1. Dendroclimatic Analyses

2. You now have the climate variables. What’s the next step? Statistical analyses to select the ONE climate variable to eventually reconstruct. We must first carefully analyze the climate/tree growth relationship 1. Response function analysis: biological model of tree growth/climate relationship developed by Hal Fritts in early 1970s uses the final tree-ring chronology developed after standardization uses monthly temperature and precipitation (others possible) uses months from the previous year as well (why?)

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

4. Response function analysis:

5. Response Function Analysis

6. 2. 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 coefficients SAS output below: r-value (top), p-value (middle), n size (bottom) 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 technique Why do the two series diverge here?

12. Climate Reconstruction You’ve chosen your ONE climate variable to reconstruct based on these analyses. Use ordinary least squares regression techniques, which says: Tree growth is a function of climate, but we want to reconstruct climate. Instead, we state climate is a function of tree growth. x-values are the predictor variable = tree-ring chronology y-values are the predictand variable = climate variable ^ y = ax + b + eis the form of the regression line 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 and the equation used for reconstruction.

13. In SAS: proc reg; model jult = std; where “jult” = July temperature being reconstructed, and “std” = the tree-ring (standard) chronology 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. Do this for the full length of the tree-ring record for each year. predict = (9.59154*std) + 32.96236; 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 Water Year Rainfall, New Mexico

16. Reconstructed Nov-Apr average temp, Tasmania

17. Reconstructed Blue River Annual Streamflow, Colorado

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