Simulation of Crop Yields Using ERA-40: Limits to Skill and Nonstationarity in Weather–Yield Relationships

The crop model

The crop model used in this study was the General Large-Area Model for annual crops. It is fully described in GLAM2004. It is a model of intermediate complexity, with parameterizations that seek to avoid a large crop model input data requirement, while capturing the interactions between climate and crop. It is designed to run on any spatial scale at which a relaionship exists between crop and climate (Challinor et al. 2003), and it has been run successfully over India at a 2.5° resolution using observed gridded data (GLAM2004) and GCM ensemble output (Challinor et al. 2004a).

GLAM is a process-based crop model with a daily time step, allowing it to resolve the impacts of subseasonal variability in weather. It has a soil water balance with 25 layers, which simulates evaporation, transpiration, and drainage. Transpirative demand is simulated according to Priestly and Taylor (1972), and the supply of water according to root water uptake. Roots grow with a constant extraction-front velocity and a profile that is linearly related to leaf area index (LAI). LAI evolves using a constant maximum rate of change of LAI that is modified by a soil water stress factor (the ratio of water supply to transpirative demand). Separate simulation of biomass accumulation, by the use of transpiration efficiency [an input parameter, normalized by the vapor pressure deficit (VPD) and based on observations], allows specific leaf area (SLA; the mass of leaf per unit area of leaf) to be used as an internal consistency check: leaf area and leaf mass can be derived independently of each other and can be used to calculate values of SLA that can be compared to the typical observed values. The objective of the model is to reproduce the impact of weather on observed crop yield. This aim leads to two particular model characteristics: first, complexity at a level that is far removed from the yield-determining processes is omitted (see Sinclair and Seligman 2000). In general, simple parameterizations are favored over more complex methods. Second, of the impacts on yield due to factors other than weather (biotic stresses such as pests, diseases, weeds, and abiotic management factors), only two are modeled explicitly—(i) planting date, which occurs on the first day within the prescribed planting window for which the available soil moisture is over 50% of the maximum, or at the end of the window if no such day is found; and (ii) soil hydrological properties, which are derived from the prescribed saturated upper limit and drained lower limit of the soil. GLAM uses a single parameter to account for the yield gap (the reduction in yield from climatically determined attainable values to actual values due to the impact of biotic stresses and suboptimal management). While this is a simplification, it allows the model to focus on the crop–climate interaction.

Weather and yield data

Weather inputs for the crop model are daily mean values of vapor pressure and mean temperature, and daily total rainfall and solar irradiance. These inputs came from ERA-40 (http://www.ecmwf.int/research/era/). ERA-40 is a global reanalysis at T159 resolution, which equates approximately to a 1.1° × 1.1° square grid. The data cover the period from September 1957 to August 2002. Solar radiation and precipitation are accumulated over 0000–2400 coordinated universal time (UTC) and are input to the crop model without modification. Daily mean temperature is calculated as the average of the ERA-40 six-hourly temperature. Six-houly dewpoint temperature is used to calculate daylight mean vapor pressure by averaging over data between sunrise and sunset only. This method resulted in the use of at least two values for each daily value.

Precipitation is a key determinant of rain-fed groundnut yields (e.g., Camberlin and Diop 1999). It is also a difficult variable for climate models to reproduce accurately. Hence, this variable merits particular attention. During the ERA-40 data period there are differing amounts of observational data used in the analysis: ERA-40 can be characterized as having three separate periods, each with more assimilated data than the last as more satellite data became available. One such period starts in 1973, and another in 1987. The introduction of new data has resulted in differences in the hydrological cycle between the three identified periods (Andersson et al. 2005). These differences are most pronounced over the ocean (Troccoli and Kållberg 2004), although changes also occur over land. The results of Andersson et al. (2005) suggest that the largest change in precipitation over land is likely to be around 1973. This issue is revisited briefly in section 3a, where the ERA-40 dataset is compared with the dataset of the Indian Institute of Tropical Meteorology (IITM; http://www.tropmet.res.in/). Rather than regrid either dataset and degrade the information, ERA-40 grid cells were assigned uniquely to an IITM grid cell according to the region of the greatest overlap. Both data sources have associated errors, but the IITM dataset is based solely on observations, and is expected to provide a better estimate of rainfall over the area covered.

