Effect of uncertainty in temperature and precipitation inputs and spatial resolution on the crop model

This study addresses the effect of uncertainty in temperature and precipitation inputs and spatial resolution on crop simulation results for Hungary and Romania. Crop yield and harvested area for maize and winter-wheat were simulated using the improved Global Agro-Ecological Zones model (iGAEZ) for the years 1990–1999 with two climate inputs (Climatic Research Units Global 0.5°C Monthly Time Series, Version 2.1 (CRU TS 2.1) and Meteorological Research Institute Global Climate Model with the 20-km mesh horizontal resolution (MRI-GCM20)). The mean, standard deviation and RMSE of the differences between constraint-free and moisture-limited crop yield demonstrate that uncertainty in temperature and precipitation is a significant cause of the considerable uncertainty on crop simulation results at 0.5-degree grid. This uncertainty decreases when simulation results are spatially aggregated to the country scale. Next, to assess the effects of spatial averaging of climate input data, we performed the crop simulations at 0.5 and 0.25-degree grid using MRI-GCM20. The results showed that the correlation of the simulation results at 0.5-degree and at 0.25-degree grid scale is very weak. It seems that within-grid variability in climatic data significantly affects the crop simulation results. Moreover, the comparison of the Food and Agriculture Organization (FAO) yield statistics with crop simulation results shows that simulation results at 0.25-degree grid are much better than that of 0.5-degree grid.


INTRODUCTION
Many studies have emphasized the impact of input and model error on the actual simulated outcomes of complex simulation models.Wirz (2000) presented a solution to scaling of a complex photosynthesis model, including the variation associated with daily weather variables.Complex crop models are being used to predict and quantify the effects of climate change on crop yield at the regional or national scale (Tan and Shibasaki, 2003;Parry et al., 2004;Stehfest et al., 2007).Tatsumi et al. (2011) developed a new global crop yields modeling methodology -improved Global Agro-Ecological Zones model (hereafter referred to as 'iGAEZ') based on Global Agro-Ecological Zones (GAEZ) (Fischer et al., 2000).Moreover, considerable research into the effects of uncertainty in climate, soil and crop management on crop simulation model outputs has been carried out.In recent years, there have been many studies to assess uncertainty in climate, soil and management (Bouman, 1994;Nonhebel, 1994;Pachepsky and Acock, 1998;Soltani et al., 2004;Fodor and Kovacs, 2005;Masutomi et al., 2009).These studies have contributed greatly to the understanding that (1) the main drivers for the uncertainty in model outputs are climate and soil data, and (2) crop models are sensitive to the variability of temperature and precipitation inputs and spatial scale of climate inputs (Mearns et al., 1997;Semenov and Porter, 1995).However, these studies don't represent the quantitative assessment of uncertainty in further detail in regional and global scale crop yield models.Additionally, much less work has been done on the global crop simulation using a high-resolution database.
Guiding research questions were as follows.( 1) To what extent does uncertainty in climate inputs and spatial resolution affect the iGAEZ model?, (2) How accurately can crop yield and the harvested area for small countries be reproduced by iGAEZ?
The objectives of this study are: (1) to quantify the influence of uncertainty in temperature and precipitation on crop simulations with different spatial resolutions (0.25 and 0.5-degrees) and the national yields for Hungary and Romania, (2) to evaluate the influence of spatial averaging of temperature and precipitation values on model outputs, and (3) to assess the effect of spatial scale and uncertainty in climate on model outputs.In global-scale numerical simulations, especially for countries with large croplands, there are no significant differences in the crop yields result between two datasets with low-resolution (0.5-degree) and high-resolution (0.25-degree).A few examples are shown in Figures S1 and S2, in which we examined results for China.No significant difference was found in using the two datasets with different spatial resolutions.Moreover, good agreement was obtained between crop model outputs obtained with low-resolution datasets (0.5-degree) and statistical values among continental scales (Tatsumi et al., 2011).On the other hand, few attempts have been made to evaluate our model in small countries such as Hungary and Romania.We need to examine the impacts of the spatial resolution in dataset on yield estimation for countries with smaller croplands.This paper attempts to validate our model performance in terms of spatial resolution of dataset by comparing model outputs with high-resolution (0.25-degree) and low-resolution (0.5-degree) for a case study in small countries.

