1. science
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INTERNATIONAL JOURNAL OF CLIMATOLOGY
Int. J. Climatol. 19: 365–378 (1999)
SPATIAL INTERPOLATION OF AIR TEMPERATURE ACCORDING TO
ATMOSPHERIC CIRCULATION PATTERNS IN SOUTHEAST FRANCE
a
DOMINIQUE COURAULTa,* and PASCAL MONESTIEZb
INRA, Unite´ de Bioclimatologie, Domaine St Paul, Site Agroparc, 84914 A6ignon, Cedex 9, France
b
INRA, Unite´ de Biome´trie, Domaine St Paul, Site Agroparc, 84914 A6ignon, Cedex 9, France
Recei6ed 13 January 1998
Re6ised 1 August 1998
Accepted 3 September 1998
ABSTRACT
A method is proposed for the interpolation of daily maximum and minimum air temperatures (Tx and Tn,
respectively) at the regional scale, taking into account the atmospheric circulation patterns (CPs). The study region
was in southeast France (150 × 250 km2). Daily temperatures measured at 152 meteorological stations were available,
and CPs from automatic classification performed every day by Me´te´o France from forecast model outputs were used.
For the whole of Europe, ten classes centred on France are defined. A geostatistical approach (ordinary kriging) was
chosen, because it permits the mapping of the estimation variance for interpolation and consideration of several days
at once. Different data processing methods were compared: raw temperatures without correction; temperatures
converted to sea level by applying a constant or varying coefficient according to the CP; and sorting days in relation
to CP and season. Cross-validation analyses were performed, separating the data set in two independent parts (62
stations for the model calibration and 90 for the validation). These sets of data showed errors from 0.6° to 2°C. An
improvement of 0.5°C was observed for the maximum temperature if it was corrected with regard to the elevation and
the days sorted according to CP; however, correction of the elevation had a greater effect on improving the results
than does CP sorting. The results obtained for the minimum temperatures fluctuate more from day to day. Copyright
© 1999 Royal Meteorological Society.
KEY WORDS: air
temperature; atmospheric circulation patterns; kriging; spatial interpolation; France, southeast; geostatistics
1. INTRODUCTION
The air temperature (Tair) measured at 2 m is one of the main input data for many models, such as
agrometeorological models for water balance monitoring, crop models for yield prediction, and hydrological models. This variable plays an important role in the energetic and hydric exchanges at the interfaces
between the soil, plants and the atmosphere. Plant growth depends on air temperature, and in crop
models, the different phenological stages are determined according to accumulated air temperatures from
the sowing date. Temperature thresholds are defined as the temperatures below which there is no
development for some crops. In southeast France for example, the threshold for wheat is 0°C, while for
maize it is 6°C. When these crop models are applied on a large scale (regional or continental), it is
necessary to have sufficiently accurate temperature data. For example, the GOA model (Brisson et al.,
1992) used to estimate yield potentials on a European scale for different crops and climates divides the
entire territory into 30-km pixels, for which a mean climate is obtained from one to five meteorological
stations. Sensitivity studies performed by Ruget et al. (1995) showed that if a systematic error of
9 1°C/day is made on air temperature during the entire growth cycle of maize, then a yield estimation
error of 0.5–1 t/ha will arise, which is significant (Dele´colle et al., 1995); accurate climatic data are
therefore very important.
* Correspondence to: INRA, Unite´ de Bioclimatologie, Domaine St Paul, Site Agroparc, 84914 Avignon, Cedex 9, France. Tel.:
+33 4 90316206; fax: +33 4 90899810; e-mail: [email protected]
CCC 0899–8418/99/040365 – 14$17.50
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D. COURAULT AND P. MONESTIEZ
A problem exists in that there is an insufficient number of meteorological stations providing climatic
data, and they have an irregular geographical distribution (in France the mean distance between
meteorological stations is about 30 km); therefore, spatial interpolation methods must be used. Some
methods are only based upon distance criteria, such as the Thiessen Polygons which correspond to the
defined homogeneous areas in which the temperature is assumed to be constant. This technique has been
used frequently in hydrological studies. The geostatistical approach, based on regionalised variables
theory (Wackernagel, 1995) is more difficult to use because it requires structural analysis of the data set.
