Towards ice-core-based synoptic reconstructions of west antarctic climate with artificial neural ...

30 Pages·2005·1.32 MB·English

INTERNATIONALJOURNALOFCLIMATOLOGY
Int.J.Climatol.25:581–610(2005)
PublishedonlineinWileyInterScience(www.interscience.wiley.com).DOI:10.1002/joc.1143
TOWARDS ICE-CORE-BASED SYNOPTIC RECONSTRUCTIONS OF WEST
ANTARCTIC CLIMATE WITH ARTIFICIAL NEURAL NETWORKS
DAVIDB.REUSCH,a,*BRUCEC.HEWITSONb andRICHARDB.ALLEYa
aDepartmentofGeosciencesandEMSEnvironmentInstitute,ThePennsylvaniaStateUniversity,UniversityPark,PA16802USA
bDepartmentofEnvironmentalandGeographicalSciences,UniversityofCapeTown,PrivateBag,Rondebosch7701,SouthAfrica
Received9March2004
Revised22August2004
Accepted12November2004
ABSTRACT
Ice cores have, in recent decades, produced a wealth of palaeoclimatic insights over widely ranging temporal and
spatial scales. Nonetheless,interpretation ofice-core-based climate proxies is stillproblematic dueto a variety ofissues
unrelated to the quality of the ice-core data. Instead, many of these problems are related to our poor understanding
of key transfer functions that link the atmosphere to the ice. This study uses two tools from the field of artificial
neural networks (ANNs) to investigate the relationship between the atmosphere and surface records of climate in West
Antarctica. The first, self-organizing maps (SOMs), provides an unsupervised classification of variables from the mid-
troposphere (700 hPa temperature, geopotential height and specific humidity) into groups of similar synoptic patterns.
An SOM-based climatology at annual resolution (to match ice-core data) has been developed for the period 1979–93
based on the European Centre for Medium-Range Weather Forecasts (ECMWF) 15-year reanalysis (ERA-15) dataset.
This analysis produced a robust mapping of years to annual-average synoptic conditions as generalized atmospheric
patterns or states. Feed-forward ANNs, our second ANN-based tool, were then used to upscale from surface data to
the SOM-based classifications, thereby relating the surface sampling of the atmosphere to the large-scale circulation of
the mid-troposphere. Two recorders of surface climate were used in this step: automatic weather stations (AWSs) and
ice cores. Six AWS sites provided 15 years of near-surface temperature and pressure data. Four ice-core sites provided
40 yearsofannualaccumulationandmajorionchemistry.AlthoughtheANNtrainingmethodologywasproperlydesigned
and followed standard principles, limited training data and noise in the ice-core data reduced the effectiveness of the
upscaling predictions. Despite these shortcomings, which might be expected to preclude successful analyses, we find
that the combined techniques do allow ice-core reconstruction of annual-average synoptic conditions with some skill.
We thus consider the ANN-based approach to upscaling to be a useful tool, but one that would benefit from additional
training data. Copyright  2005 Royal Meteorological Society.
KEYWORDS: icecores;synopticreconstruction;artificialneuralnetworks;self-organizingmaps;WestAntarctica
1. INTRODUCTION
This work seeks to use ice-core proxy datasets to reconstruct 40 years (1954–93) of West Antarctic annual
climate as seen in the mid-tropospheric circulation using the well-known but poorly understood link between
the atmosphere and ice cores. Ice-core proxy data is calibrated to atmospheric circulation data for the period
1979–93 and then used to predict the latter for the period 1954–78. As an additional test of our method,
automatic weather station (AWS) data are also used for a limited reconstruction in the 1979–93 period. As
described in further detail in the following sections, our approach to this problem consists of four steps.
1. Simplify the atmosphere: self-organizing maps (SOMs) extract patterns of variability by doing a
classification into generalized states. These patterns are useful both for studying the recent atmosphere
and as components of the subsequent reconstruction.
*Correspondence to: DavidB.Reusch, Department of Geosciences and EMS Environmental Institute, The Pennsylvania State
University,UniversityPark,PA16802,USA;e-mail:[email protected]
Copyright  2005 Royal Meteorological Society
582 D.B.REUSCH,B.C.HEWITSONANDR.B.ALLEY
2. Link ice-core proxy and AWS datasets to the atmosphere: a feed-forward artificial neural network (FF
ANN) is trained to predict the patterns from (1) using either ice-core or AWS data. This step calibrates
the upscaling tool.
