Physics-based models are grounded on the solution of fundamental physical equations
describing streamflow and sediment and nutrient generation within the catchment.
Standard equations used in such physics-based models are the equations of conservation
of mass and momentum for flow and the equation of conservation of mass for sediment
(e.g. Bennett 1974).
In theory, the parameters used in physics-based models are measurable within the
catchment and so are ‘known’. However, in practice, the large number of parameters
involved and the heterogeneity of important characteristics within the catchment means
that these parameters must typically be calibrated against observed data. This creates
additional uncertainty in parameter values. Also, even in situations where parameters can
be ‘measured’ within the catchment, errors in the measurement of important
characteristics will create additional uncertainty as to the veracity of model outcomes.
Where parameters cannot be measured within the catchment they must be determined
through calibration against observed data. Given the large number (possibly hundreds) of
parameter values needed to be estimated using such a process, problems with the lack of
identifiability of model parameters and non-uniqueness of ‘best fit’ solutions can be
expected. There is likely to be a large number of parameter values for which the model
gives an adequate fit. Thus the physical interpretability of model parameters is
questionable. In the case of large simulation models, where many possible ‘best’
parameter sets are available, there are ‘clear limitations on how one might interpret the
technical or scientific significance of any particular set of parameters that lead to a good
fit’ (Spear 1995). In the case of physics-based models this means that the necessity to
calibrate some or all parameter values will undermine the physical interpretability of the
entire parameter set.
An additional problem with estimating model parameters in physics-based models is the
necessity to lump together spatially distributed variables into data at a single point. Lane
et al. (1995) state that ‘model parameters derived in this manner represent nothing more
than fitted coefficients distorted beyond any physical significance’. In general the
equations governing the processes in physics-based models are derived for small-scale
models under very specific physical conditions. However, in physically based models
these equations are used at much greater scales, and under different physical conditions.
The equations are generally derived for use with continuous spatial and temporal data, but
the data used in these models is often point-source data taken to represent an entire grid
cell within the catchment. The derivation of mathematical expressions describing
individual processes in physics-based models is subject to numerous assumptions that
may not be relevant in many real-world situations (Dunin 1975). The viability of lumping
up small-scale physics to the scale of the spatial grid used in many physics-based models
is also questionable (Beven 1989). Specifically there is a lack of theoretical justification
for assuming that equations apply equally well at the grid scale, at which they are
representing the lumped aggregate of heterogeneous subgrid processes (Beven 1989).
Physics-based models also tend to have greater data and computational requirements than
other model types. Parameter values must be measured both spatially and temporally
within the catchment. The use of such models has been limited by the lack of observed
physical and biological data within catchments, and by the larger computing costs
involved in their use.
The tradeoff between model complexity and accuracy is not simply that increased model
complexity increases model accuracy. Simpler catchment models perform equally well or
at least are not substantially outperformed by more complex models (Loague and Freeze
1985). Jakeman and Hornberger (1993) confirmed this result for different levels of
complexity in conceptual models.
3.2 Specific erosion and sediment/nutrient models
Many different erosion and sediment/nutrient transport models are currently available.
These models differ in complexity, the catchment processes modelled and the
assumptions on which they are based. This section provides an outline of a number of
currently available models, including information on their cost, availability and hardware
The Adaptive Environmental Assessment and Measurement program (AEAM) is a
process for the development and exploration of management options for complex
systems. One of the main outcomes of the AEAM process is the development of a model
based on expert knowledge of the system. The complexity of the model developed
depends on the relationships within the system considered to be necessary by the expert
groups consulted. Grayson et al. (1994) identifies AEAM as being ‘a philosophical and
methodological framework designed to deal with the uncertainties inherent in
environmental changes’. The AEAM approach relies on expert knowledge along with
historical variability and patterns of change to characterise the system. The initial
simulation model developed from this characterisation is used to design management
programs which measure responses to management actions, which are used to refine the
initial model. In this way, the model is an adaptive approach to catchment management.
There is not a set model structure for AEAM. Instead, the program can be thought of as a
guideline for catchment management groups to approach their water quality problem.
The basic design of the AEAM program is in two parts. The ‘shell’ handles the
input/output and provides the structure to manage the spatial and temporal data, while the
‘dynamic simulation’ performs the numerical simulation of the system (Grayson et al.
1994). The shell tends to be generic between AEAM models, while the dynamic
simulation is developed for the specific application.
AEAM, although widely used elsewhere, has not been used to a large extent in Australia
(Grayson et al. 1993; Grayson et al. 1994). AEAM models of catchment behaviour are
generally simple balance-type representations based on rainfall and evaporation input
data. The models developed do not normally attempt to quantify the processes involved
in water quality and are not formulated as predictive or forecasting tools. Instead, they
are a more trial-and-error approach to catchment management, generally relying on
empirical and simple conceptual models. Like CMSS, these models rely on calibration of
parameter estimates and are intended only as planning tools (Walton and Hunter 1996).
The model has been used for integrated catchment management on the Latrobe and
Goulburn River catchments (Grayson et al. 1994 and Grayson and Doolan 1995
respectively) and for the improved integration of planned riparian-zone research in the
North Johnstone catchment in Queensland (Argent and Wilson 1996).