However, this approach gives an interpolation error, thus allowing the possibility of introducing some
explanatory factors of spatial variability, e.g. the topography (Dodson and Marks, 1997)—which can be
entered as an external drift in kriging (Hudson and Wackenagel, 1994)—or the lake effect (Holdaway,
1996). Although elevation is the main variation factor for air temperature (a decrease of about 0.6°C/100
m is generally accepted), it is influenced by other factors. Both local and regional effects exist;
meteorological stations can modify the measurement (Fury and Joly, 1995). Seguin et al. (1982) observed
a temperature difference of the close environment of 2° and 4°C between wet and dry areas, respectively.
Proximity to the sea, topography, and the general atmospheric circulation patterns (CPs; Huard, 1993)
also influence spatial variations of air temperature. All these factors are not easy to integrate using
interpolation methods, and the spatial scale of the study, the available information and the level of
accuracy required must also be taken into account.
The objective of this paper is to propose a methodology for spatial interpolation of air temperature,
taking into account the effect of CPs in order to provide more accurate input data for crop models
applied on a large scale. The relationship between CPs and climatic data is the subject of many papers
(Bardossy and Caspary, 1990; Hay et al., 1991; Bardossy and Plate, 1992; Knapp, 1992; Huard, 1993;
Jones et al., 1993; Buishand and Brandsma, 1997). It seems obvious that the CP plays a role in the spatial
variation of air temperature. Indeed, according to the dominant wind direction and the topographic
situation, spatial correlations between stations are different.
From a data set of 152 meteorological stations located in southeast France, ordinary kriging was used
to determine whether CPs modify the thermal gradients on a regional scale and improve the air
temperature estimations at any point in the area under study. In the first part of this paper, the data are
presented and a brief review of the kriging method and the different processes performed on the data is
given. In the second part, interpolated temperature maps are shown. The accuracy of the procedure is
discussed, based on a cross-validation study.
2. THE DATA SET
2.1. The circulation pattern
The CP data come from outputs of large-scale forecast models running in Me´te´o France (EMERAUDE-ARPEGE). Fifteen variables, among them the geopotentials at different levels: 500, 700 and 1000
hPa, are classified via an automatic procedure based on dynamic clouds (block clustering). The values
obtained at 100 grid points cover Europe and are centred on France. Ten classes are proposed for each
variable which are associated with the main atmospheric CPs (Be´nichou, 1985). In this study, it was
decided to study the classes issued from the 1000 and 700 hPa geopotentials, because these present high
correlations with the climatic conditions observed at the surface (Be´nichou, 1985). Daily values obtained
for the 2 years between 1993 and 1994 were used. A longer sample would be more significant, but the
entire series for all 152 meteorological stations was not available, and the aim of the study is to propose
a methodology which can subsequently be applied to other years. Figure 1 shows an example of the main
CP classes encountered during this period for the 1000 hPa geopotential. Class 9 (CA9) represents more
than 16% of situations, and corresponds to an anticyclone occurring in winter or autumn involving cold
snaps and sometimes frost; therefore, it is important for agriculture. Class 5 (CA5) is of the meridian type,
with a flux oriented north – south and sometimes producing strong winds. A frequency analysis of the CP
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 365 – 378 (1999)
SPATIAL INTERPOLATION OF AIR TEMPERATURE
367
showed that the distribution varies according to the season; some CPs are dominant in summer (the same
Class 4 can be observed (anticyclonic, 700 hPa geopotential) for 30 consecutive days Figure 2). The
temporal variations of the 1000 hPa geopotential are more important than those of the 700 hPa
geopotential, because the 700 hPa level is less-dependent on topography and surface conditions such as
proximity to the sea.
Figure 1. Main circulation pattern classes obtained from the 1000 hPa geopotential by automatic classification performed daily at
Me´te´o France. The contours represent the elevation (in geopotential meters) at 1000 hPa, the bold line (120) corresponds to 1015
hPa. (a) Anticyclone with cold snaps occurring in winter (CA9); (b) oceanic anticyclone (CA1); (c) anticyclonic type on the North
Sea (CA6); (d) meridian type depression over East Europe (CA5); and (e) continental anticyclone over East Europe (CA7)
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 365 – 378 (1999)
368
D. COURAULT AND P. MONESTIEZ
Figure 2. Temporal variations of the CP classes obtained from the 1000 hPa geopotential (a) and the 700 hPa geopotential (b) for
1993 – 1994
2.2. The meteorological data
Maximum and minimum daily temperatures (Tx and Tn, respectively) at 152 stations covering an area
of 150× 250 km2 in southeast France (Figure 3) were provided by Me´te´o France. From this data set, 62
stations were extracted for the model calibration. These stations belong to the automatic and synoptic
network, i.e. the data are available at actual times. The 90 remaining stations, which deliver delayed data,
were used for model validation. The two data sets were compared using statistical tests in order to check
whether a significant difference existed between these two groups. The two data sets have similar
characteristics (Table I). The spatial density of the stations is globally homogeneous over the entire area,
i.e. that there are not more stations in the south of the area under study than in the north, east or west.
