Spatially-explicit modelling of biophysical parameters for the Shoshone National Forest, WY

Niklaus E. Zimmermann & David W. Roberts
Dept. of Forest Resources and Ecology Center
Utah State University, Logan, UT 84322-5215





High resolution climate maps were generated for NW-Wyoming in order to measure tree species realized niches. The goal of this study is to define species parameters for a spatially-explicit, dynamic forest simulation model.

First, high resolution maps of monthly normals for average temperature and precipitation were generated, based on a downscaling of coarse resolution (PRISM-) precipitation maps and of spatially interpolating temperature variables from climate stations. The coarse resolution maps were downscaled using least square regressions between elevation and climate parameters in a moving window of variable size. Consequently the resolution was refined from ~4.5km to 90m cell-size. Inverse distance weighted smoothing techniques were applied to spatially interpolate regression intercepts between temperature and elevation in order to adjust for local deviations from the regional adiabatic lapse rate.

Second, direct and indirect solar radiation was calculated on the basis of a 90m DEM (Digital Elevation Model). Hourly intervals per day and 10 day intervals over the year were used to calculate monthly mean values of irradiation.

Next, monthly potential evapotranspiration, and annual heat sum (daydegrees) were calculated, and finally, a map of available site water was generated, integrating the balance of precipitation and potential evapotranspiration over a topographically and geologically defined soil bucket size. Calculations were adjusted to local water year.

The maps of site water balance and heat sum were then sampled using a forest inventory database of 3500 plots to define tree species realized niches for the study area, and to define the necessary parameters for the forest dynamics model.



Biogeographers and ecologist have long recognized the relationship between plant distribution and climate (Humboldt,1807, Humboldt & Bonpland,1805, de Candolle, 1855, see Woodward, 1987 for an over-view). Schimper, (1898) was the first to rigorously relate the influence of climate on plant distribution to physiological processes. Temperature in particular was recognized for having a strong influence on plant distribution, primarily through frost frequencies and heat sum. Larcher, (1982) and Woodward, (1987) discuss the influence of low temperatures on physiological adaptations and natural selection.

Box 1: Limiting effects of temperature  
In general, many biogeographers and ecophysiologists believe that species are limited at their upper elevational or poleward latitudinal limits by climatic effects on reproduction and establishment (Woodward, 1992). The limiting  effect of high temperature on the distribution and dynamics of forests is less clear, however. High temperatures do not seem to be directly physiologically limiting in most ecosystems (Larcher, 1980, Woodward, 1987).  Trees have been long noted to grow south of their latitudinal limits in the northern hemisphere (Loehle & LeBlanc, 1996), and physiological (Bonan & Sirois, 1992), dendrochonological (Cook & Cole, 1990), and tree growth (Larsen, 1965) data all show that maximum relative growth rates often occur at a species southern range limit.  Lower elevational or lower latitudinal limits appear to have other causes than climate.

Aim of the study

A series of climate maps was generated in order to test the relationships between individual tree species and important bioclimatic parameters that:

The LAASIM model is sensitive to both available site water and minimum heat sum (total of day-degrees). Therefore two maps were developed that aim at synthesizing this information. A series of climate maps had to be derived to prepare this synthesis.

Box 2: Large scale climate mapping   
Significant success in simulating large-scale high-resolution climate maps has become possible recently due to (1) the increased computational power of workstations, (2) the better availability of climate data, (3) the development of spatial statistics and their integration into GIS software, and (4) the availability of large scale high resolution digital elevation models (DEM). This combination resulted in the first statistically derived climate maps for large areas about 10 years ago (Hutchinson & Bischof, 1983, Running et al., 1987). Although presently there is a variety of statistical and methodological approaches in use, generally they all use elevation as a major variable to explain climate parameters along spatial gradients (Daly et al., 1994; Hutchinson, 1995, Lennon & Turner, 1995, Running et al., 1989). Three models are widely distributed: ANUSPLIN, developed by M.F. Hutchinson, MT-CLIM-3D (Running & Thornton, 1993, Thornton et al., 1997), and PRISM (Daly et al., 1994).  Although these models employ different techniques to develop gridded climate surfaces from published climate station data and digital elevation models (DEMs), they exhibit very similar results, with slightly higher mean absolute errors for ANUSPLIN and with the highest differences among methods in high elevations, late fall and winter (Wilson et al., 1996).

