1. Dendroclimatic Analyses

2. You’ve downloaded or obtained all the climate data. What’s the next step? Statistical analyses to select the ONE climate variable to eventually reconstruct.Statistical analyses to select the ONE climate variable to eventually reconstruct. We must first carefully analyze the climate/tree growth relationshipWe must first carefully analyze the climate/tree growth relationship Response function analysis:Response function analysis: biological model of tree growth/climate relationshipbiological model of tree growth/climate relationship developed by Hal Fritts in early 1970sdeveloped by Hal Fritts in early 1970s uses the final tree-ring chronology developed after standardizationuses the final tree-ring chronology developed after standardization uses monthly temperature and precipitationuses monthly temperature and precipitation uses months from the previous year as well (why?)uses months from the previous year as well (why?)

3. Response function analysis: uses principal components (PC) multiple regressionuses principal components (PC) multiple regression PC analysis removes effects of interdependence among climate variablesPC analysis removes effects of interdependence among climate variables more recent software (PRECON) also uses bootstrapping to calculate confidence intervalsmore recent software (PRECON) also uses bootstrapping to calculate confidence intervals notice r-squared values due to climate and prior growthnotice r-squared values due to climate and prior growth interpret the diagram. Look for bumps, humps, dips, and dumps.interpret the diagram. Look for bumps, humps, dips, and dumps. Bump = single positive monthly variableBump = single positive monthly variable Hump = two or more consecutive positive monthly variablesHump = two or more consecutive positive monthly variables Dip = single negative monthly variableDip = single negative monthly variable Dump = two or more consecutive negative monthly variablesDump = two or more consecutive negative monthly variables

4. Response function analysis:

5. Response Function Analysis

6. Correlation analysis Correlation analysis complements results from response function analysis. RFA primarily concerned with temp and precip. Correlation analysis can be done on ALL climate variables (PDSI, ENSO, PDO, etc.) Correlation analysis best done with stats packages (SAS, Systat) or PRECON. Range of values = -1.0 < r < +1.0 Associated with each r-value is its p-value which tests for statistical significance. In general, we want p-values less than 0.05, or p < 0.05. As in response function analysis, we also analyze months from the previous growing season (why?). As in response function analysis, we look for groupings of monthly variables to indicate seasonal response by trees.

7. Correlation analysis Graphical output from PRECON. Any value above +0.2 or below -0.2 is significant. Positive! Negative!

8. Note how response function analysis (top) and correlation analysis (bottom) are complementary (but different).

9. Pearson Correlation Coefficients Prob > |r| under H0: Rho=0 Number of Observations lmayt ljunt ljult laugt lsept loctt lnovt -0.08019 -0.03131 -0.34233 -0.16914 -0.29516 -0.09849 -0.02712 0.4941 0.7897 0.0023 0.1414 0.0096 0.4071 0.8173 75 75 77 77 76 73 75 Correlation analysis R-values also known as Pearson correlation coefficientsR-values also known as Pearson correlation coefficients SAS output below: r-value (top), p-value (middle), n size (bottom)SAS output below: r-value (top), p-value (middle), n size (bottom) How do you interpret negative correlations?How do you interpret negative correlations?

10. Pearson Correlation Coefficients Prob > |r| under H0: Rho=0 Number of Observations jult augt sept octt novt dect -0.41391 -0.18258 -0.21850 -0.08422 -0.02171 -0.13367 0.0002 0.1120 0.0579 0.4756 0.8534 0.2562 77 77 76 74 75 74 Correlation analysis

11. Stepwise multiple regression analysis Another complementary techniqueAnother complementary technique Why do the two series diverge here?

12. Climate Reconstruction You’ve chosen your ONE climate variable to reconstruct based on these analyses.You’ve chosen your ONE climate variable to reconstruct based on these analyses. Use ordinary least squares regression techniques, which says:Use ordinary least squares regression techniques, which says: Tree growth is a function of climate, but we want to reconstruct climate.Tree growth is a function of climate, but we want to reconstruct climate. Instead, we state climate is a function of tree growth.Instead, we state climate is a function of tree growth. x-values are the predictor variable = tree-ring chronologyx-values are the predictor variable = tree-ring chronology y-values are the predicted variable = climate variabley-values are the predicted variable = climate variable ^ y = ax + b + eis the form of the regression liney = ax + b + eis the form of the regression line In many older studies, it was common to conduct a regression over a calibration period (e.g. 1951-1990), and verify this equation against data in a verification period (e.g. 1910-1949) to ensure the robustness of the predicted values.In many older studies, it was common to conduct a regression over a calibration period (e.g. 1951-1990), and verify this equation against data in a verification period (e.g. 1910-1949) to ensure the robustness of the predicted values.

13. In SAS:In SAS: proc reg; model jult = std;proc reg; model jult = std; where “jult” = July temperature being reconstructed, andwhere “jult” = July temperature being reconstructed, and “std” = the tree-ring (standard) chronology“std” = the tree-ring (standard) chronology In the regression output, you will be given the regression coefficient (a) and the constant (b).In the regression output, you will be given the regression coefficient (a) and the constant (b). To generate predicted climate data before the calibration period, plug these two values into an equation to predict July temperature.To generate predicted climate data before the calibration period, plug these two values into an equation to predict July temperature. Do this for the full length of the tree-ring record for each year.Do this for the full length of the tree-ring record for each year. predict = (9.59154*std) + 32.96236;predict = (9.59154*std) + 32.96236; where “predict” is predicted July temperature and “std” = the tree-ring data.where “predict” is predicted July temperature and “std” = the tree-ring data. Climate Reconstruction

14. Reconstructed Bemidji Feb-May Mean Monthly Max Temp Climate Reconstruction

15. Reconstructed Blue River Annual Streamflow, Colorado

16. Reconstructed Temperatures from Multiple Proxies, the famous “Hockey Stick” graph