The procedure used for crop model site specific adjustment

58 M. Gu´erif, C.L. Duke Agriculture, Ecosystems and Environment 81 2000 57–69 conditions for each field in order to apply the model to each point of the domain, and these may vary con- siderably from one point to another. This information is generally not available, but remote sensing, espe- cially in the optical domain, which gives extensive spatial information on the real crop growth status, is a practical way of estimating it. Several methods have been explored Delécolle et al., 1992. One of them Bouman and Goudriaan, 1990; Guérif and Duke, 1998 consists of coupling a radiative transfer model to the crop model through a canopy structure variable like LAI, which makes it possible to simulate remote sensing variables like reflectance in the visible and near-infrared for each point of the spatial domain, at the times when remotely sensed reflectance data are available. Comparison of the simulated and measured variables allows re-estimation of some of the parame- ters or initial conditions of the model, leading to better simulation of yield. This process is called the assim- ilation of remote sensing data into the crop model; it provides a local adjustment of the crop model. Such a procedure was developed in a previous study on sugar beet Guérif and Duke, 1998 that employed the SUCROS model Spitters et al., 1989 and the SAIL model Verhoef, 1984 for simulating radiative transfer into the canopy. The parameters describing the establishment of the crop time between sowing and emergence, number of plants emerged, initial leaf area, which vary greatly according to soil, weather and sowing techniques were re-estimated for specific situations. However, there is a need to know the value of the parameters of the radiative transfer model other than LAI, which are specific to the status of canopies and soils optical properties and geometry of the leaves, reflectance of the soil, and so vary greatly from place to place over a large domain. One should think about estimating them within the assimilation of remote sensing data technique also, but it would increase the number of parameters to be estimated and require a high amount of remote sensing data which is hardly available in operational situations. It was shown that it is possible to develop a method for estimating the values of these parameters, based on prior analysis of their regional variations Duke and Guérif, 1998. Using this method, instead of standard values, can re- duce the errors in spectral reflectance estimates made by the radiative transfer model. The objective of this paper is to measure the in- fluence of these remaining errors due to uncertainty of soil and canopy parameters on the result of re- mote sensing data assimilation process, and hence on the estimates of crop model parameters, initial conditions and yield. The overall performance of the method was evaluated for estimating crop parameters and yield in virtual regional conditions where neither the initial condition sowing date nor some important crop parameters crop establishment characteristics are known. The study is restricted to sugar beet crops in northern France Picardie. In the first part of the paper, the main statements of the previous mentioned studies are presented, then the methodology used and the results obtained in this work of error propagation analysis are presented and discussed.

2. The procedure used for crop model site specific adjustment

2.1. Variations in sowing dates, emergence and early growth characteristics Farmers have tended to sow sugar beet earlier each spring during the past decade, in order to maximise the potential growth of the crop and the final root dry mass. These early sowing dates raised the probabil- ity of more difficult conditions during the sowing– emergence phase, leading to the appearance of mecha- nical obstacles for young plants large soil aggregates due to soil humidity while drilling or crust formation due to rainfall after sowing. These difficult condi- tions may delay emergence the temperature sum req- uired for emergence may rise from 100 to 180 ◦ C day, base 0 ◦ C, decrease the proportion of plants which can emerge 50 emergence rates compared to nor- mal rates of 95, and therefore, result in fewer and smaller plants at emergence Boiffin et al., 1992. These characteristics of crop establishment are key parameters of the SUCROS module for emergence and early growth, as they determine the initial LAI growth Eq. 1: LAI = LAI init exp RGRL×ST−SEMERG 1 where SEMERG is the thermal time from sowing to emergence ST is the thermal time from sowing, LAI init the initial leaf area index at emergence deter- M. Gu´erif, C.L. Duke Agriculture, Ecosystems and Environment 81 2000 57–69 59 mined by the number of plants emerged and the initial leaf area per plant and RGRL is the relative