cc: Ilona.Liesner@gkss.de
date: Sun, 26 Sep 1999 18:58:02 +0200
from: Hans von Storch <Hans.von.Storch@gkss.de>
subject: TAR10.6
to: tar10@egs.uct.ac.za

Dear Tar10ers,
attached please find as WORD documents the revised version of section 10.6,
the appendix with the list of applications of empirical downscaling
studies, and the list of references for the whole section 10, as it exists
presently. In 10.6 the example for a transfer function design is still
missing: Bruce was supposed to provide this example. He is presently not
responding -I hope that this no reason for
concern - and I could provide an example with short term notice on Tuesday.
Also one figure caption is missing; I have asked Rick Katz, from whom the
example is taken, for a proper formulation.

The reference list is the basis for further compilations by my secretayry,
Mrs Ilona Liesner. Please send her your input for additional references,
updates and deletions.

For those of you, who don't like reading WORD, I am adding the texts as
ascii as well. But, we should
not edit the ascii files but only the WORD files, as otherwise the spelling
of nn-English authors
and, in case of the reference list, titles of papers would be damaged.

I want to take the opportunity to thank Linda and Filippo for their
cooperation during the last few days.

Can somebody tell me where to send the figures? I have eps-files, but other
formats could also be produced.

Cheers

Hans

-----------------------------------------------------


10.6 Empirical/statistical and statistical/dynamical methods

10.6.1 Introduction

Formally, the concept of regional climate being conditioned by the
large-scale state may be written as a stochastic and/or deterministic
mapping of a predictor (a set of large-scale variables) on a  predictand (a
set of regional climate variables In general, the mapping is unknown is
unknown and is modeled dynamically (i.e., through regional climate models)
or empirically from observational (or modeled) data sets. In some cases the
predictor and predictand are the same variables but on different spatial
scales (for example the disaggregation schemes of Brger, 1997; Wilks,
1999; and Widmann and Bretherton, 1999), but in most cases they are
different. The mapping commonly employed is, in general, not designed to
fully model all ranges of temporal scales.

When using downscaling for assessing regional climate change, three
implicit assumptions are made:

-	The predictors are variables of relevance and are realistically modeled
by the GCM.    Since different variables have different characteristic
spatial scales, some variables are considered more realistically simulated
by GCMs than others.  For instance, derived variables (not fundamental to
the GCM physics, but derived from the physics) such as precipitation are
usually not considered as robust information at the regional and grid scale
(e.g., Osborn and Hulme, 1997; Trigo and Palutikof, 1999). Conversely,
tropospheric quantities like temperature or geopotential height are
intrinsic parameters of the GCM physics and are more skillfully represented
by GCMs. However, there is no consensus in the community about what level
of spatial aggregation (in terms of number of grid cells) is required for
the GCM to be considered skillful. For example Widmann and Bretherton
(1999) find monthly precipitation on spatial scales of three grid lengths
(in their case: 500 km) reliably simulated.
 
- The transfer function is valid also under altered climatic conditions.
This is an assumption that in principle can not be proven in advance. In
the case of empirical functions, the observational record should cover a
wide range of variations in the past; ideally, all expected future
realizations of the predictors should be contained in the observational
record. 

-	Critical is the assumption that the predictors employed fully represent
the climate change signal. Too little attention has in the past been paid
to this assumption, but Hewitson (1999) and Charles et. al. (1999) have
made progress in this respect.

A diverse range of downscaling methods has been developed, but in principle
fall into three categories, which are based upon the application of
- weather generators, which are random number generators of realistically
looking sequences conditioned upon the large-scale state (10.6.2.1). 
- transfer functions, where a direct quantitative relationship is derived
through, for example, regression (10.6.2.2).
- weather typing schemes based on the more traditional synoptic climatology
concept (including analogs and phase space partitioning) and which relate a
particular atmospheric state to a set of local climate variables (10.6.2.3).

Each of these approaches has relative strength and weaknesses in
representing the range of temporal variance of the local climate
predictand. Consequently, the above approaches are often to some degree
merged in order to compensate for the relative deficiencies in one method.

Most downscaling applications have dealt with temperature and
precipitation.  However, a wide array of studies exists in which other
variables have been investigated. Appendix XX provides a non-exhaustive
list of past studies indicating predictands, geographic domain, and
technique category. We are concentrating on references to applications
since to 1995, since studies prior to that date made use of now outdated
global climate change scenarios.