Naturally, this distribution is less homogeneous vertically, because there are only a few stations at high
altitudes. More than 50% of the stations are below 200 m, and less than 8% are located above 1000 m.
The highest elevation is at 1567 m in the west of the study area, while the lowest values correspond to the
Rhoˆne valley in the centre and close to the coast. The trend over the whole area is not high, and therefore,
it can be assumed that the station sample is representative of the region.
3. BRIEF REVIEW OF KRIGING
The aim is to estimate the temperature at any point x0 in the region of interest, knowing the temperatures
at a set of stations (in this case, 62 stations, xi ). The measured variable, T(x), is spatially dependent, i.e.
it is a regionalised variable. It is assumed to be the realisation of a random spatial function. An estimator,
called kriging, is computed as a linear combination as follows:
ns
T*(x0)= % li T(xi )
i=1
where T(x) is a random function, xi is the location of the station i, ns is the station number (in this case
ns =62), and T*(x0) is the best unbiased linear predictor of T(x) in x0. The coefficients li (weights) do not
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 365 – 378 (1999)
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SPATIAL INTERPOLATION OF AIR TEMPERATURE
Figure 3. Locations of the meteorological stations
depend on the values of T(xi ), but only on the covariance between measured stations, cov(T(xi ), T(xi%)),
and between measured and estimated stations, cov(T(xi ), T(x0)). In order to be unbiased, li must sum to
1. External drift is not taken into account.
In the following, all stations in the neighbourhood of x0 were used for the computation of estimations,
which is usually called ‘unique neighbourhood’.
The spatial covariance of T(x) can be modelled through the semivariogram. The experimental
semivariogram computed from observed values is expressed as follows:
nd
% (Ti, j −Ti%, j )2
gi,i% =
j=1
2nd
where Tij is the temperature measured at xi on day j and nd is the number of days measured. The plot of
gi,i% versus the distance di,i% =d(xi, xi%) gives a variogram cloud. Then, a model of semivariogram g(h),
which is a measure of the similarity between points at a given distance h apart, is fitted. Different models
are proposed in the literature where it is important to define certain parameters such as the nugget effect,
which is the limit of g(h) when the distance (h) is zero. The range is the maximum distance at which there
Table I. Characteristics of the two data sets: 62 stations are used for the model
calibration, and 90 for the validation
Tn 62 (90)
Minimum
Maximum
Mean
S.D.
−16.2
26.9
8.3
6.6
(−15)
(27.2)
(7.8)
(6.6)
Tx 62 (90)°C
−8.3
39.6
18.8
7.9
(−6)
(40.6)
(18.8)
(8)
z 62 (90) m
1
1567
292
300
(1)
(1047)
(284)
(284)
Tx, maximum daily temperature; Tn, minimum daily temperature for 2 years (1993–1994); z, station
elevation.
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 365 – 378 (1999)
370
D. COURAULT AND P. MONESTIEZ
Table II. The slope coefficients of the regressions performed between daily temperatures and elevations for the 62
calibration stations in the different situations studied
Slope coefficient (°C/100 m)
Tn
Tx
All days (730 days)
Season sorting (184 days)
Seasonal and CP sorting
( ¡ days)
0.64
0.53 (winter), 0.62 (summer)
0.31 (CA6 summer),
0.85 (CA1 spring)
0.66
0.63 (autumn), 0.70 (spring)
0.43 (CA9 autumn),
0.84 (CA5 autumn)
Ti,d = adzi+bd: i, 62 stations; d, days; CA: the CP class for the 1000 hPa geopotential. Only the extreme values are given for the
sorted days.
is no variation and the sill is the g(h) value at the range value. Kriging then uses the variogram g(h) to
assign weights to neighbouring observations in the interpolation process (Wackernagel, 1995).
In general, when only 1 day of data is available, a stationarity and isotropy assumption is used to
compute the experimental variogram, averaging all pairs (xi, xi%) for similar distances. Here, replications in
time allow estimation of gii% for every pair, and point dispersion in the variogram cloud around the fitted
semivariogram g(h) — which is stationary and isotropic—can be checked.
