Predictive Models
The conceptual model forms the foundation for further field investigations as well as the development of predictive models. These are essentially mathematical models or simple tools that contain equations that represent the physical processes of water movement in a catchment. Encapsulating the hydrological processes using governing mathematical equations, boundary conditions and estimates of catchment parameters can provide a powerful predictive tool.
The conceptual model outlines the dominant processes and underlying simplifying assumptions to be implemented by the predictive model. It is important to clarify the complexity of the solution required, as an oversimplified model may not be adequately robust and an over-complex model may be costly, time-consuming and have intractable data requirements. The level of conceptualisation and requirements of the predictive model depends on the management objectives, available resources and field data, and the legal and regulatory framework (Bear et al, 1992).
Mathematical models can vary in form and complexity and include analytical, analytical element, boundary integral and numerical techniques.
Analytical Models
In analytical models the partial differential equations that govern water flow are directly solved. Analytical models are useful in providing simple, quick and approximate solutions to one- or two-dimensional flow problems, with relatively small data requirements. However, simplifying assumptions such as straight boundaries or homogenous aquifers are required that may not be valid in reality. Analytical models are often used in preliminary investigations and for validating other modelling efforts. Initial development of analytical models focused on stream depletion due to groundwater extraction (Theis, 1941; Glover & Balmer, 1954; Jenkins, 1968). Later refinements include existence of a semipermeable layer (Hantush, 1965), analysis of cyclic pumping wells (Wallace et al, 1999), a stream that only partially penetrates the aquifer (Hunt, 1999) and estimation of the baseflow reduction and stream infiltration components of stream depletion as well as the timing of hydraulic gradient reversal (Chen, 2003). Analytical solutions that represent the hydraulic interaction between streams and a range of different aquifer types (confined, leaky or watertable) are publicly available (Barlow and Moench, 1998). Analytical models can be constrained by assumptions that oversimplify the conceptual model or are invalid for the catchment.
In analytical element models, analytical solutions for different processes (such as groundwater pumping, recharge, seepage boundaries) are spatially combined and superimposed. This allows greater capability in simulating the complexity of hydrological processes in a catchment, and to accommodate layering and inhomogeneity in aquifer properties. Examples of available analytical element modelling tools include QUICKFLOW, WINFLOW, TWODAN, GFLOW and Visual Bluebird (Table 1).
Boundary integral equation models involve the combination of analytical and numerical solutions, but are not commonly used.
Numerical Models
Numerical models use approximation and iterative techniques to solve the governing equations. Gridded methods such as finite difference or finite elements are used to discretise the model region into smaller increments. This allows better handling of complexity in terms of spatial and temporal variability (such as boundary conditions, aquifer structure and hydraulic parameters, recharge and discharge processes) and for three-dimensional solutions to be constructed. As such, numerical models tend to be more complicated and time-consuming, and require a larger array of inputs and careful calibration.
There are four possible alternatives in terms of the numerical modelling of connected groundwater-surface water systems (CDM, 2001). These are:
- using a developed fully-integrated surface water and groundwater hydrological model. Only a few fully-integrated models that encompass surface, unsaturated and saturated zone flow have been developed; such as MIKE SHE, IHSim and IWFM (Table 1);
- using or expanding the surface water capabilities of developed groundwater modelling software. Many groundwater numerical models omit or oversimplify surface-groundwater interaction processes. The commonly used groundwater flow model MODFLOW (Harbaugh et al, 2000) does include packages that represent interactions with various surface water features. For example, the MODFLOW River package calculates seepage flux using Darcy's Law with estimates of a leakage coefficient as well as the head difference between the groundwater elevation in the model cell and the specified stream elevation;
- using or expanding the groundwater capabilities of developed surface water modelling software. Many surface water models combine all unmeasured fluxes (such as evaporation, in-stream use, ungauged tributary inflows, unlicensed abstractions) into one term, which also includes seepage with the groundwater system. The urban runoff model SWMM (US EPA) and the Integrated Quantity and Quality Model IQQM (NSW DNR) are surface water models with limited representation of groundwater processes. IQQM simulates surface water movement using a series of interconnected nodes to simulate water movement from one point in the river or stream to the next; and
- using or developing an intermediate modelling package linking established groundwater and surface water models. Models such as MODBRANCH linking MODFLOW and the stream network model BRANCH (Swain & Wexler, 1996) and ISGW linking MODFLOW and HSPF have been designed in this way. Software to link the surface water model IQQM to the MODFLOW groundwater package have recently been developed and trialled (REM, 2002).
