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Keywords:

  • regional crop simulation;
  • large-area crop modeling;
  • model calibration

Abstract

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Method and Data
  5. 3 Results
  6. 4 Discussion
  7. 5 Conclusions
  8. Acknowledgment
  9. References
  10. Supporting Information

Reliable regional-scale representation of crop growth and yields has been increasingly important in earth system modeling for the simulation of atmosphere-vegetation-soil interactions in managed ecosystems. While the parameter values in many crop models are location specific or cultivar specific, the validity of such values for regional simulation is in question. We present the scale dependency of likely parameter values that are related to the responses of growth rate and yield to temperature, using the paddy rice model applied to Japan as an example. For all regions, values of the two parameters that determine the degree of yield response to low temperature (the base temperature for calculating cooling degree days and the curvature factor of spikelet sterility caused by low temperature) appeared to change relative to the grid interval. Two additional parameters (the air temperature at which the developmental rate is half of the maximum rate at the optimum temperature and the value of developmental index at which point the crop becomes sensitive to the photoperiod) showed scale dependency in a limited region, whereas the remaining three parameters that determine the phenological characteristics of a rice cultivar and the technological level show no clear scale dependency. These results indicate the importance of using appropriate parameter values for the spatial scale at which a crop model operates. We recommend avoiding the use of location-specific or cultivar-specific parameter values for regional crop simulation, unless a rationale is presented suggesting these values are insensitive to spatial scale.


1 Introduction

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Method and Data
  5. 3 Results
  6. 4 Discussion
  7. 5 Conclusions
  8. Acknowledgment
  9. References
  10. Supporting Information

The grid interval of global climate models (GCMs) is in general hundreds of kilometers in latitude and longitude. In contrast, most crop models [e.g., Jones et al., 2003] are designed at a far smaller field scale than that of a GCM grid cell. Scale incompatibility between climate and crop models is a major issue when simulating crop growth and yield at a GCM grid scale [Baron et al., 2005]. As over 34% of the Earth's ice-free land surface is covered by cropland or pasture [Ramankutty et al., 2008], the reliable representation of crop growth and atmosphere-vegetation-soil interaction in managed ecosystems is a priority in earth system modeling [Levis et al., 2012]. Therefore, designing crop models at such a scale [Challinor et al., 2004; Iizumi et al., 2009] has been increasingly important.

Crop model parameters that are important in determining the sensitivity of crop growth rate and yield to environmental and management conditions are in many cases specific to the location or cultivar. The validity of using such parameter values for simulation at a GCM grid scale is questionable. Indeed, theoretically, all numerical models including crop model should be calibrated at a given spatial scale before its application. However, this procedure is often impeded for regional crop simulation because of limited availability of crop data covering a large spatial domain. A study exploring the impacts of the spatial aggregation of data on weather and emergence dates on the simulated length of growth period for winter wheat in Germany [van Bussel et al., 2011] showed that the use of aggregated data and an identical set of cultivar-specific parameter across Germany has little effect on the simulated crop phenological events by up to 100 km grid size. However, van Bussel et al. [2011] also showed that the error in the simulated length of the period from emergence till ear emergence increased as grid size becomes coarser and, in contrast, the error in the simulated entire growth period decreased as grid size becomes coarser. The result for the period from emergence till ear emergence suggests that the value of phenological parameters that results in the best fit to observations potentially changes with the spatial scale of the simulation. Such a hypothesis has been made in other studies. Xiong et al. [2008] proposed representative parameter values for each agro-ecological zone for regional simulations using the Crop Environment Resource Synthesis (CERES)-rice model. Iizumi et al. [2011] revealed that likely parameter values at a regional scale could differ from those determined at a field scale (i.e., cultivar specific). While there is much evidence to justify the use of regional-scale parameter values in regional crop simulations, no systematic evaluation has been performed to understand the relationship between likely parameter values and the spatial scale of a simulation (i.e., the grid interval). The knowledge gap still remains to answer the questions: how and which parameter values in a crop model are sensitive to grid interval? To close the knowledge gap, we examined the dependency of likely parameter values related to crop growth rate and yield on the spatial scales of simulation, using relatively dense rice crop data and a paddy rice model applied to Japan as an example. Most rice in Japan is grown under sufficiently irrigated conditions; hence, temperature (or solar radiation), rather than precipitation, is a key driver of interannual variability of yield [Horie et al., 1995; Iizumi et al., 2009]. For this reason, our study mainly examined parameters that determine the sensitivity of rice growth and yield to temperature conditions. Note, however, that some parameters considered here (e.g., τ; see Table 1 for symbols) are not necessarily the case, but important in the calibration of the crop model used.