Examples of model users:
LWRRDC; Centre for Environmental Applied Hydrology at the University of Melbourne
Run under QuickBASIC or VisualBASIC on PC
Models are generally adapted from a model used in a similar AEAM application elsewhere.
LWRRDC and the Centre for Environmental Applied Hydrology at the University of
Melbourne have prepared Occasional Paper 01/95, ‘Adaptive Environmental Assessment
and Measurement [AEAM] and Integrated Catchment Management’ ($28), providing more
detailed information and two Victorian applications for the Latrobe River and Goulburn
and Broken Rivers catchments on PC-format floppy discs.
For further information contact:
Dr Rodger Grayson
Phone: (03) 9344 7305
The Agricultural Non-Point Source model (AGNPS) is an event-based, non-point source
pollution model developed by the US Department of Agriculture’s Agricultural Research
Service (USDA-ARS) in cooperation with the Minnesota Pollution Control Agency and
the US Soil Conservation Service (SCS). The model was developed to predict and
analyse runoff water quality from rural catchments ranging from a few to over 20 000 ha.
AGNPS uses a grid cell representation of the catchment, with cell resolution ranging
from 0.4 to 16 hectares. Runoff and transport of sediment, nutrient and chemical oxygen
demand are simulated for each grid cell, with potential pollutants being routed through
cells to the catchment outlet.
Runoff within the catchment is simulated using the SCS curve number method, an
empirical rainfall-runoff modelling technique. This method deals with baseflow
separately and combines channel runoff, surface runoff and subsurface flow into ‘direct’
runoff. The rainfall-runoff equation is
is the annual rainfall, Q
is the potential maximum runoff, I
is the initial
abstraction (often assumed to be 0.2S
) and S
is the potential maximum retention. The
value of S
is related to a curve number CN by the relationship:
Erosion and sediment transport are modelled using a modified version of the Universal
Soil Loss Equation (USLE), which is discussed in sections 3.2.14 and 3.2.17. Two
different versions of the AGNPS model have been developed by the USDA-ARS. One
uses the USLE, the other the RUSLE (AGNPS98). A version is currently being
developed using the USLE-M (Kinnell and Risse 1998, Kinnell, 1998a and 1998b). Soil
loss is calculated within AGNPS for each cell in the catchment. The chemical transport
component of AGNPS models the transport of nitrogen, phosphorus and chemical
oxygen throughout the catchment, using relationships adapted from the CREAMS model
and from a feedlot evaluation model. The nitrogen cycle is considered explicitly in
AGNPS (Ball and Trudgill 1995). The model treats nutrients and chemical oxygen
delivered from feedlots as point sources, and routes them with contributions from non-
point sources. Other point source inputs of pollutants and water are modelled by
inputting incoming flow and nutrients to the cells in which they occur.
Input data for the AGNPS model includes variables describing catchment morphology,
land use variables and precipitation data, generally input for each cell in the catchment
grid. The model outputs total volumes associated with runoff, sediment yield and
chemical output in a number of different forms, including graphical and numerical
AGNPS was developed and tested on catchments in the USDA but has been applied in a
number of different studies on catchments in Australia (Rosewell 1995) and around the
AGNPS is generally more accurate in its predictions and analysis of sediment yield than
models such as CMSS, but the greater data requirements and computational complexity
of AGNPS must be weighed against this improvement in accuracy.
Examples of Model Users:
Department of Conservation and Land Management - Gunnedah Research Station
PC or Unix/Solaris 2.5×
Freely available from USDA-ARS via the Internet at
For further information contact:
Mr. Richard Beecham
Phone: (02) 9895 7169
From the mid 1980s, advances in sediment and nutrient transport modelling included the
development of a grid or cellular approach, dividing the landscape into cells which were
modelled individually and totalled for the catchment. This approach subsequently
provided a common basis for the structure of process-based hydrologic and water quality
models (Moore and Gallant 1991). The pioneering model was the Areal Non-Point
Source Watershed Environment Response Simulation (ANSWERS) program, a precursor
to GIS (Zhang et al. 1995). The primary outputs of model simulation are runoff and
erosion (Fisher et al. 1997), although the model has been extended to include nutrients
(Moore and Gallant 1991).
The model uses four main categories of landform parameters: soil, land uses, elevation-
based slope and aspect, and channel descriptions in addition to the storm event details
(Fisher et al. 1997). Within these broad categories many parameters are required. For
example, for each soil type the following eight variables are required: total porosity, field
capacity, steady state infiltration, the difference between steady state and maximum
infiltration, the rate of decrease in infiltration with an increase in soil moisture,
infiltration control zone depth, antecedent soil moisture, and erodibility.
The erosion module in ANSWERS is governed by the continuity equation
is the net detachment or deposition rate and q
is the lateral inflow of sediment
load to the channel. Detachment of soil particles by raindrop impact is calculated using
= 0.027 C K A
is the rainfall impact detachment rate, C is the cropping and management factor
of the USLE, K is the soil erodibility factor, A
is the area increment and R
is the rainfall
ANSWERS uses a form of the Yalins’ (1963) bedload transport equation to predict the
transport of cohesionless grains over a movable bed for steady uniform flow of a viscous
fluid (Loch et al. 1989b). The extended version of ANSWERS is capable of simulating
the transport of individual particle size classes (Rose and Ghadiri 1991).
Documents you may be interested
Documents you may be interested