Introduction to stormwater modeling

The foundation of stormwater management is an understanding of how a particular land area and drainage system can affect, and can be affected by, the stormwater passing through it. In particular, when (or preferably before) alterations are made to the land area or drainage network, stormwater managers need to understand and anticipate how the alteration is likely to affect the volume, flow rate, and quality of runoff moving through the system, and in turn, how the stormwater is likely to impact the people, property, and natural resources of the area. Modeling is a tool that can be used to understand and evaluate complex processes.

Purpose of stormwater modeling

Some kind of stormwater model is needed whenever an estimate of the expected volume, rate, or quality of stormwater is desired. Modeling is also often necessary for the design of BMPs and hydraulic structures and for evaluation of the effectiveness of water quality treatment by BMPs. If monitoring data exists for the specific combination of precipitation and site conditions under consideration, modeling may not be necessary. However, in many cases the conditions to be analyzed do not fit precisely with the conditions monitored in the past and modeling will be necessary.

In general models can be physical or numerical. A physical model is a constructed replica of the system whereas a numerical model is based on equations that approximate the processes occurring in the system. Typically, it is not realistic to construct a physical model that would provide reliable hydrologic predictions for a watershed or drainage system, so numerical (nearly always computer-based) models are the standard tool for stormwater management.

Note that this Manual cannot possibly contain a thorough analysis of modeling. Instead, the purpose is to introduce a stormwater manager to the terms of modeling and some cursory assessment of model calibration.

In practice, stormwater models are most commonly used either as planning and decision making aids for water management authorities, or as tools for developers who wish to design for and demonstrate compliance with regulations and principles governing protection of water and waterways. They are used, for example, to predict:

• Water quality effects of various land management scenarios
• Effects of water control structures on water surface elevations in a channel
• Performance of stormwater management structures such as ponds, wetlands, trenches, etc.
• Wetland impacts resulting from channel excavation
• Lateral extents of a floodplain along a channel

These examples show some of the potential uses of modeling, but the list is by no means exhaustive. Modeling in general is a versatile tool that can be applied to any number of situations.

Types of models

The most commonly used stormwater models can generally be classified as either hydrologic, hydraulic, or water quality models.

• Hydrologic models are used to estimate runoff volumes, peak flows, and the temporal distribution of runoff at a particular location resulting from a given precipitation record or event. Essentially, hydrologic models are used to predict how the site topography, soil characteristics, and land cover will cause runoff either to flow relatively unhindered through the system to a point of interest, or to be delayed or retained somewhere upstream. Many hydrologic models also include relatively simple procedures to route runoff hydrographs through storage areas or channels, and to combine hydrographs from multiple watersheds.
• Hydraulic models are used to predict the water surface elevations, energy grade lines, flow rates, velocities, and other flow characteristics throughout a drainage network that result from a given runoff hydrograph or steady flow input. Generally, the output (runoff) from a hydrologic model is used in one way or another as the input to a hydraulic model. The hydraulic model then uses various computational routines to route the runoff through the drainage network, which may include channels, pipes, control structures, and storage areas. Combined hydraulic and hydrologic models provide the functions of both hydraulic models and hydrologic models in one framework. A combined model takes the results from the hydrologic portion of the model and routes it through the hydraulic portion of the model to provide the desired estimates.
• Water quality models are used to evaluate the effectiveness of a BMP, simulate water quality conditions in a lake, stream, or wetland, and to estimate the loadings to water bodies. Often the goal is to evaluate how some external factor (such as a change in land use or land cover, the use of best management practices, or a change in lake internal loading) will affect water quality. Parameters that are frequently modeled include total phosphorus, total suspended solids, and dissolved oxygen.

Limitations of modeling and the importance of calibration

Hydrologic, hydraulic, and water quality models are not exact simulations of the processes occurring in nature. Rather, they are approximate representations of natural processes based on a set of equations simplifying the system and making use of estimated or measured data. The accuracy of a model, therefore, is limited by the quality of the simplifications made to approximate the system processes and the quality of the input data. In some cases, the impact of these limitations can be reduced by using a more complex model or paying to acquire more or better input data. However, it is also important to recognize that oftentimes, it is simply not possible to significantly increase accuracy with such means, because the necessary computational and data collection technology does not exist, and in any case the climatic forces driving the simulation can only be roughly predicted. There also could be time and funding constraints.

File:Illustration of model calibration.jpg

importance of model calibration. Models that are not calibrated to data are likely to be in serious error.

