A Climate-Based Model to Predict Potential Treeline Position around the Globe. Paulsen, J. & Körner, C. Alpine Botany, 124(1):1–12, 2014.
doi  abstract   bibtex   
In situ temperature measurements revealed that the position of the high-elevation treeline is associated with a minimum seasonal mean air temperature within a temperature-defined minimum season length across latitudes. Here, we build upon this experience and present the results of a global statistical analysis and a predictive model for low temperature treeline positions. We identified 376 natural treelines from satellite images across the globe, and searched for their closest climatic proxies using a climate database. The analysis included a snow and a water balance submodel to account for season length constraints by snow pack and drought. We arrive at thermal treeline criteria almost identical to those that emerged from the earlier in situ measurements: tree growth requires a minimum length of the growing season of 94 days. The model yields best fit when the season is defined as all days with a daily mean temperature $>$0.9 °C, and a mean of 6.4 °C across all these days. The resultant treeline model 'TREELIM' offers a robust estimation of potential treeline elevation based on climate data only. Error terms include imprecise treeline position in satellite images and climate approximations in mountainous terrain. The algorithm permits constraining low temperature limits of forest growth worldwide (including polar treelines) and also permits a bioclimatic stratification of mountain biota, for instance, for biodiversity assessments. As a side product, the model yields the global potentially forested area. The results support the isotherm theory for natural treeline formation. This completely independent statistical assessment of the climatic drivers of the global treeline phenomenon confirmed the results of a multi-year measurement campaign. [Excerpt: Basic model assumptions and definition of climatic treeline proxies] From our earlier works with data loggers (Körner and Paulsen 2004), it emerged that only three independent parameters are necessary to model treeline elevation by standardized meteorological data: (a) a threshold temperature DTMIN that constrains the growing season; (b) a minimum mean temperature for all days of the growing season SMT as defined in (a); (c) a minimum length of the growing season LGS. The definition of the growing season is a central issue, because temperatures outside the growing season have no predictive value (Körner 2012). The model, thus, needs to select periods suitable for tree growth, which means, warm enough conditions with sufficient soil moisture and no snow cover. [\n] Defining the beginning and end of the growing season by a critical air temperature only (as in Körner and Paulsen 2004) turned out to be problematic at a global scale because this procedure does not account for irregular seasonal temperatures at equatorial latitudes, and it does not account for snow pack and drought. Therefore, the TREELIM model presented here uses a LGS representing the sum of days with a daily mean temperature above a defined threshold temperature (DTMIN). The mean temperature of the growing season (SMT) for any site is then calculated by averaging the daily means for all these days. Days during which snow is present or during which soil water is not available do not count for season length [...] [\n] [...] [::Snowpack] The snow module of TREELIM accounts for the assumption that trees do not exert significant growth as long as there is late-laying snow on the ground. Snow pack may thus constrain the length of the growing period, despite warm air temperatures. It was assumed that all precipitation that falls at daily mean temperatures $\leq$0 °C fall as snow, and snow was assumed to stay and accumulate on the ground as long as daily mean temperatures remained $<$0 °C. If a snow layer is present, snow is assumed to melt whenever daily mean temperatures are $>$0 °C at a rate of 0.84 kg m-2 day-1 for each degree $>$0 °C (the WATFLOOD model; http://www.civil.uwaterloo.ca/watflood/). Sublimation was ignored. [\n] Whenever rain falls on an existing snow layer, this water cools to 0 °C and the thermal energy (4.186 kJ kg-1 K-1) is used to melt snow (333.5 kJ kg-1 snow). Thus, 1 mm of rain