Statistical regression models for assessing climate impacts on crop yields: A validation study for winter wheat and silage maize in Germany
Introduction
Crop yield assessments for upcoming climate anomalies or a systematic climate shift are of general interest for farmers, traders (e.g., grain mills, retailers), insurance companies, and policy makers. Statistical models (Ray et al., 2015, Iizumi et al., 2013, Mueller et al., 2012, Roberts et al., 2012, Schlenker and Roberts, 2009) and process based models (Asseng et al., 2013, Angulo et al., 2013, Palosuo et al., 2011) are model types for such assessments. Both model types are parametrized for past weather records. For future projections, they need weather records from climate simulation models. These climate models very often require a bias correction of the simulated output before they allow a reasonable yield projection (Lobell, 2013).
Process based crop models may not include all climate related effects on crop yields. There are many yield effects, which simply cannot be captured in process based models, because of limited spatial information about these effects. Examples are climate triggered effects on agronomic adaptation (irrigation, crop varieties, agronomic technics) or on pests, weeds, and diseases (Mueller et al., 2012). These climate triggered effects can be collinear with the climate variables. Since crop yields also contain climate triggered effects, statistical crop yield models estimate in their parameter values not only the sole, but also the triggered effect of the climate variable. Process based models do not capture these climate triggered effects as long as they are not explicitly embedded in the models (Estes et al., 2013, Lobell and Burke, 2010). In the assessment of farm scale yield effects, this is an important disadvantage of process based models in comparison to statistical models.
Statistical yield models also allow relating inter-annual yield and yield factor changes (i.e., first order temporal ratios) instead of absolute values to each other (You et al., 2009, Lobell, 2007, Lobell and Asner, 2003). Considering changes instead of absolute values eliminates the trend of the variables and it allows neglecting systematic biases for exogenous variables for example when using simulated climate data from circulation models (Lobell, 2013). However, the neglected absolute level by using changes ignores a possible level dependency of yield and climate conditions. This limits the suitability to climate change assessments for changes within the range of recent climate variability. For yield projections beyond the yield variability of the dataset used for model estimation, process based models might be more appropriate (Rötter et al., 2011). At least, process based models should complement the statistical assessments under such circumstances.
The impact of climate on crop yields can be subdivided into two variable groups: variables that primarily determine potential growth and those that can be related to stress influences. The distinction is not disjunctive, overlaps might exist. We focus on the main influences that can contribute to a statistical explanation of the yield variability. The potential yield is determined mainly by the incoming solar radiation (Monteith, 1977, Long et al., 2006). The best usage of this incoming solar radiation requires an optimal mix of agronomic measures to establish the crop, to supply the necessary nutrients and water, and to keep biotic stress factors under control. Any divergence from this optimal mix will result in stress that reduces the potential yield. For these potential stress factors, we distinguish two groups: climate and management driven stress factors.
Among all possible climate driven stress factors, we hypothesize water stress as the most relevant stress factor for German winter wheat and silage maize yields (Wessolek and Asseng, 2006, Kersebaum and Nendel, 2014, Wolf and Diepen, 1994). Other possible influences, like temperature stress, might also exist in single years (Rötter and van de Geijn, 1999, Lobell et al., 2013), but are less generally associable with German climatic conditions. Management driven stress factors, like the crop variety, fertilizer, plant protection, and machinery, are reflected in the mean yield level and the yield trend. However, there are also economic conditions, e.g., statutory set-aside quotas or renewable energy subsidies for biogas and biodiesel, which influence the annual yield variability (Krause, 2008, Bakker et al., 2005). We use the fertilizer price and the acreage of the respective crops as proxy variables to control the economic yield impacts in the models. The fertilizer price represents the varying profitability of production factor inputs (e.g., seeds, plant protection, fuel, and fertilizer) and may directly affect the yield variability. The acreage of winter wheat and silage maize represents changes in the Common Agricultural Policy (CAP) of the European Union. An expanded acreage might generally suppress the yield level of both crops due to the inclusion of marginal productive land.
