Supplementary Materials:
Full Methods
Table S1-3
Figures S1-S11
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Downscaling reveals diverse effects of anthropogenic climate warming on the
potential for local environments to support malaria transmission
Krijn P. Paaijmans, Justine I. Blanford, Robert G. Crane, Michael E. Mann, Liang Ning,
Kathleen V. Schreiber, Matthew B. Thomas
Supplemental Material
1. Climate Downscaling
1.1 Data and Methodology
The climate in a local area (in this case, a meteorological reporting station) is a
function of the large-scale atmospheric forcing, local forcing (such as topography,
water bodies and land use) and stochastic variability. General Circulation Models
(GCMs) are most effective at capturing the larger-scale processes, and climate
downscaling involves the development of an empirical or dynamically-based
transfer function that relates the larger-scale climatic state to local weather
statistics. In the methodology described here, Self-Organizing Maps (SOMs) are
used to characterize the larger-scale atmospheric state using 2.5o gridded reanalysis
data from the U.S. National Center for Environmental Prediction (Kanamitsu, et al.,
2002). Reanalysis data are generated using a global atmospheric forecast model,
where a data assimilation scheme is used to constrain or “nudge” the model output
toward the available global observations (derived from the global network of
surface and upper air reporting stations, aircraft and satellite observations). The
reanalysis variables tend to be more accurate where observational data densities
are greatest, but they are also the most reliable “observations” available in data
sparse regions.
SOMs are a category of artificial neural networks that serves as both a data analysis
and a data visualization technique. The SOM takes a multi-dimensional data set--in
this case a time series of regional atmospheric parameters--and partitions it by
defining a set of locations (nodes) in the multidimensional data space where each
node is the multivariate mean of the surrounding cluster of data points, and where
nodes are unevenly distributed through the data space such that there are more
nodes where data densities are greatest. All data points, to a greater or lesser
extent, contribute to the definition of each node, so the nodes do not represent a
discrete partitioning of the data space. In this respect, SOMs are analogous to a
fuzzy clustering algorithm.
The NCEP reanalysis data are regridded to a nominal 2o x 2o grid surrounding the
meteorological station. The 19 hexagonal cells centered on and surrounding the
station are used to train the SOM, and for each of the 19 cells we use standardized
values of the surface air temperature, the specific and relative humidities at 850 hPa
and the sine of the Julian day to give a total of 76 variables (19 cells X 4 atmospheric
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variables) that define the large-scale atmospheric state (the weighting given to the
day of year is somewhat arbitrary, but compensates for the degree of spatial
autocorrelation in the atmospheric parameters). For each station, one SOM is
trained with an n x m data matrix input where m is the number of variables (76) and
n is the number of days in the data set (for the period 1979-2007). In this
application we use an 11 x 9 array for the SOM, giving 99 nodes. Smaller SOM arrays
produce more generalized groupings, while larger arrays allow for more subtle
differences between groups. Each node in the SOM is defined by a 76-element
reference vector that corresponds to the 76 variables in the input data matrix.
The training procedure starts by randomly assigning values to each reference
vector. We then take the 76 variables from day one and compare it to each of the
SOM node reference vectors. The winning node is the node that is closest to the data
(using Euclidian distance) and the reference vector for that node is nudged slightly
in the direction of that day’s data. The reference nodes for the surrounding nodes
are also nudged in the same direction, but by a smaller amount. Every row (day) in
the data matrix is passed through the SOM in the same manner, and the procedure
repeated iteratively until there is essentially no change in the SOM reference
vectors. Updating the surrounding nodes as well as the winning node forces nodes
that represent very different parts of the data space to move further apart in SOM
space, while nodes that are very similar are located close together. If the data set
consisted of two very different clusters or "atmospheric states" for example, the two
groups would map to opposite corners of the SOM, and the nodes between would
represent the transition states from one to the other. The procedure for training
SOMs in this fashion and using them as a type of fuzzy clustering algorithm is
described in Hewitson and Crane (2002) and Crane and Hewitson (2003). SOMs are
particularly useful in this context because they assume no underlying statistical
distribution for the data and they are very forgiving of missing data. A continuous
data set is not required, and if there are missing data within a row of the data
matrix, the comparison with the reference vectors is carried out on whichever pairs
of data elements are present for that day.
For each station, once the SOM has been trained on the reanalysis data and every
day is mapped to a SOM node, we take all the days on a given node, extract the local
(meteorological station) observed temperature for those days, and construct a
cumulative frequency distribution of observed local temperatures associated with
that particular historical large-scale atmospheric state. We can then take any day,
map it to the SOM and then randomly extract a (downscaled) temperature value
from the associated cumulative frequency distribution. We can also take GCM daily
data (re-gridded to the same 2o x 2o grid) for the present and future time periods
and map those to the same SOM created from the reanalysis, and again extract an
observed temperature associated with the model simulated atmospheric state.
