from both buffer-areas. In selecting representative subregional tributary stream-aquifer interactions for the ANN training, datasets include only data from grouping areas that have a total tributary stream length longer than 1 km in all its buffer-areas. Figs. 7 and 8 provide typical ANN training and testing prediction performance for Arkansas River stream-aquifer interaction modeling, including: the forecast bias in modeling units (F. Bias = Observed mean – Predicted mean), root mean squared error (RMSE) in modeling units for testing, noise-to-signal ratio ( = RMSE/variance), and coefficient of determination (r2). Similar results are obtained for ANN prediction performance of net return flows and TDS concentrations for tributaries located within the grouping areas. The large number of testing cases as compared with the training cases and the performance statistics indicate a respectable extrapolation capability of the ANNs by providing reasonable performance when tested over portions of the MODFLOW–MTD3MS modeled subregion that were not included in the training dataset. As a representative example of the results, Fig. 9 gives a comparison of the ANN predicted versus the MODFLOW calculated return flow volume and TDS concentration time series for Grouping Area 7. The temporary, transient return flow responses during initialization of the MODFLOW simulations are due to incomplete consideration of recharge and pumping stresses occurring prior to the start of the simulation period. 4.4. ANN performance evaluation

4.3. Stream-aquifer ANN training Experimentation with several ANN architectures and configurations for this study resulted in selection of the radial basis function neural network (RBFNN) as best suited for stream-aquifer model-

Performance for each water management scenario and grouping area simulation was evaluated separately to observe general performance trends. Each simulation event consisted of 133 weekly predictions under a given water management alternative.

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Fig. 7. Performance summary of the Arkansas River stream-aquifer ANN training and testing for return flow rates.

Fig. 8. Performance summary of the Arkansas River stream-aquifer ANN training and testing for return flow TDS concentrations.

In the MODFLOW–MT3DMS modeled area, 143 main stem river simulations and 98 tributary regime simulations were used for performance evaluation. The RMSE computed for weekly return flow predictions in both cases range from 0 to 37  103 m3/wk, with the majority of the Arkansas River return flow RMSE values below 25  103 m3/wk. The majority of RMSE values computed for salinity load predictions range from 20 to 400 mg/L, with larger errors found in the tributary regime. Analysis of the coefficients of correlation (r2) for all cases show that most training and testing values exceed 0.85, with higher correlations observed in the Arkansas River predictions. Lower performance was observed in the tributary TDS concentration predictions due to higher variability in the modeled salinity concentrations in small tributaries to the Arkansas River. The time-lagged ‘‘memory” from previous predictions included as explanatory variables has a positive influence on the ability of the ANN to make accurate predictions. However, a challenge arises during simulation of river basin management strategies using GeoMODSIM when linked with the trained stream-aquifer ANNs since there are no previous predictions to initiate the simulation. Starting the simulation using average predicted values increases the uncertainty in ANN return flow and TDS concentration predictions due to the inaccurate initialization. Simulation results show that sequential accumulation of errors can occur where RMSE increases

by a factor of two for both the Arkansas River and tributary regime predictions, with the range of RMSE for concentration predictions for the Arkansas River increasing by a factor of three. Future work will focus on development of training methodologies to reduce this negative effect.

4.5. Basin-scale water management modeling with stream-aquifer ANN The trained river and tributary stream-aquifer ANNs were linked with the GeoMODSIM river basin network flow model within the River GeoDSS for analyzing the performance of improved water management scenarios over the entire Lower Arkansas River basin in Colorado (Triana et al., 2010b). In these management scenarios, adjustments in the surface water system are transmitted through the ANN explanatory variables to the groundwater system, producing spatially distributed responses at the stream-aquifer interface affecting surface water availability, reservoir storage, and water quality (salinity). The GeoMODSIM river basin network model simulates the distribution of available flows in the basin according to adjudicated water rights, established water trading mechanisms in the basin such as exchanges and plans for augmentation, and compliance with the Interstate Compact Agreement

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Fig. 9. Comparison of ANN predicted and MODFLOW–MTD3MS calculated return flows and TDS concentrations for Grouping Area 7.

between Kansas and Colorado over Arkansas River flows at the state line. Results from simulated performance of water management strategies involving various combinations of alternatives for percent of canal seepage reduction (Seep%), improved irrigation efficiency (Rech% = percent of recharge reduction), and installation of subsurface drains (Drain-m) (drain spacing in meters) are given in Figs. 10 and 11. Fig. 10 shows that implementation of improved

water management alternatives results in various degrees of reduction in canal diversions, implying more efficient water use, while still satisfying irrigation demands in accordance with specified water right priorities. In addition, dilution from retaining more flow in the river and reducing saline irrigation return flows results in significant reductions in the average TDS concentration of the canal diversions (Fig. 11). Clearly, stream-aquifer interactions play a significant role in the conjunctive management of surface and

Fig. 10. Total basin-wide canal diversions for selected combined management alternatives.

