1
Article title: Climate change mitigation policies reduce the rate and magnitude
2
of ecosystem impacts
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Short running title: Climate change mitigation and global ecosystem impacts
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Author names: Andrew J. Hartley12, Richard J. J. Gilham1, Carlo Buontempo1 and
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Richard A. Betts12
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Author research addresses:
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1
Met Office Hadley Centre, FitzRoy Road, Exeter, EX1 3PB, UK
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2
Department of Geography, University of Exeter, The Queen's Drive, Exeter,
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Devon, EX4 4QJ, UK
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Correspondence author address and e-mail:
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Met Office Hadley Centre, FitzRoy Road, Exeter, EX1 3PB, UK
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andrew.hartley@metoffice.gov.uk
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Article type: Research Paper
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1
1
ABSTRACT
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Aim
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To show the impacts of climate change mitigation on the rate and magnitude of
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change in the climate that influences large-scale ecosystems.
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Location
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Results are calculated for all terrestrial land areas free of ice, and summarized
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for 35 places of high conservation priority. We focus on 6 areas of high
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conservation priority: Altai-Sayan Montane Forests, Orinoco River and Flooded
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Forests, Chihuahuan Deserts, Congo Basin, Southwest Australia, and Coastal
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West Africa.
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Methods
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We use a simple metric of change based on statistical distance within the
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Holdridge Life Zone classification space (Hdistance) to quantify ecosystem-
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relevant change in climate between a baseline average climate (1961-1990) and
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each year in a 150 year time series (1950-2099). We apply this metric to a 58
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member ensemble of GCM projections, for a business as usual scenario and an
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aggressive climate change mitigation scenario. The rate and magnitude of change
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in the Hdistance is calculated for each ensemble member.
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Results
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We find that more than 50% of high conservation priority areas show divergence
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in the rate and magnitude of change in the Hdistance metric when comparing a
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business as usual emissions scenario (A1B) with an aggressive carbon dioxide
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mitigation scenario (RCP2.6). In other high priority areas we find that potentially
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important thresholds are exceeded even with small changes in the Hdistance
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under scenario A1B.
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1
Main conclusions
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We conclude that potentially dangerous impacts to high priority ecosystems can
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be avoided in many parts of the world by a global policy of aggressive climate
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change mitigation. Even though in some cases, the long term magnitude of
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change threshold is exceeded under RCP2.6, this generally occurs later in the
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century, allowing more time for ecosystems to adapt.
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8
KEYWORDS
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Climate change; mitigation; conservation planning; ecosystem impacts; potential
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ecosystems; Holdridge Life Zones; Perturbed Parameter Ensemble; WWF
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Priority Places; Biodiversity
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3
1
INTRODUCTION
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Conservation planners need to know what challenges lie ahead for global
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ecosystems and biodiversity if different courses of action are taken by the
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world’s governments in response to anthropogenic climate change. This presents
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challenges to climate scientists to ensure that policy relevant climate modeling
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experiments are conducted and communicated effectively to users in the
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conservation community. Likewise, in order for conservation science to progress
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from the bioclimatic envelope approach, new methods need to be developed to
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incorporate higher temporal resolutions of climate data into models of species’
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population dynamics (Huntley et al., 2010; Keith et al., 2008; Anderson et al.,
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2009).
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To date, the majority of biodiversity impacts studies have chosen to use
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temporally aggregated and spatially disaggregated changes derived from General
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Circulation Models (GCMs; e.g. Tabor & Williams, 2010) under a variety of future
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socio-economic scenarios (N. Nakicenovic et al., 2000). In doing so, potentially
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important information on inter-annual or intra-seasonal variability has been
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disregarded in biodiversity projections. Additionally, the spatial disaggregation
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of GCM data creates greater uncertainty in conservation policies at ecoregion
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and local scales (Wiens & Bachelet, 2010). As models for predicting the impact
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of climate change on global biodiversity begin to consider interactions
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between population dynamics and species’ ranges (Anderson et al., 2009),
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conservation scientists must develop more robust methods to integrate
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projections from large ensembles of GCMs that have been designed to
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address specific climate change policy questions. Huntley et al. (2010)
4
1
propose that the next generation of integrated model should include climatic
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and habitat suitability, population dynamics and dispersal ability. They
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present this in the context of the range of species responses to the magnitude
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and rate of change. They also argue that there is a role to play for models of
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intermediate
6
information on species’ population responses to change.
