Bioclimatic Predictors for Supporting Ecological

Applications in the Conterminous United States

Data Series 691

U.S. Department of the Interior

U.S. Geological Survey
Bioclimatic Predictors for
Supporting Ecological Applications
in the Conterminous United States

By Michael S. ODonnell and Drew A. Ignizio

Data Series 691

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior
KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2012

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Suggested citation:
ODonnell, M.S., and Ignizio, D.A., 2012, Bioclimatic predictors for supporting ecological applications in the conterminous
United States: U.S. Geological Survey Data Series 691, 10 p.
 iii

Contents
Abstract............................................................................................................................................................1
Background.....................................................................................................................................................1
Climatological Terms.............................................................................................................................2
Definition of Quarterly Indices.............................................................................................................2
Methodology....................................................................................................................................................2
Downscaled PRISM Data.....................................................................................................................2
Data That Accompanies This Report..................................................................................................3
Modifications to Original Bioclimatic Calculations..........................................................................3
Notation for Equations..........................................................................................................................4
Product Description for Bioclimatic Predictors........................................................................................4
Bio 1Annual Mean Temperature.....................................................................................................4
Bio 2Annual Mean Diurnal Range..................................................................................................4
Bio 3Isothermality.............................................................................................................................5
Bio 4Temperature Seasonality (Standard Deviation) .................................................................5
Bio 4aTemperature Seasonality (CV).............................................................................................5
Bio 5Max Temperature of Warmest Month..................................................................................6
Bio 6Min Temperature of Coldest Month......................................................................................6
Bio 7Annual Temperature Range....................................................................................................6
Bio 8Mean Temperature of Wettest Quarter................................................................................6
Bio 9Mean Temperature of Driest Quarter....................................................................................6
Bio 10Mean Temperature of Warmest Quarter............................................................................7
Bio 11Mean Temperature of Coldest Quarter...............................................................................7
Bio 12Annual Precipitation..............................................................................................................7
Bio 13Precipitation of Wettest Month............................................................................................8
Bio 14Precipitation of Driest Month...............................................................................................8
Bio 15Precipitation Seasonality (CV).............................................................................................8
Bio 16Precipitation of Wettest Quarter..........................................................................................8
Bio 17Precipitation of Driest Quarter.............................................................................................8
Bio 18Precipitation of Warmest Quarter.......................................................................................9
Bio 19Precipitation of Coldest Quarter .........................................................................................9
Summary..........................................................................................................................................................9
Acknowledgments........................................................................................................................................10
References.....................................................................................................................................................10

Tables
1. Climate data inputs used to derive the bioclimatic predictors for the conterminous
United States.........................................................................................................................................2
2. Data series file naming convention..................................................................................................2
3. Example of applying quarterly calculations to normals and time-series climate data..........4
iv

Conversion Factors
Inch/Pound to SI
Multiply By To obtain
Length
inch (in.) 25.4 millimeter (mm)
foot (ft) 0.3048 meter (m)

SI to Inch/Pound
Multiply By To obtain
Length
millimeter (mm) 0.03937 inch (in.)
meter (m) 3.281 foot (ft)
kilometer (km) 0.6214 mile (mi)
Temperature in degrees Celsius (C) may be converted to degrees Fahrenheit (F) as follows:
F = (1.8 C) + 32
Temperature in degrees Fahrenheit (F) may be converted to degrees Celsius (C) as follows:
C = (F 32)/1.8
Temperature in degrees Celsius (C) may be converted to degrees Kelvin (K) as follows:
K = C + 273.15
Temperature in degrees Fahrenheit (F) may be converted to degrees Kelvin (K) as follows:
K = (F + 459.67)/1.8
Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83)
and the World Geographic System of 1972 (WGS 72).
Bioclimatic Predictors for Supporting Ecological
Applications in the Conterminous United States