Table 1. Descriptions of Parameters of the Paddy Rice Crop Model Studied in This Study
SymbolUnitDescription
GdayMinimum number of days required for heading under 350 ppm of atmospheric [CO2] concentration
AT Sensitivity of developmental rate (DVR) to air temperature
Th°CAir temperature at which DVR is half of the maximum rate at the optimum temperature
DVI*day−1Value of developmental index at which point the crop becomes sensitive to the photoperiod
T*°CBase temperature for calculating cooling degree days
Ccool Curvature factor of spikelet sterility caused by low temperature
τ Technical coefficient

2 Method and Data

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Method and Data
  5. 3 Results
  6. 4 Discussion
  7. 5 Conclusions
  8. Acknowledgment
  9. References
  10. Supporting Information

2.1 Paddy Rice Model

For this study, we used the paddy rice model (called the process-based regional-scale yield simulator with Bayesian influence version 1, PRYSBI-1) presented in Iizumi et al. [2009], which demonstrated the upscaling of a field-scale model through the calibration of 13 parameters using area-mean weather and crop data. This model uses the same growth processes as those in the field-scale model of Horie et al. [1995]. The model accounts for processes of phenological development, dry matter production, and yield formation. Daily maximum and minimum temperatures, solar radiation, atmospheric [CO2], and transplanting date are required model inputs. Precipitation is not incorporated because the irrigation is assumed sufficient.

Of the 13 parameters calibrated by Iizumi et al. [2009], we selected seven parameters as the calibration parameters for this study (Table 1). The selected parameters were related to phenology (G, AT, Th, and DVI*), the sensitivity of spikelet sterility to low temperature (T* and Ccool), or technological level (τ). Initial conditions for developmental index (DVI0), dry weight (DW0), and leaf area index (LAI0), which appeared in Iizumi et al. [2009], were removed from the calibration parameters. Instead, the values determined in the previous study [Iizumi et al., 2009] were used here because these initial conditions have influences to model output, but it is too complex to analyze the interaction of initial conditions and the scale dependency of other parameter values at once. The sensitivity of developmental rate (DVR) to day length (BL) and critical day length (Lc) was also eliminated because the variability of day length across spatial scales may be negligible when considering a spatial scale under 100 km. Finally, the curvature factor of spikelet sterility caused by high temperature (Chot) was removed because, as discussed in Iizumi et al. [2009], the value of this parameter on a regional scale under the given regional crop data was highly uncertain. This is likely because a lack of heat-induced yield loss events in the data. Considering the large uncertainty of Chot value even on a single spatial scale, we were conservative to explore the scale dependency of Chot value.

2.1.1 Modeling of Developmental Index and Rate

In the PRYSBI-1 model, the developmental index (DVI) was used to model the progress of growth stage of rice crop in a numerical manner. The DVI value of zero, one, and two indicates transplanting, heading, and maturity, respectively. The DVI at day i after transplanting, DVIi (day−1), is given as a summation of developmental rate (DVR) from the transplanting date till day j:

  • display math(1)

The four parameters (G, AT, Th, and DVI*), out of seven parameters considered in this study, appeared in the equations for developmental rate:

  • display math(2)

where DVR is the developmental rate at day j (day−1), Gv is the minimum number of days required for heading (day), AT is the sensitivity of the developmental rate to air temperature (dimensionless), T is the daily mean air temperature (°C), Th is the air temperature at which the developmental rate is half of the maximum rate at the optimum temperature (°C), G is the value of Gv when the [CO2] concentration is 350 ppm (day), Ca is the atmospheric [CO2] concentration (ppm), and α is the empirical constant (1.14 × 10−4). DVI* is the value of developmental index at which the crop becomes sensitive to photoperiod (day−1), L is the day length (h), Lc is the critical day length (h), and Kr (0.118) and Tcr (12.7) are empirical constants. The developmental rate basically depends on temperature condition. Also the developmental rate changes depending on whether the developmental index is below or above the value of DVI* and whether the day length is below and above the value of Lc.

2.1.2 Modeling of the Effect of Management and Low Temperature on Harvest Index

In the PRYSBI-1 model, actual grain yield is calculated as a multiplicative form of the total dry matter production including roots (t ha−1), Wtotal, harvest index (dimensionless), h, and technical coefficient (dimensionless), τ:

  • display math(3)

The technical coefficient works to adjust the gap between potential and actual yields, although it does not represent any biological process. The total dry matter production including roots is a sum of daily increment of dry weight calculated from incident solar radiation, canopy reflectance, leaf area index, and radiation-use efficiency for the period from transplanting till harvesting [Iizumi et al., 2009].