melts 1/80 kg m-2 snow per degree air temperature above 0 °C. The quantity of snow pack (in kg m-2) was calculated by a simple input-output model with a daily resolution: snow layer at day (i) = snow layer at day (i - 1) + snowfall at day (i) - snow melt at day (i). [\n] [...] [::Site water balance] [...] The water balance equation was solved by a submodel of TREELIM that accounts for precipitation (liquid and solid), evapotranspiration, and the resulting soil water content. Since climate databases offer only monthly precipitation, we had to approximate actual rainfall regimes, assuming that air temperature determines saturated vapour content of the air. We then adopted a temperature-related stepwise interpolation of mean daily rainfall from annual data with a monthly resolution. This given amount of precipitation water was allocated by plausibility to precipitation events in the following way: The mean per day event was assumed to be 5 mm if the monthly mean T was $<$5 °C, 10 mm for 5-10 °C, 15 mm for 10-15 °C, 20 mm for $>$15 °C. For instance, if the monthly mean temperature is 7.3 °C and the monthly precipitation is 27.4 mm, precipitation events are assumed to be 10 mm each, one on day 7, one on day 14, and the remaining 7.4 mm are assumed to fall on day 21. [\n] This procedure is more realistic than for instance splitting monthly precipitation into 30 events. Since soil moisture is buffering moisture availability, the actual fragmentation of monthly precipitation is not very critical, except for conditions where drought is critical, which is rare at alpine treeline elevations. Errors introduced by this procedure are certainly small compared to the uncertainty of actual precipitation at treeline, based on climatic layers derived from low elevation climate stations. [::Daily Potential evapotranspiration] (DPET) was estimated using the Hargreaves equation (Hargreaves and Samani 1985) in the FAO-56 form as adopted by Allen et al. (1998), again with a daily resolution. [...] [::The water balance] for a given day was then calculated with a two-layer bucket model for a given soil water holding capacity as defined by the International Geosphere-Biosphere Programme (IGBP 2000). [...] [\n] [...]
@article{paulsenClimatebasedModelPredict2014,
  title = {A Climate-Based Model to Predict Potential Treeline Position around the Globe},
  author = {Paulsen, Jens and K{\"o}rner, Christian},
  year = {2014},
  volume = {124},
  pages = {1--12},
  issn = {1664-221X},
  doi = {10.1007/s00035-014-0124-0},
  abstract = {In situ temperature measurements revealed that the position of the high-elevation treeline is associated with a minimum seasonal mean air temperature within a temperature-defined minimum season length across latitudes. Here, we build upon this experience and present the results of a global statistical analysis and a predictive model for low temperature treeline positions. We identified 376 natural treelines from satellite images across the globe, and searched for their closest climatic proxies using a climate database. The analysis included a snow and a water balance submodel to account for season length constraints by snow pack and drought. We arrive at thermal treeline criteria almost identical to those that emerged from the earlier in situ measurements: tree growth requires a minimum length of the growing season of 94 days. The model yields best fit when the season is defined as all days with a daily mean temperature {$>$}0.9 \textdegree C, and a mean of 6.4 \textdegree C across all these days. The resultant treeline model 'TREELIM' offers a robust estimation of potential treeline elevation based on climate data only. Error terms include imprecise treeline position in satellite images and climate approximations in mountainous terrain. The algorithm permits constraining low temperature limits of forest growth worldwide (including polar treelines) and also permits a bioclimatic stratification of mountain biota, for instance, for biodiversity assessments. As a side product, the model yields the global potentially forested area. The results support the isotherm theory for natural treeline formation. This completely independent statistical assessment of the climatic drivers of the global treeline phenomenon confirmed the results of a multi-year measurement campaign.

