1
Agricultural
Effects an Grown! and Surface Water. ;: Research at tlie Edge af Science and Society
(Proceedings o f a symposium held al Wageningen. October 2000). lAIIs'l'ubl. no. 273. 2002.
397
Models and monitoring: scaling-up cause-andeffect relationships in nutrient pollution to the
catchment scale
P A U L QUINN
Water Resources Systems Research Laboratory, Department of Civil
University of Newcastle, Newcastle upon TyneNEi 7RU, UK
Engineering,
e-mail: [email protected]
Abstract Laboratory and small-scale field observations have yielded
fundamental insights into the causes of nutrient pollution. Detection of
downstream, off-site impacts of nutrient pollution reveals its effects. However,
there is a gulf in our knowledge and practice that prevents the rational scalingup of findings made at one scale so that they contribute to establishing a sound
scientific basis for planning at the catchment scale. Many modellers may thus
rely on simple models when simulating nutrient pollution at the catchment
scale as these models can reflect their judgments and uncertainties. The only
way for planners and scientists to advance in harmony is to create robust
scaling-up techniques, which can call upon a range of scale-appropriate
models (including complex physically-based, distributed models and lumped
Minimum Information Requirement (MIR) models). This goal will not be
achieved unless an extensive set of nested, multi-scale experiments are
undertaken to examine how processes and model parameters change over
space and time. This paper shows that any hydrological flow path and nutrient
source area analysis must pay respect to the effects of the model grid scale and
the size of the study area.
Key words Minimum Information Requirement models; modelling; monitoring;
nutrient pollution; scaling
INTRODUCTION
When changing scale, from a point to a catchment, the processes that can be measured
and simulated change radically. Thus, a thorough understanding of the scaling issues
that relate to measurements, processes, model parameters and data is needed. This paper
addresses two fundamental scaling issues by describing the sensitivity of model output
to model grid resolution and the changes seen in hydrological flow processes when
moving from the point scale through to the plot, hillslope, catchment and basin scales.
It is widely recognised that environmental measurements cannot b e scaled-up
directly (Beven, 1989). The types of measurements taken at a point ( 1 n r ) may differ
radically from measurements made at the hillslope scale (1 ha), in small catchments
(1 Ion") or in large catchments (1000 km"). However, some environmental measure­
ments can be made accurately at all scales, for instance water and nutrient balances,
and as such they can form the basis of a combined monitoring and modelling strategy
for addressing scale issues. In principle, synchronous determinations of the water and
nutrient fluxes made at the point, plot, hillslope, catchment and basin scales, offer the
best hope of understanding scale dependent effects and determining modelling
strategies appropriate to specific scales of application.
398
Paul Quinn
This paper suggests that the scaling-up of cause-and-effect relationships can be
achieved by combining the use of physically-based models at the "local" scale (i.e. the
point, plot scale and hillslope scales) with use of simple Minimum Information Require­
ment (MIR) models at the catchment/basin scale. A MIR model can be defined as the
simplest model structure that satisfies the modelling needs of the policy maker whilst
still ensuring that the model parameters retain physical significance (Quinn et al, 1999).
Physically-based models can be used effectively at the point, plot and hillslope
scale where the acquisition of data is appropriate to the structure of the model
(Birkenshaw & Ewen, 2000). Problems of parameterizing physical models at the
catchment scale, due to heterogeneity and uncertainty, are reported elsewhere (Franks
et al, 1997). At the hillslope scale or small catchment scale, many modellers may
decide that quasi-physical, semi-distributed models are more appropriate (Beven et al.,
1995), but even simple models may not be applicable at the larger catchment scale. As
a result, modellers often choose to use a simple, parsimonious model structure at the
catchment scale. In the MIR approach the simplest model structure is sought which
satisfies the condition that the chosen MIR must be able to mimic the output of
whichever physical or quasi-physical models have been used at the point, plot,
hillslope or catchment scale. Since the physical or quasi-physical models always yield
time series of water and nutrient fluxes, the common denominator at all scales is the
water and nutrient flux as predicted by both a scale-appropriate model and also by a
simple MIR model. Any change in the MIR calibrated model parameter values when it
is applied over a range of scales has to be due to a scaling-up effect.
T H E CHOICE OF GRID SCALE AND GRID SCALE D E P E N D E N C Y
The choice of grid scale has important implications for flow path simulations:
Information may be lost by averaging as the grid resolution becomes coarser.
Flow accumulation algorithms can create apparent patterns that turn out to be
artefacts of the grid resolution chosen (Quinn et al, 1995).
