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Appendix A. Meteorological calculations and data sets.

In order to derive estimates of mean temperature (T_a), vapour pressure deficit (VPD) and incoming solar radiation (RAD) we implement well tested models from the literature. T_a was derived through the relationship provided in Thornton et al. (1997):

T_a = 0.606T_max + 0.394T_min

We derive VPD through a locally calibrated version of Murray’s formula (Murray 1967):

Where e_s is the saturation vapor pressure, e_m 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 R_A 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). K_r 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 T_min, T_max 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 h_u and h_t are the separation lags in space and time respectively, z(u,t) is the observed variable at a given spatio-temporal coordinate, N(h_u, h_t ) 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:

1. Initialize a random visiting schedule for the grid of G locations, with a data heap of n observations.
2. Visit the i^th node of the grid and estimate the mean and variance via Kriging conditioned on the values in the data heap.
3. Draw a random value from the Gaussian distribution of the node, defined by the Kriging estimate (mean) and Kriging variance. The resultant value was the SGS estimate ^*_i
4. The realization ^*_i was then treated as an observation for subsequent estimates, and added to the data heap (n + i conditioning data).
5. Iterate from 2 until all grid locations were visited (i = G).

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 T_min, T_max and P. We modeled the spatial variation of T_min and T_max with a nested spherical (φ_u._sph T_min = 23.8 km, φ_u.sph T_max = 9.67 km), exponential model (φ_u.exp T_min = 154.2 km, φ_u.exp T_max  = 196.6 km). For P, a Gaussian model (φ_u.gaus P = 34.7 km) with a small nugget effect (τ_u 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 T_min and T_max, 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 sill_u = 6.4, sill_t = 11.69 and sill_g = 12.8 for T_min; sill_u = 10, sill_t = 23.1 and sill_g = 32.46 for T_max ; and sill_u = 20.0, sill_t = 38.44 and sill_g = 49.3 for precipitation (Fig. A1).

The indicator semivariogram for P_i in space consisted of a nested spherical (φ_u._sph P_i = 21.3 km), exponential model (φ_u._exp P_i = 190.9 km), with a nugget effect (τ_u P_i = 0.06). Temporal autocorrelation was accounted for with an exponential semivariogram (φ_t._exp P_i = 4 days) with a nugget effect (τ_t P_i = 0.06). The sill parameters were sill_u = 0.17, sill_t = 0.18 , sill_g = 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.

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. is the number of observations
% Series is the completeness of observations
T_max is daily maximum temperature, T_min 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 (γ_{hu = 0}) were constructed by considering pairs of observations from the same day at increasing spatial separations. Temporal semivariograms (γ_{ht = 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.

LITERATURE CITED

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.

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Wackernagel, H. 1998. Multivariate Geostatistics: An Introduction with Applications. Springer, Berlin, Germany.