Subalpine fir populations were sampled at 3 elevations on southwest-facing slopes on Klahhane Ridge, Blue Mountain, Mount Dana, and Dodger Point: the upper (treeline), middle, and lower extent of its elevation range. At least 25 trees were sampled from 20 m-wide band transects at each site. Only trees with dominant or codominant crown classification (Spurr and Barnes 1980) were sampled to reduce variation in growth trends related to competition. Trees with major stem or crown deformities were avoided.
Two cores were extracted with an increment borer at 1.1-1.4 m height on the cross-slope sides of each tree, Cores were mounted in wooden blocks and sanded until individual tracheids were visible. All cores were crossdated (visually -- Swetnam et al. 1985. and verified with COFECHA -- Holmes 1983), and one core from each tree (the core with the fewest instances of reaction wood) was measured to the nearest 0.01 mm with an incremental measuring machine (Robinson and Evans 1980). Measurements were verified by remeasuring a randomly-selected 21-year segment of each core, and cores were completely remeasured if the sum of the squared difference of these measurements was greater than .073 mm² (after Fritts 1976). The mean measurement error is approximately 2% of ring widths for all cores that were not rejected.
Washington State Division 4 climate data tan average of weather stations from the northeastern Olympic Peninsula and the west slope of the Cascade Mountains) for 1895-1990 were used in analyses (National Climatic Data Center Data, WeatherDisc Associates, Inc. 1990). While a comparison of divisional data and growth is one step removed from the local climate's direct effects on growth, divisional data were selected in favor of local weather station data because the nearest stations to the study sites (Port Angeles and Port Townsend) are near sea level and heavily influenced by maritime climate, including coastal fog, and are not representative of climate at the study sites at higher elevations. Divisional weather stations provide monthly summaries of precipitation and temperature that are often more reliable sources of climatic information than local weather stations, because the average of many climatic stations reduces the influence of anomalous and missing data points. In addition, divisional data have been shown to more closely correlate with tree-ring data than individual climate stations (Blasing et at. 1981).
Mean monthly temperature and total monthly precipitation were used in analyses. Analyses were based on a hydrologic year (October through September) to represent the period of influences of climate on tree growth. September is the latest possible time that subalpine fir accumulates stem wood at the lower elevation study sites (personal observation). Climate-growth correlations are described using this hydrologic year.
This study compares the average year-to-year growth response of the twelve sites to climate for the time period 1895-1990. In order to obtain twelve mean site chronologies, individual ring-width series were standardized so that trees of different age, size, and growth trend (growth suppression and/or release periods) could be averaged. Standardization with a cubic smoothing spline (20-year 50% frequency response) was used to eliminate tree specific growth trends that resulted from age and size differences, and competition effects of trees growing in closed canopy conditions (Cook and Peters 1981, Cook et al. 1990). Spline stiffness was selected by subjectively eyeballing spline fits of 5, 10, 20, 35, and 50 year 50% frequency responses until a stiffness was found that eliminated most trends in growth through time. For most cores, this required eliminating endogenous disturbance trends (i.e., competition related growth trends) that occurred over as little as a 10-year period and therefore a flexible spline was chosen. A spline of 20-year 50% frequency was used in standardization of all cores to accommodate cores with higher low frequency growth trends. Although the 20-year 50% frequency spline is flexible, it provides consistent standardization of cores to year-to-year (high frequency) variation by eliminating differences in low-frequency growth trends. The ring-width measurements of each core were divided by the fitted spline values to produce a standardized tree-ring series for each core with a mean of one and constant variance. These individual standardized series were then averaged together using a biweight robust mean (Cook 1985, Cook et al. 1990) to produce a mean standardized chronology for each site for the 1895-1990 time period for which climatic data are available.
The 20-year 50% frequency spline almost certainly-removes trends in growth that are related to trends in climate, but the competition among individuals sampled from closed canopy conditions requires removing longer-term trends in growth. Exploratory analyses of climate-growth relationships with mean site chronologies created with 5, 10, 20, 35, and 50-year 50% frequency splines showed little difference in results, however the 20-year frequency spline was selected because it is the stiffest spline that eliminates low-frequency growth trends.
Multivariate time-series modeling including autocorrelation and partial correlation coefficients, Yule-Walker estimates of pooled autoregression, and Akaike Information Criterion (from the program ARSTAN, Cook 1985), were used to evaluate autocorrelation in the 12 standardized site chronologies. Four of the 12 sites showed persistent autocorrelation after initial standardization, and individual cores from these sites were fit with univariate autoregressive modeling. Mean site chronologies were then created with a robust mean estimation of residual series for these 4 sites.
Divisional climatic data were also standardized using the 20-year 50% frequency response cubic smoothing spline to eliminate trends in climate data and allow comparisons of year-to-year variation in climate and growth. Climatic data were standardized to remove trends in climate that may have been shared in common with the growth trends that would have been eliminated in creating site chronologies. Therefore, this analysis focuses on comparing year-to-year variation in growth and climate because longer-term trends in growth and climate have been removed. Monthly temperature and precipitation, and winter precipitation (sum of December to March precipitation - i.e., snowfall) variables were divided by fitted spline values of each series to produce standardized climate series. The 12 mean growth chronologies were correlated with standardized climatic variables.
Descriptive statistics were calculated to compare growth among sites. Basal area increment was calculated for each core from ring-width measurements and estimates of the distance from the innermost ring to the pith. Basal area increments of all cores were then averaged with a simple arithmetic mean for the time period 1940- 1990 to calculate the mean basal increment for each site. Mean basal area increment allows for a comparison of growth rates at each site that is not possible solely with ring width measurements. Correlations among mean site chronologies were also calculated to determine similarities in year-to-year variability in growth among sites. A preliminary analysis of these correlations suggested that correlations are higher among environmentally similar sites, and principal component analysis (Jolliffe 1986) was used to determine the proportion of this variation that is common to all sites and to groups of sites with similar growth characteristics.
