J. Meteor. Res.  2019, Vol. 33 Issue (4): 777-783 PDF
http://dx.doi.org/10.1007/s13351-019-8143-9
The Chinese Meteorological Society
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Article Information

ZHAO, Yanxia, Chunyi WANG, and Yi ZHANG, 2019.
Uncertainties in the Effects of Climate Change on Maize Yield Simulation in Jilin Province: A Case Study. 2019.
J. Meteor. Res., 33(4): 777-783
http://dx.doi.org/10.1007/s13351-019-8143-9

Article History

in final form March 20, 2019
Uncertainties in the Effects of Climate Change on Maize Yield Simulation in Jilin Province: A Case Study
Yanxia ZHAO, Chunyi WANG, Yi ZHANG
State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, China Meteorological Administration, Beijing 100081
ABSTRACT: Measuring the impacts of uncertainties identified from different global climate models (GCMs), representative concentration pathways (RCPs), and parameters of statistical crop models on the projected effects of climate change on crop yields can help to improve the availability of simulation results. The quantification and separation of different sources of uncertainty also help to improve understanding of impacts of uncertainties and provide a theoretical basis for their reduction. In this study, uncertainties of maize yield predictions are evaluated by using 30 sets of parameters from statistical crop models together with eight GCMs with reference to three emission scenarios for Jilin Province of northeastern China. Regression models using replicates based on bootstrap resampling reveal that yields are maximized when the optimum average growing season temperature is 20.1°C for 1990–2009. The results of multi-model ensemble simulations show a maize yield reduction of 11%, with 75% probability for 2040–69 relative to the baseline period of 1976–2005. We decompose the variance so as to understand the relative importance of different sources of uncertainty, such as GCMs, RCPs, and statistical model parameters. The greatest proportion of uncertainty (> 50%) is derived from GCMs, followed by RCPs with a proportion of 28% and statistical crop model parameters with a proportion of 20% of total ensemble uncertainty.
Key words: analysis of variance (ANOVA)     climate change     ensemble simulation     maize yield     uncertainty
1 Introduction

Crop models and climate projections are essential tools in the examination of impacts of climate change on crop yields although simulation results are inherently uncertain (Godfray et al., 2010; Wang et al., 2017). The uncertainty intrinsic of crop models can be attributed to differences in physical and biological processes considered in these models and to the ways in which physical parameters are set (Li T. et al., 2015; He et al., 2017). The uncertainty derived from climate projections is mainly related to the use of different global climate models (GCMs), downscaling techniques, and emission scenar-ios (Li R. Q. et al., 2015; Wu et al., 2016; Okoro et al., 2017). Therefore, different sources of the uncertainty may affect projections of the impacts of climate change on crop yields. An understanding of these sources of the uncertainty is central to improving the applicability of climate change impact studies (Asseng et al., 2015; Wallach et al., 2016).

The use of ensemble probabilistic simulation, which involves the operation of several GCMs under multiple emission scenarios and different crop model parameterizations, or of multiple crop models has been proposed as a way to address the uncertainty in climate impact assessments (Tao and Zhang, 2013; Yang et al., 2017; Wang et al., 2018; Aryal et al., 2019). Weighting of sources of the uncertainty enables the prioritization of relatively important sources in analysis and reduces the uncertainty in the presence of limited resources. However, recent studies have presented inconsistent results on dominant sources of the uncertainty in projections of climate change effects on crop yields. For instance, Zhang et al. (2017) reported that the uncertainty from climate projections is much more pronounced than that from crop model parameters, for which results are based on simulations conducted from two crop models with 100 sets of parameters in each model driven by 24 climate projections consisting of eight GCMs and three representative concentration pathways (RCPs). Similarly, Ceglar and Kajfež-Bogataj (2012) noted that the uncertainty from crop model parameters can be regarded as negligible compared to that from regional climate models (RCMs). By contrast, almost equivalent uncertainties from GCMs and crop model parameters were found in Zhou and Wang (2015). Furthermore, Tao et al. (2018) found that contributions of crop model parameters and climate projections to the total variance in ensemble outputs varies greatly depending on crop model structures and site conditions. Despite the perceived importance of sources of the uncertainty, the majority of previous studies have considered uncertainties from climate projections consisting of GCM/RCM and RCPs, which are not disaggregated from uncertainties of RCPs.

