## 3 Results
### Trend of Cropland Productivity  
To examine the spatial-temporal variation of cropland productivity, we conducted the trend analysis using the M-K test at the pixel level. Figure 6a shows the trend of CFAPAR from 2000 through 2013 represented by the M-K z-score. Results show that the \(z\)-score in most crop areas is above zero (Figure 6a), indicating a general increasing trend of cropland productivity from 2000 to 2013. The z-score in some areas such as the southern and central regions of SK and AB was higher than in other cropland areas. Some small areas such as the area in the northern part of MB and northwestern part of AB, show a decreasing trend (\(z\)-score \(<0\)). At the significance level of 0.05 (\(\mid\)\(z\)-score \(\mid\)\(\geqslant\) 1.96), a significant increasing trend of cropland productivity was observed in AB and SK, as seen from the  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **CFAPAR** & **Rainfall** & **Temperature** & **Radiation** \\ \hline
**CFAPAR** & \(-1.00\) & \(0.60\) & \(-0.46\) & \(0.00\) \\
**Rainfall** & & \(-1.00\) & \(0.39\) & \(0.49\) \\
**Temperature** & & & \(-1.00\) & \(-0.64\) \\
**Radiation** & & & & \(-1.00\) \\ \hline \end{tabular}
\end{table}
Table 1: Partial Correlation Matrix, a partial correlation analysis was conducted between average annual CFAPAR and average annual cumulative rainfall, average annual growing season mean temperature and average annual cumulative short wave radiation during 2000–2013. The dataset is shown in Figure 5.  
Figure 5: The overall relationship between average annual CFAPAR and average annual cumulative rainfall (**a**); growing season mean temperature (**b**); and average annual cumulative short wave radiation during 2000–2013 (**c**). Samples located inside cropland mask were randomly selected using the Create Random Points tool of ArcGIS software.  
Theil-Sen median slope (>0.10) in Figure 6b. A significant decreasing trend of cropland productivity at the 0.05 level was observed in small areas scattered throughout MB (TS slope < \(-0.05\)).  
To further analyze the trend of annual cropland productivity at larger scales, the M-K test was also performed at the provincial level and for agro-climatic zones. Figure 7 shows the trends of cropland productivity in the three provinces. Cropland productivity showed a strong increasing trend in AB (\(Z\)-score = 2.08 > 1.96, slope = 0.91 year\({}^{-1}\), Figure 7a) and SK (\(Z\)-score = 2.85 > 1.96, slope = 0.96 year\({}^{-1}\), Figure 7b). No significant trend was observed for cropland productivity in MB at the 0.05 significance level. Figure 8 shows that cropland productivity had a significant increasing trend in the sub-humid zone (\(Z\)-score = 2.74 > 1.96, slope = 0.71 year\({}^{-1}\)), the semi-arid zone (\(Z\)-score = 2.63 > 1.96, slope = 1.23 year\({}^{-1}\)) and the arid zone (\(Z\)-score = 2.52 > 1.96, slope = 1.20 year\({}^{-1}\)), with the largest increase in the semi-arid zone and the smallest in the semi-humid zone. This indicates a general increasing trend of cropland productivity in the Canadian Prairies. Figure 8 also shows that cropland productivity in the sub-humid zone is always higher than that in the other two zones. By comparing Figures 7 and 8 it is apparent that trends in cropland productivity were more clearly observed when evaluated using the climatological districts than using the administrative boundaries.  
Figure 6: Spatial patterns of crop productivity trends from 2000 to 2013 using MK method; Mann–Kendall \(Z\)-score (a) and the Theil-Sen median slope of the trend in CFAPAR significant at \(p\) < 0.05 (b).  
Figure 7: _Cont._