Recognizing the high degree of error or uncertainty inherent in many aspects of stormwater modeling can help to focus efforts where they do the most good. Generally, the goal of stormwater modeling is to provide a reasonable prediction of the way a system will respond to a given set of conditions. The modeling goal may be to precisely predict this response or to compare the relative difference in response between a number of scenarios. The best way to verify that a model fulfills this need (to the required degree of accuracy) is to check it against actual monitoring data or observations (Figure 8.1).

The process of model calibration involves changing the estimated input variables so that the output variables match well with observed results under similar conditions. The process of checking the model against actual data can vary greatly in complexity, depending on the confidence needed and the amount of data available. In some cases, the only feasible or necessary action may be a simple “reality check,” using one or two data points to verify that the model is at least providing results that fall within the proper range. In other cases, it may be necessary to perform a detailed model calibration, to ensure the highest possible accuracy for the output data. For some models, calibration is unnecessary due to the design of the model.

Calibration should not result in the use of model parameters that are outside a reasonable range. Additionally, models should not be calibrated to fit so tightly with observed data that the model loses its flexibility to make estimates under other climatic conditions.

Minnesota model input guide

The section on unified sizing criteria, outlines recommendations for sizing best management practices. The following sources of information will allow designers to use the above referenced models for estimating hydrologic, hydraulic, or water quality parameters.

Data resources

Precipitation

The most commonly referenced precipitation frequency study in Minnesota is the U.S. Weather Bureau’s 1961 Technical Publication 40 (TP-40, Hershfield, 1961). Despite potential doubts regarding the adequacy of TP-40, which is viewed by some as outdated and not reflective of recent climate trends, TP-40 remains the dominant source for Minnesota precipitation magnitude and return frequency. Isopluvial maps showing precipitation depths corresponding to the following 24-hour return events over the entire state are included in TP-40.

• 1-year design storm
• 2-year design storm
• 5-year design storm
• 10-year design storm
• 25-year design storm
• 100-year design storm

Design engineers typically make use of precipitation exceedence probability to calculate the risks of design failure for channel protection, over-bank flooding, and extreme flooding. A storm magnitude of a return period (T) has the probability of being equaled or exceeded in any given year is equal to 1/T. For example a “100-year” event at a given location has a chance of 1/100 or 0.01 or 1% of being equaled or exceeded in any given year.

More recent work by others to update, test and/or validate the TP-40 findings include precipitation frequency studies conducted by the Midwest Climate Center (Huff and Angels’ 1992 Bulletin 71), Metropolitan Council’s Precipitation Frequency Analysis for the Twin Cities Metropolitan Area (study updates in 1984, 1989, and 1995), and Mn/DOT’s November 1998 study Intensity of Extreme Rainfall over Minnesota in coordination with Richard Skaggs from the University of Minnesota.

In addition to the frequency analysis studies, an impressive source of historical (and current) precipitation data and other climate data for Minnesota has been compiled by the Minnesota Climatology Working Group.

Climate trends

According to Dr. Mark Seeley, University of Minnesota, sufficient data exist to support recently observed trends of climate change in Minnesota. Notable changes over the last 30 years include:

• Warmer winters.
• Higher minimum temperatures.
• Increased frequency of tropical dew points.
• Greater annual precipitation with:
  • More snowfall.
  • More frequent heavy rainstorm events.
  • More days with rain.

The increasing precipitation and snowfall trends suggest the need for an updated Minnesota precipitation study.

Topographic data

General topographic information can be obtained from USGS topographic maps. The USGS topographic maps display topographic information as well as the location of roads, lakes, rivers, buildings, and urban land use. Paper or digital maps can be purchased from local vendors or ordered on the USGS Web site. Counties often have more detailed topographic information available in a format suitable for use in Geographic Information systems (GIS). Additionally, topographic data suitable for GIS use for the metro area and statewide may be available from MetroGIS and the MN DNR. To acquire detailed topographic data for a site, a local survey may need to be completed.

Soils and surficial geology

Data on soils can be obtained from county soil surveys completed by the USDA Natural Resources Conservation Service (NRCS). These reports describe each soil type in detail and include maps showing the soil type present at any given location. A list of soil surveys available for Minnesota can be found on the NRCS Web site. Soils information could also be obtained by conducting an onsite soil survey, by conducting soil borings, and by evaluating well logs. Other sources of soils information, such as dominant soil orders, may be obtained from the Land Management Information Center, the MN DNR, or from MetroGIS. Information on [[|surficial geology can be obtained from the Minnesota Geological Survey.