The harvest index is proportional to the inverse of the percentage of spikelet sterility caused by temperature stress induced by (hc) low or (hh) high temperature:

  • display math(4)

In this study, only the parameters related to low temperature stress were studied because Iizumi et al. [2009] suggested that the parameters related to high temperature stress were not well determined due to the lack of marked heat-induced yield losses in the regional crop data, although parameter values related to heat stress on a smaller spatial scale is intensively studied on the basis of the chamber experimental results [e.g., Nakagawa et al., 2003]. The omission of hh in the calibration does not deteriorate the quality of this study as the analysis of regional crop data suggests that heat-induced yield losses can be negligible at least in the regions and period studied here. The harvest index due to low temperature stress is calculated:

  • display math(5)

where hm is the maximum harvest index obtained under optimum climatic and management conditions (dimensionless), γc is the sterile spikelet (dimensionless), and Kh (= 5.57) is the empirical constant (day).

The two parameters (T* and Ccool), out of seven parameters considered in this study, appeared in the modeling of the impacts of low temperature stress to harvest index. The relationship between the daily mean temperature and the percentage of sterility of rice crop is parameterized:

  • display math(6)
  • display math(7)

where γ0 (= 4.6, dimensionless) and Kq (0.054, °C−1) are empirical constants, Ccool is the curvature factor of spikelet sterility relating to low temperature (dimensionless), Q is the cooling degree days (°C day), and T* is the base temperature (°C). The summation in equation (7) is done for the period in which the rice panicle is sensitive to low temperature (0.75 ≤ DVI ≤ 1.20).

2.2 Data

Observed daily maximum and minimum temperatures and solar radiation from the gridded daily weather data set at a resolution of 1 km × 1 km over terrestrial Japan for 1979–2010 were used [Seino, 1993]. In the data set, daily anomalies of a climatic variable at observational sites relative to the 30 year climatological mean values at corresponding locations were spatially interpolated by using the inverse distance weighted averaging method [Seino, 1993]. Historical land use/land-cover maps at the same resolution as that of weather data from the National Land Numerical Information database, compiled by the Ministry of Land, Infrastructure, Transportation, and Tourism of Japan (http://nlftp.mlit.go.jp/ksj-e/index.html), were used to identify the locations of rice paddies. Atmospheric [CO2] data from the Carbon Dioxide Information Analysis Center [Keeling et al., 2009] were used: values for the [CO2] data changed yearly but were identical across spatial scales.

For 1979–2010, dates of rice transplanting, heading, and harvesting, as well as yield values, at a subnational level were obtained from the governmental crop statistics yearbooks, compiled by the Ministry of Agriculture, Forestry, and Fisheries of Japan [Iizumi et al., 2013a]. The land area of political units used by the subnational statistical units for crop data ranged from 290 to 17,906 km2 (the mean value being 2658 km2; Figures 1b and 1c), roughly corresponding to 1–29 regular 25 km grid cells (the mean number was 4).

image

Figure 1. Locations of two study regions within: (a) Japan, (b and d) Tohoku, and (c and e) Kyushu. For the full map of Japan, a green shaded area indicates rice paddy in 2000: a contour line indicates elevation at every 500 m. In regional maps, a square indicates a 25 km × 25 km regular grid cell; (Figures 1b and 1c) subnational statistical unit; (Figures 1d and 1e) planting dates in 2000 overlaid with paddy area in that year; gray shaded area indicates nonpaddy; a solid (dashed) red box indicates the 25 km grid cell where the smallest (largest) long-term mean value of transplanting date was observed.

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To match the spatial scales between the crop and weather data, data values of each climatic variable were spatially aggregated day by day, from the original resolution (1 km × 1 km) to each of four coarser resolutions (the grid interval of 25, 50, 75, and 100 km; Figures 1b and 1c), using the box averaging method. As grid cells overlapped each other, the number of grid cells located within a 100 km × 100 km grid presented in Figures 1b and 1c was 16, 9, 4, and 1 for the grid intervals of 25, 50, 75, and 100 km, respectively. The extent of paddy area located within a 1 km × 1 km grid cell was used as a weight to calculate the harvested area-mean values of the climatic data for a given grid interval. This is because the crop data used for the model calibration were weighted by harvested area and thus the crop data from major rice-cropping area located within a grid cell contributed more to the area-mean value than those from minor rice-cropping area; and therefore, the use of harvested area-weighted climatic data is more reasonable than a use of simple area-mean climatic data to model the climate-crop relationship on a given grid interval. Again note that this study focuses to simulate typical growth and yield in a given area instead of the simulation of spatial heterogeneity of crop in a given area [e.g., Iizumi et al., 2013b]. For the crop data, dates of transplanting, heading, and harvesting, as well as yield values, were spatially aggregated for each of the coarser resolutions in a similar fashion. However, note that the values of the crop data are identical across the grid cells located in a political unit (Figures 1d and 1e).

