A Drain Spacing Tool That Estimates the Optimum Subsurface Drain Spacing for Maximum Profit

Ehsan Ghane^1,*, A. Pouyan Nejadhashemi¹, Ian Kropp²

---

Published in Journal of the ASABE 66(2): 397-402 (doi: 10.13031/ja.15406). Copyright 2023 American Society of Agricultural and Biological Engineers.

---

¹Biosystems and Agricultural Engineering, Michigan State University, East Lansing, Michigan, USA.

²Computer Science, Ohio Northern University, Ada, Ohio, USA.

^*Correspondence: ghane@msu.edu

The authors have paid for open access for this article. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License https://creative commons.org/licenses/by-nc-nd/4.0/

Submitted for review on 16 October 2022 as manuscript number NRES 15406; approved for publication as a Research Brief and as part of the “Advances in Drainage: Selected Works from the 11th International Drainage Symposium” Collection by Community Editor Dr. Zhiming Qi of the Natural Resources & Environmental Systems Community of ASABE on 18 January 2023.

Highlights

• An empirical equation was embedded in a user-friendly tool to estimate the site-specific design drainage rate.
• The site-specific design drainage rate was based on the local soil, weather, and economics of the area of interest.
• The tool uses the site-specific design drainage rate to estimate the optimum drain spacing.
• The optimum drain spacing maximizes the economic return on investment.

Abstract. Properly estimating the subsurface drain spacing is critical to optimizing crop production. The Hooghoudt equation can be used in humid climates to approximate the drain spacing. However, the application of this equation has been limited due to site-specific data requirements and because it is a complicated process that is not usually practical for practitioners. Traditionally, drainage contractors have chosen a drain spacing without using the Hooghoudt equation. The objective of this article is to develop a user-friendly decision-support tool that estimates the site-specific optimum drain spacing for maximum economic return on investment. We developed the Drain Spacing Tool for the Midwest USA based on the Hooghoudt equation and site-specific inputs. The tool automatically acquires the site-specific equivalent saturated hydraulic conductivity of the soil profile and depth to the restrictive layer from the gSSURGO database, and the user manually enters the desired drain depth. The site-specific input of design drainage rate (DDR), that is required in the Hooghoudt equation, is estimated from an empirical equation that was developed from a DRAINMOD modeling study. The site-specific inputs for the empirical equation include site-specific 30-year average growing-season rainfall, drain depth, equivalent saturated hydraulic conductivity, and depth to the restrictive layer, all of which are automatically acquired from gSSURGO, except for the rainfall data, which was acquired from the PRISM Climate Group. The site-specific DDR value from the empirical equation was then used in the Hooghoudt equation to estimate the optimum drain spacing that maximizes economic return on investment. In conclusion, the tool estimates the site-specific optimum drain spacing based on the local soil, weather, and economics of the area of interest.

Keywords. Decision-support tool, Design drainage rate, DRAINMOD, Farm profitability, Tile drainage.

The design of the subsurface drain spacing is important to optimize crop production. Drain spacing is an important design decision that affects crop productivity by dictating how fast water is removed from the soil (Ghane and Askar, 2021; Skaggs, 2017). Choosing a drain spacing that is too wide leads to under-designing the drainage system, resulting in overly slow water removal and a potential decline in crop yield (Skaggs, 2007). On the other hand, choosing a drain spacing that is too narrow leads to an over-designed drainage system. As a result, this would lead to more nutrient loss, extra unnecessary capital costs for the drainage system, and overly quick water removal that may cause yield decline due to depriving the crop of much-needed water during the growing season (Skaggs, 2007). The overly quick water removal will also increase peak flow and the chance of downstream flooding (Ghane and Askar, 2021). Therefore, there is a need to estimate the drain spacing that removes no more or less than the necessary amount of water to optimize crop production.

The Hooghoudt equation can be used in humid climates to approximate drain spacing (Ghane, 2022a). However, the application of the Hooghoudt equation in drainage design has been limited due to its requiring site-specific inputs and being a complicated process, which is not usually practical for practitioners. Traditionally, drainage contractors have chosen a drain spacing without using the Hooghoudt equation. A decision-support tool allows for easy use of complicated equations to estimate drain spacing. Therefore, there is a critical need for a decision-support tool to estimate the optimum drain spacing that maximizes economic return on investment (i.e., maximum profit).