By Michael S. ODonnell1 and Drew A. Ignizio2

Abstract Bioclimatic predictors (as defined by Nix, 1986 and

Hijmans, 2004) were derived from two climate data sources
The U.S. Geological Survey (USGS) has developed (Climate Source, 2011; Oregon State University, 2011) to bet-
climate indices, referred to as bioclimatic predictors, which ter represent the types of seasonal trends pertinent to the phys-
highlight climate conditions best related to species physiol- iological constraints of different species. For example, wettest
ogy. A set of 20 bioclimatic predictors were developed as month and seasonal anomalies will generally capture broader
Geographic Information Systems (GIS) continuous raster biological trends better than the temperature or the amount
surfaces for each year between 1895 and 2009. The Parameter- of precipitation for a given day due to the inherent variability
elevation Regression on Independent Slopes Model (PRISM) associated with weather. Some of these variables are poten-
and down-scaled PRISM data, which included both averaged tially multicollinear (more prominent at local regions), and
multi-year and averaged monthly climate summaries, was used therefore, caution is advised when including multiple biocli-
to develop these multi-scale bioclimatic predictors. Bioclimatic matic predictors within species distribution models.
predictors capture information about annual conditions (annual The 20 bioclimatic predictors were derived using an
mean temperature, annual precipitation, annual range in tem- open source programming language, Python, which is based
perature and precipitation), as well as seasonal mean climate on the Environmental Systems Research Institutes (ESRI) Arc
conditions and intra-year seasonality (temperature of the coldest Macro Language (AML) program written by RobertHijmans
and warmest months, precipitation of the wettest and driest (2004). The input data are in the geographic coordinate sys-
quarters). Examining climate over time is useful when quantify- tem latitude/longitude and rely on two datums (table 1). To
ing the effects of climate changes on species distributions for minimize introducing errors while projecting these data from
past, current, and forecasted scenarios. These data, which have latitude/longitude to a map projection, which can introduce
not been readily available to scientists, can provide biologists errors resulting from the distortions associated with the
and ecologists with relevant and multi-scaled climate data selected map projections and data characteristics (for example,
to augment research on the responses of species to changing scale, heterogeneity), the bioclimatic variables remain in the
climate conditions. The relationships established between spe- climate datas native coordinate system. However, in most
cies demographics and distributions with bioclimatic predictors analysis scenarios, these data will need to be converted to a
can inform land managers of climatic effects on species during map projection.
decisionmaking processes. Due to the volume of data, the datas spatial extent (conter-
minous United States), the spatial resolution, and the temporal
resolution, we used High Throughput Computing (HTC) via
the Condor middleware (http://research.cs.wisc.edu/condor/)
Background to distribute the processing tasks. For example, each set of 20
bioclimatic predictors (20 products are derived for each year)
Species are affected by both climatic and non-climatic require the development of approximately 200 interim datasets
factors. Climatic change can impose physiological constraints for a total of 576,000 datasets to obtain the final derived prod-
on species and therefore can affect species distributions to ucts. As a result, we were able to reduce the level of process-
varying degrees. The relationship between climate and the ing time by using high throughput computing. All climate data
distribution of a species throughout a landscape varies due to
inputs required conversion to GIS data formats (native climate
local adaptation and other factors, such as dispersion con-
data is stored in ASCII format), conversion of units (accounts
straints related to habitat availability.
for scale factors used to compress data), assignment of a defined
coordinate system, and the importation and editing of metadata
1
U.S. Geological Survey for the final product. We then developed multi-band GeoTiff
2
Cherokee Services Group, Fort Collins, Colo. raster datasets (table 2) where each of the 20 bioclimatic
2 Bioclimatic Predictors for Supporting Ecological Applications in the Conterminous United States

Table 1. Climate data inputs used to derive the bioclimatic predictors for the conterminous United States.
Data source Years Resolution Coordinate System
Climate Source1 Monthly averages across years 19712000 400 m (15 arc seconds) Geographic Coordinate System
and NAD 83 datum
Oregon State University Monthly averages across year 19712000 800 m (30 arc seconds) Geographic Coordinate System
and NAD 83 datum
Climate Source2 Monthly, 19712009 2000 m (1.25 arc-minutes) Geographic Coordinate System
and WGS 72 datum
Oregon State University Monthly, 18952007 4000 m (2.5 arc-minutes) Geographic Coordinate System
and WGS 72 datum
1
Climate Source downscaled the Oregon State University PRISM 800 m climate data.
2
Climate Source downscaled the Oregon State University PRISM 4 km climate data.