For example, Fig. 1 (a) shows a map of a commonly used topographic wetness index
ln(a/tan P) (where a is the upslope accumulated area and tan (3 the gradient of the local
slope (Quinn et al, 1995). This type of index is commonly used to represent source
area activity. Two grid-scale dependent phenomena are revealed on Fig. 1. Firstly, the
detail of the micro-topography and the effects of field boundaries are lost when
changing from a 2-m grid resolution to a 15-m grid resolution. Secondly, the change
in grid resolution changes the mean and distribution of the ln(a/tan P) wetness index
pattern, which in turn alters the apparent likelihood of sources and sinks for nutrients.
The change in wetness index patterns is quantified in Fig. 1 (b), in which the change in
the average value of ln(a/tan (3) is calculated using a range of grid sizes. The result is a
systematic shift in the calculated average value with respect to grid size. This type of
grid scale analysis offers us an opportunity to understand and resolve the scaling-up
effect (see Quinn et al, 1995). The effects of grid scale choice must be understood if
modellers wish to relate their findings back to reality or if a comparison is to be made
between models that have used differing grid resolutions. This is particularly true if
any form of parameter calibration has been performed, as the resulting parameters will
be dependent on grid scale.
Models and monitoring: scaling-up cause-and-effect relationships in nutrient pollution
L e g e n d t o Fig
Field Boundaries
399
1(a).
In (a/tan b) value
r—|
4.046 - 7.473
7.473 - 9.382
9 . 3 8 2 - 10.84
10.84-12.414
;.T>i
'
g
12.414-14.926
•
14.926 - 24.845
1
5
10
15
DTM G r i d C e l l S i z e
15m
(b)
Fig. 1 (a) The ln(a/tan (3) wetness index map for a 2 m and a 15 m digital elevation
model (DEM), (b) The systematic shift in the mean of the wetness index caused by an
increase in DEM grid resolution.
SCALING-UP O F PROCESSES, M O N I T O R I N G A N D M O D E L L I N G
Process representation is arguably the most fundamental problem of scaling. As scale
increases, processes integrate to yield responses which require different data sets, and
simulation strategies which differ markedly from those appropriate to smaller scales.
By showing the processes at each scale, it is possible to look at some problems of
process simulation and measurement, paving the way for an idealized design for a
catchment-scale experiment.
In Fig. 2, 1 n r of soil is assumed to be the "point" scale. In Fig. 2(a), the soil, roots
and macropores are shown, all of which control the soil moisture and nutrient regime.
To these are added influxes of overland flow and subsurface flow from upslope, which
sustains a water table. In Fig. 2(b), a typical laboratory experiment for deducing
nutrient mobilization processes is shown. In this experiment, a sealed soil column is
used to study the susceptibility of nutrients to leaching. It differs significantly from the
processes shown in Fig. 2(a) since it is missing the three-dimensional lateral inputs and
outputs of flow seen in reality. In Fig. 2(c), an in situ suite of point scale measure­
ments, with open boundary conditions, is proposed to observe flow and nutrient
dynamics as influenced by both upslope and downslope flow conditions. As stated in the
400
Paul Quinn
Fig. 2 The point scale, (a) The features of a typical 1 m" soil column, (b) A typical soil
column experiment, (c) An in situ suite of point scale measurements, (d) Examples of
moisture and nutrient fluxes that can be determined at a point.
introduction, the water balance and nutrient balance can be determined at this point.
Hence, Fig. 2(d) shows a subset of measurements that can be made at the point scale. It
is fundamental that each component of the flow is captured and that a long time series
of measurements is made. Given the localised nature of the measurements, fully
physically-based models can reasonably be developed to test basic ideas and physical
relationships.
A similar approach should also be taken in experiments at the plot scale, assumed
to be 10 x 10 m to 50 x 50 m, in that the upper and lower boundaries of the plot should
not be sealed. Within a plot scale experiment, multiple repetitions of the same point
measurements should be set up in order to characterize the means and variances of the
water and nutrient balances.
At the hillslope scale (1-5 ha), we are faced with our greatest problem, as many
differing macroscale processes are in operation. Figure 3 shows the hydrological
processes anticipated in two typical UK hillslope scenarios, (i.e. with and without land
drainage). In general, hydrological processes tend to vary greatly between the catch­
ment divide and the main channel, reflecting the change in landscape. The dynamics of
both the unsaturated and saturated flow processes are spatially and temporally complex
(and result in spatially and temporally variable sources of hydrological connection to
Models and monitoring: scaling-up cause-and-effect relationships in nutrient pollution
401
Fig. 3 The hillslope scale, (a) A typical set of hydrological features in a UK hillslope
without land drains, (b) A typical UK hillslope with land drains.
