b
A NONPARAMETRIC APPROACH TO DETERMINE
THE NUMBER OF OBSERVATIONS REQUIRED
FOR ESTIMATING BASINSCALE
SOIL TEST PHOSPHOROUS
By
WI LLiAM RAY MARSHALL
Bachelor of Science
University of Kentucky
Lexington, Kentucky
1992
Submitted to the Faculty of the
Graduate College of the
Oklahoma State University
in partial fulfillment of
the requirements for
the Degree of
MASTER OF SCIENCE
July, 1998
h
OKLAHOMA STATE UNIVERSITY
A NONPARAMETRIC APPROACH TO DETERMINE
THE NUMBER OF OBSERVATIONS REQUIRED
FOR ESTIMATING BASINSCALE
SOIL TEST PHOSPHOROUS
Thesis Approved:
ii
ACKNOWLEDGMENTS
I would like to thank Dr. Daniel Storm for serving as my major advisor. His
guidance and encouragement helped me reach this goal. I would also like to
thank Dr. Tom Haan and' Dr. Mike Smolen for serving on my committee.. Their
thoughts, comments, and suggestions are greatly appreciated. My sincere
thanks is also extended to Dr. Ronald Elliott, who provided me work experiences,
opportunities, and direction. To the people of the Biosystems and Agricultural
Engineering Department, especially Dr. Bill Barfield, I extend my warmest wishes
and gratitude for the experiences and.friendships you have provided.
This research would not have been possible without the data and support
supplied by the Oklahoma Conservation Commission, the Arkansas Soil and
Water Conservation Commission, the Adair and Delaware County Oklahoma
State University Cooperative Extension Service offices, and the City of Tulsa
Public Works Department. My thanks to all of them.
I would Ilike to thank my parents for their love, encouragement, and
understanding. I give my love and admiration to my wife, Patricia, and to our
new daughter, Haley Brooke. They are both treasured gifts. I thank God for my
blessings and give praise to Him.
iii
Chapter
TA.BLE OF CONTENTS
Page
L
1. INTRODUCTION 1
Background and Need 1
Objectives 4
2. LITEIRATURE REVIEW 6
Soil Phosphorous 6
Soil Phosphorous Cycle 7
Soil Test Phosphorous 9
Number of Soil Samples 10
Fieldscale 11
Underlying Distributions 11
Geostatistics 13
3.. WATERSHED DATA DESCRIPTIONS 16
Upper Little Deep Fork Creek 18
Soills 19
Land Use 20
Soil Test Phosphorous 20
Battle Branch and Peacheater Creek 26
Soils 27
Land Use 30
Soil Test Phosphorous 30
Haw Creek 36
Soils 36
Land U1se 37
Soil Test Phosphorous 37
Lake Eucha (Arkansas) 38
Soils 38
Land Use 38
Soil Test Phosphorous 39
iv
Chapter Page
4. NONPARAMETRIC METHOD DEVELOPMENT .40
Data AnalysIs 41
Soi:1 Test Phosphorous Probabiility Distributions .42
Soil Test Phosphorous by Soil Mapping Unit and Soil
Characteristics ' 51
Empirical Distributions 53
Comparison of Classic to Nonparametric Techniques , 62
Nonparametric Method , 68
5. APPLICATION OF METHOD 71
Lalke Eucha (Oklahoma) Basin 72
Hydrolog!icallWater Quality Model 75
Confidence Intervals 75
Number of Observations and Confidence Intervals 85
6. SUMMARY. CONCLUSIONS, AND RECOMMENDATIONS 87
Summary and Conclusions 87
Recommendations 89
REFERENCES " 90
APPENDiCES 94
Appendix A: Soil Data 95
Appendix B: Soil Test Phosphorous Data 105
v
Table
LIST OF TABLES
Pag:e
l
3.1. Upper Little Deep Fork Creek Soil Test Phosphorous Summary 25
3.2. Battle Branch Soil Test Phosphorous Summary 33
3.3.. Peacheater Creek Soil Test Phosphorous Summary 33
3.4. Haw Creek Soil Test Phosphorous Summary 37
3.5.. Lake Eucha (AR) Soil Test Phosphorous Summary 39
4.1. Summary of GoodnessofFit Tests for a Lognormal Distribution 50
4.2. Summary of Regression of Soil Test Phosphorous by
Soill Mapping Unit 53
4.3. Summary of Regresslion of Soil Test Phosphorous by
Selected Soil Characteristics 53
4.4. Constant, C, for Equation 4.3 59
4.5. Constant, C, for Equation 4.7 to Determine Sample Size for
Estimating Basinscale Soil Test Phosphorous within a
90% Confidence Interval 70
5,.1. Lake Eucha Basin (Oklahoma) MajlOr Land Use
and Poultry tnventory 74
5.2. Input Parameters for SIMPLE Single Cell Runs for Forest 77
5.3. Input Parameters for SIMPLE Single Cell Runs for Pasture 78
5.4. Lak.e Eucha Basin (Oklahoma) Sample Sizes and
90% Confidence Intervals for the Soil Sampling Plan 86
vi
Figure
LIST OF FIGURES
Page
3.1. Watershed/basin locations 17
3.2. Upp,er little Deep Fork Creek Basin soil associations 21
3.3. Upper little Deep Fork Creek Basin land use 22
3.4. Upper Little Deep Fork Creek Basin
composite soil sample locations 24
3.5. Battle Branch Watershed soil associations 28
3.6. Peacheater Creek Watershed soil associations 29
3.7. Battle Branch Watershed land use 31
3.8. Peacheater Creek Watershed land use 32
3.9. Battle Branch Watershed field boundaries 34
3.10. Peacheater Cr,eek Watershed field boundaries 35
4.1. Relative frequency distribution of soil test phosphorous for forest
in the Upper little Deep Fork Creek Basin 44
4.2. Relative frequency distribution of soil test phosphorous for pasture
in the Upper little Deep Fork Creek Basin 44
4.3. Relative frequency distribution of soil test phosphorous for pasture
in the Battle Branch Watershed 45
4.4. Relative frequency distribution of soU test phosphorous for pasture
in the Peacheater Creek Watershed .45
vii
Figure Page
4.5. Relative frequency distribution of soil test phosphorous for pasture
in the Haw Cree:k Watershed 46
4.6. Relative frequency distribution of soil test phosphorous for pasture
in the Lake Eucha Basin (AR portion) 46
4..7. Lognormal probability plot of soil test phosphorous for forest
in the Upper little Deep Fork Creek Basin .47
4.8. Lognormal probability plot of soil test phosphorous for pasture
in the Upper Little Deep Fork Creek Basin .47
4.9. Lognormal probability plot of soiil test phosphorous for pasture
in the Battle Branch Watershed .48
4.10. Lognormal probabiHty plot of soil test phosphorous for pasture
in the Peacheater Creek Watershed 48
4.11. Lognormal probability plot of soil test phosphorous for pasture
in the Haw Creek Watershed .49
4.12. Lognormal probability plot of soil test phosphorous for pasture
in the Lake Eucha Basin (AR portion) .49
4.13. Empirical distributions of mean soil test phosphorous for various
sample sizes for forest in the Upper Little Deep Fork Creek Basin 56
4.14. Empirical distributions of mean soil test phosphorous for various
sample sizes for pasture in the Upper Little Deep Fork Creek Basin....... 56
4.15. Empirical distributions of mean soil test phosphorous for various
sample sizes for pasture in tine Battle Branch Watershed 57
4.16. Empirical distributions of mean soil test phosphorous for various
sample sizes for pasture in the Peacheater Creek Watershed 57
4.17. Empirical distributions of mean soil test phosphorous for various
sample sizes for pasture in the Haw Creek Watershed 58
4.18. Empirical distributions of mean soil test phosphorous for various
sample sizes for pasture in the Lake Eucha Basin (AR portion) 58
viii
Figure Page
4.19. Estimated 90% confidenoe intervals for mean
soil test phosphorous for forest fOil" varying sample sizes 60
4.20. Estimated 90% confidence intervals for mean
soil test phosphorous for pasture for varying samp·le sizes 61
4.21. Comparison of confidence intervals computed by the
classical and nonparametric methods for varying sample sizes
for Upper Little Deep Fork Creek forest. 65
4.22. Comparison of confidence intervals computed by the
classical and nonparametric methods for varying sample sizes
for Upper Little Deep Fork Creek pasture 65
4.23. Comparison of confidence intervals computed by the
classical: and nonparametric methods for varying sample sizes
for Battle Branch pasture 66
4.24. Comparison of confidence intervals computed by the
classical and nonparametric methods for varying sample sizes
for Peacheater Greek pastyre 66
4.25. Comparison of confidence intervals computed by the
classical and nonparametric methods for varying sample sizes
for Haw Creek pasture 67
4.26. Comparison of confidence intervals computed by the
classical and nonparametric methods for varying sample sizes
for Lake Eucha (AR portion) pasture 67
5.1. Lake Eucha Basin 73
5.2. SIMPLE initial P versus P loading for forest.. 79
5.3. SIMPLE initial P versus P loading for pasture 80
5.4. Confidence Interval determination for forest 83
5.5. Confidence Interval determination for pasture 84
ix
CHAPTER 1
IINTRODUCTION
Background and Need
Surface runoff from agricultural related activiUes and other potential
nonpoint pollution sources, if not properly managed, can contribute significant
loadings of phosphorous and sediments to receiving surface waters. Soil
phosphorous can contribute to nonpoint source pollution through runoff in soluble
and sedimentbound ~orms. Excessive levels of phosphorous in surface waters
can lead to eutrophication, an increase in the fertility status of natural waters that
causes accelerated growth of allgae or other water plants (Pierzynski at aI.,
1994).
As more emphasis is plaoed on nonpoint source pollution determination
and prevention, the use of computer modeling and geographic information
systems has Dome to the forefront of pollution management and evaluation
technology. Computer models can be used to target critical source areas of
sediment and phosphorous for priority treatment (Storm et al., 1996). Spedal
emphas,is can then be given to these critical areas to help minimize the potential
for detrimental offsite water quality impacts.
1
Since many of these computer models are used to determine
phosphorous loadings to receivingi waters, an important model input parameter is
soil phosphorous level. Some hydrologicat/water quality models require soil test
phosphorous as an input parameter. Soil test phosphorous is that portion of soil
phosphorous that is availabl!e for plant uptake or is in a form to readily become
available during a growing season.
At present, there is no established procedure or method to predict the soil
test, or plant available, phosphorous levels for various land uses, land covers,
and/or soil types without employing a sit.especific soil sampling program. When
addressing nonpoint source pollution problems, the geographic area of interest is
very often on the basinscale of several thousand to several hundred thousand
hectares. With sampling areas of thlis magnitude, soil sampling and analysis
costs can begin to be a major part of the overall project budget.
Soil samples that are eventually collected are typically used to provide an
estimate of the average, or mean, soil test phosphorous. As with any estimate,
there wHl be some uncertainty due to the spatial variability of soil test
phosphorous and soil sampling procedures. Quantifying this uncertainty will
provide a measure, or degree of confidence, for the estimated mean soil test
phosphorous and aid in quantifying the output uncertainty for the
hydrologicallwater quality model emp!loyed. Thus, them is a need to predict the
minimum number of soil samples required, within some specified confidence
interval, to obtain an estimate of the mean soil test phosphorous level.
2
Classical statistical techniques are availab:le for predicting the number of
soil samples required, but are based on the assumption of a 'known underlying
distribution, or normal distribution, of the data means. Sometimes, the
assumptions associated with this approach do not apply or are not completely
valid. It has been found that data from highlevel soil test phosphorous basins
with fields that receive poultry litter may not adhere to all the assumptions
needed to use classical statistics.
The purpose of this research was· to evaluate soil test phosphorous
probability distributions from s,everal watersheds and/or basins and develop a
nonparametric approach for determining the minimum number of soil samples
required, within a specified confidence interval, to obtain an estimate of the mean
soil test phosphorous. The method was developed for basinscale applications.
Empirical distributions of the data were used so that no assumption had to be
made regarding the underlying distribution of the means.
Another important component of estimating sample sizes is determining
an acceptable confidence interval. An approach was also developed for
identifying the confidence interval based on the expected output variance due to
initial phosphorous input of a hydrological/water quality model. The Spatially
Integrated Model for Phosphorous Loading and Erosion (SIMPLE) (Sabbagh et
aI., 1995) was the model employed. It is a continuous simulation, distributedparameter
modeling system developed to estimate watershed and/or basinscale
sediment and phosphorous loading to surface waters. The technique used
to determine the confidence interval for predicting sample size can also be used
3
to estimate the confidenoe interval and model output variance associated with a
predetermined sample size.
The method developed for predicting the number of soi'l samples required
within a specified confidence interval was then used to develop a soil sampling
plan for the Oklahoma portion of the Lake Eucha basin, which is located in
northeastern Oklahoma.
Objectives
The overall objectives of this research were to examine the probability
distributions of soil test phosphorous data and develop a nonparametric method
to determine the number of observations required to estimate basinscale soil
test phosphorous. The results could also be used to apply a confidence interval
to a predetermined number of samples. The empirical results were then used to
develop a soil sampling plan. More specifically, the objectives were:
1. Evaluate the underlying probability distributions of soil test phosphorous
data sets from four Oklahoma watersheds and the Arkansas side of the
la'ke Eucha basin;
2. Use regression statistics to evaluate the relationship, if any, between soil
test phosphorous and soil mapping units, and soil test phosphorous and
selected soil parameters, for three Oklahoma watersheds;
4
3. Develop a nonparametric method to determine the minimum number of
soil samples required., within a specified confidence interval, to obtain an
estimate of the basinscale mean soil test phosphorous by major land use;
4. Apply the nonparametricmethod from objective 3 to develop a soil
sampling plan for the Oklahoma portion of the lake Eucha basin using the
SIMPLE distributed parameter water quality computer model.
5
CHAPTER 2
LITERATURE REVIEW
SoU Phosphorous
Phosphorous is essential to all forms of life on earth. The lack of available
phosphorous in soils can be a limiting factor in plant growth. Over the years, the
addition of phosphorous to soils in the form of manures, minerals, or fertilizers
has contributed to locations with elevated levels of soil phosphorous. Soils with
highlevel phosphorous have greater potential for phosphorous transport offsite
through surface runoff in soluble and sedimentbound forms. While phosphorous
ils not toxic and does not represent a direct health threat to human or other
organisms, it does mpresent a serlious indirect threat to water quality (Peavy et
aI., 1985). Phosphorous is often the limiting nutrient in surface waters. When an
increase in phosphorous occurs in a phosphorouslimited water body, the growth
of algae and/or water plants can be accelerated, thus, beginning the process of
eutrophication. Eutrophic conditions can negatively affect water quality by
causing low dissolved oxygen levels. excess.ive aquatic growth, increased
sedimentation, and greater turbidi.ty. Managing our soil and water resources
requires an understanding of the soil phosphorous cycfe.
6
Soil Phosphorous Cycle
The literature is quite extensive and contains very detailed information on
the topic of the soi'l phosphorous cycle. Rather than present such an exhaustive
review on the subject, an overview of the soil phosphorous cycle is g,iven.
Pierzynski et 801. (1994) presents a discussion of the soli phosphorous
cycle. Phosphorous, found in all terrestrial environments, primarily originates
from the weathering: of soil minerals and other more stable geological materials.
