Pestic. Sci. 1981, 12, 123-132

Simulation of Herbicide Persistence in Soil; a Revised Computer Model

Allan Walker and Anthony Barnes

National Vegetable Research Station, Wellesbourne, Warwick CV35 9EF

(Manuscript received 19 February 1980)

Empirical equations were used to calculate the moisture content of surface soil from measurements of rainfall and daily maximum and minimum air temperatures. Air temperatures were also used to calculate soil temperatures. There was good agree- ment between calculated and measured moisture contents and temperatures from Wellesbourne and from some sites in North America. The equations were incor- porated into a simulation model for the prediction of herbicide persistence. Results from the model were essentially the same, whether calculated or measured soil moistures and temperatures were used in the calculations.

1. Introduction

A mathematical model described by Walker1 has been shown to predict the persistence of a number of herbicides in soil in the field, once the rates of degradation have been established in the same soil in the lab0ratory.2-~ The basis of the model was to estimate the fluctuations in temperature and moisture content of surface soil in the field from weather records, and to combine these with the laboratory measurements of herbicide degradation rates. The original program was written in the simulation language CSMP,B for which the weather records of daily soil temperatures at 10-cm depth, the rate of evaporation from an open water surface (Eo, mm day-') and the rainfall (mm day-1) were required. Soil temperatures and evaporation measurements are not always available and the model has therefore been revised to use daily measurements of maximum and minimum air temperatures and rainfall as the input variables. These data are more readily available from a wide range of sites. Other minor modifications have been made to the original model to simplify its use and the program has been rewritten in FORTRAN. The purpose of this paper is to describe and validate the revisions that have been made.

2. Soil moisture content 2.1. The original model To predict soil moisture content, the surface layer of soil was considered to be independent of any soil beneath it. Incoming water (rainfall or irrigation) was added to that already present in the soil until field capacity was reached and any further incoming water was ignored. Loss of water from the soil was calculated by multiplication of the evaporation of water from an open water surface by a weighting factor which varied with soil water stress. It was assumed that the soil would lose water at the same rate as an open water surface when moisture content was at or near to field capacity, but that as the soil dried, the rate of water loss would be a progressively smaller proportion of the open water loss. Rainfall and evaporation were assumed to occur at even rates throughout the day, and the change in soil moisture content was calculated at short time intervals from the difference between input of water (rainfall) and output of water (evaporation multiplied by the weighting factor). The soil moisture content was updated at the end of each time interval by addition

0031-613X/81/0400-0123 $02.00 0 1981 Society of Chemical Industry

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124 A. Walker and A. Barnes

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of the change in moisture to that present in the soil at the beginning of the time interval. Slight errors could occur with this approach when evaporation was relatively high. The model did not permit small amounts of rain to wet the soil before being evaporated; this could overestimate evaporation under such circumstances. The model has therefore been modified to improve this particular aspect.

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- - -

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2.2. The revised model In the revised program, any rain is assumed to fall at an even rate during the first half of each day, and evaporation is assumed to occur at an even rate during the second half of each day. This pro- cedure permits all rain, irrespective of the amount, to wet the soil and then to evaporate, thus simulating more closely the real situation.

The main change that has been made to the model, however, concerns the original requirement for values of the rate of evaporation from an open water surface (E,,). This has been replaced by a series of equations derived by L i n a ~ r e , ~ which permits calculation of Eo from the daily maximum and minimum air temperatures and the altitude and latitude of the site. The validity of these equa- tions was examined using weather data from Wellesbourne for summer 1977. Daily values of Eo for the period 1 May to 30 September were calculated from the daily maximum and minimum air temperatures and the latitude and altitude of the National Vegetable Research Station. and these

0

I I I I 1 I 1 > I I I

Figure 1. Observed ( 0 ) and predicted (---) soil moisture contents at three sites: A, in 0-3 cm soil at Wellesbourne, time 0 = 1 May 1973; B, in 0-4 cm noil at Regina, Saskatchewan, time 0=1 June 1976; C , in 0-4 crn soil at Regina, Saskatchewan, time 0 = I July 1977.

Simulation of herbicide persistence in soil 125

were compared by linear regression analysis with measured values. In general, the observed EO was lower than that predicted, and the equation which best described the data (r=0.805) was:

Em = 0.5 1 + (0.59 x Ec) ( 1 )

where Em is the measured evaporation (mm day-1) and E, is that calculated using the equation of Linacre7 (mm day-1). Equation (1) was incorporated into the computer program.