complexity,
especially
given
the
shortage
of
suitable
7
8
In this paper we report the outcome of using a relatively simple metric for
9
ecosystem change with an ensemble of GCM projections to assess the possible
10
rate and magnitude of ecosystem change. We compare the results obtained from
11
using both a 'business as usual' and an aggressive mitigation future scenario
12
with the aim of demonstrating the possible effect of policy decisions on
13
ecosystems. In addition, we aim to show projected changes in the context of
14
thresholds in the rate and magnitude of change. This is investigated using a
15
large ensemble of GCMs to explore uncertainties due to the parameterization
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of the Hadley Centre model HadCM3C. The rate and magnitude of ecosystem
17
change is quantified using a new measure, defined as the distance of change
18
within the Holdridge Life Zone conceptual space.
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5
1
METHODS
2
A new measure of ecosystem change
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The Holdridge Life Zone system (Holdridge, 1967) was one of the first
4
classifications to relate climatic variables to large-scale ecosystems. It has the
5
advantage of being relatively simple to implement whilst allowing the objective
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relation of temperature and precipitation variables to either potential biomes,
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altitudinal zones or potential vegetation types (the combination of which was
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termed “Life Zones” by Holdridge). An important caveat in this approach is
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acknowledged in the term 'potential'. Climate is only one of many factors that
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contribute towards determining the existence of a particular vegetation type at a
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given time and location. Other factors that may influence vegetation type, such as
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CO2 effects, ozone, nutrient availability and soil condition are not accounted for
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by the Holdridge system. Nevertheless, we argue that the general approach is
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still relevant, as many existing studies use temperature and precipitation
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variables to quantify the impacts of climate change on species or ecosystems
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(Velarde et al., 2005; Lugo et al., 1999; Good et al., 2011).
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Rather than classifying particular grid cells into discrete Life Zones, we use the
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axes of Mean Annual Biotemperature and Annual Precipitation as a means of
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defining a statistical space that is relevant to ecosystems (see Appendix S1 in
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Supporting Information for calculations). Within this statistical space, we
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calculate the distance of change between a baseline climate and a future climate
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(see Appendix S2). Since these axes are not orthogonal, a trigonometric
24
transformation is used to obtain the distance of separation between the baseline
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and a given point in time (see Appendix S3).
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1
2
This distance metric (Hdistance) can be thought of as a vector of movement
3
between two points within the Holdridge diagram (see Appendix S2). It provides
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an objective measure of change between two time periods that allows
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comparison of changes between different ecosystems in different climatic zones.
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The use of Hdistance provides a continuous metric for evaluating the GCM
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output. This represents an advantage over measuring discrete transitions from
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one vegetation class to another. This will help to compare the ecosystem impacts
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in different parts of the world, for example, whether the projected large warming
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of the Russian tundra is a more or less disruptive ecosystem perturbation than
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the wetting of the eastern Sahara.
12
13
Climate change projections
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In this study we apply the Hdistance measure to a large ensemble of climate
15
change projections based on the HadCM3C General Circulation Model (GCM;
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Booth et al., 2012). This is an atmosphere-ocean-carbon cycle coupled
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configuration of the original HadCM3 model (Gordon et al., 2000). It is
18
configured to include additionally the main elements of the carbon cycle, via
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dynamic vegetation and ocean exchange, as well as an interactive sulfur cycle
20
scheme to account for emissions-based air pollution. The model includes flux
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adjustments to account for biases in the model sea surface temperatures and
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salinity compared to historical observations, as described in Collins et al. (2010).