As phosphorous is solubilized in soils by the chemical and physical processes of
weathering, it is accumulated by plants and animals, reverts to stable forms in
the landscape, or is eroded from soils and deposited as sediments in freshwaters
or oceans. Soil factors that control the conversion rate of phosphorous between
the inorganic and organic forms regulate the short and longterm fate of
phosphorous in the environment. The soil phosphorous cycle consists of many
complex chemical and microbiological reactions.
Organic soil phosphorous includes both biologically available organic
phosphorous and resistant organic phosphorous (Foth and Ellis, 1997).
Common ~orms of organic phosphorous found in soils include inosital
phosphates, phospholipids, phosphoproteins, sugar phosphates, and nucleic
acids. Soil organic phosphorous transformations are primarily mineralizationimmobilization
reactions mediated by soil microorganisms and phosphorous
uptake by plant roots. Studies have shown that as much as 50% of the
phosphorous transported in runoff can be soluble organic phosphorous
(Pierzynski et al., 1994). It has also been found that organic phosphorous has
7
been somewhat correlated to extractable, soil test phosphorous (Sharpley" 1985;
Sharpley et al., 1987).
Inorganic soil phosphorous can make up to 50  70% of the total
phosphorous in soils; the major soil inorganic phosphorous transformat1ons of
importance include the fixation of phosphorous in insoluble forms by adsorption
and precipitation reactions, and the solubilization of phosphorous by desorption
reactions and mineralization dissolution (Pierzynski et aI., 1994). In soils that are
moderately weathered, the dominant minerals are apatites. In highly weathered
soils, iron (Fe) and aluminum (AI) precipitates become the major mineral sources
of phosphorous.
The pH is a controlling factor that determines phosphorous solubility, as
described by (Johnson et aI., 1997). Maximum phosphorous availability occurs
in a pH range of 5.5 to 7.2, where the ions present will be either monovalent
(HZP04) or divalent (HPO/), both of which are readily available for plant uptake.
At soil pH levels below 5.5, iron (Fe), aluminum (AI), and manganese (Mn) react
with phosphorous to form insoluble compounds. When soil pH exceeds 7.2,
phosphorous will complex with calcium (Ca) to form plant unavailable
phosphorous.
The transport of phosphorous in runoff can occur in both particulate and
soluble forms. Particulate phosphorous includes all solid phase forms and
phosphorous sorbed by soil particles and organic matter eroded during runoff
and is the major contributor (7590%) of phosphorous transported from
cultivated land (Burwell et aI., 1977). Runoff from pasture and grassland tends to
8
have higher fractions of soluble phosphorous forms. Edwards et at (19'96)
reported greater than 74% of total phosphorous runoff from fescue plots treated
with poultry litter was in the soluble 10rm.
Soil Test Phosphorous
Soil test phosphorous is an availability index that is correlated to the
amount of phosphorus that will be avai'lable, or become available, to a plant
during a growing season. The fra.ction of soil phosphorous that the plant can
readily use, available soil phosphorous, makes up about one percent of the total
phosphorous in soils (Johnson et at, 1997). The compound solubilities present
in the soil effect the availability of inorganic phosphorous. As more phosphorous
from solution is extracted, it may be replaced from the precipitated or solid
phase. The chance for phosphorous in soil solution increases as the amount of
total soil phosphorous increases.
There are several methods used to estimate the available soil
phosphorous. The overwhelmingly largest fraction of soil samples are tested for
available phosphorus by extraction with dilute acid solutions (Fixen and Grove,
1990). The Mehlich III soil test method (Mehlich, 1984) is one extraction
procedure that is used to measure plant available phosphorous. Cai et al. (1997)
found from a comparison of four extractants (Modified Troug, Mehlrich III, Olsen,
and ionexchange resin) that Mehlich III provided better detection of
phosphoroussufficient and phosphorousdeficient soils under the conditions
tested. Bray P is another standard extractant method commonly used. The Soil,
9
Water, and Forage Laboratory at Oklahoma State Univers.ity uses the Mehlich HI
extractant method to obtain and report soil test phosphorous.
Available soil phosphorous is a vital input parameter for many
hydrological/water quality models. It is used in predicting soluble phosphorous
transport using. a soil extraction coefficient and in sedimentbound phosphorous
transport using phosphorous ennichment ratios (Sharpley et aI., 1982).
Number of Soil Samples
The goal of most soil sampling programs is to obtain an average value for
some soil property over the area being sampled. When presented with this task,
one will inevitably need to know how many soil samples are needed and the
associated level of confidence in the estimated mean. The level of variation in
the parameter being sampled will impact the number of observations needed to
estimate the mean. Soils, by nature, are heterogeneous and have high spatial
variability.
The literature review revealed that most work to date, pertaining to
estimating; sample size and confidence intervals, may be generally grouped into
three categories: fieldscale sampling procedures, assumed underlying
probability distributions, and geostatistics. Each of these categories is addressed
in the following sections.
10
Fieldscale
Classical statisticali approaches to soil sampling have assumed each
observation to be independent and identically distributed (Sabbe and Marx,
1987). Numerous studies have examined the spatial variability of soil properties
and have described soil sampling methods for obtaining representative estimates
(Cline, 1944; Rigney, 1956; Peterson and Calvin, 1983; Russo and Bresler,
1981; Sisson and Wierenga, 1981; Webster and Oliver; 1992). While different
methods of sampling may have been studied, all of these cited works have
focused on fieldscale variations and sampling.
A study by Keogh and Maples (1967) suggested that the size of the field
did not affect the coefficient of variation appreciably, especially above a minimum
size of 8.1 to 12.2 ha (20 to 30 acres). It was also determined that more samples
were required to determine soil test phosphorous than other soil fertility
parameters. Cameron et aL (19171) also reported that the number of samples
needed to estimate the field average did not increase drastically with an increase
in field size. It is recommended by Zhang and Johnson (1997) to collect at least
15 random core samples per field to comprtse a representative composite field
soil sample.
Underlying Distributions
A known, or assumed, underlying probability distribution of the data
means is the basis of classical statistical methods for estimating the required
sample size, or number of observations, needed for estimating a soil parameter.
11

When the data tend to follow a known distribution, using classicall statistical
methods is a good approach. The number of observations, n, needed to achieve
a desired estimation variance is given by Cline (1944),
n = t«282/ (x _p)2 (2.1)
where fa is Student's t at the chosen level of probability, a, 8
2 is the estimated
variance, and x  f.l is the acceptable deviation from the true mean, p. Of course.
Student's t is based on the assumption of normality (Steel and Torrie, 1980).
Warrick et al. (1986) states the appropriate Student t value should only be used
to estimate confidence intervals; for estimating n, the twotaHed normalized
deviate, Za, should be used instead of Student's t. This method would require an
estimate of the expected mean and variance for the property being sampled.
These methods assume that the means of the data follow a normal
distribution. This assumption is explained by the Central Limit Theorem, and is
quoted by Ott (1984) as,
"lf random samples of n measurements are repeatedly drawn from a
population with a finite mean f.l and a standard deviation (7, then, when n is
large, the relative frequency histogram for the sample means (calculated
from the sample means) will be approximately normal with mean f.1 and
standard deviation a/Jfi .."
Haan (1.977) expands the explanation of the Central Limit Theorem by stating
that the population must consist of identically and independently distributed
random variables and discusses some generalized conditions under which it can
appfy.
12

Many physical, chemical, and biological properties of soils display skewed
distributions that are better approximated by the two parameter lognorma'i
distribution (Parkin et al." 1988). Parkin et a!. (1990) evaluated five methods for
calculating confidence intervals for a lognormally di'stributed. variable. They used
four test ,Iognonnal populations, each with known means and variances. A
nonparametric method was developed and was determined to be a good
alternative to the others for calculating confidence intervals when sample siz,es
were grater than 20 and the underlying population deviated from true
lognormality.
Geostatistics
Another focus in the literature pertaining to soil sampling was on the use
of geostatistics, which is a form of statistics dealing with spatially referenced
data. Geostatistics assumes data properties are correlated over space, so that
data points close together tend to be more alike than those that are far apart. In
other words, it can be used where the assumption of independent observations
may not be valid.
The theory of regionalized variables, those distributed in space, was
developed by G. Matheron (1963) in the 1960s. The application of this theory led
to the methodology for geostatistics, which began in mining and geology for the
assessment of are bodies. The term "kriging" after O.G. Krige, described the
method of producing the best estimate of the unknown value of a parameter at
13
some location within an ore deposit. (Warrick et aI., 1986; Sabbe and Marx,
1987).
McBratney and Webster (1983) presented a method for determining the
required number of observations, or soil samples, needed for regional estimation
of soH properties based on regionalized variables. They created semivariograms
for soil properties and showed how kriging could be used to estimate
a soil property at unvisited sites. If the semivariogram is already known, the
kriging variance for any particular sampling scheme can be determined. They
demonstrated the advantages of kriging from grid samples when estimating the
soil properties over a region. When computing the required sample size, threeand
halffold to ninefold gains in efficiency over that estimated by classical
theory for simple random sampling was reported.
Grid sampling was used by Gupta et al. (1997) to examine spatial
variability and sampling strategies for sitespecific farming at two farms. Semivariogram
models were used to describe the correlation structure of nutrients.
Determination of sample size and optimum sampling interval, considering the
correlation and semivariance characteristics of the nutrients, were considered.
Optimal. sampling grids were determined for the nutrients based on spatiaf
variability.
Geostatistics can be used successfully on the basinscale where there is a
gradual change spatially of the measured parameter, such as soil phosphorous.
When abrupt changes occur, as along field or property boundaries, the use of
geostatistics becomes limited. Basins, or watersheds, that contain poultry
14
related activities where the I~tter is spread on the fields may not be suited to
geostatistics for estimating soil sampling size because there may exist significant
differences in soil phosphorous levels from one field to the next. These
differences are based on the history and levels of litter application that differ
across field boundaries.
15
........_
CHAPTER 3
WATERSHED DATA DESCRIPTIONS
Data from four Oklahoma watersheds and the Arkansas portion of the
Lake Eucha basIn were examined and used for this research. The
watershed/basin data were chosen based on the availability and diversity of
geographic location and land use. The watersheds/basins (locations) used in
this study are listed below.
• Upper Little Deep Fork Creek Basin (Easterncentral Oklahoma)
• Battle Branch Watershed (Northeastern Oklahoma)
• Peacheater Creek. Watershed (Northeastern Oklahoma)
• Haw Greek Watershed (Southeastern Oklahoma)
• Lake Eucha Basin (AR portion) (Northwestern Arkansas)
In general, an of the watersheds are mostly rural agricultural settings.
Four of the five watersheds contain poultry production activities and have had
varying time lengths of involvement in the industry. The watersheds are in close
enough proximity that they experience similar dimates and growing seasons.
The general locations are shown in Figure 3.1.
The same types of data were not available from each watershed. For two
of the locations, Lake Eucha (Arkansas portion) and Haw Creek (Oklahoma),
16
COLORADO I K A N S A S
I
2:
NEW I
4 MEXICO Ii
OKLAHOMA TEXAS I ...
Nt . Tulsfl ~; 1.
Not to scale 1~
®Oklahoma City
»
I
z
>.
1. Upper Little Deep Fork Creek Basin I ""J C/)
»
en
2. Battle Branch Watershed I " . 5 ..
3. Peacheater Creek Watershed
4. Lake Eucha Basin  ~' ....
T E X A 5. Haw Creek Watershed (OK portion) I s
Figure 3.1. WatershedlBasin locations.
only soil test phosphorous data were available. Data layers for each of the
watersheds/basins were originally obtained and developed for other projects
pertaining to nonpoint source assessment of phosphorous and sediment
loadings, where the computer modeling was, or is to be, performed by the
Biosystems and Agricultural Engineering Department, Oklahoma State
University. The watershed/basin data sets used in this study are described in the
following sections. The Geographical Resource Analysis Support System
(GRASS) geographic information system (GIS) developed by the U.S. Army
Corps of Engineers (U.S. Army, 1,991) was used to compile and organize the GIS
data.
Upper Little Deep Fork Creek
The Upper Little De,ep Fork Creek basin is located in the southwest corner
of the northeast quadrant of Oklahoma (Figure 3.1). It covers approximately
39,500 ha (97,500 acres) and lies almost entirely in Creek County. The western
2000 ha (5,,000 acres) stretch into neighboring Lincoln County. The Little Deep
Fork Creek flows general}y east and into the Deep Fork River, which is a tributary
of the North Canadian River. A site tour of the basin revealed the major
industries to include oil and gas exploration and agriculture. The agricultural
activities are hay production, grazed cattle, and small grain production. The
basin is approximately 40% forest and 55% grasslands, with the remaining 5%
urban or other.
18
SoUs
The soils are described by the USDA Soil Survey for Creek County. The
soils are in three broad, general associations, which are sandy soils of the
forested areas, dark soils of the prairies, and soils of the bottom lands. Each
association is dominated by soils that developed from similar or related parent
materials, have some characteristics in common, and contain many smaU areas
that belong to one of the other two associations (SCS, 1958).
Digital soil type data boundaries for Creek and Lincoln Counties were
obtained from Oklahoma soH surveys that had been digitally scanned. The
attributed soil characteristic information was obtained from the U.S. Department
of Agriculture, Natural Resources Conservation Service's National Map Unit
Interpretation Record (MUIR) Database (USDANRCS, 1994) for Creek and
Lincoln Counties. The MUIR data set is a collection of soil and soilrelated
properties, interpretations, and performance data for a soil survey area that is to
be used in conjunction with county soil surveys. The data are stored in a
retrievable relational database with information for most of the U.S. counties. A
list of the soils within the ~tudy area, with selected attributes, can be found in
AppendiX A.
The majority of the soils within the basin are from the Darnell and
Stephenville series. The Darnell series are very shallow acid soils developed
over reddish sandstones. They are too shallow for cropping and are used mainly
for woodland pasture. The Stephenville series are of medium depth over the
parent materials of soft reddish sandstone and are stightly acid. Sandstone
19
outcrops are common in both series (SCS, 1958). The distribution of the three
general soil associations are depicted in Figure 3.2.
land Use
The land use data were obtained from the Oklahoma Conservation
Commission (OeG), Water Quality Division in digital format. The watershed was
field inspected by oce personnel and was divided into 29 categories. The major
category ratings consisted of "poor" to "good" for grasslands and forestlands,
croplands, and a few other smaller agricultural categories. S'ince the oce land
use data did not contain urban areas, there were some "holes" in the data set
where urban activities were present. To make a comp,lete land use data file, Soil
Conservation Service (1985) Okl.ahoma land use digital data were used to fill in
the lacking portions. This facilitated the creation of a comp\ete land use data set.
Grasslands cover approximately 55% of the basin, forestlands cover about 40%,
and the remaining 5% is made up of cropland, urban, oilfield activities, and
"other" land uses. Figure 3.3 shows the distribution of the major land uses.
SoU Test Phosphorous
The soil sampling was performed by oce personnel. The soil sampling
plan called for collecting a proportionate number of samples based on the
percentage of land use type. The exception to this was forest land use, which
was assumed to have relatively uniform soil nutrient levels. This was done for a
predetermined number of composite samples over the entire basin. The basin
20
=
o
I
4
I
8km
I
Soil Associations o Soils of the bottom lands r.., Sandy soils of forested areas
• Dark soils of the prairies
 Stream network
• Water
Figure 3.2. Upper Little Deep Fork Creek Basin soil associations.