Land cover and land use

Land cover and land use information can be obtained from the local planning agency such as the county or city of interest but may also be available in the sources listed by the Land Management Information Center www.lmic.state.mn.us/chouse/land_use.html, the DNR http://deli.dnr.state.mn.us/data_catalog.html, and MetroGIS www.datafinder.org/index.asp.

Monitoring data

Monitoring data can be used as model input and for model calibration. Data on lake levels, ground water levels, stream flow, and water quality can be obtained from local monitoring studies or from such agencies as the Department of Natural Resources (DNR), United States Geologic Survey (USGS), Minnesota Pollution Control Agency (MPCA), and the Metropolitan Council for the Twin Cities metro area.

Input guidance

Rainfall distribution

Storm distribution is a measure of how the intensity of rainfall varies over a given period of time. For example, in a given 24 hour period, a certain amount of rainfall is measured. Rainfall distribution describes where that rain fell over that 24 hour period; that is, whether the precipitation occurred over a one hour period or over the entire 24 hours.

The standard rainfall distribution used for urban areas in Minnesota for sizing and evaluation of BMPs is the Natural Resource Conservation Service’s (NRCS) recommended SCS Type II rainfall distribution for urban areas. This is a synthetic event, created by the SCS (now the NRCS), of a 24-hour duration rainfall event in which the peak intensity falls in the center of the event (at 12 hours).

The advantage of using the synthetic event is that it is appropriate for determining both peak runoff rate and runoff volume. Drawbacks of using a synthetic event are that they rarely occur in nature and are difficult to explain. Observed precipitation data can be used if analysis with a natural distribution is desired.

Further information regarding rainfall distribution can be found in the Minnesota Department of Transportation’s Drainage Manual and in the Hydrology Guide for Minnesota prepared by the Soil Conservation Service (now the NRCS).

Water quality event

Small storms are often the focus of water quality analysis because research has shown that pollution migration associated with frequently occurring events accounts for a large percentage of the annual load. This is because of the “first flush” phenomenon of early storm wash-off and the large number of events with frequent return intervals. Rain events between 0.5 inches and 1.5 inches are responsible for about 75 percent of runoff pollutant discharges (MPCA, 2000).

The rainfall depth corresponding to 90 percent and 95 percent of the annual total rainfall depth shows surprising consistency among six stations chosen to represent regional precipitation across the State. The six stations analyzed were Minneapolis/St. Paul International Airport, St. Cloud Airport, Rochester Airport, Cloquet, Itasca, and the Lamberton SW Experiment Station. The rainfall depth which represents 90% and 95% of runoff producing events was 1.09 inches (+/- 0.04 inches) and 1.46 inches (+/- 0.08 inches), respectively. This rainfall depth can be used for water quality analysis throughout the state.

Larger events such as the spring snowmelt, however, can be the single largest water and pollutant loading event in the year. In Minnesota, this spring snowmelt occurs over a comparatively short period of time (i.e., approximately two weeks) in March or April of each year – depending on the region of the state. The large flow volume during this event may be the critical water quality design event in much of the state. See Chapter 2 for a further discussion of snowmelt runoff variation across the state and Chapter 9 for the problems associated with snowmelt.

Technical Bulletin 333, Climate of Minnesota (Kuehnast, 1982), shows that the average annual date of snowmelt can be represented by the last date of a 3 inch snow cover. This document also includes figures that allow estimation of the average depth of snowpack at the start of spring snowmelt plus the water content of the snowpack during the month of March.

The estimated infiltration volume can be determined from research in cold climates by Baker (1997), Buttle and Xu (1988), Bengtsson (1981), Dunne and Black (1971), Granger et al. (1984) and Novotny (1988). This research shows that infiltration does in fact occur during a melt at volumes that vary considerably depending upon multiple factors including: moisture content of the snow pack, soil moisture content at the time the soil froze, plowing, sublimation, vegetative cover, soil properties, and other snowpack features. For example, snowmelt investigations by Granger et al. (1984) took measurements from 90 sites, located in Saskatchewan Canada, representing a wide range of land use, soil textures, and climatic conditions. From this work, general findings showed that even under conservative conditions (wet soils, ~35 percent moisture content, at the time of freeze) about 0.4 inches of water infiltrated during the melt period from a one-foot snowpack with a 10 percent moisture content (1.2 inches of equivalent moisture) in areas with pervious cover. This would not apply to impervious surfaces.