variables for a given year was represented as a different band. subsequent years (time-series), but rather uses months from
The process for developing the multi-band bioclimatic predictor the beginning of the same year. We believe the AML was
raster datasets is discussed within this document as well as the intended to be used on normals climate data and not time-
accompanying Federal Geographic Data Committee (FGDC) series climate data. Our analysis has been adapted to handle
metadata (http://www.fgdc.gov/metadata). both time-series and normals climate data.
In the unlikely event that the same precipitation/
temperature was recorded for different quarters (constituting
Climatological Terms a quarterly tie), precipitation/temperature data will be selected
Climate normals are 30-year monthly averaged temperature from the first chronological quarter. This applies for quarterly
and precipitation data between 1971 and 2000 (30 years bioclimatic variables, which identify and summarize the wet-
inclusive). test, driest, warmest, and coldest periods of the year.
Climate time-series are monthly data for each year. That is to
say the years are not averaged over a 30-year span as with
the climate normals data.
Methodology
The maximum temperature (Tmax) and minimum temper- Downscaled PRISM Data
ature (Tmin) for monthly data reflect the monthly means
of daily maximum temperatures and monthly means of PRISM is an analytical model that uses point data and a
daily minimum temperatures. Tmax and Tmin can define digital elevation model (DEM) to generate gridded estimates of
either a single month for a specific year (time-series) monthly temperature and monthly total precipitation. PRISM
or the mean of a single month across a span of years is well suited to regions with mountainous terrain, because it
(normals). incorporates a conceptual framework that addresses the spatial
The total monthly precipitation (PPT) defines the total pre- scale and pattern of orographic processes (Daly and Phillips,
cipitation for a single month within a specific year (time- 1994). To improve upon the 4 km and 800 m PRISM data
series) or it is defined as the monthly mean total precipita- that were developed by the Climate Group at Oregon State
tion of a single month across a span of years (normals). University, Climate Source applied a Gaussian filter, which was
a modification of the Barnes filter (Barnes, 1964), to increase
the resolution of the original grids from the base resolution of
Definition of Quarterly Indices 4km to 2 km (time-series) and 800 m to 400 m (normals).
Quarterly indices are based on 3 month intervals. For Table 2. Data series file naming convention.
each month, the two subsequent months are evaluated. To
produce indices at the end of the year, the quarterly period is [One dataset exists for Composites_400m and one dataset exists for
Composites_800m. The dataset filenames for the 2 km and 4 km data will
defined using the months in the beginning of the year (when
denote a different year for each dataset]
using climate normals). For example, if December is the target
month, then January and February of the same averaged time Root folder Example dataset name
period are included in the quarter. When time-series climate Composites_400m BioClimComposite_1971_2000_400m.tif
data is evaluated, we have permitted the quarterly period to
extend across two years. The exception to this description is Composites_800m BioClimComposite_1971_2000_800m.tif
when we are evaluating the final year for time-series data. Composites_2km BioClimComposite_(Year)_2km.tif
When the latter scenario occurs, we will use months within
the same year. Hijmans (2004) does not include months from Composites_4km BioClimComposite_(Year)_4km.tif
 Methodology3

users will find a zip file called Composites_2km_1980_1989.

Prior to interpolation, the gridded surface is first re-
zip, which contains ten composite raster datasets (one for each
sampled to one-half the x- and y-distance of its original resolu-
year) of the 2 km resolution derived bioclimatic variables.
tion (4 km to 2 km and 800 m to 400 m), hereafter referred to
The authors scrutinized these data carefully using sev-
as half-resolution. The re-sampled grid is then shifted the dis-
eral methods. We first evaluated each bioclimatic predictor to
tance of its half-resolution in both the x- and y-directions, such
determine that the output correctly represented the resolution
that the center of every third cell in the shifted half-resolution
and information relevant to the predictor in question (based on
grid falls directly over a node (or corner) of original input
definitions outlined within this document). Second, we wrote a
data. The filter then interpolates the shifted half-resolution
script that flagged datasets where values assigned to pixels fell
grid from the original grid by calculating a distance weighted
outside a typical range. For example, any bioclimatic variables
average from neighboring grid cells. The resampled cell
describing temperature and that did not fall within the U.S.
values thus come from those pixel values of the underlining
temperature extremes (66.7C and 57C) where highlighted as
original grid that fall within the boundary of the shifted half-
a potential error. Any bioclimatic variables describing precipita-
resolution grid.
tion were flagged as a potential error when values fell outside
The following cases were considered when deriving
of the range of 0 mm and 9000 mm. If the bioclimatic predictor
the surface using the Gaussian filter. When the shifted half-
represented a percentage, we flagged any datasets that produced
resolution grid is equidistant from four original input grid cells
results greater than 100 percent. The datasets that were flagged
(that is, over a node), then the four original cells are averaged
using this method were investigated to ensure that pixel values
to create the new downscaled grid cell. If the shifted half-
were not a result of mis-calculating the bioclimatic predic-
resolution grid cell falls completely within an original grid
tor, but rather a result of the input data. We explain within this
cell, the downscaled grid cell is assigned the same value as the document (for example, see Bio 15 description) why this might
original grid cell. In the case of calculating the value of a new occur (where it pertains to a bioclimatic predictor) and where
downscaled grid cell where the shifted half-resolution grid these anomalies typically occur (spatially).
cells falls between two original grid cells at the same longitude
or latitude, then the two adjacent original grid cells are aver-
aged to create the downscaled grid cell. Modifications to Original Bioclimatic
The Climate Source downscaling approach does not Calculations
add new features to the spatial patterns in the original grid;
rather, it simply interpolates between existing grid cells using Several minor modifications to the original AML
Gaussian-weighted averaging to produce a higher resolution written by Robert Hijmans (posted on the Bioclim website;
grid that preserves local detail. http://www.worldclim.org/bioclim) were implemented to
derive these data products. We also added one bioclimatic
variable to the original 19 that Hijmans developed. The modi-
Data That Accompanies This Report fications were as follows:
A suite of GIS raster datasets (GeoTiff), which are 1. The original AML multiplies the result of Bio 4
available for download accompany this report. Each raster (Temperature Seasonality) by 100, which appears to have
dataset is a multiband composite that includes 20 bioclimatic been applied to preserve significant digits for some other
variables (20 bands within each composite raster dataset). application. Our data does not multiply this result by 100.
The bioclimatic variables are derived from 400 m and 800 m
2. We do not round data inputs or outputs (that is, data
resolution climate normals (table 1), and 2 km and 4 km reso-
inputs are floating point to the degree that the source data
lution climate time-series (table 1). Each dataset consists of
accuracy is preserved).
a world file (.tfw), an FGDC metadata file (.xml), a pyramids
overview file (.ovr), an auxiliary file (.aux.xml), a summary 3. Quarterly indices are based on running 3-month intervals
statistics file (.aux.xml) and a GeoTiff file (.tif). Users only (much like a running sum). For each month, the two sub-
require the GeoTiff file, but auxiliary files are provided for sequent months are evaluated. When time-series climate
metadata, faster rendering display time (which is the purpose data are evaluated, we have permitted the quarterly period
of overview file), and dataset summary statistics (aux.xml). to extend across two years. The exception to this is when
These data are organized and bundled in zip compres- we are evaluating the final year for time-series data.
sion files for download within each of the four bioclimatic When this occurs, we will use months within the same
composite folders (Composites_400m, Composites_800m, year. Similarly, when working with climate normals, at
Composites_2km, and Composites_4km). The composite the end of the year the quarterly period is defined using
folders for the 400m and 800 m bioclimatic data contain a the months in the beginning of the year. An example of
single zip file. The 2km and 4 km time-series data contain applying a quarterly measurement to climate normals and
multiple zip files that bundle a range of years. For instance, climate time-series data is provided in table 3.
4 Bioclimatic Predictors for Supporting Ecological Applications in the Conterminous United States

