# **4. Sensitivity of cropping patterns to seasonal perturbations in climate**

Results for the regression coefficients based on the cropland sensitivity models capture the effect of the predictor variables on cropland share and are shown in Table 2 for each of the six cropland models (MODIS, GLCF, GLC2K, ORNL, SAGE, IFPRI). The coefficients indicate the change in the log of the odds ratio per unit change of the predictor variables ( _[10mm]_ for precipitation and _[°C]_ for temperature; refer to table caption for details). Model diagnostics are provided at the bottom of each column. Model fits ( _R_<sup>_2_</sup> ) range from .22 (GLCF) to .39 (SAGE) and the majority of coefficients are statistically significant (p < .05, non-significant coefficients are indicated by *). Coefficients smaller than .001 (marginal effect < 0.1%) are omitted for clarity.

To summarize these results, the marginal effect of each variable was evaluated by combining both linear and quadratic terms and calculating the slope (sensitivity) at the sample mean (Table 3). Also, log odds were converted to odds ( _Q_ ) for interpretability. Thus, values greater than one indicate a positive marginal effect and values smaller than 1 indicate a negative marginal effect. For example, an odds ratio coefficient of 1.05 indicates that the odds of having croplands at a given location increases by 5% for each unit increase in the predictor variable. The combined effect of temperature and precipitation across all seasons and soil variables is shown in italics, and the multi-model mean is shown is the last column.

The results show that, for current climate conditions, the cropland models predict a positive effect for precipitation (1.048 – 1.233, with the exception of GLC2K, .775) and a negative effect for temperature (.812 – .951) when compounding all seasonal coefficients. That is, increases/decreases in seasonal precipitation result in a higher/lower cropland share, whereas increases/decreases in temperature are associated with lower/higher cropland share.

Moreover, interesting patterns are revealed in the seasonal breakdown of climate effects. While increases in precipitation during spring, summer and fall tend to have a positive marginal effect, additional rainfall during winter is negative. This is intuitive, as moisture requirements are most critical during the crops’ main growing season, but are less important during soil preparation and regeneration. Temperature coefficients, on the other hand, exhibit an opposing seasonal pattern, whereby warmer temperatures during the winter are positive, but higher temperatures during spring, summer and fall tend to decrease cropping. This is consonant with the notion that there is an optimum temperature for cropping systems, beyond which increases in temperature have adverse effects (i.e. a hill-shaped functional relationship). During the coldest season, however, warmer temperatures can have positive effects as they influence soil regenerative processes during the fallow period.

The marginal effects of the chemical, hydraulic and thermal properties of soils are consistently positive. That is, the ability of soils to retain water and store heat tends to be beneficial for crops and increases the likelihood of croplands. Similarly, higher soil fertility (C:N ratio) makes it more probable that land will be used for cropping. By extension, active management and preservation of soil properties is critical for maintaining cropland suitability.

The effect of changes in growing season length is very small (.999), which is not surprising as these effects are known to be most important in higher latitudes. Also, the marginal effect of topography is negative (.987), which indicates that steeper slopes tend to reduce the density of croplands. However, the magnitude of this effect is relatively small at the scale of this analysis (.5 grid cell). Lastly, population density tends to increase with cropland density 8