Karynn Sebesta

May 2014

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Table of Contents

List of Figures………………………………………………………………………………………………………………………………………….2

List of Tables……………………………………………………………………………………………………………………………………………3

Executive Summary…………………………………………………………………………………………………………………………………4

Introduction and Background………………………………………………………………………………………………………………….5

County Ditch 57 Background………………………………………………………………………………………………………5

Improvement Features………………………………………………………………………………………………………………5

Background of the Hydrologic Model…………………………………………………………………………………………6

Significance of Hydrologic Modeling………………………………………………………………………………………….6

Methodology…………………………………………………………………………………………………………………………………………11

Vflo™ Requirements…………………………………………………………………………………………………………………11

Development of Parameter Maps…………………………………………………………………………………………….11

Rainfall Data……………………………………………………………………………………………………………………………..15

Channel Data…………………………………………………………………………………………………………………………….15

Additional Data…………………………………………………………………………………………………………………………16

Model Calibration……………………………………………………………………………………………………………………..16

Results…………………………………………………………………………………………………………………………………………………..17

Vflo™ Parameter Maps……………………………………………………………………………………………………………..17

Vflo™ Model……………………………………………………………………………………………………………………………..20

Analysis………………………………………………………………………………………………………………………………………………….43

Spring Storm………………………………………………………………………………………………………………………..……43

Summer Storm………………………………………………………………………………………………………………………….43

Fall Storm………………………………………………………………………………………………………………………………....44

Effectiveness of Installed Structures…………………………………………………………………………………………45

Recommendations for Future Analysis………………………………………………………………………………………………….47

References…………………………………………………………………………………………………………………………………………….48

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List of Figures

Figure 1: Location of County Ditch 57 Watershed……………………………………………………………………………………8

Figure 2: Improvement Features of CD 57 Watershed…………………………………………………………………………….9

Figure 3: Monitoring Site Locations of CD 57 Watershed……………………………………………………………………….10

Figure 4: Digital Elevation Model of CD 57 Watershed…………………………………………………………………………..22

Figure 5: Slope Percent of CD 57 Watershed………………………………………………………………………………………….23

Figure 6: Land Use and Land Cover of CD 57 Watershed………………………………………………………………………..24

Figure 7: Roughness of CD 57 Watershed………………………………………………………………………………………………25

Figure 8: Soil Texture of CD 57 Watershed…………………………………………………………………………………………….26

Figure 9: Effective Porosity of CD 57 Watershed……………………………………………………………………………………27

Figure 10: Hydraulic Conductivity of CD 57 Watershed………………………………………………………………………….28

Figure 11: Wetting Front of CD 57 Watershed……………………………………………………………………………………….29

Figure 12: Hydrologic Soil Groups of CD 57 Watershed………………………………………………………………………….30

Figure 13: Curve Numbers of CD 57 Watershed…………………………………………………………………………………….31

Figure 14: Initial Abstraction of CD 57 Watershed………………………………………………………………………………….32

Figure 15: Vflo™ Model of CD 57 Watershed…………………………………………………………………………………………33

Figure 16: Spring Storm Spatially Distributed Rainfall Map…………………………………………………………………….34

Figure 17: Spring Storm Discharge Hydrographs…………………………………………………………………………………….35

Figure 18: Spring Storm Stage Hydrographs…………………………………………………………………………………………..36

Figure 19: Summer Storm Spatially Distributed Rainfall Map……………………………………………….………………..37

Figure 20: Summer Storm Discharge Hydrographs…………………………………………………………………………………38

Figure 21: Summer Storm Stage Hydrographs……………………………………………………………………………………….39

Figure 22: Fall Storm Spatially Distributed Rainfall Map…………………………………………………………………………40

Figure 23: Fall Storm Discharge Hydrographs…………………………………………………………………………………………41

Figure 24: Fall Storm Stage Hydrographs……………………………………………………………………………………………….42

Figure 25: Site 1 Discharge and Stage Hydrographs……………………………………………………………………………….46

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List of Tables

Table 1: Manning’s Roughness Coefficient……………………………………………………………………………………………12

Table 2: Green-Ampt Infiltration Parameters for Soil Texture Classes…………………………………………………..13

Table 3: Curve Numbers for CD 57…………………………………………………………………………………………………………14

Table 4: Initial Abstraction Values………………………………………………………………………………………………………….14

Table 5: Acreage and Percentage of Land in each Land Use/Land Cover Classification………………………….17

Table 6: Acreage and Percentage of Land Associated with each Roughness Value………………………………..18

Table 7: Soil Textures found in CD 57 with Corresponding Green-Ampt Infilitration Parameters

Acreage and Percentage of Land……………………………………………………………………………………………….19

Table 8: Curve Number and Initial Abstraction Values Acreage and Percentage of Land……………………….20

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Executive Summary

The County Ditch 57 watershed, located in Mapleton, Minnesota, was modeled using the

watershed modeling software Vflo™. The purpose of the study was to conduct hydrologic modeling for

the watershed and analyze the observed and simulated hydrographs for stage and discharge. The

observed and simulated hydrographs were compared to determine if installed structures throughout the

channel were effective in decreasing stage and discharge. The channel is subjected to flooding events

which has decreased agricultural yield and water quality. Structures were installed to help improve

water quality and reduce flooding events. County Ditch 57 is a tributary for the Cobb River and

eventually the water that flows through County Ditch 57 flows into the Mississippi River. The hopes of

this study and the ongoing project from I&S Group is that by improving County Ditch 57 the same

structures can be built along other waterways that will eventually improve the water quality of all river

systems in Minnesota.

Comparing and analyzing the simulated and observed hydrographs for both stage and discharge

found that the installed structures are effective in decreasing stage and discharge. Spring, summer and

fall storms were modeled and analyzed. In determining the effectiveness of the structures only the

spring and fall storm events were used. The summer storm wasn’t used because the simulated and

observed hydrographs did not match close enough to give a definite conclusion.

An additional monitoring site is recommended to be added along with modeling different types

of storm events to ensure the model is working properly. The additional monitoring site, which should

be added at the channel’s outlet, would give better insight as to how much water would be discharging

without the structures compared to what is actually discharging with the structures. The modeling of

different types of storm events is recommended to ensure the model is calibrated correctly and giving

the best results to compare to observed data.

