## 3 Results
### The Relationships between Cropland Productivity and Climatic Variables  
The spatial patterns of average annual CFAPAR from 2000 to 2013 in Section 3.2 highlighted the potential connections between cropland productivity and climate variability. Figure 9 shows the partial correlation coefficients of the three climatic variables with annual cropland productivity from 2000 to 2013. Figure 8: Temporal trends of annual CFPAR in three agro-climatic zones in the Canadian Praities, sub-humid zone (**a**); semi-arid zone (**b**); and arid zone (**c**); respectively. Figure 7: Temporal trends of annual CFPAR in Alberta (AB) (**a**); Saskatchewan (SK) (**b**); and Manitoba (MB) (**c**); respectively. For cumulative rainfall in a growing season (Figure 9a), the variability of cropland productivity is generally sensitive to rainfall variability with a positive relationship in more than 70% of the study areas (Figure 9a). The partial correlation coefficient (\(r\)) over most cropland areas in the Canadian Prairies was higher than 0.55, especially in AB and SK. Cropland productivity in most areas was negatively affected by growing season mean temperature (Figure 9b); however, except for areas in the arid zone located mainly in southern SK and southeast AB, the effect was not significant. For the cumulative radiation during the growing season (Figure 9c), there was no significant correlation between cropland productivity and radiation at the 0.05 level in most areas, indicating that cropland productivity in these areas was not normally limited by radiation. However, cropland productivity in some localized croplands of central AB and northeast SK was sensitive to radiation with a positive partial correlation coefficient greater than 0.55 (\(p<0.01\), \(n=14\)). For AB and SK, it could be observed that rainfall played the most important role in variation of cropland productivity with a positive relationship, followed by temperature variability and radiation variability (Figure 9). The variation of cropland productivity in MB was more affected by the temperature variability (\(p<0.10\)) and the limiting factors were more complicated than that in AB and SK. In summary, the analysis in this section demonstrated that cropland productivity variability in most areas of the Canadian Prairies was mainly driven by the amount of rainfall. Figure 9: Spatial patterns of the partial correlation coefficient (\(r\)) between CFAPAR and climatic variables during the crop growing season; cumulative rainfall (**a**); growing season mean (**b**) temperature; and cumulative radiation (**c**), respectively. To further determine the trend of cumulative rainfall during observed years, the analysis was conducted using the M-K test and the results are shown in Figure 10. Areas with a positive \(z\)-score, indicating an increasing trend, were distributed in most areas of the Canadian Prairie region. However, the increasing trend was not significant at the level of 0.05 (\(\mid\)Z-score \(\mid\)\(\leqslant\)1.96) except in some localized areas. To further evaluate the relationship between cropland productivity and rainfall, the spatial distribution of the coefficient of variation (CV) of rainfall is shown in Figure 11 and compared with that of cropland productivity. Although there was no apparent trend for rainfall, the CV of rainfall showed strong fluctuation. Rainfall variability ranged from 40% to 60% across the three agro-climatic zones, with a higher variability in the semi-arid zone than in the sub-humid zone. The CV distribution of cropland productivity (Figure 12) shows a consistent pattern as in [PERSON], _et al._ (2012), and has a similar spatial pattern to that of rainfall (Figure 11). A strong and positive linear correlation between the CV of CFAPAR and that of rainfall (\(r\) = 0.66, \(n\) = 593, \(p\) < 0.01) was observed (Figure 13). Hence, these results indicate that the cropland productivity variability was partly determined by the rainfall variability.