DATA AND METHODS
We used the iGAEZ model (Tatsumi et al., 2011) to calculate crop yield and assess the effect of uncertainty in temperature and precipitation on crop yield and harvested area.The iGAEZ requires daily climate inputs for mean, maximum, and minimum temperature, precipitation, vapor pressure, and solar radiation.Document S1 provides the iGAEZ framework.The study area is located in Hungary and Romania.These countries have a small land area, with which the difference of spatial resolution may make differences in the model simulation.Production of maize and winter-wheat is done briskly in these countries.Further, agriculture in these countries is almost entirely achieved through rain-fed cultivation (Portmann et al., 2010).Thus, we need not take the effect of irrigation into consideration and time series of yield statistics are available.These are the reasons for the choice of the study area.
This study employs several sets of climate and static data as shown in Table SI.The Climate Research Units Global 0.5°C Monthly Time Series, Version 2.1 (CRU TS 2.1) is the observed monthly climate dataset that was published by Climatic Research Units (Mitcell and Jones, 2005).On the other hand, the Meteorological Research Institute Global Climate Model with the 20-km mesh horizontal resolution (MRI-GCM20) is a 0.1875 degree grid global climate model which was newly developed for the KAKUSHIN program (Kitoh et al., 2009).These data were interpolated to daily values using linear interpolation.Moreover, we resampled the static data (elevation, soil, etc.) to 0.5 and 0.25-degree spatial resolution using the nearest neighbor method.
In the beginning, we determined the uncertainty in the MRI-GCM20 temperature and precipitation by calculating the average temperature and total precipitation over a month in 1990-1999 for both CRU TS 2.1 and MRI-GCM20 databases.These results provided information which explained the differences of crop simulation results when using CRU TS 2.1 and MRI-GCM20 climate inputs.Here, the average temperature and precipitation values of MRI-GCM20 grid points within a CRU TS 2.1 grid cell were used (hereafter referred to as 'MRI-GCM20-0.5').Next, we carried out the crop yield simulation at the 0.5-degree grid using CRU TS 2.1 and averaged climate variables of MRI-GCM20.Thereby, we can estimate the influence of uncertainty in the temperature and precipitation inputs on iGAEZ.Third, we simulated the crop yield at the highresolution 0.25-degree grid using MRI-GCM20 (hereafter referred to as 'MRI-GCM20-0.25'),with each 0.5-degree grid box containing four 0.25-degree grids.Each 0.25-degree grid received the climate variables of the nearest MRI-GCM20 grid point.These simulations allowed us to estimate the within-grid variability of the crop yield in order to infer if simulation at the high-resolution has more effect on the crop yield and harvested area.
The experiment was applied for the years 1990-1999 in order to simulate the crop yields of maize and winter-wheat for Hungary and Romania.To evaluate the influence of the climate inputs on the crop simulation results at the national scale we used the Food and Agriculture Organization (FAO) yield statistics (FAOSTAT, 2005).

Differences of CRU TS 2.1 and MRI-GCM20 temperature and precipitation
We examined the differences between the CRU TS 2.1 and the MRI-GCM20-0.5 databases for temperature and precipitation in Hungary and Romania (Table SII in the supplement).It demonstrates that MRI-GCM20-0.5 has a tendency to overestimate temperature compared to CRU TS 2.1 in July-October for both countries.On the other hand, MRI-GCM20-0.5 underestimated temperature by 0.32-2.64°C in February-June for both countries.Moreover, the standard deviation of the differences in temperature indicates that the largest variability is in August.Monthly total precipitation values by MRI-GCM20-0.5 have a tendency to overestimate precipitation for all months compared to CRU TS 2.1, except for September-November in Hungary, and August-September in Romania.Of note is that precipitation values in June for MRI-GCM20-0.5 are more than 100 mm/month, and about twice that of CRU TS 2.1.