4. DATA PROCESSING
4.1. Ele6ation correction
In order to eliminate the effect of elevation on temperature (and because a digital elevation model
(DEM) was not available in the study area), a simplified approach was used. A constant coefficient
obtained from the relationship between temperature and elevation was applied to transform the temperature to an ‘equivalent temperature at sea level’. The temperature decrease value of 0.6°C/100 m is the most
common found in the literature. If the 2-year series are pooled together, coefficients for Tx and Tn are
close to this theoretical value (Table II). When each day is analysed separately, important variations of
this coefficient are observed (Figure 4). Even a few days present a positive slope, which explains why the
mean values found for all days (first line in the Table II) are outside the range given for the days sorted
by season (second line, Table II). This temporal variability is due in part to the fact that the gradient of
0.6°C/100 m corresponds to the free atmosphere, which is not immediately close to the surface. Various
parameters modify thermal gradients, i.e. air moisture, atmospheric stability, hydric surface status, slope
and exposure (Douguedroit and de Saintignon, 1974; Arya, 1988; Carrega, 1994). The models accounting
for these factors are more complex and more difficult to extrapolate, because they require more input data
(Chen and Robinson, 1991). In order to improve our ‘simplified’ correction, variation of the global slope
coefficient in relation to the main CP was analysed.
4.2. Day sorting for CP and season
Days were sorted both according to the CP and to the season, because the effects of atmospheric
circulation are not the same throughout the year; for example, an anticyclone can increase the
temperature in summer and decreases it in winter (Courault et al., 1996). For each day group, the mean
slope coefficient resulting from the regression performed between temperature and elevation was computed. Table II displays the results for the extreme values of the main groups. The coefficients vary from
0.31° to 0.85°C, meaning that if a station located at a 600 m elevation measures a temperature of 15°C,
its sea-level temperature will be 17° or 20°C, depending on the season and the CP. This correction still
remains ‘simplified’, but is easy to use everywhere when no information other than the temperature and
the elevation at the observation stations is available.
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 365 – 378 (1999)
SPATIAL INTERPOLATION OF AIR TEMPERATURE
371
5. SPATIAL ANALYSIS
5.1. Semi6ariogram analysis
Variograms for the following cases have been computed:
(i) temperatures directly measured at the stations without corrections (730 days were considered in this
case; Figure 5a);
(ii) temperatures corrected for elevation using a constant coefficient (730 days; Figure 5b); and
(iii) temperatures corrected for elevation using different coefficients for the different seasons and the CPs,
(the number of days varies; Figure 5c).
In the last two cases, temperatures are converted to sea level (Tsea
residuals:
Tsea
i, j
i, j
) and g is computed from the
=Ti, j −aj zi
where i is the station number (1 – 62), j is the day (1–730), zi is the station elevation and aj is the slope
coefficient (chosen as either a constant or a variable depending on the CP and season; Table II).
It was observed that the point dispersion and g values decrease when the temperatures are converted to
the sea level (Figure 5a – c). The day sorting by CP and season does not decrease the dispersion. This is
due to two phenomena: the ‘natural’ variability of each g (which depends on the length of the series for
a stationary case) and the variability due to being ‘non-stationary in time’, which we attempt to reduce.
When the days are sorted according to the CP, the second term decreases (if stationality is assumed within
groups), but the first term increases because the series are shorter and the grouped days are nonhomogeneous.
Figure 4. Relationships obtained between the maximum daily temperature (Tx ) and the elevation of the 62 calibration stations (z)
for 2 days; a and b are the parameters obtained for the regression Tx =az +b, a is the slope, b represents the residues corresponding
to the sea-level temperature for the day studied and r 2 is the correlation coefficient
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 365 – 378 (1999)
372
D. COURAULT AND P. MONESTIEZ
Figure 5. (a) Semivariogram performed using the raw data from the 62 stations; maximum daily temperatures for the 2 years
(1993 – 1994); (b) semivariogram performed on the maximum daily temperatures converted to sea-level values using a constant
coefficient (0.66°C/100 m) for the 2 years (730 days); and (c) semivariograms performed on daily maximum temperatures converted
to sea-level values when the days are sorted according to the main CP and the season (spring on the graph)
Copyright © 1999 Royal Meteorological Society
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SPATIAL INTERPOLATION OF AIR TEMPERATURE
373
Figure 6. Models fitted to the semivariograms for different situations: (i) using raw data and corrected elevation data for Tn (a) and
Tx (b) over all 730 days; and (ii) using temperatures converted to sea-level values in spring for different CPs for Tn (c) and Tx (d)
5.2. Fitting the models
The models fitted to the semivariograms describe the spatial structure of the air temperature. The data
is smoothed in order to see the trend and curve shape more clearly. A non-linear regression method
adjusted by the least squares method is then used to determine the parameter models. The choice of model
results from a compromise between the best fit visually and the smaller standard error. In most cases,
linear or exponential models with ‘range parameters’ (or ‘scale parameters’ for linear models) varying
from 120 to 300 km (Figure 6) were found to be most suitable. For example, the exponential model is as
follows:
g = b+a× 1 − exp
−3 × h
p
where b is the nugget (when h =0), p is the distance from which g does not vary, and a is the value of
g at p minus the nugget; a, b and p are determined by the least squares method.