The humidity analysis of the ECMWF causes overprediction of the tropical precipitation used in ERA-40. Rapid adjustment of the Hadley circulation, and adjustment of the precipitation to observed values, take place in the first 6–12 h of each forecast. This “spindown” problem can result in daily precipitation being higher than that observed (for a detailed analysis see Andersson et al. 2005). However, comparisons with the IITM data show that the ERA-40 high precipitation bias is not generally a problem for the Indian summer monsoon over this period (section 3a).

The yield data for calibration and evaluation of the model came from the database of agricultural returns compiled by the International Crops Research Institute for the Semi-Arid Tropics (ICRISAT) in Patancheru, India. Yields tend to increase over time, as improved varieties and management methods are employed. This trend will not be predicted by the model, and some assumptions must be made in order to remove this trend. In this study we have taken the common step of assuming a linear technology trend. Hence, all yields shown and referred to, unless otherwise stated, have been linearly detrended. The results of this study may depend to some degree on how the technology trend is modeled; it is, therefore, worth considering other options. Because explicit modeling of the underlying technological processes would require a knowledge of crop variety and management, two practical options for modeling the yield technology trend remain—(i) fitting a given trend parameterization (e.g., polynomial) using least squares (Just and Weninger 1999), and (ii) assuming the form of the probability density function (PDF) of detrended yield, and of the form of the technology trend, with subsequent determination of the trend using maximum likelihood (Moss and Shonkwiler 1993; Ramirez et al. 2003). Because the form of the PDF of yield cannot be determined a priori (e.g., Atwood et al. 2003), we use the first of these methods to determine alternative technology trends; linear (y = a + bt), quadratic (y = a + bt + ct²), and cubic (y = a + bt + ct² + dt³) trends were fitted to either the whole time series or piecewise to each half of the time series (section 3b).

The weather and yield datasets overlap for the period of 1966–89 for 132 grid cells across India. Hence, this is the spatiotemporal domain used for this study. Figure 1 shows the mean and standard deviation of ERA-40 rainfall, as well as the same statistics for the yield data.

Crop model calibration

GLAM is used here to simulate groundnut (Arachis hypogaea L.) yield. Soil hydrological properties were derived from FAO/UNESCO (1974) and planting windows were from Reddy (1988)following GLAM2004. Control planting windows are of a 30-day duration. The crop-specific parameters for the control run in this study came directly from GLAM2004. In that study, these parameter values minimized root-mean-square error (rmse) in yield for simulations of groundnut yield across India. These optimal parameters all fall within the range of the observed values. The parameters are not genotype specific, although many are broadly based on the TMV-2 cultivar, which is commonly grown in India.

A sensitivity analysis using the ERA-40 data showed that rmse in crop yield could not be systematically reduced across all model grid cells by changing any parameters in the crop model from the GLAM2004 values. This implies that this parameter set is suitable for use with ERA-40 data. Note, however, that calibration of each grid cell individually would reduce rmse in yield, because it would result in spatially variable optimal parameters. This spatial variability in optimal parameters is in contrast to the results using the 2.5° grid in GLAM2004, where the optimal parameter set was relatively constant over space. Likely reasons for the spatial variability of optimal parameters observed here include the finer spatial and temporal resolution of the ERA-40 data. For the current study, a global (India-wide) groundnut parameterization was retained because there is insufficient data on the spatiotemporal pattern of groundnut varieties that are grown to justify local parameterization.

GLAM2004 found that the impact of the inclusion of the irrigated fraction of groundnut crop on the skill of the simulations was small. The irrigated fraction has a mean, over the period of 1966–89, of less than 15% in 48 of the 82 grid cells where there are data (ICRISAT; see, e.g., GLAM2004), and a mean of less than 30% in 64 grid cells. Two cells [at Andhra Pradesh (AP) and Gujarat (GJ)] are considered in particular detail in the analyses that are presented (see Fig. 1 for their location): irrigation in grid cell AP accounts for an average of 12% of the area under cultivation. Because irrigated yields tend to be a factor of 0.4–1 times greater than rain-fed yields in this region (Virmani and Shurpali 1999), irrigation is not expected to significantly alter the results. Mean irrigation in GJ is even less significant, at 1%. Hence, the irrigated fraction was not simulated for this study.