21
oI
4
I
8 km
I
Figure 3.3. Upper Little Deep Fork Creek Basin land use.
22
 Stream network
Other: crops, water, farmstead, oil wasteland, urban,
impervious surfaces
Forest
Major Land Uses
Pasture/Grasslands •D
was divided into one square mile grids and at least one composite soil sample
was collected from each grid. General locations of where the samples were
taken were recorded and a digital soil sample location map was developed by
OCC. Originally, approximately 150 composite samples were collected. Later,
due to the similar magnitudes of forest and range land soil phosphorous levels,
20 additional composite samples were obtained over the basin from the forested
areas to improve the variability and mean estimates. The soil samples were
collected from the Summer of 1996 through the Spring of 1997. All of the
samples were analyzed by the Oklahoma State University Soil, Water, and
Forage Laboratory. The results are reported as soil test phosphorous as
measured by the Mehlich III ,extraction test method. Figure 3.4 shows the
approximate locations where the composite soil samples were taken. A
summary of the soil test phosphorous data is shown in Table 3.1. The complete
soil test phosphorous data can be found in Appendix B.
23
•
•• •+ • • • •
• • + • • • +• • + .. + • • • + + • • • • + • • • • •
• • : • + • • +. • • • •
. • • • • + • • • + • •• + + + • • • + • •• • • + + • • • + • + • • • • • • • + • • •• • • • + + • \ • • • + •• • • • •+ • • • +
+
o
I
4
I
8 km
I
• Midpoint of composite soil sample
Figure 3.4. Upper Little Deep Fork Creek Basin composite soil sample locations.
24
Table 3.1. Upper Little Deep Fork Creek Soil Test Phosphorous· Summary
Land use Mean Median Std. Dev. Range Count
(mg/kg) (mg/kg) (mg/kg) (mg/kg) (no.)
Forestland"
Stable 19 19 4 13  25 8
Moderately used 17 16 5 7  27 14
Heavily used 19 17 6 11  29 12
Grassland"
Good condition 16 14 7 7  35 41
Fair condition 15 14 5 8  30 38
Poor condition 16 13 9 4  53 45
Unmanaged 17 13 11 6  38 6
Cropland
Small grains 1,6 19 7 9  49 3
Salt or Oilfield 9 9 3
Induced Erosion
Feedlot 275 275 304 60490 2
• Mehlich III phosphorous
.. Forestland
Stable: undisturbed. 0  1% bare soil
Moderate use: 1; 10% bare soli
Heavy use: > 10% bare soli
Grassfand
Good condition: < 1% bare soil
Fair condition: 1  5% bare soli
Poor condition: 5  20% bare soil
Unmanaged: 20  100% bare soil with erosive areas
25

Battle Branch and Peacheater Creek
An extensive soil sampling plan for these watersheds was implemented as
part a United States Department of Agriculture (USDA) hydrologic unit area
project for the Illinois River Basin, which is located in northwest Arkansas and
northeast Oklahoma. The project sanctioned the delineation of individual pasture
fields and the soil samp ing of each, as reported by Sabbagh et al. (1995). Battle
Branch and Peacheater Creek watersheds are located within the Illinois River
Basin. These watersheds contain extensive poultry industry activities. The data
were used for this study and are described below as in the referenced report.
The Battle Branch Watershed is located in southern Delaware County in
northeastern Oklahoma (Figure 3.1). The watershed area covers about 2,200 ha
(5,500 acres). The topography is primarily rough steep hills with a blackjackpostoak
tree cover. The major land use is agriculture. Poultry industry activities
including broilers, layers, breeder hens, and pullets, are present. The survey
data indicates there are approximately 25 poultry houses within the watershed.
The Peacheater Creek Watershed is located in Adair County in
northeastern Oklahoma (Figure 3.1). The watershed area covers approximately
6,500 ha (16,000 acres). The watershed is in the Ozark Highland land
Resource Area. The topography is primarily rough steep hills with a blackjackpostoak
tree cover and the major land use is agriculture. There are 59 poultry
houses located within the Peacheater Creek watershed. These operations
maintain an average of 1.1 million broilers, layers, breeder hens, and pullets per
26
year. In addition there are nine dairies with a total of 800 dairy and about 3000
unconfined beef cattle located within the watershed.
Soils
Digital soil type data for Battle Branch and Peacheater Cre,ek watersheds
were obtained from the soil surveys for Adair County and Delaware County
(SCS, 1965; SCS, 1970) that had been digitally scanned. Values for other soil
characteristic, such as clay content, bulk density, slope length, erodibility factor,
organic carbon content, and hydrologic group were estimated from the same soil
surveys.
The Battle Branch watershed includes 19 different soil types. A complete
list of the soils for Battle Branch are in Appendix A. The predominant soils in the
watershed are in the Clarksville and BaxterLocust associations. The Clarksville
soils are cherty silt clay loam soils and generally have high steep slopes with
high runoff potential. The Baxter and Locust soils are cherty silty clay loam soils
and are found on the nearly level to gently sloping ridge tops (SCS, 1970).
Figure 3.5 depicts the distribution of the soil associations within the watershed.
The Peacheater Creek watershed includes 18 different soil types and are
listed in Appendix A. The predominant soils are in the BodineDickson
association. The Bodine soils are loamy soils and generally have steep slopes
with high runoff potential (SCS, 1965). The spatial distribution of soil types are
shown in Figure 3.6.
27
2 km
I
 Stream network
oI
Figure 3.5. Battle Branch Watershed soil associations.
28
Soil Associations
[] EJdoradoNewtoniaOkemah
SallisawElsahStaser
• Clarksville
• BaxterLocust
 Stream network
Soil Associations
D HectorLinker
oI
2I
4km
I
BodineDickson
• EtowahHuntington
• SummitJay
Figure 3.6. Peacheater Creek Watershed soil associations.
29
d

A comprehensive land use inventory for Battle Branch and Peacheater
Creek Watersheds was conducted in the early 1990's by the Oklahoma State
Univers!ity Cooperative Extension Service. The watersheds were divided i,nto
individual fields, based on land ownership, land uses, and cover types. The
detailed land' use inventory with field boundaries was combined with Agricultural
Stability and Conservation Service (ASCS) black and white aerial photography.
These boundaries were then digitized and labeled. Spatial representations of
soil and land use characteristics were then generated with a GIS. Figures 3.7
and 3.8 indicate the distribution of land uses within the watersheds. There is
approximately 60% pasture in both Battle Branch and Peacheater Creek
watersheds.
Soil Test Phosphorous
The pasture fields in the study areas were the fields of interest, since the
effects of poultry liter application to pasture were under evaluation. Soil sampling
for most of the fields was done so that at least one composite sample was
obtained for each of the fields sampled. Soil sampling was performed by the
Oklahoma State University Cooperative Extension Service. The samples were
collected over the period of 1991 through 1994. The resultant soil test
phosphorus level for the composite sample was then assigned to the respective
field. All of the samples were analyzed by the Oklahoma State University Soil,
30
Major Land Uses
r~l",:j Pasture/Meadow  Stream network
• Forest
[ 1 Other: crops, water, farmstead, urban, impervious surfaces
2 km
I
oI
Figure 3.7. Battle Branch Watershed land use.
l
31
32
4km
I
2I
 Stream network
aI
Pasture/Meadow
Figure 3.8. Peacheater Creek Watershed land use.
Major Land Uses
• Forest
D Other: crops, water, farmstead, urban, impervious surfaces
_L :.:......
boundaries of pastures within the watersh,eds that were sampled.
as measured by the Mehlich III extraction test method. A summary of the
Water, and Forage Laboratory. The results are reported as soil test phosphorous
230
255
Count
(no.)
Count
(no.)
9  490
7 164
Range
(mg/kg)
Range
(mg/kg)
38
89
Std. Dev.
(mg/kg)
Std. Dev.
(mg/kg)
74
33
52
Median
(mg/kg)
Median
(mg/kg)
54
93
Mean
(mg/kg)
Mean
(mg/kg)
Pasture
Pasture
Land use
Land use
• Mehllch III pllosphorous
• Mehlich III phosphorous
completed soil test phosphorous resul:ts is reported in Tables 3.2 and 3.3. The
detailed results are found in Appendix B. Figures 3.9 and 3.10 show the field
Table 3.3. Peacheater Creek Soil Test Phosphorous· Summary
Table 3.2. Battle Branch Soil Test Phosphorous· Summary
3.. .........
34
2 km
I
oI
Figure 3.9. Battle Branch Watershed field boundaries.
oI
2
I
4 km
I
l
Figure 3.10. Peacheater Creek Watershed field boundaries.
35
Haw Creek
Haw Creek Watershed, part of the Wister lake Basin, is located in eastern
LeFlore County in southeastern Oklahoma and stretches into Arkansas (Figure
3.1). Only data from the Oklahoma portion was used for this study. It covers
approximately 2,000 ha (5,000 acres) on the Oklahoma s:ide. It is a rural
watershed containing poultry industry activities. There am 20 poultry houses
(approximately 20,000 birds per house) located within the Oklahoma portion of
the watershed (Joe Bullard, Oklahoma State University Cooperative Extension
Service, personal communication).
Soils
Soils within the watershed can be grouped into three general soil
associations, and are described by the Soil Survey of LeFlore County (SCS,
1981 ). The NeffKennCeda association is described as nearly level to gently
slopingl, moderately drained loamy soils. They are located on the flood plains
and are subjected to occasional flooding. The CarnasawOctaviaPirum
association is deep, gently sloping to steep, well drained stony soils. They are
located on ridges and mountains. The SallisawStigler association is deep,
nearly level to moderately steep, well drained loamy soils. They are located on
the uplands. Most of this association is in pasture.
36
Land Use
The major land use within the watershed is forest. Haw Creek is locat.ed
within the Ouachita Mountains National Forest area, but also contains private
land ownership. There is approximately 560 ha (1,400 acres) of pasture on the
Oklahoma side (Joe Bullard, Oklahoma Cooperative Extension Service, personal
communicat'ion), located mostly in the valleys and along the stream banks.
Soil Test Phosphorous
The pasture fields were soil sampled by the Oklahoma State University
Cooperative Extension Service during the Summer and Fall of 1995.
Approximately 90% of the pasture area within Haw Creek Watershed was
sampled (Joe Bullard, Oklahoma State University Cooperative Extension
Service, personal communication). The samples were analyzed by the
Oklahoma State University Soil, Water, and Forage Laboratory. The results are
reported as soil test phosphorous as measured by the Mehlich III extraction test
method. Table 3.4 summarizes the soil test phosphorous results. The complete
data set is found in Appendix B.
Table 3.4. Haw Creek Soi Test Phosphorous' Summary
Land use
Pasture
• Mehllch III phosphorous
Mean
(mg/kg)
104
Median
(mg/kg)
54
Std. Dev.
(mg/kg)
110
Range
(mg/kg)
2 ~ 515
Count
(no.)
82
1 37 ._.
Lake Eucha (Arkansas)
Lake Eucha Basin is located in northeastern Oklahoma and northwestern
Arkansas (Figure 3.1). The Lake Eucha basin is approximately 93,000 ha
(230,000 acres), with 40% in Benton County, Arkansas and the remainder in
Delaware County, Oklahoma. This basin is generally known for its extensive
poultry industry activities. Soil sampling of all pasture tor the Arkansas portion
has been completed and the results were used in this study.
A 1996 survey by the Water Quality Division, Oklahoma Conservation
Commission concluded there were 489 poultry houses on the Arkansas side of
the basin (OCC, 1996). These include houses for layers and broilers.
Soils
The soil types within the Arkansas portion of the basin are reported and
discussed by Wagner and Woodruff (1997). The soils are part of the ClarksvilleNixa
Captina and the ClarksvilleNoarkNixa soil mapping units. Each mapping
unit contains numerous soil types, where the majority of soils within both units
are cherty to very cherty silt loams. Soil thickness can range from less than one
meter to several meters, but the soils are generally thin.
Land Use
Land use is primarily forest and pasture while poultry is the major
agricultural commodity produced in the basin (Wagner and Woodruff, 1997). A
survey performed by the Oklahoma Conservation Commission during the Spring
38
of 1996 (OCC, 1996) found a total of 714 poultry houses in the basin, with 489
located on the Arkansas side. The survey also fOl!Jnd 18 hog houses and 5
turkey houses in production on the Arkansas portion. Approximately 40% of the
Arkansas portion is pasture/hay, 55% forest, 3% crop, 1% urban, and 1% other
(NRCS, 1995). This corresponds to approximately 14,900 ha (37,000 acres) of
pasture/hay land use.
Soil Test Phosphorous
The pastures within the Arkansas portion of the Lake Eucha basin have
shown in Table 3.5. The complete data set is found in Appendix B.
measured by the Mehlich III extraction test method. The summarized results are
been soil sampled. Samples were collected by the Arkansas Soil and Water
261
Count
(no.)
5  490
Range
(mg/kg)
118
Std. Dev.
(mg/kg)
152
39
Median
(mg/kg)
164
Mean
(mg/kg)
Pasture
Land use
• Mehlich III phosphorous
Conservation Commission and analyzed by the University of Arkansas Soil and
Water Laboratory. The sampling occurred during the period of 1994 through
1997. The soil phosphorous results are reported as soil test phosphorous as
Table 3.5. Lake Eucha (AR) Soil Test Phosphorous· Summary
l
CHAPTER 4
NONPARAMETRIC METHOD DEVELOPMENT
Classic statistical techniques of predicting sample size are based on a
normal distribution of the data means and identical and independent distributions
of the original population. The data from highlevel soil test phosphorous basins
with poultryrelated activities, such as the case for this study, may not meet all
the assumptions required for the classical approach. Soil test phosphorous
levels from these basins may not be independent from field to field within a basin.
In other words, information from one sample may be partially duplicated in a
sample close by. In addition, the data may not be identically distributed. The
application of poultry litter to fields has created a basinscale data set of soil test
phosphorus that may contain multipl,e, nonidentical distributions.
It would appear that the use of geostatistics might be applicable in these
cases. Geostatistics assume a gradual, or at least measurable, change of the
interested variable over space. Basins, or watersheds, with fields that receive
poultry litter applications probably will not, however, readily lend themselves to
geostatistics. This is because soil test phosphorous levels can abruptly change
from field to field based on field ownership, litter application rates, and litter
application histories. Yet, there is no current mathematical method to account
40
I
IIII
iII
for, or model, where and when this abrupt variance from field to field will be
present.
The above discussion is the basis for development of a nonparametric
approach for estimating soil sample size for "poultry" watersheds or bas,ins. Soil
test phosphorous from watersheds with poultryrelated activities may be elevated
and exhibit bimodal distributions, due to the fact some pastures receive poultry
litter and some do not. Also, there may be a high variability of soil phosphorous
among pastures that do receive litter.
Data Analysis
The initial steps in the process of developing the nonparametric method of
predicting required sample sizes were to evaluate the existing data sets, and
evaluate the distributions to determine if they foHowed typical distributions.