Effect on crop yield of uncertainty in climate variables
In this section, we assessed climatic uncertainty by comparing constraint-free and moisture-limited crop yields using the CRU TS 2.1 and MRI-GCM20-0.5 projection.For constraint-free maize yields, yield using CRU TS 2.1 is slightly less than that using MRI-GCM20-0.5 (Table I).
Table I.Summary statistics of the crop yield at 0.5-degree grids using CRU TS 2.1 and MRI-GCM20-0.5 for 1990-1999 a Yield averaged over all 0.5-degree grids b CRU TS 2.1 minus MRI-GCM20-0.5 c Standard deviation of the differences in yield of all 0.5-degree grids d RMSE of the differences in yield of all 0.5-degree grids  et al., 2010).In this period, average temperature by MRI-GCM20-0.5 is slightly higher than that of CRU TS 2.1.Moreover, the growing degree day accumulation (degree C × days, referred to as 'DDA') between planting and harvest date by MRI-GCM20-0.5 is slightly larger than CRU-TS 2.1.Consequently, we can explain this result by the overestimation of temperature and DDA with MRI-GCM20-0.5 compared to CRU TS 2.1 in days between planting and harvest.On the other hand, moisture-limited maize yields using MRI-GCM20-0.5 is larger than that using CRU TS 2.1 by 419 kg/ha due to the overestimation of precipitation by MRI-GCM20-0.5 compared to CRU TS 2.1 in days between planting and harvest date.Winter-wheat in Europe is generally planted in September and October, and the number of days between planting and harvest is about 240-300 days (Portmann et al., 2010).Because the DDA of winter-wheat under the constraint-free yields for CRU TS 2.1 is larger than that for MRI-GCM20-0.5,we realize that the differences of the constraint-free yield (CRU TS 2.1 minus MRI-GCM20-0.5)are positive.The effect of uncertainty in precipitation on maize is larger than that predicted on winter-wheat, because the standard deviation and RMSE of the differences are three times larger than that of constraint-free yield (Table I).It is observed that uncertainty in precipitation is particularly large for May-August (Table SII in the supplement).Since maize grows in this period, the effect of uncertainty in precipitation is strong for maize, which is greatly influenced by evapotranspiration.
Crop simulation results at the 0.5-degree grid were spatially aggregated to country scale (Table II).For moisturelimited maize yields, the mean of the differences (CRU TS 2.1 minus MRI-GCM20-0.5)changed in magnitude from −419 kg/ha (Table I) at 0.5-degree grid scale to −721kg/ha in Hungary and −242 kg/ha in Romania (Table II).RMSE decreases from 420.3 kg/ha at 0.5-degree grid scale to 320.4, and 330.7 kg/ha at country scale.Moreover, the standard deviation decreases from 412.1 kg/ha at 0.5-degree grid scale to 276.1, and 290.8 kg/ha at country scale.For moisture-limited winter-wheat, RMSE and standard deviation decrease from 393.1 and 386.4 kg/ha to 289.8, 327.2 kg/ha and 274.4,318.8 kg/ha at country scale (Tables I and  II).These results indicate a considerable decrease in variability.The influence of uncertainty in temperature and precipitation inputs on the aggregated yields will be smaller at country scale compared to 0.5-degree grid scale as a result of spatial averaging.This may deteriorate model ability to evaluate crop yields on 0.5-degree grid scale compared to country scale.

Validity of model and influence of spatial resolution on the crop yield simulation
Table III shows the adjusted coefficients of determination values describing the results from the regression between the observed statistics and the crop simulation results over the period 1990-1999.R 2 for the relationship between the realistic yield, which takes into consideration pests, animals, crop-management, soil and irrigation as yield reducing factors, using MRI-GCM20-0.5 and MRI-GCM20-0.25 by a linear regression reaches values of 0.28-0.53for both maize and winter-wheat.Similarly, R 2 for the relationship between the harvested area using MRI-GCM20-0.5 and MRI-GCM20-0.25 reaches values of 0.06-0.86 for both crops.These values are not necessarily large compared with Wit et al. (2005).For this reason, we believe that the weak correlation of simulation results using MRI-GCM20-0.5 and MRI-GCM20-0.25 is mainly due to a difference in spatial duplicability of temperature and precipitation input data.
Next we consider the results from the linear regression between the FAO yield statistics (FAOSTAT, 2005) and the realistic yield of the MRI-GCM20-0.5 or MRI-GCM20-0.25 experiment.Strong relationships could be found which improved the R 2 value from 0.71 and 0.29 (MRI-GCM20-0.5),to 0.88 and 0.86 (MRI-GCM20-0.25)for maize yields in Hungary and Romania.Moreover, for winter-wheat yields in Hungary, R 2 is 0.84 in MRI-GCM20-0.5 and 0.88 in MRI-GCM20-0.25.However, for winter-wheat yields in Romania, the R 2 value could not be improved, with results giving 0.69 for MRI-GCM20-0.5 and 0.55 for MRI-GCM20-0.25.For maize and winter-wheat harvested area, R 2 between MRI-GCM20-0.5 and FAO statistics value is on average 0.49 = (0.89 + 0.09 + 0.04 + 0.95)/4 in Table III.However, the R 2 value in MRI-GCM20-0.25 is on average 0.64 (Table III).It seems that this is an eligible application of the highresolution climatic data in iGAEZ model.However, adjusted coefficients of determination on harvested area between FAO and CRU TS 2.1, which use observation-based data, are less than those for between FAO and MRI-GCM20-0.5 in some cases (Table III).Here we assume the root cause to be the influence of uncertainty in FAO statistics, which has values influenced by political, economic, and extreme climate conditions.Our model does not consider socio-economic Table II.Summary of the average crop yields at Hungary and Romania using CRU TS 2.1 and MRI-GCM20-0.5 aggregated to the country scale for 1990-1999 a Average crop yields (left: constraint-free, right: moisture-limited) b Standard deviation of the differences in yield (left: constraint-free, right: moisture-limited) c RMSE of the differences in yield (left: constraint-free, right: moisture-limited) a Adjusted coefficients of determination from linear regression analysis between FAO statistics and the realistic yield of the MRI-GCM20-0.5 experiment for the 1990-1999 b Adjusted coefficients of determination from linear regression analysis between FAO statistics and the realistic yield of the MRI-GCM20-0.25 experiment for the 1990-1999 c Adjusted coefficients of determination from linear regression between the realistic yield of the MRI-GCM20-0.5 and MRI-GCM20-0.25 experiment for the 1990-1999 d Adjusted coefficients of determination from linear regression between FAO statistics and the realistic yield of the CRU TS 2.1 experiment for the 1990-1999 e Average of the differences in yield (kg/ha) and harvested area (km 2 ) f Standard deviation of the differences in yield (kg/ha) and harvested area (km framework.Moreover, both CRU TS 2.1 and MRI-GCM20-0.5 have uncertainty in climate variables.The diagrams in Figures 1 and 2 show a comparison of the maize and winterwheat yields and harvested area for Hungary and Romania between results using MRI-GCM20-0.5 and MRI-GCM20-0.25 projection for 1990-1999, with FAO statistics given for reference.We show the geographic distribution of maize and winter-wheat yields per grid cell in 1990-1999 (Figure S3 in the supplement).Simulation with MRI-GCM20-0.5 greatly overestimated harvested area, and at the same time, underestimated yields compared to FAO yield statistics, where results using MRI-GCM20-0.25 grid spacing significantly improved even though there are still differences with FAO yield statistics. Simulated results using MRI-GCM20-0.25 show that maize crop yields are 19% and 53% greater for Romania and Hungary compared to the results using MRI-GCM20-0.5.Harvested area also decreases by 32% and 23% relative to MRI-GCM20-0.5, and as a result agreement with FAO yield statistics improved significantly, even though there are still discrepancies (Figures 1 and 2).On the other hand, winter-wheat yields increased by 15% and 13% and harvested area decreased by 17% and 21% compared to MRI-GCM20-0.5, for Romania and Hungary respectively (Figures 1 and 2).In this case, iGAEZ is highly likely to accurately predict the yield across the field when the high-resolution inputs are used (Figure S3 in the supplement).