Study area and data sources

All maps were generated on a 90m grid, based on the spatial resolution of the DEM we used to translate climate information into geographical space for the study area of NW-Wyoming (Fig.1). We used three sources of climate information:


Fig. 1: Study Area in NW-Wyoming. The site is part of the Greater Yellowstone Ecosystem. Click on map to view a larger version.

Box 3: Data error analysis   
NCDC stations data were assumed to be error-checked. The SnoTel stations data however were analyzed for 9 different types of errors that have been addressed during the evaluation period; erroneous records were eliminated before further analysis. Monthly mean values were derived from corrected data for precipitation sum (80 stations), and minimum and maximum temperature (59 stations) for the study area. Mean monthly average temperature was derived by simply averaging minimum and maximum temperature values. The monthly mean values were calculated for the period of 1961 to 1990 (1979 to 1990 for SnoTel sites).



Downscaling PRISM precipitation maps

The PRISM climate modelling program (Daly et al., 1994) employs a unique hybrid approach of statistical modelling with meteorological first principles to produce maps of climatic parameters on monthly time steps. However, the PRISM maps have insufficient spatial resolution for modeling purposes.

Accordingly, a procedure was developed (Fig. 2) for downscaling the coarse resolution maps (Fig. 3) to a grid size of 90 meters by regression between the PRISM climate maps and elevation in a moving window. A variety of moving-window sizes was tested for best fit of the generated high resolution maps by jackknifing the data from the climate stations. Precipitation maps were best fit at a window size of 13 x 13 PRISM cells. This results in two new maps of locally derived regression parameters (intercept & lapse rate). These maps allow to generate high-resolution precipitation maps by reprojecting the values to actual elevation using the fine-scale DEM and the maps of the regression parameters.

Fig. 2: Procedures for downscaling coarse resolution climate maps. Click on map to view a larger version.

Fig. 3: PRISM - average temperature map for July. The resolution is ~4.5km. Click on map to view a larger version.

Generating temperature maps

Least squares regressions of climate station monthly temperatures on elevation were calculated. The regression slopes (temperature lapse rates) showed balanced residuals and slopes in agreement with known seasonal trends. Accordingly, the resulting monthly lapse rates were assumed to be sufficiently accurate.

The regression intercepts, however, showed regional variability, and were adjusted to reflect spatial autocorrelation by spatially interpolating the regression residuals to adjust the intercepts (see Fig. 4). Tests for interpolating the relatively few and unequally scattered residuals from station locations included kriging, thin plate splines and inverse distance weighted interpolations.

The last approach resulted in lowest prediction errors and was used to generate temperature maps (Fig. 5), based on regionally adjusted regression parameters and the 90 meter DEM.

Fig. 4: Procedures for generating high resolution temperature maps. Click on map to view a larger version.

Fig. 5: Downscaled high resolution map for average temperature (July).Click on map to view a larger version.

Box 4: Error assessment of temperature and precipitation maps   
Jackknifed mean absolute errors for the downscaled monthly mean precipitation maps range from 0.44mm (August) to 0.82mm (May), with an overall mean of 0.58mm. For the generated temperature maps the mean monthly errors range from 1.9°F (May) to 2.4°F (February), with an overall mean of 2.1°F. Downscaled PRISM-temperature maps showed slightly higher error rates than the selected approach.


Solar Radiation

Direct insolation was calculated using the SOLARFLUX model (Dubayah & Rich, 1995; Rich et al., 1995) and the 90m DEM (Fig. 6). Diffuse solar radiation was derived from a procedure described in Kumar et al., (1997). Both modeling approaches were based on:

to calculate mean monthly values of radiation (kj · m-2 · day-1). Monthly values were derived by interpolating the 10-day interval data over time using the Simpson's 3/8-rule (four-point integration) and Bode's rule (five-point integration).

Fig. 6: Direct solar radiation on the winter solstice for the Grand Tetons National Park, WY. Black color designates areas in the shadow of high mountains without direct irradiation for this date. Click on map to view a larger version.


