Anthony Jakeman

How much complexity is warranted in a rainfall-runoff model?

Development of mathematical models relating the precipitation incident upon a catchment to the streamflow emanating from the catchment has been a major focus of surface water hydrology for decades. Generally, values for parameters in such models must be selected so that runoff calculated from the model “matches” recorded runoff from some historical period. Despite the fact that the physics governing the path of a drop of water through a catchment to the stream involves complex relationships, evidence indicates that the information content in a rainfall-runoff record is sufficient to support models of only very limited complexity. This begs the question of what limits the observed data place on the allowable complexity of rainfall-runoff models. Time series techniques are applied for estimating transfer functions to determine how many parameters are appropriate to describe the relationship between precipitation and streamflow in the case where data on only precipitation, air temperature, and streamflow are available. Statistics from an “information matrix” provide the clues necessary for determining allowable model complexity. Time series models are developed for seven catchments with widely varying physical characteristics in different temperate climatic regimes to demonstrate the method. It is found that after modulating the measured rainfall using a nonlinear loss function, the rainfall-runoff response of all catchments is well represented using a linear model. Also, for all catchments a two-component linear model with four parameters is the model of choice. The two components can be interpreted as defining a “quick flow” and “slow flow” response of the given catchment. The method therefore provides a statistically rigorous way to separate hydrographs and parameterize their response behavior. The ability to construct reliable transfer function models for describing the rainfall-runoff process offers a new approach to investigate empirically the controls of physical catchment descriptors, land use change, climate change, etc., on the dynamic response of catchments through the extensive analysis of historical data sets.

Position Paper11Position papers aim to synthesise some key aspect of the knowledge platform for environmental modelling and software issues. The review process is twofold - a normal external review process followed by extensive review by EMS Board members. See the Editorial in this issue.: Ten iterative steps in development and evaluation of environmental models

Models are increasingly being relied upon to inform and support natural resource management. They are incorporating an ever broader range of disciplines and now often confront people without strong quantitative or model-building backgrounds. These trends imply a need for wider awareness of what constitutes good model-development practice, including reporting of models to users and sceptical review of models by users. To this end the paper outlines ten basic steps of good, disciplined model practice. The aim is to develop purposeful, credible models from data and prior knowledge, in consort with end-users, with every stage open to critical review and revision. Best practice entails identifying clearly the clients and objectives of the modelling exercise; documenting the nature (quantity, quality, limitations) of the data used to construct and test the model; providing a strong rationale for the choice of model family and features (encompassing review of alternative approaches); justifying the techniques used to calibrate the model; serious analysis, testing and discussion of model performance; and making a resultant statement of model assumptions, utility, accuracy, limitations, and scope for improvement. In natural resource management applications, these steps will be a learning process, even a partnership, between model developers, clients and other interested parties.

A review of erosion and sediment transport models

Abstract Information on sediment and nutrient export from catchments and about related erosive processes is required by catchment managers and decision-makers. Many models exist for the consideration of these processes. However, these models differ greatly in terms of their complexity, their inputs and requirements, the processes they represent and the manner in which these processes are represented, the scale of their intended use and the types of output information they provide. This paper reviews several different erosion and sediment and sediment-associated nutrient transport models with regard to these factors. The review of models is limited to those models with explicit considerations of either the sediment generation or transport process.

Computation of the instantaneous unit hydrograph and identifiable component flows with application to two small upland catchments

Abstract Our approach is based upon three factors: (i) the representation of total streamflow response as a linear convolution of the instantaneous unit hydrograph with rainfall excess; (ii) approximation of this representation in discrete time by a rational transfer function relationship which involves an efficient and flexible parameterisation; (iii) use of a simple refined version of the instrumental variable method of parameter estimation as the major tool to determine the number of identifiable flow components in the representation and to estimate their dynamic contributions to the instantaneous unit hydrograph. Stream hydrograph separation is undertaken by convoluting rainfall excess with the identified components of the unit hydrograph. The procedure is applied to two small upland catchments in Wales. The results demonstrate that at sampling intervals of the order of one hour, successful separation of quick and slow flow components can be achieved with short time series of rainfall and streamflow.

Integrated Assessment and Modelling: Features, Principles and Examples for Catchment Management

Abstract To meet the challenges of sustainability and catchment management requires an approach that assesses resource usage options and environmental impacts integratively. Assessment must be able to integrate several dimensions: the consideration of multiple issues and stakeholders, the key disciplines within and between the human and natural sciences, multiple scales of system behaviour, cascading effects both spatially and temporally, models of the different system components, and multiple databases. Integrated assessment (IA) is an emerging discipline and process that attempts to address the demands of decision makers for management that has ecological, social and economic values and considerations. This paper summarises the features of IA and argues the role for models and information systems as a prime activity. Given the complex nature of IA problems, the broad objectives of IA modelling should be to understand the directions and magnitudes of change in relation to management interventions so as to be able to differentiate between associated outcome sets. Central to this broad objective is the need for improved techniques of uncertainty and sensitivity analysis that can provide a measure of confidence in the ability to differentiate between different decisions. Three examples of problems treated with an IA approach are presented. The variations in the way that the different dimensions are integrated in the modelling are discussed to highlight the sorts of choices that can be made in model construction. The conclusions stress the importance of IA as a process, not just as a set of outcomes, and define some of the deficiencies to be overcome.