[Appendix XX = Table 10.6.1]

10.6.2 Methodological options

10.6.2.1 Weather generators

Weather generators are statistical models of observed sequences of weather
variables.  They can also be regarded as complex random number generators
(Katz and Parlange, 1996), the outputs of which resemble daily weather data
at a particular location (Wilks and Wilby, 1999). There are various  types
of daily weather generators, based on the approach to modeling daily
precipitation occurrence: but the types usually fundamentally rely on
stochastic  processes. Two of these include the Markov chain approach
(e.g., Richardson, 1981; Hughes et al., 1993, Lettenmaier, 1995; Hughes et
al., 1999, Bellone et al., 1999) and the spell length approach (Racksko et
al., 1991; Wilks, 1999a).  In the spell length approach, which can be
viewed as a natural way of extending the Markov chain approach, the length
x of the spell lengths are simulated based on a probability distribution of
the lengths. In the Markov chain approach precipitation occurrence is
simulated day by day. Wilks (1999a) and Semenov et al. (1998) compare these
methods. An additional approach is the so-called ``conceptual model''
approach, which involves chance mechanisms (e.g., clustering) by which
storms arise and  which is often used by hydrologists (O'Connell et al.
1999). 

Weather generators have been used for generating climate change scenarios
that incorporate changes in climate variability (e.g., Katz, 1996; see
Chapter 13, this volume) and for statistical downscaling, or for both
simultaneously (Semenov and Barrow, 1997, Wilks 1999b).  In the context of
statistical downscaling the parameters of the weather generator are
conditioned upon a large-scale state (see Katz and Parlange, 1996;  Wilby
et al., 1998; Charles et al., 1999), or relationships can be developed
between large scale parameters sets of the weather generators and local
scale parameters (Wilks, 1999b). Conditioning on large-scale states
alleviates to some degree one of the chronic flaws of many weather
generators, which is the underestimation of interannual variations of the
weather variables (Wilks, 1989), and, to a degree, induces spatial
correlation (Hughes and Guttorp, 1994).

As is the case with other downscaling methods the success of this method is
dependent upon the strength of the relationship between the stochastic
generator parameters and the large-scale circulation index, and the
stability of this relationship over time.

As an illustration, the analysis of Katz and Parlange (1993, 1996) is
discussed in some detail. They conditioned daily precipitation amount for a
location in California on a circulation index, based on sea level pressure
off the coast of California.  They modeled the daily time series of
precipitation as a chain dependent process, modeling occurrence as a first
order Markov chain, and a power transform of intensity as normally
distributed. The circulation index was allowed only two states, above and
below normal pressure over a 78-year record.  Using the Akaike and Bayesian
Information Criteria  they determined  that model parameters such as mean
intensity, standard deviation of intensity, and the probability of
precipitation varied significantly with the circulation index state (high
versus low pressure). They found that the conditioned model reproduced the
precipitation variance statistics of the observations better than the
unconditioned model, for example,  interannual variance  of monthly total
precipitation. They went on to describe the use of their model for climate
change  scenario formation, i.e., conditions where the probability of
obtaining a  particular circulation index state is shifted.  The mean
precipitation changes linearly with the probability of the circulation
state, but the standard deviation of the precipitation amount changes
nonlinearly  (Figure 10.6.1). These relationships  indicate  that the model
allows for changes in the coefficient of variation of monthly total
precipitation, which increases under mean drier conditions and decreases
under mean wetter conditions. This method thus also allows for change in
variability of precipitation along with the mean. 


Figure 10.6.1-  Figure 2 from  K and P  96


10.6.2.2 Transfer functions
The more common approaches found in the literature are regression-like
techniques or piecewise interpolations using a linear or nonlinear
formulation.  The simplest approach is to build multiple regression models
relating free atmosphere grid point values to surface variables.  For
example Sailor and Li (1999) have in this manner modeled local temperature
at a series of US stations. Other regression models use field of spatially
distributed variables to specify local temperatures in Sweden (e.g.: Chen
et al., 1999), or principal components of regional geopotential height
fields (e.g.: Hewitson, 1992).

Canonical Correlation Analysis (e.g., von Storch and Zwiers, 1999) has
found wide application. A variant of CCA is redundancy analysis, which is
theoretically attractive as it maximizes the predictands variance; however,
in practical terms it seems similar to CCA (WASA, 1998). Also Singular
Value Decomposition has been used (Huth, 1999). 

Most applications have dealt with precipitation; for instance Busuioc and
von Storch (1996) with Rumanian monthly precipitation amounts, or Dehn and
Buma (1999) with a French Alpine site. Kaas et al (1996) have successfully
specified local pressure tendencies, as a proxy for local storminess, from
large-scale monthly mean air pressure fields. 

Oceanic climate and climate impact variables have also been dealt with:
salinity in the German Bight (Heyen and Dippner, 1998); and salinity and
oxygen in the Baltic (Zorita and Laine, 1999); sea level (e.g., Cui at al.,
1996); and a number of ecological variables such as abundances of species
(e.g., Kroencke et al., 1998).  In addition statistics of extreme events,
expressed as percentiles within a month or season, have been modeled: storm
surge levels (e.g., von Storch and Reichardt, 1997) and ocean wave heights
(WASA, 1998).