The objective of this study is to create a user-friendly decision-support tool that estimates the ideal drain spacing for a given site in order to maximize the financial return on investment. The value of this tool lies in its ability to predict the site-specific optimum drain spacing based on the soil, climate, and economics of the field of interest.

Description of the Tool

An empirical Equation for Estimating the Design Drainage Rate

The Drain Spacing Tool estimates the Design Drainage Rate (DDR) using an empirical equation developed by Ghane et al. (2021). The equation maximizes economic return on investment based on the local soil, weather, and economics of the field of interest. Furthermore, the equation was developed based on DRAINMOD modeling results from simulating continuous corn production with three drain depths, three effective radii, and five soils at four locations in the northeast USA. The four locations were chosen to cover a wide range of climates, and those included Waseca, Minnesota; Urbana, Illinois; Lansing, Michigan; and Albany, New York. Modeling data were used to select the optimum drain spacings that maximized the annual return on investment for each combination of factors. The economic analysis considered annual corn production income, annual corn production costs, and annual drainage system costs. Then, the optimum drain spacing for each combination of factors was used to calculate the DDR that maximized the economic return on investment. The results were then used in a multiple linear regression analysis to develop an empirical equation. For the Midwest USA, the equation is written as:

(1)

where

DDR = design drainage rate, defined as the rate when the water table is midway between lateral drain pipes and is at the soil surface (cm/day)

P_g = long-term average growing-season precipitation from one month prior to planting to four months after planting (mm)

D_d = drain depth from the soil surface to the drain center (cm)

K_e = equivalent saturated hydraulic conductivity of the soil profile (cm/day)

D = depth to restrictive layer from the soil surface (cm).

Growing-season precipitation (Pg)

The 30-year average precipitation was obtained from the PRISM Climate Group (PRISM Climate Group, 2021) in the form of an 800-m gridded dataset. The dataset was resampled into 10-m cells to match the spatial resolution of the soil dataset. The tool uses input dates for calculating precipitation during the growing season. If the user draws an area of interest that covers two or more cells, the tool calculates the area-weighted precipitation for that area of interest.

Depth to restrictive layer (D)

We used the gSSURGO database to provide the 10-m cells of the depth to the restrictive layer (Soil Survey Staff, 2020). If the user draws an area of interest that covers two or more 10-m cells, the tool calculates the area-weighted D for that area of interest. If the gSSURGO database provides a depth to the restrictive layer greater than 200 cm, we used 305 cm as the depth to the restrictive layer (MN Drainage Guide 1984).

Equivalent saturated hydraulic conductivity (Ke)

We used the gSSURGO database to create a K_e raster. The K_e is the depth-weighted average saturated hydraulic conductivity from the soil surface to the restrictive layer. To create the K_e raster, we used the Soil Data Development Toolbox (USDA-NRCS, 2016). The Soil Data Development Toolbox is an open-source plugin to ArcGIS Desktop and allows users to easily extract data from the raw gSSURGO database. Each tool includes an easy-to-use user interface that walks users through the required steps for data extraction. Among the many tools within the Soil Data Development Toolbox, this project utilized the Create Soil Map tool to create the required K_e raster. However, the Create Soil Map tool requires a depth for the restricted layer (D) to create the K_e and only accepts a single D value. Since the study area covers the Midwest, there is a large spatial variation in the D value. To develop a unique K_e value for each raster point, we performed a custom-made analysis within ArcGIS desktop. To the best of our knowledge, this was a novel procedure for generating a multi-state K_e raster. This analysis began by first calculating K_e for 31 different D scenarios using the Create Soil Map Tool. The 31 different D scenarios included 0-50 cm, 0-55 cm, and at 5 cm intervals up to 0-200 cm. Using the D raster, we chose the respective K_e that was closest to the D raster among the multiple K_e values for each raster point. For example, for a given raster point, our algorithm chooses among 31 possible K_e values for each of the 0-50 cm, 0-55 cm, 0-60 cm, 0-65 cm, and so on up to 0-200 cm at 5-cm intervals. Then, in this example, if the D value for that respective raster is 64 cm, we chose the K_e that was calculated for the 0-65 cm. As a result, we generated a raster map of K_e values for the entire study area, where each K_e raster point corresponds with its respective D value. If the user draws an area of interest that covers two or more cells, the tool calculates the area-weighted K_e for that area of interest.

