Variational approach to homogenization of doubly-nonlinear flow in a periodic structure

This work deals with the homogenization of an initial- and boundary-value problem for the doubly-nonlinear system D(t)w - del.(z) over right arrow = g(x, t, x/epsilon) (0.1) w is an element of alpha(u, x/epsilon) (0.2) (z) over right arrow is an element of (gamma) over right arrow (del u, x/epsilon) (0.3) Here epsilon is a positive parameter; alpha and (gamma) over right arrow are maximal monotone with respect to the first variable and periodic with respect to the second one. The inclusions (0.2) and (0.3) are here formulated as null-minimization principles, via the theory of Fitzpatrick MR 1009594]. As epsilon -> 0, a two-scale formulation is derived via Nguetseng's notion of two-scale convergence, and a (single-scale) homogenized problem is then retrieved. (C) 2015 Elsevier Ltd. All rights reserved.

Implications of using On-Farm Flood Flow Capture to recharge groundwater and mitigate flood risks along the Kings River, CA

Two large hydrologic issues face the Kings Basin, severe and chronic overdraft of about 0.16M ac-ft annually, and flood risks along the Kings River and the downstream San Joaquin River. Since 1983, these floods have caused over $1B in damage in today’s dollars. Capturing flood flows of sufficient volume could help address these two pressing issues which are relevant to many regions of the Central Valley and will only be exacerbated with climate change. However, the Kings River has high variability associated with flow magnitudes which suggests that standard engineering approaches and acquisition of sufficient acreage through purchase and easements to capture and recharge flood waters would not be cost effective. An alternative approach investigated in this study, termed On-Farm Flood Flow Capture, involved leveraging large areas of private farmland to capture flood flows for both direct and in lieu recharge. This study investigated the technical and logistical feasibility of best management practices (BMPs) associated with On-Farm Flood Flow Capture. The investigation was conducted near Helm, CA, about 20 miles west of Fresno, CA. The experimental design identified a coordinated plan to determine infiltration rates for different soil series and different crops; develop a water budget for water applied throughout the program and estimate direct and in lieu recharge; provide a preliminary assessment of potential water quality impacts; assess logistical issues associated with implementation; and provide an economic summary of the program. At check locations, we measured average infiltration rates of 4.2 in/d for all fields and noted that infiltration rates decreased asymptotically over time to about 2 – 2.5 in/d. Rates did not differ significantly between the different crops and soils tested, but were found to be about an order of magnitude higher in one field. At a 2.5 in/d infiltration rate, 100 acres are required to infiltrate 10 CFS of captured flood flows. Water quality of applied flood flows from the Kings River had concentrations of COC (constituents of concern; i.e. nitrate, electrical conductivity or EC, phosphate, ammonium, total dissolved solids or TDS) one order of magnitude or more lower than for pumped groundwater at Terranova Ranch and similarly for a broader survey of regional groundwater. Applied flood flows flushed the root zone and upper vadose zone of nitrate and salts, leading to much lower EC and nitrate concentrations to a depth of 8 feet when compared to fields in which more limited flood flows were applied or for which drip irrigation with groundwater was the sole water source. In demonstrating this technology on the farm, approximately 3,100 ac-ft was diverted, primarily from April through mid-July, with about 70% towards in lieu and 30% towards direct recharge. Substantial flood flow volumes were applied to alfalfa, wine grapes and pistachio fields. A subset of those fields, primarily wine grapes and pistachios, were used primarily to demonstrate direct recharge. For those fields about 50 – 75% of water applied was calculated going to direct recharge. Data from the check studies suggests more flood flows could have been applied and infiltrated, effectively driving up the amount of water towards direct recharge. Costs to capture flood flows for in lieu and direct recharge for this project were low compared to recharge costs for other nearby systems and in comparison to irrigating with groundwater. Moreover, the potentially high flood capture capacity of this project suggests significant flood avoidance costs savings to downstream communities along the Kings and San Joaquin Rivers. Our analyses for Terranova Ranch suggest that allocating 25% or more flood flow water towards in lieu recharge and the rest toward direct recharge will result in an economically sustainable recharge approach paid through savings from reduced groundwater pumping. Two important issues need further consideration. First, these practices are likely to leach legacy salts and nitrates from the unsaturated zone into groundwater. We develop a conceptual model of EC movement through the unsaturated zone and estimated through mass balance calculations that approximately 10 kilograms per square meter of salts will be flushed into the groundwater through displacing 12 cubic meters per square meter of unsaturated zone pore water. This flux would increase groundwater salinity but an equivalent amount of water added subsequently is predicted as needed to return to current groundwater salinity levels. All subsequent flood flow capture and recharge is expected to further decrease groundwater salinity levels. Second, the project identified important farm-scale logistical issues including irrigator training; developing cropping plans to integrate farming and recharge activities; upgrading conveyance; and quantifying results. Regional logistical issues also exist related to conveyance, integration with agricultural management, economics, required acreage and Operation and Maintenance (O&M).

On-Farm Flood Flow Capture – addressing flood risks and groundwater overdraft in the Kings Basin, with potential applications throughout the Central Valley

Project fact sheet prepared in cooperation with the USDA Natural Resources Conservation Service and the Kings River Conservation District.

An Integrated Approach to Quantifying Groundwater and Surface Water Contributions of Stream Flow

The management of water resources in Ireland prior to the Water Framework Directive (WFD) has focussed on surface water and groundwater as separate entities. A critical element to the successful implementation of the
WFD is to improve our understanding of the interaction between the two and flow mechanisms by which groundwaters discharge to surface waters. An improved understanding of the contribution of groundwater to surface water is required for the classification of groundwater body status and the determination of groundwater quality thresholds. The results of the study will also have a wider application to many areas of the WFD.
A subcommittee of the WFD Groundwater Working Group (GWWG) has been formed to develop a methodology to estimate the groundwater contribution to Irish Rivers. The group has selected a number of analytical techniques to quantify components of stream flow in an Irish context (Master Recession Curve, Unit Hydrograph, Flood Studies Report methodologies and
hydrogeological analytical modelling). The components of stream flow that can be identified include deep groundwater, intermediate and overland. These analyses have been tested on seven pilot catchments that have a variety of hydrogeological settings and have been used to inform and constrain a mathematical model. The mathematical model used was the NAM (NedbØr-AfstrØmnings-Model) rainfall-runoff model which is a module of DHIs MIKE 11 modelling suite. The results from these pilot catchments have been used to develop a decision model based on catchment descriptors from GIS datasets for the selection of NAM parameters. The datasets used include the mapping of aquifers, vulnerability and subsoils, soils, the Digital Terrain Model, CORINE and lakes. The national coverage of the GIS datasets has allowed the extrapolation of the mathematical model to regional catchments across Ireland.