2.3. Validation of the revised model Measured values of soil moisture content in 0-3 cm of the soil were used by Walker to predict persistence of napropamidel and propyzamides in the soil, and measured values in 0-4 cm were used by Smith and Walker,g and Walker and Smith,lo in studies of the persistence of asulam and 2,4,5-T. The extent to which some of these measured data can be predicted from the daily maximum and minimum air temperatures, the daily rainfall, and the altitude and latitude of the different sites is illustrated in Figure 1 . There was generally good agreement between calculated and observed data, and the model predicted with reasonable accuracy the times of wet and dry soil conditions. The observed lower limits of soil moisture were also predicted accurately by the model.

I 3. Soil temperature

3.1. The original model In order to use records of 10-cm soil temperatures to predict temperatures in the surface layer of soil, an empirical additive adjustment was employed. Use of this was based on the observation that the mean temperature at 2-cm depth (measured with buried thermocouples) was similar to that at 10 cm in early April and late September, but during June and July, was from 3 to 7°C higher. When the temperatures at 10 cm were used in the program, 0°C was added on 1 April, 5°C on 1 July, and 0°C on I October. In between these dates, the addition increased or decreased linearly with time.

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25 - !2 1

s 20 + D a

15 - 0 m

10

5

C I I I I I 1 I 0 10 20 30 40 50

Days

Figure 2. Observed (--) and predicted (- - -) daily maximum and minimum temperatures at 2-cm depth in soil at Wellesbourne; time O = 1 May 1973.

126 A. Walker and A. Barnes

3.2. The revised model The two basic assumptions of the revised method of simulation were: (a) that the daily mean temperature is constant with depth; and (b) that the daily amplitude about the mean varies with depth according to :

A d = As x e(-dIJ)) (2)

where A d is the amplitude at depth d, As is the amplitude at the soil surface, and D is a parameter, the damping depth, which is a measure of the rate at which the amplitude is reduced with depth in the soil and is a function of the thermal diffusivity of the soil.11 Soil temperatures at depths of 2, 5 and 10 cm were measured continuously at Wellesbourne during the period May to August 1973 using thermocouples buried in the soil.12 Analysis of these temperature data confirmed that the above assumptions were reasonable. Estimates of the mean temperatures and amplitudes at the different depths were obtained for 40 separate days, 10 randomly selected from each of the 4 months. By regression analysis of In(Ad) against d, daily values of As and D were estimated. The best common value of D was 9.3 cm and the coefficient of variation of daily estimates of D was 26%, very low considering that each estimate was derived from a straight line fit to only three points. This suggests that as a first approximation, D can be considered constant. By a series of regression-fitting procedures,13 the following relationships were derived :

Soil mean temperature Sm= 1.70 + 0.994Am+ 0.466Ao (3)

Amplitude at soil surface As = 0.53 + 1 .62Ao (4)

where Am and A. are the daily mean air temperature and the daily amplitude about the mean, respectively.

Therefore, using daily air temperatures, the mean temperature of the soil can be estimated from equation (3) and the amplitude of the temperature at the soil surface can be estimated from equation (4). The amplitude at depth d can be calculated from equation (2) with 0 = 9 . 3 cm, and therefore :

Maximum soil temperature at depth d= Sm + Ad

Minimum soil temperature at depth d = S, - A d

( 5 )

(6)

I 1’ I I I I I

0 10 20 3 0 40 50

Days Figure 3. Observed (-) and predicted (- - -) daily maximum and minimum temperatures (“C) at 2.5-cm

depth in soil at Regina, Saskatchewan; time O = I June 1976.

Simulation of herbicide persistence in soil 121

4 0

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30

25

20

Further evaluation of the observed soil temperature data showed that the effect of depth on the times at which the daily minimum and maximum temperatures occurred could be estimated,13 but this was not essential for the present purposes. For use in the simulation model, it is assumed that minimum and maximum temperatures are separated by 12 h, and half-sine curves are fitted between appropriate minimum and maximum temperatures.