Model calibration follows the same procedure as GLAM2004. The yield gap parameter (YGP) is determined for each individual grid cell by cross validation, with the period of 1966–77 being used to determine the 1978–89 YGP, and vice versa. Calibrated values of YGP are values that minimize the rmse between the observed and simulated crop yields.

Crop growth simulations

In addition to the control run that is described above, a number of other simulations were carried out. Key parameters relating to the crop, its management, and the input weather data were varied. To examine the impact of crop duration in the southern peninsula the four genetic coefficients, which determine the thermal time for each of the four growth stages in GLAM, were altered. Each was increased by an equal fraction such that the mean duration from planting to harvest increased from 90–100 days (control run) to 120–130 days. These increased values allow the simulation of an extended duration crop (simulation E1).

To examine the impact of the choice of planting window, a delayed window was used in grid cells in two key regions: Gujarat (where the control planting window of 30 days starts on 15 June, and the delayed planting window P1 is 1–10 August) and Andhra Pradesh (where the control planting window is 1–30 June, and the delayed planting window P2 is 1–30 July). These two regions have the largest groundnut production over the study period (Challinor et al. 2003).

Because ERA-40 precipitation is not expected to be as accurate as the observed values, two bias corrections of the ERA-40 precipitation were carried out: simulation B1 corrects the mean climatology (it shifts the ERA-40 June–September rainfall totals by a constant factor for each location, such that the 1966–89 mean rainfall agrees with the IITM data), and simulation B2 corrects the interannual variability (it shifts the seasonal total by a time-varying amount such that it agrees with the IITM data). These simulations allow the impact of precipitation inaccuracies to be assessed. Simulations with input precipitation bias correction using the extended duration crop were also carried out (E1B1). Because YGP is calibrated on rmse in yields, it will have some component of bias correction, which may include input weather data bias (Challinor et al. 2004a). Because all of the simulations (control, P1, P2, B1, B2, E1, E1B1) differ in terms of the exact input weather time series, each simulation has its own calibrated spatial distribution of YGP.

Analysis of simulated yields

The relationship between monthly mean weather during the growing season and the observed yield (i.e., the observed relationship between yield and weather) may be different than the relationship between the monthly mean weather and the simulated yield (i.e., the modeled relationship between yield and weather). Comparisons between modeled and observed yield–weather relationships enable the assessment of the crop model’s ability to correctly simulate the response of the crop to weather. Section 3b compares the simulated and observed weather–yield relationships, using the ERA-40 weather variables. Section 3c goes on to compare the observed and simulated yields directly, using correlation coefficients and rmse of the former relative to the latter.

Evaluation of the Indian summer monsoon in ERA-40

To assess the potential impact of the introduction of satellite data into the reanalysis, the June–July–August–September (JJAS) precipitation from the IITM and ERA-40 were compared by averaging each across two periods—1966–72 and 1974–89 (see section 2b). The difference between the mean ERA-40 and mean IITM values (d) is an indication of systematic bias. A change in the sign of d is an indication of a potentially serious drift in the ERA-40 data; such a drift represents a change in the bias of the ERA-40 precipitation (note, however, that bias correction B2 does correct for this). Over 80% of the 159 grid cells over India (which include the 132 for which there are yield data) have the same sign of d for the two periods. A Kolmogorov–Smirnov test on the two distributions of total JJAS precipitation shows that 80% of the grid cells for which there are yield data cannot be said to have different distributions for the two periods (at a significance level of 5%). Hence, the impact of the changes in the ERA-40 hydrological cycle on the simulation of the Indian summer monsoon appears not to seriously question the validity of the precipitation data.