Several reviews have highlighted the complexities of process-based crop models, which must be used to meet requirements for extensive input parametric applications (White et al., 2011; Bassu et al., 2014) but which increase uncertainties of the simulation results (Zhou and Wang, 2015). Alternatively, statistical crop models have been employed to analyse crop response uncertainties related to model parameters (Zhang et al., 2017; Zhou et al., 2017). Primary advantages of statistical models are rooted in their partial dependence on extensive field experimental data and in their simple regression equations, which can be used to easily quantify the model uncertainty (Asseng et al., 2013). Furthermore, statistical models account for yield responses to effects of the pests, diseases, and air pollution during the growing season, which are not considered in most process-based models (Lobell et al., 2006; Shi et al., 2012). In this study, statistical crop models based on information taken from both time series and multiple sites in space, namely the panel regression models, are adopted to assess maize yields, an approach that has only recently been emphasized (Lobell and Burke, 2010; Tack et al., 2015; Liu et al., 2016). This has been attributed to the high accuracy of panel regression models in predicting crop responses to temperature changes relative to time-series models, which are only based on time series data for each site (Schlenker and Lobell, 2010; Tao et al., 2013).

Jilin Province (40.9°–46.3°N, 121.6°–131.3°E; Fig. 1) of northeastern China is examined as a case study of the uncertainty regarding the impacts of climate change on the maize yield simulation. Jilin Province is the largest commercial grain production area in China. The maize production plays an important role in local and national food security, which contributes more than 70% of the total grain production and occupies 65% of the crop-sown area of Jilin Province (National Bureau of Statistics of China 2013–17). Hence, the projected future responses of maize yields to climate change in this region are a significant determining factor relevant to the future food production in Jilin Province and to national grain supplies.

 Figure 1 The major maize-growing area and locations of the selected study stations in Jilin Province.

The purposes of this study are to estimate the effects of climate change on maize yields, to evaluate the overall uncertainty in this estimate attributable to three sources (GCMs, RCPs, and crop regression model parameters), and to evaluate the separate contributions of these sources. First, the crop yield and meteorological data for 1990–2009 taken from eight study sites are combined to estimate the panel regression models, and the bootstrap method is used to estimate 30 sets of parameters to fit the model representing parameter uncertainty. Then, 24 climate projections representing the uncertainty, are constructed by using eight GCMs and three RCPs. Finally, multiple climate projections are used to drive the regression model with multiple sets of parameters to assess the complete responses of maize yields to climate change. Moreover, the variance is decomposed to analyze contributions of different sources of the uncertainty from GCMs, RCPs, and parameters of the crop regression model to maize yield ensemble simulations.

2 Materials and methods 2.1 Study area

This study is conducted at eight sites selected from agrometeorological stations of the China Meteorological Administration (CMA) in Jilin Province (Fig. 1): Baicheng (45.4°N, 122.5°E), Changling (44.2°N, 123.6°E), Nongan (44.3°N, 125.1°E), Yongji (43.4°N, 126.3°E), Shuangyang (43.3°N, 125.4°E), Lishu (43.2°N, 124.2°E), Huadian (42.6°N, 126.5°E), and Meihekou (42.3°N, 125.4°E). These sites are chosen because of their locations in the major maize production area of Jilin Province (counties with > 5,000 ha of maize planting acreage consecutively from 2005 to 2012) and the high-quality data recorded.

2.2 Crop and climate data

The crop yield and meteorological (daily temperature and precipitation) data collected at the study stations from 1990 to 2009 are obtained from the National Meteorological Information Center of CMA.

GCM simulation data archived by CMIP5 are obtained. Daily temperature and precipitation data for 1976–2005 (the baseline period) and for 2040–69 (the future period) are used in this study and are derived from 24 climate projections of eight GCMs under three RCPs (RCP2.6, RCP4.5, and RCP8.5). The eight GCMs are BCC-CSM1-1 (China), CCSM4 (USA), CSIRO-MK3.6.0 (Australia), EC-EARTH (Europe), GFDL-ESM2G (USA), IPSL-CM5A-MR (France), MRICGCM3 (Japan), and NorESM1-M (Norway).

