Effects of interannual climate variability on tropical tree cover

Transcription

1 Effects of interannual climate variability on tropical tree cover Milena Holmgren, Marina Hirota, Egbert H. Van Nes & Marten Scheffer Correspondence to: Contents: 1. Climate Indexes. 2. Correlation of climate variables and multi-collinearity analysis (Tables S1, S2) 3. Interactive effects of MAP and CV on tropical tree cover (Table S3, S4). 4. Models for the distribution of tree cover in wet tropics (MAP > 600 mm) as a function of MAP, CV and MSI (Table S5, S6, S7). 5. Non-spatial models for the distribution of tree cover in dry tropics (MAP 600 mm) as a function of climate (Tables S8, S9, S10, S11). 6. Spatial models for the distribution of tree cover in dry tropics (MAP 600 mm) as a function of climate (Tables S12, S13, S14). 7. Analysis of the residuals for dry-land models. NATURE CLIMATE CHANGE 1

2 1. Climatic indexes Standardized Precipitation Index (SPI) The Standardized Precipitation Index estimates the probability of an anomalous precipitation event at a particular time scale 30. The SPI is defined as the number of standard deviations above or below the climatological mean precipitation for that period. Depending on the SPI value, the anomalous climatic event is classified as follows: SPI values +2σ +1.50σ to +1.99σ +1.00σ to +1.49σ -0.99σ to +0.99σ -1.00σ to -1.49σ -1.50σ to -1.99σ -2σ Category Extremely wet Severely wet Moderately wet Close to normal Moderately dry Severely dry Extremely dry Because we were interested in evaluating inter-annual variability, SPI values were calculated for each year as the deviations of the yearly mean precipitation from the long term Mean Annual Precipitation (MAP) for the period from 1961 to 2002 (42 years). Severely wet years were defined for our purpose as those with SPI +1.5σ (thus including the years classified as extremely wet in the original SPI system). For each pixel, we calculated the percentage of severely wet years (SPIW). Conversely, severely dry years were defined as those with SPI - 1.5σ to calculate the percentage of severely dry years (SPID). SPIW and SPID are good indicators of inter-annual variability because they are not correlated with MAP (see Table S1). Coefficient of Variation (CV) and Standard Deviation (SD) Coefficient of variation (CV) and standard deviation (SD) of mean annual precipitation (MAP) were calculated according to the usual statistical equations for the years Markham s Seasonality Index (MSI) The Markham s Seasonality Index was proposed to show the tendency a certain location has to concentrate more precipitation in certain months of the year compared to others 31. Its calculation assumes that monthly rainfall totals are vectors, with the rainfall as the length, and the month as the direction of the vector. We calculated the magnitude of the summed vector of all months per year (which is an indication of the seasonal variation) and standardized this by dividing it by the mean annual precipitation. Subsequently we averaged the yearly values over the period of 1961 to NATURE CLIMATE CHANGE

3 SUPPLEMENTARY INFORMATION 2. Correlation between climate variables and multi-collinearity analysis. Table S1 Pearson correlation coefficients among Mean Annual Precipitation (MAP) and the other climate variables: percentage of severely wet years (SPIW), percentage of severely dry years (SPID), Coefficient of Variation (CV), Standard Deviation (SD) and Markham Seasonality Index (MSI). Indexes SPIW SPID CV SD MSI MAP Table S2 Variance Inflation Factor (VIF) values for the explanatory variables (MAP, SPIW, SPID, CV, MSI) to test for multi-collinearity. All VIF < 5 indicating there is no multicollinearity affecting the effect size and signal of the linear coefficients. Continent/ precipitation classification VIF for each linear regression setup f(map, SPIW, MSI) f(map, SPID, MSI) f(map, CV, MSI) /drylands (1.01, 1.06, 1.06) (1.00, 1.05, 1.05) (1.79, 1.79, 1.01) /wetlands (1.48, 1.00, 1.48) (1.48, 1.03, 1.50) (2.27, 1.82, 1.48) /drylands (1.38, 1.05, 1.41) (1.40, 1.04, 1.38) (2.52, 2.41, 3.11) /wetlands (1.23, 1.21, 1.36) (1.15, 1.12, 1.28) (1.71, 2.15, 2.30) /drylands (1.24, 1.08, 1.30) (1.35, 1.42, 1.42) (1.96, 2.30, 1.47) /wetlands (1.32, 1.02, 1.33) (1.34, 1.02, 1.33) (1.60, 1.25, 1.32) NATURE CLIMATE CHANGE 3

4 3. Interactive effects of MAP and CV on tropical tree cover. Table S3. Non-spatial generalized least square (GLS) models fitting tree cover percent (arcsin-squared-root transformed) to Mean Annual Precipitation (log MAP) and the Coefficient of Variation (log CV) and their interaction for tropical regions in each continent. Significance of the explanatory variables assessed with L-Ratio (* p < 0.05). Estimates and confidence intervals () are presented for each factor. Continent Intercontinental AIC Pseudo Adj Constant * MAP * CV * MAP*CV * Constant * MAP * CV MAP*CV Constant * MAP * CV * MAP*CV * Constant * MAP * CV * MAP*CV * NATURE CLIMATE CHANGE

5 SUPPLEMENTARY INFORMATION Table S4. Spatial generalized least square (GLS) models fitting tree cover percent (arcsinsquared-root transformed) to Mean Annual Precipitation (log MAP), the Coefficient of Variation (log CV) and their interaction for tropical regions in each continent. Significance of the explanatory variables assessed with L-Ratio (* p < 0.05). Estimates and confidence intervals () are presented for each factor. Continent Intercontinental AIC Pseudo Adj Constant MAP CV MAP*CV Constant * - - MAP * - - CV MAP*CV Constant MAP * CV * MAP*CV * Constant MAP * CV * MAP*CV * NATURE CLIMATE CHANGE 5