A properly constructed mathematical model can be a powerful analysis tool for a range of purposes (Middlemis, 2001), including to:
- improve understanding of the key hydrological processes. The behaviour of groundwater-surface water systems can be evaluated and the water balance components quantified in terms of storage and flux;
- help predict the impact of various water management options or changes to catchment condition, assist in the optimisation of management solutions and provide input to the engineering design of on-ground works. Models have been used to simulate the effect of changes to water allocations, increased groundwater development, water trade, long term climatic trends or land use change, by comparing with a baseline status quo scenario. Developing models that simulate linked physical, biological and economic systems under different scenarios is an invaluable way of understanding catchment processes and their response to change; and
- help synthesise data and encapsulate the existing understanding of the groundwater and surface water systems. Models are often used to interpolate the available (but limited) data both in space and time, as a cheaper and quicker option than intense data collection. Information gaps can be identified and sensitivity and uncertainty analysis undertaken to guide data gathering and risk management. Models can be used as a visualisation and communication tool.
However, mathematical models need a robust understanding of the key hydrological processes. A model can have significant errors because of the need to:
- simplify complex natural systems by making key assumptions. Model results can be called into question if the basic assumptions are not valid;
- interpolate between often sparse data points (such as monitoring bores or stream gauges);
- integrate hydrological processes that operate at different scales in space and time. Surface water processes tend to occur at much shorter timescales than groundwater processes;
- assess the natural variability in fluxes (such as episodic recharge or flood events) often with inadequate time series monitoring;
- deal with parameters (such as transmissivity) that can vary significantly over the model area; and
- use modelling code that intrinsically does not have a unique solution.
A predictive modelling example
The area of the catchment can be represented as an interconnected 3D grid of cells, which are assigned a number of different parameters to represent natural variation in hydrogeological properties. Groundwater fluxes into and out of these cells can be simulated using the numerical groundwater flow modelling code MODFLOW (Harbaugh et al, 2000).
Once calibrated against empirical data (ie. historical records of groundwater recharge and extraction and water level monitoring) the model can be used to develop predictions of what future groundwater levels will be for any projected changes in groundwater extraction. This response function can be developed for a variety of different projections of what future pumping scenarios may be.
An environmental component can be incorporated into the response function that allows for the environmental water requirements of each connected ecosystem. As well as this, a water resource management component can be used to allocate the remaining water between surface water withdrawal and groundwater extraction based on different water property right arrangements and the seasonal stream flows and groundwater recharge.
An economic component is incorporated into the model that allocates water extracted on-farm between various cropping enterprises. At the farm level, the decision maker is faced with an intermediate-term decision of allocating land versus short-term decisions of allocating water between crops within the season, as the actual allocation of water may be different from farmers' expectation at the beginning of the season. In this manner the impact on farmer decisions of uncertainty in water supply throughout the season is captured. The farmer is assumed to maximise profits subject to land and water resources available for a given set of prices and production technologies.
Modelling Guidelines
General guidelines have been developed by the Murray-Darling Basin Commission relating to groundwater flow modelling (Middlemis, 2001). This is a useful resource for the non-specialist client in scoping and developing model project specifications, project management and the model review process. The guidelines also have comprehensive technical information relating to the different stages of the modelling process such as conceptualisation, calibration, prediction, uncertainty analysis and reporting. Although principally designed for groundwater flow models, the guidelines have general principles useful for more integrated modelling initiatives.
The HarmoniQuA project involves a consortium of European agencies and universities working to develop a user-friendly guidance and quality assurance framework for best-practice river basin modelling. This involves:
- a harmonised methodology with associated guidelines (generic, domain specific and integrated) for good modelling practice;
- a computer based toolbox to provide guidance, monitoring and reporting functionality to the HarmoniQuA knowledge base and support the model user/water manager throughout the quality assurance process;
- results of two sets of real life test case studies; and
- infrastructure for exploitation and dissemination, including training material.
The two main products are the Modelling Support Tool (MoST) and Knowledge Base (KB) which are available as a free download. The overall modelling process has been structured into five key processes (Figure 2). The 'Knowledge Base' relates to various components of catchment water management including groundwater, precipitation-runoff, river hydrodynamics, flood forecasting, water quality, ecology, and socio-economics. The HarmiQuA project aims to support the implementation of the EU Water Framework Directive.