Descriptive statistics for each data set were presented in Chapter 3. For Upper
Little Deep Fork Creek, the soil test phosphorous data were statistically analyzed
and it was found that there was no significant (a = 0.05) difference among the
means of various conditions (good, fair, poor, unmanaged) for the Grasslands
land use. The same was found among the means of the various conditions
(stable, moderate use, heavy use) for Forest land use. Since there were no
significant differences between the means, the various pasture/grassland
conditions were combined into one pasture land use and the various forest land
use conditions were combined into one forest land use. The other data sets
were used as previously presented.
41
The ability to predict tile expected soil test phosphorous level's based on
physical soil properties was also examined. Regression statistics were
performed on three of the data sets in an attempt to develop a prediction
equation of soil test phosp,horous derived from soi!1 mapping units and selected
soill characteristics.
Soil Test Phosphorous Probability Distributions
Haan (1977) presents three ways to determine if data follows a certain
probability distribution. The first is to plot the data as frequency histograms, the
second is to evaluate the linearity of the data plotted on the appropriate
probability paper, and the third is to use statistical tests. All three have been
performed with the data for this study.
The data sets were first plotted as frequency histograms, as shown in
figures 4.1 through 4.6. Since the literature revealed that soil properties tend to
follow lognormal distributions, the theoretical lognormal distribution was also
plotted for each data set and included on each figure. Then, the data were
plotted on lognormal probability paper. If the data corresponds to the distribution
as represented by the probability paper, the data will plot as a straight line. The
Weibull plotting position formula was used to rank and plot the data, as
presented by Haan (1977). Rather than using cumulative probability as the xaxis,
the standardized normal variable, Z, was used. Figures 4.7 through 4.12
show the lognormal probability plots.
42
Lastly, the data sets were statistically tested to determine if they were from
a lognormal distribution. The KolmogorovSmirnov (KS) and Ch:isquare tests
wer,e used. The KS test is used by oomparing the maximum deviation between
the cumulative distribution function under the nuU hypothesis and the sample
cumulative density function based on the number of observations to a tabulated
value for the chosen significance.. If the maximum deviation is less than the
tabullated value, the null hypothesis is accepted. In this case" the nulll hypothesis
was that the data were from a lognormal distribution. The Chisquare test makes
comparison between the actual number of observations and the expected
number of observations (expected according to the distribution under lest) that
fall in the class intervals. The class intervals were defined so that the expected
number of observatlions in each c1'ass Interval were the same, as suggested by
Haan (1977). The results of the statistical tests are summarized in Table 4.1.
The tests were conducted at 0: = 0.05 significance level.
43
. Lognormal
distribution
_ Observed data
Observed data
. Lognormal
distribution
0.30 i,,,L.
0.05 +f
130 observations
0.05 /f
0.35 ,.
0.30 +
o 2 6 10 14 18 22 26 30 34 38 42 46
Soli Test Phosphorous (mg/kg)
0.35 .,,
34 observations
~g 0.25 11
Q>
::J go 0.20 11 ....
u..
~ 0.15 \f:
t=l
.!!
CD 0.10 \+
!l:
g>. 0.25 +
CD
::::J
~ 0.20
u.
~ 0.15 11
:t=l
!!!
CD 0.10 I}
0::
Figure 4.1. Relative frequency distribution of soil test phosphorous for forest in
the Upper Utile Deep Fork Creek Basin.

o 2 6 10 14 1B 22 26 30 34 38 42 46
Soil Test Phosphorous (mg/kg)
Figure 4.2. Relative frequency distribution of soil test phosphorous for pasture in
the Upper Little Deep Fork Creek Basin.·
44
0.35 r
. Lognormal
distribution
O.30 i;=====23=0 ob=serv=atio=ns :l
Observed data
0.00
g> 0.25 j
G)
;:, g 0.20 4 ...
LL
G) 0.15 1
~
.!2
~ 0.10
0.05
o 15 35 55 75 95 115 135 155 175 195 215 235
Soil Test Phosphorous (mg/kg)
Figure 4.3. Re'ative frequency distribution of soil test phosphorous for pasture in
the Battle Branch Watershed.
0.35
0.30
g> 0.25
CIl)
:::J .g.. 0.20
LL
~ 0.15
~
~~
0.10
0.05
0.00
255 observations
 1 Observed data

. Lognormal
~ distribution 1,\'
I
1;
i
>
~ b,~ "..,...  I
~
o 30 70 110 150 190 230 270 310 350 390 430 470
Soil Test Phosphorous (mg/kg)
Figure 4.4. Relative frequency distribution of soil test phosphorous for pasture in
the Peacheater Creek Watershed.
45
Observed data
...... Lognormal
distribution
261 observations
. Lognormal
82 observations
0.30 tItr==========,!
Observed data
110 150 190 230 270 310 350 390 430 470
Soil Test Phosphorous (mg/kg)
0.00
46
0.05
o 30 70 110 150 190 230 270 310 350 390 430 470
Soil Test Phosphorous (mg/kg)
0.35 .r~......,
>. g 0.25 itt1
CLl
~e0.20
u..
~ 0.15
:i:i
."
Gi 0.10
0::
0.35
0.30
>.
0c:: 0.25
a>
::J
C'" 0.20  a..>.
LL
Q) 0.15 > :fj
eu Qi 0.10
0::
0.05
0.00
0 30 70
Figure 4.5. Relative frequency distribution of soi'! test phosphorous for pasture in
the Haw Creek. Watershed.
Figure 4.6. Relative frequency distribution of soil test phosphorous for pasture in
the Lake Eucha Basin (AR portion).
100 ._:C.:.:')
C')
Em
::::J
0...
0
.!: 0 10
m0
.c a. m
(1)
l .0 en
..............I· •
•••••• ~.............
• •• 
47
Figure 4.7. Lognormal probabUity plot of soil test phosphorous for forest in the
Upper Little Deep Fork Creek Basin.
Figure 4.8. Lognormal probability pilot of soil test phosphorous for pasture in the
Upper Little Deep Fork Creek Basin.
2.50
2.50
1.50
1.50
0.50
0.50
0.50
0.50
Standardized Normal Variable, Z
Standardized Normal Variable, Z
1.50
1.50
. . .......
~~
I
• •
...
1 , ,
2.50
1
2.50
100 C) .:.:: C)
EfI) ::s e0
.!: 0 10
I/)
0
.!:
Q. I/)
CI)
I
0 en

48
Figure 4.9. Lognormal probability plot of soil test phosphorous for pasture in the
Battle Branch Watershed.
2.50
2.50
1.50
1.50
0.50
0.50
0.50
0.50
Standardized Normal Variable, Z
Standardized Normal Variable, Z
1.50
1.50
.,
........ 
.
~ r
~
I
I
................
., *" ~
...r'
.........
~
" 1.. ~.JI'."
 I
1
2.50
1
2.50
1000 tD
~C)
Etn 100 ::J e0
J:
Co en
0
J:
.D..... 10 '
Ch
CD
t .0 en
1000 tD
~C)
ECI) :::J 100 e0
J:
C.
00
J:
D...... 10 en
CI)
to
tIJ
Figure 4.10. Lognormal probabmty plot of soil test phosphorous for pasture in the
Peacheater Creek Watershed.
.,..
...... ~
~ "'., 
.~ .~
'
 .....'
,
Standardized Normal Variable, Z
1000 C)
c1!!:
C)
Een 100 ~
00 .r=
Co
en
0 .r=
D. 10 en
CD
~
0
tn
1
2.50 1.50 0.50 0.50 1.50 2.50
Figure 4.11. Lognormal probability plot of soil test phosphorous for pasture in the
Haw Creek Watershed.
1000 C)
~C)
Een 100 ::J e0
.r=
Co
en
0 .r=
a. 10 en
(I)
~
0
tn
~
I' 1'"
~.""
I"" ......
1
2.50 1.50 0.50 0.50 1.50 2.50

Standardized Normal Variable, Z
Figure 4.12.. Lognormal probability plot of soil test phosphorous for pasture in the
Lake Eucha Basin (AR portion).
49
c
Table 4.1:. Summary of GoodnessofFit Tests for a Lognormal Distribution
Ho: Data are from a lognormal distribution
Location/Data Set Land Use KolmogorovSmimov Chisquare
Test Test
Upper Little Deep Forest Do Not Reject Ho Do Not Reject Ho
Fork Creek
Upper Little Deep Pasture Do Not Reject Ho Do Not Reject Ho
Fork Creek
Battle Branch Pasture Reject Ho Reject He
(p < 0.01) (p < 0.005)
Peacheater Creek Pasture Reject He Reject Ho
(p < 0.01;) (p < 0.05)
Haw Creek Pasture Do Not Reject Ho Do Not Reject Ho
Lake Eucha Pasture Reject Ho Reject He
(AR portion) (p < 0.01) (p < 0.05)
Notes: 0: =0.05
Ho =null hypothesis
The two visual methods (frequency histograms and probability plots) tend
to agree with the statistical tests for each of the data sets. The Upper Little Deep
Fork Creek data, both forest and pasture, appear to be lognormally distributed.
The watersheds with poultry industry activities, Battle Branch, Peacheater Creek,
and Lak'8 Eucha (AR portion) rejected the null hypothesis of a lognormal
distribution. These data sets appear to exhibit some type of bimodal
distributions. Haw Creek, which also has poultry activities, did not reject the null
hypothesis of lognormaUy distributed soil test phosphorous. The frequency
histogram and probability plot (figures 4.6 and 4.12) do appear, however, to
50
.,Ii
d
indicate that there may be some bimodal tendency, but apparently not enough to
reject lognormality in the statistical tests.
Soil Test Phosphorous by Soil Mapping Unit and Soil Characteristics
It was desired to evaluate predicting soil test phosphorous levels based on
soil mapping units or soil characteristics. If successful, soil phosphorous levels
could then be estimated from soil mapping units or soil characteristic information.
This would be advantageous since digital soil data sets exist for many areas.
The three data sets were used where soil sample or field locations were known.
For the Upper Little Deep Fork Creek, the soil data layer was overlain with the
soil sample location data using GIS. This resulted in a soil mapping unit, or soil
type, assignment for each soil sample. The same was performed with Battle
Branch and Peacheater Creek, except the pasture field boundaries were used,
since each field had been sampled separately. Where more than one soil
mapping unit was present in a field, the dominant soil based on coverage area
was sel.ected.
Regression statistics were then performed. The first regression involved
the use of dummy variables because the soil type was designated by a letter and
not an associated numeric value, or in other words, qualitative rather than
quantitative independent variables were used. The method of using dummy
variables as presented by Ott (1984) was used as follows:
I I
1' 
(4.1 )
where,
1 51 C.
y = the dependent variable;
p= the unknown parameter;
X1 = 1 if treatment 2, X1 = 0 otherwise;
X2 =1 if treatment 3, X2 =0 otherwise;
Xn =1 if treatment n+1, Xn =0 otherwise;
E =the random error term.
The result is an expression for soil test phosphorous based on soil types.
The second regression performed on each data set was based on the
associated soil characteristics of each soil mapping unit. This involved multiple
linear regression. The results of both regressions are summarized in Tables 4.2
and 4.3. There was no apparent correlation between soil test phosphorous and
soil mapping units, or betweHn soil test phosphorous and the soil characteristics.
It turned out that there was no significant difference (0:; = 0.05) of soil test
phosphorus among soil types for data from Upper Little Deep Fork Creek, which
included forest and pasture data. The regression is denoted by liN/A" for "not
applicable" in Table 4.2. The coefficients of determination from the regressions
are shown in the tables, but there were no significant parameters for any of the
regressions.
The results of the regression analysis indicate that soil test phosphorous
levels for these data sets are not related to soil type and are probably influenced
primarily by the land management activities. The soil type does, however, playa
role in the transport fate of phosphorous once it reaches the soil, as discussed in
the literature review.
52
<
Table 4.2.. Summary of Regression of Soil Test Phosphorous by Soil Mapping
Unit
tN/A: no significant difference (0: = 0.05) in soil test phosphorous means among soil mapping
units
Location/Data Set
Upper Little Deep
Fork Creek
Battle Branch
Peacheater Creek
0.17
0.10
Adjusted R2
0.08
0.05
Table 4.3. Summary of Regression of Soil Test Phosphorous by Selected Soil
Characteristicst
Location/Data Set
Upper Little Deep
Fork Creek
Battle Branch
Peacheater Creek
0.01
0.10
0.01
Adjusted R2
0.04
0.07
0.02

f Soil Characteristics: K, Organic matter or Organic Carbon content, Clay content, Bulk density
Empirical Distributions
Empirical methods were used to develop a nonparametric method for
determining the sample size, or number of observations, required for estimating
53
<


basinscale soil test phosphorous within a 90% confidence interval. MonteCarlo
sampling was employed to develop distributions of the soil test phosphorous
means for various sample sizes from the observed data.
The data sets of interest for this study were those watersheds or basins
that contained poultry industry activities, where the soil test phosphorous data did
not appear to follow a lognormal or standardtype distribution. Using classical
statistics, which assumes a normal distribution of the means, would be an
, approximation, at best, to estimate sample size for the bimodal distributed data.
It was assumed that the data represented the parent populations for each
data set since almost all pasture fields had been sampled. The data from the
Upper Little Deep Fork Creek Basin for pasture, which does not contain poultry
activities, was likewise used. The only data set available for forest land use was
also from the Upper Little Deep Fork Creek basin.
A personal computer spreadsheet application was adapted to perform the
Monte Carlo sampling for creating the empirical distributions. For each data set,
the soil test phosphorous was ranked from low to high and an associated
probability, from zero to one, was assigned to each data point based on its rank.
A macro was written that would randomly choose a probability from a uniform
distribution of zero to one and then select the corresponding soil test
phosphorous value. This was performed a number of times equal to the current
sample size, Le. 25 times for a sample size of 25. Then, a mean and standard
deviation were calculated for the empirical distribution of randomly chosen
values. This procedure was repeatedly performed for each sample size of 5 to
54
j'.
«
l
250, in increments of fi:ve. The entire process was repeated 250 times for each
sample size,.
Once the new empirical distributions were developed, the 90% confidence
intervals were calculated. They were chosen so that they were symmetrical in
probability, L'8. for tile 90% confidence interval, 5% of the area of the distribution
is to the left and 5% is to the riglht. The 90% confidence interval was chosen, but
any confidence interval could have been used. Figures 4.13 through 4.18 are the
resultant empirical distributions for each data set for the various sample sizes.
55
I
. !
<
e Q ~~~~a .. ~_~.~~~~~~".~_
f] J u n n n ~ u E '~!..!l ,I:
V
.." o~~wv~Y~~.VVV~TT~ •
0 Monte Carlo Simulation Mean 
II 90% Confidence Interval 
 ,
30
27 C) 24 ,~ E' 21 Q. 18 tn {!!. 15
'0 12
t:/)
c 9
cu :E 6
3
o
o 25 50 75 100 125 150 175 200 225 250
Sample Size, n
Figure 4.13. Empirical distributions of mean soil test phosphorous for various
sample stzes for forest in the Upper Little Deep Fork Creek Basin.

i\ if
..... ( ,
,
,,,"~f,jQ.a~~~ ... ~
I~ i ~ iJ D ! D n B !) B D
'/ ,. ~ <> V T ~ .~ .... 'V 'ill .....
,/
,
Monte Carlo Simulation Mean  0
II 90% Confidence Interval 
, I
30
27 ~ 24 CE) 21 Q. 18 tn {!!. 15
'0 12
en
c 9
eu
eli) ,6
:E
3
o
o 25 50 75 1:00 125 150 175 200 225 250
Sample Size, n
Figure 4.14. Empirical distributions of mean soil test phosphorous for various
sample sizes for pasture in the Upper Little Deep Fork Creek Basin.