From this point, we create a suite of data sets for each meteorological observing
station that includes daily time series of: the observed station temperature, the
temperature downscaled from the reanalysis data, the temperature downscaled
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from a suite of present-day GCM runs, and the temperature downscaled from a suite
of GCMs projecting mid-century climate change.
A separate SOM mapping and downscaling is carried out for each meteorological
station and for each station we downscale the daily maximum and minimum
temperatures, and the daily average temperature (max+min / 2). We then construct
a joint frequency distribution of paired maximum and minimum temperatures to
downscale the diurnal range. For the future projections, the GCM simulated
temperature difference (Future – Present) is added back to the downscaled
temperatures. In this way, the change in the GCM large-scale mean captures changes
due to direct radiative forcing and a generally warmer world, while the downscaling
captures the regional variation in those changes as a function of atmospheric state
and local variability.
In summary, the downscaling procedure involves:
For each target location (meteorological station):
1) Defining the large scale atmospheric state using NCEP reanalysis data
 Standardize the data and regrid to an approximate 2o grid. Extract the
training data for the 19 hexagonal cells centered on and surrounding the
station location.
 Train a SOM to group days with similar atmospheric characteristics
2) Defining the temperature regime associated with each group (SOM node)
 Take each day that maps to a group, extract the target meteorological
station's observed temperature for those days, and define the temperature
frequency distribution for the node
3) Downscaling temperature
 Standardize and regrid the GCM present-day and future projection climate
data using the same variables that were used to train the SOM
 Map these data to the SOM trained on the NCEP reanalysis data
 Randomly select a temperature value from the nodes temperature
distribution function, and add the temperature delta values for the future
projection
This is then repeated for each GCM and for all meteorological stations.
Full details on the downscaling procedure and its application to downscaling
precipitation in South Africa and in Pennsylvania can be found in Hewitson and
Crane (2006) and Ning et al. (2012 a; b). The meteorological stations used for the
East Africa analysis are listed in Table S1 and the GCMs used for the projection of
present-day (1961-2000) and future (2046-2065) climates are given in Table S2.
The present-day simulation uses historical atmospheric greenhouse gas
concentrations from the World Climate Research Programme (WCRP) Coupled
Model Intercomparison Project (CMIP3) 20c3m scenario. The mid-century
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projections are based on the A2 emissions scenario. The data and descriptions of
the GCMs can be found at the WCRP CMIP3 Multi-Model Data website1 and the GCMs
used are those that archived the daily data necessary for the precipitation
downscaling described in Ning et al. (2012a; b).
1.2 Downscaling Validation and Results
The close agreement between the observed meteorological station data and the
downscaled temperatures derived using the NCEP reanalysis data is shown in
Figure S1, which compares the two probability distributions, Observed and
Downscaled, for mean daily temperature and the diurnal temperature range at all
four stations. By randomly selecting values from the observed temperature
frequency distribution, and by constructing individual SOMs for each target location,
the downscaling not only captures the local forcing constrained by the larger-scale
atmospheric state, but also incorporates the stochastic variability present in the
observations and is able to match both the means and the extremes of the
distributions. The ability of the downscaling to effectively recreate the monthly
means and the seasonal cycle in temperature is shown in Figure S2. Figure S3
shows the fractional mean square error (MSE) between the observed temperatures
and the temperatures downscaled from the NCEP reanalysis data and present-day
GCM data and from the raw GCM simulations. The fractional MSE for the
downscaled GCM data is very close to that of the NCEP recreated temperatures (in
the range of 10-25%), and much smaller than the errors for the raw GCM simulation
data (typically > 100%) at all four stations. The actual downscaled projections
averaged across all eight GCMs are shown in Figure S4 for maximum, minimum and
mean temperatures, as well as the diurnal temperature range at all four stations.
References
Crane, R. G. and B. C. Hewitson. Clustering and upscaling of station precipitation
records to regional patterns using self-organizing maps (SOMs). Climate
Research, 25:95-107 (2003).
Hewitson, B. C. and R. G. Crane. Self-Organizing Maps: Applications to synoptic
climatology. Climate Research, 22:13-26 (2002).
Ning, L., M. E. Mann, R. G. Crane, T. Wagener. Probabilistic Projections of Climate
Change for the Mid-Atlantic Region of the United States—Validation of
Precipitation Downscaling During the Historical Era. J. Climate, 25:509-526
(2012a).
Ning, L., M. E. Mann, R. G. Crane, T. Wagener, R. Najjar, R. Singh. Probabilistic
Projections of Anthropogenic Climate Impacts on Precipitation for the MidAtlantic Region of the United States. J. Climate, 25:5273-5291 (2012b).
Kanamitsu, M., W. Ebisuzaki, J. Woollen, S-K Yang, J.J. Hnilo, M. Fiorino, and G. L.