The average snowmelt volume can then be estimated using the equation below (see Chapter 2, Figures 2.6 and 2.7 for input variables)

Other procedures for estimating water quality treatment volume based on annual snow depth are described by the Center for Watershed Protection (CWP) (Caraco and Claytor, 1997), which is available as a free download from the CWP Web page at www.cwp.org/cold-climates.htm. More snowfall and snowmelt data can be found in the a [www.climate.umn.edu/snow_fence/Components/SWE/marswe.htm# report] sponsored by the Minnesota Department of Transportation.

For purposes of determining the volume of runoff or snowmelt that should be managed by the site BMPs, designers must make two water quality volume computations: snowmelt and rainfall runoff. The BMP would then be sized for the larger of the two results. Areas with low snowfall will likely find that the rainfall based computations are the larger value, while those areas with greater snowpack will find that snowmelt is larger.

In some cases snowmelt would be selected as the design parameter for computing the volume, whereas other options lead to rainfall as the critical design parameter (see Unified sizing criteria.

Extreme flood events

Because a spring melt event generates a large volume of water over an extended period of time, evaluation of the snowmelt event for channel protection and over-bank flood protection is generally not as important as the extreme event analysis. This warrants attention because of the possibility that a major melt flooding event could, and sometimes does, happen somewhere in the state.

Conservative design for extreme storms can be driven by either a peak rate or volume event depending upon multiple hydraulic factors. Therefore, depending upon the situation, either the 100-yr, 24-hr rain event or the 100-yr, 10-day snowmelt runoff event can result in more extreme conditions. For this reason, both events should be analyzed.

Protocol for simulation of the 100-yr, 24-hr rainfall event is well established in Minnesota. High water elevations (HWL) and peak discharge rates are computed with storm magnitudes based on TP-40 frequency analysis and the SCS Type II storm distribution. Protocol has been established for the analysis of HWL and peak discharge resulting from a 7.2 inch 100-yr, 10-day snowmelt runoff event. However, this event has received a considerable amount of criticism. Although not well documented, it is thought that the theoretical snowmelt event was devised by assuming a six inch 100-yr, 24-hr rainfall event occurs during a 10-day melt period in which one foot of snow (with a 10 percent moisture content) exists at the onset. A typical assumption accompanying the event is that of completely frozen ground (no infiltration) during the melt period for which the result is 100 percent delivery of volumes. So what do we use? Climate records show that the highest rain event during this common melt period over the past 100+ years was 4.75 inches. An alternative method to consider is to add 4.75 inches of precipitation to the site’s snowmelt volume (including infiltration). Designers should compare this to the 7.2 inch, 10-day snowmelt volumes and then determine which is best for the site.

Protocols for computation of extreme snowmelt events should be established as part of a state-wide precipitation study that has been discussed to update TP-40.

Runoff coefficient

The Rational Method is used to estimate peak runoff rates for very small sites. The simple equation for peak discharge (cubic feet per second) is Q=CiA, where C is a runoff coefficient, i is rainfall intensity in inches per hour, and A is drainage area in acres. The chosen value of C must represent losses to infiltration, detention, and antecedent moisture conditions. Additionally, C varies with the frequency of the rainfall event. Tabled values for C are shown below.

Runoff coefficients for 5 to 10 year storms Template:Runoff coefficients for 5 to 10 year storms

Curve numbers

Curve numbers are used in the SCS Method to represent the runoff expected after initial abstractions and infiltration into the soil. Curve numbers are based on land use and hydrologic soil group. The SCS (now the NRCS) developed tables with curve numbers appropriate for urban, agricultural, arid and semiarid rangeland, and undisturbed land uses. Hydrologic soil group can be determined from soil surveys.

Curve number tables are published in TR-55: Urban Hydrology for Small Watersheds (ftp://ftp.wcc.nrcs.usda.gov/downloads/hydrology_hydraulics/tr55/tr55.pdf) but are also available in textbooks and within modeling software.

Curve numbers vary for smaller storms (see discussion in SLAMM documentation: http://www.unix.eng.ua.edu/~rpitt/SLAMMDETPOND/WinSlamm/Ch2/Ch2.html.) A short summary of some more commonly used curve numbers is given in Table 8.4.