An alternative to linear regression is to use piecewise linear or nonlinear
interpolation; geostatistics offers elegant "kriging" tools to this end
(e.g., Wackernagel, 1995). The potential of this approach has been
demonstrated by Biau et al. (1999), who related local precipitation to
large-scale pressure distributions. Another approach is to use cubic
splines, as was done by Buishand and Klein Tank (1996) for specifying
precipitation in Switzerland. Also Hantel et al. (1998) adopt a nonlinear
design for modelling snow cover duration in Austria with European mean
temperature and altitude.

Another non-linear approach is based on artificial neural networks (ANN;
Hewitson and Crane,1996), which are generally more powerful than other
techniques, although the interpretation of the dynamical character of the
relationships is less easy. For example, Trigo and Palutikof (1999) map
with an ANN SLP and 500 hPa height values on daily temperature at a station
in Portugal and find significantly improved specification as compared to a
linear ANNs. 

Figure 10.6.2

10.6.2.3 Weather typing
The synoptic downscaling approach empirically defines weather classes
related to local and regional climate variations. These weather classes may
be defined synoptically or fitted specifically for downscaling purposes by
constructing indices of airflow (Conway et al., 1996). The frequency
distributions of local or regional climate are then derived by weighting
the local climate states with the relative frequencies of the weather
classes. Climate change is then estimated by determining the change of the
frequency of weather classes.

In many cases, the local and regional climate states are derived from the
observational record. Wanner et al. (1997) used changing global to
continental scale synoptic structures for understanding and reconstructing
Alpine climate variations, while Widmann and Schaer (1997) could not relate
changing Swiss precipitation to changing statistics of weather classes.
Kidson and Watterson (1995) made a similar analysis for New Zealand.  Jones
and Davies (1999) apply the technique for studying changing air pollution
mechanisms.

The analog method was introduced into the downscaling context by Zorita et
al (1995). Conceptually similar, but mathematically more demanding are
techniques which partition the large-scale state phase space, for instance
with Classification Tree Analysis, and use a randomized design for picking
regional distributions. This technique was pioneered by Hughes et al
(1993). Lettenmaier (1995) gives a general overview of these techniques.
Both analog and CART approaches return the right level of variance and
correct spatial correlation structures. 

In the following, we discuss in some more detail a case of
statistical-dynamical downscaling as suggested first by (Frey-Buness et
al., 1995): Statistical-dynamical downscaling (SDD) is a hybrid approach
with statistical and dynamical elements. In a first step GCM results of a
multi-year climate period are disaggregated into non-overlapping multi-day
episodes of quasi-stationary large-scale flow patterns. Once defined,
similar episodes are grouped in classes of different weather types. Typical
members of these classes, i.e. episodes which in total comprise only a
small fraction of the complete period, are simulated with a regional
climate model (RCM). It is driven at its boundaries by the GCM results of
the respective episodes. Eventually, the RCM results are statistically
evaluated where the frequency of occurrence of the respective classes
determines their statistical weight. An advantage over the SSD technique
over other empirical downscaling techniques is that in this way spatially
distributed local climates are specified. Its feasibility has been
demonstrated by a series of studies on climate and climate change in the
European Alps (see Appendix XX).

As compared with conventional continous RCM simulations (Section 10.5), the
computational effort of SDD is small and almost independent of the length
of the climate period. That this reduction of computational demands is not
combined with a reduction is accuracy, at least in terms of time-mean
distributions, is demonstrated by a comparison of mean precipitation
distributions as simulated by a continuous RCM simulation and by the SSD
technique. Figure 10.6.3 displays correlation coefficients and mean
absolute differences, conditional upon the degree of disaggregation. When
the computational oad is reduced to 20%, the mean absolute error amounts to
about 0.4 mm/day, whereas the correlation coefficient is about 0.96. Thus,
in practical applications the intrinsic error of SDD is acceptable if the
overall error is largely determined by the error of the used models (GCM
and RCM).



Figure 10.6.3. Similarity of time mean precipitation distributions obtained
in a continuous RCM simulation and through SSD for different levels of
disaggregation. Top: mean absolute difference [mm/day], bottom: spatial
correlation coefficient. Horizontal axis: computational load of SSD.  is
the number of days simulated in SSD, N the number of days simulated win the
continuous RCM simulation.


10.6.3 Issues in Statistical Downscaling

10.6.3.1 Temporal variance
Transfer function approaches and some of the weather typing approaches
suffer to varying degrees from an under-prediction of temporal climate
variability, since only part of the regional and local temporal variability
of a climate variable is related to large scale climate variations, while
another part is generated regionally. (For the case of regression the
mathematics of this principle are worked out by Katz and Parlange (1996).)
Two approaches for bringing the downscaled climate variables to the right
level of variability are in use: inflation and randomization. In the
inflation approach, originally suggested by Karl et al. (1990), the
variation is increased by the multiplication of a suitable factor; a more
sophisticated approach, named "expanded downscaling", was developed by
Brger (1996). It is a variant of Canonical Correlation Analysis that
ensures the right level of variability. This approach is utilized by Huth
(1999) and Dehn et al. (1999). In the randomization approach the
unrepresented variability is added as unconditional noise; that is, in the
simplest case, the "missing" variance is added in the form of white noise
(Hewitson, 1998). The concept is worked out in von Storch (2000), and
applications are offered by Dehn and Buma (1999) and Buma and Dehn (1998).

