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JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY
VOLUME 49
Spatial Predictions of Extreme Wind Speeds over Switzerland Using
Generalized Additive Models
CHRISTOPHE ETIENNE, ANTHONY LEHMANN, AND STÉPHANE GOYETTE
Climatic Change and Climate Impacts Group, Institute for Environmental Sciences,
University of Geneva, Geneva, Switzerland
JUAN-IGNACIO LOPEZ-MORENO
Instituto Pirenaico de Ecologı´a, CSIC, Campus de Aula Dei, Zaragoza, Spain
MARTIN BENISTON
Climatic Change and Climate Impacts Group, Institute for Environmental Sciences,
University of Geneva, Geneva, Switzerland
(Manuscript received 3 March 2009, in final form 14 April 2010)
ABSTRACT
The purpose of this work is to present a methodology aimed at predicting extreme wind speeds over
Switzerland. Generalized additive models are used to regionalize wind statistics for Swiss weather stations
using a number of variables that describe the main physiographical features of the country. This procedure
enables one to present the results for Switzerland in the form of a map that provides the 98th percentiles of
daily maximum wind speeds (W98) at a 10-m anemometer height for cells with a 50-m grid interval. This
investigation comprises three major steps. First, meteorological data recorded by the weather stations was
gathered to build local wind statistics at each station. Then, data describing the topographic and landscape
characteristics of the country were prepared using geographic information systems (GIS). Third, appropriate
regression models were selected to make spatially explicit predictions of extreme wind speeds in Switzerland.
The predictions undertaken in this study provide realistic values of the W98. The effects of topography on the
results are particularly conspicuous. Wind speeds increase with altitude and are greatest on mountain peaks in
the Alps, as would be intuitively expected. Relative errors between observations and model results calculated
for the meteorological stations do not exceed 30%, and only 12 out of 70 stations exhibit errors that exceed
20%. The combination of GIS techniques and statistical models used to predict a highly uncertain variable,
such as extreme wind speed, yields interesting results that can be extended to other fields, such as the assessment of storm damage on infrastructures.
1. Introduction
Wind storms can generate severe damage to infrastructure and therefore lead to large economic losses (SwissRe
2007; MunichRe 2008). In the past two decades, two
major storms affected Switzerland. The February 1990
‘‘Vivian’’ storm resulted in severe damage in the Alps
(Schüepp et al. 1994) and economic losses related to
Corresponding author’s address: Christophe Etienne, Climatic
Change and Climate Impacts Group, Institute for Environmental
Sciences, University of Geneva, Battelle/D, Chemin de Drize 7,
1227 Carouge, Geneva, Switzerland.
E-mail: [email protected]
DOI: 10.1175/2010JAMC2206.1
Ó 2010 American Meteorological Society
infrastructure (Schraft et al. 1993). In December 1999, the
‘‘Lothar’’ storm caused even higher damage in France,
Germany, and Switzerland (Bresch et al. 2000; MunichRe
2001), with total economic losses estimated at about
US$12 billion.
Damage functions have been investigated in the past
two decades to assess the damage to buildings resulting
from wind storms (Heneka and Ruck 2004). Losses related to storm events can be assessed through empirical
formulas that take into account variables describing the
characteristics of a windstorm event, such as mean or
maximum wind speeds (Dorland et al. 1999; Unanwa
et al. 2000; Huang et al. 2001) or storm duration (Schraft
et al. 1993). The most important parameter remains
SEPTEMBER 2010
ETIENNE ET AL.
wind speed at the standard anemometer height of 10 m
(maximum wind gusts) that is often the dominant factor
leading to damage (Heneka and Ruck 2004). Gust values
are frequently normalized as a function of local climate
conditions, essentially taking into account relative wind
speeds rather than absolute wind speeds to assess storm
damage (Klawa and Ulbrich 2003; Pinto et al. 2007). The
underlying hypothesis is that in wind-prone areas, buildings (and also forests) are generally well adapted to
conditions where strong winds are frequent; as a result,
the vulnerability of these regions to strong wind events is
generally less than in other regions where these events
are rare. The 98th percentile of daily maximum wind
speed data (W98) is a key parameter that provides information on local wind conditions; in addition, W98 is
often used as a threshold in empirical formulas that attempt to translate the damage caused by wind storms into
monetary terms (Klawa and Ulbrich 2003).
In mountain areas such as the Alps, wind flows show
high spatial variability. As discussed by Barry (1992) or
Mortensen and Petersen (1998), topography has a strong
influence on the estimation of wind speeds. Ridge crests,
deep valleys, or other irregular landscapes are important
orographic features capable of exerting an influence on
boundary layer flows. Many local climate phenomena as
well as natural channeling effects or thermally induced
circulations are found within the alpine domain. Wind
flows can be very strong at one location but very weak in
a neighboring valley, thus exhibiting major discontinuities within small areas. These discontinuities make the
spatial interpolation of wind speed values difficult (Tveito
et al. 2008). Working with wind speeds within the atmospheric boundary layer always remains a challenge, since
it is a highly fluctuating and nonlinear element of atmospheric flows, where the variability in both time and space
can be high. Because of many turbulence effects and the
presence of numerous roughness elements (Stull 1988),
modeling wind and extreme events, as well as attempting
to regionalize wind speed and direction remains a difficult
task, even with the help of numerical models (Goyette
et al. 2001). However, a number of methods have been
developed helping to address the issues related to the
regionalization of wind speeds (Porch and Rodriguez
1987; Palomino and Martin 1995; Nielsen 1999; Schaffner
et al. 2006). Many correction factors related to topographic features, such as slope angles, altitude, or landform characteristics, have been added to the calculation
of wind speeds in order to adjust the results and thus
enable these to be in better agreement with observations.
