Sources of error in model predictions of pesticide
leaching: a case study using the MACRO model
N.J. Jarvis
a,*, C.D. Brown
b, E. Granitza
c aDepartment of Soil Sciences, SLU, Box 7014, 750 07 Uppsala, SwedenbSoil Survey and Land Research Centre, Cran®eld University, Silsoe, Bedford MK45 4DT, UK cHoechst Schering AgrEvo GmbH, Hoechst Works, D-65926 Frankfurt, Germany
Abstract
Uncalibrated predictions of soil water balance, water content, non-reactive solute transport (bromide) and pesticide leaching (bentazone) made by three users of a comprehensive mechanistic model (MACRO) are compared to measured data obtained for a sandy soil at Vredepeel in the Netherlands. The objective was to assess the signi®cance of different sources of error for making predictions of pesticide leaching. Objective statistical indices were used to compare the simulations made by different users and to evaluate overall model performance. All three users predicted very similar water balances. Soil water contents were in good agreement with the measurements, with the simulation based on measured hydraulic functions giving somewhat better predictions than those based on automatic estimation procedures (pedo-transfer functions). Bromide movement was also satisfactorily predicted by all three users despite an inability to reproduce the strong retention near the soil surface caused by ®nger ¯ow. Bentazone dissipation in the ®eld was severely underpredicted by all three users based on laboratory measurements of degradation. This error overshadowed the effects of differences in parameterisation between users. # 2000 Elsevier Science B.V. All rights reserved.
Keywords:Model; Pesticide; Leaching; MACRO; Predictive errors
1. Introduction
Reliable information on pesticide fate and mobility can be obtained from field or lysimeter experiments. However, such experiments are time-consuming, site-specific and expensive. For these reasons, simulation models are now being increasingly used in pesticide registration programs as potentially effective and inexpensive screening tools
*Corresponding author. Fax:46-18-672795.
E-mail address: nicholas.jarvis@mv.slu.se (N.J. Jarvis).
(Russell et al., 1994). With this increasing use of simulation models, it is vital that confidence can be placed in model outputs. In a review of the literature, Jarvis et al. (1995) concluded that most applications to date have involved some degree of calibration to improve model performance so that the predictive accuracy of pesticide leaching models is still unclear.
There are two main sources of error in simulation model outputs: model error and parameter error (Loague and Green, 1991). Model errors result from incorrect or undue simplification of process descriptions in the model and neglect of significant processes (Russell et al., 1994). Clearly, some degree of model error is inevitable, since by definition models are simplifications of reality. However, in principle, model errors should be minimised when mechanistic process descriptions are used (Wauchope, 1992) and in detailed models which include as many relevant processes as possible. Parameter error is the use of inappropriate parameter values. These errors arise either because the required data is not available, because they are interpreted in different ways by different users, or because the measurements are themselves subject to error or for some reason do not adequately reflect the prevailing field conditions. This may be potentially serious for comprehensive data-demanding simulation models and for those parameters for which the relevant model outcome (e.g. leaching) is especially sensitive. Parameter error is particularly critical where models are used predictively, since methods for parameter estimation (e.g. default values, pedo-transfer functions) may introduce additional sources of error. In a model `ring test', Brown et al. (1996) demonstrated that errors in parameterising pesticide leaching models resulted in significant variations in model predictions, even among `expert-users'. These potential errors are magnified for users of the more complex simulation models, who may be specialists in some aspects of the subject (e.g. pesticide chemistry) but relatively inexperienced in others (e.g. soil physics). In this paper, we investigate the relative significance of different sources of error for one of the more detailed mechanistic models available (MACRO, version 4.0) using independent predictions made by three users of water balance, non-reactive solute transport (bromide) and pesticide leaching in a sandy soil (Vredepeel, Netherlands).