Mean sensitivity (Fritts 1976), a measure of year-to-year growth variation, and the standard deviation of standardized chronologies were calculated for each site. Two measures of the growth variation shared among cores on each site were also calculated. Pearson product-moment correlation coefficients were calculated among individual standardized tree chronologies growing on the same site. This mean "intrasite" correlation is a measure of the amount of year-to-year variation in growth that is shared among the trees growing on each site. The percentage of growth variation explained by the first principal component of the correlation matrix for a common time interval was also calculated using ARSTAN (Cook 1985) as an additional measure of the variance held in common among trees growing on each site (Graumlich 1993).
Climate-growth relationships were examined using Pearson product-moment correlation coefficients. The 12 site chronologies were correlated with monthly total precipitation and monthly mean temperatures for two hydrologic years ending in September of the current growing season for the period 1895-1990 (1895-1989 for Mount Dana). Climate-growth correlations were lagged two hydrologic years, because current year growth is partially attributable to year-to-year carbohydrate storage and changes in photosynthetic biomass (Fritts 1976). Monthly climate variables were initially used instead of seasonal climatic variables because the influence of climate on tree growth and other important physiological processes is difficult to predict prior to data collection (Cook and Cole 1991). A preliminary analysis indicated that precipitation for the months December through March were negatively correlated with growth on most sites. These months were summarized into a winter precipitation variable (2 hydrologic years) and correlated with growth. I recognize that the growth of each individual is determined by the specific climate conditions that the individual encounters. Divisional data is used as a substitute for site specific data, and results should be viewed with this fact in mind.
Although interpretation of the significance level of climate-growth correlations is difficult because of the large number of climatic variables and intercorrelation among variables, correlations exceeding r = ±.205 (á < .05, two-tailed test, df=90) are considered to be potentially important. Only correlations that show consistent patterns among similar study sites are considered to be meaningful, because spurious correlations are possible given the large number of comparisons (55 climatic variables and 12 tree growth indices). Scatterplots of significantly correlated climatic variables were examined for non-linearities and for the influence of extreme climatic variables on climate-growth relationships.
A correlation matrix of the climatic variables was examined for significant intercorrelations among variables and for potential spurious correlations with site chronologies. Fifty-five variables produced a matrix of 1485 ((55*54)/2) correlation coefficients. Using a r= .201 cutoff(á = .05, two-tailed test, df=94), 173 correlations were significant. These 173 significant correlations are more than twice the. 74 significant correlations expected if significant correlations were obtained at random (á = .05), indicating that climatic variables are intercorrelated. The highest correlations are between precipitation and temperature variables of the same month. Precipitation is negatively correlated with temperature for the months March-October, and positively correlated with December and January precipitation. Intercorrelation among the 55 climatic variables suggests that spurious correlations could make interpretations of the correlation analysis difficult. Partial correlation analysis was therefore used to evaluate potential spurious correlations by determining the correlation between each site chronology and climatic variable while holding the values of all other correlations constant (Zar 1984, Stahle et al. 1991). The initial Pearson product-moment correlation analysis determined 16 climatic variables that are significantly correlated with site chronologies. Partial correlation coefficients exceeding r = ±.226 (á < .05, two-tailed test, df=74) are considered potentially important when results are consistent across sites.
A secondary goal of this study is to compare the growth response of subalpine fir to temperature, with the parabolic growth function used in many JABOWA-based models. Subalpine fir growth during the growing season was summarized graphically, with growth response at all elevations plotted to represent the growth 20 response over a range of temperatures. Growing season temperature s positively correlated with growth in July for low and middle elevation sites, and August at high elevation sites, and plots were therefore created using these months at respective elevations. In order to create a growth response curve to growing season temperature across the elevation range of sample sites, monthly divisional data were adjusted for an environmental lapse rate of 5° C/1000m (after Henderson et al. 1989) at each elevation. Mean indexed growth was first plotted with all 3 sample elevations at each of the 4 mountains, and the 4 high, middle, and low elevation sites were subsequently averaged together because they showed a similar growth response. An overall growth response to growing season temperature was constructed by averaging these values at 0.5° C intervals (1° C intervals at temperature extremes in order to incorporate at least 5 values for each point) without regard to elevation.
The growth-climate relationships used in JABOWA-based models often describe species response to one limiting climate factor (frequently growing degree days - Botkin et al. 1972, Solomon and West 1987), and although relationships are often assumed to be parabolic, other relationships could be used in the models. My intention is not to evaluate JABOWA-based models or the parabolic growth curve per se, but rather to explore the potential limitations of using generalized growth functions to describe a species response to climate change.
There are limitations to creating a growth response curve from tree ring data First, the tree ring measurements used in this study represent growth responses to local climate, microsite conditions and competition, and the use of divisional climatic data as well as a lack of detailed information on microsite conditions and competition effects) provide growth information that differs from the actual conditions affecting growth on each sire. Second. the parabolic growth curve described by JABOWA- based models is based on actual unsmoothed growth data, in contrast to the year-to- year variation in (standardized) growth used in this study. While basal increment measurements may be more comparable to the empirical data used in JABOWA-based models, a preliminary comparison of individual basal area measurements showed that large differences in individual growth trend and rate (some trees grow up to 10 times faster than others on the same site) required standardization of individual cores prior to comparison. A growth response curve based on year-to-year growth variation is a good approximation of species growth response to summer temperature, and provides a starring point for examining the growth equations used to model species response to climate change.