There have been several studies aimed at assessing wind
speeds over Switzerland (Jungo et al. 2002; Schaffner et al.
2006), including within the topographically complex Alpine domain (Schaffner et al. 2006), in other regions
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(Troen and Petersen 1989; Frank and Landberg 1997;
Wei et al. 2006) or for specific types of surfaces (Dellwik
et al. 2005; Reutter et al. 2005). There has even been an
attempt at interpolating wind over the entire globe by
Paulo et al. (2000). The resulting maps provide wind
velocities at different altitudes (10, 50, 100 m, or more).
Past studies of the spatial distribution of wind speeds
have used interpolation methods with the help of correction factors related to elevation or slope values
(Schaffner et al. 2006), or statistical relationships between gust factors and mean wind speeds (Jungo et al.
2002). Unlike these past studies, this paper focuses on
the maximum wind speeds rather than the mean wind
speeds, in order to pave the way for future work on
damage costs related to severe wind storms.
The method presented in this paper discusses a new
approach to regionalize wind speeds measured at weather
stations distributed throughout Switzerland. It aims to
test the use of spatial prediction derived from state-ofthe-art statistical models in the field of meteorological
applications. A regression-based model is proposed that
is capable of predicting W98 values in the complex terrain characteristic of Switzerland, based on variables
that describe topographic characteristics (Barry 1992;
Mortensen and Petersen 1998). One of the objectives of
the present work is thus to investigate to what extent wind
velocities can be explained at the local scale by surrounding landscape characteristics. This research also
assesses a regression model for wind analysis, assuming
that the local relationship between the predicted pattern
(e.g., wind speed) and its direct or neighboring environment is stronger than the relationships with measurements obtained from other, more distant weather
stations.
Statistical models such as generalized additive models
(GAMs; Hastie and Tibshirani 1990) have been widely
used in the past for a range of scientific domains (Lehmann
et al. 2002a). GAMs represent a nonparametric extension
of generalized linear models (GLMs) that themselves are
an extension of multiple linear regression models (MLR).
Just as in the case of GLMs, GAMs can fit response data
following Gaussian, binomial, Poisson, or gamma statistical distributions. However, smooth functions rather than
parametric terms are used to estimate response curves in
GAMs (Yee and Mitchell 1991). These smooth functions
provide a better fit to environmental fields than linear or
parabolic curves, as several other response shapes are
commonly observed (e.g., logarithmic, plateau, bimodal).
The statistical tool generalized regression analysis and
spatial predictions (GRASP) is used for this study, allowing both an investigation of spatial predictions and a link
with geographic information systems (GIS; Lehmann et al.
2002b). This paper applies these statistical methods to
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FIG. 1. Map of Switzerland, showing the Jura Mountains along the northeast border and the
Alps in the south. The river Rhone basin is located in the Canton of Valais. The Anetz weather
stations and the main lakes are also shown.
regionalize meteorological data over heterogeneous terrain in Switzerland, using fine GIS layers that describe the
topographic, geographic, and landscape characteristics of
the country.
GIS applications yield valuable information that helps
improve statistical models and their derived spatial predictions by considering data layers that are of relevance
to explain the meteorological phenomena under study.
With the help of digital elevation models (DEMs), GIS
tools enable the development of detailed data layers that
accurately describe the complex terrain of Switzerland.
Slope and curvature layers are often employed, but a
combination of these layers through a powerful GIS extension (Weiss 2001; Jenness 2006) leads to a precise
classification of the terrain according to topographic
characteristics, distinguishing high ridges from hills, deep
and shallow valleys or plains. This fine representation of
complex terrain is of key importance when dealing with
wind characteristics.
Results provide reliable wind data over the country,
allowing previous work on past heavy windstorm events or
climate extremes (Beniston 2007). In addition, the method
can also be adapted to predict mean wind speeds or return
periods (Johnson and Watson 1999; Palutikof et al. 1999;
Della-Marta et al. 2009), and can be investigated at different resolutions. Besides evaluating windstorm damage,
this work can lead to other applications, such as the
evaluation of the potential for wind-generated energy
production (Schaffner and Gravdahl 2003).
In the following sections, an overview of the different
GIS procedures is provided, followed by a description of
the meteorological and physiographical data. In addition, a detailed explanation of the important preparation steps is given, with the resulting maps for different
regions of Switzerland. Following the compilation of this
information, various model selection methods have been
tested using the variables by separately including different groups of predictors. The main statistical model selection results are listed, from which daily maximum wind
speeds have been predicted and wind maps have been
created. Finally, results are discussed and an outlook for
future research is presented.
