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Tree-ring carbon isotope data and drought maps
for the U.S. Southwest


Calculation of Drought Indices
The long-term trend of each site was originally fitted with a spline with stiffness of 50 to each of the 14 chronologies (Fig. 1) and then isotopic indices (Leavitt and Long, 1989a) were calculated as the ratio of each measured δ13C to corresponding δ13C of the spline:

Isotopic Index = δ13C measured/δ13C spline

"Del Indices" (Leavitt and Long, 1989a) were then calculated as follows to provide larger numbers easier to compare with one another:

Del Index = (isotopic index - 1) x 1000

This Del Index can be interpreted such that moisture conditions near average (measured δ13C values near the spline values) have Del Index values close to zero, progressively more negative Del Index values (δ13C values above the corresponding spline values) indicate greater moisture stress, and progressively more Del Index positive values (δ13C below the spline) indicate greater moisture excess. Del Index values usually range between -50 to +50. Various tests of the 14-site isotopic data with Palmer Drought Indices and streamflow in various temporal and spatial modes suggested a significant relationship with Del Index (Leavitt and Long, 1989a). The spatial network was used to produce hand-contoured drought maps for the 1900-04 and 1950-54 (Fig. 3) pentads in Leavitt and Long (1989a), which appear very similar to drought maps based on instrumental-based measurements and reconstructions from tree-ring width measurements.

figure 2. Example of spline curve fitted to Kane Spring Pentad isotope chronology
Fig. 2. Example of spline curve (stiffness=50) fitted to the Kane Spring pentad isotope chronology (δ13C on y-axis) (Leavitt and Long, 1989a). The δ13C values above the spline are interpreted as above-average moisture stress, and those below the spline are above-average moisture excess. The Isotopic Indices, Del Indices and Drought Indices are calculated from the ratio of actual δ13C values to the corresponding spline values.

Figure 3.  Contour Map of Isotopic Del Indices for 1950-54
Fig. 3. Contour map of isotopic Del Indices (top) for 1950-54 around the Southwest based on carbon isotope composition of pinyon pine tree rings (contours here are guided by the Del Indices at each of the 14 sites, as opposed to the new data and maps available at this site produced by gridded interpolation). For comparison, the instrumentally measured Palmer Drought Indices (middle) and Palmer Drought Indices reconstructed from tree-ring widths (bottom) are shown (after Fig. 2 of Leavitt and Long, 1989a). In all maps, the more negative values indicate more severed drought, and vice versa for positive values.


Beginning in 1999 and continuing until November 2004, all 14 sites were revisited and re-sampled to bring the chronologies up to at least 1999 (Leavitt, in prep.). In this case, the 1970-74, 1975-79 and 1980-84 pentads were sampled and analyzed to compare with the original chronologies and adjust for offsets related to natural isotopic variability among trees, and then individual years were analyzed beginning in 1985 until the final year of growth. In this manner, not only was the isotope chronology extended, but the relationships at both annual and pentad scales could be examined, which had not been possible in the earlier studies.

A set of drought maps for all pentads and for single years was developed from the complete suite of tree-ring isotope results. Rather than using Del Index as originally used, however, the Del Indices were converted to Drought Indices (Appendix A) by:

Drought Index = Del Index/10

This produces pentad Drought Indices falling between about -5 to +5, similar in range to Palmer Drought Indices, although no linear correspondence has been established. Drought Indices were calculated from the original Del Indices from the 14 sites through 1980-84. New splines were fitted to the complete set of pentads through 1995-99, and Drought Indices were calculated for 1985-89, 1990-94 and 1995-99. Rather than a stiffness of 50, splines with either 4, 5 or 6 nodes were chosen depending on which produced values most closely matched to the original Del Indices. Because of edge effect differences between the original spline fit to the data ending in 1980-84 and the new spline curves fit to data ending in 1995-99, the Del Indices/Drought Indices for the 1980-84 pentad are from the new spline and not those originally determined in 1989.

Drought Indices were also calculated for individual years from 1985 to 1999 using straight-line standardization because the period was only 15 years in length, and fit well in all cases with a straight line. This brought the record up to 1999, and because of resampling dates, there were enough isotopic measurements from tree rings to also produce Drought Index maps for 2000 and 2001 (calculated relative to the 1985-99 straight-line regressions). A few values from 2000 and 2001 fell outside the more typical range of -5 to +5 for the Drought Indices calculated from the pentad data.

Furthermore, rather than contouring the values at the 14 sites, gridded interpolations (txt files of values) and contour maps (both lines and color fields) were generated for grid points using the statistical computation package R (version 2.3.1). The inverse distance weighting methodology being used is not the same as that of Cook et al. (1999), which produced continental U.S. gridded PDSI data from tree rings, but the Cook et al. methodology is a special case of this methodology (Appendix C).

For purposes of smooth contouring, maps were interpolated to 0.1° x 0.1° grids, but the text files contain interpolations at 1° x 1° grids points deemed sufficient to represent variability over the map field. The data and maps are available in Appendix B.


Sites Contributing to Each of the Maps
Because the tree-ring chronologies are of varying lengths, the number of sites contributing Drought Indices to the interpolation algorithm progressively decreases for maps of older pentads (as well as for the most recent years as a result of the resampling). The contributions are summarized in Table 1. Thus, for example, only 4 sites contributed to the map for the 1600-1604 pentad. The Kane Springs, Alton and Gate Canyon sites all extend earlier than 1600 (1490, 1520 and 1580, respectively) but maps earlier than 1600 were not created.

Table 1. Approximate site elevations and the beginning year contributing to the isotope drought maps.

SITE Elevation (m) Beginning Year Final Year
Kane Springs, UT 1965 1600 2001
Alton, UT 2245 1600 1999
Dry Canyon, CO 2150 1625 2000
Lower Colonias, NM 2375 1655 2001
Aztec, NM 2080 1710 2001
Cerro Colorado, NM 2500 1650 2001
Ozena, CA 1370 1750 2000
Hawthorne, NV 2330 1620 2001
Mimbres, NM 2025 1790 2001
Owl Canyon, CO 1860 1600 2001
NC AZ, AZ 1470 1725 2001
NE AZ, AZ 2090 1700 2000
Gate Canyon, UT 2220 1600 1999
Lamoille, NV 2130 1685 2000


Limitations
Mapping and data at grid points outside the field of 14 sites (i.e., toward the edges of the maps) should be interpreted very carefully and in many cases is not likely valid or rational, e.g., Drought Indices very far outside the more typical range of -5 to +5. The gridded interpolation also calculated standard error variance at each of the grid points (see Appendix C), so maps of those errors have also been generated and available in the list below.

Additionally, the color schemes used in the maps cover Isotope Drought Index Values between -5 and +5. As not colors outside this range have been assigned, when values are interpolated beyond this range, they plot as white fields in the maps. Thus the white fields do not indicate that there is no interpolated data in those grid points, but rather that the interpolated values are outside (sometimes far outside) the more typical range of -5 to +5 in the original site data.
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