The nugget effect is different for maximum and minimum temperatures; it is low when the temperatures
are not corrected for elevation both for Tx and Tn (in the order of 0.5–2°C), and high (close to 4°C) for
Tn when they are corrected for elevation (Figure 6a). In this case, the variogram is ‘flat’, indicating a lack
of structure. This difference can be explained by the spatial variability of Tn which must be more ‘local’
than that of Tx. It is possible that the ‘micro topography’ or the local environment plays a more
important role for Tn than for Tx. Maximum temperatures have a larger spatial range; when it is warmer,
a larger area is involved in the study area. Ashraf et al., (1997) noticed from a geostatistical study
conducted in USA with 17 stations, that Tx show less scatter in their correlation functions than Tn,
because Tn are ‘more affected by local features of landscape or localised weather patterns’. The models
show variations according to the CP and the season (Figure 6c,d).
5.3. Thermal maps resulting from ordinary kriging
The following stage is the estimation of the air temperature in the region of interest. Temperatures are
interpolated at each node of a 1×1 km grid, using kriging on the calibration stations. Figure 7 shows
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 365 – 378 (1999)
374
D. COURAULT AND P. MONESTIEZ
examples of temperature maps for the main classes. The standard error gives values varying from 0.5° to
2°C. The magnitude and direction of thermal gradients vary within the same day between the maximum
and minimum temperatures, and according to the different CPs in a given season. The differences between
Tn and Tx maps are due to several phenomena; proximity to the sea attenuates thermal gradients in the
middle of the day during spring and summer, hence the maximum temperatures of coastal stations are
Figure 7. Thermal maps obtained by ordinary kriging from data converted to sea-level values for different CP classes for some days
in spring (the map axes are in Lambert coordinates)
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 365 – 378 (1999)
SPATIAL INTERPOLATION OF AIR TEMPERATURE
375
often lower than those of continental stations. At night, the sea releases the stored heat, and the minimum
temperatures at coastal stations are higher than those of continental ones, the sea being like a reservoir
with a high thermal inertia (Holdaway, 1996). The type of surface also induces differences between Tn and
Tx. Dense vegetation has a high evapotranspiration rate, which tends to decrease air temperature in the
middle of the day (Tx ), while during the night, vegetation acts as insulation and thus, minimum
temperatures are generally lower on non-vegetated than on vegetated surfaces. With regard to the
differences between the CPs, thermal gradients are oriented either parallel or perpendicular to the coast,
and vary from 2° to 6°C according to the season. Thermal gradients are different in each season for the
same CP class (Figure 8a) and for several days in a same season and CP class (Figure 8b). The days of
a given CP class can not be considered as a repetition of the same phenomenon; the groups remain
heterogeneous. Therefore, we cannot assign a ‘characteristic thermal map’ to each CP class. An
investigation into whether this additional information improves the daily temperature estimation is
presented below.
6. VALIDATION STUDY
Temperatures at the 90 validation stations were estimated using kriging. These stations were not taken
into account either in the semivariogram computations or in the model fittings. Different cases were
compared in order to determine whether the estimations are more accurate when taking more information
into account. The first case corresponds to interpolations performed on the raw temperatures without
elevation correction (one model for 730 days; Figure 5a). In the second case, the model obtained for the
temperatures at sea level (one model for 730 days) is used. The third case corresponds to the sea-level
temperatures and to the days sorted according to seasonal CP. The residual mean squares error (RMSE)
was computed for each case. The results are presented in Table III for some typical days of the main CP.