Potential Evapotranspiration

Potential evapotranspiration was calculated for the study area (Fig. 7) using the empirical equation of Jensen & Haise (1963), which was derived from data of the arid western United States. This method is based on monthly mean values for daily solar radiation and temperature:

(1)            ETp = Rs / 2450 · (0.025 Ta + 0.08)

where: ETp = mean daily potential evapotranspiration (mm · day-1), Rs = daily total solar radiation (kjoules · m-2 · day-1), Ta = mean daily air temperature (°C).

Comparative calculations based on the Solar Thermal Unit method (Caprio, 1974) and the Turc method (Turc, 1963), both based on the same independent parameters, revealed very similar results. The empirical formula of Jensen & Haise was selected because it was especially designed for the arid Western States, and revealed the most likely values.

Fig. 7: Map of the potential evapotranspiration based on the empirical equation of Jensen-Haise (1963). Click on map to view a larger version.


Topographic Position, Soil Properties, and Bucket Size

Topographic position, necessary to classify soil properties over large areas, was calculated using a hierarchically nested approach. Using circular moving-windows with a radius ranging from 180m up to 6120m in the 90m DEM, the difference between mean elevation in the window and the elevation of the center cell of the window was calculated. The resulting maps were interpreted as relative exposure at different spatial scales. A hierarchical integration into a single map was achieved starting with the standardized exposure values of the largest window, adding standardized values from smaller windows where these smaller scale values exceed values of the larger scale map.

Fig. 8: Map of the hierarchically nested topographic position. Click on map to view a larger version.

The resulting map was classified into 4 principal topographic classes (Fig.8):

These topographic characteristics were used (R.F. Fisher, unpubl.; Roberts et al., 1993), together with an ecological classification of the surface geology, to define:

The following equation was used to calculate the soil bucket size thereof:

(2)             Bucket Size = D · SSMC · (1 - (CFC / 100))

where: D = soil depth (meter), SSMC = specific soil moisture holding capacity (mm · m-1) and CFC = coarse fragment content (%). SSMC represents the difference between field capacity and permanent wilting point of specific soil textures, reflecting differences in pore volume and pore diameter distributions by texture.


Site Water Balance

Bucket size, potential evapotranspiration and precipitation were combined to calculate the spatially-explicit site water balance (Fig. 9) similar to the approach first employed by Grier & Running (1977). Beginning with the first month in fall when precipitation exceeds potential evapotranspiration (after a possible drought period), the difference between precipitation and potential evapotranspiration is summed for 12 months. The running sum is never allowed to exceed the bucket size, and water in excess of the bucket size is presumed to run off.

Fig. 9: Map of the site water balance. Click on map to view a larger version.

When potential evapotranspiration begins to exceed precipitation the difference is subtracted from water in the bucket, often achieving significant negative values over the course of a year. Site water balance is an estimate of the water available to plants during the a year, and integrates both climatic and soil parameters. The method differs from Grier & Running (1977) in the determination of the appropriate water year, and in not assuming that soils begin the water year with full recharge.



Day-degree totals are calculated by multiplying the number of days for which the mean temperature exceeds an arbitrary standard of 0°C by the mean temperature over this period. While different threshold values have been used by various authors, we used a 0°C-threshold in accordance with Woodward (1992). The minimum number of day-degrees necessary to complete vegetative and reproductive life cycles differs among tree species and is an expression of the minimum heat sum required to grow, mature and compete with other trees (Woodward, 1992).


Number of Frost-free Days

A map of the number of Frost-free days was derived using the same procedure as was used to calculate Day-degree totals. However, instead of adding up heat values above freezing levels, the simple number of days exceeding 0°C were accumulated pixel by pixel. The values for daily temperatures were derived from linear interpolation of monthly mean temperature values.


Average Temperature of the Coldest Month

The study area is situated at the crossroads of three major climatic influences, namely the maritime weather of the Pacific Northwest, the weather systems of the Great Basin (Intermountain West), and of the Great Plains east of the Rocky Mountains. This results in a highly variable pattern of the temperature course during a year. We have derived a map of the average temperature of the coldest month as a synthesis of local temperature constraints on plant growth. These pattern show significant deviations from monthly temperature maps.