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Introduction and Background

The purpose of this study is to conduct and analyze hydrologic modeling for County Ditch 57, CD

57, watershed in Mapleton, Minnesota. The hydrologic modeling conducted on CD 57 is part of larger

ongoing project by I&S Group. This study will also determine if water quality improvement features

install in CD 57 are helping to decrease peak flow and discharge. The physics based model Vflo™, will be

used to conduct hydrologic modeling. In the following sections CD 57’s background, an introduction to

Vflo™ and the significance of hydrologic modeling will be discussed.

County Ditch 57 Background

CD 57 is located in Mapleton, Minnesota which is part of Blue Earth County in south-central

Minnesota (Figure 1). CD 57 was built in 1921 to increase agricultural yield by draining fields of excess

water. Over the last 90 years the original tile system has deteriorated and failed resulting in construction

of an open ditch in the lower part of the ditch. CD 57 was unable to hold the amount of water it was

needed to drain which caused flooding, poor agricultural yields, and poor water quality.

CD 57 isn’t only a problem for the farmers in the area, but a problem for all the other channels

and rivers it is a tributary for. CD 57 drains into the Cobb River which is a tributary for the Le Sueur River.

The Le Sueur River empties into the Blue Earth River which converges with the Minnesota River and

eventually empties into the Mississippi River. CD 57 has been listed by the Pollution Control Agency to

be impaired water, meaning the amount of sediment and other pollutants that are being carried

throughout the channel are too high and thus resulting in pollution of other river systems. CD 57 can be

called a starting point of solving the water quality issues in Minnesota. If the water quality issue can be

solved for CD 57, then the same type of work can be completed on other river systems to clean

Minnesota’s surface water.

Improvement Features

I&S Group has been working with the watershed for quite some time, monitoring water quality

and flow to determine what the channel needs in order to decrease sediment load and other pollutants.

Five water quality improvement features have been installed and or constructed throughout the

channel. Buffer strips were placed along 4.1 miles of the ditch. Their purpose is to regulate water flow,

dissipate high water events and stabilize the stream banks. A surge pond was added which created

storage for the upper part of the watershed. The purpose of the pond is to decrease flow and flooding

events within CD 57 and the downstream rivers. Mapleton has an existing stormwater pond that was

expanded. The pond was expanded and dug deeper. The purpose of this pond is to provide additional

water treatment by requiring the pond to reach a higher water level before it can drain to the channel.

The pond holds runoff water from the city. A two-stage ditch was installed. The concept of a two-stage

ditch is to create a channel within a channel. The smaller inner channel accommodates low flow events

and the upper wider channel serves as a floodplain for high flow events. Native buffers and buffer strips

were implemented throughout the two-stage ditch to allow for additional filtration and uptake of

nutrients and sediment. A sediment trap has also been implemented to provide a sediment storage

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basin within the channel and decrease suspended sediment throughout the channel. The last of the

improvement features that were install into CD 57 are overflow weirs. The first weir directs flow into the

surge pond. The second weir, located towards the outlet near Cobb River, is to reduce the flow rate

before it discharges into the Cobb River. The reduced flow will also reduce frequency and intensity of

flooding events resulting in a decrease of nutrients and sediment load being discharged in the Cobb

River. The preceding information regarding structures constructed and installed for the improvement of

CD 57 came from I&S Group’s Water Quality Sampling and Monitoring Work Plan. For the location of

each structure please see Figure 2.

Post-installment of the water quality features, twelve monitoring locations were set. For the

hydrologic model only four of those twelve locations were used. The locations were chosen because

they were located within the open channel and all data that was needed to operate and calibrate the

model was available. It is important to note here that the hydrologic model could not take into account

the structures that have been installed within the ditch. To view the locations of the monitoring sites

please see Figure 3.

Background of the Hydrologic Model

The software used to create a hydrologic model for CD 57 water was Vflo™. Vflo™ is a physics-

based distributed hydrologic model. Vflo™ is an extension of the original model called r.water.fea, which

was a finite element approach to watershed modeling. The purpose of the model was to provide a

hydrologic modeling tool that used GIS maps of parameters directly within the GIS environment (Vflo™

Model Theoretical Background, 2014). The difference between Vflo™ and other hydrologic models is

that it “represents roughness and slope as nodal rather than elemental parameters” which allows the

model to simulate the watershed as a whole rather than breaking it into equivalent conceptual

cascades, planes or sub-areas (Vflo™ Model Theoretical Background, 2014).

Vflo™ uses a variety of equations to solve the simulated results, these include the kinematic

wave analogy for overland flow, the Green-Ampt method for infiltration among others. Vflo™ uses

“spatial and temporal characteristics of a watershed that govern the transformation of rainfall into

runoff” (Vflo™ Model Theoretical Background, 2014). It needs various data from topography, land

use/land cover, soils and precipitation to simulate the runoff accurately.

In addition to the various data needed to define the watershed, observed data can also be

loaded into Vflo™ and used to calibrate the model. The calibration results in slightly changing various

input parameters so the simulated hydrographs match the observed hydrographs. As stated before,

Vflo™ is not capable of uploading information regarding man-made structures that may alter stage or

discharge of the channel.

Significance of Hydrologic Modeling

Hydrologic modeling is described by Bedient, Huber and Vieux as “the most logical and

scientifically advanced approach to understanding the hydrologic behavior of complex watershed and

water resources systems.” Hydrologic modeling allows us to understand how water flows throughout a

watershed system. It simulates results from different input parameters and allows a prediction of how a

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watershed may change with urban development or flooding control options. These models can also be

used to continually monitor locations that may not have the safest conditions for field technicians to be

gathering data in.

Although hydrologic modeling does have many advantages, that are some disadvantages to

using them as well. Models can only be as accurate as the data that is used to create the model,

therefore if data is outdated or in accurate the model may not simulated correct results. Also, in the

case of Vflo™ the model can be calibrated to match observed data, which changes the input parameters

thus changing the data for the watershed. The calibration may not be as big of an error factor when

modeling smaller watersheds, but could pose a problem in larger watershed, or areas where overland

properties and infiltration properties change drastically throughout the watershed.

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Figure 1. Location of County Ditch 57 Watershed. The above map shows where CD 57

watershed is located within Blue Earth County in Minnesota.

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Figure 2. Improvement Features of CD 57 Watershed. This map displays the structures that

were installed within the watershed to improve water quality and decrease flooding events.

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Figure 3. Monitoring Site Locations of CD 57 Watershed. The above map shows the

locations of the monitoring sites used for modeling CD 57 watershed.