23
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In order to capture uncertainties related to configuration of the GCM, a 58
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member perturbed parameter ensemble was created. Each member of this
7
1
ensemble was configured with a set of parameters designed to explore the range
2
of uncertainty in the atmosphere, ocean, land carbon cycle and sulfur cycle. A
3
framework for such an approach can be found in Murphy et al. (2007), and this
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Earth System Ensemble (ESE) is described in full by Lambert et al. (2012). Each
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ensemble member was run using historical climate forcing from 1950 to 2000,
6
and two different scenarios between 2000 and 2099 (discussed below). While
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the ensemble has a large number of members, the experiment was not designed
8
to provide probabilities of particular outcomes. It should be interpreted as a
9
means of exploring the range of credible outcomes from a GCM by sampling from
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a large range of uncertainty.
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12
We assessed the impacts of a climate change mitigation strategy by using two
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distinct future greenhouse gas emissions scenarios. Firstly, the IPCC Special
14
Report on Emissions Scenarios (SRES) A1B scenario (N. Nakicenovic et al., 2000)
15
was used to represent a ‘business as usual’ scenario in which the world
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continues to be more integrated with a balanced emphasis on all energy sources.
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Secondly, the Representative Concentration Pathway 2.6 (RCP 2.6, also referred
18
to as RCP 3PD) was used to simulate a scenario of aggressive greenhouse gas
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mitigation policy (Moss et al., 2010; see Fig. 1). Each scenario was used to force
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the 58 member ESE, with the resulting difference used to show the effect an
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aggressive mitigation policy may have on global ecosystems. It should be noted
22
that while each ensemble member is forced by two different emissions scenarios,
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the total radiative forcing depends on the perturbed parameters for the
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interactive carbon and sulfur cycles in each ensemble member. Additionally,
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since the emissions from RCP2.6 effectively remain constant from approximately
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1
2020 and then reduce after 2050 (see Fig. 1), the ecosystem changes from
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RCP2.6 show the changes that we have already committed to as a result of the
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delayed response of the Earth system to historic greenhouse gas emissions.
4
5
6
Distance of change
7
For each ensemble member and emissions scenario, the Hdistance was
8
calculated (see Appendix S3). Mean annual biotemperature and mean annual
9
precipitation were calculated for a period of 1961 to 1990 (beginning in January
10
1961 ending in December 1990), and used to calculate the Hdistance between
11
this baseline period and each individual year in the 150 year time series (from
12
1950 to 2099). By calculating Hdistance over the historical period, we obtain a
13
measure of how much we would expect Hdistance to vary under normal climatic
14
conditions. If we make the reasonable assumption that ecosystems are in
15
equilibrium with the current climate, we may regard the Hdistance over the
16
observed period as an indication of the natural variability of this measure. In
17
other words, this is the degree to which we would expect the climate to vary
18
year-to-year without inducing an ecosystem change.
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20
Rate and magnitude of change
21
We calculated the mean Hdistance for each decade in the 150 year time series,
22
relative to the 1961-1990 baseline, to give the decadal magnitude of change. The
23
rate of change is calculated for each year (t0) by subtracting the mean annual
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Hdistance for the previous 10 years (t-11 to t0) from the mean annual Hdistance
25
for the next 10 years (t0 to t11). This annual rate of change was then averaged for
9
1
each decade to give the mean decadal rate of change in the Hdistance. The time
2
series of magnitude of change in the Hdistance is presented according to a
3
selection of WWF Priority Places. These are areas selected as a focus for
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conservation activity by WWF, based on a combination of their diversity and
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abundance of life, threats they face and WWF’s ability to make a positive impact
6
within the next decade (see Fig. 2).
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1
RESULTS
2
3
We present here results for the following 6 WWF Priority Places: Altai-Sayan
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Montane Forests, Orinoco River and Flooded Forests, Chihuahuan Deserts and
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Freshwater, Congo Basin, Southwest Australia and West Africa Marine
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(Terrestrial part). These regions (see Fig. 2) were selected as examples of the
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variety of change in the rate and magnitude of Hdistance. A summary of the
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changes found in all Priority Places can be found in Table 1. This summarises
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whether or not divergence was found between the two scenarios, and whether
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or not the A1B crossed a threshold of rate or magnitude.