The selection of appropriate curve numbers is of great importance when using the SCS Method. Sizing of facilities and comparisons of existing or pre-development conditions to proposed developed conditions can depend highly on the selected curve numbers. MPCA uses the land cover in place immediately before the proposed project as the “pre-development condition”. Many other regulators use a more natural condition to reflect change from pre-European settlement times (See box on previous page). The hydrologic soil group of the native soils should be used for pre-development conditions, but developed conditions may alter the soil condition by compaction, fill, or soil amendments. In the more conservative, natural definition of pre-development condition, land use would be meadow or woods in good condition as appropriate to the natural state of the site. Chapter 10 contains further discussion of the option for defining pre-development conditions. Special care should be taken to identify areas of soil group D and areas of open water as these areas have high levels of runoff. Care must also be taken when selecting curve numbers for agricultural land as its use can change considerably annually and even over the course of a season.

:A. Composite Curve Numbers According to the NRCS (TR-55, 1986), curve numbers describe average conditions for certain land uses. Urban area curve numbers are a composite of grass areas (assumed to be pasture in good condition) and directly connected impervious areas. TR-55 guidance documentation recommends that curve numbers be adjusted under certain conditions:

• When the percentage of impervious cover differs from the land use contained in curve number tables.
• When the impervious area is unconnected.
• When weighted curve number is less than 40.
• When computing snowmelt on frozen ground.

:NRCS advises that the curve number procedure is less accurate when runoff is less than ½ inch. Other procedures should be followed to check runoff from these smaller events. One technique could be to compute runoff from pervious and impervious areas separately, with unique rather than composite curve numbers. Specific guidance is available in NRCS Technical Release 55 (available at NRCS National Water and Climate Center).

B. Antecedent Moisture Conditions

Antecedent moisture conditions (AMC) describe the moisture already present in the soil at the time of the rain event. AMC level I represents dry conditions, level II represents normal conditions, and level III represents wet conditions. Normal conditions are defined as 1.4 to 2.1 inches of rainfall in the growing season in the five days preceding the event of interest. Most evaluations of expected future site conditions use the curve numbers appropriate to AMC II. However, if the specific conditions of interest are expected to differ, curve numbers appropriate to AMC I or III should be used.

Infiltration rates

Infiltration is the process of water entering the soil matrix. The rate of infiltration depends on soil properties, vegetation, and the slope of the surface, among other factors. Discussions of infiltration often include a discussion of hydraulic conductivity. Hydraulic conductivity is a measure of ease with which a fluid flows through the soil, but it is not the infiltration rate. The infiltration rate can be determined using the hydraulic conductivity through the use of the Green-Ampt equation. The Green-Ampt equation relates the infiltration rate as it changes over time to the hydraulic conductivity, the pressure head, the effective porosity, and the total porosity. Typical values used in the Green-Ampt equation can be found in Rawls, et al. (1983).

A simple estimate of infiltration rates can be made based on the hydrologic soil group or soil texture (Table 8.5). These infiltration rates represent the long-term infiltration capacity of a constructed infiltration practice and are not meant to exhibit the capacity of the soils in the natural state. The recommended design infiltration rates fit within the range of infiltration rates observed in infiltration practices operating in Minnesota (Table 8.6). The length of time a practice has been in operation, the location within the basin, the type of practice, localized soil conditions and observed hydraulic conditions all affect the infiltration rate measured at a given time and a given location within a practice. The range of rates summarized in Table 8.6 reflects the variation in infiltration rate based on these types of factors. Information on measuring infiltration rates and the use of the numbers presented in Table 8.5 can be found in the infiltration section in Chapter 12 of this manual.

Event mean concentrations

Event mean concentrations (EMCs) of a particular pollutant (i.e. total phosphorus, total suspended solids) are the expected concentration of that pollutant in a runoff event. Along with runoff volume, EMCs can be used to calculate the total load of a pollutant from a specific period of time. EMCs are frequently based on land use and land cover, with different predicted pollutant concentrations based on the land use and/or land cover of the modeled area.

Table 8.7 lists EMCs for total phosphorus (TP) that were reported in Pitt et al. (2004). EMCs can range by an order of magnitude for a given land use, an it is therefore best to have site-specific or comparable local data for calibration purposes. The EMCs in the Pitt et al. study were from the National Stormwater Quality Database (NQSD, Version 1.1). Note also that EMCs are concentration data, which are only part of the overall loading equation. Although some land uses might have a high EMC, for example open space at 0.27-0.31 mg/l, little runoff occurs from this land so overall phosphorus loading is low.