56
<> Monte Carlo Simulation Mean 
 90% Confidence Interval 
I)
t 1 ~ ~ .~.a:£Gl"'.Q;~Iil< ... .f!J, ... ~__ ... ..... D_ • Ii ~~mRR ~~E~~~~~=I~~
v ~
~~~~~~Wq~~~~~~vv~
75
50
25
o
o
250
225
Oi 200
..llI:: ~ 175 0.. 150 t/) {!!. 125
'0 100
f/J
cm
:E
25 50 75 100 125 1150 175 200 225 250
Sample Size, n
FiQiure 4.15. Empirical distributions of mean soil test phosphorous for various
sample sizes for pasture in the Battle Branch Watershed.
<;.
~ <>
"
l' 'I ,"
~ r, <> (:>
 I 0 <; /,;
G' / () , "
FV
<> './
v ~
// '7
'/
Monte Carlo Simulation Mean 1 <>
<>
_.  90% Confidence Interval 1,
,
250
225
Oi 200
..llI:: OEJ 175 0..
150 t/)
~ 125
'0 100
t.IJ
c: 75
as
CI) :s 50
25
o
o 25 50 75 100 125 150 175 200 225 250
Sample Size, n
Figure 4.16. Empirical distributions of mean soil test phosphorous for various
sample sizes for pasture in the Peacheater Creek Watershed.
57
()
<>
<>
 A
' 1\ $ 8 <> <> <
~  ~
'
~
<>
l I  I
: 9 ' <>
v ',' <> v
8 <> Monte Carlo Simulation Mean 1
  90% Confidence Interval 1
, ,
250
225
'Ci200
.:Ell:: 175 a. 150 en
CD 125
I
'0 100
tJ'J
c 75
ca
~ 50
25
o
o 25 50 75 100 125 150 175 200 225 250
Sample Size, n
Figure 4.17. Empirical distributions of mean soil test phosphorous for various
sample sizes for pasture in the Haw Creek Watershed.
25 50 75 100 125 150 175 200 225 250

 F~~~\
~ <>
t'.. ~, 8 ,'  ,
, . I.i ,
I I 1 1'
 ~ ,
;...J!' , ,
V
~ v <>
 .:) Monte Carlo Simulation Mean 
 90% Confidence Interval 
250
225 ~ 200 E175 a.
150 (/I
{!!. 125
'0 100
tJ'J
cco 75
CD
:E 50
25
o
o
Sample Size, n
Figure 4.18. Empirical distributions of mean soil test phosphorous for various
sample sizes for pasture in the Lake Eucha Basin (AR portion).
58
The 90% confidence interval widths were empirically determined for each
sample size from each empirical distribution and plotted on a single graph.
Figure 4.19 is the plot of the 90% confidence intervals for forest and Figure 4.20
is for pasture. Regression was then performed on each data set to develop an
equation for each respective curve. The bestfit regression lines were of the
form:
y = CnD.S (4.2)
where y represents the 90% confidence interval, C is a constant specific to each
curve, and n is the sample size. Solving for n yields:
n = (c/yl (4.3)
A unique equation for n was developed for each of the data sets. The only
difference was the constant, C. Table 4.4 lists the constants for equation 4.3
developed from each data set.
Table 4.4. Constant, C, for Equation 4.3
Constant, C
Location/Data Set Land Use for Eqn. 4.3 R2
Upper Little Deep Forest 16.8 0.99
Fork Creek
Upper Little Deep Grasslands, 27 0.99
Fork Creek Pasture
Battle Branch Pasture 125 0.99
Peacheater Creek Pasture 295 0.99
Haw Creek Pasture 377 0.98
Lake Eucha Pasture 390 0.99
(AR portion)
59
10 I I
ma
m IV
~ ~
m Q) .E.....C..
Q. Q)
.... CJ
til C
Q) Q)
.'"'" "ICi: o 0
~ 0
C
IV ~
Q) ~
:i c:n
9 
8
7
6
5
4
3 ~
2 
1
Forest Location/Data Set
.. Upper Little Deep Fork
Creek
PredictiQnJ;_guation
90% CI = 16.8no·s
R2 =0.99
25 50 75 100 125 150 175 200 225 250
o ' I \ j IiiI
o
Sample Size, n
Figure 4.19. Estimated 90% confidence intervals for mean soil test phosphorous for forest
for varying sample sizes.
20
140
I
~
Pasture Location/Data Set Prediction Equation
120 1 ~ tJ. Lake Eucha (AR portion) 90% CI =390n0
.
5
R2 =0.99
 _ 100
:( Haw Creek 90% CI =377n0
.
5
en C'O R2 = 0.98
~ ~
Q) G) 90% CI =295n0
.
E=.... • Peacheater Creek 5 Q. Q) 80 R2 = 0.99
.... (J
II) C 90% CI = 125nO
.
5 G) G) • Battle Branch
~ " It:
. C 60 R2 = 0.99 o 0
0) U)(J
x Upper Little Deep Fork 90% CI =27n0
.
5
'> C
C'O ~
Q) 0 Creek R2
;;;: 0.99
:E ~ 40
25 50 75 100 125 150 175 200 225 250
J lit( E  o i) ~( )( H )( H ~. ~( t( H H 'iE l( )! I:1E H I,E H H i U H ~,{ I
o
Sample Size, n
Figure 4.20. Estimated 90% confidence intervals for mean soil test phosphorous for pasture
for varying sample sizes.
Comparison of Classic to Nonp,arametric Techniques
The form of the regression equation derived from the nonparametric
approach is very similar to what would be used for an approximation of n for a
normal distribution of means. For a normal distribution the lower and upper
confidence limits are found from classic statistics to be:
L  Z ax =x  al21ii
U  Z ax =X+ alllii
(4.4)
(4.5)
where L is the lower limit, U is the upper limit, x is the sample mean, Zal2 is the
value from the standard normal distribution for the specified error level, ct, and ax
is the standard deviation. Subtracting equation 4.4 from equation 4.5 for the
interval width and solving for n, yields:
(4.6)
where CI is the required confidence interval. Equation 4.6 is the same as that
given by Steel and Torrie (1980) for estimating required sample sizes and is
bas,ed on the Central Limit Theorem.
It appears that the consta.nt, C, obtained from the nonparametric approach
is comprised of a variance and probability variable. The nonparametric method
does not distinguish between the two components. However, use of the
nonparametric equation does not requilre the assumption of a known underlying
distribution. As deviation from normality increases, the efficiency of parametric
tests decreases, but the efficiency of nonparametric tests is not affected
62
s
(Mcintyre and Tanner, 1958). Use of classical statistical techniques to calculate
n also requires a direct estimate of the variation, or standard deviation, which is
typically very difficult to estimate without sufficient data.
The nonparametric approach for determining sample size was
investigated because it was not fully evident that the data sets obtained from
highlevel soil test phosphorous watersheds/basins would adhere to the
assumptions required for using c1assi:cal statistical techniques. The assumptions
referred to are those related to the Central Limit Theorem, such as identically and
independently distributed data. Also, application of the Central Limiit Theorem is
used as an approximation. assuming the means of the population are normally
distributed.
To compare the two approaches, the differences in confidence intervals
determined from each method were compared. For each sample size, the 90%
confidence interval was computed from classical statistics for a normal
distribution using equation 4.6. For (Y x' the standard deviations from the original
data sets were used. The resultant interval was then compared to that obtained
from the nonparametric approach. Figures 4.21 through 4.26 are plots of the
percent differences of the classical 90% confidence interval to that computed by
the nonparametric approach. The comparison was made for each data set. The
results of the comparisons indicate there is approximately a 10% difference
between the two methods for all the sample sizes. There was no definite sample
size where the two converged for any data set.
63  
I.......
As it has turned out, use of the Central Limit Theorem is probably general
enough to apply to slituatiions I:ike those presented in this study.. Due to the
relative small differences, the classic approach would probably be acceptable for
future estimations of sample size under the conditions studied.
64 
25 50 75 100 125 150 175 200 225 250
Mean Deviation: 1.0 %
Mean Absolute Deviation: 4.0% •
• • • • • • • • • • • • • • • • • • • • •
•
•
o
5
5
1:0
15
10
15
o
(.)
....o~ 0;
~ E
c e
~ CG
~g.
._ 0
cz
1:.2
Q)o
C'lS ; .~
Q. U)
U)
CG (J
Sample Size, n
Figure 4.21. Comparison of confidence intervals computed by the classical and
nonparametric methods for varying sample sizes for Upper Little
Deep Fork Creek forest.
15 ,,
•
•
• • •
• •
•
•
• •
•
• •
•
• • •
Mean Deviation: 4.4 %
Mean Absolute Deviation: 5.0 %
•
o
_ 'Lo: 10
oC;
Q) E
(c) .CG. 5
Q) CG
; Q.
.lI_: 0C 0 +,,+r.,r.,rr,..rl
Cz. •
.C.. '"0 • • •
Q)  5 ~ CG
Q) .~
Q. ~ 10 (
3
25 50 75 100 125 150 175 200 225 250
Sample Size, n
15 ..1.... '
o
Figure 4.22. Comparison of confidence intervals computed by the classical and
nonparametric methods for varying sample sizes for Upper Little
Deep Fork Creek pasture.

65
<


Sample S'ze, n
Figur,e 4.23. Comparison of confidence intervals computed by the classical and
nonparametric methods for varying sample sizes for Battle Branch
pasture.
15
(,) Mean Deviation: 1.6 %
0 10 Mean Absolute Deviation: 3.5 % 'i:
0 CD
CD E • c0 C'G 5  • I CD C'G • • l e. • • :CtD: c • • • ._ 0 0 .... cz • c 0 • • • • • • CD «U 5 • • • • • • 0
I <J • • (I)
10. /1J
~10
u
15 
0 25 50 75 100 125 150 175 200 225 250
Sample Size, n
Figure 4.24. Comparison of confidence intervals computed by the classical and
nonparametric methods for varying sample sizes for Peacheater
Creek pasture.
66
«
15 ,,
+
+
+
+
+
+
• •
+
+
•
+
• +
+
• •
• •
•
•
Mean Deviation: 3.7 %
Mean Absolute Deviation: 5.9 %
(.)
CJ 10
'0:5Q) B E
c::: f! 5
~ ns + + +
~ ~ 0 +,,,,,_____._,........,..,.1
cz
'E.2
Q)  5 CJ ns
Q) .~
,e. =ns10  +
o
15 ' '
o 25 50 75 100 125 150 175 200 225 250
Sample Size, n
Figure 4.25. Comparison of confidence intervals computed by the classical and
nonparametric methods for varying sample sizes for Haw Creek
pasture.
15 ..,,
o +.~,...,:.rr,•.:: • .......,,_."'....y+,+..• •
Mean Deviation: 1.7 %
10  Mean Absolute Devilation: 3.5 %
5
5
10
+
•
+
•
•
•
+
•
•
•
•
• • • •
25 50 75 100 125 150 175 200 225 250
Sample Size, n
15 1. . .J
o
Figure 4.26. Comparison of confidence intervals computed by the classical and
nonparametric methods for varying sample sizes for Lake Eucha
(AR portion) pasture.
67 J. <

Nonparametric Method
The previous sections present the steps to develop a nonparametric
approach to determine the sample size for estimating basinscale soil test
phosphorus within a 90%, confidence interval. The same nonparametric
approach can also be used to determine the 90% confidence interval associated
with a predetermined sample size for similar watersheds or basins. These two
options for using the nonparametric method are termed Option A and Option B,
respectively. The method was derived assuming the soil sample locations, or
fields to be sampled, are randomly selected.
Option A can be used to determine the required number of observations,
or sample size. To do this, an acceptable interval of soil test phosphorous levels
must first be determined. This can be thought of as an allowable plus or minus
deviation from the exp,ected mean. Since the soil phosphorous data will most
likely be used as input into a hydrological/water quality model, an acceptable
interval of soil test phosphorous should be determined from the chosen model.
This can be obtained by running the model for varying initial soil test
phosphorous levels to develop a relationship between input soil test phosphorous
and output phosphorus loading. Then, after choosing an acceptable interval of
phosphorous loading from the model output, an input soil test phosphorous
interval can he obtained from the developed relationship. Allowing this interval
width to be the acceptable 90% confidence interval, the required sample size can
68
II
then be computed using the following equation and the appropriate constant, C,
value from Table 4.5:
(4.7)
where n is the required sample size, C is the nonparametric constant from Table
4.5, and the 90% confidence interval of soi'l test phosphorous is in mg/kg.
Option B can be used when there is a predetermined number of samples
to be collected. This may be the case when budget or time constraints limit the
total number of samples available for a particular project. For this case, the
appropriate constant, C, from Table 4.5 must be chosen and equation 4.7 solved
for the 90% confidence inte:rval. Then, based on the input versus output curve
from the chosen computer model as developed and described in the previous
paragraph, the expected model output phosphorous loading interval can be
determined. AppUcation of the method using Option B is demonstrated in the
next chapter on a soil sampling: plan for a basinscale modeling study.
Nonparametric method for determining sample size and the 90%
confidence interval for estimating basinscale soil test phosphorous:
Option A: Determine the required sample size for the 90% confidence interval.
Option B: Determine the 90% confidence interval given a predetermined sample
size.
Steps:
1. Option A: Determi,ne an acceptable soil test phosphorous interval and let it be
the 90%, confidence interval.
Option B: Use a predetermined number of soil samples.
2. Option A: Chose the appropriate constant, C, from Table 4.5 based on major
land use, poultry house density, or other basin characteristics.
Option B: Chose the appropriate constant, C, from Table 4.5 based on major
land use, poultry house density, or other basin characteristics.
3. Option A: Solve equation 4.7 for the required sample size within the 90%
confidenoe interval.
Option B: Solve equation 4.7 for the 90% confidence interval using the
predetermined sample size.
Table 4.5. Constant, C, for Equation 4.7 to Determine Sample Size for Estimating
Basinscale Soil Test Phosphorous within a 90% Confidence Interval
Location/Data Set Land Use
Poultry House
Density1
Constant, C,
For Equation 4.7 2
Upper Little Deep Forest No Poultry 16.8
Fork Creek
Upper Little Deep Grasslands, No Poultry 27
Fork Creek Pasture
Battle Branch Pasture 0.018 125
houses/ha
Peacheater Creek Pasture 0.015 295
houses/ha
Haw Creek : Pasture 0.014 377
houses/ha
Lake Eucha Pasture 0.03 390
(AR portion) houses/ha
1. Density based on pasture/grassland coverage
2. Constant, C, for use with equation 4.7 with 90% Confidence Interval in mg/kg
70
CHAPTER 5
APPLICATION OF METHOD
The Biosystems and Agricultural Engineering Depa.rtment, Oklahoma
State University has contracted with the City of Tulsa, Oklahoma to perform a
nonpoint source computer model assessment of the Lake Eucha basin. The
focus of the assessment will be on sediment and phosphorous loadings. In order
to perform the modeling, initial soil! test phosphorous levels are needed. To
estimate basinscale soil test phosphorous levels, the nonparametric method for
determining the 90% confidence interval for sample size was used to develop a
soil sampling plan for the Oklahoma portion of the lake Eucha basin.