growth rate, which is quite stable whatever the crop establish- ment conditions Boiffin et al., 1992. Both SEMERG and LAI init may vary considerably and be strongly intercorrelated over a large spatial domain, depend- ing on the emergence conditions. Moreover, sowing dates may also vary greatly according to soil traffica- bility and farmers decisions. This was confirmed by measurements that were made on two growing areas in Northern France in 1995 Fig. 1. The time be- tween the earliest and latest sowing dates was about 6 weeks in both cases and the resulting emergence characteristics thermal time from sowing to emer- gence and number of plants varied as widely as that observed during experiments made on various sites and years Boiffin et al., 1992. These variations have major effects on subsequent growth, as is shown by Fig. 1. Frequency histograms of sowing dates, thermal time from sowing to emergence ◦ C days, base 3 ◦ C and number of plants emerged per m 2 over 50 fields in two sugar factory areas; j : Eppeville and : Marle in 1995. field experiments and by SUCROS sensitivity analysis Guérif et al., 1998; Dürr et al., 1999. Thus, the real emergence parameter values are of major importance for simulation of subsequent growth: remote sensing is a powerful tool for estimating these parameters. 2.2. Crop model emergence and early growth module recalibration using assimilation of remote sensing data The method was tested first on a local scale. SUCROS-sugar beet and SAIL models were coupled by means of the LAI variable Fig. 2. Experimental data obtained for a ‘reference crop’, grown in poten- tial conditions, were used to calibrate the models in a previous phase, to adapt some of their coefficients to the regional context Duke, 1997. The method was tested on a different set of experi- mental data, for which crop establishment was inten- tionally disturbed. The default values for the parame- ters of emergence and early growth phases SEMERG and LAI init were used in the SUCROS+SAIL model to simulate the spectral reflectance in three bands green 500–590 nm; red 620–680 nm; near-infrared 790–890 nm, which was compared to four measure- ments made during crop establishment. Minimisation of a criterion based on the differences between sim- ulated and measured spectral reflectance using an optimisation software FSEOPT designed by Stol et al. 1992, enabled the method to re-estimate properly the emergence and early growth parameters as well Fig. 2. Flowchart showing the assimilation of remote sensing data into the crop model. 60 M. Gu´erif, C.L. Duke Agriculture, Ecosystems and Environment 81 2000 57–69 as the crop yield of the test crop Guérif and Duke, 1998. The initial condition sowing date and the SAIL model parameters of crop leaf angles and soil optical properties were known in this local scale application of the method. Transposition of this method to large spatial domains requires estimating such crop and soil parameters, which may vary considerably from one place to another. Furthermore, at this scale, sowing date is not available for each field and has to be esti- mated. 2.3. Variability of SAIL parameters on large spatial domains due to variations in soils and crops 2.3.1. Soil parameters Soil spectral reflectance is an important parameter of the SAIL model. Its role is very strong during crop establishment until the canopy completely covers the soil surface. Soil spectral reflectance depends princi- pally on three soil characteristics: 1. Surface soil texture, which may be considered to be a permanent characteristic of soils. The infor- mation on soil texture spatial distribution is gen- erally available from soils maps: the predominant soil type in the region is a silty loam, with zones of clay loam and chalk classified as an Haplic Luvisol FAO classification. 2. Surface humidity 0–1 mm, which changes quickly, depending on soil texture and the rain evaporation patterns from 5 to 30 of soil dry mass. This information may be empirically de- rived from climatology number of days since the last rainfall for a given evaporative regime or from a crop model including a water balance module. 3. Surface rugosity, which depends mainly on soil tillage operations and changes over time due to the action of the rain. Rugosity is low for seedbeds, but scuffling, which is done before canopy closure to eliminate weeds, may substantially increase it. Information on soil rugosity is quite difficult to ob- tain. Scuffling appeared to be applied to about 20 of the fields in the area. Field measurements on different soil types in the area, with varying humidity and rugosity, were used to derive parameters for soil spectral reflectance ρ soil as a decreasing exponential function of soil surface hu- midity H, dry mass ρ soil = ρ smin + ρ smin + ρ smax − Table 1 Parameters for exponentially decreasing soil reflectance–humidity functions for three main soil types and the two roughness classes Parameters Rugosity Low non-scuffled High scuffled Green Red NIR Green Red NIR Silty loam soil ρ smax 0.25 0.06 0.76 0.16 0.05 0.11 ρ smin 0.33 0.12 0.08 0.24 0.09 0.12 α 0.47 0.16 0.07 0.34 0.14 0.10 Clay loam soil ρ smax 0.19 0.26 0.39 0.19 0.26 0.34 ρ smin 0.09 0.12 0.22 0.06 0.09 0.12 α 0.14 0.13 0.12 0.09 0.08 0.05 Chalky soil ρ smax 0.39 0.44 0.54 0.79 0.79 0.47 ρ smin 0.16 0.21 0.30 0.16 0.20 0.28 α 0.10 0.10 0.16 0.82 0.77 0.16 ρ smin exp−αH, for each soil type and level of rugosity Table 1 Duke and Guérif, 1998. 