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Mathematical Models of Crop Growth and Yield (Books in Soils, Plants, and the Environment)
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An Anarchy of Chillies. Cannabis For Dummies For Dummies. View Wishlist. Our Awards Booktopia's Charities. To do so, we computed Yp for maize Zea mays L. We ran the simulation models for all locations in a global weather database to compute Yp. We then divided the weather station locations into training and testing locations and made predictions for the testing locations with data from the training locations. The two models have been widely used and they were chosen because of their differences in complexity, and because both models were implemented as R packages R Core Team, , which facilitates their use for this type of study.
Both models operate on a daily time step and require daily solar radiation S rad and maximum temperature T min and minimum temperature T max to compute Yp. LINTUL is a relatively simple model that simulates the development of leaf area index as a function of thermal time and then uses a fixed radiation use efficiency to estimate biomass production. These data were derived from satellite observations coupled with the Goddard Earth Observing System climate model to obtain complete terrestrial coverage. The quality of the Prediction of Worldwide Energy Resource data as input for crop models has been evaluated, with mixed results Bai et al.
We note that these evaluations are problematic, as they compared weather station data at a particular site with the average values for large grid cells but we do not dispute that the data have some error and bias. Though the quality of these data could be important considerations for a particular study, region, or crop model, this is not a major concern for our study, as our purpose is not to provide the most accurate estimates of Yp, but rather to compare different spatial estimation methods that all use the same input data. We also computed monthly climate averages from the daily data to use as an input for the metamodel and the weather generator.
Spatial Prediction Methods and Evaluation We ran the two simulation models for each of the two crops for all 18, terrestrial weather stations excluding Antarctica using an emergence day on the 15th of each month for each of 30 yr — To select a plausible growing season, we then computed the average yield for each month, then the maximum of the resulting 12 values was used as the observed Yp for a crop and model combination. In other words, for each weather station, we selected the sowing date that on average, gave the highest Yp during the yr period.
We evaluated the performance of five main methods to estimate Yp at the testing locations by comparing the results with observed Yp, computed with the crop simulation models. We also evaluated the effect of distance to the nearest station on RMSE. Five main spatial estimation methods were used; eight methods one counts the within-method variations Fig. Interpolated weather W INT : Daily weather data were interpolated to the testing data sites for which the crop model was run.
Interpolation was done via thin plate spline TPS models with longitude, latitude, and elevation as independent variables. The TPS model was used here and in the interpolations described below, because of its ease of use and because it has been successfully used for spatial interpolation of climate data Hutchinson, ; Jarvis and Stuart, ; Fick and Hijmans Interpolated yield: Simulated Yp at the training sites was interpolated via TPS to estimate yield at the testing sites.
Random Forest has the benefit of flexibility for fitting potentially irregular surfaces resulting from complex interactions. These variables have been shown to be of great practical value in spatial predictive modeling of the distribution of species and in related ecological modeling techniques Booth et al.
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The bioclimatic variables represent annual trends e. Weather generator: Daily weather data were generated from long-term averages in two ways. Comparing these two variations allows us to separate the effect of the climate interpolation and the weather simulation. The weather generator was extremely simple.
Monthly averages were assigned to the 15th of each month or 14 February and values for intermediate days were obtained by linear interpolation. These generated values were used to run the crop model. Flow diagram showing different approaches for creating crop model predictions with high spatial resolution from spatially sparse weather station data. Here, we focus on the average results. The M BIO model performed best by far. It had an average correlation coefficient of 0. The I NN model was the worst methods with an averaged correlation coefficient of 0.
Quality of predicted yield potential for nine prediction methods. In general, the methods overestimated the observed yield values Table 1, Supplemental Table S1. The G WTH model tended towards underestimation for low observed Yps and overestimation for observed Yps higher than about kg ha —1 Fig. S1, Supplemental Fig. S4, Supplemental Fig. With the I XY method, for low observed Yp values, higher values were often predicted, whereas for high observed values, lower values were often predicted.
Correlation between predicted and observed long-term average yield potential at each location for maize and the WOFOST model. There were large differences between the variants within the main methods. Thus interpolation of the climate had a negative effect in the performance of the weather generator method. S2S, Supplemental Fig. S5, Supplemental Fig. For the poorest performing methods I XY , M CLM , and I NN , the largest differences between the observed and predicted Yp, were found in mountains regions such as the Rocky Mountains, Andes, and Himalayas, as well as in places where there were fewer nearby training sites because of edge effects along the coast Fig.
S3, Supplemental Fig. S6S, Supplemental Fig. Maize yield potential Yp; 10 3 kg ha —1 simulated with the WOFOST model and predictions based on training sites black points on map via eight methods. Differences between maize yield potential Yp; 10 3 kg ha —1 simulated with the WOFOST model and Yp predicted via eight different spatial methods using training sites white points on map. The I NN model was the only method for which there was a clear relationship between RMSE and the distance to the nearest weather station. Unsurprisingly, the performance was better at shorter distances.
For example, RMSE was kg ha —1 at km but kg ha —1 at 50 km and it would be zero at 0 m distance to the nearest weather station. In other words, for each km increase in the distance from a weather station, the RMSE will increase by 9. Most crop simulation models require long-term daily weather data as input but for many regions, weather station data are not available at a high spatial resolution.
We compared the performance of five main methods eight methods if one counts the within-method variants that can be used to estimate yield potential in places where there are no weather stations. An advantage of this approach is that such a metamodel is mathematically much simpler than the dynamic crop simulation models and therefore is very fast. This can be an important time-saver when modeling on the global scale and at a high spatial resolution e.