2.3 Calibration of the Model

The Markov chain Monte Carlo (MCMC) method [Metropolis et al., 1953; Hastings, 1970] was used to estimate posterior distributions of the seven selected parameters employed in the PRYSBI-1 model (Table 1). In this method, parameter values distributed within a known possible range (represented by a uniform distribution; Table S1) were updated using the calibration data to form a posterior distribution of a parameter value according to Bayes' theorem:

  • display math(8)

where p(θ|D) is the posterior probability distribution of parameter θ under a given data D, π(D|θ) is the likelihood function, p(θ) is the prior probability distribution of parameter θ, and the denominator of the right-hand side is the normalizing constant. The possible parameter values ranges used in this study (Table S1) were as per the prior distributions used in Iizumi et al. [2009], which cover values of the parameters determined for major cultivars grown in the study regions [Iizumi et al., 2011].

The likelihood function was specified as:

  • display math(9)

where N is the sample size, and Yi and inline image are the vectors of the calibration data and model outputs (for yield, heading date, or harvesting date), respectively. The variances of error ( inline image) were estimated in parallel with the crop parameters. The suffix i denotes the ith metric number of the calibration data (i.e., 1, yield; 2, heading date; and 3, harvesting date). The error distribution was assumed to be a multivariate normal distribution, with nondiagonal elements of the variance-covariance matrix equal to zero. Although a more complex assumption on the form of error distribution is possible [e.g., Hue et al., 2008], the assumption used here is the simplest and frequently used in the previous studies [Iizumi et al., 2009, 2013b].

The procedures of the MCMC method were basically identical to those described in Iizumi et al. [2009]. However, the differential evolution adaptive Metropolis (DREAM) algorithm [Vrugt et al., 2009] was adopted for this study, which has a more rapid convergence than the Metropolis-Hastings algorithm used in Iizumi et al. [2009]. Iterations of 50,000 Monte Carlo steps with three parallel Markov chains were conducted. The convergence was diagnosed on the basis of Gelman and Rubin (G-R) statistics [Gelman and Rubin, 1992]. The setup of the MCMC method was identical across the spatial scales of model calibrations, although the weather and crop data used for model inputs and calibration data changed by grid interval.

2.4 Analyses

To compare amplitudes between the interannual and spatial variability of observed crop and climatic data, we provided box plots for each grid interval from 25 to 100 km, for all variables and for both regions (Tohoku and Kyushu), as shown in Figures 2, 3, and S1. The variables include the dates of transplanting, heading, harvesting, and yields, as well as the vegetative and reproductive growth period-mean values of temperature and solar radiation. In these figures, data for two grid cells were presented (for instance, see Figures 1b–1e for transplanting date; note that the locations of two grid cells compared could change depending on the variable and grid interval), with the exception of the 100 km grid interval, at a given interval where the largest or smallest observed values on a long-term mean basis emerged. Although an analysis for other grid cells is possible, we presented these grid cells where both sides of the extremes of crop data were observed because the results for remaining grid cells distributed within these two results. A box plot indicates the interannual variability of a crop or climatic variable at a given grid interval for the study period (i.e., 1979–2010), whereas the difference between two box plots at a given grid interval indicates the spatial variability of a crop or climatic variable on a given grid interval.

image

Figure 2. Box plots of the observed dates of (a and b) transplanting, (c and d) heading, (e and f) harvesting, and (g and h) yields for two grid cells at a given grid interval in two regions for the 1979–2010 period with four grid intervals. Data for two grid cells (one grid cell for the grid interval of 100 km) where the largest (gray) or smallest (white) long-term mean value of each crop variable was observed were presented. The vertical line of a box plot indicates the 90% confidence interval; the lower and upper hinge indicate the 25-percentile and 75-percentile values, respectively; a horizontal line indicates the median; and crosses indicate the minimum and maximum values.

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image

Figure 3. Box plots of the observed vegetative and reproductive growth period temperatures ((a) TVGP; (c) TRGP) and solar radiations ((b) SRVGP; (d) SRRGP) for two grid cells at a given grid interval in the Tohoku region for the 1979–2010 period with four grid intervals. Data for the grid cells in Figure 1 are shown. A description of a box plot presented in Figure 2 can be applied to this figure.