4. The AML calculates temperature seasonality (referred Table 3. Example of applying quarterly calculations to normals
to as Bio 4 in this report) using the standard deviation and time-series climate data.
of the mean monthly temperature instead of deriving
[Normals data are averaged climate indices of a single month across multiple
the temperature seasonality coefficient of variation. The years. For example, precipitation is averaged across all January measurements to
standard deviation was used instead of the coefficient of produce a single measurement that represents January 19712009. Calculating the
variation because degrees Fahrenheit and degrees Celsius quarterly for normals data that occurs during December requires using January
and February data averaged across 19712009. Quarterlies calculated for time-
may have negative values and the coefficient of variation
series data do not use normalized monthly indices and therefore these quarterlies
is not interpretable under these circumstances. Also, if are calculated using monthly climate data from subsequent years. For example,
the mean temperature is zero, the coefficient of variation quarterlies calculated for December require monthly data across two different
cannot be calculated (that is, you cannot divide by zero). years. The example below shows the data inputs that would be used to calculate
a quarterly index for normals data (for the time period 19712009), and for time-
Although we provide the original temperature seasonal-
series data (for December, 2000).]
ity bioclimatic predictor (standard deviation), as outlined
by Hijmans, we also converted temperature to degrees Normals Time-series
Kelvin and calculated temperature seasonality using the December, 19712009 December, 2000
January, 19712009 January, 2001
coefficient of variation. This additional bioclimatic vari- February, 19712009 February, 2001
able is included in the data and referred to as Bio 4a.

5. Metadata was dynamically developed for all derived Product Description for Bioclimatic
products with the use of metadata templates. For each
dataset, parameters unique to the GIS data were extracted Predictors
from that specific dataset and inserted into the template to
produce a unique metadata record. Bio 1Annual Mean Temperature
6. Detailed documentation on the methods used for deriving Definition: The annual mean temperature.
these products is provided, which had not been published
Units: Degrees Celsius
by the original developers.
Data Inputs: The average temperature for each month
(Tavgi)
Notation for Equations Calculation:

i = month ii ==12 Tavgi

Bio 1 = (1)
1

12
Tmax = monthly mean of daily maximum temperatures (C)
The climate inputs are averaged across the year to
Tmin = monthly mean of daily minimum temperatures (C) acquire the annual mean temperature. We calculate the
Tmax i + Tmini average temperature for each month, and then average
Tavgi = is the average temperature these results over twelve months.
2
(C) for the given month (i). Interpretation: The annual mean temperature approxi-
mates the total energy inputs for an ecosystem.
TKmax = monthly mean of daily maximum temperatures (K)

TKmin = monthly mean of daily minimum temperatures (K) Bio 2Annual Mean Diurnal Range
Tkavgi = the average temperature (K) for the given Definition: The mean of the monthly temperature
month (i). ranges (monthly maximum minus monthly minimum).
Since the climate data inputs are monthly or aver-
PPT = total monthly precipitation (mm)
aged months across multiple years, this calculation
ii ==12
1
is the summation of a climate measurement across uses recorded temperature fluctuation within a month
all months within a given year (e.g., Jan., Feb., to capture diurnal temperature range. Using monthly
, Dec.). averages in this manner is mathematically equivalent
to calculating the temperature range for each day in a
ii ==12
2
is the summation of a climate measurement for month, and averaging these values for the month.
months of December in year1, January
in year2, and Februaryin year 2. These Units: Degrees Celsius
calculations are used for the quarterly indices Data Inputs: Monthly maximum temperatures (C) and
described below (see also: table 3). monthly minimum temperatures (C)
 Product Description for Bioclimatic Predictors 5

