INTRODUCTION
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).
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.
LITERATURE REVIEW
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.
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Unexplained Variation in Simple, Non-Spatially Explicit Models when Compared to Stream Total
Phosphorus Concentration
There have been several major efforts to quantify the dominant controls on water quality at the
basin scale. Few of these studies have been able to clearly define what variables are controlling water
quality . Robertson et al. (2006) compared summer median concentrations of phosphorus and other water
quality measures at 250 wadeable stream monitoring sites across Wisconsin to a wide variety of soil,
landscape, and land cover characteristics. The percent of agricultural lands explained 44% of the variance
in the observed total phosphorous concentrations. The addition of point-source loading and loam deposit
terms in a multiple linear regression accounted for 56% of the variation. The author attributed the
remainder of the variance to interactions among categories. This study provides an interesting case study
in which a large amount of variation can be explained by a single variable, but the addition of more model
terms provides little additional explanation. How can the additional variation be explained?
Van der Perk et al. (2007) compared baseflow samples from 1st to 4th order streams distributed
evenly across a 370mi2 basin in England (predominately grassland) to a series of explanatory variables .
Streambed phosphorous concentrations, stream sediment chemistry, and sewage treatment works only
described only 25% of the variation in stream total phosphorous concentrations. The inability to explain
stream water concentrations was attributed to poor spatial data and complex interactions between
transport and in-stream processes. It is a very common practice for researchers to attribute poor results to
inadequate spatial data (Hunsaker et al. 1995; Soranno et al. 1996; Jain et al. 2000; Jones et al. 2001;
Richards et al. 2006; Boomer et al. 2008). What sort of spatial resolution is required to describe these
processes?
Inconsistent Model Terms Used to Predict Sediment with Multiple Linear Regression
Several other researchers have reached limitations in the ability to model observed water quality
data using multiple linear regression and non-spatially explicit terms. A summary of the results of several
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multiple linear regression equations that predict sediment yields is found below. Although some of the
coefficients of determination approach acceptable levels, the inconsistency in model variables indicates
these models are very specific to the observed data and area of study they were derived from. This is an
indication that the major forces that control water quality at the basin scale have yet to be defined
(Boomer et al. 2008).
Table 1. Adapted summary of efficiency of six different sediment models and the varying model terms (Boomer et al.
2008).
Summary of Study and Model
R2 (%)
78 catchments in Chesapeake Bay watershed, USA
Boomer et al. 2008
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log(SY kg/ha/yr) = 30.71(mean soil erodibility) +0.86log((Q)-0.23(relief ratio)-0.68(sqrt(%forest))
+0.33(Appalachian Plateau)
32 catchments in the Magdalena River watershed, Columbian Andes in South America
Restrepo et al. 2006
log(SY Mg/Km/yr)=-0.884+0.814log(runoff mm/yr)-0.3906log(average max Q)
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23 catchments in the Patuxent River watershed, MD
Weller et al. 2003
TSS(mg/L)=1(%cropland)+0.6(%development)+0.7(Coastal Plain) +11.5(Week)
+17.2(%cropland*week) +7.8(%development*week) +11.8(Coastal Plain*week)
+6.9(%cropland*Coastal Plain*week)
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26 catchments in Central Belgium
Verstraeten et al. 2001
log(SY Mg/ha/yr)=3.7-0.7log(area ha)-0.84log(hypsometric integral)+0.11log(drainage length in m)
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21 catchments in the Fish River watershed, Al
Basnyat et al. 1999
log(TSS mg/L)=3.7(%forest)+17.33(%development)-20.7(%orchard) +11.5(%cropland)
+17.66(%pasture)
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17 catchments in the Chesapeake Bay watershed
Jones et al. 2001
log(SY kg/ha/yr)=8.472+0.079(%development)-0.116(%wetland)-0.038(riparian forest)
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(Weller et al. 1998; Basny at et al. 19 99; J ones et al. 2001; Verstraeten et al. 2001 ; Res trepo et al. 2 006)
(Van der Perk et al. 2007)
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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.