Examining now the study period as a whole, Fig. 2 compares the seasonal total ERA-40 monsoon rainfall with that of the IITM. The mean June–September ERA-40 rainfall is mostly lower than IITM values, and many standard deviations are lower also. ERA-40 overestimates the frequency of light rains, and underestimates heavy rains (Fig. 3). Overall, the number of rain days in ERA-40 is greater than that of the IITM data. Mean monsoon onset is in broad agreement over much of India, although the southern peninsula shows a tendency for earlier onset in ERA-40 (Fig. 3c). Onset here is defined after Zhang et al. (2002): a criterion of rainfall >5 mm day⁻¹ is fulfilled first for 5 days, then consecutively for 10 out of 20 days.

The subseasonal variability is compared for two ERA-40 grid cells (in regions where much of India’s groundnut is grown) in Fig. 4. For one of these cells (GJ), the seasonal cycle is well simulated, despite the mean values that are underestimated. In cell AP, June and September totals are well simulated, but July and August are deficient; thus, the seasonal cycle is poorly simulated. These differences in the subseasonal variability have consequences for the model simulations in these regions (section 3c).

The subseasonal variability of the precipitation also changes over time, as the following example shows. The seasonal cycle of rainfall in western Gujarat (the 13 westernmost grid cells in Fig. 3c) was tested for changes across the periods of 1966–77 and 1978–89, using the Wilcoxon rank sum test (Wilcoxon 1945). Five grid cells showed a change, at a 5% significance level, in the 14-day-summed values of precipitation that were centered on either 17 August (which showed increased precipitation) or 31 August (which showed decreased precipitation). All of the IITM grid cells for western Gujarat showed one of these changes, which was significant at 5%.

Relationships between weather and yield

Figure 5 shows that modeled yields are more rainfall dependent than the observed yields. Given that rainfall is one of the few input variables in the model, but one of many in reality, this is not surprising. The same pattern of overcorrelation can be seen between simulated yield and VPD (Fig. 6), although some of the lower correlations in the far south are reproduced by the model. Correlations between yield and VPD do not imply causality because VPD and rainfall are highly correlated (Fig. 6c). However, looking at the differences between correlations in the first and second half of the time series (Table 1) reveals that for GJ, observed correlations with VPD can be more robust than correlations with precipitation. Note that for both GJ and AP the changes in correlation are not related to changes in the calibration parameter YGP, because YGP is constant over time in both cases.

Yields in the GJ region have been shown to have a stronger climate signal (defined as the strength of the detectable impact of climate on yield, as measured by a correlation coefficient, e.g.) than yield in the AP region (GLAM2004; Challinor et al. 2003), and this is reflected in correlations between the June–September meteorological variables and yields (Table 1). All of the observed statistically significant correlations over the 1966–89 time period are reproduced as statistically significant correlations by the model. Four of the six observed significant correlations for the two 12-yr subperiods are reproduced as statistically significant correlations by the model. However, differences between the first and second half of the time series are not well represented. This issue is revisited below.

Correlating, in turn, monthly mean values of precipitation, the VPD and net radiation from ERA-40 with yield in the Gujarat region (Fig. 7) show that the simulations pick out correctly the months during which weather has the most impact on yield (July, August, and September). The crop model overpredicts precipitation and radiation correlations early in the season. This suggests that a later planting date may be used in the simulations for this region, because reduced early season correlations would result. Using a planting window of 1–10 August (simulation P1) reduces the June and July weather–yield correlations (Fig. 7). The same simulation also produces a change in the correlation between rainfall and yield over the two halves of the time series (0.46 for 1966–77 and 0.65 for 1978–89), which agrees more closely with the observed change (c.f. Table 1). A similar result is obtained with bias-corrected input weather data in simulation B2 (Fig. 7); B2 has a correlation between yield and rainfall for 1966–77 of 0.43, and the value for 1978–89 is 0.65.