Topographically
Fig. 4 Catchment scale to basin scale, (a) Possible distributions of source areas in a
small catchment, (b) Broad classifications of land use, climate and topography as seen
at the basin scale.
receiving waters). Along with leaching, a key cause of nutrient mobilization is related
to the existence of source areas that have a high nutrient transport capacity. Surface
source areas for nitrate and phosphate have been referred to as critical source areas
(CSAs) while subsurface controlled sources are probably synonymous with runoff gen­
erating variable source areas (VSAs). The role of topography, soil and human influences
are at their greatest at the hillslope scale. The temporal dynamics of source area opera­
tion and the connectivity of the source areas to the receiving waters need to be
addressed. This is probably best achieved using simple, functional quasi-physical models
that reflect the likely functioning of the CSAs and VSAs (Heathwaite et al, 2000).
Paul Quinn
402
Point scale
1D Physically based model with
boundary conditions. Physical
Properties in each layers e.g.
conductivity
K(1), K(2) K(3) K(4) K(5)
3D Physically based
Model with boundary
conditions. Physical
properties in each cell
e.g. K(x,y,z)
Plot scale
Quasi-physical probability
distribution function model.
E.g. a topographic function
and a soil function:K = Exp (wetness/
drainage rate)
Hillslope and
Catchment
scale
MIR models
based on
statistical
distributions for
each
subcatchment
Basin or
Regional
scale
Weather stations
l\ Flow and water quality
TT gauges
•
Plot experiments
A source area/
leaching function
model
land use / nutrient
input distribution
function
A nutrient index and transport model
Fig. 5 An ideal experimental design to address flow and nutrient pollution needs,
including the spatial distribution of multi-scale experiments and a recommendation of
the type of model suitable for application at each scale. Note that a simple MIR model
can be run at all scales.
A good experiment at the catchment scale ( 1 - 1 0 Ian") should encompass the range
of typical hillslopes and source areas that exist within the region. In Fig. 4(a), the
likely operation of VSAs, which are controlled by the topography, can be monitored
and simulated. Equally, some attempt must be made to quantify the prevalence and
hydrological activity of CSAs in the area, which are related to husbandry. In Fig. 4(b),
the scale is increased once again from a single catchment to the basin scale (1000 k m " 10 000 km"). The key influence of nutrient release at this scale is the large-scale
variability of land use, rainfall regime and topography. Any model or measurement
should try to reflect this variability, albeit the uncertainty will remain high, since it is
neither technically or economically feasible to measure and simulate everything. At the
basin scale a broad re-classification of the landscape is needed to reflect the differing
regimes of nutrient inputs, the gross variability of the rainfall/evaporation regime and
the hydrological potential for the transport of nutrients in each zone (including both
Models and monitoring: scaling-up cause-and-effect relationships in nutrient pollution
403
natural and man made factors). Hence, the model becomes a spatial index of nutrient
availability and an index of nutrient transport potential (Heathwaite et al, 2000). This
type of model can be coupled to a GIS so that the overall model structure can be a
simple MIR model fed by statistical distributions of land use characteristics (Quinn et
al, 1999).
TOWARDS AN INTEGRATED MULTI-SCALE APPROACH
It is argued that a nested, multi-scale set of representative experiments can be made
from point to basin scale and that a mixture of model types can be applied dependent
on scale. Figure 5 shows the proposed experimental design and the type of model to be
ran at each scale. Application of the appropriate models at each scale gives a modeller
the basic understanding of cause-and-effect relationships. A common MIR model is
then applied at each scale, which will attempt to mimic the output of each scaleappropriate physical or quasi-physical model. Thus, the MIR parameters derived,
should reflect both the changes in the process caused by scaling-up and capture any
artefacts of scaling-up caused by the choice of grid resolution.
REFERENCES
Beven, K. J., Lamb, R., Quinn, P. P., Romanowicz, R. & Freer, J. (1995) TOPMODEL. In: Computer Models of
Watershed Hydrology (ed. by V. P. Singh), 627-668. Water Resources Publications.
Birkenshaw, S. & Ewen, .1. E. (2000) Modelling nitrate transport in the Slapton Wood catchment using SHETRAN.
./. Hydro!. 230, 18-33.
Franks, S. W., Beven, K. J., Quinn, P. F. & Wright, I. R. (1997) On the sensitivity of soil-vegetation-atmosphere transfer
(SVAT) schemes: equifinality and the problem of robust calibration. Agric. For, Meleoro! 86, 63-75.
Heathwaite, A. L., Sharpley, A. N. & Gbureck, W. .1. (2000) Conceptual approach for integrating phosphorous and
nitrogen management at watershed scales. J. Environ. 29( 1 ), 158-166.
Quinn, P., Beven, K. J. & Lamb, R. (1995) The ln(a/tan (3) index: how to calculate it and how to use it within the
TOPMODEL framework. Hydro! Processes 9(2), 161-182.
Quinn, P. F., Anthony, S. & Lord, E. (1999) Basin scale nitrate modelling using a Minimum information Requirement
approach. In: Water Quality: Processes and Policy (ed. by S. Trudgill, D. Walling & B. Webb), 101—117. Wiley,
Chichester, UK.