Patterns of crop cover under future climates

We study changes in crop cover under future climate and socio-economic projections. This study is not only organised around the global and regional adaptation or vulnerability to climate change but also includes the influence of projected changes in socio-economic, technological and biophysical drivers, especially regional gross domestic product. The climatic data are obtained from simulations of RCP4.5 and 8.5 by four global circulation models/earth system models from 2000 to 2100. We use Random Forest, an empirical statistical model, to project the future crop cover. Our results show that, at the global scale, increases and decreases in crop cover cancel each other out. Crop cover in the Northern Hemisphere is projected to be impacted more by future climate than the in Southern Hemisphere because of the disparity in the warming rate and precipitation patterns between the two Hemispheres. We found that crop cover in temperate regions is projected to decrease more than in tropical regions. We identified regions of concern and opportunities for climate change adaptation and investment. Electronic supplementary material The online version of this article (doi:10.1007/s13280-016-0818-1) contains supplementary material, which is available to authorized users.


Material and Methods
The RF algorithm contains three major steps: (1) n 'bootstrap' samples are drawn from the original training data with each sample comprising 70%, of the data. The remaining 30% of the data are used to estimate model errors and accuracy and later used for cross-validation; (2) an unpruned regression tree is grown for each of the bootstrap samples. However, rather than using the best split among all p predictors, only m of the p predictors are randomly sampled and the best split is chosen from among these m variables. And (3), the prediction is formed by averaging the output of the n trees. RF also produces scores measuring the relative importance of each explanatory variable on the response variable. This score is estimated by calculating the mean decrease in accuracy due to the permutation of one explanatory variable while leaving the others unchanged (Liaw and Wiener 2002). An overall measure of the mean squared errors (sum of squared residuals divided by number of trees) is also calculated within RF.
The climate projections from each of the four GCMs were used independently in Random Forest. That is, we did not calculate a climate model ensemble, but ran the RF model for each GCM and each RCP separately.

AEZ
The agro-ecological-zones (AEZs) dataset is widely used in agronomic, economic and integrated assessment models to determine where different crops could be grown. For example, the Global Trade Analysis Project (GTAP) model determines for each economic region an endowment of land in each of the 18 AEZ's. In this study, we used AEZs calculated by Harman (in prep.) based on a methodology that reproduces the results of Ramankutty and Foley (1999) for the reference period . Their original method divides the total global land surface into 18 AEZs in a two-step process. First is a partitioning into three climate zones, tropical, temperate and boreal, based on two climate metrics: the minimum over the year of the daily minimum temperature and growing degree days (GDD), a measure of heat accumulation used by agronomist to predict plant growth rates and phenological stages. Second, each climate zone is further sub-divided into 6 land types according to the length of the growing period (LGP).
LGP is defined as the period of time in a given year when the climate is optimal for plants to grow and complete a phenological cycle. GDD and LGP are well-established metrics from agronomy research though it should be recognised that there is an inherent scale issue between the plot-scale research that underpins their definition and their use in global scale climate models and economic models.
Although an AEZ map developed by Ramankutty and Foley (1999), which input data have been reproduced by IIASA and FAO and known as GAEZ (v3) (Fischer and Nachtergaele 2008) is already in relatively wide use, the GAEZ data set cannot be extrapolated to account for climates different to that of its baseline period, 1969-1999. Hence we have used a generic, objective and replicable methodology to reconstruct the AEZs. This methodology accommodates changes in the climatic factors that are determinants of the AEZs (Harman in prep.). The defining climate metrics and the resultant AEZ distribution for the GAEZ 1969-1999 base period have been reconstructed using readily obtainable, curated and assured datasets, but it was necessary to modify some aspects of the definitions of GDD and LGP to be numerically more robust. Our baseline AEZs are based on the gridded, re-analysed, monthly-averaged, daily minimum and near-surface air temperature from the Climate Research Unit CRU-TS3.21 data (Jones and Harris 2008). Differences between GTAP-AEZ and

Biophysical variables
Terrain elevation and dominant soil maps were used both as direct explanatory variables in the Random Forest model and also as inputs to the AEZs and PAEZs. These variables were assumed to be unchanged between the baseline and future periods.

GDP
We use a set of two normalised (ranking from 0 to 1) GDP projections that corresponds to the two RCPs, 4.5 and 8.5 (Cai et al. 2015). These GDP projections were generated using GTEM-C, the CSIRO variant of the Global Trade and Environment model (Cai et al. 2015). In the first scenario, global population was assumed to follow the median variant of the United Nations World Population Projections, reaching 10.6 billion people in 2100 (UN 2012). The supply of fossil fuels was assumed to continue the current trend of growth while assumptions about industrial and household energy efficiency improvements were conservative, ranging from 0.15% to 0.75% per year Cai et al. (2015). As such, global greenhouse gas (GHG) emissions followed RCP8.5, reaching 130 gigatonnes GtCO2 in 2100. Based on the above assumptions, regional total factor productivities (TFP) were iteratively derived such that regional Gross Domestic Products (GDP) will continue the momentum of growth, with world GDP reaching 450 trillion in constant 2007US dollars (2007. The second scenario adopted the same assumptions about demographic change, energy efficiency improvement and regional TFP, but imposed a (uniform) global carbon price, to ensure that global GHG emissions followed RCP4.5. In this 4 scenario, the economy responded by switching away from energy and carbon intensive industrial practice and consumption patterns. However, the overall differences in GDP between the two scenarios were minor. This is because the economic cost of decarbonisation was contained by the uptake of renewable energy generation and carbon sequestration technologies in the short term and offset by the avoidance of climate damages in the long term. As a result, the ranking of GDP by region did not change (Fig. A2 in Supplementary information file), although there were differences in the actual monetary values (for further details, see Cai et al. 2015).

Technology
Nitrogen and phosphorus Fertiliser Application data were sourced from the Global Fertilizer and Manure dataset v1 for the period 1994-1999 obtained from the Socioeconomic Data and Applications Center (SEDAC). Units: Kg/Ha (Potter and Ramankutty, 2010).
See Partial Dependence Plot foo all variables ( Figure S7).  Table 1.  Figure S2. GDP estimates for the baseline periods and projections to 2080 based on the RCPs 4.5 and 8.5.
Source: projections obtained from the GTEM-C model (Cai et al., 2015). Figure S3. Zero crop cover in the baseline and projected in the future predictions. Each map shows any pixel that was zero in the baseline period and its crop cover was projected to have very small value, e.g. smaller than 0.05%.
8 Figure S4. Ensemble mean of projected novel agricultural systems. The maps show areas that present zero crop cover in the baseline period increase to greater than 10% cover in the projections by the 2070-2100 period. Each pixel shows the average value for the 4 GCM, the two maps show ensembles of projected agricultural systems for the 2 RCPs.
9 Figure S5. Magnitude of change in the projected crop cover using information from the 4GCMs under the RCP4.5 scenario. Figure S7. Partial plots for the trained Random Forest model.