Results & Discussion


The database of the Shoshone Ecosystem Project containing information on the abundance and distribution of both individual species and habitat types was dropped through these bioclimatic maps. In different projects a series of hypotheses were tested concerning the driving forces that govern the distribution and dynamics of plant species (Wendel, in prep.; Roberts et al., in prep.). These analyses revealed the importance of heat sum, cold temperatures, evapotranspiration and site water balance to predict the distribution of individual species.

Consequently, we used the climate variables to define the tree species realized niches using the environmental envelope approach (Holdridge, 1967; Box, 1982; Busby, 1986; Walker & Cocks, 1991; Carpenter et al., 1993; Shao & Halpin, 1995). Two-dimensional rectilinear environmental envelopes for tree species of the Shoshone Nat. Forest were derived from heat sum and site water balance.

Additionally, the environmental envelope technique is used to define tree species parameters for the spatially-explicit forest succession model LAASIM (see Roberts et al., 1993 for a preliminary version).

Generally, we found that the more the derived variables were dependent of slope, aspect, and topographic position, the less significant they correlated with species patterns. The two most likely reasons for this are:

We thus selected only those points for the analyses where field observed and digital topographic situation didn't exceed threshold values. 



Bonan, G.B. & Sirois, L. 1992. Air temperature, tree growth, and the northern and southern range limits to Picea mariana. J. Veg. Sci. 3(4): 495-506.

Box, E.O. 1981. Macroclimate and Plant Forms: An Introduction to Predictive Modelling in Phytogeography. Junk, The Hague, NL.

Busby, J.R. 1986. A biogeographical analysis of Nothofagus cunninghamii (Hook.) Oerst. In southeastern Australia. Australian Journal of Ecology 11: 1-7.

Candolle, A.I., de 1855. Géographique Botanique Raisonnée. Masson, Paris.

Caprio, J.M. 1974. The solar thermal unit concept in problems related to plant development and potential evapotranspiration . In Lieth, H. (ed.). Phenology and Seasonality Modeling. Springer, New York, pp. 353-364.

Carpenter, G., Gillison, A.N. & Winter, J. 1993. DOMAIN: a flexible modelling procedure for mapping potential distributions of plants and animals. Biodiversity and Conservation 2: 667-680..

Cook, E.R. & Cole, J. 1990. On predicting the response of forests in eastern North America to future climate change. Climatic Change 19: 271-282.

Daly, C., Neilson, R.P. & Phillips, D.L. 1994. A Statistical-Topographic Model for Mapping Climatological Precipitation over Mountainous Terrain. J. Appl. Meteorol. 33: 140-158.

Dubayah, R. & Rich, P.M. 1995. Topographic solar radiation models for GIS. Int. J. Geographical Information Systems , 9: 405-419.

Grier, C.C. & Running, S.W. 1977. Leaf area of mature north-western coniferous forests: relations to site water balance. Ecology 58: 893-899.

Holdridge, L.R. 1967. Life Zone Ecology , Tropical Science Center, San José, Costa Rica.

Humboldt, A. von 1807. Ideen zu einer Geographie der Pflanzen nebst einem Naturgemaelde der Tropenlaender. Tuebingen.

Humboldt, A. von & Bonpland, A. 1805. Essai sur la Géographie des Plantes; Accompagne d'un Tableau Physique des Régions Equinoxiales. Paris.

Hutchinson, M.F. 1995. Interpolating mean rainfall using thin plate smoothing splines. Int. J. Geographical Information Systems 9: 385-403.

Hutchinson, M.F. & Bischof, R.J. 1983. A new method for estimating the spatial distribution of mean seasonal and annual rainfall applied to Hunter Valley, New South Wales. Aust. Meteorol. Mag. 31: 179-184.

Jensen, M.E. & Haise, H.R. 1963. Estimating evapotranspiration from solar radiation. J. Irrig. Drainage Div. ASCE 89: 15-41.

Kumar, L., Skidmore, A.K. & Knowles, E. 1997. Modelling topographic variation in solar radiation in a GIS environment. Int. J. Geographic Information Science 11: 475-497.