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Methodology

Vflo™ has a number of data requirements needed in order to make a model and have it operate

correctly with accurate results. Each of the requirements and some non-requirements are described

below as well as the steps taken in order to create or manipulate the data into what is needed.

Vflo™ Requirements

Vflo™ has two components that work together to make the model. The first is the Basin

Overland Properties file, BOP, and the other is the rain rate property file, RRP. The BOP file contains land

surface data and infiltration properties. Land surface data includes watershed slope, flow direction,

watershed roughness, channel width and side slope and baseflow. Infiltration properties include

hydraulic conductivity, wetting front, effective porosity, soil depth, initial saturation, percent impervious

and abstraction. The RRP file contains spatially distributed rainfall data across the watershed.

Vflo™ can be run with or without GIS parameter maps to make the BOP file. In the case of a

larger watershed, it is easier to create GIS parameter maps to easily manipulate and change data

according to needs that present themselves. In order for the model to correctly input the data from GIS

parameter maps all data must be in American Standard Code Information Interchange, ASCII, which is

clipped to the same domain, sampled to the same grid cell size and projected in the same projection

(Vflo™ Online User Guide, 2014). For the CD 57 watershed all data was resampled from 1 meter to 50

meters and projected in NAD 83/UTM Zone 15N. The watershed data was resampled to 50 meters after

determining that 10 meters was too large of a file for Vflo™ to process with the amount of rainfall data

that was being input. For the most accurate data, all parameter maps were first created with a cell size

of 1 meter and then resampled to a cell size of 50 meters. By waiting until all maps were completed it

ensured the most accurate data would be input into the model.

Development of parameter maps

A Vflo™ model can be created without using GIS parameter maps, however for the size of CD 57

and for accuracy of the model GIS parameter maps were created and then imported into Vflo™. The first

step to creating these maps was to delineate the watershed. Multiple high resolution digital elevation

models, DEMs, were obtained through the United States Geological Survey, USGS, website. The DEMs

were then pieced together as one using the mosaic tool in ARCMap.

Multiple steps had to be taken in order to delineate the watershed. I used directions from Trent

University in California, found from google, to help guide me throughout the process. The first step to

delineating a watershed is to create a depressionless DEM using the fill tool in the Hydrology toolbox. It

fills in sinks, a cell with an undefined drainage direction, to remove any imperfections in the data (ArcGIS

Online Help 2014). After the DEM has been filled the flow direction tool can be used to create a flow

direction map. According to ERSI’s online help for ArcGIS, the flow direction tool creates a raster of flow

direction from each cell to its steepest down slope neighbor. After the flow direction map has been

made the flow accumulation tool is applied. It creates a raster of accumulated flow into each cell. After

the flow accumulation raster has been created a pour point is identified to let ArcMap know where the

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accumulated flow is eventually going. The pour point for the CD 57 watershed is the point at which the

open channel flows into the Cobb River. After the pour point has been selected and created, the snap

pour point tool is used to put your chosen pour point to the cell with the highest flow accumulation

within a specified distance (ArcGIS Online Help, 2014). If you run the tool with a search radius of zero,

the pour point will remain at the exact location you have established. The last step in delineating the

watershed is to use the watershed tool. All of the previously made maps are inputted and the tool

determines the contributing area. After the watershed has been delineated all other parameters maps

can be created and clipped to the extent of the watershed map.

In order to create parameter maps for the basin overland properties and infiltration properties

both land cover/land use map and soil data maps are needed, as well as the delineated watershed map.

The land cover/land use map was needed to determine Manning’s roughness coefficient, and percent

impervious surface of the land. The soil data maps were needed to determine curve numbers hydraulic

conductivity, effective porosity and wetting front. Initial abstraction was calculated using Manning’s

roughness coefficient and curve numbers. The watershed map was needed to determine surface slope

of the watershed.

The land cover/land use map was downloaded from the Multi-Resolution Land Characteristics

Consortium, MRLC, and the National Land Cover Database, NLCD, 2006 map was used. The NLCD map is

based on a 16-class land cover classification scheme that has been applied consistently across the

United States at a spatial resolution of 30 meters (mrlc.gov/nlcd2006). The land use map was of the

continental United States and was first clipped to the watershed extent, and then re-projected in NAD

83/UTM Zone 15N.

The land use map was already classified in the 16-class land cover classification scheme that is

most widely used. The map needed to be transformed from a raster to a polygon in order to edit the

attribute table and add in manning’s roughness coefficients, and percent impervious surface of the land.

Manning’s roughness coefficients were added first and determined using Chow (1959). Roughness

coefficients, n values, represent the degree to which land use creates a frictional drag over the land

surface when water flows over it. Table 1 shows the roughness values and land use characteristics

associated with CD 57. To determine the percent imperviousness of the land the descriptions of land

use/land cover characteristics were used from NLCD 2006 legend. The numbers were interpolated and

then could be calibrated as needed within the model.

Table 1. Manning’s Roughness Coefficient (Chow 1959).

Land Use/Land Cover Manning’s Roughness Coefficient

Bare Rock/Sand/Clay 0.04

Deciduous Forest 0.1

Developed, Open Space 0.015

Emergent Herbaceous Wetland 0.055

Herbaceous Grassland 0.055

High Intensity Residential 0.015

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Low Intensity Residential 0.015

Medium Intensity Residential 0.015

Open Water 0.015

Row Crops 0.035

Woody Wetlands 0.1

After roughness and percent impervious were determined using land use/land cover data, soil

data needed to be downloaded. Soil data maps were downloaded from the Web Soil Survey through the

Natural Resource Conservation Service, NRCS. Data was collected for Blue Earth County and then clipped

to the watershed extent and projected in NAD 83, UTM Zone 15N. Soil texture classification and

hydrologic soil groups were needed in order to determine the rest of the parameters needed to run

Vflo™. The maps came in raster form and had to be transformed into a polygon in order to edit the

attribute table and add in the needed parameters.

The Green-Ampt infiltration method was used to determine effective porosity, wetting front and

hydraulic conductivity of the various soil textures found in the CD 57 watershed. These numbers, which

have already been calculated, can be found in the text Hydrology and Floodplain Analysis by Bedient,

Huber and Vieux on page 149 in table 2-4. Effective porosity is defined as the space between soil and or

rock particles available for water to flow and is a unit-less number. Wetting front, also known as suction

head, is the difference between atmospheric and hydrostatic pressures and pulls water downward into

unsaturated soil (Bedient, Huber and Vieux, 147). Hydraulic conductivity is defined by Bedient, Huber

and Vieux as the ratio of velocity to hydraulic gradient indicating the permeability of the material.