Figure 2: HarmoniQuA flowchart of the process of modelling river basin processes
Modelling Software
Outlined in Table 1 are some examples of modelling code with varying levels of surface water and groundwater capabilities
| Model | Source | Description |
|---|---|---|
| Analytical Models | ||
| GWFLOW | http://typhoon.mines.edu/software/igwmcsoft/ | Suite of 7 analytical solutions for groundwater flow problems including streamflow depletion |
| STRMDEPL | http://smig.usgs.gov/SMIG/models/strmdepl_code.html | FORTRAN program to calculate time-varying streamflow depletion caused by a pumped well. |
| WALTON35 | http://typhoon.mines.edu/software/igwmcsoft/ | Series of 35 simple analytical/numerical models for flow, solute and heat transport including streamflow depletion and saltwater intrusion |
| Analytical Element Models | ||
| GFLOW | http://www.haitjema.com/ | Models stready state flow in a single heterogenous aquifer Uses stream networks with calculated streamflow |
| TWODAN | http://www.fittsgeosolutions.com/ | Two-Dimensional analytical groundwater flow model |
| Visual Bluebird | http://www.eng.buffalo.edu/groundwater/software/software.html | Interface for 2-D single-layer analytical element groundwater flow |
| WINFLOW | http://www.groundwatermodels.com/software/Software.asp | Analytical model for 2-D steady state and transient groundwater flow. |
| Integrated Numerical Models | ||
| IHSim | http://www.modhms.com/software.htm | Integrated finite element model for 3-D subsurface and 2-D overland/stream flow and transport |
| InHM | http://inhm.org | Integrated Hydrology Model integrates surface and subsurface flow and transport processes using physically-based first-order flux relationships |
| IWFM | http://baydeltaoffice.water.ca.gov/modeling/hydrology/IWFM/index.cfm | Integrated Water Flow Model is a water resources management and planning model that simulates groundwater, stream flow and interactions, soil moisture etc. Includes a land use based approach of calculating water demand |
| MIKE BASIN | http://www.dhisoftware.com/mikebasin/ | GIS-based water resource modelling framework at river-basin level including surface water, groundwater, rainfall, water quality etc |
| MIKE-SHE | http://www.dhisoftware.com/mikeshe/ | Modelling system with modules for 3-D groundwater flow, overland flow, unsaturated flow, solute transport, water quality, irrigation, particle tracking etc |
| MODHMS | http://www.modhms.com/software.htm | MODFLOW-based groundwater flow integrated with dynamic interactions with overland flow and channel flow analysis |
| WASH123D | http://chl.erdc.usace.army.mil/CHL.aspx?p=s&a=Software;1 | Watershed Systems of 1D Stream-River Network, 2D Overland Regime and 3D Subsurface Media. Finite element integrated model supported by GMS graphical environment |
| ZOOMQ3D | http://www.bgs.ac.uk/science/3Dmodelling/zoom.html | Saturated groundwater flow model using object oriented programming and able to integrate surface water components |
| Surface Water Focused Numerical Models | ||
| HSPF | http://water.usgs.gov/software/hspf.html | Hydrological Simulation Program for modelling the hydrologic and water quality processes, including groundwater recharge and baseflow |
| SWMM | http://www.epa.gov/ednnrmrl/models/swmm/index.htm | Dynamic rainfall-runoff model for water flow and quality in urban areas, included interflow between groundwater and drainage system |
| Groundwater Focused Numerical Models | ||
| DYNFLOW | http://www.dynsystem.com/system/dynflow.html | 3-D finite element groundwater flow model with stream/river package |
| FESEEP | http://www.civil.usyd.edu.au/cgr/software.shtml | 2-D finite element steady state seepage analysis |
| FLOWNET | http://www.microfem.com/ | Generates 2-D flow net using finite difference approximation |
| GGU-SS FLOW 2D/3D | http://www.ggu-software.com | Steady state 2-D or 3-D groundwater flow using finite element analysis |
| MicroFEM | http://www.microfem.nl/products/microfemw.html | Finite element groundwater model with drain, river and wadi top systems |
| MODFLOW 2000 | http://water.usgs.gov/nrp/gwsoftware/modflow2000/modflow2000.html | 3-D finite difference groundwater flow model with various modules including groundwater-surface water interactions. De facto industry standard |
| MODRET | http://www.scientificsoftwaregroup.com/ | Modified version of MODFLOW for calculating infiltration from retention ponds to unconfined shallow aquifers |
| PLASM | http://typhoon.mines.edu/software/igwmcsoft/ | 2-D nonsteady finite difference groundwater flow model including option for stream leakage |
| SefWeir | http://www.ogi.co.uk/ | Finite element analysis of groundwater flow beneath a dam or weir |
