Mark Breunig
GEOG 681
Introduction
The overall purpose of this model topic is to increase the effectiveness of watershed-scale
phosphorus water quality modeling. Most watershed-scale phosphorus water quality models perform
poorly when compared to observed data sets, because the scientific community does not properly
understand the complex interactions that occur at this scale. The goal of this model is to develop
“spatially explicit” variables that more accurately represent what controls the long term average
phosphorus concentration in a stream.
Background Information
Importance of Phosphorus
Phosphorous is of major concern to water quality managers in agricultural watersheds because
it can cause eutrophication in surface waters. Agricultural fertilizers and animal waste contain
phosphorus. This chemical has a tendency to absorb to soil particles, and is transported to surface
water primarily during runoff events. In cases of chronic over-application, it can be transported
independently of soil particles (USEPA 2007).
The Consideration of Spatial Configuration in Models
Water Quality Models can be separated into two major categories, spatially explicit models and
non-spatially explicit models. A spatially explicit model includes variables and parameters that describe
how features are arranged on the landscape. Runoff flow length or travel time to a stream network is
an example of this type of variable. A non-spatially explicit model includes variables and parameters
that do not specifically consider spatial arrangement. Percent of a particular class of land cover is an
example of this.
Previous Studies
Numerous studies have attempted to quantify the complex interactions between basin scale
processes, landscape features, and anthropogenic activity to observed sediment and phosphorous
measures in streams (Band et al. 1993; Srinivasan et al. 1994; Ferro et al. 1995; Hunsaker et al. 1995;
Johnes et al. 1996; Mattikalli et al. 1996; Soranno et al. 1996; Worrall et al. 1999; Jain et al. 2000; Liu
2000; Tong et al. 2001; Reed et al. 2002; Robertson et al. 2006; Boomer et al. 2008). Despite these
attempts, a model has yet to be defined that can be used to reliably predict sediment and phosphorous
in ungauged watersheds. This represents a collective misunderstanding of the fundamental processes
that control water quality at the catchment scale (Boomer et al. 2008). Achieving a more accurate
representation of these processes is essential if effective management decisions are to be made.
Improper use of the Universal Soil Loss Equation at the Basin Scale
While the Universal Soil Loss Equations (USLE) and its derivatives have been extensively
validated at the field scale, there is little evidence that its application is valid when used at the basin
scale with course resolution data sets. Regardless of this fact, the USLE and its derivatives continue to
be improperly applied (Kinnell 2004; Boomer et al. 2008) by both scientists (Kim et al. 2005; Wang et al.
2005)and policymakers (USEPA 2005; Donigian et al. 2006) across the globe. This misguided work is so
common it is difficult to provide a complete summary of its applications. A simple query of the
Wisconsin Department of Natural Resources online publications (Wisconsin Department of Natural
Resources 2008) results in a list of about 30 or more applications of the Soil and Water Assessment Tool
(SWAT) at the basin scale within recent years alone. SWAT is one of the many models that uses USLE
and its derivatives to perform sediment load and yield calculations. Boomer et al. (2008) urge the
scientific community that the USLE was not developed for basin scale use. It is a field scale tool, and it
requires field scale observations and applications. Its use in ungauged basins can lead to improper
management decisions. When compared to observed data by Boomer et al. (2008), it has performed
very poorly. Sediment delivery ratios that range from complex to simple in nature often accompany the
USLE. They represent arbitrary mathematical attempts at rectifying an invalid conceptual framework
(Kinnell 2004; Boomer et al. 2008), and add additional parameters to an already over-parameterized
model.
Model Details
Goal of the Model
In an attempt to improve over previous research and improper techniques, examine the utility of
spatially explicit parameters in phosphorus water quality by testing the performance of the most
fundamental spatially explicit parameter – surface overland flow length to perennial stream.
Model Taxonomy
This model is classified as a deterministic, empirical, and inductive model.