Below, in Table 2, each of the three parameters is listed with their accompanying soil texture class for

the CD 57 watershed. These are the average values, and if needed could be calibrated within the model.

Table 2. Green-Ampt Infiltration Parameters for Soil Texture Classes (Bedient, Huber and Vieux, 149).

Soil Texture Class Effective Porosity Wetting Front (cm) Hydraulic Conductivity (cm/hr)

Clay 0.385 31.63 0.03

Clay Loam 0.309 20.88 0.10

Loam 0.434 8.89 0.34

Muck 0.309 20.88 0.10

Silt Loam 0.486 16.68 0.65

Silty Clay 0.323 29.22 0.05

Silty Clay Loam 0.432 27.30 0.10

The hydrologic soil map was needed to determine the curve numbers of the land. Curve

numbers weren’t needed to run the Vflo™ model however, in order to calculate initial abstraction, curve

numbers were needed. Curve numbers were determined using table 2-1 on page 90 in the Hydrology

and Floodplain Analysis text. The curve number is dependent on both land use characteristics and

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hydrologic soil group. The curve number associated with the land use/ land cover for CD 57 can be seen

in Table 3 below.

Table 3. Curve Numbers for CD 57.

Land Use/ Land Cover Curve Number

Bare Rock/Sand/Clay 86

Deciduous Forest 77

Developed Open Space 74

Emergent Herbaceous Wetland 74

Herbaceous Grassland 74

High Intensity Residential 90

Low Intensity Residential 81

Medium Intensity Residential 83

Open Water 0

Row Crops 80

Woody Wetlands 70

After curve numbers and roughness have been determined initial abstraction values can be

calculated. Abstraction is the initial loss of water prior to infiltration (Bedient, Huber, Vieux 111).

Abstraction is dependent on the curve number of the surface and is calculated using equation below:

Initial abstraction values were calculated and then added to the attribute table of the land use/ land

cover map. In Table 4 below the initial abstraction values associated with each land use/ land cover

classification is shown.

Table 4. Initial Abstraction Values.

Land Use/ Land Cover Initial Abstraction

Bare Rock/Sand/Clay 0.326

Deciduous Forest 0.597

Developed Open Space 0.703

Equation 1. Initial Abstraction Equation.

Initial Abstraction, Ia, (in inches) = 0.2S

Where:

S = (1000/CN) -10

CN = Curve Number

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Emergent Herbaceous Wetlands 0.703

Herbaceous Grassland 0.703

High Intensity Residential 0.222

Low Intensity Residential 0.469

Medium Intensity Residential 0.4096

Open Water 0

Row Crops 0.5

Woody Wetlands 0.857

Rainfall Data

The second component to Vflo™ is the input of rainfall data. Rainfall data can be input in

different forms, however for this study NEXRAD Level II data was used. Three different rainfall storms

were collected, one from each season. To determine when these storms occurred dates were collected

from the Minnesota Climatology Working Group from the University of Minnesota. After the dates were

chosen, data was collected from the National Climatic Data Center, NCDC, through the National Oceanic

and Atmospheric Administration, NOAA, website. Each day contained roughly 100-200 zipped files of

rainfall data. Each file had to be unzipped in order to be uploaded into Vflo™. The spring storm was April

9-11. 2013. The summer storm was June 21-23, 2013 and the fall storm was October 3-6, 2013. 2013

data was used because stage and discharge had been collected throughout the year and could be

compared to the simulated data. The files were uploaded into Vflo™, for each event, and then saved as

an RRP file. A complete list of all files used to compile the RRP files is available upon request.

Channel Data

Channel data was collected from I&S Group and Richard Moore of the Water Resource Center at

Minnesota State University, Mankato. I&S Group gave me a large excel file that contained stage,

elevation and discharge data for each monitoring site throughout 2012 and 2013. Richard Moore gave

me shapefiles for the channel and field tiles of CD 57.

Although not part of a requirement for the Vflo™ model, the stream data was needed to

properly calibrate the model and achieve the most accurate results. The shapefiles were uploaded into

Vflo and used only to ensure all cells within the channel were correctly named a channel cell. I&S

monitoring sites 2, 4, 5 and 7 were used within the model from the excel file. I copied the data

associated with each storm event for each monitoring site and input it into a separate excel

spreadsheet. Each excel file had to be saved in tab delimited format for Vflo to read it correctly. Each file

contained, date and time in GMT, stage in feet, and discharge in cubic feet per second.

Each of the four monitoring locations was classified as a rated channel cell within Vflo. This

meant that additional data would be needed in order for the model to correctly calculate those cells.

Rated channel cells need a stage-area curve and a stage-discharge curve. The data from I&S Group was

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used to create the stage-discharge curve. I&S Group also created channel cross sections that were used

to create the stage-area curve.

Additional Data

Some data was input directly into Vflo™ without the need for parameter maps. The soil depth,

initial saturation, channel width, channel side slope and baseflow are among these. It was discussed

with Dr. Bryce Hoppie that these factors could easily be calibrated within Vflo™ and uniform values

could be used and changed if needed. Soil depth was set at 60 inches, the average value for south-

central Minnesota. Initial saturation was 100 percent because for the first storm the ground was fully

saturated as the snow had just recently melted, saturating the ground. For channel side slope and width

average values were again used and calibrated as needed. Channel side slope was a 30 percent grade

and channel width was set at 3 feet. Baseflow was estimated to be 0.004 cfs and from there was

adjusted as needed for each storm event and for different locations in the channel.

Model Calibration

After all parameters maps, rainfall data, and all other additional data have been collected the

Vflo™ model can be made. The model is created by inputting all parameters for the BOP file and the RRP

file. Watch points are chosen in order for the model to display simulated results. Watch points can be

anywhere within the channel. For this study the four monitoring locations were used as watch points so

observed data could be uploaded.

Once all parameters have been input and watch points selected the model is solved. Observed

data is loaded to compare to the simulated data. The model is then calibrated by adjusting various

infiltration parameters so the simulated data matches the observed data. Initial saturation, hydraulic

conductivity and soil depth are adjusted to calibrate to volume. Overland roughness is adjusted to

calibrate to flow peak and channel roughness is adjusted to calibrate to timing. The process of solving

the model and calibrating factors is continued until the best matching hydrographs are achieved.