Economic component

In the basic version of the tool, the economic input option is turned off. In that case, the default equation 1 regression coefficients are used to estimate the design drainage rate (Ghane et al., 2021).

When the economic input option is turned on, the tool calculates customized equation 1 regression coefficients based on the economic user inputs related to the corn and drainage system (see subsection Optional advanced economic inputs). In other words, the tool performs a custom multiple linear regression to replace the default regression coefficients of equation 1 every time the user enters a set of economic inputs. The regression variables P_g, D_d, K_e, and D would remain constant with every set of economic user inputs for a given site, and only the DDR would vary because it is a function of the economic inputs. The economic inputs influence the DDR calculation by affecting the drain spacing at which the maximum annual return on investment (i.e., optimum drain spacing) is achieved for every set of economic user inputs. To determine the optimum drain spacing for every set of economic user inputs without having to run DRAINMOD on the fly, we stored a database of DRAINMOD simulations that included relative yields for every 0.5-m-interval drain spacing for each combination of factor (drain depth, effective radius, location, soil). Then, the results are used in a multiple linear analysis to determine a custom empirical equation that will replace the default equation 1.

Figure 1. User interface of Drain Spacing Tool. Steps are shown for using basic version of tool to determine optimum drain spacing (image courtesy of [Ghane, 2022b]).

Equation for Estimating the Optimum Drain Spacing

The design drainage rate from the default empirical equation 1 (when economic inputs are turned off) or the custom empirical equation (when economic inputs are turned on) is used in the Hooghoudt equation to estimate the optimum drain spacing. The Hooghoudt equation is written as calculated by Ghane et al. (2021):

(2)

where

S_o = optimum drain spacing (cm)

DDR = design drainage rate estimated from equation 1 (cm/day)

K_e = equivalent saturated hydraulic conductivity of the soil profile (cm/day)

d_e = equivalent depth (cm)

D_d = drain depth from the soil surface to the drain center (cm).

An empirical Equation for Estimating Drainage Discharge

The Drain Spacing Tool estimates drainage discharge based on an empirical equation developed by Ghane and Askar (2021). This empirical equation was developed based on stepwise regression of the same DRAINMOD simulation data described in the previous section. The empirical equation is written as:

(3)

where

DD = long-term average annual drainage discharge (cm)

P = 30-year average annual precipitation (cm)

DDR = design drainage rate that is equal to drainage intensity (cm/day)

S_o = optimum drain spacing (cm)

K_e = equivalent saturated hydraulic conductivity (cm/day).

The 30-year average annual precipitation was obtained following the same procedure as the growing-season precipitation.

Tool Inputs and Outputs

The online tool has two main geographical layers (Soil Survey Staff, 2020) (fig. 1). The first layer includes information about the drainage class along with other soil properties. The second layer shows shaded areas that do not need subsurface drainage because of their drainage class. This layer is a combination of three drainage classes, including excessively drained, somewhat excessively drained, and well-drained soils. For soils that fall outside of that shaded layer, there may be a need for subsurface drainage. For these soils, the user will use the tool to estimate the optimum drain spacing based on local conditions for any rotation of corn and soybean.

A summary of the inputs and outputs of the tool is presented in table 1. The design drain depth is the distance from the soil surface to the bottom of the drain. To convert the design drain depth to the drain depth (D_d) used in equation 1, we considered an outside radius of 5.8 cm for a 100-mm (4-inch) drain pipe. The target corn planting date is the 30-year average corn planting date for the region where the point of interest is located. On the outputs page, the drainage intensity output is equal to the design drainage rate estimated from equation 1.