The observation of a change in the relationship between weather and yield in India at this time (1977–78) is not unique to this study, and has also been observed by Parthasarathy et al. (1992), Challinor et al. (2003), Selvaraju (2003), and Kulkarni and Pandit (1988). Further evidence of such changes in weather–yield relationships can be found by examining the correlation of all-India groundnut yield (produced by the Food and Agriculture Organization of the United Nations) with El Niño region sea surface temperatures (SSTs). For example, using the Niño-1 and -2 regions (0°–10°S, 90°–80°W) September SSTs from the Climate Prediction Center (http://www.cpc.noaa.gov), and linearly detrending the FAO yield data between 1966 and 1989, the correlation for the period of 1966–77 is −0.78, and the 1978–89 value is −0.26. A similar analysis with all-India rainfall data (Parthasarathy et al. 1995) reveals a change in correlation between rainfall and yield, across the same two time periods, from 0.96 to 0.67.

The skewness of the yield and rainfall time series also suggests a change in the nature of the relationship between weather and yield: the skewness of yield shows more variability over both space and time than the skewness in rainfall (Fig. 8). The change in yield skewness suggests a systematic shift in the PDF of yields. That the rainfall does not show a change in skewness over time, while the yield does, suggests that the shift in the PDF has a nonclimatic component (or, at least, a component that is unrelated to rainfall). Changes in irrigation levels or in the form of the technology trend are two of the numerous possible nonclimatic factors that could contribute to the change in skewness.

To determine whether the observed nonstationarity was due solely to the chosen form of the yield technology trend, a number of other forms of trend were considered. Linear, quadratic, and cubic trends, together with the yield data and the yield residuals, are shown in Fig. 9. Running means over 5, 7, or 9 yr were also used to detrend. The analysis was applied to the GJ and AP grid cells, and to all-India yields used in the SST and rainfall correlation analysis above. The character of the results (i.e., the changes in correlation) was not altered in any case. Most of the computed trends in GJ and AP were not statistically significant, and so the all-India case is chosen to illustrate this (Table 2).

An analysis of the ratio of yield to rainfall (Fig. 10) shows that over Gujarat and much of the southern peninsula, the apparent water-use efficiency (AWUE) is particularly high—in some places unrealistically so. To place an approximate upper limit on AWUE, we take an average-to-high yield for India (1000 kg ha⁻¹), and an average-to-low value of water use (400 mm for a groundnut crop cycle; Sivakumar and Sarma 1986), giving a value of 30 kg ha⁻¹ cm⁻¹. Frequent occurrence of higher values could be indicative of errors in the rainfall, which is underestimated by ERA-40 (Fig. 2). In the southern peninsula, however, AWUE values are high without frequently being unrealistic. This may be due to differences in the seasonal cycle. In the AP grid cell (see Fig. 1), for instance, an average of 56% of the rainfall between (simulated) planting and harvest falls during pod filling, compared to less than 30% for three grid boxes in Gujarat. A similar value can be found in the GLAM2004 simulations (using IITM rainfall) for the grid cell corresponding to AP (59%). A higher percentage of rainfall during pod filling will contribute to higher AWUE.

Relationship between observed and simulated yields

The control simulation output is shown in Fig. 11. Mean yields across many regions are well simulated, with the notable exceptions being much of the southern peninsula and Gujarat. The GLAM2004 simulations, which used observed gridded data, showed closer agreement with observations for both the southern peninsula and Gujarat. For the control simulation, 33% of the grid cells have mean yields within 5% of observed values, 53% are within 10% of observations, and 83% are within 50% of observations. The fact that mean yields have been well simulated across a range of environments is not due simply to a tuning of YGP to an appropriate value: narrow ranges of YGP for which mean yields are simulated accurately show diversity in the June–September precipitation characteristics (Fig. 12). Mean simulated LAIs for the control simulation across India are mostly less than one (not shown), which is realistic for an Indian groundnut crop (Kakani 2001).

Standard deviations in yield (σ_y) are harder to simulate than the mean, with values over most of India being underpredicted, and values in the southern peninsula being strongly overpredicted. Similar results were found in GLAM2004. Observed values of σ_y in the current study are higher than in GLAM2004 because of the finer spatial scale of the ERA-40 grid; yield data aggregated to a finer resolution tend to have higher standard deviations (Hansen and Jones 2000). The ERA-40-driven simulations do have higher values of σ_y than the GLAM2004 simulations. This is partly due to the use of daily, as opposed to monthly, VPD, radiation, and temperature data.