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We further presented comparisons between observed and simulated time courses of heading dates and yields over the study period for both regions at all grid intervals (Figures 4 and S2). In these figures, data were presented for two grid cells (one grid cell for the 100 km interval) that were identical with that of previously mentioned comparisons. Therefore, Figures 4 and S2 demonstrate the model performance for two representative grid cells at a given grid interval. Although the time courses of the harvesting dates were omitted due to the limited space, goodness of fit statistics for all crop variables, including harvesting dates, are available in Table 2.

image

Figure 4. Temporal dynamics of the observed (circle and cross) and simulated (solid line) heading dates and yields in the Toshoku region for the 1979–2010 period with four grid intervals. Results for the grid cells in Figure 1 are shown. Blue (red) color indicates the data for the grid cells where the largest (smallest) long-term mean value of each crop variable was observed.

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Table 2. Root-Mean-Square Errors (RMSE) Calculated Between Observed and Simulated Data in Two Regions for the Period 1979–2010 at Four Grid Intervalsa
RegionGrid Interval (km)RMSE
Heading DateHarvesting DateYield
Days(%)Days(%)t ha−1(%)
  1. a

    Relative RMSE (in %) were calculated against the long-term mean observed data.

Tohoku251–6(0.6–2.8)5–15(1.8–5.5)0.331–0.411(7.1–6.6)
502(0.7–0.8)6–7(2.2–2.5)0.351–0.334(6.0–7.1)
751(0.6)6–7(2.3–2.4)0.289–0.281(5.2–5.7)
1001(0.6)6(2.1)0.283(5.4)
Kyushu258–12(3.1–5.2)7–13(3.0–4.4)0.516–0.625(10.3–12.7)
508–10(3.2–4.5)7(2.3–2.6)0.284–0.367(7.4–6.1)
756–7(2.6–3.0)7–11(2.6–3.8)0.283–0.332(6.0–6.9)
1006(2.6)7(2.6)0.303(6.4)

Figures 5 and S3 present the parameters posterior distributions (including the variances of errors in the observed crop data) estimated using the MCMC method for all grid intervals and regions. In these figures, data were presented for two grid cells (one grid cell for the 100 km interval) that were identical with that of previously mentioned to be consistent comparisons as much as possible, if the G-R statistics for the grid cells suggested convergence (<1.2). If the posterior distributions for the grid cells did not meet the convergence, we sought another grid cell that met the convergence and had larger (or smaller) observed crop data values. However, this does not largely affect the results because most parameters in over nearly 80% of grid cells showed the convergence, with one exception (Th for grid cells with 75 km interval in Tohoku region, Table S1). The form and range of prior distributions, the length of iteration, imperfect modeling, or lack of information in the calibration data are possible reasons for the fail in meeting the convergence. We used the observed heading dates for parameters related predominantly to the phenology (G, AT, Th, DVI*, inline image, and inline image), whereas observed yields were used for remaining parameters (T*, Ccool, τ, and inline image). A box plot of the figures indicates the posterior distribution of a parameter that represents the uncertainty in the likely value of a parameter for given calibration data, whereas the difference between two box plots at a given grid interval indicates the spatial variability of likely parameter values.

image

Figure 5. Posterior distributions of (a–g) the seven parameters and (h–j) the three variances of errors in the observed data for two grid cells at a given grid interval in the Tohoku region with four grid intervals. Data for the grid cells in Figure 1 are shown (see also section 2.4). A description of a box plot presented in Figure 2 can be applied to this figure.

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To examine if scale dependency of a parameter occurs or not, we further calculated the probability that likely values of a parameter at the grid interval of 100 km were larger than those at each of the finer grid intervals (25, 50, and 75 km). This was done by comparing a couple of posterior distributions of a parameter at a given finer grid interval and grid intervals of 100 km using the bootstrap method. For each finer grid interval, all posterior distributions of a parameter in all grid cells that met the convergence were combined and then compared to the posterior distribution in the 100 km grid interval. A summary of the calculated probabilities is presented in Table 3.

Table 3. Probabilities That Likely Parameter Values at the Grid Interval of 100 km Are Greater Than Those at Finer Grid Intervals (25, 50, or 75 km), Calculated on the Basis of the Posterior Distributionsa
ParameterProbability
25 km Versus 100 km50 km Versus 100 km75 km Versus 100 km
  1. a

    A bold font indicates consistent increase or decrease in the probability with the grid interval.