2. Materials and methods
2.1. Site details and measurements
Simulations are presented of experiments carried out in a sandy soil (Vredepeel) in Netherlands under winter wheat. In this paper, simulation results are compared to contents of soil water, bromide and bentazone measured in the soil profile by coring on three occasions during a 14-month experimental period. For site descriptions and detailed information concerning the measurements, the reader is referred to Boesten and van der Pas (2000).
2.2. Description of the model
boundary between the domains defined by a soil water pressure head close to saturation and its associated water content and hydraulic conductivity. Water flow in micropores is calculated by the Richards' equation while simple gravity flow is assumed in the macropores. Solute transport in micropores is given by the convection±dispersion equation (CDE), with pesticide assumed to obey first-order kinetics for degradation and linear instantaneous, reversible, sorption. In the case of the sandy soil at Vredepeel, the hydraulic conductivity of the micropore region is sufficiently large to prevent the macropores acting as a preferential flow region so that the model effectively reduces to the classical Richards/CDE approach. For a full description of the model, the reader is referred to Jarvis (1994) and Saxena et al. (1994).
2.3. Modelling strategy
For the simulations presented in this paper, no model calibration against the measurements was allowed. Apart from this, each model user was given the freedom to parameterise the model in any way considered appropriate. In practice, this meant that the users could derive parameter values either from the available measurements, from default values in the model, from previous experience, or from automatic estimation procedures (pedo-transfer functions). Table 1 summarises the methods chosen by the three users for different parameter groups in the model.
In this study, model performance is assessed objectively by comparing the degree of agreement of the model with the measurements using statistical indices (Loague and Green, 1991). Four such indices are used, the modelling efficiency EF, the non-normalised root mean square error NRMSE, the coefficient of shape CD and the coefficient of residual mass CRM (Vanclooster et al., 2000). The NRMSE is defined as
NRMSE
The ideal value of CD is unity. The ideal values of NRMSE and CRM are zero. If CRM takes large positive or negative values, then the mass of the substance is strongly underestimated and overestimated, respectively. In the case of pesticide residues, this implies errors in predicting degradation.
Table 1
Methods used to parameterise the modela
Parameter group
aA: direct measurements/®eld observations; B: pedo-transfer functions in MACRO_DB (Jarvis et al., 1997); C: default values in the model; D: experience/general knowledge.
The modelling results obtained by the different users were compared to the measurements using the stepwise test procedure adopted for the COST modelling exercise (Vanclooster et al., 2000). In this procedure, the water balance and soil hydrology are compared first, followed by non-reactive solute transport, heat flow and soil temperatures, and finally, pesticide movement and persistence.
3. Results and discussion
3.1. Soil water balance
The calculated soil water balance depends strongly on evapotranspiration which, in turn, depends on the crop parameterisation chosen by the user. For most model applications, little information is available concerning crop development, and Vredepeel is no exception in this respect. All three users set emergence and harvest dates to known values. Also, apart from the parameters discussed below, all crop parameters were set to default values in MACRO 4.0 by all three users. User 1 set the maximum root depth to 0.6 m despite the reported root depth of 0.4 m (Boesten and van der Pas, 2000). From past experience in using the model, this user concluded that the effective root depth is usually somewhat deeper than that observed. The maximum leaf area index was also reduced from the default value in the model of 5 to 3, based on comments in Boesten and van der Pas (2000) that wheat growth during the experiment was poor due to drought stress. The critical water tension for uptake was reduced from the default value of 10 to 2 m, a typical value for sandy soils. User 2 set all crop parameters, except emergence and harvest dates, to default values in MACRO 4.0. Thus, in contrast to user 1, the maximum root depth was assumed 1 m, the maximum leaf area index was 5.0, and the critical tension for water uptake was 10 m. User 3 derived crop parameters from the estimation routines in the MACRO_DB database version of the model (Jarvis et al., 1997). The maximum root depth was 0.5 m, the maximum leaf area index 4.4 and the critical tension for water uptake 1.37 m.
