A simulation model for predicting soil moisture status

Soil & Tillage Research, 2 (1982) 67--80

67

Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

A SIMULATION MODEL FOR PREDICTING SOIL MOISTURE STATUS

B.D. W I T N E Y

~ , K. E R A D A T

OSKOUP

and R.B. S P E I R S 2

IDepartment of Agricultural Engineering and Mechanisation, and 2 Department of Soil Science, Edinburgh School of Agriculture, Edinburgh E H 9 3JG (Great Britain) (Accepted 14 October 1981)

ABSTRACT

Witney, B.D., Eradat Oskoui, K. and Speirs, R.B., 1982. A simulation model for predicting soil moisture status. Soil Tillage Res., 2: 67--80. A simulation model has been developed to predict dally values of soil moisture content in the top 300 m m of the soil profile from simple meteorological and soil data. Daily precipitation is balanced against runoff, evapotranspirtation and drainage. Proven procedures were adapted to calculate both runoff and evapotranspiration, the selection of the methods being influenced by the simplicity of the input data requirement and the essential accuracy of the results in relation to the complete model. Drainage for a given moisture content was calculated by means of exponential functions derived from experimental data of the hydraulic conductivities at field capacity and at saturation assuming a homogeneous soil profile. Good agreement was obtained between the predicted values of the soil moisture content and experimental data over a 4-year period for three typical Scottish soils both fallow and grass covered.

INTRODUCTION

For the selection of farm power and tillage machinery, it is necessary to balance the inflated costs in future years of the timeliness penalties of an inadequate agricultural production system with the annual cost surcharge of over-investment in farm equipment and drainage. As tillage operations largely dictate the total power requirement of the tractor fleet on arable farms, the estimation of suitable days for field work, especially in the autumn to spring period, forms an essential part of the machinery selection process. Although a number of simulation models have been developed to predict the various elements of the soil moisture balance equation (evaporation, drainage and runoff), the extension and combination of these models to provide work day probabilities has received less attention. Several theories, such as some for evaluating evaporation, are overcomplex for application in areas where only limited meteorological data is available, whilst the estimation of drainage in the mathematical models for predicting field work days is often based on the over-simplified concept of constant flow, which bears little relation to the actual fluctuations in soil water movement. 0167-1987/82/0000--0000/$02.75 © 1982 Elsevier Scientific Publishing Company

68 To overcome some of these limitations, a general model for predicting the moisture status of unsaturated soils has been developed but the estimation of drainage is currently restricted to homogeneous soil profiles and that of runoff to non-sloping areas. SOIL MOISTURE STATUS MODEL The soil moisture status model was based on the qualitative moisture balance equation proposed by Krimgold {1954) for a given soil segment of given depth (h): m h = P + Ca + ( R i - - R o )

+ (Qssi - - Q s s o ) + ( V i - V o )

-(E+L)

(1)

where: m h = soil moisture status for the segment ( m m ) ; P = precipitation or irrigation water (mm); Ca = amount of water condensing on the soil from the air entering the soil (mm); Ri, R o = surface runoff o n t o / f r o m the segment of relief (mm); Qssi, Qsso = amount of water entering/leaving the segment as subsurface liquid flow (mm); Vi, Vo = amount of water vapour entering/leaving the segment (mm); E = evapotranspiration (mm); and L = interception by vegetation (mm). For the purpose of the present study to evaluate the moisture status (m) in the plough layer to a depth of 300 mm, equation (1) was simplified to the modified form: m =rap + P - - R - - D - - E

(2)

where: m p = soil moisture content on previous day (mm); P-- precipitation (mm); R = runoff (mm); D = drainage (mm); and E = evapotranspiration (mm). In this way, the soil moisture content on the previous day (rap) was adjusted for soil moisture gains and losses to provide a revised soil moisture status on a cumulative basis. Only water entering the soil as precipitation (rainfall, sleet or snow) or irrigation water (P) was considered because worldwide meteorological data is readily available. The amount of water condensing onto the soil from the air entering the soil (Ca) was neglected. Provided that the soil does n o t receive runoff from adjacent areas, only the c o m p o n e n t of precipitation lost as runoff (R) from the surface area of the soil segment influences its soil moisture status. Similarly, it is assumed that drainage (D) accounts for all subsurface water flow. The differential transmission of water vapour through the soil (Vi -- Vo) is assumed to be negligible in comparison with the evapotranspiration (E) and, at the early stages of plant establishment, the moisture intercepted by vegetation (L) can be discounted. SURFACE RUNOFF Surface runoff is calculated by means of the antecedent rainfall index m e t h o d which incorporates rainfall, soil and soil moisture data (Hartman et