[Excerpt: Basic model assumptions and definition of climatic treeline proxies]

From our earlier works with data loggers (K\"orner and Paulsen 2004), it emerged that only three independent parameters are necessary to model treeline elevation by standardized meteorological data: (a) a threshold temperature DTMIN that constrains the growing season; (b) a minimum mean temperature for all days of the growing season SMT as defined in (a); (c) a minimum length of the growing season LGS. The definition of the growing season is a central issue, because temperatures outside the growing season have no predictive value (K\"orner 2012). The model, thus, needs to select periods suitable for tree growth, which means, warm enough conditions with sufficient soil moisture and no snow cover.

[\textbackslash n] Defining the beginning and end of the growing season by a critical air temperature only (as in K\"orner and Paulsen 2004) turned out to be problematic at a global scale because this procedure does not account for irregular seasonal temperatures at equatorial latitudes, and it does not account for snow pack and drought. Therefore, the TREELIM model presented here uses a LGS representing the sum of days with a daily mean temperature above a defined threshold temperature (DTMIN). The mean temperature of the growing season (SMT) for any site is then calculated by averaging the daily means for all these days. Days during which snow is present or during which soil water is not available do not count for season length [...]

[\textbackslash n] [...]

[::Snowpack] The snow module of TREELIM accounts for the assumption that trees do not exert significant growth as long as there is late-laying snow on the ground. Snow pack may thus constrain the length of the growing period, despite warm air temperatures. It was assumed that all precipitation that falls at daily mean temperatures {$\leq$}0 \textdegree C fall as snow, and snow was assumed to stay and accumulate on the ground as long as daily mean temperatures remained {$<$}0 \textdegree C. If a snow layer is present, snow is assumed to melt whenever daily mean temperatures are {$>$}0 \textdegree C at a rate of 0.84 kg m-2 day-1 for each degree {$>$}0 \textdegree C (the WATFLOOD model; http://www.civil.uwaterloo.ca/watflood/). Sublimation was ignored.

[\textbackslash n] Whenever rain falls on an existing snow layer, this water cools to 0 \textdegree C and the thermal energy (4.186 kJ kg-1 K-1) is used to melt snow (333.5 kJ kg-1 snow). Thus, 1 mm of rain melts 1/80 kg m-2 snow per degree air temperature above 0 \textdegree C. The quantity of snow pack (in kg m-2) was calculated by a simple input-output model with a daily resolution: snow layer at day (i) = snow layer at day (i - 1) + snowfall at day (i) - snow melt at day (i).

[\textbackslash n] [...]

[::Site water balance] [...] The water balance equation was solved by a submodel of TREELIM that accounts for precipitation (liquid and solid), evapotranspiration, and the resulting soil water content. Since climate databases offer only monthly precipitation, we had to approximate actual rainfall regimes, assuming that air temperature determines saturated vapour content of the air. We then adopted a temperature-related stepwise interpolation of mean daily rainfall from annual data with a monthly resolution. This given amount of precipitation water was allocated by plausibility to precipitation events in the following way: The mean per day event was assumed to be 5 mm if the monthly mean T was {$<$}5 \textdegree C, 10 mm for 5-10 \textdegree C, 15 mm for 10-15 \textdegree C, 20 mm for {$>$}15 \textdegree C. For instance, if the monthly mean temperature is 7.3 \textdegree C and the monthly precipitation is 27.4 mm, precipitation events are assumed to be 10 mm each, one on day 7, one on day 14, and the remaining 7.4 mm are assumed to fall on day 21.

[\textbackslash n] This procedure is more realistic than for instance splitting monthly precipitation into 30 events. Since soil moisture is buffering moisture availability, the actual fragmentation of monthly precipitation is not very critical, except for conditions where drought is critical, which is rare at alpine treeline elevations. Errors introduced by this procedure are certainly small compared to the uncertainty of actual precipitation at treeline, based on climatic layers derived from low elevation climate stations.

[::Daily Potential evapotranspiration] (DPET) was estimated using the Hargreaves equation (Hargreaves and Samani 1985) in the FAO-56 form as adopted by Allen et al. (1998), again with a daily resolution. [...]

[::The water balance] for a given day was then calculated with a two-layer bucket model for a given soil water holding capacity as defined by the International Geosphere-Biosphere Programme (IGBP 2000). [...]

[\textbackslash n] [...]},
  journal = {Alpine Botany},
  keywords = {*imported-from-citeulike-INRMM,~INRMM-MiD:c-14127697,bioclimatic-predictors,climate,ecological-zones,environmental-modelling,forest-resources,global-scale,landscape-dynamics,precipitation,snow,temperature,tree-line},
  lccn = {INRMM-MiD:c-14127697},
  number = {1}
}
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