Topographic Indices
In contrast to non-spatially explicit over-parameterized models, topographic indices are simple
and can be mapped spatially (Beven 1998). This allows a manager to be able to locate specific areas
within a watershed to focus management (Beven 1998; Tomer et al. 2003; Dosskey et al. 2005). There
are a variety of topographic indices for certain applications. TOPMODEL, which is a runoff model
developed for shallow soils with moderate topography in areas that do not experience long dry periods,
represents the most frequently used and long-lived topographic index model. It has been shown to
perform well in many case studies, when applied appropriately (Beven 1998). Somewhat similar indices
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have been used to identify areas to focus conservation precision, such as the wetness index and the
erosion index (Tomer et al. 2003; Dosskey et al. 2005). However these models are relatively new, lack
sufficient quantitative assessment, and are not specifically designed to quantitatively predict water quality.
Much work is yet to be done in developing a simple, yet effective sediment/total phosphorous model that
has utility in ungauged basins.
OBJECTIVES
1. Test the accuracy of a topographically based model to identify locations of ephemeral channels
throughout Waupaca County.
2. Compare the efficiency of a simple, non-spatially explicit phosphorous model to different
topographically based models when compared to observed phosphorous yields in potential
contributing areas of roughly 400 acres.
3. Compare the predictive capability of four different topographically based phosphorous models to
observed phosphorous yields in contributing areas of roughly 400 acres.
a. Determine if including a transport-decay term will enhance model efficiency.
b. Test whether using the SNAP-Plus phosphorous index instead of generic export
coefficients provides enhanced model performance.
4. Assess to what extent the spatial resolution of the digital elevation model effects the prediction of
locations of ephemeral channels and accuracy of phosphorous loads made by the simple nonspatially explicit model and the 4 topographically based models.
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METHODS
Site Selection
Approximately 7-11 ephemeral channel monitoring sites will be selected within Waupaca County.
The exact number of sites is yet to be determined due to funding and land access logistics. For a site to be
considered, it must satisfy a series of hierarchical criteria. The initial screening will identify potential
contributing area of approximately 400 acres. Potential contributing areas will be estimated using
ArcGIS 9.3 and a 3m resolution digital elevation model obtained from the Waupaca County GIS
department. The specifics of the GIS analysis can be found in the Spatial Analysis section below. For a
contributing area to be considered, it must be connected to a stream network via an ephemeral channel.
The area around the ephemeral channel must have the correct morphology to ensure a flat-crested longthroated flume can collect a representative water quality sample and volume of runoff. See the Flume
Installation section for more details on the installation process and requirements. A land use assessment
will be done on the remaining potential sites. The success of the regression analysis, discussed in the
statistical methods section, will depend heavily on an evenly spaced distribution of observed phosphorous
loads. Using land cover as a predictor of this distribution will be useful for the comparison of the simple
and topographic based models. Land cover is a reasonable preliminary screening tool for establishing a
desirable range in observed phosphorous loads. Potential sites will be grouped in categories based on
percent cultivated fields. The next phase of site selection will involve working with the Waupaca County
Conservation Department during the winter of 2008-2009 to identify land owners within these categories
that already use SNAP-Plus. More information on this software can be found in the SNAP-Plus section
below. The county conservation department will also be consulted to obtain land owner and operator
contact information. Depending on recommendations of the conservation department, land owners will
be contacted via phone, letter, in person, or email. Landowner cooperation with the SNAP-Plus data
collection process and monitoring flume installation will determine which potential sites from the percent
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cultivated field categories will be selected as field sites. Sites that represent the ideal distribution of
percent agriculture will be pursued to as much degree as feasible.
Preliminary Spatial Analysis
Delineation of potential contributing areas will done using the spatial analyst extension found
within ArcGIS 9.x. A high resolution (3m) digital elevation model (DEM) will be used as input data for
this delineation. The DEM was derived from XYZ points collected via Light Detection and Ranging
(LIDAR) by Ayres and Associates in 2005. Since this DEM has a high degree of both horizontal and
vertical accuracy, no filling will be done prior to generating the flow direction grid. A flow accumulation
grid will then be derived from the flow direction grid. The contributing areas will be delineated with the
watershed delineation tool using the flow direction grid based on the un-filled DEM serves as the input.
