Prediction of soil moisture characteristics from mechanical analysis and bulk density data

Agricultural Water Management, 10 (1985) 305--312

305

Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

P R E D I C T I O N O F SOIL M O I S T U R E C H A R A C T E R I S T I C S F R O M MECHANICAL ANALYSIS AND BULK DENSITY DATA

N. MADANKUMAR

Water and Land Management Training and Research Institute (Walamtari), Himayatsagar, Hyderabad- 500 030 (India) (Accepted 17 September 1985)

ABSTRACT

Madankumar, N., 1985. Prediction of soil moisture characteristics from mechanical analysis and bulk density data. Agric. Water Manage., 10: 305--312. Soil moisture characteristics can be established directly from the physical properties of soils such as mechanical analysis and bulk densities. Multiple regression equations were worked out by taking first fractions of sand (E 1), silt + clay (E' = E~ + E~) and bulk density (P), and second fractions of sand (El), silt (E2), clay (E3) and bulk density (P) as independent variables to predict the parameter b, the air-entry potential~ e and the saturation moisture content 8 s of the soil-moisture characteristics equation. Regression equations were tested for soils of different textural and structural compositions and showed good agreement between estimated and experimentally determined values.

INTRODUCTION

Knowledge of soil-moisture characteristics or ~--0 curves is of great importance in the investigation of the plant soil--water relationship. The relationship provides information on water stored in the root-zone and moisture depletion at a particular tension. It also provides a link in the formulation of flow problems in terms of either ~ or 0, which can be used for the determination of hydraulic conductivity and are essential for calculating soil--moisture diffusivity from moisture content data (EI-Komos et al.,1979; Madankumar et al.,1979, 1981). Childs (1940) observed that the physical properties of soils govern the soil moisture characteristic. Many workers have studied dependence of water relations on physical properties of soils from various angles (Subba Rao et al., 1955; Chibber, 1964; All and Biswas, 1968) and reached more or less similar conclusions. Hillel (1971) quotes several empirical equations proposed in the past but these equations have a number of limitations. Ghosh (1976) recommended an empirical equation based on the sand and siltcontent of the soil, which is only applicable for sandy soils.More recent, Ghosh (1980) recommended an empirical equation based on mechanical analysis

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data, b u t no account has been made in his model for the bulk density. Moisture retentions are influenced by bulk density at lower tensions, i.e., less than 1 bar (Hillel, 1971, pp. 61--65.). (The soil parameter b from Ghosh (1980) is more influenced by the silt/sand ratio than by the clay content.) Madankumar et al. (1979, 1981) established functional relationships between soil physical properties and the parameters in the equation for water retentivity for different softs in India. The present paper is an extension of this work and gives an empirical technique that has wider applicability in establishing the soil-moisture characteristic from mechanical properties and bulk density data. In the present study the data of Madankumar et al. (1979, 1981) were used for developing the regression equations. THEORY

A general expression relating water potential $ (cm o f water) and moistue content O (cm3/cm 3) is given by Campbell (1974): =

exp

(1)

Ce where Se is the suction corresponding to air entry value; ¢ the soil moisture tension corresponding to moisture content; 0 saturated moisture content; and b a parameter characterising the soil. To evaluate the constants ~be and b equation (1) can be modified as: log ~ = log ¢ e + b log (0 s/0 )

(2)

= log ~ e + b log 0 r

where 0J~ is the relative moisture content. The values of $ e and b can be determined from the intercept and slope of a best fit line obtained when log ¢ is plotted against log 0 r- The experimental data of Madankumar et al. (1979, 1981) for the soils numbered 1 to 22 were used to determine Ce, #s and b. Next, the same data were used for developing multiple regression equations. Sample numbers 23 to 35 were then used as a test o f the developed equations. T w o types of regression equations were applied. For the first type the sand fraction E~ and the sum o f the silt fraction E2 and clay fraction E3 (E' = E2 + E3) were used together with bulk density, P, yielding: b = 4.79 - 4 . 0 1 2 6 E ~ + 1.5404E' + 1.3953P ~ e = - 3 0 . 1 4 8 3 + 58.4856E1 + 107.7303E' - 5.4278P 0s = 0.1254 + 0.08856E~ + 0.76654E' + 0 . 0 2 1 8 3 P For the second type El, E2, E3 and P were used separately giving: b = 5.5 - 4.793E1 + 2.8148E2 -- 0.41E3 + 1.459P ¢ e = 172.267 - 165.86E1 - 112.679E2 -- 95.324E3 + 5.35aP" 0s = 2.693 - 2.711E, - 2.01E2 - 1.9E3 + 0.148P