69 al., 1960; Knisel et al., 1969). For values of the antecedent precipitation index (API) of less than 200 mm, the daily runoff is: P(615.0356 mm -- 2.847 API)

R~ = P

P + 529.4376 mm -- 2.437 API

mm

(3)

mm

(4)

and above that limit:

R2 = P

P(219.6338 mm -- 0.904 API) ....

P + 134.0358 mm -- 0.494 API

The antecedent precipitation index is calculated from the equation: API = rnp -- PWP- h- BD

(5)

where: PWP = permanent wilting point in the soil profile (cm 3 • g-~); h = depth of the soil profile (mm); and BD = soil bulk density (g. cm-3). DRAINAGE Water movement through unsaturated soils is governed by the hydraulic conductivity in accordance with Darcy's equation: D

=

where: D = soil water flux (mm. day-l); K = hydraulic conductivity (mm. day -1 }; (P = soil water pressure head (mm); and h = soil depth measured downwards positively (mm). In a uniform soil, the term dq)/dh is negligible because very large changes in hydraulic conductivity occur for only small changes in soil water c o n t e n t (Davidson et al., 1969). At a hydraulic gradient of unity in homogeneous soils, Black et al., {1969) confirmed t h a t the drainage flow is equal to the hydraulic conductivity and further proved that the hydraulic conductivity is an exponent of the soil moisture content. These assumptions, together with experimental data for hydraulic conductivities and soil moisture contents (Cassel, 1975), were used to derive the equation for the drainage (D): lnD=cl

lnmp+C2

(7)

where cl and c2 are constants representing soil type. The hydraulic conductivity and hence the drainage rate reaches a constant upper limit when the soil is at saturation and either ceases or reaches a negligible value when the soil moisture c o n t e n t approaches field capacity. Solving equation (7) for the upper and lower limits of hydraulic conductivity (Ksat and Kfc) when the soil moisture c o n t e n t is at saturation (rnsat) and at field capacity (mfc), the drainage equation can be presented in the following form: D

= Kfc(mp/mfc)

c~

where: a = (ln Ksat -- In Kfc)/(ln msat -- In mfc ).

(8)

70 • Regr~ss:~oi~ equation • Theoretical equation

i00

5O

Y 10

5

•

0.5

m

i

!

i

I

i

5

i0

50

Measured drainage

(mm.day-1 )

Fig. 1. Measured and predicted drainage using regression and theoretical equations for Macmerry soil se~es.

The results predicted by the drainage equation explained 96% of the experimental data for the two soil types investigated with a correlation coefficient of 0.982 in each case. Although the deviation between theory and practice (Fig. 1) was greater than with the use of a regression equation in the form of equation (7), the main advantage of equation (8) is that soil water flux can be accurately estimated from a knowlege of simple soil water properties. In layered soils or in the presence of a low water table where the hydraulic gradient is less than unity, this equation can be used to estimate unsaturated hydraulic conductivity of soils from which drainage can be calcu!ated by means of equation (6). EVAPOTRANSPIRATION

The potential evaporation (PE) was calculated by means of Thornthwaite's

71

formula (1948) requiring only the mean m o n t h l y air temperature (t): PE = 16(10 t/I) a

(9)

where: a = (0.675/3 -- 77.1/2 + 0.017920/+ 492390) × 10 -6 I=il i

=

+i2 +i3 + . . . + i l 2

(10)

(t/5) 1-s14

(11)

with the subscripts 1, 2 . . . . . 12 defining the months of the year. The monthly evaporation calculated from equation (9) was divided by the number of days (30) in a standard m o n t h to give the daily potential evaporation (DPE) and adjusted using Pierce's procedure (1966) to yield the actual evapotranspiration (E): E = DPE. K 1 K d K r K c K s