Table 2 shows that accumulated actual evapotranspiration was similar for all three users (448±468 mm), giving a very similar water balance, despite the documented differences in crop parameterisation particularly between user 2 and users 1 and 3. The reason for this is that potential evapotranspiration (PET) was calculated in different ways: users 1 and 3 took the meteorological data supplied and calculated PET by the Penman±
Table 2
Monteith equation internally in the model, while user 2 supplied the model with the Makkink estimates of PET given in Boesten and van der Pas (2000). It can be noted that MACRO allows the user both options. PET calculated by the Penman±Monteith equation was larger than the Makkink estimates, so that the ratio between actual transpiration and potential transpiration was smaller for users 1 and 3 than for user 2. Supplementary calculations showed that if user 2 had calculated PET with the Penman±Monteith equation, then actual evapotranspiration would have been ca. 12% larger than that estimated by user 1, and the net recharge to groundwater reduced by a corresponding amount.
3.2. Soil hydraulic properties
User 1 derived the soil hydraulic parameter values from the reported measurements using the RETC program (Yates et al., 1992), fitting the data simultaneously to the Brooks and Corey (1964) water retention function and the Mualem (1976) model of unsaturated hydraulic conductivity. In contrast, users 2 and 3 made use of the pedo-transfer functions available in the auxiliary shell program MACRO_DB (Jarvis et al., 1997) to predict the hydraulic properties from soil texture, bulk density and organic carbon content. On the whole, these pedo-transfer functions succeeded quite well in reproducing the parameter values derived from least-squares fitting to the measured water retention and hydraulic conductivity functions. However, in one important respect, they failed to match the data. The air-entry pressures were overestimated by the pedo-transfer functions, and the pore size distribution index strongly underestimated. The reason for this is that the pedo-transfer functions are based only on total sand, silt and clay contents, and cannot therefore discriminate between soils dominated by fine, medium or coarse sand fractions. In sandy soils, the distribution and relative abundance of these sand fractions has very important implications for the shape of the hydraulic functions near saturation. It is clear from the measured water retention data (Boesten and van der Pas, 2000) that Vredepeel is dominated by the finer sand fraction and is also quite narrowly
graded (especially in the subsoil), giving small values of air-entry pressure (ÿ39 cm in
the topsoil andÿ45 cm in the subsoil), and large values of the pore size distribution index (0.85 and 1.96, respectively). In contrast, the pedo-transfer functions gave air-entry
pressures varying fromÿ8 toÿ10 cm and pore size distribution indices of ca. 0.2±0.3.
These values may be considered to represent an `average' sand, in effect, one that is characterised by a broader pore size distribution.
All three users assumed similar values for the limiting water content for root water uptake (`extractable' water content, Fig. 1). All three users also assumed similar values for the saturated water content (Fig. 1). The small differences result from differences in defining how the bulk density varied with depth in the soil profile. However, Fig. 1 shows that the pedo-transfer functions adopted by users 2 and 3 result in significantly larger
water contents at intermediate pressure heads (e.g.ÿ100 cm in Fig. 1) compared to the
values calculated by user 1 based on the measurements, especially in the subsoil. This is largely due to the underestimate in pore size distribution index discussed above. Fig. 2 shows that the pedo-transfer functions (users 2 and 3) gave reasonable estimates of saturated hydraulic conductivity based on calculated values of effective porosity
(saturated water content minus water content at a pressure head ofÿ50 cm). In contrast, due to the errors in estimating the air-entry pressure and pore size distribution index, the
unsaturated conductivity at ÿ50 cm was underestimated by up to two orders of
magnitude.
3.3. Water ¯ow and water contents
All three users predicted similar flow patterns at Vredepeel, with the two main
recharge periods characterised by typical flow rates of ca. 0.1±0.4 mm hÿ1(see Fig. 3).