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Results

Vflo™ needs various parameters maps, rainfall data and observed data to be operated and

calibrated correctly. In order to understand the simulated data and to be able to further analyze that

data it is required to know and understand the data that has been input in the model. This section will

briefly go over all the results of all parameter maps that were map as well as simulated data from the

created Vflo™ model.

Vflo™ Parameter Maps

A DEM was needed to delineate the watershed for CD 57. Figure 4 illustrates the delineated

watershed in DEM form. Elevation is presented in meters and ranges from 297 meters to 322 meters.

The watershed contains approximately 6,378 acres of land. The original delineation created from

ArcMap wasn’t completely accurate because of the field tiles that change the watershed extent. The

south-east border had to be slightly edited to account for the field tiles and the additional drainage area

those would include. The DEM map was the used to clip all other maps created.

From the DEM a slope map was created. Minnesota’s land, especially in south-central

Minnesota, is relatively flat with minor hills scattered throughout. The slope map created for Vflo is

shown in Figure 5. Most of the land has a percent rise of zero to five. The areas with the largest percent

rise can be found on channel banks or areas that have been excavated. In CD 57’s watershed areas with

larger slopes are near the channel bank and near field tile. It is apparent from Figure 5 why field tiles

were needed in this area, field tiles drain the land of excess water. Majority of the land has a very low

slope grade and thus water would flow very slowly if at all off from the fields.

Land use and land cover data was needed to determine other parameters used in Vflo. South-

central Minnesota consists mainly of farm fields and small towns. It was not surprising that majority of

CD 57’s watershed consists of row crops and some developed space. Almost 85 percent of the land is

classified as row crops and 13 percent was classified as various stages in development. The rest of the

land is classified into bare rock/sand/clay, deciduous forest, emergent herbaceous wetlands, herbaceous

grassland, open water and woody wetlands. Figure 6 illustrates the land cover and use that is associated

with the CD 57 watershed. Mapleton, the town located within the watershed is not highly developed

thus we see the town mostly classified as low to medium residential. In Table 5 below the land use and

cover is broken down into acreage and percentage to further illustrate the amount of land in each

classification.

Table 5. Acreage and Percentage of Land in each Land Use/Land Cover Classification.

Land Use/ Land Cover Acreage Percentage of Land

Bare Rock/Sand/Clay 3.26 0.05%

Deciduous Forest 7.96 0.13%

Developed, Open Space 472.24 7.4%

Emergent Herbaceous Wetlands 6.12 0.096%

Herbaceous Grassland 77.31 1.22%

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High Intensity Residential 15.91 0.25%

Low Intensity Residential 259.07 4.08%

Medium Intensity Residential 55.28 0.87%

Open Water 55.08 0.867%

Row Crops 5386.62 84.9%

Woody Wetlands 7.34 0.12%

Roughness was determined using Chow’s (1959) table for various roughness coefficients

associated with different land use and cover classifications. As stated previous, roughness represents

the degree to which land use and cover create a frictional drag over the land surface when water flows

over it. From the characteristics of the land use previously discussed it was hypothesized that majority of

the land would have relatively low to intermediate roughness values. The roughness for CD 57’s

watershed ranged from 0.015-0.1 with most of the land having a value of 0.035. This information is

illustrated in Figure 7. It is important to understand that roughness can vary with season, especially in

this area of Minnesota. During the spring, the row crops have not been planted yet or if they have they

are still seedlings thus their roughness will be slightly lower. During the summer and fall roughness will

increase as the crops grow taller and thicker. Overland and channel roughness effect the amount of

runoff and discharge greatly within a watershed and is an important calibration factor when working

with Vflo™. In Table 6 below, acreage and percentage of land is shown for each roughness value.

Table 6. Acreage and Percentage of Land Associated with each

Roughness Value.

Roughness Value Acreage Percentage of Land

0.015 857.58 13.5%

0.035 5386.62 84.9%

0.04 80.57 1.27%

0.055 6.12 0.96%

0.06 7.34 0.12%

0.1 7.96 0.13%

The next map created was the soil texture map (Figure 8). This map was needed to understand

what types of soils are represented within CD 57’s watershed. The soil texture determines the effective

porosity, wetting front and hydraulic conductivity of the land. These parameters, among others, are

needed to determine infiltration rates and needed within Vflo™ to operate the model and calibrate it to

observed data. Soil data was downloaded from the NRCS web soil survey. CD 57’s watershed contains

seven different soils. These soils include clay, clay loam, loam, muck, silt loam, silty clay and silty clay

loam. The areas classified as muck had to be joined with areas classified as clay loam because the table

for the Green-Ampt infiltration parameters of various soil textures found in the text Hydrology and

19

Floodplain Analysis did not include muck. Additional research found no Green-Ampt infilitration

parameters for the soil texture muck.

From previous experience with soils, I hypothesized that the hydraulic conductivity and effective

porosity would be relatively low in majority of the watershed. Soils with clay and silt tend to have a

lower effective porosity because the individual grains are packed closer together. The grains are able to

closely pack together because of their shape which tends to be more oval and flat than round like a sand

grain. The shape of the grains will also affect how fast water will move through the subsurface. A smaller

effective porosity is related to a lower hydraulic conductivity. Wetting front, also known as suction head,

pulls water into the subsurface. Clay rich soils will suction more water into the subsurface because of

their absorbent minerals that act as sponges. Wetting front has an inverse relationship with effective

porosity and hydraulic conductivity.

Effective porosity for the watershed is represented in Figure 9 and ranges from 0.309 to 0.486.

Areas with higher effective porosity are associated with soils that contain loam, which tends to carry

equal parts sand, silt and clay. Hydraulic conductivity is represented in Figure 10 and ranges from 0.03

centimeters per hour to 0.65 centimeters per hour. Wetting front for CD 57 watershed is represented in

Figure 11 and ranges from 8.89 centimeters to 31.63 centimeters. Table 7 below displays the acreage

and percent of land that is associated with each value. Much of the land in the watershed consists of

clay and silty clay loam. From Figure 8 and Table 7 the soils with higher effective porosity and hydraulic

conductivity are located closer to the channel and the soils with lower effective porosity and hydraulic

conductivity are located further away from the channel.

Table 7. Soil Textures found in CD 57 Watershed with Their Corresponding Green-Ampt Infiltration Parameters

Acreage and Percentage of Land.