(12)

where KI, Kd, Kr, Kc and Ks are correction factors for day length, soil dryness, number of rainy days, crop stage of growth and surface cover, respectively. The day length correction factor (KI) was calculated from the equation: (13)

KI = u / N

where n is the duration of sunshine and N is the duration of daylight from the Smithsonian table (List, 1958). The soil dryness factor (Kd) is defined as the ratio of the actual evaporation to the potential evaporation. The relation with soft moisture deficit in a 300-ram profile is shown in Fig. 2. The rainy 1.0

~= 0.8 o u~

o

0.6

o.4 i

I

c:l 0.2

FIELD CAPACITY

PERMANENT WILTING POINT I

(FC) O

; iO

(ewe) ; 20

& 30

I 40

; 50

Soil moisture deficit (mm)

Fig. 2. Dryness correction factor, K d (Source: Pierce, 1960).

72 TABLE I R a i n y day c o r r e c t i o n factors, K r Number of consecutive days with precipitation

Kr

0 1 2 3 and more

1.00 0.75 0.65 0.55

day correction factors (Kr) are listed in Table I. Crop stage correction factors were developed by Pierce {1966) and an example of those for grass is shown in Fig. 3. The effect of soil surface cover on evaporation is also accounted for by using a soil surface cover correction factor (Ks) proposed by Gerb (1966), which states that the rate of evaporation decreases linearly as the percentage surface cover (PSC) increases to 100%: Ks = 1 -- 0.005 PSC

(14)

This correction factor is particularly relevant to row crops. COMPUTATIONAL PROCEDURE

A computer programme was written in FORTRAN IV language to calculate the soil moisture status from the following input data: daily precipitation and sunshine hours; mean m o n t h l y air temperature; latitude; hydraulic conductivities and soil moisture contents at both field capacity and saturation; soil bulk density. EXPERIMENTAL WORK

Although there is no published data for the daily fluctuations in moisture content of Scottish soils, weekly values of soil moisture tension in two soil series in Central Scotland -- Macmerry and Darvel series .... for 1972, 1974, and 1976 were abstracted from records of the Soil Survey of Scotland (Duncan, 1979). Owing to inadequacies in these data, a further experiment was carried o u t in 1978 to record, over a period of one year, the fluctuation in soil moisture content of two soil types: Winton and Macmerry. The Winton series are an imperfectly drained sandy clay loam soil with a very slowly permeable subsoil. The Macmerry series are a loamy soil overlying a slowly permeable sandy clay loam subsoil at a depth of around 500 mm, and Darvel series are a freely drained sandy loam. A full description of these softs is presented by Ragg and F u t t y (1967).

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74 T A B L E II Soil test data Soil series

Hydraulic conductivity in 3 0 0 m m soil profile

Winton Macmerry Darvel

Bulk density (g. cm -3)

At field capacity ( m m . day -1 )

At saturation ( m m . day -~ )

0.5 0.8 1.0

21.3 32.3 38.2

1.1 1.1 1.2

The soil test data is presented in Table II. The field capacity for the Winton and Macmerry soils is at 0.05-bar water tension whilst for the Darvel soil it is at 0.1-bar water tension. The corresponding moisture contents were taken from the soil moisture characteristics using a logarithmic regression equation (Fig. 4). Using these soil moisture characteristic curves and bulk density values, the soil moisture tensions were converted to soil moisture contents in terms of % (w/w) and mm of moisture in the top 300 mm of the soil profile. Daily rainfall figures were obtained from the nearest meteorological station. One of limitations of the earlier experiments was that the meteorological data were collected from stations 3--5 km remote from the soil site whereas weather information for the 1978 experiment was obtained from a station only 1 km away. 100

• DARVE L MACME RRY • WINTON

50 e~

30 ~e

20 ,--t o m

lO

I 0.05

I 0.1 Soil

moisture

tension

I

I

I

!

1.0

2

3

4

(bar)

Fig. 4. Soil moisture content at different tensions for Darvel, Maemerry and Winton soil series in the plough layer.

