Methods Based on Statistical Analysis to Improve Water Retention in

Sub-surface Irrigation

Visala Tallavarjula

9th Grade, Wilcox High School

Santa Clara, CA

Abstract

In many different parts of the world including California and other arid states in the US, there is water

shortage due to droughts. Subsurface irrigation is effectively used in drought ridden areas. The purpose

of this experiment is to explore ways to improve further subsurface watering efficiency. Improved water

retention leads to lower cost of pumping water. Reduced evaporation loss means more water availability

for transpiration resulting in greater crop yield. Fine grain soils, like clay and silt, block water infiltration.

In the small pores of fine soils, water is held strongly by adhesion forces. The water held by the soil stops

additional water from passing through and infiltrate down. The idea of this work is to use the same

principle in the reverse direction and show that the upward movement of water by evaporation can be

blocked by fine grain top soil bed. The goal of the project is to develop a method that is simple and can

be easily implemented using readily available materials in all regions including those in the developing

world.

Testable Question

How do different top soil grain sizes and bed thicknesses affect water loss due to evaporation for sub-

surface irrigation?

Introduction

If watered from top surface, wet soil is exposed to atmosphere. Evaporation is controlled by the

exposed area, wind speed, humidity, and temperature. A certain fraction of water is lost due to

evaporation. In sub-surface irrigation watering pipe is buried underneath the soil surface. By watering

below the surface, wet soil is not exposed to sun and wind. However, even in subsurface irrigation there

is evaporation loss.

Figure-1: Subsurface irrigation concept and fine grain and coarse grain soil details

This project explores methods by which evaporation can be reduced further. Fine grain soil has large

surface area of soil particles. Adhesion is the force of attraction between water molecules and soil

particles. Due to adhesion, a thin film of water is tightly held around the soil particles [2]. The finer the

soil particles, the greater the surface area and the thin water film is held more tightly. In the case of fine

grain soil, tightly held water film resists any further water movement through the pores. Fine grain soils

like clay and silt block water infiltration. When fine grain soil is used on the top surface, it reduced water

infiltration [1], [6]. The idea of this project is to use the same principle in the reverse direction and resist

the upward movement of water by evaporation using a fine grain top soil bed. Depth of watering has an

impact of evaporation loss in sub-surface irrigation [3], [4], [5] and [7].

Hypotheses

(i) The smaller the grain size of the top soil bed, the lower the evaporation loss.

(ii) The thicker the top soil bed, the lower the evaporation loss.

Screening Design of Experiments

In the first phase of the experimentation, the objective was to determine the important variables that

affect the evaporation loss. The experiments take a month due to slow evaporation rate in a closed

room. Hence, it is important to find out which variable have the most impact and test them with several

data points. The three independent variables: depth of watering (Dw), top soil bed thickness (tB)and top

soil bed grain size index (Gsz), are selected for the Design of Experiments or DOE. Eight plastic containers

are prepared with watering depth at 1cm and 4 cm; top soil bed thickness at 1cm and 3 cm, top soil

beds with fine grain, 𝐺𝑠𝑧 =0 (fine grain: Seed Starter Mix) and coarse grain, 𝐺𝑠𝑧 =100 (coarse grain:

Volcanic Pumice). One center point sample is prepared with a watering depth of 5cm, bed thickness of 2

cm, 50/50 mixture of the fine grain and coarse grain soils. This design considers all the eight corners and

the center of the body of a cube in 3 dimensional space with the variables (𝐷𝑤, 𝑡𝐵, 𝐺𝑠𝑧) as axes as

shown in Figure-2. Amount of soil in each container, temperature of the samples, humidity, and surface

area exposed to air, and amount of water added are the control variables that are kept constant.

Figure-2: Three dimensional space of the independent variables screened in Design of Experiments.

Screening Experiments Method

Sample Preparation:

All the plastic containers are filled to a predetermined height (hw) with Natural & Organic Potting Soil.