| SHARP | http://water.usgs.gov/software/ground_water.html | Finite-difference model to simulate freshwater/salt water flow in layered coastal aquifers |
| SFWMD | http://www.sfwmd.gov/org/pld/hsm/modflow/index.htm | South Florida Water Management Model. Development of MODFLOW packages for providing better capability in simulating connectivity |
| Hybrid Numerical Models | ||
| Ground Water Simulator | http://www.artesiansoftware.com/ | Integrates MODFLOW 2000, MODPATH particle tracking and MT3DMs mass transport model |
| IFMMike | http://www.wasy.de/english/produkte/feflow/ifmmike11.html | Links FeFlow finite element subsurface flow and transport model with Mike11 1-D surface water flow model |
| IHM | http://www.intera.com/technology_ihm.php | Integrated Hydrological Model linking HSPF surface water model with MODFLOW groundwater model |
| ISGW | http://www.isgw.com/about_isgw.html | Integrated Surface and Ground Water Model linking HSPF surface water model with MODFLOW groundwater model |
| MODBRNCH | http://water.usgs.gov/software/modbrnch.html | Linking of MODFLOW3-D groundwater flow package with BRANCH which models 1-D unsteady flow in open-channel networks |
| MODFLOW/DAFLOW | http://water.usgs.gov/nrp/gwsoftware/daflow/daflow.html | Coupled Flow Model using USGS MODFLOW and DAFLOW Models |
Case Studies
Relevant Links
eWater CRC Catchment Modelling Toolkit
Murray Darling Basin Commission Groundwater flow modelling guideline
NHT Practical Index of Salinity Models (PRISM)
Environment Canterbury NZ Groundwater Analysis Tools
International Association for Environmental Hydrology HydroWeb
IGMC International Groundwater Modeling Center
IGMC JUPITER - Joint Universal Parameter Identification and Evaluation of Reliability
IWMI SWIM Paper 6 Modeling water resources management at the basin level
European Commission HarmoniQuA
ISEM Europe ECOBAS - Register of Ecological Models
UK Environment Agency Groundwater Resources Modelling
Dominion University CEML Environmental Model Library
US Department of Agriculture George E Brown Jr Salinity Laboratory
Pacific Northwest National Laboratory Hydrology Web Computing
US Environmental Protection Agency GWERD Software
US Environmental Protection Agency Fundamentals of ground-water modeling
US Geological Survey Analytical modelling of flow and transport in aquifers
US Geological Survey Surface-water quality and flow Modeling Interest Group (SMIG)
US Geological Survey Water Resources Software
US Geological Survey Guidelines for evaluating groundwater flow models
GGSD Geotechnical and Geoenvironmental Software Directory
The Hydrogeologist Software for Hydrogeologists
Richard B Winston Groundwater Modeling Links
References
Barlow PM, Moench AF, 1998. Analytical solutions and computer programs for hydraulic interaction of stream-aquifer systems. Open-File Report 98-415. US Geological Survey.
Bear J, Beljin MS, Ross RR, 1992. Fundamentals of ground-water modelling. EPA Ground Water Issue EPA/540/S-92/005. US Environmental Protection Agency.
CDM, 2001. Evaluation of integrated surface water and groundwater modelling tools. Camp Dresser and McKee.
Chen X, 2003. Analysis of pumping-induced stream-aquifer interactions for gaining streams. Journal of Hydrology 275:1-11.
Glover RE, Balmer CG, 1954. Stream depletion resulting from pumping a well near a stream. American Geophysical Union Transactions 35(3), 168-470.
Hantush MS, 1965. Wells near stream with semipervious beds. Journal of Geophysical Research 70(12), 2829-2838.
Harbaugh AW, Banta ER, Hill MC, McDonald MG, 2000. MODFLOW-2000, The U.S.Geological Survey Modular Groundwater model - user guide to modularisation concepts and the groundwater flow process. US Geological Survey Report 00-92.
Hunt B, 1999. Unsteady stream depletion from ground water pumping. Ground Water 37(1), 98-104.
Jenkins CT, 1968. Techniques for computing rate and volume of stream depletion by wells. Ground Water 6(2), 37-46.
Middlemis H, 2001. Groundwater flow modelling guideline. Murray Darling Basin Commission.
REM 2002. Watermark: Sustainable groundwater use within irrigated regions. Project 2: Conjunctive resource management, milestone 2 final report. Prepared for the Murray Darling Basin Commission, Australia.
Swain ED, Wexler EJ, 1996. A coupled surface-water and ground-water flow model (MODBRNCH) for simulation of stream-aquifer interaction: U.S. Geological Survey Techniques of Water-Resources Investigations, book 6, chap. A6, 125 p.
Theis CV, 1941. The effect of a well on the flow of a nearby stream. American Geophysical Union Transactions 22 (3), 734-738.
Wallace R, Darama BY, Annable MD, 1999. Stream depletion by cyclic pumping of wells. Water Resources Research 26 (6), 1263-1270.