Calculation: Calculation:

Bio 2 =
ii ==12
1 (Tmax i Tmini ) (2)
Bio 4 = SD{Tavg1, ..., Tavg12} (4)
The standard deviation of the 12 mean monthly tem-
12 perature values is calculated. The original AML multi-
Each monthly diurnal range is the difference between plies the result by 100, which was designed to preserve
that months maximum and minimum temperature. significant digits, but in our calculations we do not do
This difference is then averaged over the twelve multiply by 100.
months of the year. Interpretation: Temperature seasonality is a measure
Interpretation: This index can help provide information of temperature change over the course of the year. The
pertaining to the relevance of temperature fluctuation AML developed by Robert Hijmans and posted on
for different species. Bioclim (http://www.worldclim.org/bioclim) calculates
temperature seasonality using the standard deviation of
the mean monthly temperature instead of deriving the
Bio 3Isothermality temperature seasonality coefficient of variation. The
larger the standard deviation, the greater the variability
Definition: Isothermality quantifies how large the day- of temperature.
to-night temperatures oscillate relative to the summer-
to-winter (annual) oscillations. Bio 4aTemperature Seasonality (CV)
Units: Percent Definition: The amount of temperature variation over a
given period based on the ratio of the standard devia-
Data Inputs: Results from equation 2 and equation 8 tion of the monthly mean temperatures to the mean
monthly temperature (also known as the coefficient of
Calculation:
variation (CV)).
Bio 2 Units: Percent
Bio 3 = x 100 (3)
Bio 7 Data Inputs: The average temperature for each month
Isothermality is derived by calculating the ratio of the (Tavgi) and the annual mean temperature in K (Bio 1).
mean diurnal range (Bio 2) to the annual temperature Calculation:
range (Bio 7, discussed below), and then multiplying
by 100. Bio 4a =
{ } x 100
SD Tkavg1,...,Tkavg12
(5)
Interpretation: Isothermality is generally useful for (Bio 1 + 273.15)
tropical, insular, and maritime environments (Nix, For this calculation, temperature values are converted
1986). Isothermality quantifies how large the day-to- to degrees Kelvin so negative temperatures values do
night temperatures oscillate relative to the summer- not occur and it avoids the possibility of having to
to-winter (annual) oscillations. An isothermal value of divide by zero. CV is calculated by first averaging the
100 indicates the diurnal temperature range is equiva- minimum temperature and maximum temperature val-
lent to the annual temperature range, while anything ues for each month. Then the standard deviation of the
less than 100 indicates a smaller level of temperature 12 mean monthly temperature values is calculated. We
variability within an average month relative to the then divide the standard deviation by the mean monthly
year. A species distribution may be influenced by temperature (Bio 1 in K) and multiply this by 100.
larger or smaller temperature fluctuations within a
Interpretation: Temperature seasonality is a measure
month relative to the year and this predictor is useful
of temperature change over the course of the year.
for ascertaining such information.
The temperature Coefficient of Variation (CV) is the
ratio of the standard deviation of the monthly mean
Bio 4Temperature Seasonality temperatures to the mean of the monthly temperatures
(also known as the relative standard deviation) and is
(Standard Deviation) expressed as a percentage. CV therefore captures the
dispersion in relative terms because standard deviation
Definition: The amount of temperature variation over
can produce two similar values while the means may
a given year (or averaged years) based on the standard
be different. However, if variance is the same, an area
deviation (variation) of monthly temperature averages.
with a lower mean temperature is distinguishable from
Units: Temperature (degrees Celsius) an area with similar variance but with a higher mean
Data Inputs: The average temperature for each temperature. The larger the percentage, the greater the
month (Tavgi) variability of temperature.
6 Bioclimatic Predictors for Supporting Ecological Applications in the Conterminous United States

Bio 5Max Temperature of Warmest Month Data Inputs: The average temperature and the total
precipitation for each month
Definition: The maximum monthly temperature occur- Calculation:
rence over a given year (time-series) or averaged span
of years (normal). ii ==13 PPTi , (9)
Units: Degrees Celsius
ii == 24 PPTi , Where precipitation n is
Data Inputs: Monthly maximum temperatures (C) evaluated for 12 consecutive
...,
Calculation: QPPTmax = max sets of 3 months. The laast
ii ==12
10
PPTi two sets span two years for
Bio 5 = max({Tmax1, ..., Tmax12}) (6) ii ==111 PPTi , time-series data

This is calculated by selecting the maximum tempera- ii ==12
2
PPTi
ture value across all months within a given year.
Interpretation: This information is useful when examin-
ing whether species distributions are affected by warm ii ==13 Tavgi Where monthly temperature
temperature anomalies throughout the year.
Bio 8 = averages are baased on the
3 three selected months of QPPTmax