11
12
We plotted the time series of change in the ensemble mean of Hdistance for each
13
Priority Place and both emissions scenarios (Fig. 3), with the shaded area
14
showing 1 standard deviation around the mean for each scenario. Additionally,
15
based on the information in Fig. 3, we plot for each decade, the mean rate of
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change in the Hdistance against the total magnitude of change relative to the
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1961-90 baseline (Fig. 4). Error bars show 1 standard deviation around the
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decadal mean rate and magnitude of change in Hdistance. This figure also shows
19
the changes in relation to potentially important thresholds. These thresholds
20
represent the baseline variability in the Hdistance and can be interpreted as the
21
upper limits to variability in Hdistance between 1961-1990. The thresholds for
22
both magnitude and rate of change in Hdistance are based on all ensemble
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members and scenarios for the 1961-1990 period compared to the 1961-1990
24
mean climate. For a given ensemble member and scenario, the Hdistance
25
between each year and the 1961-1990 mean climate was calculated, with the
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1
threshold magnitude being the mean magnitude of change plus 1 standard
2
deviation. For rate of change, the upper threshold was set at 1 standard
3
deviation greater than the mean.
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1
DISCUSSION
2
3
All WWF Priority Places show a steady increase in the Hdistance over time,
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irrespective of greenhouse gas emissions scenario (Fig. 3). However, a clear
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divergence emerges between the A1B scenario and RCP2.6 scenarios from
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approximately 2050 in most Priority Places. Fig. 4 shows that this divergence is
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more pronounced in the Altai-Sayan Montane Forests and Orinoco River Priority
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Places (the full list of places where this occurs can be found in table 1). It is
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notable that in the Altai-Sayan, the threshold for the rate of change is
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considerably lower (0.025) than in the Orinoco River Priority Place (0.044). This
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has a consequence of the mean rate of change exceeding the threshold between
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the 1990s and 2030s in Altai-Sayan under RCP2.6. In contrast, the mean rate of
13
change under RCP 2.6 does not exceed the threshold in Orinoco River. It is also
14
notable that while the rate and magnitude thresholds are exceeded in the
15
ensemble mean for A1B, the uncertainty, shown by horizontal and vertical bars
16
around each decade, is much greater in Orinoco River Priority Place.
17
18
The Chihuahuan Desert, Congo Basin and Southwest Australia Priority Places are
19
examples of places where there is little or no divergence between A1B and
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RCP2.6. While there is some divergence between the ensemble mean, the range
21
of uncertainty from the GCM ensemble overlaps considerably. However, these
22
locations also show the importance of the threshold value. For all 3 places, the
23
rate and magnitude thresholds are not exceeded under RCP2.6, because either
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the inter-decadal change is minimal (Congo Basin), or because the thresholds are
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relatively high (Chihuahuan Desert and Southwest Australia). In contrast, the
13
1
low threshold for the Congo Basin is exceeded under A1B, albeit due to a modest
2
increase in rate and magnitude. We also observe that despite high thresholds in
3
the terrestrial part of the West Africa Marine Priority Place, the magnitude of
4
change under A1B still exceeds the threshold of rate and magnitude.
5
6
A main advantage of this approach is the ability to compare changes across very
7
different ecosystems. We propose that the Hdistance is used as a measure for
8
setting global scale conservation priorities for adaptation to climate change. In
9
comparison to results from assessments of velocity of climate change
10
(Dobrowski et al., 2012; Loarie et al., 2009), the Hdistance is a continuous
11
measure of the magnitude and rate of change at a certain location. Also, in
12
contrast to the majority of biodiversity impacts assessments that rely on the
13
identification of suitable habitats (e.g. Thomas et al., 2004; G.F. Midgley et al.,
14
2002), this approach is compatible with the coarser resolution of GCMs without
15
relying on uncertain downscaling techniques (Wiens & Bachelet, 2010; Trivedi et
16
al., 2008). Furthermore, in comparing A1B to RCP2.6, we provide conservation
17
planners and policy makers with information on the impacts of aggressive
18
climate change mitigation policies. Using the examples that we present, it is clear
19
that ecosystem impacts are not globally uniform, and in many cases can be
20
avoided if carbon dioxide emissions peak in approximately 2020 and decline
21
thereafter.