75 DISCUSSION T h e results o f t h e c o r r e l a t i o n analysis b e t w e e n the p r e d i c t e d a n d m e a s u r e d values o f t h e soil m o i s t u r e c o n t e n t are v e r y e n c o u r a g i n g (Table I I I ) . F o r t h e ten experiments with a total of 820 data points, correlation coefficients range f r o m 0 . 9 9 0 to 0.999. In all b u t t w o e x p e r i m e n t s , MG 78 and WB 78, the soil m o i s t u r e c o n t e n t is slightly u n d e r e s t i m a t e d . F r o m a m o r e detailed e x a m i n a t i o n o f the individual d a t a it is e v i d e n t t h a t t h e r e is a close agreeTABLE III Correlation analysis of predicted and experimental values of soil moisture c o n t e n t

Code No. DG DG DG MG MG MG MG MB WG WB

Soil series Type of cover

72 Darvel 74 76 72 Macmerry 74 76 78 78 78 Winton 78

Grass Grass Grass Grass Grass Grass Grass Fallow Grass Fallow

Year

No. of measurements

Regression coefficient

Standard error

Correlation coefficient

1972 1974 1976 1972 1974 1976 1978 1978 1978 1978

52 51 49 51 52 46 133 134 125 116

0.9707 0.9808 0.9823 0.9930 0.9214 0.9594 1.0132 0.9922 0.9785 1.0082

0.0189 0.0131 0.0103 0.0138 0.0104 0.0147 0.0084 0.0038 0.0076 0.0053

0.990 0.996 0.997 0.995 0.997 0.995 0.996 0.999 0.996 0.998

m e n t d u r i n g t h e w e t t e r p a r t o f the y e a r f r o m the beginning of O c t o b e r until t h e e n d o f April (Fig. 5). A l t h o u g h a n u m b e r o f m a j o r discrepancies d o occur, p a r t i c u l a r l y d u r i n g the g r o w i n g season, these are as f r e q u e n t l y a t t r i b u t able to inconsistencies b e t w e e n the field values and w e a t h e r p a t t e r n s or t o i n t e r m i t t e n t failure o f the m o n i t o r i n g e q u i p m e n t as to a n y inaccuracies o f t h e analytical t e c h n i q u e s . A significant i n c o n s i s t e n c y b e t w e e n field m o i s t u r e c o n t e n t s and the weather p a t t e r n occurs on Darvel f r o m m i d May to early J u n e and on M a c m e r r y t h r o u g h o u t M a y (Fig. 5). T h e m e a s u r e d soil m o i s t u r e c o n t e n t on Darvel declined a n d on M a c m e r r y r e m a i n e d u n c h a n g e d during the s e c o n d h a l f o f May in r e s p o n s e to six rainfall events with a t o t a l p r e c i p i t a t i o n o f 21 m m recorded at the m e t e o r o l o g i c a l station. T h e m e a s u r e d soil m o i s t u r e c o n t e n t is also c o n s i s t e n t l y b e l o w p r e d i c t e d values in the t h r e e - m o n t h p e r i o d u p t o late M a y f o r M a c m e r r y . A l t h o u g h local w e a t h e r v a r i a t i o n b e t w e e n the sites and the m e t e o r o l o g i c a l s t a t i o n c o u l d a c c o u n t f o r the f o r m e r occasional differences, it is m o r e likely in the l a t t e r case t h a t the dense r o o t m a t o f the p e r m a n e n t p a s t u r e site i n t e r c e p t e d m u c h o f the rainfall b e f o r e it r e a c h e d the t e n s i o m e ters, an e f f e c t w h i c h w o u l d be tess p r o n o u n c e d on t h e m o r e highle p e r m e a b l e Darvel soil. This e x p l a n a t i o n is c o n f i r m e d b y the e x c e l l e n t c o r r e l a t i o n be-

78

~

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O (~

00~/~)