Soil Texture Effective Porosity

Wetting Front (cm)

Hydraulic Conductivity

(cm/h)

Acreage Percentage of Land

Clay 0.385 31.63 0.03 2055.12 32.2%

Clay Loam 0.309 20.88 0.10 216.55 3.4%

Loam 0.434 8.89 0.34 160.12 2.5%

Silt Loam 0.486 16.68 0.65 121.80 1.9%

Silty Clay 0.423 29.22 0.05 850.98 13.3%

Silty Clay Loam 0.432 27.30 0.10 2973.43 46.7%

In addition to effective porosity, wetting front and hydraulic conductivity, initial abstraction is

needed. To calculate initial abstraction the hydrologic soil groups and curve numbers of the watershed

must first be defined. The hydrologic soil groups are based off the soil’s run off potential and infiltration

rate when thoroughly wetted. The CD 57 watershed contains hydrologic soil groups B, C and D with

mixtures of the three as well. Soil group B consists mainly of silt loam and silt with moderate infiltration

when thoroughly wetted. Group C soils are sandy clay loam and have low infiltration rates when

thoroughly wetted. Group D soils consists of clay loam, silty clay loam, silty clay or clay and has the

highest run off potential with very low infiltration rates when thoroughly wetted. Figure 12 shows the

20

locations of each hydrologic soil group within CD 57 watershed. Soils with the highest run off potential

are located on the outskirts of the watershed and represent most of the land. Majority of the CD 57

watershed contains soils with low to very low infiltration rates.

Curve numbers are determined using the hydrologic soil group in addition to the land use/ land

cover. It is an empirical parameter used to predict direct runoff or infiltration from rainfall. Curve

numbers aren’t used directly in Vflo™, but are needed to calculate initial abstraction. The higher the

curve number the greater the runoff potential. Figure 13 shows the various curve numbers associated

with CD 57 watershed. Curve numbers are highest in the town of Mapleton and slightly decrease

throughout the rest of the watershed. Most of the watershed contains a curve number of 80.

Initial abstraction was calculated using Equation 1 previously shown. Initial abstraction is the

initial loss of water prior to infiltration. It is the last of the infiltration parameters needed to operate

Vflo™. Abstraction values in CD 57 watershed range from 0 inches to 0.857 inches. Initial abstraction

values for the watershed are shown in Figure 14. Most of the watershed contains an abstraction value of

0.5 inches. Table 8 below shows how much of the watershed is associated with each curve number and

initial abstraction value.

Table 8. Curve Number and Initial Abstraction Values Acreage and Percentage of Land.

Curve Number Initial Abstraction (in) Acreage Percentage of Land

0 0 55.08 0.867%

70 0.857 7.34 0.12%

74 0.703 555.67 8.76%

77 0.597 7.96 0.13%

80 0.5 5386.62 84.9%

81 0.469 259.07 4.08%

83 0.4096 55.28 0.87%

86 0.326 3.26 0.05%

90 0.222 15.91 0.25%

Vflo™ Model

The Vflo™ model was created by inputting all parameter maps and channel data. Figure 15

displays the model without the rainfall data added. Green lines represent flow direction for overland

cells and blue lines represent flow direction for channel cells. Flow is generally in the Northeast direction

for the channel and overland cells flow into the channel. Not all areas have a flow direction because of

the relatively flat land.

Spring, summer and fall seasons were modeled using the heaviest rainfall that occurred during

that season. Figure 16 illustrates the rainfall that occurred during the spring storm, April 9-11, 2013.

Over the three days of rainfall the watershed had 3.257 to 4.342 inches of rain. The model generated

stage and discharge hydrographs and plotted simulated and observed stage and discharge for each of

the sites. Sites 2, 4 and 5 were used for the spring storm. Site 7 was not used because data was not

available for the specified dates. The model was calibrated to simulate hydrographs that best fit the

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observed data. Discharge hydrographs for the spring storm can be found in Figure 17 and the stage

hydrographs for the same storm can be found in Figure 18.

The summer season was modeled using the storm that occurred from June 21 through June 23,

2013. Rainfall over the watershed ranged from 1.954 to 3.908 inches with most of the watershed in the

range of 2.28 to 3.256 inches. The spatially distributed rainfall can be seen in Figure 19. Sites 2, 4, 5 and

7 were used to model the summer storm. Figure 20 displays the discharge hydrographs for the summer

storm and Figure 21 displays the stage hydrographs for the same storm. The simulated and observed

data does not match for these sites and will be explained in further detail in the analysis section.

The fall season was modeled using the storm that occurred from October 3 through October 6,

2013. Rainfall over the watershed ranged from 2.447 to 4.195 inches of rain. Majority of the watershed

was in the range of 3.146 to 4.195 inches of rain. Figure 22 displays the spatially distributed rainfall over

the watershed. All four sites were used to model the fall storm event. Figure 23 shows the discharge

hydrographs for the fall storm and Figure 24 shows the stage hydrographs for the same storm.

22

Figure 4. Digital Elevation Model for CD 57 Watershed. The above map shows the elevation

of the watershed in meters. Lowest elevation is found within the channel. The difference in

elevation from the highest to the lowest point is about 25 meters.

23

Figure 5. Slope Percent of CD 57 Watershed. Slope percent or percent rise of the land is

shown in this map. From this map it is obvious that the land is relatively flat. Most of the

land has a slope percent of 0-5 percent.

24

Figure 6. Land Use and Land Cover of CD 57 Watershed. This watershed was clipped from

the NLCD 2006 map and is based on a 16-class land cover classification scheme. Majority of

the land is classified as row crops.

25

Figure 7. Roughness Values for CD 57 Watershed. Values were determined using Manning’s

roughness coefficient based on land cover and use classifications from Chow (1959).

26

Figure 8. Soil Texture of CD 57 Watershed. A soil texture map from the NRCS was clipped to

the watershed extent to make this map. The watershed consists mostly of clay and silty clay

loam.

27

Figure 9. Effective Porosity of CD 57 Watershed. The effective porosity of the soil depends

on the soil texture. Values were determined using the Green-Ampt Infilitration Parameters

for Soil Texture Classes table from Bedient, Huber and Vieux.

28

Figure 10. Hydraulic Conductivity for CD 57 Watershed. Values are based on the soil texture

class and were determined using the same table used for Figure 9.

29

Figure 11. Wetting Front Values for CD 57 Watershed. Like figure 9 and 10 values are based

off of the soil texture class and were determined using the table stated in Figure 9.

30

Figure 12. Hydrologic Soil Groups of CD 57 Watershed. A hydrologic soil group map was

downloaded from the NRCS web soil survey and then clipped to the watershed extent.