Tohoku Region
G0.4510.4070.528
AT0.7420.6670.889
Th0.4100.6780.345
DVI*0.5960.4830.340
T*0.8050.7440.784
Ccool0.3640.4120.552
τ0.4400.3570.563
inline image0.3420.3660.553
inline image0.9320.9760.729
inline image0.6610.5950.726
Kyushu Region
G0.6390.7280.699
AT0.3580.5300.417
Th0.4110.3330.278
DVI*0.5620.4430.457
T*0.8110.7240.792
Ccool0.3470.4850.354
τ0.4660.5440.512
inline image0.4330.5210.580
inline image0.2820.2830.421
inline image0.4620.5200.529

3 Results

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Method and Data
  5. 3 Results
  6. 4 Discussion
  7. 5 Conclusions
  8. Acknowledgment
  9. References
  10. Supporting Information

3.1 Impacts of Spatial Aggregation on Interannual Variability of Crop and Climate Data

For both regions, the amplitudes of the spatial variability for transplanting dates across 25 km grid cells, within a 100 km grid (represented by the difference between two box plots at a given grid interval) were larger than the interannual variability of the 25 km grid cells (represented by a box plot; Figures 2a and 2b). As expected, the spatial variability of the transplanting dates decreased as the grid interval became coarser, and converged to the value at the 100 km grid cell. By contrast, the majority of the interannual variability of transplanting dates still remained even after spatial aggregation. Similar tendencies were revealed for heading and harvesting dates in both regions (Figures 2c–2f). Almost identical tendencies as noted above were observed for the yields in both regions (Figures 2g and 2h). The less impacts of the spatial aggregation on the interannual variability of a variable of interest noted above were consistent for growing-season climatic variables in both regions (Figures 3 and S1).

3.2 Performance of the Calibrated Model at Four Spatial Scales

For all grid intervals, overall performance of the calibrated model in capturing the spatial and temporal variability of heading dates, harvesting dates, and yields in Tohoku region was good (Figure 4). For Kyushu region, the performance of the calibrated model was in general good; although comparatively large errors were found for the simulated heading dates (Figure S2). In the Tohoku region, the root-mean-square error (RMSE) values calculated between observed and simulated heading dates for the period 1979–2010 were 1–6 days for 25 km grid cells (Table 2) and 1 day for the 100 km grid cell. RMSE values for 50 and 75 km grid cells fell between those for 25 and 100 km grid cells (Table 2). In the Tohoku region, RMSE values for harvesting dates and yields for the 25 km grid cells ranged from 5 to 15 days and from 0.331 to 0.411 t ha−1, respectively, whereas those for the 100 km grid cell were 6 days and 0.283 t ha−1, respectively (Table 2).

As observed in the Tohoku region, RMSE values for all crop variables tended to decrease as the grid interval became coarser. Similar tendencies were found in the Kyushu region, with larger RMSE values than in the Tohoku region (Table 2). For instance, for yields in the Kyushu region, the RMSE value was 0.516 to 0.625 t ha−1 across the 25 km grid cells and was 0.303 t ha−1 for the 100 km grid cell. Most RMSE values for yields over 50 and 75 km grid cells were midway between 25 and 100 km grid cell values (Table 2), as observed in the Tohoku region.

3.3 Differences in Parameter Values Across Spatial Scales

As shown in Table 3, consistent increases in the probability that parameter values at the 100 km grid interval are larger than those of finer grid intervals (i.e., 25, 50, and 75 km) emerged for the curvature factor of spikelet sterility caused by low temperature (Ccool), and error variance in the observed yields ( inline image) in the Tohoku region: in fact, likely values of these parameters became larger as the grid interval became coarser. Such a tendency appeared for the variances of errors in the observed yields ( inline image), heading dates ( inline image), and harvesting dates ( inline image) in the Kyushu region.

By contrast, consistent decreases in the probability that parameter values at the 100 km grid interval are larger than those at the finer grid intervals were found for the DVI value at which point the crop becomes sensitive to the photoperiod (DVI*) in the Tohoku region and the air temperature at which DVR is half the maximum rate at the optimum temperature (Th) in the Kyushu region (Table 3): this corresponds to values of these parameters getting smaller as the grid interval became coarser.

In addition, visually, the likely values of base temperature for calculating cooling degree days (T*) in both regions and those of Ccool in the Kyushu region appeared to level out as the grid intervals approach 75 km or coarser (Figures 5e, S3e, and S3f). Although a somewhat similar tendency was observed for the minimum number of days required for heading under 350 ppm of atmospheric [CO2] (G) in both regions (Figures 5a and S3a), the large spread in value of the parameter (represented by the posterior distribution) hindered the extraction of a clear dependency of parameter values on grid interval. For remaining parameters (AT and τ), no relationship between the parameter values and grid interval was found. The limited spatial details of crop data used here may in part help to explain the unclear spatial dependency of some parameters.