2. Study area
Switzerland is a small country in central Europe covering approximately 41 000 km2 that stretches roughly
350 km from east to west and 220 km from north to
south (Fig. 1). The landscape is extremely diversified
and irregular, with a relatively low and narrow mountain
range in the north (the Jura), the very high mountain
peaks of the Alps that often exceed 4000 m above mean
sea level in the south, and a relatively flat area (the Swiss
Plateau) stretching from east to west between the two
mountain ranges. South of the Alps begins the Po valley,
which is the lowest region of the country. As mountain
areas occupy more than 60% of the surface of the
country, the altitudinal gradient is very high. The Alps
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act as a climate barrier between northern Switzerland,
which is under the influence of both Atlantic and continental air masses, and southern Switzerland, where
the Mediterranean Sea exerts a substantial influence.
Schüepp (1978) has compiled over 40 different climate
types over the Alps. Furthermore, winds can be determined by synoptic situations as discussed by Jungo
et al. (2002); most of the important damaging historical
storms have occurred during the winter period (Pfister
1999; Alexandersson et al. 2000).
3. Data and methods
a. Weather stations network
Figure 1 shows the distribution of the automatic network of the Anetz (Automatisches Netzwerk) meteorological stations, managed by the Swiss weather service
(MeteoSwiss). The network provides reliable and quality checked weather data in digital form (Bantle 1989;
Begert et al. 2005). Seventy stations have been measuring
daily maximum wind speeds since 1981 and were used for
this study. Wind speeds are recorded every 3 s, and mean
and maximum wind speeds are archived each 10 min;
daily maximum wind speeds were recorded at each station for the 1981–2005 period. The W98 values were then
calculated from the listed data for each Anetz station,
providing information on the different wind conditions
over the country.
b. Topographic data
All physical factors likely to disturb wind flows need
to be included in the regression analysis and accurately
represented by GIS layers. The main input datasets was
the DEM of Switzerland at a resolution of 50 m provided by the Swiss Federal Office of Topography (more
information available online at www.swisstopo.ch). Using
a GIS function tool (Weiss 2001; Jenness 2006), relevant
data layers at different scale levels were generated for the
study.
From the original DEM, various elevation-related parameters were calculated, each of them at the same resolution of 50 m. First, surface elevation, which has an
obvious influence on wind speeds (Tennekes 1973; Miller
and Davenport 1998; Winstral et al. 2009), was estimated
at different spatial scales that may influence flow characteristics. To take into account the surrounding topographic characteristics, different maps were created by
considering all elevation values in a radius of 100 m,
200 m, 500 m, 1 km, and 2 km respectively. For example,
each 50-m cell of the dem500 layer reflects mean elevation values within a radius of 500 m.
Slopes and curvature (including profile and plane
curvature) were also calculated to provide further
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topographic information, and the rescaling steps were
carried out for each. Curvature describes the shape of the
ground, whether the land is convex or concave, whereas
plane and profile curvature describe the curvatures perpendicular and transverse to the mountain, respectively.
Wind flows are affected by terrain undulations, which
explain why all mountain shapes need to be taken into
account to accurately describe wind speeds. Effects of
curvature on wind flows have been pointed out by
McKee and O’Neal (1989); slope influence was assessed
by Petkovsek and Hocevar (1971), McNider and Pielke
(1984), and Smith (1985). In addition, the orientation of
the mountains was considered, as the main airflow directions are likely to be related to the major morphological characteristics. Orientation angles were transformed
using sine and cosine functions, leading to two separate
variables—northings and eastings—again assessed at different scale levels.
Topographic characteristics of the surface have a
marked influence on the wind velocity (Barry 1992).
Canyon shapes, midslope areas as well as high ridges can
disrupt wind flows and thus explain channeling effects
(Kaufmann and Weber 1998). Studies showing the importance of mountain geometry on wind speeds were
made by Nappo (1977), Steinacker (1984), and Vergeiner
and Dreiseitl (1987). Based on the DEM and the slope
map at 50 m, simple procedures can lead to a classification of the surface into several landform categories
which can then be used as inputs for regression models.
This procedure creates topographic position indices
(TPI) for each cell of the DEM (Weiss 2001; Jenness
2006). TPI compares the cell elevation with the average
cell elevation in the neighborhood; positive differences
imply that the position is on a hill, whereas negative values
would rather describe a valley. Null values represent either flat areas or midslopes.
For this work, two TPIs have been constructed with
mean altitudes located within a 250-m and 2-km radius,
respectively. These two indices are compared in a first
classification step. For instance, a high TPI value in a small
neighborhood associated with a low TPI value in a larger
neighborhood would correspond to a small hill located
within a larger valley. This first step may not be sufficient
for the analysis, as two different surfaces may lead to the
same TPI. To avoid this confusion, the results are combined with the slope values. This combination produces
the final landform map that describes the topographic
characteristics of Switzerland according to 10 different
categories. Further information as well as a more detailed
explanation on the algorithms used in this procedure can
be found in Jenness (2006).
The final landform map can be seen in Fig. 2. An
overall view of Switzerland is shown, and also an
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FIG. 2. (top) Classification of landforms into 10 categories for Switzerland. (bottom) An example is shown
for the Aletsch Glacier.
enhanced view over the Aletsch Glacier in the Alps. In
the large-scale view, a clear difference can be observed
between the mountain regions and the Swiss Plateau.