3. Reconstruct earlier climate: ice-core data outside the calibration period are used with the trained FF ANN
topredicttheassociatedatmosphericpatternsfortherestoftheice-coreperiod.Givensufficientconfidence
in these predictions, they would be used to develop a full time series of reconstructed climate.
4. Evaluate the methodology: confidence in a climate reconstruction is tied to the data and steps involved in
creatingit. We thus evaluate the reliability of the SOM-basedanalysis and FF ANN-basedupscaling steps
and comment on issues associated with the ice-core data that reduce skill in the upscaling step.
1.1. Icecoresand climate
Decades of research have shown ice cores to be extremely valuable records of the Earth’s climate from
subannual to millenial time scales and beyond (e.g. Wolff and Peel, 1985; Legrand etal., 1988; Mayewski
etal., 1988, 1997; Zielinski etal., 1994; White etal., 1999). As with marine sediment cores, tree rings and
other climate proxies, interpretation of the ice-core record of palaeoclimate is not always straightforward.
In many cases, although the data are of unquestionably high quality and temporal resolution, our poor
knowledge of the relevant transfer functions can greatly reduce the value of the record. This is a recognized
problem (Waddington, 1996) and, although process studies and field work have helped greatly in some areas
(e.g. in improving our understanding of how δ18O records temperature), there are still many gaps in the
ice
knowledge we need to understand the proxy records fully. This is particularly true in the Antarctic, where
directobservationaldatafortheatmospherearehardtoobtainand,whenavailable,tendtoberelativelyshort
(by climatological standards) and spatially limited.
Ice cores record many different aspects of the climate system, sometimes in multiple ways. Each proxy
captures one or more climate features in a way that will likely differ in both space and time to varying
degrees. For example, the relationship between δ18O and temperature can be different at different places
ice
and times (Alley and Cuffey, 2001; Jouzel etal., 2003) as other influences on δ18O vary in their relative
ice
effect. Furthermore, many proxies are only captured during precipitation events. This can lead to biases in
the proxy when precipitation is seasonally variable. For example, if wet deposition is the dominant capture
process for a chemical species and snow only falls during the summer, then the ice-core record for that
species will be biased towards a picture of the summer atmosphere. Unfortunately, the subannual character
of precipitation is typically not very well known at West Antarctic ice-core sites, and we are often forced
to assume that snow falls uniformly throughout the year. Subannual sampling is still possible, and indeed
necessary to reconstruct annual cycles of chemical species, but it must be remembered that these data are
projected onto an underlying assumption about uniform snowfall. Thus, unless detailed subannual process
data are available (e.g. Kreutz etal., 1999), we are limited to studies of ice-coreproxies at annual resolution.
High-resolution meteorological data (reanalysis and/or observational) provide a means to study relationships
between ice-core proxies and the atmosphere over subannual intervals, but we remain limited to annual (or
possibly semiannual)-resolution climate reconstructions from the proxies.
1.2. The meteorologicalrecordand reanalysisdatasets
The best meteorological datasets in the Antarctic are typically from two areas: the coastal stations, such as
McMurdo, Mawson and Halley Bay, and the two long-term interior plateau stations, South Pole and Vostok
(Figure 1). Records from elsewhere in the Antarctic interior are limited, with few exceptions, to AWSs and
short-term data collection during traversesandice-coredrilling operations (e.g.Siple Dome).The latter often
only represent the summer field season (when the sites are occupied). AWSs provide year-round data, apart
from instrument problems, but only measure the near-surface environment in a limited manner. The AWS
network, nonetheless, provides an invaluable sampling of the West Antarctic atmosphere.
The shortage of direct observational data has, in turn, increased the importance and utility of numerical
forecast/dataassimilation/analysisproductsforAntarcticclimateresearch.Thetwomostwidelyuseddatasets
of this type are from the National Centers for Environmental Prediction–National Center for Atmospheric
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ICE-CORE-BASEDSYNOPTICRECONSTRUCTIONS 583
Figure 1. Site map showing AWS (solid circles) and ice-core sites (squares) of this study, and other sites (open circles) and regions
mentionedinthetext.CWA(centralWestAntarctica)collectivelydescribesfouricecoresites(A,B,C,D)publishedinReuschetal.