In summary, for both regions, values of the three parameters (T*, Ccool, and inline image) appeared to change relative to the grid interval, while values of three other parameters (G, AT, and τ) seemed independent of the grid interval. For the remaining four parameters (Th, DVI*, inline image, and inline image), the dependency of parameter values on grid interval varied by region.

4 Discussion

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Method and Data
  5. 3 Results
  6. 4 Discussion
  7. 5 Conclusions
  8. Acknowledgment
  9. References
  10. Supporting Information

Results show the powerful capability of the MCMC method in fitting the crop model to observations at various spatial scales, ranging from grid intervals of 25–100 km, as previously presented for limited spatial scales [Makowski et al., 2002; Iizumi et al., 2009]. Importantly, errors in the simulated dates of phenological events and yields became smaller as grid intervals became coarser (Table 2). Such results were the opposite of van Bussel et al. [2011] who found that errors in the simulated dates of winter wheat ear emergence increased as the grid interval become coarser. Both van Bussel et al. [2011] and this study used the spatially aggregated values of planting (or transplanting) dates and daily temperature as the inputs. However, van Bussel et al. [2011] used an identical set of parameters determined on a site level for all simulations with varying spatial scales. In contrast, this study calibrated parameter values from one spatial scale to another. This difference makes the discrepancy between van Bussel et al. [2011] and our study reasonable. This suggests that the scale dependency of parameter values is associated with the calibration of a set of parameters to address the climate-crop relationship under given spatial scale; this indicates the importance of using appropriate values of crop model parameters for regional simulations.

A possible reason for decreased error in model outcomes at larger spatial scales is that the spatial heterogeneity of crop conditions induced by soil and management, which could lower the performance of simpler models that do not account for such information, is ameliorated through the spatial aggregation [Lobell and Burke, 2010]. Challinor et al. [2005] suggests that decreased errors in model outcomes at larger spatial scales can be attributed to the decreased interannual variability of crop and climate data associated with spatial aggregation. Such a decrease in temporal variability is expected to counteract nonlinear climate-crop relationships and increase the model performance (even for simpler models) in capturing the interannual variability of yields, as has been previously noted [Challinor et al., 2005; Lobell and Burke, 2010]. However, in this study, the interannual variability of crop and climate data at coarser grid intervals remains almost similar level with that at a finer grid interval (Figures 2, 3, and S1) and thus the effects of decreased interannual variability of crop and climate data on the calibrated model outcome is unclear.

As shown in section 3, errors in simulated heading dates in the Kyushu region (RMSE of 7–13 days) are not greatly improved by spatial aggregation (Table 2 and Figure S2). RMSE values presented here are almost double those of previous studies (3–6 days) [Iizumi et al., 2009]. Iizumi et al. [2009] included two parameters in the calibration, which were related to the effect of day length on growth rate (BL and Lc), in addition to the parameters calibrated in this study. Because major rice cultivars grown in the Kyushu region are in general more sensitive to day length than those in the Tohoku region [Horie et al., 1995], the omission of BL and Lc from the calibration parameters is likely responsible for the larger errors in heading date in the Kyushu region, even at the larger spatial scale. In addition, the higher variability of dates of heading and harvesting across smaller scales for Kyushu region compared to that for Tohoku region (Figures 2b, 2d, and 2f) could be a factor in the poor performance of the model at Kyushu region (though the simulated yields for that region are not sensitive to the disagreement in the timing of these phenological events (Figure S2)). The findings also suggest that key parameters could vary by region because the heading dates in the Tohoku region are simulated accurately without the calibration of BL and Lc.

Scale dependency of parameter values was found across the regions for the parameters related to the yield response to low temperature (T* and Ccool; Table 3; Figures 5 and S3). This indicates that parameters that are important in determining the degree of yield response to a major driver of interannual yield variability in a given region are primary candidates of calibration parameters for the regional-scale crop model calibration. Simultaneously, the error variances in the observed crop data ( inline image, inline image, and inline image) are potential calibration parameters candidates since, in general, errors in crop data can be reduced through spatial aggregation and these parameters, in part, represent such an effect on crop data in the model calibration. By contrast, the parameters that determine the phenological characteristics of a rice cultivar (G and AT) and technological level (τ), have no likely scale dependency or weak scale dependency (e.g., G); this seems reasonable as these parameters are not sensitive to temperature in nature. However, note that other parameters (Th and DVI*) were scale dependent in a limited region, emphasizing the fact that key processes that govern the interannual variability of crop growth and yield differ by region, and the associated parameters therefore need to be calibrated for a given spatial scale.