The classification procedure yields the different shapes
of the topography, by distinguishing between the uppermost mountain ridges and the adjoining upper slopes
and upland drainages. The tool also highlights the shallow valleys and the open slopes beneath the high peaks,
highlighting the shape of the mountain. It is thus seen
that, starting from a basic DEM associated with a slope
layer, simple algorithms can lead to a fine classification of
highly heterogeneous terrain. This landform classification
map will be further introduced as a factor type variable in
the regression procedure by sampling information around
weather station locations.
c. Sampling physiographical conditions at the
meteorological stations
Values of all the physiographical variables mentioned
above and prepared for the study (Table 1) were sampled by reading the information found for each Anetz
station on a 50-m grid. To describe the landform characteristics, 10 categories were originally used. Unfortunately, these 10 categories are not all represented
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TABLE 1. List of all the maps prepared at different resolutions
(XX 5 50, 100, 200, 500, 1000, 2000 m) and used as predictors in the
regression models to estimate wind speed.
Predictor name
Description
Resolutions (m)
Data class
demXXm
cuXXm
cuXXpl
cuXXpr
sloXXm
eaXX
noXX
ldXXm
Altitude
Curvature
Plane curvature
Profile curvature
Slope
Easting
Northing
Landform
classification
XX 5 50–2000
XX 5 50–2000
XX 5 50–2000
XX 5 50–2000
XX 5 50–2000
XX 5 50–2000
XX 5 50–2000
50
Numeric
Numeric
Numeric
Numeric
Numeric
Numeric
Numeric
Factor
within the Anetz network, and thus work was conducted
for just 7 categories. Table 1 lists all the variables at the
different scales that were introduced in the regression
process.
d. Generalized regression analysis and spatial
predictions
As GAMs have been previously used in different
environmental fields (Lehmann et al. 2002a), they were
employed in this work to predict wind speeds using the
GRASP extension tool. GRASP is a statistical package
that has been developed to automate the production of
spatial predictions from point observations using GAMs
(Lehmann et al. 2002b), and it can be used in the S-Plus
software package or as an extension for the statistical
software package known as R. This tool is made up of
a number of functions designed to facilitate regression
analysis aimed at spatial predictions, and is associated
with a user-friendly graphical interface. As GRASP was
originally created to predict the spatial distribution of
vegetation (Zaniewski et al. 2002; Maggini et al. 2006) or
animal species (Castella et al. 2001; Ray et al. 2002; Luoto
et al. 2006), this tool has been adapted from its original
use in spatial predictions in ecology to predictions in
meteorology. Indeed, GRASP is a generalized method
for predicting any point observations from statistically
and spatially related explanatory variables, and thus can
be used in a range of environmental fields.
The true challenge in selecting a regression model remains a complex issue (Burnham and Anderson 2002).
These authors have listed the selection methods in three
categories: 1) optimization of Akaike’s information criterion (AIC) or Bayesian information criterion (BIC), 2)
tests of hypotheses (chi-square and F tests), and 3) ad hoc
methods. The AIC (Akaike 1973) relies on an empirical
log-likelihood function that assesses the relative distance
between the fitted model and the observed data (Burnham
and Anderson 2002). The log-likelihood value is penalized
by the number of parameters in the fitted model, favoring
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models with fewer selected predictors. As for AIC, BIC is
also penalized by the number of observations (Schwarz
1978). Statistical tests such as chi square or F help to understand the consequences of including or excluding
a term from the model.
A cross-validation is a frequently used solution for
a model selection (Stone 1977; Maggini et al. 2006). The
main advantage of this procedure is that no other observation dataset is required for the model validation.
Other datasets are usually rare and, if available, are generally used directly for the analyses (Araùjo et al. 2005).
The cross-validation process creates random subsets of
the main dataset to validate the model results (Lehmann
et al. 2002b) and includes all the available data in the
modeling process. The K-fold cross validation (Franklin
et al. 2000) and the bootstrap technique (Efron and
Tibshirani 1993; Guisan and Harrell 2000) are considered as the most interesting compromise, since they assess model stability without any loss of information.
e. Model selection steps
For this analysis, the W98 data calculated from the
70 meteorological stations was fitted to a Poisson distribution because of the skewed shape of its strictly positive
distribution (also tested by the chi-square goodness-of-fit
test). This assumption implies that only positive values of
wind speeds can be predicted.
In the context of this analysis, correlation between
variables must be taken into account, as two variables
might lead to the same result (Lehmann et al. 2002b). To
address this issue of orthogonality, maximum correlation between variables was set to 0.8 for all the selection
tools (Leathwick et al. 2005, 2006). Beyond this threshold, one of the two correlated variables is automatically
removed from the selection.
Several model selection methods were tested using
different sets of candidate variables. Available selection methods in the GRASP package (AIC, BIC, and F
and chi-square tests, as well as cross validation) were
tested on several groups of variables (Table 2), and the
results were analyzed for each method through validation
statistics: correlation and cross-correlation coefficients.
In all cases, stepwise procedures were used for the selection of significant predictors, with a backward direction
for the cross-validation method.
Some of the main results are described in this paper
and only one ‘‘best’’ model is fully detailed. In fact the
notion of best model is fairly subjective with so many
potential predictors. It is of course possible to fit a wide
range of models with all possible combinations of variables. The general rule in regression analysis is to avoid
overfitting the data with too many variables. The best
way to avoid overfitting is to cross validate each model
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JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY
TABLE 2. List of the five different groups of variables that were
tested in the regression process.