Potter. NCEP-DEO AMIP-II Reanalysis (R-2). Bulletin of the American
Meteorological Society, 83:1631-1643 (2002)
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https://esg.llnl.gov:8443/index.jsp
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Table S1: Location of the Downscaled Meteorological Stations
Station
Latitude
Longitude
Altitude (m)
Kitale
1.02
35.00
1,875
Kisumu
-0.10
34.75
1,146
Kericho
-0.37
35.35
2,184
Garissa
-0.47
39.63
147
Observation
time period
1982/122005/10
1978/122010/04
1987/021998/02
1980/062010/04
Table S2: GCMs Used for the Temperature Downscaling Over Kenya
Model
CCCMA_CGCM 3.1
CNRM_CM 3
CSIRO_MK 3.0
GFDL_CM 2.0
IPSL_CM4
MIUB_ECHO_G
Country
Canada
France
Australia
USA
France
Germany/Korea
MPI_ECHAM 5
MRI_CGCM 2.3.2A.
Germany
Japan
Resolution (long x lat)
Spectral T47 (2.5o x 2.5o)
Spectral T63 (1.9o x 1.9o)
Spectral T63 (1.9o x 1.9o)
2.5o x 2o
3.75o x 2.5o
Spectral T30 (3.75o x
3.75o)
Spectral T63 (1.9o x 1.9o)
Spectral T44 (2.7o x 2.7o)
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Table S3. Mean temperature and diurnal temperature range (DTR) as estimated by
the raw GCMs or the downscaled (DS) models, for recent historic (1981-2000) and
future climates (2046-2065), for 4 sites across Kenya. Data represent 20-years
averages from the ensemble of individual models, and the standard error of the
mean. Values between parentheses are the lowest and highest average value
reported by any model.
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Fig. S1. The observed (blue) and NCEP downscaled (red) probability distributions of
daily average temperatures (left column) and diurnal temperature ranges (DTRs;
right column) over the 4 stations: 1. Kitale; 2. Kisumu; 3. Kericho; 4. Garissa. The
vertical scales are different in order to fit the results.
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Fig. S2. The observed (blue) and NCEP downscaled (red) annual cycles of daily
average temperatures (left column) and diurnal temperature ranges (DTRs; right
column) over the 4 stations: 1. Kitale; 2. Kisumu; 3. Kericho; 4. Garissa (Unit: °C).
The vertical scales are different in order to fit the results.
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Fig. S3. The average fractional MSE from NCEP-downscaled data (blue), GCMdownscaled (green), and raw GCM simulations (red) over the 4 stations, and the
average across the 4 stations: 1. Kitale; 2. Kisumu; 3. Kericho; 4. Garissa.
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Fig. S4. Projected changes of the annual average maximum temperature, minimum
temperature, average temperature, and DTR between the period 2046-2065 and the
period 1981- 2000 for each of the four stations: 1. Kitale; 2. Kisumu; 3. Kericho; 4.
Garissa (Unit: °C). The squares are the ensemble downscaled average across the
eight GCMs, and the whiskers are the inter- GCM uncertainties.
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Fig. S5. Mean temperature and diurnal temperature range (DTR) as estimated by
the raw GCMs or the downscaled (DS) models, for recent historic and future
climates for Kericho in western Kenya. The grey shading indicates the range outputs
from individual climate models (full details of models in Table S2). The dotted black
line represents the average from the ensemble of models; the solid black line the
available weather station data recorded at Kericho for a subset of the historic time
series.
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Fig. S6. Mean temperature and diurnal temperature range (DTR) as estimated by
the raw GCMs or the downscaled (DS) models, for recent historic and future
climates for Kitale in western Kenya. The grey shading indicates the range outputs
from individual climate models (full details of models in Table S2). The dotted black
line represents the average from the ensemble of models; the solid black line the
available weather station data recorded at Kitale for a subset of the historic time
series.
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Fig. S7. Mean temperature and diurnal temperature range (DTR) as estimated by
the raw GCMs or the downscaled (DS) models, for recent historic and future
climates for Garissa in western Kenya. The grey shading indicates the range outputs
from individual climate models (full details of models in Table S2). The dotted black
line represents the average from the ensemble of models; the solid black line the
available weather station data recorded at Garissa for a subset of the historic time
series.
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Fig. S8. Mean temperature and diurnal temperature range (DTR) as estimated by
the raw GCMs or the downscaled (DS) models, for recent historic and future
climates for Kericho in western Kenya. Different colored lines represent outputs
from individual climate models (full details of models in Table S2).
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Fig. S9. Mean temperature and diurnal temperature range (DTR) as estimated by
the raw GCMs or the downscaled (DS) models, for recent historic and future
climates for Kitale in western Kenya. Different colored lines represent outputs from
individual climate models (full details of models in Table S2).
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Fig. S10. Mean temperature and diurnal temperature range (DTR) as estimated by
the raw GCMs or the downscaled (DS) models, for recent historic and future
climates for Kisumu in western Kenya. Different colored lines represent outputs
from individual climate models (full details of models in Table S2).
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Fig. S11. Mean temperature and diurnal temperature range (DTR) as estimated by
the raw GCMs or the downscaled (DS) models, for recent historic and future
climates for Garissa in western Kenya. Different colored lines represent outputs
from individual climate models (full details of models in Table S2).
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