Bio 6Min Temperature of Coldest Month To calculate this bioclimatic predictor we first identify
the three consecutive months with the highest cumula-
Definition: The minimum monthly temperature occur- tive precipitation total. In the unlikely event that the
rence over a given year (time-series) or averaged span
exact same amount of precipitation was recorded for
of years (normal).
two different quarters (constituting a quarterly tie for
Units: Degrees Celsius maximum precipitation), temperature data will be taken
Data Inputs: Monthly minimum temperatures (C) from the quarter that comes first chronologically. We
Calculation: then calculate the average temperature for the three
months with the highest cumulative precipitation.
Bio 6 = min({Tmin1, ..., Tmin12}) (7)
Interpretation: This index provides mean temperatures
This is calculated by selecting the minimum tempera- during the wettest three months of the year, which can
ture value across all months within a given year. be useful for examining how such environmental fac-
Interpretation: This information is useful when examin- tors may affect species seasonal distributions.
ing whether species distributions are affected by cold
temperature anomalies throughout the year.
Bio 9Mean Temperature of Driest Quarter
Bio 7Annual Temperature Range
Definition: This quarterly index approximates mean
Definition: A measure of temperature variation over a temperatures that prevail during the driest quarter.
given period. Units: Degrees Celsius
Units: Degrees Celsius
Data Inputs: The average temperature and the total
Data Inputs: Results from equation 6 and equation 7 precipitation for each month
Calculation:
Calculation:
Bio 7 = Bio 5 Bio 6 (8)
This is calculated by subtracting Bio 6 (Minimum PPTi ,
i =3
(10)
i =1
Temperature of Coldest Month) from Bio 5 (Maximum i =4
PPTi , Where precipitation
i =2 n is
Temperature of Warmest Month). evaluated for 12 consecutive
...,
Interpretation: This information is useful when examin- QPPTmin = min sets of 3 months. The laast
ing whether species distributions are affected by ranges ii ==12
10
PPTi two sets span two years for
ii ==111 PPTi , time-series data
of extreme temperature conditions.
ii ==12
2
PPTi
Bio 8Mean Temperature of Wettest Quarter
Definition: This quarterly index approximates mean ii ==13 Tavgi Where monthly temperature
temperatures that prevail during the wettest season. Bio 9 = averages are baased on the
3 three selected months of QPPTmin
Units: Degrees Celsius
 Product Description for Bioclimatic Predictors 7

To calculate this bioclimatic predictor we first iden- Bio 11Mean Temperature of Coldest Quarter
tify the three consecutive months with the lowest
cumulative precipitation total. In the unlikely event Definition: This quarterly index approximates mean
that the exact same amount of precipitation was temperatures that prevail during the coldest quarter.
recorded for two different quarters (constituting a
Units: Degrees Celsius
quarterly tie for minimum precipitation), temperature
data will be taken from the quarter that comes Data Inputs: The average temperature for each month
first chronologically. We then calculate the average Calculation:
temperature for the three months with the lowest
cumulative precipitation. i =3
Tavgi , (12)
i =1

Interpretation: This index provides mean tem-
i =4
Tavgi , Where temperaturres are
i =2
peratures during the driest three months of the ..., evaluated for 12 consecutive
year, which can be useful for examining how QTmin = min sets of 3 months. Th
he last
ii ==12 Tavgi two sets span two years for
such environmental factors may affect species
10

seasonal distributions. ii ==111 Tavgi , time-series data

ii ==12
2
Tavgi

Bio 10Mean Temperature of Warmest Quarter

ii ==13 Tavgi Where monthly temperature
Definition: This quarterly index approximates mean Bio 11 = averages are based on the
3 three selected months of QTmin
temperatures that prevail during the warmest quarter.
Units: Degrees Celsius
To calculate this bioclimatic predictor we first identify
Data Inputs: The average temperature for each month the coolest quarter of the year (the average tempera-
Calculation: tures of each month in the quarter are summed; the
quarter with the lowest value is selected). If quarterly

ties occur, the first chronological quarter is selected as
ii ==13 Tavgi , (11)
the coolest quarter. We then calculate the average tem-
ii == 24 Tavgi , Where temperaturres are perature for the three months in the coldest quarter.
..., evaluated for 12 consecutive
QTmax = max sets of 3 months. Thee last Interpretation: This index provides mean temperatures
ii ==12
10
Tavgi two sets span two years for during the coldest three months of the year, which can
ii ==111 Tavgi , time-series data be useful for examining how such environmental fac-

ii ==12
2
Tavgi tors may affect species seasonal distributions.