(1999)
Research (NCEP–NCAR) in the USA and the European Centre for Medium-Range Weather Forecasts
(ECMWF) in the UK. Both forecast models have problems in the Antarctic (e.g. Bromwich etal., 1995;
Genthon and Braun, 1995; Cullather etal., 1997) and the shortage of observations tends to produce analyses
that resemble the forecast more than in areas with more available observations. Nonetheless, despite their
shortcomings (e.g. Marshall, 2002; Bromwich and Fogt, 2004), these products are still much better options
thanhavingonlytheobservationaldata.ECMWFandNCEP–NCARhaveeachproducedso-calledreanalysis
versions of their model predictions (Kalnay et al., 1996; ECMWF, 2000; Kistler etal., 2001). A reanalysis
uses one version of the forecast model for the duration of the study period and thus removes changes to the
model as a source of changes in the forecasts. Other factors, such as addition and removal of observational
data over time, remain as variables affecting the skill of the reanalyses, but these are external to the model.
In short, the reanalysis datasets provide a realistic, 6 h picture of the atmosphere with reasonable horizontal
and vertical resolution in an otherwise data-sparse region.
1.3. Classification andupscaling: towards synoptic reconstructions
The focus of our study has thus been the link between annually resolved ice-core proxies, e.g. major
ion chemistry and accumulation, and the annually resolved atmosphere using two tools from the field of
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ANNs.First,SOMs(Kohonen,1990,1995)provideaclassificationofmeteorologicalvariablesfromthemid-
troposphere (from the ECMWF 15-year reanalysis, ERA-15) into groups of similar synoptic patterns. SOMs
havebeenusedforclimatedownscaling(CraneandHewitson,1998),asamechanismforclimateclassification
(Cavazos,1999,2000),andforexaminingchangesinclimateovertime(HewitsonandCrane,2002),allinmid-
latitude settings. In this study, we have developed an SOM-based climatology of mid-tropospheric variables
for annually averaged ERA-15 data. Second, FF ANNs allow us to find a possibly nonlinear relationship
between a set of predictors (e.g. upper air variables) and a set of targets (e.g. AWS surface observations).
In particular, we have used FF ANNs to upscale from AWS and ice-core predictor data to SOM-based
synopticclassificationtargets.Inthisway,pastatmosphericconditionscanbepredictedfromproxydatawith
a confidence based on the quantity and nature of the training data. Unfortunately, the short training period
(15 years) and limited spatial extent of the selected ice-core data appear to prohibit a simple, deterministic
reconstructionfromhigh-confidence,well-definedpredictions.Instead,amoreprobabilisticapproachisneeded
to make up for the shortcomings in these datasets. Pending development of a more robust methodology and
improved datasets, we are limited to an evaluation of what can be done with the current data.
In Section 2 we describe the AWS, ECMWF and ice-core datasets. An overview of the ANN tools used
is given in Section 3 (also see Hewitson and Crane (2002) and Reusch and Alley (2002). Section 4 presents
the SOM-basedannual synoptic climatology and upscaling results/atmospheric reconstructionfrom AWS and
ice-core data. Issues related to the methodologies and input data are covered in Section 5.
2. DATA
2.1. ECMWFdata
The ECMWF 15-year reanalysis data product (ERA-15) provided global-scale meteorological data for
the period 1979–93 (fully described in Gibson etal. (1999)). The original ERA-15 production system used
spectral T106 resolution with 31 vertical hybrid levels (terrain following and higher resolution in the lower
troposphere, lower resolution in the stratosphere). The lower resolution product used here was derived from
theproductionsystemandprovides2.5° horizontalresolutionforthesurfaceand17upperairpressurelevels.
Six-hourly data are available at 0, 6, 12 and 18 UTC. Annual averages of the 6-h data were normalized
to the 1979–93 baseline (by respectively subtracting and dividing by the full dataset mean and standard
deviation) prior to the SOM analysis (Section 3.1). Figure 2 is an example of the annual-average 700 hPa
temperatures used.