Conversely, weather generators suffer from the inverse of the above, and
have difficulty in representing low frequency variance.  However,
conditioning the generator parameters on the large-scale state may
alleviate this to some degree state (see Katz and Parlange, 1996; Wilks,
1999a; Wilby et al., 1998; Charles et al., 1999).

10.6.3.2 Validation

The validation of downscaling techniques is an essential but difficult
requirement.  It requires demonstrating the robustness of the downscaling
under future climates, and that the predictors used represent the climate
change signal. Both assumptions are not possible to rigorously test, as no
empirical knowledge is available so far. The analysis of historical
developments as well as simulations with GCMs can provide support for these
assumptions. However, the success of a statistical downscaling technique
for representing present day conditions does not imply legitimacy for
changed climate conditions (Charles et al., 1999).

The classical validation approach is to specify the downscaling technique
from a segment of available observational evidence and then assess the
performance of the empirical model by comparing its predictions with
independent observed values. This approach is particularly valuable when
the observational record is long and documents significant changes in the
course of time.  An example is the analysis of absolute pressure tendencies
in the North Atlantic by Kaas et al. (1996), who fitted a regression model
which related spatial air pressure patterns to pressure tendency
statistics. Similarly Wilks (1999) developed a downscaling function on dry
years and found it functioning well in wet years. Hanssen-Bauer and Frland
(1998) and Hanssen-Bauer (1999) found in their analysis that data series of
50 year length may not be sufficient to derive a valid model.

An alternative approach is to use a series of comparisons between models
and transfer functions, as demonstrated by Busuioc et al (1999), Charles et
al. (1999) and Gonzlez-Ruoco et al. (199a,b). In the former study, it was
first demonstrated that the GCM incorporated the empirical link; in the
latter, a regional climate model was used.  From these findings it was
concluded that the dynamical models would correctly "know" about the
empirical downscaling link; then the climatic change, associated with a
doubling of carbon dioxide, was estimated through the empirical link and
compared with the result of the dynamical model. In both cases, the
dynamical response was found to be consistent with the empirical link,
indicating the validity of the empirical approach and its legitimate
approach in downscaling other global climate change information.

10.6.3.3: Choice of predictors

The list of predictands in the literature is very broad and comprise direct
climate variables (e.g.: precipitation, temperature, salinity, snow pack),
monthly or yearly statistics of climate variables (distributions in wind
speeds, wave heights, water levels, frequency of thunderstorm statistics),
as well as impacted variables (e.g.: frequency of land slides). The
Appendix XX lists a  wide range of predictors, predictands, and techniques.
Useful summaries of downscaling techniques and the predictors used are also
presented in Rummukainen (1997), Wilby et al. (1998) and Wilby and Wigley
(1999).  

However, outside of passing references in many studies to the effect that a
range of predictors were evaluated, there is little systematic work that
has explicitly evaluated the relevant skill of different atmospheric
predictors (Winkler et al., 1997).   The one commonality between most
studies is, not surprisingly, the use of some indicator of the large-scale
circulation.

The choice of the predictor variables is of utmost importance. For example,
Hewitson (1997, 1998) has demonstrated how the downscaled scenario of
future change in precipitation may alter significantly depending on whether
or not humidity is included as a predictor. The implication here is that
while a predictor may or may not appear as the most significant when
developing the downscaling function under present climates, the changes in
that predictor under a future climate may be critical for determining the
climate change.  Some estimation procedures, for example stepwise
regression, are not able to recognize this and exclude variables that may
be vital for climate change.  Such exclusion may lead to misleading
scenarios of change.

A similar issue exists with respect to downscaling temperature. Werner and
von Storch (1993), Hanssen-Bauer (1999) and Mietus (1999) noted that low
frequency changes in local temperature during the 20th temperature could
not be related to changes in circulation. Schubert (1998) makes a vital
point in noting that changes of local temperature under doubled atmospheric
CO2 may not be driven by circulation changes alone, but may be dominated by
changes in the radiative properties of the atmosphere. This is a particular
vulnerability of any downscaling procedure in light of the propensity to
use circulation predictors alone that do not necessarily reflect the
changed radiative properties of the atmosphere.  

One possible solution is to incorporate the large-scale temperature field
from the GCM as a surrogate indicator of the changed radiative properties
of the atmosphere. This approach has been adopted by Dehn and Buma (1999)
in their scenario of future Alpine land slides. Another solution is to use
several large-scale predictors, such as gridded temperature and circulation
fields (e.g., Gyalistras et al., 1998; Huth, 1999).