Concentrated flow pathways will be identified from a natural breaks classification of the flow
accumulation grid. These concentrated flow pathways are linear features that have a very high probability
of being paths of ephemeral drainage. Potential contributing area size and ephemeral connectivity to
stream networks serve as the first two criteria in the site selection process. Field verification of the
ephemeral drainage ways will be conducted with differentially corrected readings from a Trimble GeoXT
GPS unit to ensure the validity of perspective sites. Discussion of spatial analysis pertaining to modeling
applications are discussed in the Models section.
Flume Installation
Site selection will depend on the feasibility of proper flume installation. The local morphology of
the ephemeral drainage way must be constricted enough to concentrate flow into the flat-crested longthroated flume. This type of morphology is easily identifiable from the high resolution DEM. Flatcrested long-throated flumes have many benefits. These flumes provide more accurate discharge
estimations (within 2% of actual value), cost less, have better technical performance, and can be computer
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designed and calibrated using WinFlume (Bos et al. 1984; Wahl et al. 2002). Actual construction will
follow specific guidelines found in (Clemmens et al. 2001).
Models
Five models will be developed for regression analysis with observed data. The specific
parameters of the topographically based models are yet to be determined, but the general structure is
outlined below. The form of the first model will consist of a simple non-spatially explicit representation
of the potential contributing area. Percent cultivated fields will be the only variable considered in this
model. The structure of the other models can be most clearly represented by Table 2 found below. They
will all include the same spatially explicit topographic index terms, but will have different variations on
phosphorous decay terms and export coefficients. The spatial variables and parameters will be developed
with ArcGIS 9.x spatial analyst, and will consist of modified forms of topographic indices and concepts
that have been previously used a variety of researchers (Ferro et al. 1995; Hunsaker et al. 1995; Soranno
et al. 1996; Beven 1998; Jain et al. 2000; Reed et al. 2002; Tomer et al. 2003; Hjerdt et al. 2004;
Richards et al. 2004; Dosskey et al. 2005).
Table 2. Summary of spatially explicit topographic index based phosphorous models that will be tested against observed
phosphorous loads in ephemeral drainage ways.
Phosphorous
Model
decay term?
Export Coefficient
II
No
III
Yes
IV
No
SNAP-Plus P Index for cultivated
V
Yes
fields, generic for other land use type
generic for all land uses
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This promises to be a very insightful comparison. By isolating smaller contributing areas defined
by a high resolution DEM, and removing variability due to in-stream processing, we hope to be able to
assess the validity of different conceptualizations of basin scale modeling. Modeling phosphorous export
from small potential contributing areas in ephemeral channels using a high resolution DEM is a unique
attempt at removing as much unwanted sources of variability as possible while still allowing for complex
interactions between export and transport to occur. This research is also unique in its scale of
measurement. Most studies either focus on the field scale (on the ground observations) or the grossly
generalized basin scale (using regional GIS data layers). We find ourselves somewhere in-between these
two extremes, as 3m a DEM is almost as precise as on a field scale survey, yet it encompasses a large
spatial extent. In addition, Models IV and V will represent the first effort to use the SNAP-Plus P Index
as an export coefficient in a spatially explicit model. The efficiency of these models will provide valuable
insight into the applicability of the P Index at the basin scale. See the SNAP-Plus section for more details.
Statistical Methods
A series of regression analysis methods will be used to evaluate the efficiency of Models I-V.
Most likely, total phosphorous load estimates will be log-transformed to account for non-normal
regression residuals. This is a common procedure done in nearly every study that involves water quality
data of this type (Tong et al. 2001; Reed et al. 2002; Robertson et al. 2006; Van der Perk et al. 2007). A
series of regression methods will be applied depending on the characteristics of the observed data.
