Appendix A. Meteorological calculations and data sets.
In order to derive estimates of mean temperature (Ta), vapour pressure deficit (VPD) and incoming solar radiation (RAD) we implement well tested models from the literature. Ta was derived through the relationship provided in Thornton et al. (1997):
Ta = 0.606Tmax + 0.394Tmin
We derive VPD through a locally calibrated version of Murray’s formula (Murray 1967):
Where es is the saturation vapor pressure, em is the ambient vapour pressure, and A, B, and C are empirical constants.
RAD was determined using the Allen model (Allen 1997), which relates the atmospheric transmissivity to daily temperature range and site elevation (through atmospheric pressure):
Where RA is the Angot (extraterrestrial) radiation in MJ m-2 day-1, P is the atmospheric pressure at the site in kPa, and P0 is the sea level atmospheric pressure (~101.3 kPa). Kr is an empirical constant, which takes values ~0.17 for inland regions, and values of ~0.20 for costal regions.
We modeled the autocorrelation structure of the Tmin, Tmax and P observations at the meteorological stations (Tables A1 and A2) by calculating their empirical semivariograms. The semivariogram γ quantifies the dissimilarity between pairs of observations separated by increasing spatiotemporal lag distances:
Where hu and ht are the separation lags in space and time respectively, z(u,t) is the observed variable at a given spatio-temporal coordinate, N(hu, ht ) is the number of pairs in the lag.
We selected and fit permissible semivariance models (Christakos 1984, McBratney and Webster 1986, Gringarten and Deutsch 2001) to summarize the empirical semivariograms. The semivariogram models include a ‘nugget’ effect or discontinuity at the origin to reflect instrument error and variations below the resolution of the sampling unit. The spatial and temporal semivariogram models were then combined using the product-sum covariance model of De Cesare et al. (De Cesare et al. 2001, De Iaco et al. 2001).
Simulation proceeded as follows:
As in all geostatistical techniques, it is possible to incorporate covariates into the simulations: We specified a linear lapse relationship between elevation and temperature, and a longitudinal gradient in precipitation, the parameters of which were estimated as part of the simulation process, via the external drift method (Hudson and Wackernagel 1994, Wackernagel 1998).
To simulate an ensemble of meteorological regimes we first calculated semivariograms for Tmin, Tmax and P. We modeled the spatial variation of Tmin and Tmax with a nested spherical (φu.sph Tmin = 23.8 km, φu.sph Tmax = 9.67 km), exponential model (φu.exp Tmin = 154.2 km, φu.exp Tmax = 196.6 km). For P, a Gaussian model (φu.gaus P = 34.7 km) with a small nugget effect (τu P = 0.2 mm) best captured the patterns of small-scale spatial variation. All three variables displayed exponential semivariance structures in time, with ranges of ~1 week for Tmin and Tmax, and a shorter temporal range of 2 days for precipitation, indicating lower temporal continuity in the time series. The sill parameters fitted for each variable were sillu = 6.4, sillt = 11.69 and sillg = 12.8 for Tmin; sillu = 10, sillt = 23.1 and sillg = 32.46 for Tmax ; and sillu = 20.0, sillt = 38.44 and sillg = 49.3 for precipitation (Fig. A1).
The indicator semivariogram for Pi in space consisted of a nested spherical (φu.sph Pi = 21.3 km), exponential model (φu.exp Pi = 190.9 km), with a nugget effect (τu Pi = 0.06). Temporal autocorrelation was accounted for with an exponential semivariogram (φt.exp Pi = 4 days) with a nugget effect (τt Pi = 0.06). The sill parameters were sillu = 0.17, sillt = 0.18 , sillg = 0.23.
The large-scale temporal trends (Fig. A1) operated on temporal separations greater than one month. This temporal separation was smaller than the implemented search strategy of ± 10 days, and was therefore irrelevant for the generation of simulations.
TABLE A1. Locations and data summary for surrounding meteorological stations.
|Tmin oC||Tmax oC||Precip. mm‡|
|Marion Forks Hatchery||583329||4939053||804||COOP||1948||35||2.0||(4.6)||15.1||(9.8)||4.3||(8.8)|
|Redmond FAA Airport||647656||4903155||935||COOP||1948||38||0.3||(6.2)||17.5||(9.7)||0.7||(2.2)|
|Metolius Intermediate Tower||614792||4923138||1253||AMERIFLUX||2001||2||4.1||(7.1)||12.4||(8.9)||0.5||(1.9)|
Mean meteorological observations. Standard deviations indicated in parentheses.
* Coordinates in meters UTM zone 10, WGS84 datum.
† Distance to Metolius Young Ponderosa pine site (km)
‡ Daily mean precipitation (mm); insufficient data at some sites for reliable annual averages.
TABLE A2. Data series completeness for meteorological stations.
|N Obs.||% Series||N Obs.||% Series||N Obs.||% Series|
|Marion Forks Hatchery||1821||99.7||1827||100.0||884||48.4|
|Redmond FAA Airport||1162||98.0||1186||100.0||987||83.2|
|Metolius Intermediate Tower||346||100.0||346||100.0||346||100.0|
N Obs. is the number of observations
% Series is the completeness of observations
Tmax is daily maximum temperature, Tmin is daily minimum temperature
FIG. A1. Semivariograms of meteorological data from the Central Cascades study area. Data were de-trended prior to analysis. Spatial semivariograms (γhu = 0) were constructed by considering pairs of observations from the same day at increasing spatial separations. Temporal semivariograms (γht = 0) were constructed from pairs of observations from the same station at increasing temporal separation, and plotted on a log axis for clarity. For all plots, detrended observations are shown as black crosses and semivariogram models are indicated as broken black lines. Grey points on the temporal plots are raw data prior to detrending.
Allen, R., 1997. Self-calibrating method for estimating solar radiation from air temperature. Journal of Hydrological Engineering 2:56–67.
Christakos, G. 1984. On the problem of permissible covariance and variogram models. Water Resources Research 20:251–265.
De Cesare, L., D. E. Myers, and D. Posa. 2001. Estimating and modeling space-time correlation structures. Statistics & Probability Letters 51:9–14.
De Iaco, S., D. E. Myers, and D. Posa. 2001. Space-time analysis using a general product-sum model. Statistics & Probability Letters 52:21–28.
Gringarten, E., and C. V. Deutsch. 2001. Variogram interpretation and modeling. Mathematical Geology 33:507–534.
Hudson, G., and H. Wackernagel. 1994. Mapping temperature using kriging with external drift - theory and an example from Scotland. International Journal of Climatology 14:77–91.
Murray, F. W. 1967. On the computation of saturation vapor pressure. Journal of Applied Meteorology 6:203–204.
McBratney, A. B., and R. Webster. 1986. Choosing functions for semi-variograms of soil properties and fitting them to sampling estimates. Journal of Soil Science 37:617–639.
Thornton, P. E., S. W. Running, and M. A. White. 1997. Generating surfaces of daily meteorological variables over large regions of complex terrain. Journal of Hydrology 190:214–251.
Wackernagel, H. 1998. Multivariate Geostatistics: An Introduction with Applications. Springer, Berlin, Germany.