Realistic forecasting of groundwater level, based on the eigenstructure of aquifer dynamics

Conference paper presented at the MODSIM03, International Congress on Modelling and Simulation, held July 2003, Jupiters Hotel and Casino, Townsville, Queensland.Short-term management of groundwater resources, especially during droughts, can be assisted by forecasts of groundwater levels. Such forecasts need to account for the natural dynamic behaviour of the aquifer, likely recharge scenarios, and recent but unknown abstractions. These requirements mean that forecasts, at say monthly intervals, need to be updated with current observations on a real-time basis. One established procedure for this kind of problem is to fit autoregressive, moving-average, exogenous-variable (ARMAX) time-series models to the history of groundwater levels in response to estimates of land surface recharge. The ARMAX difference equations are then converted into forecast equations that allow real-time updating to include recent forecast errors as an additional source of information. Some disadvantages of this pure time-series analysis approach are the apparent lack of physical concepts in the model formulation and statistical aspects of model identification and calibration that are related to the inherent structure of ARMAX equations. This paper addresses these issues by describing a method for formulating ARMAX forecast equations from a linear system description based on the eigenvalues and eigenvectors (eigenstructure) of the dynamic behaviour of an aquifer. For the piezometric response of a heterogeneous aquifer to a fixed spatial distribution of land surface recharge, with time-varying magnitude, only a few eigenvalues are significant for describing the dynamics. The resulting model has a simple robust parameter structure, and is easily calibrated and implemented in spreadsheet form. The eigenstructure approach enables transfer of some parameter information from locations with good data records to those with sparse data. This modelling approach is demonstrated with monthly values of land surface recharge, estimated from a daily water balance model, and groundwater level data from an observation well in a 2000 km² alluvial aquifer in Canterbury, New Zealand

State-space mixing cell model of unsteady solute transport in unsaturated soil

The purpose of this model is to enable implementation of the theory of linear systems control in operational management of waste and fertiliser applications onto land, so that the underlying groundwater is protected from pollution by leachate. The state-space form of the model enables use of the extensive theory and available software on stochastic linear systems. In particular, the Kalman filter is relevant to the imperfectly understood and highly variable processes of solute transport and transformation in field soils. The series of mixing cells was selected as a linear system model of one-dimensional, vertical, advective-dispersive transport, and based on cumulative soil water drainage as the index variable for application to unsteady flow in unsaturated soil. For each cell, solute transfer between mobile and immobile soil water, as well as equilibrium and nonequilibrium linear adsorption, are represented as lumped processes by two fractions linked by rate-limited transfer. The resident solute concentrations in the cell fractions are the states of the system. The complete model of solute transport and transformation for a uniform soil has four parameters, and can be described in MATLAB® with about ten lines of code. The software library can then be used to produce the discrete form of the model, which is unconditionally stable for any drainage interval as well as to implement state estimation and control algorithms. A demonstration of the model is reported for ³⁵S-labelled sulphate leached from five replicated lysimeters (800 mm diameter, l100 mm depth) of an undisturbed field soil (a free-draining silt loam) under pasture receiving rainfall and irrigation, The results show satisfactory one-step-ahead forecasts with the Kalman filter for the period of record, and a forecast is given of the complete response to the solute pulse application beyond the data record.The reported research is part of the Groundwater Quality Protection programme funded by the Foundation for Research, Science and Technology, New Zealand

Groundwater management tools : analytical procedure and case studies

This report addresses an issue of groundwater management that was identified by regional council staff, as part of a project conducted by Ministry of Agriculture & Forestry and the Ministry for the Environment for encouraging and ensuring effective and efficient water allocation in New Zealand. The issue is how to manage groundwater allocation under conditions of increasing abstraction and imperfect, but developing, knowledge of the resource. The overall objective is to maintain sustainability of the groundwater resource in terms of acceptable environmental effects. The first part of this report is a draft Best Practice Guideline, which sets the context of the nature of the groundwater resource, quality and availability of data, and an appropriate resource management approach. A recommendation from the water allocation project was that an adaptive approach to groundwater management was required, and that there was a need for appropriate analytical tools to support this approach. A companion report addresses the origin and philosophy of adaptive management in water resources. The second part of the report is concerned with the development and demonstration of a suitable analytical method, and guidelines for its implementation, which supports the recommended adaptive management strategy. The "eigenmodel" method is concerned primarily with the amount of water stored in an aquifer, and how this responds to recharge and abstraction. The resulting information about groundwater levels can be related to environmental effects such as low flow in streams, for example. It is a "whole aquifer" approach and does not purport to be suitable for detailed investigation of local effects caused by abstraction stresses. These problems require other well established modelling techniques, and their compatibility with the eigenmodel method is discussed. The issue of sparse data is addressed by the simplicity of the analytical format, which enables identification of fundamental properties of aquifer storage, sometimes from only one observation well record. Implementation of the procedure is ideally suited to spreadsheet software. These simple models can also be expressed in a form that incorporates continual monitoring of groundwater levels for "real-time" forecasting as decision support for adaptive management. Several demonstrations with observed data from two aquifer systems are presented to illustrate the capabilities of the procedure