Assessment of Model Performance
The performance of the model will be tested by comparing the coefficient of variation (R2) of two
regressions. The first regression consists of a non-spatially explicit parameter, percent agriculture, as
the independent variable and observed median phosphorus concentrations as the dependent. The
second regression consists of a spatially explicit parameter calculated by the model, “effective percent
agriculture”, as the independent variable and observed median phosphorus concentrations as the
dependent
Input Data and Reference Data
The dependent variable used to assess the model performance comes from a data set obtained from the
USGS that consists of 2001 median total phosphorus values at 241 stream monitoring sites across
Wisconsin (Figure 1). The percent agriculture parameter was calculated from the USGS 2001 NLCD
(National Land Cover Database). A 30m Digital Elevation Model (DEM) from the USGS was used to
calculate surface overland flow paths and stream locations based on flow accumulation.
Figure 1. Spatial distribution of 2001 USGS water quality monitoring sites.
Model Calculations
The following equation was used to calculate the “effective percent agriculture”.
FLag = estimated surface overland flow length to perennial stream of cultivated cropland pixels within
watershed
FLall = estimated surface overland flow length to perennial stream of all pixels within watershed
β = theoretical phosphorus decay coefficient
Watersheds were delineated by the USGS. 30m pixel size was used for the calculations.
Perennial streams were estimated by using the flow accumulation threshold technique. The resulting
effective percent agriculture value represents an attempt to calculate the proportion of phosphorus that
is likely to actually reach a stream from each cultivated cropland pixel.
The calculations were performed manually using ArcMap 9.3 spatial analyst tools. Beta values
that represented the full range of potential values found in Figure 2 were selected. The eFLag and eFLall
terms remained constant for each different trial of beta. First, the surface overland flow lengths were
calculated by using the “Flow length” (spatial analyst>hydrology) tool, using a raster input layer that
defined stream locations as the “Input weight raster”. This facilitated the calculation of only the flow
length to stream of each pixel rather than the entire flow length to the watershed outlet. Next, two
separate shapefiles were created that separated the flow lengths of the cultivated cropland pixels and
the flow lengths of the entire watershed (thus deriving FLag and FLall values). The eFLag and eFLall terms
100
90
0.05000
Pixel Value (% effective)
80
0.01000
70
0.00250
60
0.00100
50
0.00043
40
0.00022
30
0.00011
20
0.00006
10
0.00003
0.00001
0
0
2,000
4,000
6,000
8,000
10,000
0.00000
Distance (m)
β=
Distance (m)
0
30
100
200
400
500
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0.05000
100.000
22.313
0.674
0.005
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.01000
0.00250
0.00100
0.00050
0.00043
0.00022
0.00006
0.00003
0.00011
0.00001
0.00000
100.000
74.082
36.788
13.534
1.832
0.674
0.005
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
100.000
92.774
77.880
60.653
36.788
28.650
8.208
0.674
0.055
0.005
0.000
0.000
0.000
0.000
0.000
0.000
100.000
97.045
90.484
81.873
67.032
60.653
36.788
13.534
4.979
1.832
0.674
0.248
0.091
0.034
0.012
0.005
100.000
98.511
95.123
90.484
81.873
77.880
60.653
36.788
22.313
13.534
8.208
4.979
3.020
1.832
1.111
0.674
100.000
98.718
95.791
91.759
84.198
80.654
65.051
42.316
27.527
17.907
11.648
7.577
4.929
3.206
2.086
1.357
100.000
99.342
97.824
95.695
91.576
89.583
80.252
64.404
51.685
41.478
33.287
26.714
21.438
17.204
13.807
11.080
100.000
99.829
99.432
98.866
97.746
97.190
94.459
89.226
84.282
79.612
75.201
71.035
67.099
63.381
59.870
56.553
100.000
99.910
99.700
99.402
98.807
98.511
97.045
94.176
91.393
88.692
86.071
83.527
81.058
78.663
76.338
74.082
100.000
99.671
98.906
97.824
95.695
94.649
89.583
80.252
71.892
64.404
57.695
51.685
46.301
41.478
37.158
33.287
100.000
99.970
99.900
99.800
99.601
99.501
99.005
98.020
97.045
96.079
95.123
94.176
93.239
92.312
91.393
90.484
100.000
100.000
100.000
100.000
100.000
100.000
100.000
100.000
100.000
100.000
100.000
100.000
100.000
100.000
100.000
100.000
Figure 2. List of theoretical phosphorus flow length decay coefficients used to calculate the percent effectiveness of pixels.