Group
1
2
3
4
Description
All
50 m
2 km
Sort
All of the variables are included in the procedure
Local data at 50 m
Large area data within a 2-km radius
Variables were sorted by their correlation
to the W98 and their autocorrelation values
5 Model 1 km A subjective search through the variables to
use in the GRASP procedure in order to find
the best model; data are within a 1-km radius
from the simpler one to the more complex one, and to
keep the model that exhibits the best cross-validated
statistic (Maggini et al. 2006). Cross validation indeed
allows testing the stability of a model. In this study, the
final model that was chosen was one with a high correlation coefficient and that included variables that were
physically coherent.
The first step is related to the variable selection,
namely to answer the question as to which of the 43
variables should be included in the GRASP procedure.
One can work with all the variables, or focus only on
certain categories. In the present analysis, the study was
investigated with the five groups of variables shown in
Table 2. The idea behind these diverse groups is to investigate the influence of different variables on the wind
flows. The first group of variables takes into account
those without any previous manual selection (group 1).
It allows evaluating the manner in which GRASP handles the entire list and which variables are selected by
the model. Working with the local data at 50 m (group 2)
provides information on the impact of the ground characteristics on the wind speeds in the immediate neighborhood; whereas the 2-km group analyzes the influence
of the surroundings (group 3). Another possibility is to
sort the predictors by selecting variables from the list
related to both their correlation with the original W98
sample data and their autocorrelation (group 4). At each
step, the variable most correlated to the original W98
data is selected, and all other variables that have a correlation coefficient greater than 0.8 are removed. This
sorting results in a list of 15 variables. The final group
represents a subjective selection from the original list
(group 5), obtained from several tests that were made
with different groups of variables.
4. Results and discussion
a. Model selection
Table 2 lists the five groups of predictors that were
tested with the different selection methods. The first four
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groups showed no substantial result, as no convincing
model was found, either because the selected variables
were unsatisfactory, as no clear physical explanation
could be derived, or because the correlation coefficients
were unsatisfactory. A new attempt was made only with
the variables at 1 km. At this scale level, information on
the behavior of the variables is detailed in a midscale
neighborhood, which roughly corresponds to the mean of
the spatial scales chosen for the analysis. Because they
were rarely included in the models and most of the time
were removed from the selection methods, the northing
and easting predictors were excluded from final models;
these variables clearly fit better when taking into account
wind directions in the analysis. Therefore, the work was
conducted here with the following predictors: dem1km,
cu1km, cu1kmpl and cu1kmpr, slo1km, and ld2km (see
below for definitions; group 5 of Table 2). First attempts
with these variables gave interesting results, but the
landform predictor was consistently removed from the
model. As the landform characteristics were considered
to be the most influential parameter on the wind flow,
that variable was forced to be included in the model selection.
Table 3 lists the results from the different selection
tools (AIC, BIC, F, chi square, and cross validation)
applied to predictors of group 5. The model arising from
the cross-validation selection method was chosen for the
prediction of wind speeds. Apart from the landform
(ld2km) whose presence was forced in the model, three
variables were included in the model: slope (slo1km),
profile curvature (cu1kmpr), and altitude (dem1km).
This cross-validation model resulted in a Pearson’s correlation coefficient of 0.89 between observed and predicted values and a cross-correlation coefficient of 0.77
(Table 3). Correlation coefficients between the four selected predictors were all under the chosen threshold
value of 0.8.
Figure 3 shows the response curves for each of the four
selected predictors included in the model. The range of
values of the different predictors is given on the abscissa,
while the sensitivity of the model is plotted on the ordinate: this is represented on the scale of the linear
predictor before transformation by the inverse response
function.
Figure 3d emphasizes the sensitivity of the model to
altitude. As expected, wind speed values clearly increase
with altitude. The curve decreases slightly toward the end,
probably as a result of the lack of high altitude data, since
only two weather stations are located above 3000 m. Below 1500 m, wind speeds exhibit a relatively low sensitivity
to elevation. A few weather stations at altitudes of roughly
1000 m in the Alps exhibit low W98 values, because they
are located in sheltered valleys: these particular stations
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TABLE 3. Results obtained by different selection methods presenting the resulting model formula, the correlation between observed
and predicted values (COR), the cross-validated correlation (CVCOR), the percentage of explained deviance* (D2), and the number of
DFU.
Method
Selected predictors
COR
CVCOR
D2
DFU
AIC
BIC
F ( p , 0.05)
Chi square ( p , 0.05)
Cross validation
ld2km 1 dem1km
ld2km
ld2km 1 dem1km
ld2km
ld2km 1 slo1km 1
cu1kmpr 1 dem1km
0.85
0.79
0.85
0.79
0.89
—
—
—
—
0.77
0.72
0.63
0.72
0.63
0.77
10
6
10
6
18
* Deviance is a measure of deviation for GAMs, in a similar way that standard deviation is for linear regression models.
explain the flat response curve below 1500 m seen in
Fig. 3d. Above 1500 m, the weather stations are less
sheltered, thus explaining the sudden increase of wind
speeds. Uncertainties are seen to grow as altitudes increase, since points are more scattered in higher zones.
Surprisingly, slope shows an opposite trend, as wind
speeds decline when the slope increases (Fig. 3b). The
opposite could have been expected, since steep slopes
are more likely to be situated in elevated mountain
areas, leading to high wind speeds. However, because
shallow slopes represent more open areas, where wind
flows are less affected by obstacles, wind speeds can
indeed be higher than in hilly zones where many discontinuities are present.
Land shapes also have an influence on the results.