Figure-3: Details of Sample Preparation

Water Addition: 40 ml of water is added to each sample (four samples at 1cm and remaining four

samples at 4 cm watering depths). Then additional Potting Soil is added till the predetermined height

(hb) is reached. Then top soil bed is prepared in layers till the required bed thickness is formed.

Table-1: Details of sample preparation for the screening design of experiments.

Where,

W0 : Weight before water is added [g]

W1 : Weight after adding water [g]

Ww : W1 - W0 (Weight of water added) [g]

W2: Total Initial Weight with Bed cover [g] (11/27/15 4:09 PM)

Wf: Total Final Weight taken on 12/21/15 at 6:17 PM

h-bed : height of bed bottom surface [cm]

h-water : height at which watered [cm]

Watering Depth Dw =13 - h-water

Bed Thickness, tB = 13-h-bed

W is the weight loss due to evaporation after 27 days.

Weight loss is measured daily till 80% water is lost due to evaporation from the coarse grain bed sample

(27 days). The data is analyzed with statistical software (JMP) by fitting the Evaporation Loss (EL) as a

function of the three tested independent variables.

𝑬𝑳 = 𝑓(𝐷𝑤, 𝑡𝐵, 𝐺𝑠𝑧)

Weight loss is entirely due to evaporation, since the plastic wall of the container does not allow

percolation. The data from columns Dw, tB, Bed Type are entered in JMP Soft Ware under x-variables

(independent variables). W is entered as dependent y-variable. (see Appendix A1)

Statistical Analysis Results

Figure-4: Statistical Analysis Summary

From the analysis bed thickness and bed grain size have steeper slopes implying they have larger impact

on evaporation loss compared to depth of watering.

Experiments varying single variable

In the next set of experiments, the most influential variables (bed thickness and top soil bed grain size)

were varied and all the other parameters are kept constant.

Experiment-1: Dependence on top soil bed grain size (𝑮𝒔𝒛):

Six samples are prepared with watering depth, Dw =3 cm; top soil bed thickness, tB =3 cm. Top soil beds

with grain size mixtures, GSZ = 0%, 25%, 50%, 75% and 100% of coarse grain. Top soil bed texture (grain

size) is varied by mixing Seed Starter Mix (fine grain) and Volcanic Pumice (coarse grain), in varying

proportions. One reference sample is prepared with no bed, and surface watering.

Figure-5: Top soil bed grain size (texture) variation. (fg: fine grain Seed Starter Mix, cg: coarse grain

Volcanic Pumice).

Experiment-2: Dependence on top soil bed thickness(𝒕B):

Three samples are prepared with watering depth, Dw=3 cm; top soil beds with fine grain (𝐺𝑠𝑧 = 0%), and

varying top soil bed thickness, 𝒕B =1cm, 2 cm, and 4 cm. (3cm bed thickness data is used from

Experiment- 1)

Figure-6: Top Soil Bed thickness Variation

For both experiments, 60 ml of water is added to each sample (subsurface, under the bed)

All the other control variables are kept constant. Weight loss is measured daily for 4 weeks.

Figure-7: Daily weight loss due to evaporation for samples with different top soil bed grain size.

Results

The above data set is repeated for 𝐺𝑠𝑧 = 0, 50 and 100 cases.

Table-2: Grain Size variation results and repeatability data

Grain Size Index

Weight Loss (%) Average Weight Loss

(%)

Standard Deviation

Std. Dev (%) Trial-1 Trial-2 Trial-3

0 47.46 54.10 54.24 51.93 3.87 7.46

25 56.67 -- --

50 61.02 66.67 66.67 64.78 3.26 5.04

75 76.27 -- --

100 98.28 93.22 96.72 96.07 2.59 2.70

Figure-8: Box and whisker plot for grain size variation

From the Figure-8, it is clear that change from Gsz = 0 to Gsz = 50 and 100 is (12%-27%) higher than the

variability seen from range at any grain size (2.7% - 7.5%). Hence the linear change is significant.

Table-3: Top soil bed thickness variation data

Bed Thickness (cm) Weight Loss (%)

1 61.67

2 57.38

3 54.10

4 49.15

Data Interpretation and Discussion

Figure-9: Evaporation loss (%) as a function of time. It is clear that coarse grain top soil bed has highest

evaporation rate. The sample without top soil bed and surface watering is similar to 75% coarse grain

mixture.