±~±NOD 3~I~SION EIOS

(~) Z ~ N I ~

77

tween theory and experiment on bare soil in contrast with the grass site for Macmerry soil series (Fig. 6). Tensiometer accuracy is also suspect on a number of occasions. During dry period, such as July through September (Fig. 5), the higher measured soil moisture contents could be attributed to the unreliability of the Webster tensionmeters for tensions below 0.5 bar (Webster, 1965) and to soil shrinkage. As the soil dries, shrinkage occurs and there is a tendency for the soil to move away from the tensiometer cup. Tension readings are then overestimated in a dry period and underestimated in a subsequent wet period until the soil swells to regain contact with the tensiometer cup. This perhaps accounts for the very low fluctuation in the measured soil moisture content of 30 mm on Darvel in response to 60 mm of rainfall during the second half of September (Fig. 5). Discontinuities in the field data through missed readings, for example during June on Darvel, July and September 1976 on Macmerry (Fig. 5}, made comparison with the predicted value more tenuous and some data was n o t recorded because of broken equipment, for example, during August on Macmerry soil under grass for 1978 (Fig. 6). No account was taken of the capillary rise or of water retention by the growing crop as these refinements had minimal impact on the accuracy of the predicted results. Evaporation was assumed to be nil when the soil moisture c o n t e n t reached the crop wilting point. Thus, in a prolonged period without precipitation, drainage fell to zero at field capacity and the soil moisture c o n t e n t curve levelled off when at the crop wilting point, 60 mm for Macmerry soil series and 75 mm for the Darvel soil series (Fig. 5). Soil workability is directly dependent on soil moisture content. The model can be used to predict probability of occurrence of work days when the soil moisture c o n t e n t is at or below a specific value or soil workability criteria over a period of years. As soil workability varies from soil to soil, machine to machine and farm manager to farm manager, the adoption of a unique soil moisture value to differentiate between soil workability and non workability is unrealistic. A procedure has therefore been adopted to enable the number of workdays to be calculated at different levels of soil moisture c o n t e n t or workability criteria. The available days for tillage in each quarter of the year for two soil series, Macmerry and Winton, are presented in Table IV for three probability levels, 80%, 90% and 100%, and three soil workability criteria, namely, 105%, 110% and 115% of the soil moisture content at field capacity (FC). These soil moisture levels are in the region of the soil moisture contents at the upper plasticity limits of 107% and 104% of field capacity for Macmerry and Winton soils, respectively (Table V). The superposition of other weather constraints such as the probability of occurrence of frost or snow is required for a realistic comparison between predicted and practical data on work days. Fig. 5. Comparison of measured and predicted soil moisture c o n t e n t in the plough layer (300 mm) with grass cover for Darvel and Macmerry soil series in relation to precipitation during 1976.

78

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79 TABLE IV Number of days available for tillage operations at varying probability levels and workability criteria in four quarters for Macmerry and Winton soils at Langhill, Scotland Soil series Soil Number of soil workable days workability criterion 1st Quarter 2nd Quarter 3rd Quarter (% of FC) Probability level 80 90

100

80

Macmerry 105 110 115

54 27 88 81 90 89

13 58 76

67 38 10 90 83 48 91 89 61

75 48 10 91 80 48 92 91 71

63 37 10 91 82 37 92 90 67

Winton

12 4 1 83 65 32 89 87 70

22 7 2 88 66 35 91 88 52

24 14 4 80 72 31 91 90 61

17 3 1 88 71 26 92 90 57

105 ]10 ]15

90

100

80 90

100

4th Quarter

80 90

100

TABLE V Water properties of Darvel, Macmerry and Winton soil series in the plough layer Soil type

Liquid limit

Plastic limit

Field

Wilting point

capacity

(%, w/w) Darvel 32.75 Macmerry 36.00 Winton 43.75

(% of FC)

(%, w/w)

(% of FC)

(%, w/w)

(%, w/w)

(% of FC)