Figure 3a shows that categories do not seem to have an
important effect on the flows, except the far right category, which corresponds to mountain tops or high ridges.
Wind speeds on elevated peaks are higher than elsewhere, which logically corresponds to field observations
where strong winds are indeed measured close to mountain tops.
The final predictor selected is more delicate to interpret (Fig. 3c). Profile curvature describes the shape of
mountains slopes; that is, whether they are convex or
concave. Negative values indicate that the surface is upwardly convex at that cell, while positive values imply
that the surface is upwardly concave. Zero values indicate
that the side surface of the mountain is flat, therefore that
the slope is constant. Convex zones (negative values, on
the left) lead to higher wind speeds. Concave shapes are
less represented in the dataset, but the trend seems to
show increasing or constant values. In the middle, which
corresponds to flat (linear) slopes, the effect on flows is
close to neutral. Negative values of profile curvature correspond to upward convex forms, which relate to hills or
mountain tops. It is therefore coherent to find higher wind
speeds where negative curvature values are calculated,
because wind speeds are indeed higher over mountain
tops. On the contrary, positive values match with concave
shapes; that is, valleys. In these areas, wind speeds are
more likely to be low, unless there are some channeling
effects that are difficult to predict. In convex areas, two
situations can be observed: either high wind speeds due to
channeling effects, or low wind speeds because the area is
sheltered. Although few stations are located in concave
zones, the right side of Fig. 3c shows important variability,
which may indicate the different effects of concavities.
Analysis of values plotted on the ordinate suggests that
wind speeds are more sensitive to the curvature and the
slope variables than to landform and altitude.
b. Spatial predictions
Spatial predictions of wind speed were produced from
the selected model. Bootstrap techniques resulted in 200
predicted maps of W98 values, from which a mean value
was calculated to produce the final W98 map.
Bootstrap methods described in Efron and Tibshirani
(1993) enable to assess model uncertainty without the
need of additional data (Guisan and Harrell 2000). From
the original sample, random subsamples are created and
models are built from these different samples, leading to
as many maps as samples drawn. Finally, mean and
standard deviation values can be calculated on the basis
of a cell-by-cell analysis.
The W98 results present a bell-shaped curve with
a mean around 21 m s21 and a standard deviation of
roughly 43 m s21. A first appraisal shows a clear influence
of the topography on the results, as the mountain areas
are clearly taken into account in the process. Highest
values are in the Alpine region, while low results are
mostly located in the flat topography of the Swiss Plateau
or within deep valleys. In the Jura Mountains, wind
speeds are also fairly high, but lower than in the Alps.
Wind speeds derived from the methods discussed
above range from 10 to 50 m s21 (Fig. 4). A few values
reach spurious wind speeds of up to 150 m s21. Such
errors are linked to extreme negative profile curvature
values; as can be seen in the response curve, low curvature values have a positive impact on wind speeds, and
values have been extrapolated in this case, leading to
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JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY
VOLUME 49
FIG. 3. Response curves of selected model for the different predictors: (a) landform, (b) slope, (c) profile curvature,
and (d) altitude. Solid lines represent the model fit. Dashed lines represent upper and lower pointwise doublestandard-error curves.
unrealistic wind speed results. Furthermore, these high
values are all located over high peaks in the Alps. An
upper threshold wind speed of 50 m s21 has been introduced in order to avoid these problems of extrapolation. This value is a reasonable threshold since out of
nearly 20 million cells, only two exceeded 100 m s21,
and less than 0.03% of these cells were above 50 m s21.
In the canton of Valais, the lowest values of W98 are
found in narrow valleys. In the main valley of the canton
(the Rhone valley), which is wider but also lower in altitude, the map shows higher values. These results correspond to observations, as strong winds can occur in
wide valleys, but flows have more difficulty in entering
smaller or more remote valleys.
Similar conditions can be observed to the north in the
Jura, which is a lower mountain range with more open
areas. In these wide and open zones, high W98 values are
modeled. Again, as the valleys become narrower, values
decrease because strong winds rarely flow through narrow
valleys. On the mountain tops, wind speeds are at their
maximum, as for the Alps. When comparing the mean of
the W98 values within the 1000–1500-m altitude range
in the Jura and the Alps, the Jura exhibit higher values.
This difference is explained by the landscape parameter,
where the elevation range corresponds mainly to ridge
crests in the Jura but to high valleys or U-shaped
valleys in the Alps. The landform variable has an evident influence on the wind speed distributions, as the
valley shapes are clearly important in the model predictions.
Over all lakes, fairly uniform values on the order of
20 m s21 were modeled. The very small wind speed differences between the lakes are due to the elevation, but the
altitude variable does not seem to contribute sufficiently
to make a significant difference in W98 over Swiss lakes.
The standard deviation map was created by analyzing
the 200 bootstrap map results, calculating the grid-by-grid
standard deviation. Over Switzerland, minimum standard
deviation values were found around 0.46 m s21, while
some values exceeded 10 m s21. Mean values over the
country were, however, roughly 2 m s21. The highest
values are found in the Alps, in the high altitudes zone.
Low standard deviations are found over the Swiss Plateau, and also over the lakes. As explained above, values
for most of the lakes are similar and thus standard deviations are very low.
c. Model accuracy
Figure 5 displays the predicted wind speeds versus
the observations at the 70 Anetz weather stations. The
graph shows a large group of wind speed values on the
left, while only a few are over 30 m s21. The regression
SEPTEMBER 2010
ETIENNE ET AL.