Fig. 1. Soil water contents estimated at saturation (ys),ÿ100 cm pressure head (y100), and at the lower limit of root water extraction (ye).
This is to be expected because recharge is governed by the overall soil water balance, which was similar for all three users, rather than soil hydraulic properties. However, given similar water flow rates, the errors in hydraulic properties generated by the pedo-transfer functions should result in larger profile water contents. The simulations confirm that users
2 and 3 do indeed predict water contents which are ca. 0.04±0.05 m3mÿ3larger in the
upper part of the soil profile during recharge periods (see Fig. 4a,c).
It is not easy to say for certain which user produced the best simulations of soil water balance, because the data available for comparison consists of only three `snapshots' of measured water content profiles. The statistics of the goodness-of-fit of model predictions shown in Table 3 show that all three users produced acceptable simulations of soil water content with positive values of EF and NRMSE less
than 0.06 m3mÿ3. However, the simulation based on the measured data (user 1) does
give the largest overall EF and also appears subjectively to better capture the shape of the measured profiles, in particular the clear difference in water contents between topsoil and subsoil horizons (Fig. 4a±c). However, the values of coefficient of shape do not always confirm this impression (Table 3), and on one sampling occasion (Table 3, Fig. 4a), the NRMSE are larger than those obtained through the use of the pedo-transfer
functions (users 2 and 3), which are generally of the order of 0.05 m3mÿ3. The three
users made similar (and accurate) predictions of water contents on the one summer sampling occasion (Table 3), presumably because the `extractable' water content largely controls the minimum water contents attained during extended dry periods. This parameter was set to almost identical values by the three users (Fig. 1). It can be noted here that deep in the profile, water contents are controlled more by the water table position than by the hydraulic properties and surface boundary conditions. Although it is not shown here, user 2 generally predicted a deeper water table than both users 1 and 3 and thus, a drier lower subsoil. This is reflected in the slightly poorer EF obtained by user 2.
Fig. 3. Soil water ¯ow predicted at 27 cm depth in the pro®le.
3.4. Bromide transport
There were no significant differences in parameterisation of non-reactive solute transport between the three users (only the diffusion coefficient was given different values, but this is of minor significance for transport in a sand soil). Since water contents are larger, and recharge rates are similar (almost identical water balance), the pore water velocity controlling the mean convective solute displacement predicted by users 2 and 3 should be smaller (rough calculations suggest by perhaps up to 20%). This conclusion is confirmed by the comparison of predicted bromide depth profiles (Fig. 5a±c). The difference in predicted bromide transport is particularly noticeable for the profile on 27 August 1991 (Fig. 5b) which represents the system state at the end of the first recharge period.
A statistical comparison with the measured data (Table 4) shows that the use of pedo-transfer functions has resulted in apparently slightly better predictions of bromide transport, despite poorer predictions of soil water content. This is particularly the case on 27 August 1991 (Fig. 5b), when the retardation of bromide transport is captured by users 2 and 3 but not by user 1. This is probably fortuitous: the much slower bromide transport observed in the field experiment compared to the model predictions is probably due to `immobile water' and by-pass `finger flow' caused by topsoil water repellency. This is an interesting illustration of the fact that `model error' (MACRO cannot predict transport retardation due to preferential flow in sands) can sometimes fortuitously cancel out `parameter error' (underestimated pore water velocity) resulting in quite reasonable model predictions. Indeed, the overall EF values shown in Table 4 are positive for all three users indicating an acceptable model performance.