6 4. Models for the distribution of tree cover in wet tropics (MAP > 600 mm) as a function of MAP, CV and MSI (Tables S5, S6 and S7). Table S5. Non-spatial generalized least square (GLS) models fitting tree cover percent (arcsin-squared-root transformed) to Mean Annual Precipitation (MAP) and the Coefficient of Variation (CV) for tropical regions with MAP > 600 mm in each continent. Significance of the explanatory variables assessed with L-Ratio (* p < 0.05). Estimates and confidence intervals () are presented for each factor. Continent AIC Constant * MAP * CV * Constant * MAP * CV * Constant * MAP * CV * Table S6. Non-spatial generalized least square (GLS) models fitting tree cover percent (arcsin-squared-root transformed) to Mean Annual Precipitation (MAP), the Coefficient of Variation (CV) and Markham Seasonality Index (MSI) for tropical regions with MAP > 600 mm. Significance of the explanatory variables assessed with L-Ratio (* p < 0.05). Estimates and confidence intervals () are presented for each factor. f(map, CV, MSI) Constant * MAP * CV * MSI * f(map, CV, MSI) Constant * MAP * CV * MSI * f(map, CV, MSI) Constant * MAP * CV * MSI * NATURE CLIMATE CHANGE

7 SUPPLEMENTARY INFORMATION Table S7. Spatial generalized least square (GLS) models fitting tree cover percent (arcsinsquared-root transformed) to Mean Annual Precipitation (MAP), the Coefficient of Variation (CV) and Markham Seasonality Index (MSI) for tropical regions with MAP > 600 mm in each continent. Significance of the explanatory variables assessed with L-Ratio (* p < 0.05; p < 0.10 ). Estimates and confidence intervals () are presented for each factor. f(map, MSI) Constant * MAP * MSI * f(map, MSI) Constant * MAP * MSI * f(map, CV, MSI) Constant * MAP * CV MSI * NATURE CLIMATE CHANGE 7

8 5. Non-spatial models for tree cover in dry tropics (MAP 600 mm) as a function of climate (Tables S8, S9, S10, S11). Table S8. Non-spatial generalized least square (GLS) models fitting tree cover percent (arcsin-squared-root transformed) to Mean Annual Precipitation (MAP) and the Coefficient of Variation (CV) for tropical regions with MAP 600 mm in each continent. Significance of the explanatory variables assessed with L-Ratio (* p < 0.05). Estimates and confidence intervals () are presented for each factor. Continent AIC Constant * MAP * CV Constant * MAP * CV * Constant * MAP * CV * Table S9. Non-spatial generalized least square (GLS) models fitting tree cover percent (arcsin-squared-root transformed) to Mean Annual Precipitation (MAP), the Coefficient of Variation (CV) and Markham Seasonality Index (MSI) for tropical regions with MAP 600 mm in each continent. Significance of the explanatory variables assessed with L-Ratio (* p < 0.05). Estimates and confidence intervals () are presented for each factor. Continent Best Model AIC f(map, MSI) Constant * MAP * MSI * f(map, CV, MSI) Constant * MAP * CV * MSI * f(map, CV, MSI) Constant * MAP * CV * MSI * NATURE CLIMATE CHANGE

9 SUPPLEMENTARY INFORMATION Table S10. As Table S9 with the percentage of severely wet years (SPIW) based on the Standardized Precipitation Index. f(map, MSI) Constant * MAP * MSI * f(map, SPIW, MSI) Constant * MAP * SPIW * MSI * f(map, SPIW) Constant * MAP * SPIW * Table S11. As Table S9 with the percentage of severely dry years (SPID) based on the Standardized Precipitation Index. f(map, MSI) Constant * MAP * MSI * f(map, SPID, MSI) Constant * MAP * SPID MSI * f(map) Constant * MAP * * and show statistical significances of 95% (p < 0.05) and 90% (p < 0.10) respectively NATURE CLIMATE CHANGE 9

10 6. Spatial models for the distribution of tree cover in dry tropics (MAP 600 mm) as a function of climate (Tables S12, S13, S14). Table S12. Spatial generalized least square (GLS) models fitting tree cover percent (arcsinsquared-root transformed) to Mean Annual Precipitation (MAP), the Coefficient of Variation (CV) and Markham Seasonality Index (MSI) for tropical regions with MAP 600 mm in each continent. Significance of the explanatory variables assessed with L-Ratio (* p < 0.05). Estimates and confidence intervals () are presented for each factor. f(map) Constant * MAP * f(map, MSI) Constant * MAP * MSI * f(map) Constant * MAP * Table S13. As Table S12 with the percentage of severely wet years (SPIW) based on the Standardized Precipitation Index. f(map) Constant * MAP * f(map, MSI) Constant * MAP * MSI * f(map, SPIW) Constant * MAP * SPIW * Table S14. As Table S12 with the percentage of severely dry years (SPID) based on the Standardized Precipitation Index. f(map) Constant * MAP * f(map, MSI) Constant * MAP * MSI * f(map) Constant * MAP * NATURE CLIMATE CHANGE

11 SUPPLEMENTARY INFORMATION 7. Analysis of the residuals for dry-lands Figure S1: Variograms of the residuals for the models with and without the inclusion of spatial correlation. Covariates are Mean Annual Precipitation (MAP), the percentage of severely wet years (SPIW) based on the Standardized Precipitation Index, and the Markham Seasonality Index (MSI) for tropical regions with MAP 600 mm in each continent (Increases in semi-variances as a function of the distances indicate the presence of spatial correlation within the datasets. Blue and red lines represent models without and with spatial correlation respectively. NATURE CLIMATE CHANGE 11