The eigenvalue approach to groundwater modelling for resource evaluation at regional scale

A conference paper presented at ModelCARE 2002, 4th International Conference on Calibration and Reliability in Groundwater Modelling, Prague, Czech Republic, 17-29 June 2002.The dynamic response of piezometric head at any location in an aquifer to time variation of regional land surface recharge and abstraction can be expressed as a linear system comprising only a few conceptual water storages. Model structure and parameters are related to aquifer characteristics and spatial pattern of recharge by the eigenvalues and eigenfunctions of a general analytical solution to the linearised Boussinesq equation. The model is implemented as a stochastic ARMA difference equation, independently for each location. This modelling approach is demonstrated for an aquifer of 2000 km² area, yielding additional information about unobservable recharge and aquifer boundaries.Development of methodology was funded by the Foundation for Research, Science and Technology. Demonstration results are from a water resource study for Environment Canterbury, Ministry for the Environment and Ministry of Agriculture and Forestry, New Zealand

Pathways from land to stream: lessons from Pukemanga

Oral presentation at the New Zealand Hydrological Society Annual Conference, 20-23 November 2007, Rotorua, New Zealand.In the Pukemanga catchment, nitrate is leaching from soil under agricultural land use, and is being transported by subsurface water flow to surface waters. Groundwater is the suspected dominant transport pathway. This study proposes to determine the proportion of groundwater discharge to streamflow by partitioning of daily and hourly streamflow on the basis of groundwater dynamics

Groundwater recharge interface and nitrate discharge: Central Canterbury, New Zealand

Full conference paper presented at the New Zealand Hydrological Society Annual Conference, 28 November-1 December 2005, Auckland, New Zealand.Regional surveys of groundwater quality in Central Canterbury, from 1977 to the present, show widespread occurrence of nitrate contamination primarily from agricultural land use. Two reported analyses of these surveys, in 1984 and 2002, describe a general decrease of nitrate concentration with depth from the groundwater table to uncontaminated water at about 50-80 m. This high quality water is considered to be recharge from the large rivers that originate in alpine catchments. The occurrence and location of the interface between these distinctly different groundwater bodies is important for issues of access to high quality drinking water and for the quality of groundwater-fed surface waters in the down-slope areas of the Central Canterbury Plains. This paper describes the application of a prototype regional-scale model of nitrate transport in groundwater to investigation of the likely nature of this groundwater interface and the implications for quality of surface waters in the groundwater discharge zone. Results from a 2-D horizontal groundwater flow model indicate that river recharge is the major source of groundwater, from leakage rates per kilometre of river reach that are less than 1% of mean annual river flow. The vertical distribution of groundwater contaminant transport was examined with a combination of stream-function analysis of flow, and mixing-cell model simulation of contaminant dispersion. The results of a model demonstration with a realistic land use pattern, for a typical groundwater flow path, illustrate the formation of a dispersive, concentration interface between the two groundwater bodies. The demonstration example also shows how average nitrate-N concentration of about 8 mg/L in recharge from agricultural land use contributes to mean concentrations of 2- 3 mg/L in the groundwater discharge zone, due to the influence of river recharge

Working the blue gold: a personal journey with mathematical tools for water management

Keynote Address presented at the New Zealand Hydrological Society Annual Conference, 6-10 December 2010, Dunedin, New Zealand.This presentation is about mathematical models, but with a particular bias. The title refers to working the blue gold – and the models are called mathematical tools. This is about mathematical models applied to solving problems in the management of water, in terms of both quantity and quality

Development of the AquiferSim model of cumulative effect on groundwater of nitrate discharge from heterogeneous land use over large regions