2.3 Establishment of statistical maize models

Using the panel regression function available through R software, a statistical model based on information taken from multiple stations, is fitted to determine the impact of climate on maize yields. The average temperature and accumulated precipitation over the same maize growing season (21 April–30 September) across the eight sites are combined to fit the initial panel regression model as below:

 \begin{aligned} \lg \left({{\rm{Yiel}}{{\rm{d}}_{i, t}}} \right) =\; & {\beta _{i, 0}} + {\beta _1} \times {T_{i, t}} {\beta _2} \times T_{i, t}^2 \\ & + {\beta _3} \times {P_{i, t}} + {\beta _4} \times P_{i, t}^2 + {\varepsilon _{i, t}}, \end{aligned} (1)

where Yieldi,t (t ha−1), Ti,t (°C), and Pi,t (mm) are the yield, average growing temperature, and total precipitation, respectively, for year t at site i; βi, 0 represents an intercept for each site i; β1–4 represent the model parameters to be fit; and ε is an error term.

Bootstrap resampling is an effective method for regression model fitting (Lobell et al., 2006; Challinor et al., 2014; Holzkämper et al., 2015a) and is used here to estimate the regression coefficients with 1000 samples. Thirty model replications are used in consideration of the minimum R2 and moderate computation burden to represent the uncertainty in model parameters used in this study.

2.4 Uncertainty and contributions to uncertainty

The overall uncertainty is defined simply as the probabilistic yield change in simulations based on an ensemble output by using eight GCMs under three RCPs and panel regression models with 30 sets of parameters. Therefore, 8 GCMs × 3 RCPs (without considering the baseline) × 30 sets of parameters for the panel regression model × 8 sites × 30 yr = 172,800 simulations generated based on the panel regression models for the eight sites for the future climate period of 2040–69 relative to 57,600 simulations for the baseline period of 1976–2005 without considering differences in emission scenarios. The probability density function and cumulative distribution function of simulated yield changes based on multi-model ensembles are used to account for the overall uncertainty in yield changes.

An analysis of variance (ANOVA) is applied to partition the three sources of ensemble uncertainty in the projected yield changes, from GCMs, RCPs, and regression model parameters, and a ternary diagram is constructed to compare the relative importance of three sources of the uncertainty. A more detailed description of the applied ANOVA method can be found in Bosshard et al. (2013) and Vetter et al. (2017).

A three-way ANOVA is performed to calculate the total sum of squares (SST) that can be attributed to the main effect of three sources (SSGCM, SSRCP, and SSPAR) and their interactions (SSGCM×PAR, SSGCM×RCP, SSRCP×PAR, and SSGCM×RCP×PAR):

 \begin{aligned} {\rm{SST}} =\; & {\rm{S}}{{\rm{S}}_{{\rm{GCM}}}} + {\rm{S}}{{\rm{S}}_{{\rm{RCP}}}} + {\rm{S}}{{\rm{S}}_{{\rm{PAR}}}} + {\rm{S}}{{\rm{S}}_{{\rm{GCM}} \times {\rm{RCP}}}} \\ & + {\rm{S}}{{\rm{S}}_{{\rm{GCM}} \times {\rm{PAR}}}} + {\rm{S}}{{\rm{S}}_{{\rm{RCP}} \times {\rm{PAR}}}} + {\rm{S}}{{\rm{S}}_{{\rm{GCM}} \times {\rm{RCP}} \times {\rm{PAR}}}}. \end{aligned} (2)

Then, all interaction terms are split equally and added to separate factors of the GCMs, RCPs, and statistical crop model parameters:

 \begin{aligned} \;\; {\rm{S}}{{\rm{S}}_{\rm{G}}} =\; & {\rm{S}}{{\rm{S}}_{{\rm{GCM}}}} + \frac{{{\rm{S}}{{\rm{S}}_{{\rm{GCM}} \times {\rm{RCP}}}}}}{2} + \frac{{{\rm{S}}{{\rm{S}}_{{\rm{GCM}} \times {\rm{PAR}}}}}}{2} \\ & + \frac{{{\rm{S}}{{\rm{S}}_{{\rm{GCM}} \times {\rm{RCP}} \times {\rm{PAR}}}}}}{3}, \end{aligned} (3)
 \begin{aligned} {\rm{S}}{{\rm{S}}_{\rm{R}}} =\; & {\rm{S}}{{\rm{S}}_{{\rm{RCP}}}} + \frac{{{\rm{S}}{{\rm{S}}_{{\rm{GCM}} \times {\rm{RCP}}}}}}{2} + \frac{{{\rm{S}}{{\rm{S}}_{{\rm{RCP}} \times {\rm{PAR}}}}}}{2} \\ & + \frac{{{\rm{S}}{{\rm{S}}_{{\rm{GCM}} \times {\rm{RCP}} \times {\rm{PAR}}}}}}{3}, \end{aligned} (4)
 \begin{aligned} {\rm{S}}{{\rm{S}}_{\rm{P}}} =\; & {\rm{S}}{{\rm{S}}_{{\rm{PAR}}}} + \frac{{{\rm{S}}{{\rm{S}}_{{\rm{GCM}} \times {\rm{PAR}}}}}}{2} + \frac{{{\rm{S}}{{\rm{S}}_{{\rm{RCP}} \times {\rm{PAR}}}}}}{2} \\ & + \frac{{{\rm{S}}{{\rm{S}}_{{\rm{GCM}} \times {\rm{RCP}} \times {\rm{PAR}}}}}}{3}, \end{aligned} (5)
 ${\rm{SST}} = {\rm{S}}{{\rm{S}}_{\rm{G}}} + {\rm{S}}{{\rm{S}}_{\rm{R}}} + {\rm{S}}{{\rm{S}}_{\rm{P}}}, \quad\quad\quad\quad\quad\quad\quad$ (6)