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3.3. Validation of the revised model Maximum and minimum temperatures, measured at 2-cm depth in the soil, were used by Walker1.8 in studies of the persistence of napropamide and propyzamide; values measured at 2.5 cm were used by Smith and Walkerg to predict persistence of asulam in the soil. Further data at 5-cm soil depth were obtained from a site in Mississippi during studies of the persistence of metolachlor and atrazine.14 Comparisons between calculated and observed maximum and minimum tempera- tures for periods of 50 days at these different sites are shown in Figures 2, 3 and 4. Although, on

- Y F

e a

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45r A

I I I I I -I 0 10 20 3 0 4 0 50

Days

Figure 4. Observed (---) and predicted (- - -) daily maximum and minimum temperatures at 5.0-cm depth in soil at Greenville, Mississippi; time 0=1 July 1979.

occasions, there were marked differences between observed and calculated data, the general pat- terns of temperature fluctuation were predicted by the model. As mentioned before, when these soil temperatures are used in the model for simulation of herbicide persistence, sine curves are fitted between appropriate maxima and minima. Soil temperatures measured at 1-h intervals at 2-cm depth, on some days in June 1973 at Wellesbourne, are shown in Figure 5 together with the sine-curves predicted by the model. There was generally good agreement between observed and predicted daily patterns of temperature fluctuation. Similar agreement was obtained with calculated and observed data for other days.

4. The revised computer program 4.1. Details of the program A full description of the revised computer program is shown in the Appendix. Only those para- meters which are necessary input variables are defined.

4.2. Validation of the model The revised program was used to predict persistence of propyzamide, asulam and 2,4,5-T in soil. using the constants derived previously by Walker,s Smith and Walker,9 and Walker and Smith,lo respectively, together with the appropriate modifications to the program concerning temperature

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128 A. Walker and A. Barnes

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I I I 1 I I 1 I I 0 I 2 2 4 0 12 2 4 0 12 2 4

Time ( il I Figure 5. Observed ( 0 ) and predicted (- ~ -) soil temperatures at Wellesbourne. The observed data were recorded

at I-h intervals on: A, 2 June; B, 4 June; C, 9 June; D, 10 June; E, 12 June; F 17 June 1973.

optima etc. described in these previous reports. Results from the model are compared in Figure 6 with those obtained by use of the measured soil temperatures and moisture contents. With propy- zamide and asulam, the agreement was good. With 2,4,5-T, the model predicted a somewhat faster rate of loss early in the first experiment, compared with that predicted from the use of measured moistures and temperatures, but agreement was good in the other tests.

5. Discussion and conclusions

The methods used to estimate soil moisture contents and temperatures are empirical but they give good approximations to observed data from different sites. The moisture model was used to pre- dict observed data in 0-3 and 0-4 cm soil depths, and because of its empirical nature, it will probably not be accurate for other depths of soil. However, this is unlikely to restrict seriously the validity of the model because the mobility of most soil-applied herbicides is restricted during the summer months, and residues are often located in the few surface centimetres of soil. With the temperature model, constants derived from data measured in a sandy loam soil at Wellesbourne were used to predict soil temperatures in a clay soil in Regina, Saskatchewan, Canada, and in a silt loam soil in Greenville, Mississippi, USA. The degree of correspondence with observed data (Figures 3 and 4) was good considering that the differences in soil type, which would affect thermal diffusivityll and hence the value of the damping depth ( D ) in equation (21, were not allowed for in the model. It would be possible to derive more accurate estimates of the parameters for equations (2), (3) and (4) for different areas from detailed local observations, but the results in Figures 3 and 4 suggest this is not necessary. The temperature model was developed using temperatures measured in bare soil during the summer months and its use will almost certainly be restricted to these conditions. It is unlikely that the parameters derived for equations (3) and (4) will hold during the winter months when the soil may be frozen, and the presence of a crop in summer will also modify the relationship between air and soil temperatures. The results in Figure 6 confirm that the accuracy of the empirical techniques for estimating soil moisture content and temperature is sufficient for the purpose intended; there was little difference between residues predicted by the model, when

Simulation of herbicide persistence in soil 129

9 a 40

201 A b

d

L

100- Figure 6. Herbicide residues in .oil

predicted using measured (A) or calculated ( 0 ) soil moistures and tem- peratures: A, propyzamide at Welles- bourne, time 0=26 April 1973; 9, asulam at Regina, Saskatchewan, time O = 14 May 1976; C, 2,4,5-T at Regina, Saskatchewan, time 0 = 2 May 1977.