Potential problems have been noted with ECMWF (re)analysis data over Antarctica. (Comments in this
section refer to ERA-15 and operational analyses prior to development of the ERA-40 dataset, which was
unavailable for this project. Some of these issues have been resolved in ERA-40, but other problems remain,
many of which are related simply to the lack of observational data in this region prior to the satellite era
(BromwichandFogt,2004).)ThefirstrelatestotheflawedsurfaceelevationdatasetusedbyECMWFforthis
region (Genthon and Braun, 1995). Elevation errors exceeding 1000 m exist in some areas of Queen Maud
Land and the Antarctic Peninsula (e.g. Genthon and Braun, 1995: figure 3). Topography in West Antarctica
is generally much better, but errors from outside our study area will still have an influence on the reanalysis
data (e.g. an elevation error for Vostok station has broad effects on geopotential heights). The horizontal
resolution of the model also introduces unavoidable elevation errors in areas where the relief is high relative
to grid spacing (e.g. Bromwich and Fogt, 2004). The ECMWF model also suffers from two issues affecting
skillinthenear-surfaceregion:relativelylowverticalresolutionnearthesurface(evenwiththehybridlevels)
and specification of ice-shelf regions as permanent sea ice. Both lead to possible errors in the surface energy
balance due to unresolved katabatic flows and incorrect physics over the ice-shelf regions (Bromwich et al.,
2004). The latter leads to large errors in ERA-15 surface temperatures when compared with available AWS
data(ReuschandAlley,2002,2004).Evaluationsofseveraloperationalproducts(e.g.Bromwichetal.,1995,
2000; Cullather etal., 1998) and discussions with experiencedpolar meteorologists (D. Bromwich, J. Turner,
personal communications) suggest that the ECMWF analyses are the best data sets currently available for
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Figure2.Annualaverage700hPatemperatureforERA-15period(1979–93)asgrid-pointanomaliesfromthegrid-wideaverageafter
normalizing with the full-period, grid-wide average and standard deviation. Temperature generally decreases poleward; thus, darkest
shadesrepresentwarmest(coldest)temperaturesinthenorth(south).Zerocontourisinboldandvaluesclosetozeroarenotshaded
Antarctica(seealsoBromwichetal.(1998)),althoughthe ECMWF40-yearreanalysis(ECMWF,2001)may
set a new standard when it is readily available.
2.2. AWSdata
The main source of direct meteorological data in West Antarctica is the network of AWSs maintained
by the University of Wisconsin-Madison since 1980 (Lazzara, 2000). All stations provide near-surface air
temperature, pressure, and wind speed and direction; some stations also report relative humidity and multiple
vertical temperatures (e.g. for vertical temperature differences). The main instrument cluster is nominally
within 3 m above the snow surface. This distance changes with snow accumulation and removal. Pressure
is calibrated to ±0.2 hPa with a resolution of approximately 0.05 hPa. Temperature accuracy is 0.25–0.5°C,
with lowest accuracy at −70°C, i.e. accuracy decreases with decreasing temperature (M. Lazzara, personal
communication). The data used here are from the 3 h quality-controlled datasets available at the University
of Wisconsin-Madison FTP site (ice.ssec.wisc.edu). A 6 h subset of these data (for 0, 6, 12 and 18 UTC) is
used to match ECMWF time steps (see below).
TheAWSsusedinthisstudy areshowninFigure 1andsummarizedinTable I.Twoofthesites, Byrdand
Ferrell, representthe oldest two AWSs still in operation. Siple was installed at around the same time as these
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Siple
1
0.5
0
1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994
Byrd
1
0.5
0
1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994
Lettau
1
0.5
0
1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994
Marilyn
1
0.5
0
1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994
Elaine
1
0.5
0
1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994
Ferrell
1
0.5
0
1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994
Average
1
0.5
0
1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994
Figure 3. Relative proportions of observations (grey) and predictions (white) inAWS temperatureand pressure recordson a monthly
basis.SeeTableIforsiteinstallationdates
Table I. AWS locations and otheruseful data
Station Latitude Longitude Elevation (m) Date Installed Distancea (km)
Byrd Station 80.01°S 119.40°W 1530 February 1980 11.5
Elaine 83.13°S 174.17°E 60 January 1986 71
Ferrell 77.91°S 170.82°E 45 December 1980 49.5
Lettau 82.52°S 174.45°W 55 January 1986 8.3
Marilyn 79.95°S 165.13°E 75 January 1987 6.1
Siple 75.90°S 84.00°W 1054 January 1982b 103.9
aDistancetothenearestERA-15gridpoint.
bSipleAWSwasremovedinApril1992.