Optional Advanced Inputs

In the advanced interface of the tool, the user can enter optional customized inputs as presented in figure 2. The type of the drain pipe depends on the perforation pattern and shape, and the selection of a drain pipe affects water flow into the drains, thereby affecting drain spacing (Ghane et al., 2022). The tool automatically obtains the depth to the restrictive layer from the gSSURGO database. When the database-provided depth to respective layer is greater than 2.0 m or the depth is unavailable, the tool assumes a value of 3.05 m to perform the calculations. If the default depth to the restrictive layer is unsatisfactory to the user, the tool allows the user to enter a custom depth. The tool automatically obtains the equivalent saturated hydraulic conductivity from the gSSURGO database. If the default hydraulic conductivity is unsatisfactory to the user, the tool allows the user to enter a custom value to tailor the results to local conditions.

When the economic input option is turned on, the user must enter economic inputs as shown in figure 3. Once these economic inputs are entered, the annual corn production income is calculated by multiplying relative yield by potential yield by corn price. The potential yield is a user input that represents the regional yield of the Midwest USA. The potential yield is the maximum yield possible if soil water stresses are eliminated (that is, if the crop is planted on time, and there is no deficit and excessive water stresses) (Skaggs et al., 2006). The relative yield is automatically provided by the tool’s database (see subsection, An empirical equation for estimating the design drainage rate).

Figure 2. Screenshot of advanced inputs of tool.

The annual cost is composed of the annual corn production cost and the average annual drainage system cost. The average annual drainage system cost was calculated by amortizing the initial cost (i.e., material and installation) over the life of the system at a certain interest rate plus the annual maintenance cost. The average annual drainage system (AADSC) ($/ha) cost was calculated in Ghane et al. (2021) as follows:

(4)

where

L_L= Length of lateral needed per hectare (m), which is calculated from dividing 10,000 m² by drain spacing in meter

ICDS = initial cost of the drainage system ($/m), which is the sum of the drain pipe material and installation costs

IRAI = interest rate on average investment per year (decimal)

DEP = depreciation per year based on a certain lifetime of the system (decimal). For example, a system with an assumed 30-year lifetime has a 3.3% (1/30) depreciation

MR = maintenance rate per year (decimal).

Table 1. Summary of the inputs and outputs of the Drain Spacing Tool.
Required Inputs	Optional Advanced Inputs	Optional Advanced Economic Inputs	Tool Outputs	Optional Advanced Outputs
Design drain depth	Type of 4-inch drain pipe	Potential yield	Optimum drain spacing	30-year average annual precipitation
Target corn planting date	Depth to restrictive layer	Corn price	Drainage intensity	30-year average growing-season rainfall
	Equivalent saturated hydraulic conductivity	Cost of the 4-inch drain pipe	Estimated length of 4-inch drain pipe	Depth to restrictive layer
		Cost of the 4-inch drain pipe with a knitted sock	Estimated initial cost of system	Equivalent saturated hydraulic conductivity
		Cost of 4-inch drain installation	Estimated long-term average annual drainage discharge	Design discharge
		Interest rate	Drained-field area	Corn cost
		Maintenance rate		Cost of drain installation
		Expected lifetime of system		Cost of 4-inch drain pipe

The Drain Spacing Tool estimates the optimum drain spacing. To our knowledge, this is the first GIS-based tool that estimates the site-specific optimum drain spacing based on the local soil, weather, and economics of the field of interest. This tool provides the benefit of helping avoid drain spacings that are too narrow, which would otherwise increase the amount of water drained and nitrate loss (Kladivko et al., 2004; Skaggs, 2017).

To use the tool, follow these steps:

1. Go to https://www.egr.msu.edu/bae/water/drainage/tools. Click on the Drain Spacing Tool.
2. Navigate to the field of interest. Turn on the “USA Soil Survey” layer in the bottom-right panel.
3. Enter inputs for “Target corn planting date” and “Design drain depth.” To enter additional tools, click on “Other advanced inputs.”
4. Select the polygon shape and draw on the input panel around the field of interest.
5. Click “Calculate.” Tip: If the area of interest has multiple soil types, draw a polygon inside one soil type, and click “Calculate.” Repeat this for each soil type. Finally, choose your desired spacing.

Figure 3. Screenshot of advanced economic inputs of tool.