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Davs

measured or calculated moisture contents and temperatures were used. However, the data from one of the tests (Figure 6C) suggest that under some conditions the model may be inaccurate. Further comparisons between predictions from the revised model and those from the original model have shown that, in general, results from the two are similar. Again, there are exceptions, and occasionally the new model predicts slower or faster rates of loss. Such differences are not surprising considering the empirical nature of both models. It is unlikely that the methods used to calculate soil moisture contents and temperatures will be accurate under all conditions. Discussion of the ability of the revised model to predict observed residues in the soil is not appropriate here, but the results suggest that this will be no different from that of the original p r~gram. l -~ , 8-10

Appendix

C

C C

C C C C C C C

DIMENSION TMIN(365),TMAX(365),RAlN(365),HEAD(20),SHEAD(20) READ(5,lOO) HEAD

HEAD = heading for output file READ(5,200) NS,NW

NS= day number of first input weather variable N W = day number of last input weather variable

ADPTH =depth of soil for moisture prediction (cm) SDPTH =depth of soil for temperature prediction (cm) ADD =damping depth (cm) ALT =altitude of site (m) ALAT =latitude of site (degrees) ARANN = difference between mean air temperatures in warmest and coldest

months ("C)

READ(5,300) ADPTH,SDPTH,ADD,ALT,ALAT,ARANN

READ(5,400) NRUN,NPRINT,NTINC

130 A. Walker and A. Barnes

C NRUN =Number of runs of program C NPRINT=print interval for output (days) C NTINC =number of calculations per day

TINC = 1 .O/FLOAT(NTINC) WRITE(6,900) HEAD DO 50 I = NS,NW

50 READ(5,500) TMAX(I),TMIN(I),RAIN(I) C TMAX(I)= Maximum air temperature ("C) C TMIN(1) =Minimum air temperature ("C) C RATN(1) =rainfall (mm)

DO 60 J = 1 ,NRUN READ(5,100) SHEAD

C SHEAD= subheading for particular run of model READ(5,600) AIC,AIMC,AT,BD,AFC

C AIC =initial herbicide concentration C AIMC = initial soil moisture content (% w/w) C AT =standard temperature at which moisture response of degradation C C BD =bulk density of soil (g ~ m - ~ ) C AFC =field capacity soil moisture (% w/w)

C E= Arrhenius activation energy derived from laboratory studies (cal mol-1) C A and B = constants to describe moisture dependence of degradation C derived from laboratory studies C NF= First day for simulation relative to NS and NW above C NL= Last day for simulation relative to NS and NW above C CAUTION, NL must be at least one day less than NW

measured in the laboratory ("C)

READ(5,700) E,A,B,NF,NL

WRITE(6,900) SHEAD WRITE(6,1000) E,A,B WRITE(6,llOO) WW= AIMC*BD*ADPTH*O.lO FC= AFC*BD*ADPTH*O.IO T = AT + 273.0 AK4= (0.50*AFC)/2.176

CONC = AIC DO 60 I = NF,NL R = I I J = I + 1

AK3 = AFC - AK4

C The following equations calculate soil temperature parameters. The C effect of depth on daily maximum and minimum temperatures is not C included here.

AMEAN= (TMAX(I)+ TMIN(I))/2.0 RANGE= TMAX(1) - TMIN(1) AAMP= RANGE/2.0 AMEANI = (TMAX(1J) + TMIN(IJ))/2.0

SMEAN= 1.70+ (0.994*AMEAN) + (0.466*AAMP) SMEANI = 1.70 + (0.994*AMEANl) + (0.466*AAMPI) SAMP=0.53 +(1.62*AAMP) SAMPI=0.53 +(1.62*AAMPI) SMXI = SMEAN + SAMP

AAMPI= (TMAX(1J) - TMIN(IJ))/2.0

SMNI= SMEANI - SAMPI

Simulation of herbicide persistence in soil 131

SMEANI=(SMXI+SMNI)/Z.O SAMPI= (SMXI- SMNI)/2.0

C The following equations calculate Eo using the equations derived by Linacre FACT1 = 700.0*(AMEAN+ (0.005*ALT)) FACT2= 100.0- ALAT FACT5 = 0.0023*ALT FACT6 = 0.37*AMEAN FACT7 = 0.53* RANGE FACT8 = (0.35*ARANN) - 10.9 FACT3 = 15.0*(FACT5 + FACT6+ FACT7 + FACT8) FACT4 = 80.0- AMEAN EO = (((FACTl/FACT2) + FACT3)/FACT4) EO = 0.51 + (0.59*EO) IF (EO.LE.O.0) EO = 0.0 DO 60 IP= 1, NTINC