AWSs but was removed in 1992 due to logistical problems. Siple’s remoteness from McMurdo-based field
support and the high accumulation rates in this region were the main reasons that this station was removed.
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The remaining sites were installed in 1986 and 1987. All sites are within the south/southeast Pacific sector
of West Antarctica. Figure 3 summarizes the availability of each AWS for the study period (1979–93) as the
fraction of observations recorded each month. An average for the suite of AWSs is also shown. In general,
availability is either quite high or quite low, with few monthly values in between. The absence of data from
Siple in 1985–87 were not directly related to failure of the meteorological instruments but to other factors
(primarily power related, C. Stearns, personal communication, 2002). Otherwise, most data loss is related to
winter-season failures and the subsequent wait until the austral summer field season for repair.
Because all AWS sites had periods of missing observations (due to failures or just not being active for
the full study period), we have developed an ANN-based technique to supply the missing data (Reusch and
Alley, 2002). The AWS records used in this study are thus a merger of observations and predictions based
on our technique. Numerous sources are available for ANN theory and practice (e.g. Hewitson and Crane,
1994; Gardner and Dorling, 1998; Haykin, 1999; Demuth and Beale, 2000); thus, we will provide only a
short overview of our approach here. Briefly, upper air data from ERA-15 provide predictors for available
AWS temperature and pressure observations. The training methodology explores numerous predictors, ANN
parametersandensemblesofFFANNstodevelopthemostskilfulnetwork(withinthesearchspace).Because
of variable (i.e. temperature and pressure) and site differences, a separate ANN is used for each variable at
eachsite(foratotalof12ANNs)topredictthemissingobservationsfromupperairdataatthecorresponding
time steps. The average root-mean-square errors from ANN training (i.e. calibration of the prediction tool)
for all six AWS sites were 2.9°C and 1.9 hPa for monthly average temperature and pressure respectively.
The average correlation r of monthly average ANN training predictions and AWS observations was 0.96.

The AWS-prediction ANNs were implemented with the MATLAB Neural Network Toolbox (Haykin, 1999;
Demuth andBeale,2000). The climatological/statistical propertiesof this datasetaredescribedin more detail
elsewhere (Reusch and Alley, 2004).
2.3. Ice-coredata
Four shallow firn/ice cores (<90 m) from central West Antarctica (Reusch et al., 1999) provided high-
resolutionglaciochemicalandannualaccumulationdataforcomparisonwiththeERA-15data(Figure 1).Each
corewasoriginallysampledathighresolution(continuouslyevery3 cmor10–12samplesperyear)tocapture
the annualsignalsinthe majorsoluble ionsofatmospheric chemistry:Na+,K+,Mg2+,Ca2+,Cl−,NO − and
3
SO2−. Annual averagesof the chemistry time serieswere createdfrom the original subannual resolution time
4
seriesforthisstudy.Reuschet al.(1999) providefulldetailsonthedatinganddevelopmentofthese records.
A number of other ice-core datasets are available, but most fail one or both requirements for being useful
in a study such as this: availability to the community and sufficient overlap with the calibration period
(1979–93). For example, the Byrd Station dataset of Langway et al. (1994) is not readily available and has
only a 10 year overlap with the calibration period. Overlap is also an issue with the Siple Station cores of
Mosley-Thompson et al. (1991). This situation will improve with time as datasets become available from
projectssuchastheUSITASEprogram(USITASESteeringCommittee,1996).Futureworkwillincorporate
these datasets and others with sufficient overlap with whatever calibration period is used.
3. METHODS
Our overall methodology breaks down into two main areas: development of a synoptic classification of the
atmosphericcirculationusingSOMsandtraining/applicationofFFANNstodoupscalingfromice-coreproxy
and AWS datasets to the classified atmospheric patterns.
3.1. Synoptic classification and SOMs
3.1.1. SOMs. SOMs (Kohonen, 1990, 1995) provide a means to do unsupervised classification of large,
multivariate data sets into a fixed number of distinct generalized states or modes. Hewitson and Crane
(2002) reviewed SOM applications and issues in climatology, so only a brief introduction will be given here.
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588 D.B.REUSCH,B.C.HEWITSONANDR.B.ALLEY
SOM analysis effectively quantizes a continuous input space to a finite-state output space (the SOM map).
