1 Null Hypotheses for n-way ANOVA Tree cover/grass (C3,C4) does not have significant effect on partial r If p < 0.05, tree cover/grass (C3,C4) affects partial r Effect of tree cover on r is significant If p > 0.05, tree cover/grass (C3,C4) has no effect on partial r Tree and Grass (C3,C4) interaction does not have significant effect on partial r 2 Different Tree Cover Product 3 ANOVAN (Tree vs C4) for basins with significant correlation and GPP > 0.5 Accept H 0 Reject H 0 ?? DJF JJA MAM SON Combined 4 ANOVAN (Tree GLTC vs C4) for basins with significant correlation and GPP > 0.5 Accept H 0 Reject H 0 ?? DJF JJA MAM SON Combined 5 Both products show similar results with significant contribution from both C4 cover and tree cover influencing the variation of GPP-WTD partial correlation When season are pooled together, the contribution of C4 disappear. In the long run or majority of cases, the tree cover/C4 interaction controls the variation of partial correlation (?) 6 Include Climate (Evaporation ratio = lE/Net Rad=ER changing seasonally; ER Mean is ER of annual Mean LE/Annual Mean Net Rad and it does not change seasonally) 7 ANOVAN (Tree GLTC vs C4 vs ER) for basins with significant correlation and GPP > 0.5 Accept H 0 Reject H 0 ?? DJF JJA MAM SON Combined 8 ANOVAN (Tree GLTC vs C4 vs ER Mean) for basins with significant correlation and GPP > 0.5 Accept H 0 Reject H 0 ?? DJF JJA MAM SON Combined 9 Seasonal ER: Tree and ER have significant influences on variation of r in all seasons C4 has significant influence in MAM and SON In all seasons, tree cover has the largest mean Sum of Squares (MSOS), which suggests that it has larger influence on variance of GPP-WTD r than other variables including seasonal climate Mean ER: Tree and ER still have significant influences C4 shows additional significant influence in DJF Most importantly, the MSOS is much more distributed suggesting that tree cover is more related to long-term climate rather than its seasonal variation (?) 10 Include all basins with significant and insignificant correlation 11 ANOVAN (Tree GLTC vs C4) for all basins with GPP > 0.5 Accept H 0 Reject H 0 ?? DJF JJA MAM SON Combined 12 ANOVAN (Tree GLTC vs C4) for basins with significant correlation and GPP > 0.5 Accept H 0 Reject H 0 ?? DJF JJA MAM SON Combined 13 ANOVAN (Tree GLTC vs C4 vs ER) for all basins with GPP > 0.5 Accept H 0 Reject H 0 ?? DJF JJA MAM SON Combined 14 ANOVAN (Tree GLTC vs C4 vs ER) for basins with significant correlation and GPP > 0.5 Accept H 0 Reject H 0 ?? DJF JJA MAM SON Combined 15 ANOVAN (Tree GLTC vs C4 vs ER Mean) for all basins with GPP > 0.5 Accept H 0 Reject H 0 ?? DJF JJA MAM SON Combined 16 ANOVAN (Tree GLTC vs C4 vs ER Mean) for basins with significant correlation and GPP > 0.5 Accept H 0 Reject H 0 ?? DJF JJA MAM SON Combined 17 Tree and C4: Tree and C4 both have influence seasonally, but only tree has significant influence when pooled. Including all basins does not change the result Tree C4 and Clim: Similar in case of only significant or all basins Usually, more factors have significant p when all basins are included 18 ANOVA on DIFFerence between number of basins with negative and positive correlation 19 Tree cover (X) vs Grass/C4/C4 fraction (Y) 20 ANOVAN on Diff (Tree vs C4) for basins with significant correlation and GPP > 0.5 DJF JJA MAM SON 3 CombinedCombined Accept H 0 Reject H 0 ?? 21 ANOVAN on Diff (Tree vs Grass) for basins with significant correlation and GPP > 0.5 DJF JJA MAM SON 3 CombinedCombined Accept H 0 Reject H 0 ?? 22 Seasonal: Tree has significant influences on variation of r in all seasons with largest MSOS C4 has significant influence in SON, when regions in Africa with larger C4 fraction have significant negative GPP-WTD relationship. Tree and C4 interactions are insignificant in all seasons Even using total C4 shows the same. Total grass has significant influence in MAM but not in SON when C4 shows significant association Combined: When the seasons are concatenated, both tree and c4 influences are significant Might be related to sample size, as concatenating 3 seasons with insignificant p results in a significant p value Might be due to seasons not being independent from each other. Tree and C4 interaction has no significance, suggesting independence of two variables. Same with total grass, but grass and tree interactions are significant as well. 23 Until 09/10 24 Two-way vs Three-way Interaction 25 ANOVA2 (Tree GLTC vs C4 vs ER) for basins with significant correlation and GPP > 0.5 Accept H 0 Reject H 0 ?? DJF JJA MAM SON Combined 26 ANOVA3 (Tree GLTC vs C4 vs ER) for basins with significant correlation and GPP > 0.5 Accept H 0 Reject H 0 ?? DJF JJA MAM SON Combined 27 ANOVA2 (Tree GLTC vs C4 vs ER Mean) for basins with significant correlation and GPP > 0.5 Accept H 0 Reject H 0 ?? DJF JJA MAM SON Combined 28 ANOVA3 (Tree GLTC vs C4 vs ER Mean) for basins with significant correlation and GPP > 0.5 Accept H 0 Reject H 0 ?? DJF JJA MAM SON Combined 29 Full interaction results in lower MSOS of tree cover Not a lot of changes in significance 30 ANOVAN on Diff (Tree vs C4 Total) for all basins with significant correlation and GPP > 0.5 DJF JJA MAM SON 3 CombinedCombined Accept H 0 Reject H 0 ?? 31 ANOVAN on Diff (C4 vs Grass) for all basins with significant correlation and GPP > 0.5 DJF JJA MAM SON 3 CombinedCombined Accept H 0 Reject H 0 ?? 32 ANOVAN on Diff (C3 vs C4) for all basins with significant correlation and GPP > 0.5 DJF JJA MAM SON 3 CombinedCombined Accept H 0 Reject H 0 ?? 33