Overall, correlations between observed and simulated yields are comparable with observed yield–rainfall correlations (cf. Figs. 5a and 11c). However, some grid cells show a correlation between rainfall and observed yield that is not reflected in the correlation between the observed and predicted yields, and some grid cells show the converse. Further examination shows that, at least in some cases, this discrepancy is due to the VPD. If simulated yields are VPD limited, and not rainfall limited, and VPD is not correlated with rainfall, then the observed rainfall signal is not found in the simulations. Conversely, if there is a VPD signal in the observed yields, but no rainfall signal, VPD can impact yields. This effect may be a real (direct) effect, or it may be an indirect effect; larger VPDs imply drier conditions, and independently, via the GLAM formulation, tend to produce higher yields (GLAM2004).

Changes in observed and simulated weather–yield correlations over time (Table 1) are manifest in changes in skill over time. Grid cell GJ has a correlation (observed and simulated yields) of r₆₆ = 0.34 for the period of 1966–77, and r₇₈ = 0.71 for 1978–89. The corresponding grid cell in the GLAM2004 simulations showed no such change (r₆₆ = 0.79; r₇₈ = 0.70). This difference in behavior is also manifest in the correlation between ERA-40 and IITM rainfall for this location—0.41 and 0.86 for the two respective time periods. Using the August planting window (P1) reverses the sign of the change (r₆₆ = 0.91; r₇₈ = 0.47). This situation is common across Gujarat. A reduction in correlation between crop yield and weather variables across these two periods was observed by Parthasarathy et al. (1992) for cereals plus pulses, and Kulkarni and Pandit (1988) for district yields of sorghum. In the latter case the change was attributed to the introduction of new, higher-yielding, less weather-sensitive varieties in 1977–78. In the current study, it is clear that uncertainty in the planting date significantly decreases our ability to either ascribe a cause for this change in correlation, or to quantify sources of error in the input data.

The length of the growing season provides one way to assess the accuracy of the simulations. Across much of the southern peninsula both the IITM data and ERA-40 show that the growing season, as defined by rains, is longer than the crop durations that are predicted by the model. Approximately 30% of the May–November rain falls in the growing season for the control simulations in the south. In southern India, use of a planting window 1 month later than the control (simulation P2) increases this fraction to 40%. The extended-duration crop (simulation E1) has up to 50% of the May–November rainfall during the growing season. Both P2 and E1 reduce the error in mean yields in the southern peninsula. Note that a study in the Anantapur region (∼15°N, 75.5°E) by Gadgil et al. (1999) reported model results suggesting that the broad planting window used by farmers in this region (22 June–17 August) minimized the risk of failure, while a later (mid-July onward) planting window increased yields in 78% of the years. Thus, the use of a later planting window in this study does not result in planting dates beyond locally observed values.

Bias correcting the ERA-40 rainfall to IITM values can improve on the accuracy of the control simulations (Fig. 11). Figure 13a shows the results for bias correction of the mean climatology (B1). Error in mean yields in many regions, particularly Gujarat, is reduced. In Gujarat, correlations between observed and predicted yields (not shown) rise: of the 10 significant correlations in B1 in GJ, 7 are higher than those in the control run. In other regions (e.g., AP) correlations are not improved. The lack of improvement in AP is, in part, due to the smaller climate signal. The accuracy of the ERA-40 seasonal cycle of precipitation (higher in GJ than in AP; Fig. 4) may play a part in this. Simulation B2 is a further improvement on B1 across much of Gujarat and the southern peninsula (Fig. 13b). The additional improvement seen in B2 over B1 demonstrates the importance of interannual variability, which B2 corrects but B1 does not. For simulation B2, 40% of the grid cells have mean yields within 5% of observed values, 62% are within 10% of observations, and 88% are within 50% of observations.

The simulations of the extended-duration crop (E1) show a reduced rmse in yield compared to the control run (Fig. 13c). The E1B1 simulation produces a lower rmse than either B1 or E1 alone in all but two grid cells (Fig. 13d). Note that in regions with lower air temperatures, E1 can result in an unrealistically long duration. This highlights one problem with running a generalized crop parameterization across large areas.