1965
FIG. 4. Mean spatial prediction obtained from bootstrapped models. (top) The W98 over Switzerland, and
(bottom) a zoom of the Aletsch Glacier. Values are in meters per second.
slope is therefore determined by the values exceeding
30 m s21. On the left graph, lowest predicted values and
the ones over 25 m s21 seem to follow a positive trend;
whereas, no significant tendency can be observed for
values between 20 and 25 m s21.
The validation scattered graph on the right gives a
Pearson’s coefficient of R2 5 0.79. The cross-validation
graphic confirms that model results are robust, as a cross
correlation coefficient of R2 5 0.59 has been determined. As the distribution of the data does not fit perfectly to a normal distribution, calculations other than
the Pearson coefficient were made for a quantitative
validation of the results (Table 4). The Spearman rank
correlation coefficient was calculated to assess errors, as
well as the RMSE. The reliability index (RI) quantifies
the average factor by which model predictions differ
from observations (Leggett and Williams 1981), whereas
the mean average error (MAE), Willmott’s index of
agreement (D; Willmott 1982) and the modeling efficiency (MEF) are good indicators of goodness of fit
(Mayer and Butler 1993). Values of the listed indicators
confirm that the model functions correctly, but it does
not seem to explain all situations. Furthermore, a measure of the bias can be assessed when looking at the
slope and intercept of best-of-fit line equations shown
on Fig. 5.
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JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY
VOLUME 49
FIG. 5. Scatterplots of model predictions and observations at the Anetz stations. (left) The scatter graph shows the
correlation for the cross-validation selection, and (right) the result for the validation. On both graphs, the line of best
fit and its equation are shown (full line), as well as the 1:1 line (dotted line).
The absolute percentage of relative errors was assessed
at the 70 station points by calculating the difference between observed and predicted values of W98. Mean error
was 10%, maximum was 28% and the standard deviation
of these error values was 7.5 m s21. Most errors exceeding 20% occurred at stations located in the Alps. Considering the relative errors, both negative (i.e., when
predicted wind speeds overestimate observations) and
positive values were mainly located in alpine areas. Apart
from this geographical trend, the model had difficulty
approaching extreme W98 wind speeds, as can be seen
when looking at slope values of best-of-fit equations of
the scattered plots (Fig. 5). Highest positive relative errors were linked to the uppermost observed W98 values
of the weather stations, while high negative errors corresponded to lowest W98 velocities. Overall, the model
reproduced the values measured at the weather stations
in a realistic manner despite having difficulties reaching
extreme W98 wind speeds.
(Barry 1992). Turbulence effects, vorticity, or atmospheric
stability and their impact on wind flows are neglected in
this study, although they are essential when explaining
wind velocities in the boundary layer (Stull 1988; Holton
2004). These physical processes cannot be considered by
a GIS approach, but would certainly help explain errors
measured at weather stations.
Predictors used for this study have been assessed at
different spatial scales, with a maximum scale of 2 km,
assuming that local wind speeds are linked to the environmental conditions in close proximity. Nevertheless,
wind flows are also influenced by physiographical features within a larger environment, as wind speeds are
also governed by regional circulations and larger-scale
synoptic situations. Here again, GIS tools have difficulty
in describing these large scale or regional scale weather
conditions.
The number of observations in GAMs influences the
possible complexity of the model [i.e., the numbers of
d. Discussion
TABLE 4. Various indicators providing a qualitative validation of
the results. The Pearson and the Spearman rank correlation coefficients are listed, as well as the RMSE. The last columns show
three indices: RI, D, MAE, and MEF index. All of the calculations
were made for the validation and the cross-validation results. The
last line provides values of the indicators in the case of a perfect
agreement.
This part of the study investigates to what extent wind
speeds can be described by local terrain characteristics.
The focus here is thus on the relation between long-term
wind statistics at weather stations and the description of
their surrounding environment. Valleys produce their
own local wind systems as a result of thermal differences,
and topographic features interfere with the wind flow by
generating turbulent vortices (McNider and Pielke 1984;
Oke 1987), vertical air compression, and frictional drag
Pearson Spearman RMSE D
Validation
Cross validation
Perfect values
0.89
0.77
1
0.65
0.42
1
RI MAE MEF
2.78 0.94 1.05 2.19 0.80
4.05 0.86 1.07 3.15 0.58
0
1
1
0
1
SEPTEMBER 2010
ETIENNE ET AL.
degrees of freedom used (DFU) by the selected variables], which is the case for all regression techniques.
The more available data, the more complex is the model.
In this case, we used the data from 70 weather stations
and selected a final model with four variables with 18
DFU. This is a reasonable ratio between number of
observations and DFU. More observations would not
necessarily affect the resulting model but rather decrease the uncertainty in the predictions. In general,
regression results are, however, not directly influenced
by the spatial density of the observations but rather by
the representativeness of the environmental gradients
being sampled. Spatial density would be much more
significant when employing methods based on spatial
interpolation. Studies have already shown the impact of
the number of observations in similar models in ecology
(Stockwell and Peterson 2002). Distance between stations can, however, influence the independence of observations. When stations are located too close to one
another, they become spatially autocorrelated, and the
assumption of independent, identically distributed (iid)
data required by the regression technique, can be violated. In the present case, most stations are separated by
tens of kilometers and are therefore considered sufficiently independent.