Kendall’s Tau rank correlation test for small sample sizes (n<20) of non-parametric data with outliers will
be used to compare model predictions and observed results if necessary. Spearman’s p rank correlation
also provides another option in rank correlation if no outliers are present. If it is appropriate to consider
the actual values of the model predictions and the observed data, then the Pearson product moment
correlation coefficient will be used to assess the linear relationship. The coefficient of determination will
also be applied to assess the percentage of the variation in observed phosphorous yields explained by the
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various models. An adjusted R2 approach will also be implemented in order to identify the model with
the most parsimony.
Please note this is not a traditional “experimental design” that attempts to identify statistical
differences in means. The power of the test has no application in a regression context.
Spatial and Temporal Resolution Sensitivity Analysis
A spatial resolution sensitivity analysis will be conducted for each model. Based on the results of
other researchers (Hunsaker et al. 1995; Beven 1998; Richards et al. 2004), it is likely that the larger
DEM grid cell sizes will be less likely to predict the actual location of ephemeral drainage ways, hinder
model performance, and change calibrated parameter values. Even the fundamental process of defining
the potential contributing area may be affected by the DEM resolution. Three different DEM models will
be used, the 3m grid derived from LIDAR, a 30m grid derived by creating a spatial average of the 3m
data, and the USGS 30m DEM (interpolated from the 1:24,000 quadrangles or from digital stereo imagery
processes). We include the USGS 30m DEM, which is based on data from the 1970’s, to assess if
temporal scale can have as much influence on phosphorous models as spatial scale.
Observed Loads
Observed loads for several storms during the spring of 2009 will be calculated. This involves the
combination of the continuous discharge data collected by automated sensors within the flumes and flow
weighted samples collected by an ISCO automated sampler. Depending on funding constraints, multiple
fixed height siphon samplers may have to be used as a substitute for automated samplers.
Laboratory Analysis of Samples
Samples will analyzed for total suspended solids (TSS) total phosphorous (TP) and dissolved
reactive phosphorous (DRP) at the state certified University of Wisconsin Stevens Point Water and
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Environmental Analysis Laboratory. Describes the analytical methods used for analysis. Model
verification will focus on TP loads, but TSS and DRP can provide useful auxiliary information that
describes the transport processes that are dominating within areas of study.
Table 3. Summary of Analytical Methods used at the UWSP Water and Environmental Analysis Laboratory.
Category
Forms
Methods*
Solids
Total Suspended Solids
Gravimetric, 2540D
Phosphorus
Total Phosphorus
Block digester, automated 4500 P F, Lachat 8500
Dissolved Reactive
0.45 m filtration, automated colorimetric, 4500 P
Phosphorus
F, Lachat 8500
*Method numbers from Standard Methods, 19 th Ed.
SNAP-Plus
An additional component of the study involves collecting data for calculations performed by
SNAP-Plus. This will be achieved by interviewing farmers in the spring of 2009, or by obtaining the data
from a farmers SNAP database if they already use the software.
SNAP-Plus is a nutrient management software package that is gaining increased use and
recognition. It performs various calculations, the most noteworthy to this study being the P-Index. The PIndex is a phosphorous delivery risk index is being incorporated into future water quality legislation.
SNAP-Plus uses a series of algorithms to calculate the P-Index. The Revised Universal Soil Loss
Equation version 2 (RUSLE 2) estimates soil erosion, to which estimated particulate phosphorous is
partitioned. Calculations are based on field scale observations and descriptions of management strategies.
The P-Index estimates a phosphorous delivery decay based on distance to surface water, but this is a
generalized representation of the transport process. SNAP-Plus does provide a superior edge of field
export estimation to any other existing method. Therefore, exploring the potential to refine the transport
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component of the P Index using a high resolution DEM and spatially explicit transport model is an
incredibly worthwhile exercise (Ward Good 2008). To date, no other study has been designed to use
SNAP-Plus in such a context as this study. Jon Panuska and Laura Good, the two minds behind SNAPPlus, have expressed extreme interest in such a study during a recent meeting concerning phosphorous
transport and legislation. In fact, until yesterday afternoon, such an effective study design had yet to be
conceptualized.
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