where SSG, SSR, and SSP are the sum of squares for the three components, including GCMs, RCPs, and statistical crop model parameters, respectively.

Finally, simple proportions of the sum of squares attributable to the three sources (SSG, SSR, and SSP) with respect to SST are calculated with Eq. (6).

3 Results 3.1 Statistical regression model

The panel regression model trained on the dataset of yields versus the average growing season temperature for 1990–2009 at eight sites reveals a significant relationship between the yield and temperature (p < 0.05). The 30 statistical crop models are fitted to R2 values of 0.75–0.79; the fitted regression coefficients are summarized in Table 1. The models yield a positive effect for the linear term of temperature on maize yield, while a negative effect is obtained for the squared term of temperature. Figure 2 illustrates the inverted-U relationship between the yield and temperature as estimated by the regression models. This relationship implies that yields are maximized when the optimum inferred average growing season temperature is 20.1°C.

Table 1 Ensemble means and ranges of regression coefficients in the 30 replications of the panel model
 Parameter Value β1,0 –3.3870 (–3.4907, –3.3074) β2,0 –3.2981 (–3.3922, –3.2163) β3,0 –3.3980 (–3.5077, –3.2909) β4,0 –3.3589 (–3.4639, –3.2804) β5,0 –3.3565 (–3.4794, –3.2561) β6,0 –3.3869 (–3.5036, –3.3013) β7,0 –3.3480 (–3.4650, –3.2617) β8,0 –3.3075 (–3.3911, –3.2449) β1 0.4449 (0.4288, 0.4662) β2 –0.0115 (–0.0123, –0.0109)
 Figure 2 Estimated yield responses to the average growing season temperature for 1990–2009 in the 30 replications of the panel regression model.
3.2 Probabilistic changes in maize yields

The uncertainty in ensemble simulations is expressed in terms of a probability distribution, based on which the distribution form is determined visually and a probabilistic estimate is generated. Therefore, based on ensemble outputs consisting of 24 climate projections (eight GCMs under three RCPs) and 30 sets of parameters in the panel regression models, the probability distribution of the projected yield changes is analyzed to obtain potential yield changes. The probability density for changes in simulated maize yields for 2040–69 relative to 1976–2005 is presented in Fig. 3. The peak in probability density is negative, indicating a relatively high likelihood of reduced yields. From the histogram of yield changes, the maximum probability of a change in the maize yield is found in the −20% to −10% group (Fig. 3). However, probabilities of yield changes in the −10% to 0% and −20% to −10% groups are approximately the same. Overall, the ensemble simulations show that future mean yields are projected to decrease by 11% with a probability of 75% during 2040–69.

 Figure 3 The probability density of simulated maize yield changes for 2040–69 relative to the baseline period of 1976–2005.
3.3 Uncertainty and its decomposition

The simulated mean maize yield changes among 30 sets of crop parameters and eight GCMs under three RCPs are quite different. For example, the mean yield changes ranged from −32% to +1% for CSIRO-MK3.6.0 under RCP8.5 and CCSM4 under RCP2.6, respectively, with an optimal set of crop parameters found for the period 2040–69 relative to 1976–2005. These differences in the yield projection under climate change highlight uncertainties attributable to the use of different GCMs, RCPs, and model parameters.