SUMMARY AND DISCUSSION
To assess (1) the effect of the uncertainty in temperature and precipitation on crop model, and (2) the effect of spatial resolution on crop yield in countries which have a small land area, we adapted the iGAEZ model for the simulation of maize and winter-wheat on 0.5 and 0.25-degree grids.
The results of our study demonstrate that moisture-limited yields using MRI-GCM20-0.5 by crop simulation show larger yields compared to that by using CRU TS 2.1 for 1990-1999, and the effect of uncertainty in the precipitation on maize is even larger compared to winter-wheat.It is found that uncertainty in climatic inputs at this scale have a large influence on crop simulation results.We confirmed that temperature and precipitation are normally two of the key inputs for iGAEZ that predict crop yields as a function of climate conditions.When the simulation results were aggregated to country scale, uncertainty in temperature and precipitation decreased as a result of spatial averaging.Crop yield simulation results showed that crop yield and harvested area at 0.25-degree grid don't correlate strongly with results at 0.5-degree grid.Moreover, the comparison of the FAO statistics with crop yields and harvested area by MRI-GCM20-0.5,MRI-GCM20-0.25 demonstrates that simulation results at 0.25-degree grid are much better than that at 0.5-degree grid.Moreover, the harvested area is vastly overestimated and resulted in the lower crop yield at the coarse spatial resolution (0.5-degree).This is partly because spatial averaging process of the temperature and precipitation values (high-resolution to coarse-resolution) led to increased area of precipitation and decreased amount of precipitation on each grid cell.Additionally, this weak correlation may be due to missing important climate information, such as a European meso-scale precipitation which is produced only with finer spatial resolution of 0.2 degree grid (Rubel and Brugger, 2009), and uncertainty in the harvested area fraction data which indicates the fraction of each grid cell in which the crop is grown (Sacks et al., 2010).Wit et al. (2005) have reported that the crop yield simulation results at 10 × 10 km scale almost linearly with the simulation results at 50 × 50 km using averaged rainfall and radiation.Furthermore, they concluded that there is little merit in increasing the resolution.However, our simulation results at 0.25-degree grid are not only for gaining better results on yield, but also for acquiring better results on harvested area.We will have to investigate as follows: (1) the feature of the high-resolution simulation results for a large number of countries which have a large and small land area, (2) the relationship between uncertainty in model inputs and crop simulation results on a high-resolution system, and (3) an effective upscaling method.There are clear advantages in simulating crop yields at 0.25-degree grid in our research, but we found that harvested area particularly has a large error in the scale of agreement between simulated and statistical values also.Improvements of the crop simulation model should focus on harvested area fraction and the crop yield.

Figure 2 .
Figure 2. Same as in Figure 1 but for in Romania.
Maize planting in Europe generally occurs in April, and the number of days between planting and harvest is about 120-170 days (Portmann Table III.Summary statistics for country averages of maize and winter-wheat