Analysis of two variants of a spatially distributed crop model, using wavelet transforms and geostatistics

Models of crop yield are important for the assessment and optimization of agricultural systems. It is therefore necessary that crop models are suitably validated. In many circumstances, a model is required for prediction at a particular spatial scale (e.g. at a within-field scale for precision agriculture), and validation of the model should account for this. We compared spatially explicit methods to validate a grain yield model applied to a transect of 267 contiguous 0.72 - 0.72 m plots on an arable field at Silsoe, eastern England. Grain yield of wheat was determined in each plot during two growing seasons, and a crop model was used to predict the yield retrospectively. We used two variants of the model, each of which used different spatial variables as input. Observed and predicted yield were then compared with non-spatial statistics, but also with wavelet transforms (i.e. the adapted maximal overlap discrete wavelet transform) and geostatistics (i.e. a linear mixed model estimated by residual maximum likelihood). The latter two are spatially explicit statistical methods. The most successful of the variants required as input the daily evolution of leaf-area index in each plot. Validation of this variant with spatial statistics revealed that (i) the variance of the predictions tended to underestimate that of the observations, particularly at relatively coarse spatial scales, however, in relative terms, the distribution of observed variance across scales was described adequately by the model; (ii) the correlation of the predictions with the observations was weak at relatively fine scales but strong at relatively coarse scales; (iii) there was evidence that the correlation of the predictions with the observations was not uniform across the transect at relatively fine scales, which was possibly due to the underlying soil variation; and, (iv) the spatial pattern of model error suggested that some of the fine-scale yield variation, especially in the first growing season, could be attributed to soil compaction, a process not included in the model. These details were not apparent with non-spatial statistics; wavelets and geostatistics are therefore more appropriate tools for validating a spatially distributed crop model. We conclude that this variant of the model is therefore potentially useful for precision agriculture where we need to predict crop behaviour within small management zones, at the scale of tens of metres, but not to predict yield at finer scales. We outline how the most appropriate statistical technique for a particular study depends on whether the observations can be sampled regularly in space, whether we can assume the statistics are uniform across the landscape, the number of spatial scales of interest, and whether interpolation of the predictions, observations, and errors is required.