Multidimensional dataareprojectedontoa planeasarectangulargrid(ormap) ofdiscrete,generalizedstates
extractedfromthedatathroughthetrainingprocess.Thesizeofthegrid(numberofstates)directlyinfluences
theamountofgeneralization:smaller(larger)mapshavefewer(more)availablestatesinthegrid,sothefinal
states developed during training will tend to do more (less) generalization of the input. Each map state, or
node, is associated with a reference vector that represents the projection from multidimensional space to the
two-dimensional SOM space for that state. For example, in an analysis of input containing 10 variables,
each reference vector will have length 10. At the start of SOM training, reference vectors are initialized
either randomly (distributed across the input data space) or based on the first two principal eigenvectors of
the training data (Kohonen et al., 1996). The latter often has the advantage of faster subsequent training.
At the end of SOM training, each reference vector represents a generalized state extracted from the input
space. States in the SOM grid are usually identified by an (x, y) column, row coordinate pair, where x =0
to x −1 and y =0 to y −1.
max max
SOM training is based on iterative adjustment of the reference vectors during SOM training phases. Each
phasealternatesbetweenmappinginputrecordsandadjustingreferencevectors.Eachinputrecordismatched
to the closest reference vector (normally determined via Euclidean distance). The value of the matching
reference vector is then adjusted towards the value of the input record by an amount determined by the
currentlearningrate.Thelearningrateisadimensionlessparameterusedtopromotestabilityofthereference
vectors during training. The difference between an input record and its closest reference vector is scaled
by the learning rate, with the result used to adjust the reference vector. A learning rate of zero makes no
adjustments and a value of one applies the complete difference. Typical values in this work range from 0.01
to0.05. AkeyfeatureofSOMsis thatthe referencevectorsof aneighbourhood of nodesadjacenttothe best
match are also updated, but to a lesser degree. The size of the neighbourhood and the learning rate (amount
of adjustment of the reference vector) are both reduced as training progresses. This process produces vectors
representing distinct portions of the input space. Nodes will also be most similar to adjacent nodes that each
represent a nearby region of the input space. Similarity between map nodes thus decreases with increasing
internode distance. That is, adjacent nodes have the greatest similarity and diagonally opposite corners will
have the largest dissimilarity. This is a direct result of the SOM training process (Kohonen, 1995).
In turn, SOM analysis typically involves two logical training phases: ordering and refinement. During the
ordering phase, the general shape of the map is determined. The adjustment neighbourhood starts at the
value of the larger map dimension (e.g. 5 for a 5×3 SOM) so that all nodes will be initially affected. The
learning rate starts at a relatively high value (e.g. 0.05, or 5% of the difference between an input record and
its closest reference vector is applied to the reference vector) so that changes are initially relatively large.
In the refinement phase (or phases), the initial size of the adjustment neighbourhood and learning rate are
reduced (e.g. to 2 and 0.02 respectively) to attempt finer adjustments over smaller subareas. This enables
further separation of related nodes from less-related neighbours (assuming a stable configuration does not
already exist). Whereas the ordering phase may produce slightly different classifications depending on the
number of training iterations, a properly applied refinement phase will lead to a convergent solution.
Once training is complete, each reference vector is an abstraction of a portion of the input data space and
each input vector maps to one reference vector, i.e. a node of the SOM map and the data mapping to that
node share similar characteristics. Because of the quantizing nature of the SOM generalization, input data
are generallynot identical to their mappedreferencevectorsand a residual differenceremains. Depending on
the application, the residuals may be useful, e.g. to compare records mapping to the same reference vector.
The quantizing process may also lead to SOM nodes that have no mapped input vectors because there are no
training data in the region of the input space represented by the SOM node. Such SOM nodes are perfectly
valid; they just represent states intermediate between those seen in the training process. It is possible that
data not present in the training set may map to one of these nodes in the future. This is an example of the
robust nature of the SOM classification process.