307

With the aid of these equations, b, @e and Os for sample numbers 23 to 35 were determined. Next, the modified form of equation (1):

O=Os [-~]

e x p b -1

(3)

was used to generate the ~ --0 pairs by using the estimated parameters b, ~ e and Os. In this paper the observed values refer to either experimentally determined values or b, ~ e and e s-Values determined from the best fit line between log @ and log er.~The predicted values refer to the computed values obtained from the multiple regression equations• RESULTS

AND

DISCUSSION

The different soils with varying structural composition studied in this investigation are presented in Fig. 1. The predicted and observed b, @e and 0s were in good agreement (Table 1). This is further supported by the high coefficients of correlation r between the observed and calculated values (Table 2). The multiple correlation coefficients R for the combined effect of sand,

90

Clayey •

(vory fine) clay

."

clayey

(line) " I. 4C

clay

"" *. . . . . . . . . . . . . . . . . . . . .

'

' silty ClOy

.', ".. ...... "•

/

., clay loam ,. fin~ ""..19.(~.Y. . . . . . . . . . . :-.... .. sandyclay toarre - ,." ." 2 ~ ; ' " ~ " ".'-" . . . . . . . . . . . loom • "sandy"loam " silty loam

Percent sand F i g . 1.

Different types of soils studied under present investigation.

100 333 500 1 000 2 000 5000 10000 15000

100 333 500 1 000 2 000 5 000 10000 15 0 0 0

~0 (cm of water)

0.358 0.278 0.255 0.220 0.190 0.137 0.136 0.125

0.298 0.227 0.210 0.200 0.160 0.153 0.143 0.126

0.324 0.249 0.228 0.196 0.168 0.137 0.118 0.108

Soil No. 29

0.310 0.230 0.198 0.190 0.156 0.148 0.141 0.120

0.333 0.255 0.233 0.199 0.171 0.139 0.119 0.115

0.367 0.285 0.262 0.226 0.190 0.161 0.139 0.128

0.370 0.289 0.266 0.231 0.200 0.166 0.144 0.132

0.258 0.200 0.185 0.152 0.140 0.131 0.101 0.085

0.300 0.225 0.204 0.173 0.147 0.118 0.100 0.091

Soil No. 31

0.345 0.255 0.245 0.226 0.202 0.181 0.165 0.132

Soil No. 25

1

1

0.285 0.213 0.193 0.168 0.138 0.111 0.940 0.085

0.385 0.299 0.276 0.239 0.208 0.172 0.150 0.138

2

Estimated Equation

served

Ob-

0 (cm3/cm 3)

Equation 2

Estimated

Soil No. 24

served

Ob-

0 (cm3/cm 3)

1

Equation

0.348 0.270 0.247 0.217 0.184 0.152 0.131 0.120

0.296 0.200 0.212 0.175 0.516 0.140 0.133 0.133

0.316 0.240 0.219 0.187 0.160 0.219 0.110 0.101

Soil No. 32

0.340 0.252 0.243 0.205 0.170 0.151 0.132 0.116

0.314 0.236 0.215 0.182 0.155 0.125 0.106 0.096

0.358 0.278 0.255 0.221 0.191 0.157 0.136 0.125

2

Estimated

Soil No. 2 6

served

Ob-

O (cm3/cm 3)

E s t i m a t e d a n d o b s e r v e d values o f soil m o i s t u r e c h a r a c t e r i s t i c s ( 4 - - 0 pairs)