After the availability of homogeneous re-analyses (Kalnay et al., 1996),
the number of candidate predictor fields has been greatly enhanced (Solman
and Nuez, 1999); earlier, the empirical evidence about the co-variability
of regional/local predictands and large-scale predictors was very limited
and made many studies choose either gridded near surface temperature or air
pressure, or both (Gyalistras et al., 1994). These "new" data sets will
allow significant improvements in the design of empirical downscaling
techniques.



10.6.4 Inter-comparison of downscaling methodologies

An increasing number of studies comparing different downscaling studies
have emerged since SAR.  However, there is a paucity of systematic studies
that use common data sets applied to different procedures over the same
geographic region.  A number of articles discussing different empirical and
dynamical downscaling approaches (Giorgi and Mearns, 1991; Hewitson &
Crane, 1996; Wilby and Wigley, 1997; Buishand and Brandsma, 1997;
Rummukainen, 1997; Zorita and von Storch, 1997; Gyalistras et al., 1998;
Kidson and Thompson, 1998, Murphy, 1999a,b, von Storch, 1999b, Biau et al.,
1999) do present summaries of the relative merits and shortcomings of
different procedures. These intercomparisons vary widely with respect to
predictors, predictands and measures of skill. A systematic,
internationally coordinated intercomparison project would be useful.

The most systematic and comprehensive study so far is that one by Wilby et
al. (1998) and Wilby and Wigley (1997). They compared empirical transfer
functions, weather generators, and circulation classification schemes over
the same geographical region using climate change simulations and
observational data.  The study considered a demanding task to downscale
daily precipitation for six locations over North America, spanning arid,
moist tropical, maritime, mid-latitude, and continental climate regimes. A
suite of 14 measures of skill was used, strongly emphasizing daily
statistics. These included such measures as wet spell length, dry spell
length, 95th percentile values, wet-wet day probabilities, and several
measures of standard deviation.  Downscaling procedures in the study
included two different weather generators, two variants of an ANN-based
technique, and two stochastic/circulation classification schemes based on
vorticity classes.

The results prove to be illuminating, but require careful evaluation as
they are more indicative of the relative merits and shortcoming of the
different procedures, rather than a recommendation of one procedure over
another. In the validation phase of the study the downscaling results were
compared against the observational data, and indicated that the weather
generator techniques were superior to the stochastic/circulation
classification procedures, which in turn were superior to the ANNs.
However, the superiority of the weather generator when validated against
the observed data is misleading as the weather generators are constrained
to match the original data (Wilby and Wigley, 1997).  Similarly, the
improved performance of the circulation classification techniques with
regard to the ANNs is largely a reflection of the measures of skill used
and indicates the tendency of ANNs to over-predict the frequency of trace
rainfall days.  In contrast, when the inter-annual attributes of monthly
totals are examined the performance ranking of the techniques is
approximately reversed with the weather generators performing especially
poorly.

The results indicate strength by weather generators to capture the wet-day
occurrence and the amount distributions in the data, but less success at
capturing the inter-annual variability (the low frequency component).  The
important question with this procedure is thus how to perturb the weather
generator parameters under future climate conditions. At the other end of
the spectrum the ANN procedures performed well at capturing the low
frequency characteristics of the data, and showed less ability at
representing the range of magnitudes of daily events.  The
stochastic/circulation typing schemes, being somewhat a combination of the
principles underlying weather generators and ANNs, appear to be a better
all-round performer.

In application to GCM simulations of future climate, the procedures showed
some consistency with the ANN indicating the largest changes in
precipitation.  However, assessing the relative significance of the changes
is non-trivial, and at this level of inter-comparison the results of the
climate change application are perhaps more useful in a diagnostic capacity
of the GCM which appeared to show differences in the strength of the
precipitation-circulation relationship.

What is not evaluated in this study to any great degree is the range of
variance spanned by each technique. Addressing this issue Wilby et al.
(1998) and Conway et al. (1996) apply transfer functions to determine
wet/dry probabilities and then use a stochastic procedure for the magnitude
of precipitation, and in doing so capture some degree of the low frequency
and high frequency variance. Zorita et al (1995) and later Cubasch et al.
(1996) demonstrated that a suitably designed analog technique reproduces
storm interarrival terms well. Similarly, Hewitson (1998) span the range of
variance using an ANN transfer function to predict precipitation magnitude,
and then stochastically model the residual variance as a function of
atmospheric state.

An additional factor not yet fully evaluated in any comparative is that of
the temporal evolution of daily events.  In this respect the manner in
which daily events develop may be critical in some areas of impacts
analysis, for example hydrological modeling.  While a downscaling procedure
may correctly represent, for example, the number of rain days, the temporal
sequencing of these may be as important.