Bio 12Annual Precipitation

ii ==13 Tavgi Where monthly temperature
Bio 10 = averages are based on the
3 three selected months of QTmax Definition: This is the sum of all total monthly
precipitation values.
To calculate this bioclimatic predictor we first Units: Millimeters
identify the warmest quarter of the year (the aver-
age temperatures of each month in the quarter are Data Inputs: Total precipitation for each month
summed; the quarter with the highest value is selected). Calculation:
If quarterly ties occur, the first chronological quarter
is selected as the warmest quarter. We then calculate Bio 12 = ii ==12
1
PPTi (13)
the average temperature for the three months in the
warmest quarter. To calculate this bioclimatic predictor we sum the pre-
Interpretation: This index provides mean tem- cipitation values of each of the 12 months in a year.
peratures during the warmest three months of Interpretation: Annual total precipitation approximates
the year, which can be useful for examining how the total water inputs and is therefore useful when
such environmental factors may affect species ascertaining the importance of water availability to a
seasonal distributions. species distribution.
8 Bioclimatic Predictors for Supporting Ecological Applications in the Conterminous United States

Bio 13Precipitation of Wettest Month Interpretation: Since species distributions can be

strongly influenced by variability in precipitation, this
Definition: This index identifies the total precipitation index provides a percentage of precipitation variability
that prevails during the wettest month. where larger percentages represent greater variability
of precipitation. CV therefore captures the dispersion in
Units: Millimeters relative terms because standard deviation can produce
Data Inputs: Total precipitation for each month two similar values while the means may be different.
Calculation: However, if variance is the same, an area with smaller
mean is distinguishable from other areas with similar
Bio 13 = max([PPTi, ..., PPT12]) (14) variance but with a larger mean. The larger the per-
centage, the greater the variability of precipitation. We
To calculate this bioclimatic predictor we identify the
noticed that in some regions the CV values exceeded
month with the highest cumulative precipitation total.
100 percent. These regions were investigated and we
Interpretation: The wettest month is useful if extreme determined that in these areas the variance (standard
precipitation conditions during the year influence a deviation) of the precipitation throughout the year
species potential range. exceeded the average precipitation. Most likely this
can be explained by precipitation anomalies (or errors
introduced by the original PRISM models) throughout
Bio 14Precipitation of Driest Month the course of the year in these regions. These rare occur-
rences seem mostly isolated to coastal areas and islands.
Definition: This index identifies the total precipitation
that prevails during the driest month.
Units: Millimeters
Bio 16Precipitation of Wettest Quarter
Data Inputs: Total precipitation for each month Definition: This quarterly index approximates total
Calculation: precipitation that prevails during the wettest quarter.
Units: Millimeters
Bio 14 = min([PPTi, ..., PPT12]) (15)
Data Inputs: Total precipitation for each month
To calculate this bioclimatic predictor we identify the
month with the lowest cumulative precipitation total. Calculation:

Interpretation: The driest month is useful if extreme PPTi ,
i =3 (17)
precipitation conditions during the year influence a
i =1

i =4
species potential range. PPTi , Where precipitation is
i =2
..., evaluated for 12 consecutive
Bio 16 = max i = 12
sets of 3 months. The laast
Bio 15Precipitation Seasonality (CV) i =10 PPTi two sets span two years for
ii ==111 PPTi , time-series data

Definition: This is a measure of the variation in ii ==12
2
PPTi
monthly precipitation totals over the course of the year.
This index is the ratio of the standard deviation of the To derive this bioclimatic predictor we first identify the
monthly total precipitation to the mean monthly total three consecutive months with the highest cumulative
precipitation (also known as the coefficient of varia- precipitation total and then we sum the precipitation val-
tion) and is expressed as a percentage. ues for all three months. If quarterly ties occur, the first
Units: Percent chronological quarter is selected as the wettest quarter.
Data Inputs: Total monthly precipitation for each month Interpretation: This index provides total precipitation
during the wettest three months of the year, which can
Calculation:
be useful for examining how such environmental fac-

Bio 15 =
{
SD PPT1,..., PPT12 } x 100 (16)
tors may affect species seasonal distributions.

1 + (Bio 12 / 12)
Bio 17Precipitation of Driest Quarter
To derive this bioclimatic predictor we first calculate
the standard deviation of the 12 monthly precipitation Definition: This quarterly index approximates total
totals. We then divide this result by the mean monthly precipitation that prevails during the driest quarter.
precipitation value. One is added to the denominator
to avoid strange CV values where mean rainfall is less Units: Millimeters
than 1. Lastly, we multiply the result by 100. Data Inputs: Total precipitation for each month
 Summary9

Calculation: Bio 19Precipitation of Coldest Quarter

ii ==13 PPTi , (18) Definition: This quarterly index approximates total
i =4 precipitation that prevails during the coldest quarter.
i = 2 PPTi , Where precipitation is
..., evaluated for 12 consecutive Units: Millimeters
Bio 17 = min sets of 3 months. The laast
ii ==12
10
PPTi two sets span two years for Data Inputs: The average temperature and the total
ii ==111 PPTi , time-series data precipitation for each month

ii ==12
2
PPTi Calculation:

To derive this bioclimatic predictor we first identify the ii ==13 Tavgi , (20)
three consecutive months with the lowest cumulative
ii == 24 Tavgi , Where temperaturres are
precipitation total and then we sum the precipitation val- ..., evaluated for 12 consecutive
ues for all three months. If quarterly ties occur, the first QTmin = min sets of 3 months. Th
he last
chronological quarter is selected as the driest quarter. ii ==12
10
Tavgi two sets span two years for
ii ==111 Tavgi , time-series data
Interpretation: This index provides total precipitation
during the driest three months of the year, which can ii ==12
2
Tavgi
be useful for examining how such environmental fac-
tors may affect species seasonal distributions. Where monthly precipitation
i =3

Bio 19 = i values are bassed on the
PPT
i =1 three selected months of QTmin
Bio 18Precipitation of Warmest Quarter
Definition: This quarterly index approximates total To calculate this bioclimatic predictor we first identify
precipitation that prevails during the warmest quarter. the coldest quarter of the year (the average tempera-
Units: Millimeters tures of each month in the quarter are summed; the
quarter with the lowest value is selected). If quarterly
Data Inputs: The average temperature and the total ties occur, the first chronological quarter is selected
precipitation for each month as the lowest quarter. The precipitation values for the
Calculation: three months in this quarter are then summed.
Interpretation: This index provides total precipitation
(19) i = 3 Tavg , during the coldest three months of the year, which can
i =1 i
i =4

i =2 Tavg ,
i Where temperatur res are be useful for examining how such environmental fac-
..., evaluated for 12 consecutive tors may affect species seasonal distributions.
QTmax = max i =12 sets of 3 months. Th
he last
i =10 Tavgi two sets span two years for
i =1 Tavg , time-series data
i =11 i Summary
ii ==12
2
Tavgi
The bioclimatic data series provides GIS continuous
raster surfaces that represent multiple temporal and spatial
i =3 Where monthly precipitation resolutions. The source climate datasets permitted us to pro-

Bio 18 = PPT values are bassed on the
i duce bioclimatic predictors for multiple scales (400 m, 800 m,
i =1 three selected months of QTmax 2 km, 4km) and normalized/time-series climate summaries
(averaged climate indices between 19712009 and monthly
To calculate this bioclimatic predictor we first identify averaged climate indices between 18952007). Therefore,
the warmest quarter of the year (the average tempera- the bioclimatic predictors provide derived climate metrics
tures of each month in the quarter are summed; the of biological relevance for researchers and land managers to
quarter with the highest value is selected). If quarterly understand species responses to climate change. Because the
ties occur, the first chronological quarter is selected as input data used to generate these products are based on climate
the warmest quarter. The precipitation values for the models and the outputs represent summaries of climate data
three months in this quarter are then summed. at coarse resolutions, they should be used for regional assess-
Interpretation: This index provides total precipitation ments and general trends. Users should also be cognizant of
during the warmest three months of the year, which how the climate models were produced (PRISM and down-
can be useful for examining how such environmental scaled PRISM (Climate Source)) and the limitations these
factors may affect species seasonal distributions. models may have for a specific application.
10 Bioclimatic Predictors for Supporting Ecological Applications in the Conterminous United States

Acknowledgments Daly, Christopher, Neilson, Ronald P., and Phillips, Donald L.,
1994, A statistical-topographic model for mapping clima-
Funding for this project was provided by the tological precipitation over mountainous terrain: Journal of
U.S. Geological Survey, Fort Collins Science Center. We Applied Meteorology v. 33, p. 140158.
would also like to thank one of our reviewers, Travis Schmidt, Hijmans, Robert J., 2004, Arc Macro Language (AML) version
whose comments greatly improved the organization of 2.1 for calculating 19 bioclimatic predictors: Berkeley, Calif,
this document. Museum of Vertebrate Zoology, University of California at
Berkeley. Available at http://www.worldclim.org/bioclim.
Nix, Henry A., 1986, A biogeographic analysis of Australian ela-
References pid snakes, in Longmore, Richard, ed., Atlas of elapid snakes
of Australia: Canberra, Australian Flora and Fauna Series 7,
Barnes, S.L., 1964, A technique for maximizing details in
Australian Government Publishing Service, p.415.
numerical weather map analysis: Journal of Applied Meteo-
rology, v. 3, p. 396409. The PRISM Climate Group, 2011, Parameter-elevation
Climate Source, Inc, 2011, Downscaled OSU PRISM climate Regression on Independent Slopes Model (PRISM):
data: Corvallis, Oreg., The Climate Source. Available at Corvallis, Oreg, Oregon State University. Available at
http://www.climatesource.com/. http://www.prism.oregonstate.edu/.

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This report is available at: http://pubs.usgs.gov/ds/691
ODonnell and IgnizioBioclimatic Predictors for Supporting Ecological Applications in the Conterminous United StatesData Series 691