TABLE 1

1

Equation

0.408 0.324 0.300 0.262 0.229 0.192 0.168 0.156

0.375 0.306 0.271 0.230 0.200 0.180 0.140 0.125

0.377 0.295 0.271 0.235 0.204 0.169 0.147 0.133

Soil No. 33

0.337 0.263 0.253 0.242 0.208 0.187 0.163 0.152

0.388 0.303 0.279 0.242 0.210 0.174 0.151 0.139

0.427 0.341 0.316 0.278 0.244 0.206 0.181 0.167

2

Estimated

Soil No. 27

served

Ob-

0 (cm3/cm ')

O0

309

TABLE

2

r values between observed and predicted b, ~ e and ~s values Equation

(1)

(2)

b

0.934

0.960

~e

0.925 0.985

0.938 0.988

es

TABLE 3 Simple correlation coefficients r and multiple correlation coefficient R b

~

0

E,, E',P

-- 0 . 9 2 5 3 0.9253 -- 0 . 7 4 2 7 0.9559

-- 0 . 9 1 8 4 0.9184 -- 0 . 8 1 7 2 0.8507

-- 0 . 9 7 6 5 0.9765 -- 0 . 8 4 4 0 0.9869

Equation(2) E, E2 E3 P E,,E,,P

-- 0 . 9 3 0 2 0.8396 0.7715 -- 0 . 7 8 2 7 0.9610

-- 0 . 9 2 8 0 0.6356 0.8889 -- 0 . 8 3 4 9 0.9320

-- 0 . 9 8 2 1 0.6930 0.9288 -- 0 . 8 6 5 5 0.9864

Equation(l) E1 E' P

TABLE 4 r v a l u e s b e t w e e n o b s e r v e d a n d p r e d i c t e d ~---0 p a i r s

Equation

23 24 25 26 27 28 29 30 31 32 33 34 35

(I)

(2)

0.9932 0.9813 0.9875 0.9970 0.9928 0.9439 0.9899 0.9986 0.9914 0.9935 0.9961 0.9989 0.9985

0.9941 0.9823 0.9873 0.9971 0.9932 0.9414 0.9891 0.9985 0.9914 0.9944 0.9960 0.9989 0.9986

310

silt, clay contents and bulk density on b, $ e and Os were highly significant (Table 3). A comparison of predicted and observed ~--0 pairs is shown in Table 1 for the soils numbered 24, 25, 26, 27, 29, 31, 32 and 33. The high regression factors (Table 4) between the observed and calculated ~---0 pairs show that both equations give a very good agreement between the observed and predicted values. TABLE 5 C o m p a r i s o n o f t h e e q u a t i o n s (x2-test as b i n o m i a l i n d e x o f d i s p e r s i o n ; Koel, 1 9 5 4 ) Soil No.

1 2 3 4 5 6 7 8 9 10 11 12 13

1 2 3 4 5 6 7 8 9 10 11 12 13

Sample No.

23 24 25 26 27 28 29 30 31 32 33 34 35

23 24 25 26 27 28 29 30 31 32 33 34 35

Number of observations in each sample

8 8 8 8 8 8 8 8 8 8 8 8 8

8 8 8 8 8 8 8 8 8 8 8 8 8

N u m b e r of successes at ± 5%

N u m b e r o f successes at ± 10%

Equation

Equation

(1)

(2)

2 2 3 5 3 2 2 5 2 3 6 7 8

2 1 3 3 0 6 1 5 3 4 5 2 1

NS NS NS NS NS S NS NS NS NS NS S S

(1)

(2)

3 3 6 8 4 6 5 8 4 5 8 8 8

3 3 5 6 1 7 4 8 6 5 7 7 8

NS NS NS NS NS NS NS NS NS NS NS NS NS

N u m b e r o f successes at ± 15%

N u m b e r o f successes at _+ 20%

Equation

Equation

(1)

(2)

5 3 8 8 5 7 7 8 7 7 8 8 8

6 3 7 8 4 7 7 8 7 6 8 8 8

NS NS NS NS NS NS NS NS NS NS NS NS NS

(1)

(2)

6 5 8 8 8 8 8 8 8 8 8 8 8

8 5 6 8 6 7 8 8 8 7 8 8 8

NS NS NS NS NS NS NS NS NS NS NS NS NS

Significance of prediction differences between equations: S, significant at given level o f p r o b a b i l i t y (×=-test); NS, non-significant at given level o f p r o b a b i l i t y (x=-test).