In our approach, we follow the modeling concept introduced by Wechsung et al. (2008) and the validation scheme of Gornott and Wechsung (2015), who expanded the concept by two other statistical approaches. A level neutralizing transformation is applied for all variables, i.e., the crop yield, the climatic and the non-climatic variables. We utilize first order ratios and , for the years t = 2, …, M of the endogenous variable crop yield yt and the exogenous climatic and non-climatic variables xt. As functional form, we use the Cobb–Douglas function analogous to Oury (1965). The function is proven in both economic (You et al., 2009) and agronomic applications (Lee et al., 2013) and considers yield impacts arising from substitution and interaction between the exogenous variables. The first order ratios are transformed to logarithmized first order ratios of yields and yield-factors, hereafter expressed as yield and factor changes. These changes allow an intercomparison of the effects of different variables.
We test three alternative ways to incorporate the spatial heterogeneity of yield changes and yield factor changes: by separately estimated time series models (STSMs), panel data models (PDMs), and random coefficient models (RCMs). All three approaches refer to a spatial dataset consisting of N discrete subunits and M years. In our case, the subunits are German counties within a federal state, river basin, or Germany as a whole. The methodically simple STSMs are estimated independently for the N subunits resulting in N parameter sets (Butler and Huybers, 2013, Lobell and Burke, 2010). In contrast, PDMs capture directly the temporal and spatial variability by one parameter set for all of the considered N subunits (You et al., 2009). RCMs can be ranked between PDMs and STSMs. They allow individual parameter variations per subunit and a parameter set for the entire unit (Reidsma et al., 2007). The results of the estimations will be presented and evaluated at two scales: the original spatial data scale, i.e., the German county yields, and the aggregated data scale, i.e., federal states, river basins, and entire Germany. Due to the aggregation, county- and farm-individual influences are largely averaged out, which might have biased the model results otherwise (Woodard and Garcia, 2008).
We restricted the temporal and spatial resolution of all variables to a division, which is accessible for climate simulations. The model results are evaluated at a larger scale than the estimation scale. Thus, we make explicit use of spatial aggregation effects. We test and apply the approach in respect to its possible suitability for fast impact assessment of seasonal- and medium-term projections (up to 30 years) from climate models. The approach is conducted for winter wheat and silage maize because these are the major winter and summer annual crops in Germany.
Section snippets
Data
We use a spatial dataset of German crop yields per county for winter wheat and silage maize from 1991 to 2010. The dataset is supplied by the Statistical Offices of the Federation and the Länder (2013b). Climate data are available for the same period from 1218 German weather stations (DWD, 2011). The data were averaged per county to match the spatial resolution of the crop yield data. The total acreage of winter wheat and silage maize is taken from the datasets of the Statistical Offices of the
Goodness of fit
STSMs, PDMs, and RCMs are able to reproduce the measured winter wheat and silage maize yield changes at the aggregated scale for the estimations and the validations (examples shown for STSMs, RCMs, and PDMs in Fig. 2). For both crops and all models, a decrease in NSE by approximately 0.25 is common when comparing estimations with validations. The NSE decreases approximately 0.38 in the expanded validation (not shown).
For all models, crops, and aggregation scales, the goodness of fit (measured
Goodness of fit and yield variability between crops and regions
We investigated and validated three statistical models (STSM, PDM, and RCM) according their robustness for short and medium term climate assessments. These three models are tested to capture the climate-related yield variability of winter wheat and silage maize in Germany. All models are able to reproduce satisfactorily the temporal and spatial variability of yields. In general, the differences in goodness of fit between winter wheat and silage maize are low. The models of regions with higher
Conclusion
Our suggested approach can be used for seasonal forecasts and climate impact projections. For short and medium term climate assessments, we investigate and validate three statistical crop yield models (STSM, PDM, and RCM). These models are particularly suitable for a combination with biased climate simulations and avoid explicit modeling of crop yield trends. The investigated approach is thoroughly based on relative changes of yields and yield influencing factors. Our models can reproduce past
Acknowledgements
The authors would like to thank Andrea Lüttger for her contribution to the data base. We appreciate the comments of Andrea Lüttger, Katja Frieler, and Bernhard Schauberger to earlier versions of our manuscript. We are also grateful to the comments of the reviewers of this paper. The research was supported by project Trans-SEC, which is sponsored by BMBF and co-financed by BMZ.