Table 3
Statistics of goodness-of-®t for predictions of soil water content
Sampling occasion EFa NRMSEb CSc CRMd
User 1 1 ÿ1.999 0.050 0.481 ÿ0.207
2 0.948 0.018 0.791 0.005
3 0.578 0.035 0.432 ÿ0.034
All 0.771 0.034 0.756 ÿ0.070
User 2 1 ÿ0.255 0.033 5.623 ÿ0.027
2 0.563 0.052 1.874 ÿ0.234
3 ÿ0.651 0.069 9.038 0.099
All 0.397 0.055 1.084 ÿ0.049
User 3 1 ÿ0.427 0.035 7.269 ÿ0.017
2 0.615 0.049 2.494 0.03
3 ÿ0.241 0.060 5.045 0.142
All 0.498 0.050 1.732 0.059
Overall 0.555 0.047 1.039 ÿ0.02
aModel ef®ciency.
bNon-normalised root mean square error (m3mÿ3). cCoef®cient of shape.
dCoef®cient of residual mass.
3.5. Soil temperatures
Soil temperature strongly influences pesticide biodegradation so that the prediction of temperature should be an important part of any pesticide leaching model. Fig. 6 shows that the soil temperatures predicted by the three users at 1 m depth are within ca. 38C at all times. This is also the case for other depths in the profile (not shown), and is not particularly surprising since the soil thermal properties in MACRO are defined internally
Table 4
Statistics of goodness-of-®t for predictions of bromide content
Sampling occasion EFa NRMSEb CSc CRMd
User 1 1 0.272 3.511 1.906 ÿ0.459
2 ÿ1.950 3.231 0.484 ÿ0.460
3 ÿ2.257 1.596 0.502 ÿ0.603
All 0.102 2.874 1.303 ÿ0.482
User 2 1 0.468 3.001 1.085 ÿ0.233
2 ÿ1.694 3.087 0.525 ÿ0.020
3 ÿ2.588 1.675 0.992 ÿ0.702
All 0.221 2.677 0.789 ÿ0.200
User 3 1 0.434 3.096 1.924 ÿ0.162
2 ÿ0.261 2.112 1.193 0.035
3 ÿ2.036 1.541 0.306 ÿ0.456
All 0.458 2.233 1.062 ÿ0.109
Overall 0.260 2.609 0.951 ÿ0.264
aModel ef®ciency.
bNon-normalised root mean square error (mg dmÿ3). cCoef®cient of shape.
dCoef®cient of residual mass.
Fig. 6. Soil temperatures predicted at 1 m depth.
in the program so that the user cannot influence predictions of temperature to any great degree. There are only two parameters influencing temperature which the user can vary, the annual average air temperature and the annual amplitude in air temperature on a monthly basis. These parameters only influence the bottom boundary condition in the model.
3.6. Bentazone leaching
Figs. 7 and 8 show sorption distribution coefficients and degradation rate coefficients assumed by the three users. The parameter values chosen by the users should be very similar since they are largely based on the same set of laboratory measurements. This is
Fig. 7. Sorption constants for bentazone estimated by the three users.
true in the case of sorption parameters, but some significant differences are apparent in the parameterisation of degradation. This is partly because the laboratory degradation measured in the topsoil at 158C did not exactly follow the model assumption of first-order kinetics, but instead showed a two-phase pattern. Up to 157 days, bentazone degraded at a half-life of ca. 35 days, while from 157 to 450 days a half-life of 70 days was more appropriate. Users 1 and 2 selected an average value for the whole period, while user 3 fitted the rate constant to the initial, faster, degradation phase, making the reasonable assumption that the slower phase resulted from the commonly observed die-off of soil microbial populations in laboratory tests (Fig. 8). The temperature response function for degradation represents another significant difference in parameterisation between the users. User 1 sets the exponent in this function to 0.172 based on the measurements made at two temperatures in the laboratory, while users 2 and 3 chose the default value in the model (0.08), since a value of 0.172 results in an unreasonably large activation energy. Clearly, only two sets of measurements are insufficient to reliably parameterise the model. The net effects of these differences in parameterisation is that user 3 predicts the
fastest degradation at the reference temperature of 108C, while users 1 and 3 would
predict similar rates at 208C, slightly more than twice those of user 2 (the differences at cold temperatures are not so significant, because rates are low anyway).