2.3.2. Plant reflectance parameters The plant reflectance parameters in the SAIL model are the leaf optical properties leaf spectral reflectance ρ L and transmittance τ L and mean leaf angle θ L . Measurement of canopy properties to obtain a proper analysis of regional variations over a growing sea- son is extremely labour intensive. Thus, the results of a study done in 1994 on sugar beet crops expe- riencing various nitrogen regimes were used Guérif et al., 1995. It was found Guérif, unpublished results that plant optical properties and structure parameters change with the crop’s age and the water and nitrogen regimes, which also affect LAI. The canopy proper- ties were expressed as a function of LAI in such a way that they are predictable using the growth model. Two periods were used to describe the canopy characteris- tics: emergence to LAI=2.0, and LAI2.0. The means and standard deviations of θ L , ρ L and τ L are given in Table 2. This analysis of regional variations in crops and soils was used to develop a method of estimating the SAIL parameters hereafter called ‘option 2’ instead of assigning fixed standard values option 1. Soil rugosity was considered to be flat, soil texture was considered as known from soil map, and soil surface M. Gu´erif, C.L. Duke Agriculture, Ecosystems and Environment 81 2000 57–69 61 Table 2 Characteristics of sugar beet vegetation parameters for young and mature crops LAI2.0 LAI2.0 Mean S.D. Mean S.D. ρ f Green 0.14 0.015 0.15 0.014 Red 0.06 0.007 0.07 0.008 NIR 0.46 0.001 0.46 0.001 τ f Green 0.14 0.016 0.15 0.015 Red 0.05 0.011 0.06 0.071 NIR 0.49 0.001 0.49 0.001 θ L 60.0 6.0 45.0 4.5 humidity was considered as dry 5, intermediate 10, or humid 25. Therefore, the parameterisa- tions of soil reflectance–humidity relationships shown in Table 1 allowed the calculation of soil spectral re- flectance. Plant optical properties and geometry were derived from the mean values in Table 3, according to the estimate of LAI given by the model. The errors in estimating canopy reflectance using both options were quantified by a Monte Carlo tech- nique Duke and Guérif, 1998. Synthetic reflectance values which represent an ‘image’ of the regional variations in crops reflectance and will be referred to hereafter as ‘real’ reflectance were created with the SAIL model. The distributions given in Table 2 were used for the plant parameters. Uniform distributions of soil surface humidity within a class of humidity and the parameterisations of soil reflectance–humidity re- lationships in Table 1 were used for the soil parame- ters. For a given soil texture and a given class of sur- face humidity, series of 250 spectral reflectance in the green, red and near-infrared bands were simulated for a range of 10 LAI values from 0.05 to 6.0, by draw- ing parameter values from the distributions estimated from field measurements. The absolute errors on re- flectance estimate E=ρ real − τ simulated using options Table 3 Parameters defining contrasted emergence conditions and crop establishment results Emergence conditions SEMERG ◦ C day LAI init 10 − 4 m 2 m − 2 Good 75 27.0 Intermediate 110 13.9 Poor 150 2.9 1 and 2 were computed for each situation and each spectral band. Option 2 allowed the estimation of SAIL parame- ters using prior knowledge of regional variability and this had many advantages over the standard estimates Fig. 3. Option 1, with its standard values, overesti- mated reflectance for small values of LAI when soil reflectance has strong influence, while option 2 pro- vided estimates closer to the actual values. The errors might be even larger for higher or lower soil surface humidity. When expressing the errors in terms of relative RMSE Eq. 2: RRMSE= 250 P 250 1 ρ real 1 250 250 X 1 ρ real − ρ simulated 2 0.5 2 for all the range of soil surface humidity, the errors appeared to be considerably reduced with our method of estimating SAIL parameters Fig. 4, especially in the early part of the growing cycle from 30 to 15. The next major problem was to quantify the effects of the propagation of these errors due to variations in soils and crops on the results of the crop model recalibration using the assimilation of remote sensing data. This is the objective of the present work.

3. Method