A number of analyses have dealt with the relative merits of non-linear and
linear approaches.  For example, Conway et al. (1996) and Brandsma and
Buishand (1997) use circulation indicators as predictors and note that the
relationships with precipitation on daily time scales are often non-linear.
 Similarly Corte-Real et al. (1995) effectively applied multivariate
adaptive regression splines (MARS) to approximate non-linearity in the
relationships between large-scale circulation and monthly mean
precipitation. However, the application of MARS to large volume daily data
may be more problematic (Corte-Real et al., 1995). Other non-linear
techniques are kriging and analogs, whose performance were compared by Biau
et al., (1999) and von Storch (1999). Kriging resulted in better
specifications of averaged quantities but too low variance, whereas analogs
returned the right variance but lower correlations. Also analogs can be
usefully constructed only on the basis of a large data set. It appears that
downscaling of the short-term climate variance benefits significantly from
the use of non-linear models. In particular, downscaling of daily
precipitation benefits appreciably from the ability to better capture
convective events. 

Most of the comparative studies mentioned above come to the conclusion that
techniques differ in their success of specifying regional climate, and the
relative merits and shortcomings emerge differently in different studies.
This is not surprising, as there is considerable flexibility in setting up
a downscaling procedure, and the suitability of a technique and the
adaptation to the problem at hand varies.


10.6.5 Summary and Recommendations

A broad range of statistical downscaling techniques has been developed in
the past few years. Users of GCM based climate and climate change
information may choose from a large variety of methods conditional upon
their needs. Weather generators provide realistic sequences of events. With
transfer functions statistics, like conditional means or quantiles, of
regional and local climate may consistently be derived from GCM generated
data. Techniques based on weather typing serve both purposes.

Downscaling means postprocessing GCM data; it can not account for
insufficiencies in the driving GCM data. As statistical techniques are
combining the existing empirical knowledge, statistical downscaling can
describe only links which have been observed in the past. Thus, it is based
on the assumption that presently found links will prevail under different
climate conditions. It may be, in particular, that under present conditions
some predictors appear less relevant, but become significant in describing
climate change. It is recommended to test statistical downscaling methods
by comparing their estimates with simulations with high-resolution
dynamical models. The advent of decades-long homogeneous atmospheric
re-analyses have offered the community many more atmospheric large-scale
variables as possible predictors.

Statistical downscaling requires the availability of long and homogeneous
data series, while the computational resources needed are small. Therefore,
statistical downscaling techniques are suitable tools for scientific
communities without access to supercomputers and with little competence in
process-based climate modeling. Often dynamical downscaling methods are
providing much more information than may be needed in a specific
application, so that resorting to the much simpler statistical techniques
may often be advisable. Furthermore, statistical techniques may relate
directly GCM derived data to impact relevant variables, like ecological
variables or ocean wave heights, which are not simulated by contemporary
climate models.

It is concluded that statistical downscaling techniques is many cases a
viable alternative to process-based dynamical modeling, and will remain so
in the future. 

--------------------------------------------------------------

echnique category: WG (weather generator), TF (transfer function), and  WT
(weather typing). Methods utilized in these categories:  (1) For WG: M =
Markov, SM = semi-Markov, DTM = discrete-time Markov, NHMM = nonhomogeneous
hidden Markov, LARS-WG, MED = mixed exponential distribution, CP =
conditional probability.   (2) For TF: PCA = principal component analysis,
CCA = canonical correlation analysis, CPMS = Climatological Projection by
Model Statistics, LR = linear/multiple regression, IR = inflated
regression, SWR = step-wise regression, MARS = multivariate adaptive
regression splines, CS = cubic splines, PR = polynomial regression, ANN =
artificial neural networks.   (3) For WT: CA = cluster analysis, SOM =
self-organizing map, EVD = extreme value distribution.
Predictor variables: SLP (sea level pressure); Z1, Z7, Z5 (1000-, 700-,
500-hPa geopotential heights); TH1 TH8 (1000-500, 850-500 hPa thickness);
VOR (vorticity); W (wind related); Q1, Q8, Q7, Q5 (1000-, 850-, 700- and
500-hPa specific humidity);  RH8, RH7, RH5 (850-, 700-, 500-hPa relative
humidity); CC (cloud cover); ZG, MG (zonal and meridional gradients of the
predictors). Predictands: T (temperature); Tmax (maximum temperature); Tmin
(minimum temperature); P (precipitation). Region is the geographic domain.
Time is the timscale of the predictor and predictand: D (daily), M
(monthly), S (seasonal), and A (annual). 