22
23
Despite these advantages, we acknowledge that the magnitude and rate of
24
change in the Hdistance is not influenced by the resilience of ecosystems, or the
25
ability of ecosystems to adapt to climate change in situ. Therefore, we
14
1
recommend that this information be used in conjunction with species or
2
ecosystem vulnerability assessments (such as Foden et al., 2008; Wilson et al.,
3
2005; Summers et al., 2012).
4
15
1
CONCLUSIONS
2
We have presented a new annual measure of ecosystem change, Hdistance, that
3
can be used as a basis for comparing the impact of climate change on large scale
4
ecosystems across different conservation regions of the world. We calculated the
5
inter-annual variability in the rate and magnitude of change in this measure, and
6
set thresholds based on the variability during the baseline period. Using these
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thresholds, we found that an aggressive climate mitigation policy substantially
8
reduces the risk of exceeding potentially dangerous rates of change in the
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climate affecting large scale ecosytems.
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1
AKNOWLEDGEMENTS
2
We acknowledge funding from WWF and from the Joint Department of Energy
3
and Climate Change (DECC) and the Department for Environment, Food and
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Rural Affairs (Defra) Met Office Hadley Centre Climate Programme.
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1
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1
BIOSKETCH
2
Andrew Hartley is a climate impacts scientist with a particular focus on the
3
interaction between the land surface and the climate system. His current
4
research interests lie in the novel application of climate science to advise
5
conservation planners and further improvement of earth system models.
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1
TABLES WITH THEIR CAPTIONS
Scenario Divergence
No Scenario Divergence
Altai-Sayan (T)
African Rift Lakes
Amazon Guianas (T)
Atlantic Forests
Amur-Heilong (T)
Borneo
Chihuahuan Desert (T)
Cerrado-Pantanal (T)
Choco-Darien (T)
Coastal East Africa
Eastern Himalayas (T)
Congo Basin (T)
Fynbos (T)
Cora Triangle
Greater Black Sea Basin
Miombo Woodlands (T)
Lake Baikal
New Guinea
Mediterranean (T)
Southwestern Australia (T)
Mekong Complex (T)
Sumatra
Namib-Karoo (T)
Western Ghats
Northern Great Plains (T)
Orinoco (T)
South Chile (T)
Yangtze
2
Table 1. WWF Priority Places in which divergence did or did not occur between
3
scenarios. Divergence indicates locations at which a climate change mitigation
4
scenario is projected to reduce the rate and magnitude of ecosystem change
5
relative to the A1B scenario. Locations marked with (T) indicate places where
6
the A1B scenario crosses either the rate or magnitude threshold by the 2090s.
7
24
1
FIGURE LEGENDS
2
Figure 1. Carbon dioxide emissions, expressed as gigatonnes of carbon per year,
3
for SRES scenario A1B and RCP2.6.
4
5
Figure 2. Location of all WWF Priority Places, and the subset selected for this
6
study shown in Mollweide equal area map projection.
7
8
Figure 3. Time series of change in the Hdistance relative to the 1961-1990
9
baeline period. The solid lines show the ensemble mean, and semi-transparent
10
zone shows 1 standard deviation around the ensemble mean. Values are
11
smoothed using a 10-year moving average.
12
13
Figure 4. Decadal changes in rate and magnitude of change in Hdistance under
14
RCP2.6 and A1B, relative to the 1961-1990 baseline period. Black doted lines
15
denote inter-annual variability (1 standard deviation) in the rate and magnitude
16
of change during the baseline period (1961-1990) for each Priority Place.