References (61)
Implication of crop model calibration strategies for assessing regional impacts of climate change in Europe
Agric. Forest Meteorol.
(2013)- et al.
Variability in regional wheat yields as a function of climate, soil and economic variables: assessing the risk of confounding
Agric. Ecosyst. Environ.
(2005) - et al.
Emulating maize yields from global gridded crop models using statistical estimates
Agric. Forest Meteorol.
(2015) - et al.
Methods for estimating vapor pressure deficit at a regional scale depending on data availability
Agric. Forest Meteorol.
(1997) - et al.
Analysis of methods for estimating vapor pressure deficits and relative humidity
Agric. Forest Meteorol.
(1996) Evaluation of the Integrated Canadian Crop Yield Forecaster (ICCYF) model for in-season prediction of crop yield across the Canadian agricultural landscape
Agric. Forest Meteorol.
(2015)- et al.
Impact of weather on yield components of winter rye over 30 years
Agric. Forest Meteorol.
(2000) - et al.
Extending and improving regionalized winter wheat and silage maize yield regression models for Germany: enhancing the predictive skill by panel definition through cluster analysis
Agric Forest Meteorol.
(2016) - et al.
Site-specific impacts of climate change on wheat production across regions of Germany using different CO2 response functions
Eur. J. Agron.
(2014) - et al.
Pre-harvest forecasting of county wheat yield and wheat quality using weather information
Agric. Forest Meteorol.
(2013)
Changes in diurnal temperature range and national cereal yields
Agric. Forest Meteorol.
Errors in climate datasets and their effects on statistical crop models
Agric. Forest Meteorol.
On the use of statistical models to predict crop yield responses to climate change
Agric. Forest Meteorol.
Simulation of winter wheat yield and its variability in different climates of Europe: a comparison of eight crop growth models
Eur. J. Agron.
Trade-off between wheat yield and drainage under current and climate change conditions in northeast Germany
Eur. J. Agron.
Effects of climate change on silage maize production potential in the European Community
Agric. Forest Meteorol.
Impact of growing season temperature on wheat productivity in China
Agric. Forest Meteorol.
Uncertainty in simulating wheat yields under climate change
Nat. Clim. Change
Random coefficient models for time-series – cross-section data: Monte Carlo experiments
Polit. Anal.
Regression Diagnostics: Identifying Influential Data and Sources of Collinearity
Adaptation of US maize to temperature variations
Nat. Clim. Change
Variations in the sensitivity of US maize yield to extreme temperatures by region and growth phase
Environ. Res. Lett.
Panel data econometrics in R: the plm package
J. Stat. Softw.
Pooled cross-sectional and time series data: a survey of current statistical methodology
Am. Stat.
Estimating corn yield response models to predict impacts of climate change
J. Agric. Resour. Econ.
Daily Weather Data, 1951–2010
Aktueller Stand der Phänologie in Deutschland, 1992–2013
Projected climate impacts to South African maize and wheat production in 2055: a comparison of empirical and mechanistic modeling approaches
Global Change Biol.
Ackerland nach Hauptfruchtgruppen und Fruchtarten
Biases in Farm-Level Yield Risk Analysis due to Data Aggregation
German J. Agric. Econ.
Cited by (70)
Wheat yields in Kazakhstan can successfully be forecasted using a statistical crop model
2023, European Journal of AgronomyAre climate change and technology posing a challenge to food security in South Korea?
2023, South African Journal of BotanyLimited potential of irrigation to prevent potato yield losses in Germany under climate change
2023, Agricultural SystemsComparison of process-based and statistical approaches for simulation and projections of rainfed crop yields
2023, Agricultural Water ManagementBasis risk management and randomly scaled uncertainty
2022, Insurance: Mathematics and Economics