New abbreviations: NST: near surface temperature,TDS = temporal downscaling
based on Richardson-type WGSSD = statistical/dynamical downscaling

 Technique	Method	Predictor	Predictand	Region	Time	Author (s)
TF	PCA, CCA, IR: CPMS	SLP, TH8, Z5, RH8, RH5, W, K-index	Tmax, Tmin, P	5
USA stations	D	Karl et al., 1990
TF	LR	SLP, Z7 and their ZG & MG	T, P	32 stations in Oregon, USA	M	Wigley et
al., 1990
WG, WT	SM, CP	SLP	P	Stations in Germany	D	Brdossy and Plate, 1991
WG, WT	DTM	W, CC	P	Delaware River Basin, USA	D	Hay et al., 1992
TF	PCA, ANN	SLP, Z7, Z5	P	1 grid in Southeastern Mexico	D	Hewitson and
Crane, 1992
TF	PCA, CCA	SLP	P	Iberian Peninsula	S (DJF)	Zorita et al., 1992
TF	PCA, LR, IR	Z5, TH1	P, T	10 Nordic stations	M	Kaas, 1993a,b
TF	CCA	SLP	T	Central Europe	M(DJF)	Werner and von Storch, 1993
TF	CCA, LR	SLP	P	Iberian Peninsula	S (DJF)	von Storch et al., 1993
TF	PCA, PR, SWR	SLP	T	Continental USA	D	Hewitson ,1994
WG	NHMM, PCA	SLP	P	4 stations in Wash. St., USA	D	Hughes and Guttorp, 1994a
WG	NHMM, PCA	SLP, Z5	P	24 stations in Wash. St., USA	D	Hughes and Guttorp,
1994b
TF	PCA, LR, IR	Z5, TH1	P, T	10 Nordic stations	M	Jnsson et al., 1994
TF	LR, PCA, ANN		Snow pack	Colorado River Basin, USA	D	McGinnis, 1994
WT	EVD, analog	Tmax, Tmin	Tmax, Tmin	Several sites in the USA	D	Brown and
Katz, 1995
TF	PCA, regression	SLP, H500	P	Mediterranean stations	S	Jacobeit, 1994a,b
TF	PCA, CCA, LR	SLP	P	Iberian Peninsula	M	Noguer, 1994
TF	MARS, PCA	SLP	P	8 sites in Portugal	M (DJF)	Corte-Real et al., 1995
TF	PCA, LR, IR	Z5, TH1	P, T	10 Nordic stations	M	Jhannesson et al., 1995
W	PCA, CA	Z1	Tmax, Tmin, P	82 stations in New Zealand	D	Kidson and
Watterson, 1995
TF	LR	SLP, P	T	Mediterranean		Pautikof and Wigley, 1995
WG	PCA, analog, CART	SLP	P	Two regions in the USA	D	Zorita et al., 1995
TF	CCA, PCA	SLP	P	Stations in Romania	M (DJF)	Busuioc and von Storch, 1996
WT	SSD					Frey-Buness et al., 1995
WG	LR	VOR, W		Europe		Conway et al., 1996
WG	PCA, analog	SLP, Z7	P	Iberian Peninsula	D	Cubasch et al., 1996
TF	PCA, ANN	SLP, Z5	P	South Africa	D (DJF)	Hewitson and Crane, 1996
WT	SSD			Alps		Fuentes and Heimann, 1996
WT		Z7, Z5				Matyasovszky and Bogardi, 1996
WG, TF	LARS, MED, LR	SLP, P, Tmax, Tmin, solar  radiation	T, P	5 sites in
Europe	D	Semenov and Barrow, 1996
TF	CCA	SLP, NST	T,P	4 sites in the European Alps	M	Fischlin and Gyalistras,
1997
TF	PCA, regression	SLP, H500	P	Mediterranean stations	S	Jacobeit, 1996
TF	PCA, CCA	SLP	Sea level	Baltic Sea	M (DJF)	Heyen et al., 1996
TF	PCA, CCA	SLP	Sea level	Japanese coast	M (DJF)	Cui et al., 1995, 1996
	Cubic splines		P	Switzerland		Buishand and Klein Tank, 1996
WT		SLP, Z7, Z5, VOR, W	T, P	The Netherlands	D, M	Buishand and Brandsma, 1997
TF	PCA, CCA	SLP	Pressure tendencies	North Atlantic sites	M	Kaas et al. , 1996
TF	CS		P	Switzerland		Brandsma and Buishand, 1997
TF	CCA	T	Phenological event	Northern Germany		Maak and von Storch, 1997
TF	PCA, ANN	SLP, TH1, Z5, PNA	P	20 grids in NE Mexico and USA	D	Cavazos, 1997
WT	analog	Upper air fields	Snow	French Alps		Martin et al., 1997
TF	CPMS	SLP, Z5	Tmax, Tmin	2 sites: Spain and USA	D	Palutikof et al., 1997
TF	PCA, LR	SLP	Tmax, Tmin	Australia	D	Schubert  & Henderson-Sellers, 1997
	PCA			Switzerland	D	Widmann and Schr, 1997
WG, TF	ANN	Z, T, VOR	P	6 sites in the USA	D	Wilby and Wigley, 1997
TF	CPMS	SLP, Z5	Tmax, Tmin	2 sites: Spain and USA	D	Winkler et al., 1997