17
25
1
FIGURES
-1
CO2 emissions æèGtC y öø
15
10
Scenario
A1B
RCP2.6
5
0
1850
4
1900
1950
2000
Year
2
3
Figure 1.
5
26
2050
2100
27
Southwest Pacific
Choco-Darien
Amazon Guianas
Southern Chile
Southern Ocean
Southern Ocean
Atlantic
Forests
Atlantic
Forests
Orinoco River and
Flooded Forests
Southeastern Rivers
and Streams
Fynbos
Namib-KarooKaokoveld
African Rift
Lakes Region
Miombo
Woodlands
Congo Basin
West Africa Marine
Mediterranean
Coastal East Africa Southwest Australia
Madagascar
African Rift Lakes Region
Sumatra
Borneo
Mekong Complex
Yangtze Basin
Amur-Heilong
Western Ghats
Eastern Himalayas
Greater Black Sea Basin
Lake Baikal
New Guinea and
Offshore Islands
Southern Ocean
Southwest Pacific
Coral Triangle
2
Cerrado-Pantanal
Galapagos
Chihuahuan Deserts
and Freshwater
Northern Great Plains
Altai-Sayan
Montane Forests
Arctic Seas and Associated Boreal/Tundra
WWF Priority Places
1
Figure 2.
Hdistance
28
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
1975
2000
2025
Southwest Australia
2050
2075
2100
Years
1975
2000
2025
West Africa Marine
Congo Basin
2050
Orinoco River and Flooded Forests
Hdistance for WWF Priority Places
Chihuahuan Deserts and Freshwater
Altai−Sayan Montane Forests
2075
2100
RCP2.6
A1B
Scenario
1
Figure 3.
WWF Priority Places
Altai−Sayan Montane Forests
0.9
Orinoco River and Flooded Forests
0.8
0.7
0.6
●
●
2080
2080
●
●
2070
2070
●
0.5
2060
●
●
2060
2050
0.4
●
●
●
●
●
2070
2050 2040
2080
2060
0.2
●●
● ● ●●
2040
●
●
1980
1980
1960
1960
11970
970
●
●
●
0.1
2050
●
2080
2060 ●
●
2050
2040● ●
●
2030
2030
●
2020
● 2020
● 2010 ●
●
●
2010
●
●
● ● ● 2000
●
●
2000
1990
1980
1980
1990
1960
1960
1970
1970
2070
2030
2030
●
●
2020
●
2020
●
2010
●
● 2010
2000
2000
●
●
1990
1990
0.3
●
2040
0.0
Chihuahuan Deserts and Freshwater
0.9
Congo Basin
0.8
0.7
Magnitude
0.6
0.5
Scenario
●
2080
2070
●
2060
●
2050
●
a
A1B
●
0.4
●
●● ●
●
●
●
a
RCP2.6
●
2040
2050
20602070
2080
●
●2040
● 2030
●●
2030
2020
●2020
2010
2010
● ●
2000
● ● ●●
●2000
●1990
1990
19601980
1960
1970
1970 1980
0.3
0.2
●
2080
●
●
● 2070
2060
●
20502040
●●●
●
●
●
2080
2070
2060
2050●● ● 2030
2040
2030
●2020
●2020
●
2010
●●●● ●●2010
20002000
1990
1980
1960
1990
1980
1960
1970
1970
0.1
0.0
Southwest Australia
0.9
West Africa Marine
0.8
●
2080
0.7
●
2070
●
0.6
2060
●
●
0.5
2070
●
2060
2050
●
2080
●
●
0.4
●
●
●
●
2040
●2070
●
2080
2050
●
●
2060
2030
2040 ● ●2030
2020
●
2020
●
●
● ●●2000
2010
●●
2010
●
●● 1990
2000
1990
1970
1960 1960
1980
1980
1970
0.3
●
●
●
●
2050
2080 2050
2070
2060
2040
●
2040●
●
●
2030
●
2030
●
2020
●
2020
●●
●
●
2010
2010
● ●
●●
2000
2000
1990
●
1990
1980
●
1970
1980
1960 1960
1970
●
0.2
0.1
0.0
−0.025
1
2
0.000
0.025
0.050
−0.025
0.075
Rate
Figure 4.