An important point not dealt with in this study is the spatial variability of rainfall. Baron et al. [2005] showed that forcing a field-scale crop model with spatially aggregated rainfall data causes yield overestimations of 10%–50% in semiarid West Africa. Generally, the spatial variability of rainfall is high relative to other climatic variables, such as temperature. Furthermore, rainfall impacts on crop growth and yield through soil water availability where multiple processes govern, including evapotranspiration, soil water balance, and irrigation management. Similar discussion on the spatial-scale impacts of climate change scenarios (particular rainfall) on crop model outcome is available from Mearns et al. [2001]. Their results indicate that selecting candidates of calibration parameters in water-limited regions may be more complicated than in temperature-limited regions, such as Japan presented in this study. In addition, a GCM output in general represents the area-mean status of a climatic variable distributed within a grid cell, but not croplands located in a grid cell. Therefore, it is essential to conduct the statistical bias correction of a GCM output relative to weather data that represent cropland when a GCM output is used as the weather inputs for a crop model calibrated using the weather data for cropland.

While this study demonstrated the dependency of value of some specific parameters relative to grid interval for a single crop model and two locations in Japan, the findings of this study have implications for other crop models and locations in particular temperate and humid region where spatial and temporal variability of temperature plays a key role to determine crop growth and yield. As shown in this study, the parameters to determine the base temperature for calculating cooling degree days (T*) work to absorb the consequences of spatial aggregation of crop and climate data to achieve a good fit of simulated yields to the observations. Consequently, a similar scale dependency with T* can be expected for a parameter in other crop models, for instance, the base temperature for calculating heat unit in the Soil and Water Assessment Tool (SWAT) [Neitsch et al., 2005] and a series of the CERES [Singh et al., 1993] because this parameter is mathematically the same with T*. Note, however, the base temperature for calculating heat unit controls the relationship between the amount of accumulated heat above a certain threshold temperature and growth rate whereas T* controls the relationship between the amount of accumulated cooling degree days and percentage of spikelet sterility induced by low temperature.

5 Conclusions

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Method and Data
  5. 3 Results
  6. 4 Discussion
  7. 5 Conclusions
  8. Acknowledgment
  9. References
  10. Supporting Information

Given results of this study applying the paddy rice model to Japan, we conclude that values of some parameters related to temperature effects on crop yield are likely dependent on the spatial scale of a simulation. Such a dependency highlights the importance of using appropriate parameter values for the spatial scale at which a crop model operates. In turn, we recommend avoiding the use of location-specific or cultivar-specific parameter values for regional crop simulation, unless a rationale that such parameter values are insensitive to the spatial scale is presented. Otherwise, regional crop simulations need to be accompanied by downscaled climatic data and spatially dense crop database [e.g., van Bussel et al., 2011]. When parameter values are determined for a specific spatial scale, simulated yields, dates of phenological events, and thus the length of the growth period becomes more reliable with the increasing coarseness of the spatial scale of simulations. These conclusions have implications for large-area crop modeling as well as earth system modeling. Both types of modeling aim to increase the reliability of crop simulation from a GCM grid cell to global at a scale for better understanding of atmosphere-vegetation-soil interactions in managed ecosystems [e.g., Osborne et al., 2009; Levis et al., 2012] and ultimately for exploring effective adaptation measures of food systems to climate variability and change in a more process-based manner [e.g., Deryng et al., 2011; Osborne et al., 2013].

Acknowledgment

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Method and Data
  5. 3 Results
  6. 4 Discussion
  7. 5 Conclusions
  8. Acknowledgment
  9. References
  10. Supporting Information

This research was supported by the Environment Research and Technology Development Fund (S-10-2) of the Ministry of the Environment, Japan.

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  2. Abstract
  3. 1 Introduction
  4. 2 Method and Data
  5. 3 Results
  6. 4 Discussion
  7. 5 Conclusions
  8. Acknowledgment
  9. References
  10. Supporting Information
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Supporting Information

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Method and Data
  5. 3 Results
  6. 4 Discussion
  7. 5 Conclusions
  8. Acknowledgment
  9. References
  10. Supporting Information
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jame20079-sup-0001-suppinfo01.pdf9K

Readme

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Table S1

jame20079-sup-0003-suppinfofs01.pdf192K

Figure S1

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Figure S2

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Figure S3

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