A SOM classification differs from more traditional linear analysis in a number of ways that give SOMs
additional power over nonlinear datasets. For example, empirical orthogonal function (EOF) analysis, or
principalcomponentanalysis(PCA),anditsvariants,hasbeenwidelyandsuccessfullyusedformanyyearsin
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the climateandatmosphericsciencestosimplify large,multivariate datasetsfor the purposesofinterpretation
and understanding (e.g. Smith etal., 1996; Mayewski etal., 1997; Sinclair et al., 1997; Reusch et al., 1999;
von Storch and Zwiers, 1999; Schneider and Steig, 2002). Because an EOF analysis by definition produces a
linear combination of orthogonal variables, it may not always be appropriate to apply this technique to data
known to have nonlinear characteristics.The resultant EOF components may not representrealistic groups of
variables (Barry and Carleton, 2001). EOF analysis also has other pitfalls less related to nonlinearity, such
as sample size issues and determining which components to retain (e.g. North etal., 1982; von Storch and
Zwiers,1999;BarryandCarleton,2001),thatrequiresignificantexperiencewiththetechniqueandknowledge
of the input data. Although the SOM technique is not free of a learning curve, it does not force the data into
orthogonal linear combinations. SOM states are not linearly spaced, rather they represent an even coverage
of the probability density function (PDF) of the input data (Hewitson and Crane, 2002). Distances between
SOM states vary with the magnitude of the difference between the generalized patterns of each state. For
example, a subset of similar states is likely to be well separated from the remaining states in the grid but be
relatively close to one another. SOMs also interpolate into regions of the PDF without input data (Hewitson
and Crane, 2002). Lastly, the sum of the reference vectors from an SOM analysis will not reconstruct the
originalinput data,aswouldasummation ofEOFcomponents, becauseeachinput recordhasa residualwith
its closest matching reference vector. The SOM states are generalized patterns from the input data, not the
data themselves.
3.1.2. Synoptic classification. Three ERA-15 variables from the middle troposphere (700 hPa) were used
intheSOM-basedanalyses:temperatureT,geopotentialheightZ andspecifichumidityq.The700hPalevel
was selected, somewhat subjectively, to get above ERA-15 near-surface problems and the physical surface
for (most of) West Antarctica. (A continent-wide analysis would require us to move to at least 600 hPa
because this is the first pressure level fully above the surface for the full continent.) These three variables
were selected to capture the synoptic circulation and moisture transports. (Full characterization of moisture
transport, as in Bromwich et al. (2000), also requires u and v wind components.) Because of the converging
lines of longitude in polar regions, and so that grid points represented similar spatial areas, the ERA-15 data
were first resampled to an equal-area grid. Both 250 km and 125 km versions of the National Snow and
Ice Data Center EASE-Grid (Armstrong and Brodzik, 1995) were tested with the 125 km grid being used
for this study. Grid-scale means and standard deviations were then calculated from 6 h values for annual,
semiannual and seasonal time scales for each variable from the regridded data (but only annual data have
been fully analysed). Because T, Z and q have widely different mean and extreme values, each variable was
standardized to avoid scale problems in the SOM. Point-wise anomalies from the 15-year grid-point means
of the standardized values were calculated for each grid point to highlight patterns of variability. Finally, the
six variables (anomalies of the mean and standard deviation of T, Z and q) were combined for input to the
SOMsoftware.Witheachinputvariablerepresentingspatialdata,theSOMgridiseffectivelyamapofmaps.
Furthermore, since each input record contains six variables, each SOM node is actually six separate maps
representingthegeneralizedspatialstateforeachofthevariables.Forsimplicity,wewilltypicallyshowonly
one variable at a time.
The SOM analyses were performed using SOM-PAK software (Kohonenet al., 1996). We have used three
mapsizesinthisstudy:3×2,4×3and5×3.Althoughthiswasnottheprimarygoalofthiswork,theuseof
multiple sizesallows usto look athow data grouping changeswith varyingnumbers of SOMstates available
for generalization. Smaller maps have fewer states to which the input data can be mapped, so it is expected
that some grouping of input years will occur. The 5×3 map has 15 states and matches the size of our input
data (15 years); thus, it is possible, if not highly probable, for each year to map to a unique SOM state. That
is, it is expected that a 5×3 map will only group records with significant similarity, whereas smaller maps
will have some degree of forced association due to having fewer states. Thus, the 5×3 maps (15 nodes)
are preferred for our purposes. Although we are interested in the SOM’s ability to generalize, we are also
interested in its ability to classify and order without supervision. Even without substantial generalization, a
SOM analysis provides useful information about the similarities and differences in the input data through the
spatial mapping of the data on the SOM grid. Each SOM analysis produces a classification of input records
Copyright2005RoyalMeteorologicalSociety Int.J.Climatol.25:581–610(2005)
590 D.B.REUSCH,B.C.HEWITSONANDR.B.ALLEY
(calendar years) grouped by the similarity of their meteorological data (with one or more years per group).