Almost all of the land contains C or C/D soil.

31

Figure 13. Curve Numbers for CD 57 Watershed. This map displays the curve numbers for

the watershed. Curve numbers are determined using a combination of the hydrologic soil

group and land use/land cover data.

32

Vflo Model of CD 57 Watershed Figure 14. Initial Abstraction Values for CD 57 Watershed. Abstraction is the initial loss of

water prior to infiltration and is dependent on the curve number. It is calculated using the

equation on page 14.

33

Vflo Model of CD 57 Watershed

Legend

Flow Direction

Channel

Watch Points

Figure 15. Vflo™ Model for CD 57 Watershed. The above map displays the model used to

analyze the watershed. Green lines represent flow direction. Water flows into the channel

and then follows the channel to the outlet. The circle represent watch points that were used

to create the hydrographs.

34

Spring Storm Spatially Distrubted Rainfall Map

Legend

Flow Direction Lines

Channel

Watch Points

Figure 16. Spring Storm Spatially Distributed Rainfall Map. This map shows

the rain fall that occurred during the spring storm over the watershed. The

spatially distributed rainfall was acquired from noaa.gov in the form of

NEXRAD Level II data.

35

Spring Storm Discharge Hydrographs

Figure 17. Spring Discharge Hydrographs. The spring storm was

modeled from April 9-13, 2013. Blue lines are modeled discharged and

the red lines are observed discharge.

36

Spring Storm Stage Hydrographs

Figure 18. Spring Stage Hydrographs. The maps were produced at

the same time the discharge hydrographs were. The blue lines

represent simulated stage and the red lines represent observed

stage.

37

Summer Storm Spatially Distributed Rainfall Map

Figure 19. Summer Storm Spatially Distributed Rainfall Map. This map shows the spatially

distributed rainfall that occurred during the summer storm over the watershed. Rainfall data

was acquired from noaa.gov in the form of NEXRAD Level II.

38

Summer Storm Discharge Hydrographs

Figure 20. Summer Discharge Hydrographs. June 21-24, 2013 was modeled.

Blue lines represent simulated discharge and red lines represent observed

discharge.

39

Summer Storm Stage Hydrographs

Figure 21. Summer Stage Hydrographs. These graphs were produced at

the same time as the discharge hydrographs. Blue lines represent

simulated stage and red lines represent observed stage.

40

Fall Storm Spatially Distributed Rainfall Map

Figure 22. Fall Storm Spatially Distributed Rainfall Map. This map shows the spatially

distributed rainfall that occurred during the fall storm over the watershed. Rainfall data was

acquired from noaa.gov in the form of NEXRAD Level II.

41

Fall Storm Discharge Hydrographs

Figure 23. Fall Discharge Hydrographs. The storm that occurred October 3-

7, 2013 was modeled here. The blue lines represent simulated discharge

and the red lines represent observed discharge.

42

Fall Storm Stage Hydrographs

Figure 24. Fall Stage Hydrographs. These hydrographs were produced at

the same time as the fall discharge hydrographs. Here, blue lines represent

simulated stage and red lines represent observed stage.

43

Analysis

This section will discuss in further detail the results of the simulated and observed hydrographs

from the model. It will also discuss whether or not the structures that were placed within or near the

channel are working to address water quality issues regarding flooding. The observed hydrographs are

off by roughly 4-6 hours on each of the graphs. This could be due to incorrect formatting within excel

when entering time and date data or a mistake from the machine that recorded the data. When

analyzing and comparing the hydrographs I ignored the time different and looked at peak discharge and

stage.

Spring Storm

The spring storm modeled the best out of all the storms in regards to getting the hydrographs to

match. Peak discharge and peak stage were noticeably different, but quite similar, which gives insight to

the effectiveness of the structures that were built. Starting with Site 5, the site with observed data

furthest downstream, the difference was the most noticeable. Peak discharge for the model was about

35 cfs while peak discharge of the observed data roughly 14 cfs (Figure 17). Peak stage for the simulated

data was 5 feet whereas observed peak stage was 3 feet. Site 5 is located slightly downstream from the

Klein Surge Pond (Figure 2). This same difference can be seen in Site 4 and 2, although Site 2 has the

smallest difference. Again, Site 4 had a simulated peak discharge of greater than 40 cfs while the

observed data had a peak of roughly 23 cfs (Figure 17). Peak stage of the simulated data was a little over

3 feet and observed was roughly 1.7 feet. Site 4 is located within the two-stage ditch (Figure 2) and thus

it is expected to see a decreased in stage and discharge from the simulated hydrographs. Site 2 is

located within the buffer strips but before the second overflow weir (Figure 2). Difference in discharge

between the two hydrographs is roughly 25 cfs (Figure 17). The stage hydrographs for Site 2 matched

very closely as well. Peak stage showed a difference of only about 0.4 feet and the biggest difference

was after the storm had ended, the observed stage was higher than the simulated stage by about 0.7

feet (Figure 18). This could be due to the overflow weir which is slightly downstream from this site. In

cases of medium flow the weir backs up the water in the channel which would increase the stage at Site

2.

A trend for all three sites is the discharge amount after the rainfall events. Observed data has a

higher discharge than the simulated data once the rain has stopped falling. Sites 4 and 5 have a

difference of roughly 5 cfs whereas Site 2 has a difference of 25 cfs. This could be due to the installed

structures. They are holding water in the channel for a longer period of time which the model cannot

account for. The structures, especially the overflow weirs, are meant to hold water in the channel to

decrease velocity and allow the sediment load to settle out of the channel. This then decreases the

amount of sediment being discharged into the Cobb River and other channels CD 57 is a tributary for.

Summer Storm

The summer storm was the hardest storm to model. The hydrographs for both stage and

discharge hardly matched and the differences were great. There may have been calculation errors

44

within the excel file for the observed data, or the model may not have been calibrated correctly.

Another possibility is that the structures built within the channel are unable to handle large amounts of

rainfall in a short period of time or the model cannot account for large amounts of rainfall within a short

period of time. From Figures 20 and 21 we can see that a large amount of rainfall, roughly 2.5 to 1.75

inches depending on the site, fell within 15 minutes twice during the modeled summer storm. Because

of time constraints the data given from I&S Group in the excel file was not rechecked for calculation

errors and the modeled was calibrated to the best of my ability. The summer storm won’t be included in

the final analysis of the watershed or the installed structures that were put in place to improve the

channel.

