Dendroclimatic AnalysesDendroclimatic Analyses

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

Response function analysis:

Response Function AnalysisResponse Function Analysis

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

Reconstructed Bemidji Feb-May Mean Monthly Max Temp

Climate Reconstruction

Reconstructed Water Year Rainfall, New Mexico

Reconstructed Nov-Apr average temp, Tasmania

Reconstructed Blue River Annual Streamflow, Colorado

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