When the data is in analyzed for the first seven days as shown in Figure-10, the rate of evaporation loss

can be seen (shown by the slopes of equations for coarse grain and fine gran samples).

Figure-10: Evaporation loss (%) as a function of time in the first seven days

It can be seen that for fine grain soil the rate of evaporation loss is half that for the coarse grain soil bed.

Figure-11: Top soil bed grain size impact on evaporation loss

Data shows linear dependence between evaporation loss and bed grain size. As grain size increases

evaporation loss increases. This is due to the fact that for larger soil particle, adhesive forces are weaker

and water is able to move around the soil particles. This movement of water in the pores allows

evaporation to take place.

Figure-12: Top soil bed thickness impact on evaporation loss

Top soil bed thickness also shows linear relationship with evaporation loss. For thicker bed, evaporation

loss is reduced. This is due the fact that for thicker bed, there is more surface area around soil particles

that evaporating water has to overcome.

Conclusions

Evaporation loss (EL) decreased when the grain size of top soil bed is reduced. With 3 cm fine grain bed,

EL can be lowered by 30%. In the first seven days the rate of evaporation is reduced from 3.69 to 1.75 %

water lost/day when top soil bed texture is changed from coarse grain to fine grain. By increasing the

top soil bed thickness from 1 to 4 cm, EL can be reduced by 20%. Evaporation Loss is repeatable within

7.5% of the mean value. The world’s water usage is growing with demand from increasing global

population. Every drop of water conserved makes a difference. This work shows that subsurface

irrigation efficiency can be further improved by using thicker and fine grain size top soil bed. This

approach can result in water savings and reduced water pumping/production costs.

Impact

In California, for example 80% of the water is used for agriculture. Even 5% savings mean more than 400

billion gallons of water Saved! Everyone can employ this simple technique of using a fine grain soil bed

made with readily available fine grain soils like loam, clay loam etc. This method also can help conserve

water when farming on another planet like Mars where water is not easily available.

Future Work

The effect of temperature on evaporation loss suppression for fine grain top soil bed need to be studied

by exposing the samples to sun. Also the impact of wind and humidity need to be characterized.

References

[1] David M. Kopec, “Soil Characteristics and How They Affect Soil Moisture”, Extension Turfgrass Specialist, October 1995 - Volume II, Issue 10

[2] “Conservation of natural resources for sustainable Agriculture”, Water Management, Food and Agriculture Organization of the United Nations. http://www.fao.org/nr/aboutnr/nrl/en/

[3] Weikang Song, Yu-Jun Cui, Anh Minh Tang, Wenqi Ding, Thanh Danh Tran, 2014, “Experimental study on water evaporation from sand using environmental chamber”, page 123, NRC Research Press, Can. Geotech. J. Vol. 51, 2014

[4] Sakai, M., S. B. Jones, and M. Tuller (2011), “Numerical evaluation of subsurface soil water evaporation derived from sensible heat balance”, Water Resour. Res., 47, W02547, page 9, 2010

[5] C.P. Kumar, 1999, “Evaporation from Shallow water table through layered soil profiles”, Journal of Hydraulic Engineering, vol. 5, 1999.

[6] Guide to Hydrological Practices, “Evaporation, Evapotranspiration and Soil Moisture”, 1.4-8, Chapter-4. 2008. (www.whycos.org/hwrp/guide/chapters/english/original).

[7] M. Meshkat, R. C. Warner, S. R. Workman, “EVAPORATION REDUCTION POTENTIAL IN AN UNDISTURBED SOIL IRRIGATED WITH SURFACE DRIP AND SAND TUBE IRRIGATION”, American Society of Agricultural Engineers 0001-2351, Vol. 43, Pp 79-86, 2000.

Appendix A1: Statistical Analysis Data Input Details

Independent Variables Dependent Variables

Appendix A2: Regression Model and Statistical

Confidence

Appendix A3: Daily weight loss data