The basin was divided into subbasins based on major tributaries and
each subbasin will be modeled independently.. The approach for assigning initial
soil phosphorus levels in the computer model is to use mean soil test
phosphorous levels by major land use for each subbasin. Thus, the number of
composite soil samples, or rather the number of fields to sample, need to be
determined. For this project, a predetermined number of samples (30 for forest,
170 for pasture) were to be collected over the entire basin. The nonparametric
method dev,eloped in this study was used to determine the 90% confidence
intervals associated with the sample sizes to be used for each subbasin.
71
,I.
Lake Eucha (Oklahoma) Basin
Lake Eucha Basin is located in northeastern Oklahoma and northwestern
Arkansas (Figure 3.1). The Lake Eucha basin is approximately 93,000 ha
(230,000 acres), with 40% in Benton County, Arkansas and the remainder in
Delaware County, Oklahoma. This corresponds to approximately 55,800 ha
(138,000 acres) for the Oklahoma portion. This basin is generally known for its
extensive poultry industry activities, which include layers and broilers. A 1996
survey by the Water Quality Division, Oklahoma Conservation Commission found
a total of 714 poultry houses within the basin with 225 on the Oklahoma side
(OCC, 1996).
The 1:250,000 scale 1985 USGS digital elevation data were used to
delineate the subbasins. The basin was divided into six subbasins that were
similar in coverage area. The 1985 NRCS digital land use data for Oklahoma
were used to determine the pasture area.s. The poultry house inventory data
were taken from the 1996 survey by the Water Quality Division, Oklahoma
Conservation Commission (DOC, 1996). Figure 5.1 presents the Oklahoma
portion land use coverage and subbasin delineations. The tabular results along
with poultry house densities are shown in Table 5.1.
72
, ,
...
Oklahoma Arkansas
oI
8
I
16 km
I
Other: crops, water, farmstead, urban, impervious surfaces
Stream network
Subbasin boundary
Forest
Major Land Uses in Oklahoma
Pasture/Meadow •[J
Subbasins in Oklahoma
1. Lake Eucha and Rattlesnake Creek
2. Dry Creek, Teesquatnee Hollow, and Spavinaw laterals between
Rattlesnake Creek and Cloud Creek
3. Brush Creek
4. Beaty Creek
5. Cloud Creek and Spavinaw laterals between Beaty Creek and
Cheroke,e Creek
6. Hogeye Creek, Cherokee Creek, and Spavinaw laterals between
Hogeye Creek and the Oklahoma border
Figure 5.1. Lake Eucha Basin.
73
Table 5.1. Lake Eucha Basin (Oklahoma) Major Land Use and Poultry I'nventory
Total Forest Pasture Poultry
Subbasin Area Are,a Area Houses
(ha) (ha) (%) (ha) (%) (no.)
1. Lake Eucha and 7,500 6,000 79 860 11 4
Rattlesnake Creek
2. Dry Creek, Teesquatnee 9,900 7,700 77 1,800 19 8
Hollow, and Spavinaw
laterals between
Rattlesnake Creek and
Cloud Creek
3. Brush Creek 8,800 4,400 50 3,700 42 31
4. Beaty Creek 10,300 4,.500 44 5,200 50 80
(Oklahoma portion)
5. Dry Creek and Spavinaw 9,600 5,800 60 3,800 40 29
laterals between Beaty
Creek and Cherokee
Creek
6. Hogeye Creek, Cherokee 9,800 5,200 53 4,300 44 73
Creek, and Spavinaw
laterals between Hogeye I
Creek and the Oklahoma I
border I
I
74
HydrologicalJWater Quality Model
The hydrological/water quality model used for this project was the
Spatially Integrated Model for Phosphorous Loading and Erosion (SIMPLE)
(Storm et ai., 1997; Sabbagh et al., 1995). SIMPLE is a continuous simulation,
distributed parameter modeling system designed to predict sediment transport
and phosphorous loadingl to surface waters from nonpoint sources on a
watershed or basinscale. It encompasses a phosphorous transport model, a
digital terrain model, a data base manager, and a menudriven user interface.
The SIMPLE modeling system can be used in conjunction with the GIS GRASS
(CERL, 1988). The spatial component of SIMPLE is raster based, using either a
single cell or a field consisting of multiple cells as the computational unit.
SIMPLE estimates daily sediment loading, sedimentbound phosphorous, and
soluble phosphorous from each cell or field. Average loading statistics are
calculated on a daily, monthly, or annual basis.
Confidence Intervals
SIMPLE was used to develop relationship curves of "input soil P versus
output P loading". These curves are used to determine effects on model output
phosphorous loading due to variances in input soil test phosphorus. The
resultant curves illustrate how varyiing the confidence interval width on the input
initial phosphorous varies the expected output phosphorous loading interval
width. Input/output curves were developed for forest and pasture separately.
75
SIMPLE was run on a single cell basis using typical input parameter
values for forest and pasture, respectively. Ideally, the model would be run for
the entire basin of interest to obtain the input/output curve. However, as with
many modeling projects in the beginning stages, required data for the entire
basin has not yet been obtained or developed. The sensitivity analysis for
SIMPLE was used to determine the sensitive parameters. The most sensitive
parameters were:
1. initial soil phosphorous,
2. curve number,
3. soil bulk density,
4. slope, and
5. USLE C factor.
The model was first run using average, or typical, values for all input parameters
for a range of initial soil test phosphorous levels. Then, successive runs were
made while varying a sensitive input parameter. The remaining parameters were
held constant This was done for both forest and pasture, respectively. Twenty
years (19601980) of rainfall data from Siloam Springs, Arkansas were used for
all the model runs. Independent annual results were used to compute the longterm
20 year average output phosphorus loadings. Tables 5.2 and 5.3 list the
input parameters used for the model runs. The result was an "input versus
output" curve for each run, as shown in Figures 5.2 and 5.3.
76
Table 5.2. Input Parameters for SIMPLE Single Cell Runs for Forest
Parameter Input Value
Forest 1! Forest 2 Forest 3 Forest 4 Forest 5
Initial Soil Test P* 12.25 12.25 12.25 12.25 12.25
(mg/kg) to to to to to
245 245 245 245 245
Curve Number* 55 77 55 55 55
USLE C factor* 0.00053 0.0005 0.003 0.005 0.005
Slope* (%) 5 5 5 10 5
Bulk Density* 1.45 1.45 1.45 1.45 1.2
(g/cm3
)
K (English units) 0.35 0.35 0.35 0.35 0.35
Clay Content (%) 25 25 25 25 25
Organic Carbon ('%) 1 1 1 1 1
pH 6.5 6.5 6.5 6.5 6.5
Hydrologic Soil 8 B B B B
Group
Slope to Stream (%) 10 10 10 10 10
Slope Length (m) 194 194 194 194 194
* Sensitive parameter
77

Table 5.3. Input Parameters for SIMPLE Single Cel'l Runs for Pasture
Parameter Input Value
Pasture 1 Pasture 2 Pasture 3 Pasture 4 Pasture 5
Injtljal Soil Test P* 12.25 12.25 12.25 12.25 12.25
(mglkg) to to to to to
245 245 245 245 245
Curve Number* 60 80 60 60 60
USLE C factor* 0.003 0.003 0.008 0.003 0.003
Slope* (%) 5 5 5 3 5
Bulk Density* 1.45 1.45 1.45 1.45 1.2
(g/cm3
)
K (English units) 0.35 0.35 0.35 0.35 0.35
Clay Content (%) 25 25 25 25 25
Organic Carbon (%) 1 1 1 1 1
pH 6.5 6.5 6.5 6.5 6.5
Hydrologic Soil B B B B B
Group
Slope to Stream (%) 10 10 10 10 10
Slope Length (m) 194 194 194 194 194
* Sensitive parameter
78
l
4.0 i i
.. .. . , , .
  See Table 5.2 for input parameters     . . __ ., __ .
.......... ,.__ ' . __ ..,. __ .. 0. · .
. ;. i ..··~
... _..  .. _ ...  _.. . . ~. · _... _. _. .,... _.... _.. · ,.
. . .  ._ _ ., _  ,' _. _.    ,..       .    .            .,   •. ~      . _ ','  _. ., .,
'~"'
l:r Forest 1 _ ; _ ;_. __ ._: _ _ ~ .. _.. ; ; : .. _ )
* Forest 2
~Forest 3
Forest 4
~Forest 5
... ;    .    .. ..   ~    .....    ..; _ ..   ..    :                 .                           ..... _.. : . ... ~ 
3.5 t··············:··I
2.5
2.0
3.0
0.5
1.0 . ....... ...
1.5 
ca
J: ll.
0)
~0) c . 'tJ ca
.9
....J Q.
<D S0
J
20 40 60 80 100 120 140 160 180 200 220 240 260
0.0' : I : : : : I 1 I I : I I : I [I I I;: 11
o
Initial Soil Test P (mg I kg)
Figure 5.2. SIMPLE initial P versus P loading for forest.
1
4.0 , i
220 240 260
.. .} .. __ ' . , ,
. _..' , _~ ... 0._. .,_. __ 0_ .•... . , ,
, .
180 200
. .    :   .   .  .. .. ~ .......... .... . ";"   .
, ,
140 160
" .'    ..            ...              .     ~ ~   _. .  ~ .... ... .  ..
100 120
. ~ .    .  . _  _ _.     _.
.............~ ...... ~······· ..:········..····:···········..·T·..·..·······
, . ··, ...· ,,
" I ........... ~ : .. _ ~ :_ ..  _ ; ~ ..  ; : .
..................................
60 80
~Pasture 1
~Pasture 2
+ Pasture 3
Pasture 4
~Pasture 5
20 40
3.5  .
3.0 1 ..  ... .
1.5
2.5 ~  ; See Table 5.3 for input parameters
0.5 _ .
2.0 l ; .. ,  ;  .
0.0 , ' I I I I I i I : • I I I : : I' J : I " ! t J I • I , I: : t I I Ii: i I: I : i
o
1.0
.ccu a.
~0) c .
"cu
0
CO
...J
0 0..
~
~
Initial Soil Test P (mg I kg)
Figure 5.3. SIMPLE initial P versus P loading for pasture.
The slopes of the curves 011 Figures 5.2 and 5.3 vary somewhat as the
input p.arameters change. Since all the data layers for the basin had not yet
been developed, a single curve was chosen for determination of the model
output confidence interval due to input soH test phosphorous variance. A
conservative approach was taken to obtain the maximum expected model output
variance due to input initial soil test phosphorus variance. For both forest and
pasture, this corresponded to the curves for greatest expected curve numbers.
Since this soil sampling plan for the Oklahoma portion of the Lake Eucha
basin dictated that a total of 200 soil samples were to be collected, Option B of
the nonparametric method was used to determine the 90% confidence intervals.
The 200 samples (30 for forest, 170 for pasture) were proportioned among the
six subbasins based on the percentage of forest and pasture, respectively,
within each subbasin, Le. the subbas.in with the greatest pasture area will
receive the greatest number of pasture samples.
The appropriate constant, G, values from Table 4.5 had to be chosen for
use with the nonparametric equation developed, equation 4.7, to determine the
90% confidence intervals. Since some soil test phosphorous data (156 samples)
for pasture from Delaware County were available from the Soil, Water, and
Forage Laboratory, Oklahoma State University, they were used to help choose
the appropriate C value for pasture. Only soil phosphorous and land use data
were provided and sample Ilocation was not, so the data could not be directly
used as fully representative of the entire Lake Eucha (Oklahoma portion) basin
since no information was known of the individual locations and collection of
81
samples. The mean of the soil t,est phosphorous data from Delaware County
was 133 mglkg, the median was 86 mg/kg, the standard deviation was 127
mg/kg, the minimum was 2 mg/kg, the maximum was 524 mg/kg, and the C
value for these data was computed to be 418. The C value from Table 4.5 for
the Peacheater Creek data was chosen as the value to use with equation 4.7 for
pasture. This choice was based on Delaware County soil sample data
information, proximity of the watershed to the Lake Eucha basin, watershed size
similarities, and the fact that all' the pasture from Peacheater Creek had been
sampled. Due to the lack of any other available data, the C value for forest from
Upper Little Deep Fork Creek was used for forest land use. These C values and
equation 4.7 were then used to determine the 90% confidence intervals based on
the number of samples to be collected.
Using the curves as shown in Figures 5.4 and 5.5 for forest and pasture,
respectively, the expected total phosphorous loading output interval from
SIMPLE was found for each initial soil test phosphorous 90% confidence interval.
The output total phosphorous loading interval from SIMPLE does not correspond
to the expected 90% confidence interval from the model. The curves developed
in Figures 5.2 and 5.3 were based on variation in initial phosphorus input. To
obtain a true confidence interval in the model output, variance in all input
parameters and inherent variance produced within the model must be taken into
account. However, the curves produced do give an indication of the expected
effect from initial soil phosphorous input on the model output confidence interval.
The results are summarized in the next section.
82
4.0 I I
...................... _. '.
            .     .   ~          _ ~ ~ .  _ ' .      " .  .. . . _   
3.5 ~_·'''···''·;''I """'* Forest 2 1·.····:·..··.·····
See Table 5.2 for input parameters 3.0 j~ ...•••••.... , ..
............. ~.~ " .
, ,
...... ~ ~: .. " ~ ..  ~ .. ~ ._ .;.. _.
An Initial Soil Test P Confidence Interval of 8 mg/kg
gives an output Total P Loading Interval of 0.1 kg P/ha
_ .. _._.:.__ .. _ ~._...... ._.~..  _~ _ ~ .. _ _ .~._.__ "'_._
  _.  ••• _ ••••••••  •••••••• _ •••  •••••••••••: ••••••••••• ~. ~.;.. •••••• ~ •• 0 •••• _ '" :. •• _ •• __ •• ~ •• .. r    _. ~ .~ _ " '._   ..  _..  ',' .. _.'  · , · ..,
, , . · .·· ..,
1.5
2.5
2.0
C'a .c a..
en
.llI:: en
.l: 't'
C'a
0
CO
..J
0J a.. S
~
0.5
.: : ~~.: ; : ~ ~ . 1.0 ~ :: ";"':":
. . _ : ; : ~ ~ ..
20 40 60 80 100 120 140 160 180 200 220 240 260
0,0 'I I ! I I , , f : ' I , ': ,., ~ j i I I : : I' I I j , i I I , I i I ; I r , , I I , ; I I I j ,
o
Initial Soil Test P (mg I kg)
Figure 5.4. Confidence Interval determination for forest.
4.0 I I
2.5 ~ . . __ ' __ 
..............., ; , .: ..  ~    : ;   .
An Initial Soil Test P Confidence Interval of 50 mg/kg
gives an output Total P Loading Interval of 0.69 kg Plha
. ~ ·+..·..·1· 'j'" .; ~ ; ..
............... . · ·.. :· · I· · ~· ·· ..·.. ··~ ·.. I ·~· .. · .. ·· ; ..
, , ············f··········· __ ·"\······
........ _  __ ; __ _ _ .
............................., y r···· [ y '1'"''..I·· : 'f' ~ ~ ; .
· ········· 1 >< Pasture 2 I ·············· ·..·· ··..····..····..······.. · .
See Table 5.3 for input parameters . .
........•• _•..• _ _.. . .  .. __ .. _ _.....• _.  _   _.. _ _  _·· .•.••.•••• ·"0. _. __ . .. , .~_ ,
0.5 _ .