3
29
0.000
0.025
0.050
0.075
1
SUPPORTING INFORMATION
2
Additional Supporting Information may be found in the online version of this
3
article:
4
5
Appendix S1 Equations for calculation of Holdridge input variables
6
Appendix S2 The Holdridge Life Zone system
7
Appendix S3 Calculation of the Hdistance
8
9
As a service to our authors and readers, this journal provides supporting
10
information supplied by the authors. Such materials are peer-reviewed and may
11
be reorganized for online delivery, but are not copy-edited or typeset. Technical
12
support issues arising from supporting information (other than missing files)
13
should be addressed to the authors.
14
30
1
Supplementary Material
2
Appendix S1: Equations for calculation of Holdridge input variables
3
Biotemperature is calculated as the sum of all mean monthly temperatures that
4
are above freezing, divided by 12. The equation is as follows:
ti 30
Tbio 
t
ti  0
i
12
5
6
where ti = mean monthly temperature in degrees Celsius for a given 30 year
7
period.
8
9
10
Annual precipitation is calculated as the sum of total monthly precipitation. The
equation is as follows:
i 12
Pann   pi
i 1
11
12
where pi = total monthly precipitation in mm per month, averaged over a given
13
30 year period.
14
31
1
Appendix S2: The Holdridge Life Zone system
B
F
2
3
The axes used for calculating the Hdistance are shown in red (note they are not
4
orthogonal). The example shows a change from a mean baseline climate (B) to a
5
future climate (F) due to an increase in annual precipitation and mean annual
6
biotemperature. Note the log scale of both mean annual biotemperature and
7
annual precipitation. Source: Holdridge (1967)
8
32
1
Appendix S3: Calculation of the Hdistance
2
The first step in our procedure was to identify a suitable metric for calculating
3
distances between points B and F shown in Appendix S2. Given that the axis of
4
the two state variables (biotemperature and annual precipitation) are not
5
perpendicular to one another it was necessary to define an additional variable in
6
order to correctly calculate the Euclidian distance between two points in
7
Holdridge space:
8
9
10
11
d=
( b2 - b1 ) + ( r'2 - r'1 )
2
2
We used biotemperature (b) as a Y-axis and we designed the accessory variable
r' to be orthogonal to the Y-axis. This was defined by the relationship:
r' = r - btan(30°)
12
where 30° is the angle between the two axes in the original diagram and r is the
13
value of annual precipitation. Such a relationship can be obtain through
14
trigonometry, accounting for the fact that in the original Holdridge diagram, the
15
lines of constant annual precipitation do not cross the annual precipitation axis
16
at a 90° angle but rather at 120°.
17
The figure below shows the trigonometry used for calculating the distance (d)
18
between points B (baseline) and F (future).
33
r'
K
B
Bio
Temperature
R'
d
r
b
F
Annual
Precipitation
1
2
The Holdridge space is defined by the biotemperature and annual precipitation
3
axes. Since these axes are not orthogonal to one another, they cannot be used to
4
calculate the Euclidian distances within the Holdridge space. An additional
5
variable was therefore defined to overcome this problem (R'), which can be
6
constructed using the two existing axes. A mathematical relationship linking the
7
two can be identified once we consider that:
8
9
1) B-r' =BK- r'K
10
2) BKr is an equilateral triangle (all angles being 60°) from which it follows that
11
BK=Br
12
3) r'K/sin (30) =b*sin(60) with 60° being the angle in K and 30° the angle in F of
13
the triangle r'FK
14
34
1
Considering also that both axes are linear in their log form, the Euclidian
2
distances (d) in this space becomes:
3
d=
( log(b2 ) / log(b1 )) + ( log(r2 ) / log(r1 ) - log(b2 ) / log(b1 )tan(30))
2
4
35
2