were then calculated by using the “Exp” tool (spatial analysis>math). The beta values were then
multiplied by the eFLag and eFLall terms by using the “Times” tool (spatial analysis>math). The summations
of the numerator and denominator terms were made by using the “Zonal Statistics As Table” tool
(Spatial Analyst>Zonal), which allowed the calculations to made for all the sampled watersheds in
Wisconsin at once (per each beta term trialed). The data were then reorganized to facilitate the
calculation of the coefficients of determination with the observed data set. Regression plots were
analyzed for each Beta trial.
Model Outcome
Discussion of Results
Out of all the Beta values tested, not a single one showed a significant increase in the coefficient
of determination relative to the non-spatially explicit regression (percent agriculture). The effective
percent agriculture value, at least as calculated in this model, did not support the utility of spatially
explicit parameters in phosphorus water quality modeling. Figure 3 provides an example of one of the
best performing beta values (0.00022). It can be seen that even the best performing bet value offers no
improvement over the non-spatially explicit parameter. In fact, the distribution of the scatter plot for
both regressions looks almost identical, although the “effective percent agriculture” does not extend
across as wide of a range.
The comparison made in Figure 4 provides some very interesting insight on the model. It
appears that for each respective beta value, the percent effective agriculture values all change by more
or less the same amount. This explains why the graphs in Figure 3 look so similar – the spatially explicit
model does not describe any characteristic that the simpler, non-spatially explicit model represents.
% Ag vs TP
0.5
0
0.0%
20.0%
40.0%
60.0%
80.0%
100.0%
-0.5
-1
-1.5
-2
y = 0.8032x - 1.4549
R² = 0.4575
-2.5
% Effective Ag vs TP
0.5
0
0.0%
20.0%
40.0%
60.0%
80.0%
100.0%
-0.5
-1
-1.5
-2
y = 1.1042x - 1.4512
R² = 0.4501
-2.5
Figure 3. Comparison of a non-spatially explicit parameter regression (percent agriculture) and a spatially explicit parameter
regression (effective percent agriculture, β = 0.00022) with observed phosphorus stream concentrations.
0.0025
0.00022
100.0%
90.0%
80.0%
70.0%
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
100.0%
90.0%
80.0%
70.0%
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
0
50
100
150
200
250
300
200
250
300
0
0.001
100.0%
80.0%
60.0%
40.0%
20.0%
0.0%
0
50
100
150
Figure 4. Comparison of the effect of different beta values on the resulting effective percent agriculture value.
50
100
150
200
250
Potential Problems
This model certainly is a very basic representation of the complex interactions that occur on the
landscape during runoff events. It does not even consider micro-topography, rainfall, runoff coefficients,
or land uses other than cultivated cropland and “not cultivated cropland”. Perhaps the largest blunder
of this model is the assumption that the “edge of pixel” export is the same for each agricultural pixel.
Not considering agricultural management practices in phosphorus model is very problematic, as the
edge of field export can vary drastically among fields depending on presence or absence of Best
Management Practices (BMP’s). The evidence presented in Figure 4 may also suggest that the spatial
distribution of agriculture throughout most Wisconsin watersheds is random, which means solely relying
on flow length is an improper approach.
Conclusion
The poor performance of this model does not rule out the utility of spatially explicit parameters
in water quality modeling. Additional model development and comparison with multiple observed data
sets must be done in order to better assess the effectiveness of considering spatial orientation in water
quality modeling.
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