1.5
1.0 
3.0
2.0
3.5
~
J: c..
Cl
~Cl
C .
"~
0
~
.oJ
.::.. Q.
.5
.0..
20 40 60 80 100 120 140 160 180 200 220 240 260
0.0 Iii I iii T , iii I 'Pi i i J iii f; ,
o
Initial Soil Test P(mg I kg)
Figure 5.5. Confidence Interval determination for pasture.
Number of Observations and Confidence, Intervals
The steps of the nonparametric method developed in Chapter 4 were used
to determine the 9'0% confidence intervals for the predetermined soil sample
sizes for the soil sampling plan for the Oklahoma portion of the Lake Eucha
basin. The results are shown in Table 5.4.
Option B: Determine the 90% confidence interva given a predetermined sample
size.
Steps:
1. Option B: Use a predetermined number of soil samples.
» Project r,equirements: 30 samples for forest, 170 for pasture.
The samples were proportioned among the six subbasins based
on percentage of land Ulse.
2. Option B: Chose the appropriate constant, C, from Table 4.5 based on major
land use, poultry house density, or other basin characteristics.
» The C value for forest from the Upper Little Deep Fork Creek data
was chosen for forest. The C value from the Peacheater Creek
data was chosen for pasture. These were chosen based on
available data and watershed/basin characteristics.
3. Option B: Solve equation 4.7 for the 9'0% confidence interval using the
predetermined sample size.
» The samples sizes were predetermined and the corresponding 90%
confidence intervals were computed. Table 5.4 shows the subbasins,
the sample sizes, and the corresponding 90% confidence
intervals.
85
Table 5.4. Lake Eucha Basin (Oklahoma) Required Sample Sizes for the Soil
Sampling Plan
Subbasin Land
Use
Sample
Size 1
90%
Confidence
Interval 2
(mg/kg)
Expected
SIMPLE
output
interval 3
(kg P/ha)
1. Lake Eucha and Forest 5 8 0.1
Rattlesnake Creek Pasture 7 111 1.53
2. Dry Creek, Forest 7 ,6 0.05
Teesquatnee Hollow, Pasture 15 76 1.05
and Spavinaw laterals
between Rattlesnake
Creek and Cloud
Creek
3. Brush Creek Forest 4 8 0.1
Pasture 32 52 0.72
4. Beaty Creek Forest 4 8 0.1
(Oklahoma portion) Pasture 44 45 0.62
5. Dry Creek and Forest 5 8 0.1
Spavinaw laterals Pasture 34 50 0.69
between Beaty Creek
and Cherokee Creek
6. Hogeye Creek, Forest 5 8 0.1
Cherokee Creek, and Pasture 38 48 0.66
Spavinaw laterals
between Hogeye
Creek and the
Oklahoma border
1. Sample size based on a total of 30 for forest, 1170 for pasture; distributed by percent land use
coverage within each subbasin.
2. Computed from Equation 4.7 with C value from Upper Little Deep Fork Creek for forest, and C
vallue from Peacheater Creek for pasture.
3. Interval based only on effects of initial soil test phosphorous, from Figure 5.4 for forest and
Figure 5.5 for pasture.
86
CHAPTER 6
SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS
Summary and Conclusions
The main objectives of this research were to evaluate basinscale soH test
phosphorous probability distributions, develop and evaluate a nonparametric
approach for determining required sample size for estimating basinscale soil
phosphorous, and apply the results to develop a soil sampling plan for gathering
input soil phosphorous data for a hydrological/water quality computer model.
The nonparametric approach was also to be used for estimating the 90%
confidence interval for a predetermined number of soil samples. The
nonparametric approach was investigated because data from highlevel soil
phosphorous basins, such as studied in this research, may not adhere to all the
necessary assumptions to allow the valid use of classic parametric statistics or
geostatistical techniques for determining appropriate sample size.
Soil test phosphorous probability distributions from several watersheds
and basins were evaluated. The highlevel soil phosphorous data were from
watersheds containing poultry industry activities, such as pullets, layers, and
broilers. It was found that the data tend to exhibit a bimodal
87
distribution in these highlevel soil phosphorous watersheds. This is primarily
due to varying poultry litter application rates on different pasture fields and the
fact that some fields reoeive litter and some do not. There was no significant
association found between selected soil characteristics and soil test phosphorous
for the data examined.
Empirical probabillity distributions of the soil phosphorous data and
empirical 90% confidence lintervals created from the data sets were used to
develop nonparametric equations for predicting soil sample sizes for estimating
soil phosphorus levels for pasture and forest, respectively. It was found that the
nonparametric approach did not give sample size results differing greatly from
that obtained by using classic statistic techniques. The preferred use of
geostatistics, however, was prohibited from use in these poultry watersheds due
to abrupt changes in soil phosphorous levels across field or property boundaries.
The use of geostatistics relies on the gradual change in a parameter spatially.
The nonparametric equations developed were then used to form a soil
sampling plan for the Oklahoma portion of the Lake Eucha basin, which contains
poultry activiHes. The basin was divided into subbasins using a GIS. Since the
soil sampling plalll dictated a predetermined number of soil samples to be
collected, the option of the nonparametric method was used for computing the
90% confidence interval based on a predetermined sample size. The
appropriate nonparametric equation developed for computing the confidence
intervals for pasture was selected based on limited available data from the
Oklahoma portion of the Lake Eucha basin and other watershed characteristics.
88
An equation for determiining sample size and 90% confidence intervals for forest
was also dev,eloped and applied.
One difficult part was deciding which one of the developed nonparametric
sample size prediction equations to use for pasture. As with most initial soil
sampling plans, the sitespecific variance of the parameter to be measured, soill
test phosphorous in this case, is 110t known. Thus, judgement must be exercised
in choosling an appropriate variance to apply to the sample size prediction
equations.
Recommendations
Jt is recommended that classic statistic techniques be used for future
sample size determination in simi:ar watersheds or basins, since it would be
simpler and should provide similar results. It is also recommended that further
research in the area of highlevel soil phosphorous determination be placed on
ways of predicting soil phosphorous levels based on relatively easily obtained
data. Perhaps a model could be developed that could predict soil phosphorous
levels based on soil types, litter and fertilizer application history, distance of field
to poultry house, etc. This could provide a means of predicting soil phosphorous
levels without initiating extensive and expensive soil sampling plans.
89
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Foth, H.D., and B.G. Ellis. 1997. Soil fertility. 2nd ed. CRC Press. Boca Raton, FL.
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90
a
Johnson, G.V., W.R. Raun, H. Zhang, and J.A. Hattey. 1997. Ok·lahoma soil
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Neosho River; Water Quality Incentive Proposal, Benton County,
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91
Sabbe, W.E., and O.B. Marx. 11987. Soi;1 sampling: spatial and temporail
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92
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93
APPENDICES
94
APPENDIX A
SOIL DATA
Table Page
A.1. Upper Little Deep Fork Creek Soil Mapping Units 96
A.2. Upper Little Deep Fork Creek Soil Characteristics 99
A.3. Battle Branch Soil Mappng Units 101
A.4. Battle Branch Soil Characteristics 102
A.5. Peacheater Creek Soil Mapping Units 103
A.5. Peacheater Creek Soil Characteristics 104
95
r
Table A.1. Upper Little Deep ForI< Creek Soil Mapping Units
Soil Ref.
No.
Soil Description Area Coverage
(ha) (ac) (%)
1 Bates fine sandy loam, gently sloping 356 879 0..90
2 Bates fine sandy loam, sloping 17,6 436 0,45
3 Bates fine sandy loam, sloping, severely 13 32 0.03
eroded
4 Broken or Gullied sandy upland 122 302 0.31
6 Choteau very fine sandy loam, nearly level 9 22 0.02
7 Cleburne fine sandy loam 179 441 0.45
8 Collinsville and Bates soils, gently sloping 107 264 0.27
9 Collinsville and Talihina soils, sloping 895 2211 2.27
10 Collinsville and Talihina goils, strongly 554 1368 1.40
sloping
11 Dame" and Pottsville soils, sloping 9096 22477 23.06
12 Darnell and Pottsville soils, strongly 4500 11119 11.40
sloping
13 Dennis and Okemah loams,. gently slop·ing 1167 2884 2.96
14 Dennis and Okemah loams, sloping 592 1462 1.50
15 Dennis and Okemah loams, sloping, 121 300 0.31
severely eroded
16 Dougherty and Stidham fine sandy loams, 371 916 0.94
gently sloping
17 Dougherty and Stidham fine sandy loams, 24 59 0.06
nearly level:
18 Dougherty and Stidham fine sandy loams, 490 1212 1.24
sloping
23 Gullied bottom land 1224 3025 3.10
24 Mason clay loam 17 41 0.04
continued
9,6
Table A.1. (continued) Upper Little Deep Fork Creek Soil Mapping Uni:ts
SoH Ref.
No.
Soil Description Area Coverage
(ha) (ac) (%)
25 Mason silt loam 758 1873 1.92
27 OilWaste land 186 460 0.47
28 Okemah and Woodson clay loams 18 44 0.04
30 Pulaski fine sandy loam 1885 4659 4.78
33 Stephenville and Darnell fine sandy 4689 11587 11.89
loams, gently sloping
34 Stephenville and Darnell fine sandy 5360 13244 13.58
loams, sloping
35 Stephenville & Darnell fine sandy 1891 4674 4.79
loams,sloping,severely eroded
38 Teller silt loam, sloping 8 19 0.02
41 Verdi,gris day lIoam 180 444 0.46
42 Verdigris fine sandy loam 818 2022 2.07
43 Verdigris silt loam 1365 3373 3.46
1011 Bonham loam, 1 to 3 percent slopes 45 112 0.11
102 Bonham loam, 3 to 5 percent slopes 109 270 0.28
103 Bonham loam, 2 to 5 percent slopes, 142 350 0.36
eroded
104 BreaksAlluvial land complex 28 69 0.07
1105 Broken alluvial land 45 110 0.11
106 Chickasha loam,1 to 3 percent slopes 47 117 0.12
107 Chickasha loam, 3 to 5 percent slopes 17 42 0.04
108 Chickasha loam, 2 to 5 percent slopes, 153 377 0.39
eroded
continued
97
Table A.1 .. (continued) Upper Little Deep Fork Creek Soil Mapping Units
Soil Ref.
No.
Soil Description Area Coverage
(ha) (ac) (%)
109 Chickasha and Bonham soils, 2 to 6 % 370 914 0.94
slopes, severely eroded
112 DarnellStephenville fine sandy loams, 3 512 1265 1.30
to 12 % slopes
113 DarnellStephenville complex, 312 % 85 210 0.22
slopes, severely eroded
117 Konawa loamy fine sand, 0 to 3 percent 15 37 0.04
slopes
120 Mason silt clay 42 103 0.11
122 Noble fine sandy loam, 3 to 8 percent 6 16 0.02
slopes
129 Pulaski fine sandy loam 23 56 0.0'6
136 Stephenvilile fine sandy loam, 1 to 3 68 168 0.17
percent slopes
137 StephenviHe fine sandy loam, 3 to 5 121 299 0.31
percent slopes
138 Stephenville fine sandy loam, 2 to 5 54 133 0.14
percent slopes, eroded
145 Vanoss clay loam, 3 to 5 percent slopes 8 19 0.02
146 VernonCollinsville complex, 5 to 20 131 323 0.33
percent slopes
Water 264 653 0.67
Total
98
39,454 97,490 100
Tab!le A.2. Upper Little Deep Fork Creek Soil Characteristics
Soil Ref. Organic Bulk Hydrologic Slope
No. K Matter Clay Density Soil Group Range
(En9lish units) (%) (%) (g/cm3
) (%)
1 0.2 1.50 10 1.55 B 24
2 0.2 1.50 10 1.55 B 46
3 0.2 1.50 10 1:.55 B 46
4 0.24 0.75 14 1.45 B 38
6 0.43 2.00 21 1.43 C 1  4
7 0.24 0.75 15 1.45 B 1  4
8 0.32 2.00 13.5 1.43 D 24
9 0.32 2.00 13.5 1.43 0 4  12
10 0.32 2.00 13.5 1.43 0 12  20
11 0.1 0.75 15 1.48 C 4 12
12 0.1 0.75 15 1.48 C 12  20
13 0.43 2.00 18.5 1.43 C 1  4
14 0.43 2.00 18.5 1.43 C 4 6
15 0.43 2.00 18.5 1.43 C 4 6
16 0.24 0.75 14 1.45 B 25
17 0.24 0.75 14 1.45 B 02
18 0.24 0.75 14 1.45 B 58
23 0.32 2.00 23.5 1.38 B 01
24 0.32 2.00 28.5 1.45 B 01
25 0.37 2.00 19.5 1.40 B 01
27 0.24 15 1.45 D 04