Larcher, W. 1980. Physiological Plant Ecology . 2nd. Edn., Springer, Berlin.

Larcher, W. 1982. Typology of freezing phenomena among vascular plants and evolutionary trends in frost acclimation . In Li P.H. and Sakai A. (eds.). Plant Cold Hardiness and Freezing Stress: Mechanisms and Crop Implications, Vol.2. Academic Press, New York, pp. 417-426.

Larsen, J.A. 1965. The vegetation of the Ennadai Lake area, N.W.T.: studies in subarctic and arctic bioclimatology. Ecol. Monogr. 35: 37-59.

Lennon, J.J. & Turner, J.R.G. 1995. Predicting the spatial distribution of climate: Temperature in Great Britain. J. Anim. Ecol. 64: 370-392.

Loehle, C. & LeBlanc, D. 1996. Model-based assessments of climate change effects on forests: a critical review. Ecol. Modell . 90: 1-31.

Prentice, I.C., Cramer, W., Harrison, S.P., Leemans, R., Monserud, R.A. & Solomon A.M. 1992. A global biome model based on plant physiology and dominance, soil properties and climate. J. Biogeogr. 19: 117-134.

Rich, P.M., Hetrick, W.A. & Savings, S.C. 1995. Modelling topographic influences on solar radiation: manual for the SOLARFLUX model. Los Alamos National Laboratory Report: LA-12989-M.

Roberts, D.W., Fisher, R.F., Long, J.M. & Jack, S.N. 1993. The Leaf Area Allocation Model: Simulation of Rocky Mountain Forest Dynamics and Climate Change. Final Report for EPA Cooperative Agreement #817539.

Running, S.W., Nemani, R.R. & Hungerford, R.D. 1987. Extrapolation of synoptic meteorological data in mountainous terrain and its use for simulating forest evapotranspiration and photosynthesis. Can. J. For. Res. 17: 472-483.

Running, S.W., Nemani, R.R., Peterson, D.L., Band, L.E., Potts, D.F., Pierce, L.L. & Spanner, M.A. 1989. Mapping regional forest evapotranspiration and photosynthesis by coupling satellite data with ecosystem simulation. Ecology 70: 1090-1101.

Running, S.W. & Thornton, P.E. 1993. Generating Daily Surfaces of Temperature and Precipitation over Complex Terrain . In Goodchild, M.F., Parks, B.O. and Steyaert, L.T. (eds.). Environmental Modelling with GIS. Oxford University Press, New York, pp. 93-98.

Schimper, A.F.W. 1898. Pflanzengeographie auf physiologischer Grundlage. Jena.

Shao, G. & Halpin, P.N. 1995. Climatic controls of eastern North American coastal tree and shrub distributions. Journal of Biogeography 22: 1083-1089.

Thornton, P.E., Running, S.W. & White, M.A. 1997. Generating surfaces of daily meteorological variables over large regions of complex terrain. J. Hydrol. 190: 214-251.

Turc, L. 1961. Evaluation des besoin en eau d'irrigation, évapotranspiration potentielle, formule simplifié et mise an jour. Ann. Agron. 12: 13-49.

Walker, P.A. & Cocks, K.D. 1991. HABITAT: a procedure for modeling a disjoint environmental envelope for a plant or animal species. Global Ecology & Biogeography Letter 1: 108-118.

Wilson, J.P., Stillman S.T., Daly, C., Hutchinson, M.F. & Thornton, P.E. 1996. Comparison of ANUSPLIN, MTCLIM-3D and PRISM precipitation estimates. In Proceedings, Third International Conference/Workshop on Integrating GIS and Environmental Modeling, Santa Fe, NM, January 21-26, 1996. Santa Barbara, CA: National Center for Geographic Information and Analysis. CD.

Woodward, F.I. 1987. Climate and plant distribution . Cambridge Studies in Ecology, Cambridge University Press, Cambridge.

Woodward, F.I. 1992. A review of the effects of climate on vegetation: ranges, competition, and composition. In Peters, R.L. and Lovejoy, T.E. (eds.). Global Warming and Biological Diversity. Yale University Press, New Haven, CT, pp. 105-123.

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Last Updated on 10/22/00
By Niklaus E. Zimmermann