A MC = (WW* 1 O.O)/( BD*ADPTH)

SWS = EXP(SWS) AF = 0.0

C The following equations calculate soil moisture content

SWS = 2.303*(AK3-AMC)/AK4

IF (SWS.LT.600.0) AF= 0.01 - O.oooO2*(SWS- 100.0) IF (SWS.LT. 100.0) AF = 0.10 - O.O0129*(SWS - 30.0) IF (SWS.LT.30.0) AF= 1.0-0.31*(SWS- 1.0) I F (SWS.LT.l.0) AF= 1.0 EVAP= RAIN(I)*TINC*2.0 I F (R- I.GT.0.5) EVAP= - (EO*TINC*AF*2.0) IF (EVAP.GT.FC- WW) EVAP=FC- WW WW= WW+EVAP

C The following equations calculate soil temperature at the appropriate C depth and time

IF (R-I.LE.0.5) GO TO 70 SMEAN= SMEANI SAMP= SAMPI

70 CONTINUE DAMP= SAMP*EXP( - SDPTH/ADD) STEMP= SMEAN+ (DAMP*SIN(6.283*(R+ 0.75))) ST= STEMPS 273.0

C The following equations calculate the rate of herbicide degradation C at the prevailing soil temperature and moisture content

H = A*AMC**B AKI = E/(4.575*T) AK2 = AK1 *(T - ST)/ST HL=2.303*AK2 HL = H*EXP(HL)

CONC = CONC + DCDT R = R + TINC

DCDT= - (0.6932*CONC/HL)*TINC

C The following statements control the input and output

IF (MOD(II,NPRINT).EQ.O.O) GO TO 80 GO TO 60 I F (IP.NE.1) GO TO 60 WRITE(6,800) II,CONC,AMC,STEMP,H,HL

I I= I -NF

80

A. Walker and A. Barnes 132

60 100 200 300 400 500 600 700 800 900 1000 1100

CONTINUE FORMAT(ZOA4) FORMAT(215) FORMAT(3F5.1,2F5.O,F5.1) FORMATOIS) FORMAT(3F5.1) FORMAT(3F5.1 ,F5.2,F5.1) FORMAT(2FlO. 1 ,F10.4,215) FORMAT( 1 H ,18,F10.2,F10.3,F10.1,2F10.2) FORMAT( 1 H ,20A4) FORMAT(lH0,’ E = ’,F12.2,’ A = ’,F12.2,’ B = ’,F12.6) FORMAT(lH0,’ DAYS CONC MC ST H HL ’) STOP END

References I . 2. 3. 4. 5 . 6. 7. 8. 9.

10. 1 I .

12. 13. 14.

Walker, A. J . Environ. Qual. 1974, 3, 396-401. Walker, A. Pestic. Sci. 1976, I, 41-49. Walker, A. Pestic. Sci. 1976, 7, 50-58. Walker, A. Pestic. Sci. 1976, 7, 59-64. Walker, A. Weed Res. 1978, 18, 305-31 3. IBM Users Manual H20-0367-3 IBM (UK) Ltd, Croydon. Linacre, E. T. Agric. Meteorol. 1977, 18, 409424 . Walker, A. Proceedings European Weed Research Council Symposium, Herbicide and the Soil 1973, pp. 240-250. Smith, A. E.; Walker, A. Pestic. Sci. 1977, 8, 449-456. Walker, A.; Smith, A. E. Pestic. Sci. 1979, 10, 151-157. Van Wijk, W. R.; De Vries, D. A. In Physirs of Plant Environment (Van Wijk, W. R., Ed.), North Holland, Amsterdam, 1963, pp. 102-143. Rowse, H. R. Annu. Rep. Nat. Veg. Res. Stn, Wellesbourne, Engl. 1973 1974, p. 50. Barnes, A.; Walker, A,; Rose, J. A. Annu. Rep. Nat. Veg. Res. Stn, Wellesbourne, Engl. 1979 1980, 123-124. Walker, A,; Zimdahl, R. L. Weed Res. 1981, 21, In press.