28 0.37 2.00 31 1.45 C 01
30 0.2 0.75 14 1.45 B 01
33 0.24 0.75 15 1.45 B 24
34 0.24 0.75 15 1.45 B 47
35 0.24 0.75 15 1.45 B 47
continued
'99
Table A.2. (continued) Upper Little Deep Fork Creek Soil Characteristics
Soil Ref. Organic Bulk Hydrologic Slope
No. K Matter Clay Density SoU Group Range
(English units) (%) (%) (g/cm3
) (%)
38 0.37 2.00 15 1.43 B 57
41 0.32 3.00 31 1.40 B 01
42 0.24 0.75 14 1.45 B 01
43 0.32 3.00 21 1.35 B 01
101 0.43 2.00 15 1.43 D 02
102 0.43 2.00 15 1.43 0 25
103 0.43 2.00 15 1.43 D 25
104 0.37 0.75 31 1.45 0 5 12
105 0.37 2.00 19 1.43 B 03
106 0.37 2.00 20 1.45 B 1  3
107 0.37 2.00 20 1.45 B 35
108 0.37 2.00 20 1.45 B 1  5
109 0.37 2.00 20 1.45 B 1  8
112 0.2 0.75 15 1.48 C 3 12
113 0.2 0.75 15 1.48 C 3 12
11'7 0.2 0.75 6 1.43 B 03
120 0.37 2.00 19.5 1.40 B 01
122 0.2 0.75 14 1.45 B 38
129 0.2 0.75 14 1.45 B 01
136 0.24 0.75 15 1.45 B 1  3
137 0.24 0.75 15 1.45 B 35
138 0.24 0.75 15 1.45 B 25
145 0.37 0.75 31 1.45 0 35
146 0.37 0.75 31 1.45 0 5  20
100
Table A.3. Battle Branch Soil Mappng Units
Soil Ref. SoH Description Area Coverage
No. (ha) (ac) (%)
2 Baxter silt loam, 1 to 3 % slopes 119 294 5.32
3 Baxter cherty silt loam, 1 to 3 % slopes 274 678 12.26
4 Baxter Locust complex, 3 to 5 % slopes 286 706 12..77
5 Captina silt loam, 1 to 3 % slopes 161 398 7.19
8 Clarksville very cherty silt loam, 1 to 8 % 155 382 6.91
slopes
9 Clarksvillle stony silt loam, 5 to 20 % 274 677 12.25
slopes
10 Clarksville stony silt loam, 20 to 50 % 342 845 15.28
slopes
19 Jay silt loam, 0 to 2 % slopes 18 44 0.80
21 Locust cherty silt loam, 1 to 3 % slopes 57 140 2.53
22 Newtonia silt loam, 0 to 1 % slopes 16 40 0.73
23 Newtonia silt loam, 1 to 3 % slopes 38 94 1.70
33 Sallisaw silt loam, 0 to 1 % slopes 3 6 0.12
34 Sallisaw silt loam, 1 to 3 % slopes 28 69 1.25
35 Sallisaw gravelly silt loam, 1 to 3 % slopes 40 99 1.78
36 Sallisaw gravelly silt loam, 3 to 8 % slopes 129 319 5.76
37 Staser silt loam 58 144 2.61
38 Staser gravelly loam 140 346 6.25
39 Stigler silt loam, 0 to 1 % slopes 82 203 3.67
41 Taloka silt loam, 0 to 1 % slopes 18 45 0.81

Total
101
2,237 5,529 100
Table A.4. Battle Branch Soil Characteristics
Soil Ref. Organic Bulk Hydrologic Sllope
No.. K Carbon Clay Densilty Soil Group Length
(English units) (%) (%) (g/cm3
) (m)
2 0.33 1.76 19 1.37 B 152
3 0.33 1.76 19 1.37 B 152
4 0..33 1.76 19 1.37 B 121
5 0.36 1.18 12 11.43 B 152
8 0.39 0.74 12 1.46 B 15
9 0.43 0.74 25 1.43 B 60
10 0.43 0.74 25 1.43 B 30
19 0.37 1.18 18 1.51 C 167
21 0.4 0.59 12 1.48 B 152
22 0.37 1.18 18 1.41 B 182
23 0.37 1.18 18 1.41 B 152
33 0.41 0.74 33 1.46 B 15
34 0.41' 0.74 33 1.46 B 15
35 0.39 0.74 12 1.46 B 15
36 0.39 0.74 12 1.46 B 15
37 0.34 1.76 25 1.35 B 15
38 0.34 1.76 25 1.35 B 15
39 0.36 1.18 12 1.43 D 182
41 0.44 0.44 25 1.45 0 182
102

Table A5. Peacheater Creek Soil Mapping Units
Soil Ref. Soil Description Area Coverage
No. (ha) (ac) (%)
1 Bodine very cherty silt :Ioam, 18% slopes 1943 4802 30.07
2 Bodine stony silt loam, 515% slopes 487 1204 7.54
3 Bodine stony sillt loam, steep 1653 4085 25.59
5 Dickson silt loam, 13% slopes 750 1852 11.60
6 Dickson cherty silt I'oam, 03% slopes 557 1377 8.62
7 Etowah silt loam, 01% slopes 0 1 0.01
8 Etowah silt loam, 13% slopes 80 198 1.24
9 Etowah gravelly silt loam,. 13% slopes 251 620 3.88
10 Etowah and Greendall,e soils, 38% slopes 258 638 4.00
11 Gravelly alluvial land 188 464 2.91
13 HectorLinker fine sandy loams, 15% 23 56 0.35
sllopes
15 Huntington gravelly loam 49 121 0.75
16 Jay silt loam, 02% slopes 139 344 2.15
17 Lawrenoe silt loam 3 8 0.05
20 Linker loam, 35% slopes 14 34 0.21
21 Link,er loam, 35% slopes, eroded 27 68 0.42
26 Summit silty clay loam, 13% slopes 21 51 0.32
29 Taft silt loam 19 46 0.29
Total 6,461 15,966 100
103
r
Table A.6. Peacheater Creek Soil Characteristics
Soil Ref. Organic Bulk Hydrologic Slope
No. K Carbon Clay Density Soil' Group Length
(English units) (%) (%) (g/cm3
) (m)
1 0.28 0.44 14 1.45 B 122
2 0..28 0.44 14 1.45 B 61
3 0.28 0.44 14 1.45 B 61
5 0.43 0.74 25 1.43 B 152
6 0.43 0.74 25 1.43 B 152
7 0.37 1.18 25 1.39 8 189
8 0.37 1.18 25 1.39 8 152
9 0.37 1.18 25 1.39 8 152
10 0.37 1.18 25 1.39 B 122
11 0.21 0.01 1 1.34 B 15
13 0.19 0.85 17 1.5 C 152
15 0.28 2..65 24 1.34 B 15
16 0.43 0.01 18 1.51 C 189
17 0.43 1.47 18 1.39 C 152
20 0.28 1.03 19 1.48 B 122
21 0.28 1.03 19 1.48 B 122
26 0.37 0.1 33 1.34 C 152
29 0.43 2.06 18 1.34 0 15
104
APPENDIX B
SOIL TEST PHOSPHOROUS DATA
Table Page
8.1. Upper Little Deep Fork Creek Soil Test Phosphorous for Forest.. 106
B.2. Upper Little Deep ForI< Creek Soil Test Phosphorous for Grassland 107
8.3.. Upper Little Deep Fork Creek Soil Test Phosphorous for "Other"
Land Uses 111
804. Battle Branch Soil Test Phosphorous fer Pasture 112
B.5. Peacheater Creek Soil Test Phosphorous for Pasture 115
B.6. Haw Creek Soil Test Phosphorous for Pasture 119
B.7. Lake Eucha (Arkansas portion) Soil Test Phosphorous for Pasture 121
105
Table B.1. Upper Little Deep Fork Creek Soil Test Phosphorous for Forest
Sample 10. Land Use Classification Soil Test p.
No. Subclass (mg/kg) (lb/ac)
95 Stable Forest 19 38
102 (undisturbed. 0  1% bare soil) 21 42
109 2.3 47
161 18 36
165 19 3,8
166 13 26
169 19 38
172 25 51
mean: 19 40
47 Moderately Used Forest 7 15
54 (1 10% bare soil) 20 41
104 15 31
150 19 39
151 23 46
154 27 55
155 17 34
157 12 25
158 14 28
159 14 29
167 21 42
168 15 30 I 170 I 21 42 I
173 14 29
mean: 17 35
14 Heavily Used Forest 23 47
32 (> 10% bare soil) 28 57
66 12 25
72 19 38
1.52 17 34
153 29 59
156 11 23
160 16 33
162 14 29
163 17 35
164 24 48
171 18 36
mean: 19 39
. , * Mehllch III phosphorous
106
Table 8.2. Upper Little Deep Fork Creek Soil Test Phosphorous for Grassland
Sample 10. Soil Test p.
No.
1
3
5
7
11
16
17
19
26
29
40
41
44
48
53
55
57
58
61
62
65
68
70
78
79
80
84
91
98
103
111
113
114
125
126
129
130
1135
Land Use Classification
Subclass
Good Condition Grassland
« 1% bare soil)
107
(mg/kg)
29
26
13
22
11
9
13
10
9
30
14
11
13
12
18
13
15
12
19
24
14
18
10
35
14
14
8
11
15
7
14
12
20
10
11
17
12
34
(Ibs/ac)
'60
53
27
44
22
19
26
20
18
62
29
23
27
24
37
26
30
24
38
49
28
37
21
71
29
28
17
23
31
15
29
24
40
21
22
35
25
70
continued
r
Table B.2. (oontinued) Upper Little Deep Fork Creek SoU Test Phosphorous for
Grassland
Sample ID.
No.
Land Use Classification
Subclass
Soil Test p.
(mg/kg) (Iibs/ac)
138
141
144
4
6
9
10
22
31
35
39
42
45
46
51
71
74
75
76
81
82
83
85
94
96
97
99
106
115
116
120
123
128
132
133
Good Condition Gmssland
« 1% bare soil)
mean:
Fair Condition Grassland
(1 5% bare soil)
108
21
11
21
16
18
13
14
8
21
16
19
19
10
10
9
13
14
8
11
25
11
18
16
17
14
15
10
13
9
15
14
19
16
11
14
18
42
23
42
33
37
26
28
17
42
32
38
38
21
21
19
27
29
17
23
51
23
36
33
34
29
30
20
26
19
30
29
39
32
23
29
36
continued
Table B.2. (continued) Upper Little Deep Fork Creek Soil Test Phosphorous for
Grassland
Sample ID.
No.
134
139
142
143
148
149
Land Use Classi'fication
Subclass
Fair Condition Grassland
(1  5% bare soil)
mean:
Soil Test p'
(mg/kg) (Ibs/ac)
15 30
30 62
20 41
17 35
17 34
12 24
15 30
2
13
18
20
23
24
25
27
28
30
33
36
37
38
43
49
50
52
59
63
64
67
69
77
86
87
88
90
92
Poor Condition Grassland
(5  20% bare soil)
109
53
23
14
7
16
20
13
12
10
12
13
14
18
17
15
13
17
11
22
13
4
16
19
11
14
9
9
12
28
108
47
29'
15
33
41
26
25
21
24
26
29
36
34
31
26
34
22
45
27
8
32
39
22
29
18
19
25
58
continued
Table 8.2. (continued) Upper Little Deep Fork Creek Soil Test Phosphorous for
Grassland
Sample [D. Land Use Classification Soil Test p'
No. Subcliass (mg/kg) (Ibs/ac)
93 Poor Condition Grassland 17 35
100 (5  20% bare soil) 12 24
101 10 21
105 6 13
108 20 40
118 10 20
119 52 107
122 16 33
124 7 15
127 16 33
131 23 46
136 12 24
137 14 29
145 13 27
146 9 19
147 12 25
mean: 16 32
34 Unmanaged Grassland 20 41
60 (20  100% bare soil 14 28
89' with erosive areas) 6 13
110 11 22
112 13 27
140 38 78
mean: 17 35
* Mehlich '" phosphorous
110
Table B.3. Upper Little Deep Fork Creek Soil Test Phosphorous for "Other" Land
Uses
8 Salt or Oilfield Induced Erosion
73
117
Sample 10.
No.
12
15
56
107
121
" Mehlich 11/ phosphorous
Land Use Classification
Subclass
Small Grains
mean:
mean:
Dairy/Feedlot
mean:
111
Soil Test P~
(mglkg) (Ibs/ac)
9 18
22 44
19 39
17 34
9' 18
8 16
11 23
9 19
490 1000
60 122
275 561
Table 8.4. Battle Branch Soil Test Phosphorous for Pasture
Rank Soil Test P. Rank Soil Test p"
(mg/kg) (Ibs/ae) (mg/kg) (Ibs/ac)
1 5 10 41 13 26
2 5 11 42 13 26
3 6 13 43 13 27
4 7 14 44 13 27
5 7 14 45 13 27
6 7 15 46 14 28
7 7 15 47 14 28
8 8 16 48 14 28
9 8 17 49 14 29
10 8 17 50 14 29
11 8 17 51 15 30
12 8 17 52 15 30
13 9 18 53 15 30
14 9 18 54 15 30
15 9 18 55 15 30
16 9' 19 56 15 31
17 9 19 57 16 32
18 9 19 58 16 32
19 9 19 59 16 33
20 9 19 60 17 34
21 10 20 61 17 34
22 10 21 62 17 34
23 10 21 63 17 35
24 10 21 64 17 35
25 10 21 65 17 35
26 1,0 21 66 18 37
27 11 22 67 18 37
28 11 22 68 18 37
29 11 22 69 20 40
30 11 22 70 20 41
31 11 22 71 21 43
32 11 23 72 24 48
33 12 24 73 24 49
34 12 24 74 24 49
35 12 24 75 25 51
36 12 24 76 25· 51
37 12 25 77 25 52
38 12 25 78 27 56
39 13 26 79 27 56
40 13 26 80 28 58
continued
112
Table B.4. (continued) Battle Branch Soil Test Phosphorous for Pasture
Rank Soil Test P. Rank Soil Test p.
(mglkg) (Jbs/ac) (mg/kg) (Ibs/ac)
81 29 60 121 55 113
82 29 60 122 56 114
83 30 62 123 56 115
84 30 62 124 57 116
85 32 65 125 58 118
86 35 71 126 58 118
87 36 73 127 60 122
88 36 74 128 60 122
89 36 74 129 60 123
90 39 79 130 62 126
91 39 79 131 62 126
92 39 80 132 62 126
93 39 80 133 62 126
94 40 81 134 64 130
95 40 81 135 64 130
96 40 82 136 64 131
97 42 85 137 64 131
98 43 88 138 64 131
99 43 88 139 64 131
100 43 88 140 64 131
101 44 89 141 65 132
102 45 92 142 65 132
103 46 93 143 65 133
104 46 93 144 66 134
105 47 95 145 66 135
106 47 96 146 66 135
107 48 97 147 67 136
108 49 100 148 67 137
109 49 100 149 68 138
110 49 100 150 68 139
111 49 101 151 68 139
112 49 101 152 69 140
113 51 104 153 69 140
114 51 104 154 69 140
115 51 105 155 69 141
116 52 107 156 70 142
117 54 111 157 70 142
118 54 111 158 70 143
119 54 111 159 70 143
120 55 112 160 71 144
continued
113
Table BA. (continued) Battle Branch Soil Test Phosphorous for Pasture
Rank Soil Test P* Rank Soil Test P*
(mg/kg) (lbsJac) (mgJkg) (Ibs/ac)
161 71 144 201 104 212
162 72 146 202 105 214
163 73 148 203 105 214
164 73 148 204 105 215
165 73 149 205 106 216
166 73 149 206 106 216
167 73 149 207 106 216
168 74 150 208 109 222
169 74 150 209 109 222
170 74 150 210 110 224
171 74 150 211 110 224
172 74 150 212 111 226
173 74 150 213 112 228
174 77 157 214 114 232
175 7'9 162 215 114 233
176 80 163 216 114 233
177 81 165 217 117 239
178 81 165 218 119 242
179 82 167 219 119 243
180 82 168 220 120 244
181 85 174 221 120 244
182 86 175 222 131 268
183 87 177 223 135 276
184 87 178 224 137 280
185 92 187 225 138 281
186 93 189 226 140 285
187 93 189 227 140 286
188 93 190 228 147 300
189 95 194 229 154 314
190 96 196 230 164 335
191 97 197
192 97 1,97 mean: 54 110
193 98 200
194 99 203,
195 100 204
196 101 206
197 102 208
198 102 209
199 103 210
200 103 210
• Mehlich III phosphorous
114
Table B.5. Peacheater Creek Soil Test Phosphorous for Pasture
Rank Soil Test P. Rank Soil Test p.
(mg/kg) (Ibs/ac) (mg/kg) (Ibs/ac)
1 6 13 41 28 57
2 7 14 42 28 57
3 8 17 43 28 58
4 9 18 44 29 59
5 9 18 45 30 61
6 9 19 46 30 61
7 9 19 47 30 62
8 10 21 48 31 63
9 10 21 49 31 63
10 11 22 50 31 64
11 11 23 51 31 64
12 12 24 52 31 64
13 13 26 53 32 65
14 13 26 54 32 65
15 14 29 55 33 67
16 14 29 56 33 67
17 15 30 57 34 70
18 15 30 58 36 73
19 15 31 59 36 74
20 15 31 60 36 74
21 15 31 61 37 76
22 16 32 62 37 76
23 16 33 63 38 77
24 16 33 64 38 77
25 17 34 65 39 79
26 17 35 66 39 80
27 19 38 67 40 81
28 20 41 68 41 83
29 21 42 69 41 83
30 21 43 70 41 83
31 22 45 71 41 84
32 23 46 72 41 84
33 24 48 73 42 85
34 24 49 74 4