Information on land cover can also help to assess the
wind speeds. In the logarithmic wind profile commonly
used to compute wind speeds close to the ground (Tennekes 1973; Oke 1987), the influence of the type of land
cover is described by the roughness length parameter z0,
which reflects the roughness characteristics of the surface
by quantifying its impact on wind flows within the
boundary layer. Smooth surfaces such as flat ice fields are
associated with very low values of z0, while urban areas
and forests are associated with higher values. The z0 parameter is directly linked to the surface cover, and tables
relating land use to roughness length values are widely
found in the literature (Davenport 1960; Garrat 1992;
Wieringa 1993; Graefe 2003). The land-use parameter
was initially included in the regression analysis, but was
rarely selected, because it gave unsatisfactory results;
it was therefore removed from the study. Land use
would probably be a much more appropriate explanatory factor at microscale levels; whereas, at the scales
used in this study, it appears to be overshadowed by the
other physiographical variables.
5. Conclusions and outlook
Fine GIS layers combined to state-of-the-art statistical models have been used to produce a map of extreme
wind speeds over Switzerland. The resulting W98 map
provides information on local wind conditions, and
1967
calculated values may in a future step be used to assess
storm damage to infrastructure.
The following lists the most significant results that
emerge from this study.
1) GIS tools are appropriate tools to generate accurate
layers that describe the physiographical elements of
Switzerland. Powerful algorithms helped classify the
landscape into 10 categories with different topographic characteristics. The resulting landform map
successfully distinguishes between high ridges, valleys,
hills, open slopes, plains, etc. The three main geographical zones of Switzerland are highlighted, with
clear differences between the Jura Mountains, the
Swiss Plateau and the Alps. Within the latter, narrow
valleys, wide valleys, ridges, and midslope areas are
identified. This 50-m resolution map produces highresolution data that is used in the multilinear regression model to predict extreme wind speeds over
Switzerland.
2) GRASP has shown great potential for a distributed
analysis of wind speed and is clearly a promising tool
for other climatic variables. GAMs were applied to
regionalize W98 values on an elevated heterogeneous landscape.
Variables likely to have an influence on wind flows
were included in the regression process. The GRASP
tool, which allows the use of GAMs, has been applied
to the model selection. A cross-validation model selection method was chosen to select the final model.
To assess errors, bootstrap methods were used that
enabled a quantification of means and standard deviations of W98. The final model is based on a combination of data at a 1-km resolution. The altitude,
the slope, and the profile curvature were included,
and the landform map was entered into the model.
Pearson’s correlation coefficients were satisfactory,
with values of 0.89 and 0.77 for the cross correlation.
Thus, adaptation of regression models and GAMs to
predict wind speeds provides convincing results, which
can help alleviate some of the problems associated
with direct modeling of wind in the complex terrain
of Switzerland. A combination of high-resolution GIS
data associated with recent model selection methods
offers a good alternative to predict historical wind
speeds, especially over complex and heterogeneous
terrain.
3) Topography plays a major role in the spatial distribution of extreme wind speeds. The wind map shows
a clear influence of the topography, as wind velocities
for sites located above mountains are higher than
sites situated on the Swiss Plateau. In the Alps, effects of valley widths are well reproduced. There is
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JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY
a clear impact of the landform variable on the
predicted wind speeds. Slope, elevation, and profile
curvature have also been identified as significant
predictors of wind speed intensity.
Future work to improve the performance of the model
selection is under consideration. Bootstrap methods can
be more thoroughly employed in the procedure by
making a random selection within the input variables and
selecting models from the chosen variables. As suggested
by Thuiller (2007), one could investigate the mean values
of wind speeds predicted by different model selection
methods. Boosted regression tree methods can be used to
better express interactions and nonlinearities in the data.
They have been fully described in Elith et al. (2008). The
use of multivariate adaptive regression splines could
better describe nonlinear relationships between the predictors and the response. Detailed information on this
method can be found in Leathwick et al. (2005).
The W98 are defined as threshold values in many
formulas that address the issues of damage functions.
Using the results discussed in this paper, severe windstorm damage can be determined by taking into account
the wind data recorded during past wind storms in
Switzerland. Impact of climate change on future storm
events can also be estimated as part of future research,
and the associated economic losses can be quantified.
This work opens new perspectives for further research. While the research has focused on a fairly large
and heterogeneous area, similar research could be envisaged for smaller domains. Similarly, work could also
concentrate on specific altitude zones, only focusing on
high zones located in mountains, or on open plains and
flat areas, in order to investigate the behavior of winds
over more homogeneous environments.
Predicting the wind speeds over Switzerland was based
on physiographical predictors only. Investigation of wind
direction statistics at weather stations, possibly linked
to the prevailing climate conditions (Schüepp 1978;
Schmidtke and Scherrer 1997; Jungo et al. 2002) expressed by the northing and easting predictors, could help
detect regional wind systems that occur in Switzerland
such as the Bise (Wanner and Furger 1990) or the foehn
(Hoinka 1985). Inclusion of further information such as
meteorological variables (temperature, turbulence, stability, etc.) would lead to the refinement of climate
models (Goyette et al. 2001; Goyette 2008), which could
better represent the numerous atmospheric interactions
and complex physical description of wind flows.
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