Fig. 9a±c shows that user 2 does indeed predict somewhat slower dissipation of bentazone than users 1 and 3, particularly in the summer period during the experiment. The statistical comparison with the measured data (Table 5) shows that all three MACRO users considerably underestimated the observed dissipation of bentazone, with large positive values for the CRM, and negative values of EF. One explanation may be that the model underestimated leaching of bentazone below 1.1 m depth. It is difficult to test this hypothesis without flux measurements (e.g. lysimeters, drainage outflows), although the model showed no tendency to underpredict the rate of bromide leaching. Therefore, we consider that a more likely reason for the discrepancy is that bentazone degradation was underestimated either because the microbial activity in the laboratory incubation experiments did not reflect that of undisturbed populations in the field soil or because there are significant dissipation pathways and mechanisms for bentazone in the field which are not observed in the laboratory and are not included in the model. In this respect, much shorter laboratory aerobic half-lives than those used in this study are
Table 5
Statistics of goodness-of-®t for predictions of bentazone content
EFa NRMSEb CSc CRMd
User 1 ÿ1.02 21.36 0.60 0.79
User 2 ÿ2.81 29.33 0.46 1.31
User 3 ÿ0.38 17.66 0.58 0.81
Overall ÿ1.05 21.75 0.51 1.15
aModel ef®ciency.
bNon-normalised root mean square error (mg mÿ3). cCoef®cient of shape.
dCoef®cient of residual mass.
normally reported for bentazone in freshly collected field soils (on average 14 days at 208C equivalent to ca. 31 days at 108C, assuming 0.08 for the exponent in the temperature response function), while field half-lives for bentazone as short as 12 days have also been reported (Tomlin, 1997). Using MACRO, Jarvis et al. (1994) also underpredicted bentazone dissipation observed in lysimeter experiments. This was tentatively attributed to photolysis (Nilles and Zabik, 1975).
4. Conclusions
The three users introduced significant differences in parameterisation of the degradation submodel in MACRO due to (i) difficulty in estimating the reference first-order rate coefficient for degradation from laboratory incubation tests exhibiting biphasic degradation, (ii) uncertainty concerning the reliability of the laboratory degradation measurements made at two different temperatures leading to differences in parameterisa-tion of the temperature response funcparameterisa-tion. Since leaching predicparameterisa-tions are strongly dependent on degradation, it is recommended that for registration purposes, strict protocol guidelines with respect to interpretation of laboratory incubation tests should be developed and followed. The model users also adopted different methods to parameterise soil hydraulic properties. The use of pedo-transfer functions resulted in root mean square
errors in predicted soil water contents of the order of 0.06 m3mÿ3, which were only
slightly larger than the values obtained when fitting to actual measured data. Of course, whenever real data are available, it is recommended that these are used. However, this study shows that the use of such pedo-transfer functions may be sufficiently accurate for registration purposes.
Nevertheless, the main source of error was common to all three users, namely that larger dissipation rates were observed in the field compared to those predicted from the laboratory incubation measurements. This may have resulted from the exclusion of significant processes, particularly the presumed existence of additional abiotic dissipation pathways for bentazone (photolysis) or because the laboratory was not representative of field conditions either due to sampling disturbance, soil handling, the dosing method used or population die-off. Another process which is not included in the model is preferential finger flow. This was shown to influence non-reactive bromide transport, but its effect on bentazone transport could not be assessed due to the dominating influence of errors in degradation.
Acknowledgements
This study was carried out within the framework of the mathematical modelling working group of COST Action 66 `Pesticide fate in the soil environment' organised by DGXII of the EU. The authors are grateful to Jos Boesten (Winand Staring Centre, Netherlands) for supplying the dataset `Vredepeel', especially for the user-friendly way in which it was compiled. The authors also thank Allan Walker (HRI, UK) for the use of the program STATIND for calculating statistical indices of model performance.
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