AWS and ice-core data from each group were then compared for similarity within groups and differences
between groups before being used as predictors of the SOM classifications.
3.1.3. Assessmentofresults. As with manystatistical analysismethods forgrouping similar data,including
clusteranalysis,itcanbedifficulttodeterminea‘perfect’classification.AssessmentofanSOMclassification
is both a subjective and quantitative process, especially with smaller datasets (details of individual mappings
are often less important as the size of the input dataset grows). As always, it is important to bear in mind
the question being asked of the analysis method when trying to determine whether the method has given
a reliable answer. Ideally, the refinement phase produces one convergent solution from dissimilar ordering-
phase classifications. In the event that this is not possible, other criteria are required. For example, training
might be considered ‘done’ (subjectively) once mappings to the diagonal corners of the map have stabilized,
sincethesenodesareoftenthemostdistinct(althoughcontinuingbeyondthisstageisusuallyrecommended).
Sammonmaps(Sammon,1969),whichprovidetwo-dimensional projectionsofmultidimensional vectors,are
a common method for this type of evaluation. Quantization error, the difference between the input data and
the reference vectors, can be useful as a quantitive measure of SOM ‘error’, but it is unlikely to be the only
useful metric. For example, there may be little need to continue reducing the error if the mappings have
stabilized across all nodes. Similarly, there is no guaranteethat continued effortsto reduce the error will lead
to stable mappings if some data are right on the boundary between quantized states. However, in theory,
eventhose data recordscanbe separatedsuccessfullyif enough time is spent on training, though this is often
unnecessary. Examination of residuals provides another quantitative assessment approach.
After much testing and evaluation, we settled on a combination of input-data mapping stability (i.e. are
groups still changing significantly) and quantization error to determine how much training was enough. With
the small number of input records, as few as 1000 iterations were sufficient to provide initial ordering of the
input data, although 5000 were preferred. (A run of 5000 iterations typically required only a few minutes
to complete on an 867 MHz Apple Macintosh G4 Powerbook laptop.) A refinement run of up to 20000
iterations often produced useful further separation of the modes; longer run lengths had only minor benefits.
3.2. Climate upscaling
3.2.1. Overview. FF ANNs were also used for our climate upscaling studies, but with the freely available
NevProp package (Goodman, 2002). Climate upscaling uses surface data to predict corresponding SOM-
classified synoptic states. In this way, synoptic conditions can be reconstructed from a surface sampling
of the atmosphere. More surface sites and greater record length in the calibration period both improve the
quality of such reconstructions. Two surface records were used as predictors: AWS observations (six sites,
15 years) and ice-core climate proxies (four sites, 40 years). Each dataset allowed us to evaluate the surface-
to-mid-troposphere relationship, but with different levels of dating uncertainty and, thus, different temporal
resolutions. AWS observations are effectively perfectly dated records and, thus, support comparisons at up
to 6 h resolution. Thus, upscaling from AWS data allows us to test the approach under best-case conditions
for a given number of AWS sites. Because of the shortness of the AWS record, however, only very limited
testing of data not used in training is possible. As noted previously, ice-core records are generally limited
to annual or lower resolution because of assumptions about the rate of deposition and dating uncertainties.
This restricted temporal resolution is offset by the potentially much greater length of the ice-core records.
Calibration is still done for the 15 year overlap with ERA-15 data, but upscaling can be done further into
the past using the ice-core data. In this study, the four ice cores provided an additional 25 years at all sites,
taking the upscaling back to 1954.
3.2.2. Data coding. Training of an upscaling ANN requires an encoding of the predictor and target data.
Full details of how this was done are presented in Appendix A. Briefly, the predictor data are simply the
measurementsatallsites asstandardizedanomaliesfromthe study periodmean(15 yearsfor AWS,40 years
for the ice cores) at each site. To match the ice-core accumulation data (and SOM analysis data), the AWS
Copyright2005RoyalMeteorologicalSociety Int.J.Climatol.25:581–610(2005)