Considerations When Using the Tool

This tool can be used for any rotation of corn and soybeans. It should not be used for vegetables, small grains, and other crops because empirical equation 1 does not support those crops. The tool’s accuracy in estimating the optimum drain spacing relies on several factors, including empirical equation 1, PRISM weather data, gSSURGO data, and user inputs. Due to the uncertainty involved in each of those factors, we recommend using the tool’s estimate of optimum drain spacing as an initial guide for drainage design. That is, we recommend choosing a final drain spacing within 1.5 and 2.0 m of the tool’s estimated spacing. To improve the tool’s estimate, we recommend verifying the farm’s soil properties and using the advanced input setting to tailor the tool to the site-specific soil conditions.

Conclusions

Due to the lack of application of the Hooghoudt equation in subsurface drainage design, we developed a user-friendly tool to estimate the optimum drain spacing for any farm in the Midwest USA. The tool estimates the site-specific design drainage rate based on an empirical equation that maximizes the economic return on investment. Then, the tool uses the site-specific design drainage rate in the Hooghoudt equation to estimate the site-specific optimum drain spacing for maximum economic return on investment. The value of this tool lies in its ability to predict the site-specific optimum drain spacing based on the local soil, weather, and economics of the field of interest.

Acknowledgments

Dr. Ehsan Ghane contributed to the conceptualization of the tool. Ian Kropp, Dr. Amir Pouyan Nejadhashemi, and Dr. Babak Saravi contributed to the tool development at the Decision Support and Informatics Lab. Michigan State University and USDA NIFA Federal Award # 2015-68007-23193 provided funding for this tool development.

References

Ghane, E. (2022a). Choice of pipe material influences drain spacing and system cost in subsurface drainage design. Appl. Eng. Agric., 38(4), 685-695. https://doi.org/10.13031/aea.15053

Ghane, E. (2022b). Drain spacing tool (E3450). Michigan State University Extension. Retrieved from

https://www.canr.msu.edu/resources/drain-spacing-tool

Ghane, E., & Askar, M. H. (2021). Predicting the effect of drain depth on profitability and hydrology of subsurface drainage systems across the eastern USA. Agric. Water Manag., 258, 107072. https://doi.org/10.1016/j.agwat.2021.107072

Ghane, E., AbdalAal, Y., Dialameh, B., & Ghane, M. (2022). Knitted-sock geotextile envelopes increase drain inflow in subsurface drainage systems. Agric. Water Manag., 274, 107939. https://doi.org/10.1016/j.agwat.2022.107939

Ghane, E., Askar, M. H., & Skaggs, R. W. (2021). Design drainage rates to optimize crop production for subsurface-drained fields. Agric. Water Manag., 257, 107045. https://doi.org/10.1016/j.agwat.2021.107045

Kladivko, E. J., Frankenberger, J. R., Jaynes, D. B., Meek, D. W., Jenkinson, B. J., & Fausey, N. R. (2004). Nitrate leaching to subsurface drains as affected by drain spacing and changes in crop production system. J. Environ. Qual., 33(5), 1803-1813. https://doi.org/10.2134/jeq2004.1803

PRISM Climate Group. (2021). PRISM climate data. Oregon State University. Retrieved from http://www.prism.oregonstate.edu/

Skaggs, R. W. (2007). Criteria for calculating drain spacing and depth. Trans. ASABE, 50(5), 1657-1662. https://doi.org/10.13031/2013.23971

Skaggs, R. W. (2017). Coefficients for quantifying subsurface drainage rates. Appl. Eng. Agric., 33(6), 793-799. https://doi.org/10.13031/aea.12302

Skaggs, R. W., Youssef, M. A., & Chescheir, G. M. (2006). Drainage design coefficients for eastern United States. Agric. Water Manag., 86(1), 40-49. https://doi.org/10.1016/j.agwat.2006.06.007

Soil Survey Staff. (2020). Gridded soil survey geographic (gSSURGO) database for the conterminous United States. USDA, NRCS. Retrieved from https://gdg.sc.egov.usda.gov/

USDA-NRCS. (2016). Soil data development toolbox. Github repository. Retrieved from https://github.com/ncss-tech/SoilDataDevelopmentToolbox