References

• Baker, J.M., 1997. Vanishing Ponds Not a Sure Sign of Spring. Agricultural Research, April, p.9.
• Bengtsson, L., 1981. Snowmelt-Generated Runoff in Urban Areas. In Proceedings, Second International Conference on Urban Storm Drainage, Urbana, Illinois, June 14-19, 1981, pp.444-451.
• Bouwer, H. and R. C. Rice. 1989. Effect of Water Depth in Ground-water Recharge Basins on Infiltration. Journal of Irrigation and Drainage Engineering, Vol. 115, No. 4, pp. 556-567.
• Buttle, J.M. and F. Xu, 1988. Snowmelt Runoff in Suburban Environments. Nordic Hydrology, 19:19-40.
• Caraco, D. and R. Claytor, 1997. Stormwater BMP Design Supplement for Cold Climates. Center for Watershed Protection, Ellicott City, Maryland.
• Dunne, T. and R.D. Black, 1971. Runoff Processes During Snowmelt. Water Resources Research, 7(5): 1160-1172.
• Granger, R.J., D.M. Gray and G.E. Dick, 1984. Snowmelt Infiltration to Frozen Soils. Canadian Journal of Earth Science, 21:669-677.
• Haan, C., B. Barfield, J. Hayes, 1994. Design Hydrology and Sedimentology for Small Catchments. Academic Press, San Diego.
• Hershfield, D.M., 1961. Rainfall Frequency Atlas of the United States for Durations from 30 Minutes to 24 Hours and Return Periods from 1 to 100 Years. U.S. Weather Bureau, Technical Publication 40.
• Huff and Angels, 1992. Bulletin 71. Midwest Climate Center.
• Metropolitan Council, 1995. Precipitation Frequency Analysis.
• Minnehaha Creek Watershed District, 2003. Hydrologic, Hydraulic, and Pollutant Loading Study.
• Minnesota Department of Transportation, Drainage Manual, 2000.
• Minnesota Department of Transportation, 1998. Intensity of Extreme Rainfall over Minnesota.
• Minnesota Pollution Control Agency, 2000. Protecting Water Quality in Urban Areas. Best Management Practices for Dealing with Storm Water Runoff from Urban, Suburban, and Developing Areas of Minnesota. St. Paul, MN.
• Natural Resources Conservation Service, 1986. Urban Hydrology for Small Watersheds, Technical Release 55 (TR-55). ftp://ftp.wcc.nrcs.usda.gov/downloads/hydrology_hydraulics/tr55/tr55.pdf
• Natural Resources Conservation Service. 1975. Minnesota Hydrology Guide. www.mn.nrcs.usda.gov/technical/eng/pdf/mhgweb.pdf
• National Resource Conservation Service, 1997. National Engineering Handbook, Part 630, Hydrology. NRCS National Water and Climate Center. www.wcc.nrcs.usda.gov/hydro/hydro-tools-models-tr55.html
• Novotny, V., 1988. Modeling Urban Runoff Pollution During Winter and Off-Winter Periods. In Advances in Environmental Modeling, A. Marani (Editor), Elsevier Publishing, Amsterdam, pp.43-58.
• Pitt, R., A. Maestre, and R. Morquecho, 2004. The National Stormwater Quality Database (NSQD, Version 1.1). Department of Civil and Environmental Engineering. University of Alabama, Tuscaloosa.
• Rawls, W., D. Brakensiek, and N. Miller, 1983. Green-Ampt infiltration parameters from soils data. Journal of Hydraulic Engineering. Vol. 109, No. 1, pp. 62 – 70.
• Rawls, W., D. Brakensiek, and K. Saxton, 1982. Estimation of Soil Water Properties. Transactions of the American Society of Agricultural Engineers. Vol. 25, No. 5, pp. 1316 – 1320 and 1328.
• Rawls, W., D. Giminez, and R. Grossman, 1998. Use of Soil Texture, Bulk Density and Slope of water Retention Curve to Predict Saturated Hydraulic Conductivity. ASAE. Vol. 41(2), pp. 983 – 988.
• Soil Conservation Service, 1975. Hydrology Guide for Minnesota.
• U.S. Environmental Protection Agency, 1997. Compendium of Tools for Watershed Assessment and TMDL Development. EPQ 841-B-97-006, Office of Water (4503F), Washington, D.C.