Fall Storm

The fall storm modeled much like the spring storm. The observed and simulated hydrographs

matches pretty well and differences were seen in the peak discharges and stage with the simulated

being higher than the observed. Site 7 was added for the summer and fall storm events. The importance

of Site 7 is that it is located at the first overflow weir (Figure 2). This allows for better insight as to how

the overflow weir is affecting the channel and thus how the second overflow weir will affect discharge

into the Cobb River. Site 7 in Figure 24 shows a drastic difference between the observed and simulated

discharge hydrographs for the first portion of rainfall during the storm. The model has a peak discharge

of almost 100 cfs and observed data shows a peak discharge of nearly 25 cfs. The overflow weir at this

location holds water back until the water rises high enough to go over the wall. From the hydrograph we

are able to see that the structure is working because the discharge isn’t nearly as high as what the

model simulated it would be without the structure. The effectiveness of the overflow weir can also be

seen in the stage hydrograph. The simulated data shows stage changing somewhat drastically over the

storm. The observed data is steady in comparison with a peak stage of just under 6 feet.

Sites 4 and 5 are quite similar to Site 7. They show the simulated hydrographs discharging a

greater amount than what the observed data is showing. They also show the stage is significantly

lowered within the channel over the two sites. Site 5 has a simulated peak stage of 9 feet with a peak

observed stage of less than 4 feet. Site 4 is similar with a simulated peak stage of less than 8 feet and an

observed stage of about 2.5 feet. This again gives insight that the installed structures are working to

improve water quality within the channel. Site 2, which is closest to the channel’s outlet, matches the

closest with the simulated discharge hydrograph. The first peak has the biggest difference while the

second peak is less than a 10 cfs difference. There is a slight difference in the stage hydrographs, with

the simulated data being slightly higher than the observed data. Here, peak stage is just over 3 feet but

observed stage has a peak of just above 2.5 feet. With these graphs matching so well and seeing data

from the first overflow weir I was able to create a hydrograph for an additional site, Site 1, at the second

overflow weir, to have a better understand of flow leaving the channel and into the Cobb River (Figure

2).

Observed data for Site 1 was unavailable and therefore observed stage and discharge

hydrographs were unable to be produced to compare to the simulated data. Because Site 1 is located at

the second overflow weir I can assume that the same type of results found in Site 7 should occur for Site

1. Discharge for Site 1 during the first part of the storm should be significantly less than the simulated

45

data shows and may match during the second part of the storm. The same type of pattern should occur

for the stage at Site 1. If this is the case at Site 1 then it is safe to assume that the structure is working

and discharge into the Cobb River should be less than that of previous years. Stage should also decrease

and reduce flooding events into the Cobb River as well. The discharge and stage hydrographs for Site 1

can be seen in Figure 25.

Effectiveness of Installed Structures

From the gathered data and analyzing the stage and discharge hydrographs from both simulated

and observed data I have determined that the structures installed within CD 57 are working to lessen

flooding events and improve overall water quality. The spring and fall storm events showed a decrease

in stage from the observed to the simulated hydrographs. A decrease in stage means the height of the

flow in the channel is less than what the model produced meaning the installed structures are working

to decrease stage and decrease the chance of flooding events. The greatest decrease was seen in Sites 7

and 5 where two of the largest structures were installed, the first overflow weir and the Klein Surge

Pond. Both are supposed to decrease stage in the channel which is shown to be effective from the

simulated and observed stage hydrographs.

The installed structures are also supposed to clean the water; create lower slower flows to allow

for sediment load to settle before being discharged. Analyzing the simulated versus observed discharge

hydrographs this may be true. Peak discharge has decreased and discharge is occurred over a longer

period of time versus the simulated data. From the data I concluded that the structures are working to

decrease discharge throughout the channel which was seen in the simulated versus observed data for all

sites during the spring and fall storms. I cannot fully conclude that the channel is decreasing its sediment

load from these graphs; however it appears that with discharge decreasing and occurring over a longer

amount of time the flow velocity should decrease and thus decrease sediment load.

46

Site 1 Discharge and Stage Hydrographs Fall Storm

Figure 25. Site 1 Discharge and Stage Hydrographs. Simulated

hydrographs were produced for Site 1 during the Fall storm. These

hydrographs were used to see what the model produced for

discharge and stage.

47

Recommendations for Continuing Analysis

County Ditch 57 should continue to be monitored throughout the next few years to ensure the

structures are working to decrease stage and discharge throughout the channel. The observed data for

the summer storm should be rechecked to ensure no calculation errors occurred as well as continuing to

calibrate the model for better results. An additional monitoring site should be added right at the channel

outlet to determine the stage and discharge. By adding this monitoring site we would be able to

determine how much water is being discharged into the Cobb River. We could then compare that data

to the simulated data and analyze whether or not the second overflow weir is effective in decreasing

stage and discharge.

In addition to continuing the monitoring process, I recommend that different types of storms be

modeled and compared to observed data. For this study I modeled the storm in each season with the

greatest amount of rainfall. Storms that produce low to medium flows should be modeled to ensure that

the structures work in all types of rainfall amounts. Another storm that produces a large amount of

rainfall within a short period of time, like the summer storm, should be modeled to check to see if the

model was not able to accommodate for that type of storm or if the data may have been wrong for

those particular dates.

With the additional monitoring sites, rechecking data and modeling different storms the model

could be calibrated to the best of its abilities. The simulated data could then be compared to the

observed data which would give better insight to if the structures are doing their job at decreasing stage

and discharge.

48

References

"AcrGIS Online Help." ESRI, Web 2014. <http://resources.arcgis.com/en/help/main/10.1/>.

Bedient, Philip, Wayne Huber, and Baxter Vieux. Hydrology and Floodplain Analysis . 5 ed. Essex:

Pearson Education Limited, 2013. Print.

Chow. 1959.

I&S Group. Water Quality and Monitoring Work Plan. January 2012.

"Model Theoretical Background." . VFlo, 2002. Web. 2014. <http://vflo.vieuxinc.com/vflo

guide/?q=model-theoretical-background>.

"Vflo Online User Guide ." . Vflo., 2002. Web. 2014. <http://vflo.vieuxinc.com/vfloguide/?q=table-of

contents>

"Watershed Delineation with ArcGIS 10." Trent University, 2002. Jan. 2014.

<https://www.trentu.ca/library/data/DelineateWatersheds_V10.pdf>.