Variances in projected yield changes from ANOVA are divided into contributing sources (GCMs, RCPs, and regression model parameters) and are constructed in a ternary diagram (Fig. 4). Ternary plots show that the uncertainty in the projected yield changes presents a high GCM proportion with most samples clustering towards the GCMs apex. This indicates that the uncertainty is dominated by GCMs constituting 47% to 60% of the variance in ensemble yields. Contributions of RCPs to the total ensemble uncertainty also prove important, ranging from 18% to 38%. Parameters of the regression models contributed least to the uncertainty in ensemble yield changes, with most values < 25%. Averaged across all sites in the ternary graphs, the overall average values of the uncertainty attributed to GCMs, RCPs, and regression model parameters are 52% (range: 47%–60%), 28% (range: 18%–38%), and 20% (range: 15%–27%), respectively.

 Figure 4 The ternary plot showing uncertainty in projected yield changes (%) arising from the GCMs, RCPs, and statistical crop model parameters for the eight sites (denoted by small circles) for the future period of 2040–69.
4 Discussion

In the present study, the ensemble mean maize yields of eight GCMs, three RCPs, and 30 statistical crop models are used. It is noteworthy that a negative impact of climate change on maize yields is detected, which is generally consistent with previous studies of this area (Cao et al., 2010; Zhang et al., 2017). Nevertheless, magnitudes of the simulated yield change are dependent on RCPs, GCMs, crop models, and locations. Furthermore, the uncertainty arising from differences in the structure of crop models (Wang et al., 2015; Zhang et al., 2015; Tao et al., 2018) and from methods used for the downscaling and bias correction in climate models (Wilby et al., 2009; Dosio and Paruolo, 2011; Liu et al., 2017) is lacking in the present study, and should be further considered to gain a more comprehensive understanding of the impact of climate change through crop simulations.

The decomposition of sources of the uncertainty can improve understanding of the relative contributions of these sources to the projected impacts of climate change and can provide valuable information for the uncertainty reduction. The results show that GCMs are the most important source of the uncertainty and are prioritized in the ensemble simulations. This is likely found to be the case due to large divergences in the projected temperature observed among different GCMs relative to the stable statistical model structure, which result in the yield variability (Zhang et al., 2015). Improvements of GCMs can further enhance the credibility of climate change assessments and mitigate related uncertainties. The uncertainty in yield changes observed in the ensemble simulation depends largely on climate projections (consisting of GCMs and RCPs since RCPs are not isolated in previous studies) relative to the regression model parameters. This result is in agreement with those of previous studies employing statistical regression models (Lobell et al., 2006; Zhang et al., 2017), and echoes those of Tao et al. (2009) and Holzkämper et al. (2015b) derived from process-based crop models. However, these results are not consistent with those obtained by Holzkämper et al. (2015a) based on four GCM–RCMs and regression models with 50 sets of parameters. Furthermore, Zhou and Wang (2015) identified almost equivalent levels of the uncertainty from both sources in an analysis of maize yields for northeastern China. These differences highlight the importance of considering uncertainties in crop yield predictions caused by different RCPs, which have been neglected in previous studies but which might mitigate uncertainties of climate projections. Moreover, the uncertainty in ensemble yield simulations derived from RCPs proves more pronounced than that identified from the regression model parameters used in this study, further reflecting the importance of RCPs.

Panel regression models using site-specific intercepts to account for the omitted time-invariant variables are adopted rather than time-series models for each site to assess maize yields. This choice is based mainly on the high accuracy of panel regression models in predicting temperature responses relative to time-series models (Lobell and Burke, 2010; Schlenker and Lobell, 2010). Furthermore, while precipitation is an important factor shaping maize yields (Cao et al., 2010; Li et al., 2014; Zhang et al., 2017), no strong correlation between the yield and precipitation is found in this study. This result might be attributed to the varying responses of crop yields to climatic parameters at different spatial scales (Zhang et al., 2010; Shi et al., 2012). Further explorations using multivariate regression models at different spatial scales are needed to better identify the impacts of climate change on the crop production.

5 Conclusions

Ensemble responses of maize yields to projected climate changes in Jilin Province, China are evaluated after considering sources of the uncertainty from eight GCMs, three RCPs, and 30 statistical crop models derived by bootstrap resampling of the historical data. These ensemble results show that mean yields are projected to decrease by 11% with a probability of 75% during 2040–69 relative to 1976–2005. The variance decomposition shows that GCMs are the most important source of the uncertainty in the ensemble simulations, followed by RCPs and regression model parameters.

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