Development of a cross-section based streamflow routing package for MODFLOW

Highlights

• A review is given on the development of stream packages for MODFLOW.

• The new package can represent channels wider than the MODFLOW grid cell size.

• The new package can represent variability of streambed properties across channels.

• The new package can simulate spatial heterogeneity of stream-aquifer interaction.

• An example application is used to demonstrate the capability of the stream package.

Abstract

It is challenging to simulate stream-aquifer interactions for the wide channel streams with the existing stream routing packages of MODFLOW. To overcome this limitation, a Cross-Section streamflow Routing (CSR) package is developed to simulate the streamflow and the interaction between streams and aquifers for the stream with a width larger than the MODFLOW grid size. In the CSR package, streams are divided into stream segments which are formed by two consecutive cross-sections. A cross-section is described by a number of streambed points that determine the geometry and hydraulic properties of the streambed. The stream water depth and streamflow at the cross-sections are related by the Single Channel method, the Divided Channel method, a data table or a power function. A rapid algorithm is used to compute the submerged area of the MODFLOW grid. The streambed conductance of a grid cell is computed based on its submerged area, streambed hydraulic conductivity and thickness. Stream-aquifer seepage is subsequently estimated as the product of the streambed conductance and difference between the stream stage and groundwater hydraulic head. Stream-aquifer seepage is treated as lateral flow in the streamflow routing computation with the Muskingum-Cunge method or mass conservation method. A hypothetical problem is established to test the capabilities of the CSR package with steady- and transient-state models. The results compare favorably with the SFR2 package and the HEC-RAS model. However, significant difference in flood wave attenuation is observed between the CSR package and the SFR2 package. It proves that the CSR package is capable of simulating the variation of stream-aquifer interactions in both space and time efficiently. The CSR package represents a certain improvement over previous MODFLOW streamflow packages by providing the efficient cross-section based computation and the unique capability of simulating streambed heterogeneity in longitudinal and transverse directions.

Introduction

Understanding hydrological processes that occur in the stream-aquifer systems has significant importance to integrated water management, especially where streams and aquifers are hydrologically connected (Rassam, 2011, Sophocleous, 2002, Winter, 1995). The dynamics of stream-aquifer water exchanges are also important to the functioning of aquatic ecosystems (Hancock et al., 2005), pollutant and nutrient transport (Findlay, 1995, Jones and Holmes, 1996), as well as the quality and quantity of water supply to domestic, agricultural and recreational purposes (Winter, 1995). MODFLOW is the most widely used numerical model to simulate stream and groundwater interactions. However, it is challenging to represent stream-aquifer interactions for wide channel streams or for high-resolution grids, especially when the heterogeneity of streambed properties across the channel and stream morphology need to be taken into account.

The spatial variability of water and solute fluxes at the groundwater-surface water interface, the hyporheic zone, and their impacts on the stream and riparian ecosystems were studied extensively through experimental measurements in previous studies and continue as an area of active investigation (Biksey and Gross, 2001, Binley et al., 2013, Faulkner et al., 2012, Rosenberry and Pitlick, 2009, Wondzell et al., 2009). Such variability is largely attributed to streambed heterogeneity which is universal because of the streamflow dynamics and movement of streambed sediments, as well as streambed chemical reactions and invertebrate activities (Dong et al., 2012). Chen et al. (2008) discovered high spatial heterogeneity in streambed materials with depth, along the channel and cross the channel in the Platte River, Nebraska. Lu et al. (2011) also demonstrated that distribution of both horizontal and vertical hydraulic conductivities is significantly spatially dependent. Heterogeneity in permeability of streambed materials can form many flowpath connections between streams and aquifers, for both water and solutes (Conant et al., 2004), and consequently provide habitats of various scales which are important to different species (Brunke and Gonser, 1997). It has been demonstrated that neglecting streambed heterogeneity could cause significant errors in modeling results of stream-aquifer interactions (Irvine et al., 2012).

Brunner et al. (2010) pointed out the limitation in horizontal discretization of rivers could result in biased estimation of stream-aquifer exchange flux when the river width and cell size are mismatched. Mehl and Hill (2010) also examined the effect of the MODFLOW grid size on the simulation of stream-aquifer interactions. In the streamflow depletion analysis, on the other hand, Chen et al. (2008) showed that the depletion rate induced by groundwater pumping can be affected by the grid cell sizes. They all proved that refining the model grid can improve simulation accuracy. These findings underline the need for models to represent the geometry and properties both across and along stream channels with grids of high resolutions.

Because of the importance of streambed heterogeneity, and, particularly the need for simulating stream-aquifer interactions in wide channels or with refined grids, the Cross-Section based streamflow Routing (CSR) package was developed for MODFLOW. The objectives for developing the CSR package were: (1) to simulate stream-aquifer interaction and streamflow routing for the wide channel streams or with high-resolution grids; (2) to represent the heterogeneity in streambed properties not only along stream channels but also across them; (3) to physically represent the streambed geometry of high complexity. In this paper, we describe the concepts and algorithms used in the CSR package. A hypothetical stream-aquifer system is used to test the capabilities of the package. We also discuss the capabilities, assumptions and limitations, as well as potential improvement of the package.