Conference paper presented at the MODSIM07, International Congress on Modelling and Simulation, held December 2007, University of Canterbury, New Zealand.Regional-scale prediction of the effects of nitrate discharge from land use on the quality of the underlying groundwater requires two major model components: (1) a climate-driven model of agricultural land use that predicts nitrate discharge at the bottom of the plant root zone, for locations over horizontal space; and (2) a groundwater transport model, which predicts nitrate concentration at horizontal and vertical locations within the aquifer as well as the nitrate discharge to surface-water bodies. AquiferSim is a recently developed groundwater transport model, for which the inputs of recharge and nitrate from the land surface are received from a GIS user interface that accesses the root zone nitrate discharge model. The AquiferSim groundwater transport model is designed to address two particular requirements. The first is that model run times should allow for real-time examination of land use scenarios and assessment of uncertainty. The second is that dimensions of computational cells should allow for realistic transport dispersion in both horizontal and vertical dimensions, as well as allowing improved accuracy of flowpaths to surface-water bodies. These latter requirements imply very large numbers of computational cells for regional-scale studies, with associated costs in model run time. These issues are addressed in the AquiferSim model by: assuming steady-state groundwater flow and transport; solving 2D horizontal groundwater flow on ~10⁶ computational cells with a fast, fullmulti- grid solver; and then solving flow and transport on vertical sections of ~10⁴ cells along selected groundwater flowpaths, with a successive over- relaxation solver. The software was developed entirely in Microsoft Visual C# on the .NET framework. This enables the AquiferSim engine to run on modern Windows PCs and on Linux and clustered environments using the MONO platform. Computational time performance of the AquiferSim engine enables the horizontal 2D steady-flow groundwater problem and pathline tracking to be solved in about 5 s for a region occupying one third of the 1025 x 1025 computational grid. Solution for groundwater flow, nitrate transport, and groundwater age on the ~ 10⁴ cells of one vertical slice requires up to 20 s. Implementation of AquiferSim within a regional council for environmental planning purposes is the next phase of development. The major issues are likely to be: quantifying the predictive uncertainty caused by inadequate description of aquifer recharge and properties; and software design for interrogation of AquiferSim output to meet yet unspecified requirements for end-user information

Linear system model of water flow and oxygen-18 transport on a steep hillslope

The purpose of this model was to assist with the determination of the nature of water flow processes on steep (≈35°) hillslopes in a 3.8 ha forested catchment. The soils are sufficiently permeable that, for most rainstorms, streamflow responds rapidly without significant surface runoff occurring. Scientific debate had focused on whether "old water" held within the soil could be rapidly mobilised by incoming "new water" from storm rainfall. A linear system approach was taken to the analysis of the dynamic response of water flow and concentration of the natural isotope oxygen-18 in the stream to the input series of rainfall and associated oxygen-18 content from one storm. The candidate system components were bounded and unbounded water storages with first-order water flow dynamics, and bounded storages with zero-order dynamics. The upper limits on the bounded storages allow for nonlinearities in flow processes. The dynamic effect on transport of the isotopic tracer was assumed to be due to perfect mixing within each of the water storage components. The model was implemented on spreadsheet software in the form of difference equations and logical expressions. Analysis of the rainfall and streamflow data showed that the hydrometric response could be simulated with one bounded (8.5 mm) zero-order storage to account for initial rainfall loss, followed by a bounded (25.6 mm) and an unbounded first-order storage in parallel. However, this model provided insufficient attenuation of the oxygen-18 signal. Satisfactory simulation of oxygen-18 in the stream was achieved by including a bounded zero-order storage (250 mm) of specified oxygen-18 concentration. The same model structure was fItted to additional data from measurement of subsurface flow conected by troughs at four locations on the hillslopes. The results support the hypothesis that mobilisation of old water is an important component of water flow on the hillslopes. However, the degree of mixing within the old water storage has not been conclusively determined on the basis of the one storm event

Extreme ranges of groundwater level

Oral presentation at New Zealand Hydrological Society & Meteorological Society of New Zealand Joint Annual Conference, 18-20 November 2008, Shantytown/Greymouth, New Zealand.Large natural variations in groundwater levels can be an issue for selecting the depth of new water well installations or for evaluation of health risk from land treatment of waste, especially when these variations occur over periods of several years. Some parts of the Canterbury Plains show recorded variations in groundwater level that have a range of more than 30 m. In this presentation, the factors contributing to this range of groundwater level are examined and quantified. The time series of groundwater levels at selected monitoring wells in the alluvial plains area of Central Canterbury were used to calibrate a physically-based analytical groundwater model. This model is homogeneous and one-dimensional in the groundwater flow direction across the plains, and is represented for computational purposes as the eigenmodel solution to the boundary conditions of no-flow at the foothills and fixed-head at the coastal discharge zone. The results show that groundwater recharge from soil-water drainage is the dominant cause of natural groundwater level variation, even in the presence of a large component of recharge from the rivers that transect the plains. Soil-water drainage is determined by the partitioning effect of soil-plant-atmosphere processes on the rainfall climate (and, increasingly, irrigation). The time scale of dynamic response of groundwater levels and groundwater discharge to these climate-driven processes can be quantified by means of a single parameter that encapsulates the horizontal scale of the groundwater system and bulk values of the storativity and transmissivity of the aquifer. The magnitude of response is determined by the location of the monitoring well and the bulk transmissivity of the aquifer system. The geology, climate, and extent of the Canterbury Plains produce a combination of factors that result in ranges of natural dynamic groundwater level variation that are unusually large for aquifers in New Zealand