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Fig. 11. Average TDS concentrations of basin-wide canal diversions for selected combined management alternatives.

groundwater in an irrigated, alluvial river basin, requiring application of realistic and accurate modeling methods supported by dense field data collection networks. 5. Conclusions A machine-learning methodology for modeling stream-aquifer interactions at the river basin scale is presented that: (1) captures unsaturated and saturated zone modeling of return flows and salinity concentrations by training ANNs using data sets generated from MODFLOW–MT3DMS based on extensive field monitored data at the subregional scale; (2) extracts realistic stream-aquifer response information from the finite difference modeling, thereby avoiding simplifications of the stream-aquifer system behavior that are commonly used in river basin management tools; (3) defines basin-wide explanatory variables readily processed using a GIS that are spatially and temporally correlated with the quantity and quality of stream-aquifer interactions, allowing extrapolation of the stream-aquifer ANNs beyond the modeled subregion extent; (4) provides a computationally efficient framework for linking the trained stream-aquifer ANNs to comprehensive river basin management models; and (5) estimates salt loadings from the aquifer to the river system for integrated river basin quantity/quality modeling. The ANN-based methodology for modeling stream-aquifer interactions is demonstrated in the Lower Arkansas River Valley of Colorado using a well-calibrated MODFLOW–MT3DMS subregional-scale groundwater model for the historical baseline case and various improved water management alternatives. Radial basis neural networks were selected to model the stream-aquifer interactions since they provided the best performance in the testing and validation cases. The small ratio between the number of cases used in training and those used in testing indicates that the ANN develops strong relationships between the explanatory variables and return flow quantity and quality by accurately predicting a larger number of cases outside of the training datasets. Although some analysis was performed on the selection of relevant explanatory variables for the ANN, future work will attempt to perform more rigorous studies of the importance of the ANN explanatory variables to the return flow quantity and quality prediction. The overall performance of the ANNs as trained to represent stream-aquifer interactions in the Lower Arkansas River Valley demonstrates an ability to predict stream-aquifer responses under a wide range of conditions. The trained ANN can perform streamaquifer interaction modeling of water management alternatives,

periods of record, and neighboring areas not included in the detailed MODFLOW–MT3DMS model for supporting evaluation of water management alternatives at the basin scale. The trained ANN can be integrated within a river basin management modeling tool such as GeoMODSIM to assist in the water quantity and quality stream-aquifer interaction modeling for basin-scale assessment of improved water management alternatives. Acknowledgments Financial support and cooperation for this study was provided by the Southeastern Colorado Water Conservancy District, the Lower Arkansas Valley Water Conservancy District, the Colorado Agricultural Experiment Station, the Colorado Water Institute, the United States Department of Agriculture (USDA), the United States Bureau of Reclamation, and the United States Geological Survey (USGS). The authors are thankful for the cooperative assistance of more than 120 Arkansas River Valley landowners, the USDA Natural Resources Conservation Service, the Division 2 Office of the Colorado Division of Water Resources, the Pueblo Subdistrict Office of the USGS, and the USDA Farm Services Agency are highly appreciated. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the opinions or policies of the US government. Mention of trade names or commercial products does not constitute their endorsement by the US government. References Burkhalter, J.P., Gates, T.K., 2005. Agroecological impacts from salinization and waterlogging in an irrigated river valley. Journal of Irrigation and Drainage Engineering 131 (2), 197–209. Burkhalter, J.P., Gates, T.K., 2006. Evaluating regional solutions to salinization and waterlogging in an irrigated river valley. Journal of Irrigation and Drainage Engineering 132 (1), 21–30. Cosgrove, D.M., Johnson, G., 2005. Aquifer management zones based on simulated surface-water response functions. Journal of Water Resources Planning and Management 131 (2), 89–100. Draper, A., Munevar, A., Arora, S., Reyes, E., Parker, N., Chung, F., Peterson, L., 2004. CalSim: generalized model for reservoir system analysis. Journal of Water Resources Planning and Management 130 (6), 480–489. El-Beshri, M., Labadie, J., 1994. Optimal conjunctive use of surface and groundwater resources in Egypt. In: Proceedings of the VIII IWRA World Congress on Water Resources. International Water Resources Association, Cairo, Egypt, November 21–25. Elman, J.L., 1990. Finding structure in time. Cognitive Science 14 (2), 79–211. Ewen, J., Parkin, G., O’Connell, P.E., 2000. SHETRAN: distributed river basin flow and transport modeling system. Journal of Hydrologic Engineering 5 (3), 250–258. Fredericks, J., Labadie, J., Altenhofen, J., 1998. Decision support system for conjunctive stream-aquifer management. Journal of Water Resources Planning and Management 124(2), 69–78.

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