128 140 160

30.5 27.5 28.25

120 107 104

25.5 25.65 27.15

12.5 14 17

50 54 62

CONCLUSIONS T h e p r o p o s e d soil m o i s t u r e m o d e l is c u m u l a t i v e in o p e r a t i o n a n d e r r o r c o m p e n s a t i n g w h e n e v e r t h e soil r e a c h e s s a t u r a t i o n . T h e l i m i t a t i o n s o f cons t a n t f l o w i m p o s e d b y a d r a i n a g e c o e f f i c i e n t are o v e r c o m e , d r a i n a g e r a t e being r e l a t e d t o t h e h y d r a u l i c c o n d u c t i v i t y o f t h e soil b e t w e e n s a t u r a t i o n a n d field c a p a c i t y d e p e n d i n g on t h e soil m o i s t u r e c o n t e n t a n d b u l k d e n s i t y . T h e p r e d i c t e d m o i s t u r e c o n t e n t s f o r t h e t h r e e soil t y p e s o v e r several y e a r s are in close a g r e e m e n t w i t h m e a s u r e d values. T h e m o d e l has b e e n d e v e l o p e d s p e c i f i c a l l y t o f a c i l i t a t e t h e c a l c u l a t i o n o f i r r i g a t i o n r e q u i r e m e n t s , t h e p r e d i c t i o n o f d r a i n a g e flow, t h e e v a l u a t i o n o f w o r k d a y p r o b a b i l i t i e s , a n d t o f o r m o n e r o u t i n e in a m o r e c o m p r e h e n s i v e agricultural machinery selection programme. Fig. 6. Comparison of measured and predicted soil moisture content in the plough layer (300 ram) with grass cover and bare soil for Macmerry series in relation to precipitation during 1978.

80 ACKNOWLEDGEMENT T h e a u t h o r s w i s h t o e x p r e s s t h e i r a p p r e c i a t i o n t o Mr. A . C . W h i t h o r n a t t h e E d i n b u r g h S c h o o l o f A g r i c u l t u r e f o r his g u i d a n c e o n c o m p u t a t i o n a l p r o cedures. REFERENCES Black, T.A., Gardner, W.R. and Thurtell, G.W., 1969. The prediction of evaporation, drainage and soil water storage for a bare soil. Soil Sci. Soc. Am. Proc., 33: 655--660. Cassel, D.K., 1975 In situ unsaturated hydraulic conductivities for selected North Dakota soils. Univ. Agric. App. Sci., Fargo, ND, Bull. 494, 20 pp. Davidson, J.M. Stone, L.R., Nielson, D.R. and Lame, M.E., 1969. Field measurement of soil water properties. Water Resour. Res., 5: 1312--1321. Duncan, N.A., 1979. The moisture regimes of six soil series of the Central Lowlands of Scotland. J. Soil Sci., 30: 215--223. Gerb, B.W., 1966. The effect of surface applied wheat straw on soil water losses by solar distillation. Soil. Sci. Soc. Am., Proc., 30: 786--788. Hartman, M.A., Baird, R.W., Pope, J.B. and Knisel, W.G., 1960. Determining rainfall-runoff retention relationships. Texas Agric. Exp. Stn. Bull. MP-404, 7 pp. Knisel, W.G., Baird, R.W. and Hartman, M;A., 1969. Runoff volume prediction from daily climatic data. Water Resour. Res., 5: 84--94. Krimgold, D.B., 1954. General approach to the problem. In: G.W. Thorntwaite and J.R. Mather (Editors), Estimation of soil tractionability from meteorological data. Publication in Climatology, No. 7, pp. 376--378. List, R.J., 1958. Smithsonian Meteorological Tables, 6th Rev. Smithsonian Inst., 000 pp. Pierce, L.T., 1960. A practical method of determining evapotranspiration from temperature and rainfall. Trans. ASAE, 3: 77--81. Pierce, L.T., 1966. A method for estimating soil moisture under corn, meadow and wheat. Ohio Agric. Res. Dev. Cent., Wooster, OH, Res. Bull. 988, 17 pp. Ragg, J.M. and Futty, D.W., 1967. The Soils of the District around Haddington and Eyemouth. Dep. Agric. Fish. Scotland Memoirs of Soil Survey of Great Britain : Scotland. HMSO, London, 310 pp. Thornthwaite, G.W., 1948. An approach towards a rational classification of climate. Geogr. Rev., 3: 55--94. Webster, R., 1965. The measurement of soil water tension in the field. New Phytol., 65: 249--258.