1 Null Hypotheses for nway ANOVA Tree covergrass

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Null Hypotheses for n-way ANOVA • Tree cover/grass (C 3, C 4) does not have significant effect on partial r • If p < 0. 05, tree cover/grass (C 3, C 4) affects partial r Effect of tree cover on r is significant • If p > 0. 05, tree cover/grass (C 3, C 4) has no effect on partial r • Tree and Grass (C 3, C 4) interaction does not have significant effect on partial r 2

Different Tree Cover Product 3

ANOVAN (Tree vs C 4) for basins with significant correlation and GPP > 0. 5 DJF MAM JJA SON Combined Reject H 0 Accept H 0 ? ? 4

ANOVAN (Tree GLTC vs C 4) for basins with significant correlation and GPP > 0. 5 DJF MAM JJA SON Combined Reject H 0 Accept H 0 ? ? 5

• Both products show similar results with significant contribution from both C 4 cover and tree cover influencing the variation of GPP-WTD partial correlation • When season are pooled together, the contribution of C 4 disappear. • In the long run or majority of cases, the tree cover/C 4 interaction controls the variation of partial correlation (? ) 6

Include Climate (Evaporation ratio = l. E/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 C 4 vs ER) for basins with significant correlation and GPP > 0. 5 DJF MAM JJA SON Reject H 0 Combined Accept H 0 ? ? 8

ANOVAN (Tree GLTC vs C 4 vs ER Mean) for basins with significant correlation and GPP > 0. 5 DJF MAM JJA SON Reject H 0 Combined Accept H 0 ? ? 9

• Seasonal ER: • Tree and ER have significant influences on variation of r in all seasons • C 4 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 • C 4 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 C 4) for all basins with GPP > 0. 5 DJF MAM JJA SON Combined Reject H 0 Accept H 0 ? ? 12

ANOVAN (Tree GLTC vs C 4) for basins with significant correlation and GPP > 0. 5 DJF MAM JJA SON Combined Reject H 0 Accept H 0 ? ? 13

ANOVAN (Tree GLTC vs C 4 vs ER) for all basins with GPP > 0. 5 DJF MAM JJA SON Reject H 0 Combined Accept H 0 ? ? 14

ANOVAN (Tree GLTC vs C 4 vs ER) for basins with significant correlation and GPP > 0. 5 DJF MAM JJA SON Reject H 0 Combined Accept H 0 ? ? 15

ANOVAN (Tree GLTC vs C 4 vs ER Mean) for all basins with GPP > 0. 5 DJF MAM JJA SON Reject H 0 Combined Accept H 0 ? ? 16

ANOVAN (Tree GLTC vs C 4 vs ER Mean) for basins with significant correlation and GPP > 0. 5 DJF MAM JJA SON Reject H 0 Combined Accept H 0 ? ? 17

• Tree and C 4: • Tree and C 4 both have influence seasonally, but only tree has significant influence when pooled. • Including all basins does not change the result • Tree C 4 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/C 4 fraction (Y) 20

ANOVAN on Diff (Tree vs C 4) for basins with significant correlation and GPP > 0. 5 DJF MAM JJA SON 3 Combined Reject H 0 Accept H 0 ? ? 21

ANOVAN on Diff (Tree vs Grass) for basins with significant correlation and GPP > 0. 5 DJF MAM JJA SON 3 Combined Reject H 0 Accept H 0 ? ? 22

• Seasonal: • Tree has significant influences on variation of r in all seasons with largest MSOS • C 4 has significant influence in SON, when regions in Africa with larger C 4 fraction have significant negative GPP-WTD relationship. • Tree and C 4 interactions are insignificant in all seasons • Even using total C 4 shows the same. • Total grass has significant influence in MAM but not in SON when C 4 shows significant association • Combined: • When the seasons are concatenated, both tree and c 4 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 C 4 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

ANOVA 2 (Tree GLTC vs C 4 vs ER) for basins with significant correlation and GPP > 0. 5 DJF MAM JJA SON Reject H 0 Combined Accept H 0 ? ? 26

ANOVA 3 (Tree GLTC vs C 4 vs ER) for basins with significant correlation and GPP > 0. 5 DJF MAM JJA SON Reject H 0 Combined Accept H 0 ? ? 27

ANOVA 2 (Tree GLTC vs C 4 vs ER Mean) for basins with significant correlation and GPP > 0. 5 DJF MAM JJA SON Reject H 0 Combined Accept H 0 ? ? 28

ANOVA 3 (Tree GLTC vs C 4 vs ER Mean) for basins with significant correlation and GPP > 0. 5 DJF MAM JJA SON Reject H 0 Combined Accept H 0 ? ? 29

• Full interaction results in lower MSOS of tree cover • Not a lot of changes in significance 30

ANOVAN on Diff (Tree vs C 4 Total) for all basins with significant correlation and GPP > 0. 5 DJF MAM JJA SON 3 Combined Reject H 0 Accept H 0 ? ? 31

ANOVAN on Diff (C 4 vs Grass) for all basins with significant correlation and GPP > 0. 5 DJF MAM JJA SON 3 Combined Reject H 0 Accept H 0 ? ? 32

ANOVAN on Diff (C 3 vs C 4) for all basins with significant correlation and GPP > 0. 5 DJF MAM JJA SON 3 Combined Reject H 0 Accept H 0 ? ? 33