311

To investigate whether there was any differences between the results of the two, the ×2-test as binomial index of dispersion (Hoel, 1954, pp. 176-177) was used. In order to use this test, a 'Success' is defined as the result when the estimated value from a given equation is within a defined range of the true value (e.g. +- 5%, or + 10% or + 15% or +20%). Here the true value refers to observed values. As shown in Table 5, there are eight observation points (~ --0 pairs obtained for eight different values of ~ ) for each of the samples. It also shows the n u m b e r of success points by each of the regression equations. It is clear that at 15% and 20% ranges both multiple regression equations are good enough for the prediction of soil moisture characteristics. It also proves that the differences between the predicted values from the two equations are insignificant. In other words, the equations are equally good for predicting ~--0 pairs at 15% and 20% levels. At the 10% level predictions by the two equations are satisfactory but at the 5% level neither of the equations were good enough for prediction purposes. Using mechanical analysis and bulk density data, which are readily available as routine analytical data for any area, the technique developed in the present work saves considerable time and expense which would otherwise be involved in the experimental determination of soil moisture characteristics. ACKNOWLEDGEMENTS

The author acknowledges the assistance of the authorities of Sree Ram Sagar Project Command Area, Andhra Pradesh for the facilities provided. The author also thanks Mr. C. Ramanatha Chetty, Statistician, All India Coordinated Project for Dryland Agriculture, Hyderabad; and Mr. K. Sreenivasulu Reddy, Assistant Professor, Department of Statistics, Andhra Pradesh Agricultural University, Hyderabad, for their assistance in the statistical methodology, processing of data and interpretation of results.

REFERENCES

All, M.H. and Biswas, T.D., 1968. Soil water retention and release as related to mineralogy of soil clays. In: Proc. Indian Science Congress, 1968, Banaras Hindu University, Varanasi, 55(3): 633 (abstract). Cambell, G.S., 1974. A simple method for determining unsaturated conductivity from moisture retention data. Soil Sci., 177: 311--314. Chibber, R.K., 1964. Aggregate size distribution and water relationship amongst same typical Indian Soils. Bull. Bot. Inst. Sci. India, 26: 148--156. Childs, E.C., 1940. The use of soil moisture characteristics in soil studies. Soil Sci., 50: 239--252. E1-Komos, F., Oswal, M.C. and Khanna, S.S., 1979. Soil water functional relationships of some soils of Haryana State. J. Indian Soc. Soil Sci., 27 : 345--354. Ghosh, R.K., 1976. Model of the soil-moisture characteristics. J. Indian Soc. Soil Sci., 24: 353--355.

312 Ghosh, R.K., 1980. Estimation of soil-moisture characteristics from mechanical properties of soils. Soil Sci., 24: 30: 60-'-63. Hillel, D., 1971. Soil and Water: Physical Principles and Processes. Academic Press, New York, NY, 288 pp. Hoel, P.G., 1954. Introduction to Mathematical Statistics (2nd Edition). Asia Publishing House, New Delhi, 331 pp. Madankumar, N., Raman, K.V., Subbarao, I.V. and Venkatramaiah, Ch., 1979. Soil water transmission parameters and their functional relationships of some soils of College farms of Rajendranagar and Bapatla. Andhra Agric. J., 26: 154--159. Madankumar, N., Raman, K.V., Venkatramaiah, Ch., Turabul Hassan, S. and Nayeem, M.A., 1981. Water transmission parameters and their functional relationships of soils of Sree Ram Sagar Project Command Area. In: Proc. All India Sere. Minor Irrigation Prospects in 1980's, 10--11 July 1981, Lucknow (unpublished). Subba Rao, K., Ramacharlu, P.T. and Talwar, P.S., 1955. Water relations and pore size distribution in Delhi soil and Jamuna sand. J. Indian Soc. Soil Sci., 3 : 1--6.