dendroclimatic analyses. you now have the climate variables. what’s the next step? statistical...
TRANSCRIPT
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?)
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
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.
Correlation analysis
Graphical output from PRECON. Any value above +0.2 or below -0.2 is significant.
Positive!
Negative!
Note how response function analysis (top) and correlation analysis (bottom) are complementary (but different).
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?
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
Stepwise multiple regression analysis
• Another complementary technique
Why do the two series diverge here?
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 + e is 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.
• 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