TF			Ecological variables			Dippner, 1997a,b
			Slope stability			Buma nd Dehn, 1998
WT						Enke and Spekat, 1997
TF	PCA, CCA	SLP	Storm surge quantiles	German Bight	M	Von Storch and
Reichardt, 1997
WG	NHMM	Atmospheric variables	P	West Australia	D	Bates et a., 1998
TF	ANN	Z1, Z7, Q1, Q7, Q5	P	Northeast USA	D	Crane and Hewitson, 1998
TF			Sea-level variability	Chinese coast	M	Cui and Zorita, 1998
WT	SSD			Alps		Fuentes et al., 1998
TF			Salinity	South of Germany		Heyen and Dippner, 1998
TF	PCA, SR	Z1, Z5, TH1, VOR, W	T, P	Stations in New Zealand	D	Kidson and
Thompson, 1998
TF	LR	SLP, VOR, W				Kilsby et al., 1998
WT				Southeast Spain	D	Goodess and Palutikof, 1998
TF	LR	SLP, W, VOR, T8, Q8, K-index	T, P	976 European stations	M	Murphy,
1998a, b
TF	PCA, LR	SLP	Tmax, Tmin	40 sites in southeastern Australia	D	Schubert, 1998
TF	ANN, LR	Z1, Z5	Tmax, Tmin	Iberian Peninsula	D	Trigo and Palutikof, 1998
TF	PCA, LR, ANN: RBF	Z8, Z5	T, P,  vapor  pressure	A station in Central
Europe	D	Weichert and Brger, 1998
WG, TF	ANN	SLP, Z5, T, VOR	T, P	6 sites in the USA	D	Wilby et al., 1998a, b
TF			Ecol.ogical variables			Kroencke at al., 1998
TF			Ecol.ogical variables			Heyen et al., 1998
TF	CCA	SLP, NST	T,P	40 sites in the European Alps		Gyalistras et al., 1998
TF	PCA, kriging, analog		P			Biau et al., 1999
TF	PCA, redundancy an.	SLP	Wave hieghts quant.	Siite in North Atlantic	M
WASA, 1998
TF	Nonlinear fit	Regional temperature, hieght	Snow coverage	European Alps
Hantel et al., 1998
			P => Landslide	Southeast France		Buma and Dehn, 1999
WT	SSD		Thunderstorms	Southern Germany	D	Sept, V., 1998
		SLP	P => Landslide	French Alps		Dehn and Buma, 1999
TF	PCA, CCA	SLP	P	14 stations in Romania	M	Busuioc et al., 1999
TF, WT	ANN, SOM	SLP, TH1, Q0, Q7	P	20 grids in NE Mexico and USA	D (DJF)
Cavazos, 1999
WT	Analog	SLP, NST	Landslide activity	Italian Alps		Dehn, 1999a,b
						Hewitson and Crane,  1999
WT	SSD			Alps		Heinmann and Sept, 1999
WG, WT		Z7	T, P	12 sites in eastern Nebraska	D	Mearns et al., 1999
TF	LR	Z8, Z5, T8, T5, RH8, RH5, W	T	8 sites in the USA	D	Sailor and Li, 1999
WG		P	P		D	Wilks, 1999
TF	PCA, CCA	SLP	Sea level quantiles	North Sea coast	M	Langenberg et al., 1999
	Cubic splines		P	Switzerland		Buishand and Brandsma
WT	PCA, analog		P		D	Zorita and von Storch, 1999
WT	PCA, CART					Schnur and Lettenmaier, 1999
TF	CCA, redundancy analysis	SLP	T, seaa level, wave hieght, salinity, wind,
run-off	Polish coast	D/M	Mietus, 1999
TF,WG	CCA, TDS	SLP, NST	22 monthly weather statistics	2 sites in the
European Alps	M	Riedo et al., 1999
TF	Multiple regression	NST,SLP,u700,u200,v700,v200	T, max, min	Central
Argentina	M	Solman and Nuez, 1999
TF	CCA	Z500	P	16 stations in the European Alps	M (DJF)	Burkhardt, 1999
TF	CCA, SVD	NST,SLP, z500 and others	T, P and others	Norway	M(J)	Benestad ,
1999a,b
TF	Multiple regression	Various tropospheric variables	Local weather
Norwegian glaciers	D	Reichert et al., 1999
WT	SSD		P	European Alps	D	Fuentes and Heimann, 1999
WT	SSD		T, P	European Alps	D	Heimann and Sept, 1999
WT	analog	SLP, T	P	Australia		Timbal and McAvaney, 1999
WG	NHMM		P	Stations in the USA	D	Bellone et al., 1999
TF	Analog/resgression		P,NST	Iberian Peninsula		Boren et al., 1999,
Ribalaygua et al., 1999
----------------------------------------------

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Hans von Storch
Institute of Hydrophysics, GKSS, Geesthacht, Germany