Selecting among five common modelling approaches for integrated environmental assessment and management

The design and implementation of effective environmental policies need to be informed by a holistic understanding of the system processes (biophysical, social and economic), their complex interactions, and how they respond to various changes. Models, integrating different system processes into a unified framework, are seen as useful tools to help analyse alternatives with stakeholders, assess their outcomes, and communicate results in a transparent way. This paper reviews five common approaches or model types that have the capacity to integrate knowledge by developing models that can accommodate multiple issues, values, scales and uncertainty considerations, as well as facilitate stakeholder engagement. The approaches considered are: systems dynamics, Bayesian networks, coupled component models, agent-based models and knowledge-based models (also referred to as expert systems). We start by discussing several considerations in model development, such as the purpose of model building, the availability of qualitative versus quantitative data for model specification, the level of spatio-temporal detail required, and treatment of uncertainty. These considerations and a review of applications are then used to develop a framework that aims to assist modellers and model users in the choice of an appropriate modelling approach for their integrated assessment applications and that enables more effective learning in interdisciplinary settings. We review five common integrated modelling approaches.Model choice considers purpose, data type, scale and uncertainty treatment.We present a guiding framework for selecting the most appropriate approach.

Performance of conceptual rainfall-runoff models in low-yielding ephemeral catchments

Low-yielding catchments with ephemeral streams involve highly nonlinear relationships between rainfall and runoff, and there is much less documentation and appreciation of the ability to predict streamflow in these veiy difficult cases than in humid catchments. The predictions of three conceptual rainfall-runoff models are assessed in three low-yielding, emphemeral streams over a 10-year period. The models are a simple conceptual model, Generalized Surface inFiltration Baseflow (GSFB; eight parameters), a hybrid metric/conceptual model, Identification of Hydrographs and Components from Rainfall, Evaporation and Streamflow data (IHACRES; six parameters), and a complex conceptual model, the Large Scale Catchment Model (LASCAM; 22 parameters). The Salmon (0.82 km2), Stones (15 km2), and Canning (517 km2) catchments in Western Australia were selected for their range of sizes and low runoff yields (1.6–12.2% of rainfall). Their behavior is representative of a large part of Australia and semiarid regions, where antecedent conditions are critical determinants of streamflow response to rainfall. Such catchments provide a stern test of the capability of conceptual models. Five-year calibration and validation performances were assessed with a range of statistics. The models were run daily but performance was assessed on both a daily and monthly basis by aggregating daily model streamflows and observations up to monthly. The models performed well, particularly in the monthly case where often more than 90% of the variance of observed streamflow was explained in simulation on independent periods. However, while the simple conceptual model is adequate for monthly time periods, the daily simulation results indicate that a slightly more complex model (the hybrid model or the complex conceptual model) is required for daily predictions in these dry catchments. The model simulation results extend the following notion of Jakeman and Hornberger [1993] from humid to semiarid ephemeral catchments: that a model of about six parameters, albeit in an appropriate model structure, is sufficient to characterize the information in rainfall-discharge time series over a wide range of catchment sizes. Models of such modest complexity also predict runoff with good accuracy outside calibration periods, even in ephemeral, low-yielding catchments. The simulation results highlight the critical importance of the deep groundwater and antecedent moisture conditions on stream yields in ephemeral catchments and point to the desirability of accounting for these factors in arid-zone modeling.

Progress in integrated assessment and modelling

Environmental processes have been modelled for decades. However. the need for integrated assessment and modeling (IAM) has,town as the extent and severity of environmental problems in the 21st Century worsens. The scale of IAM is not restricted to the global level as in climate change models, but includes local and regional models of environmental problems. This paper discusses various definitions of IAM and identifies five different types of integration that Lire needed for the effective solution of environmental problems. The future is then depicted in the form of two brief scenarios: one optimistic and one pessimistic. The current state of IAM is then briefly reviewed. The issues of complexity and validation in IAM are recognised as more complex than in traditional disciplinary approaches. Communication is identified as a central issue both internally among team members and externally with decision-makers. stakeholders and other scientists. Finally it is concluded that the process of integrated assessment and modelling is considered as important as the product for any particular project. By learning to work together and recognise the contribution of all team members and participants, it is believed that we will have a strong scientific and social basis to address the environmental problems of the 21st Century.

Refined instrumental variable methods of recursive time-series analysis Part III. Extensions

This is the final paper in a series of three which have been concerned with the comprehensive evaluation of the refined instrumental variable (IV) method of recursive time-series analysis. The paper shows how the refined IV procedure can be extended in various important directions and how it can provide the basis for the synthesis of optimal generalized equation error (GEE) algorithms for a wide class of stochastic dynamic systems. The topics discussed include the estimation of parameters in continuous-time differential equation models from continuous or discrete data; the estimation of time-variable parameters in continuous or discrete-time models of dynamic systems ; the design of stochastic state reconstruction (Wiener-Kalman) filters direct from data ; the estimation of parameters in multi-input, single output (MISO) transfer function models ; the design of simple stochastic approximation (SA) implementations of the refined IV algorithms ; and the use of the recursive algorithms in self-adaptive (self...

Paper: An instrumental variable method for model order identification

The paper describes a simple instrumental variable method for identifying the structure of a wide class of time-series models. The method is aimed at providing a parametrically efficient (parsimonious) model structure which will lead to a combination of low residual error variance, i.e. a good explanation of the data, and low parametric estimation error variance (as measured by some norm associated with the covariance matrix of the estimation errors). It can be applied to single input-single output and multivariable systems using either discrete or continuous-time series models. It can also function as a recursive (on-line) test for reduction in model order.