RMSE=
'
1 n
% (T
−Test(i6))2
n i6 = 1 obs(i6)
i6 is the validation station number and varies from 1 to 90, Tobs is the temperature measured at the station
and Test is the temperature estimated by kriging. We did not observe the same behaviour for the maximum
and minimum temperatures. For Tx, RMSE decreases when the temperatures are converted to sea-level
values, and decreases slightly when the days are sorted according to season and CP class. The global gain
is in the order of 0.5°C, which is significant for daily values if they are used in crop models. For Tn, the
results vary according to the days; for some days the accuracy is increased when the temperatures are
corrected and the days sorted, while for other days there was no improvement in the estimation. As
previously noticed, when the minimum temperatures are converted to sea-level values, the semivariogram
becomes flat, with important noise due to the high local variability, which is not modelled. (These
calculations are illustrated only for some days in Table III. They were performed for many days and for
all seasons and CPs; the conclusions are the same.)
7. DISCUSSION AND CONCLUSION
A method is proposed for interpolation of daily air temperatures which takes into account atmospheric
CPs. A geostatistical approach consisting of fitting different models for different groups of days is used.
Ordinary kriging is then applied, either on raw data or on data converted to sea-level values. It is ‘a
simplified correction’ which can be used anywhere when only temperature and elevation are known in
addition to an atmospheric circulation classification. The first results showed that the accuracy of daily
maximum temperatures is improved by 0.5°C when the data are corrected for elevation and days sorted
by CP and season. The improvement is due more to elevation correction than to the CP sorting, which
only slightly improves the results. The results are more variable for Tn. For both cases (Tx and Tn ), it was
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 365 – 378 (1999)
376
D. COURAULT AND P. MONESTIEZ
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 365 – 378 (1999)
Figure 8. Thermal maps obtained from maximum sea-level temperatures (Tx ) for Class CA1 for different seasons (a) and different days during the spring (b)
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SPATIAL INTERPOLATION OF AIR TEMPERATURE
Table III. Errors (RMSE) computed for some days of the main CP classes using the different models
Days
CP
class
Daily
temperature
Raw data,
model 1
(RMSE)
Sea-level temperatures,
model 2 (RMSE)
Sea-level temperatures,
days sorted/CP/season,
model 3 (RMSE)
Gain
10/2/94
6
11/4/94
5
5/6/94
1
4/12/94
9
Tn
Tx
Tn
Tx
Tn
Tx
Tn
Tx
1.8
1.62
1.54
1.75
2.1
2.22
1.35
1.20
1.98
1.1
1.51
1.2
1.84
1.76
1.45
0.95
1.95
1.09
1.52
1.18
1.76
1.74
1.41
0.93
−0.15
0.53
0.02
0.57
0.46
0.48
−0.06
0.27
noticed that even if the days were sorted by season and CP, the groups were not homogeneous and the
days could not be considered as being a repetition of the same phenomenon. Therefore, there are no
characteristic thermal maps for the CP classes. This may be due to the fact that the CP classes used in this
study were defined on a too large a geographic domain (the whole of Europe, centred on France), while
the application is on a regional scale. The classes were not always relevant to southeast France. In
particular, a typical pattern of this region, characterised by an anticyclone with a regional north wind (the
Mistral) was not distinguished. The classification used in this paper is easily accessible from Me´te´o France
on a daily basis. More detailed classifications are available in the literature, e.g. the Lamb classification
(Lamb, 1972), with 29 classes for Europe. This classification requires expert knowledge, and in consequence is difficult to apply routinely for operational applications. An objective scheme, initially developed
by Jenkinson and Collison (1977) was proposed by Jones et al. (1993) to classify CPs over the British Isles
using the mean sea-level pressure data. This classification has been compared to other classical classifications (Lamb, Grossweterlagen, etc.) and shows high correlations (Jones et al., 1993; Buishand and
Brandsma, 1997). Applications outside the British Isles are possible if the grid is centred on the region of
interest. For example, this classification has been used to predict precipitation in Switzerland (Conway et
al., 1996) and temperature in the Netherlands (Buishand and Brandsma, 1997). An alternative between
automatic and expert classification is the approach proposed by Bardossy et al. (1995), where the user
defines his own classes suitable to the studied region, pointing out the centres of action (high or low
pressure). These situations are then considered as reference classes and all of the following days are
automatically classified by fuzzy rules using the geopotential data at one given level. It could be
interesting to test these classifications for our region in a further work.
Another way to improve the spatial interpolation is to take the topography more into account, using,
for example, data derived from a digital elevation model. Different studies have proposed more
sophisticated methods which undoubtedly improve the accuracy of prediction on estimations, but error
will always be present owing to the spatial resolution of the digital elevation model or the temporal
resolution of the climatic data. The method investigated in this paper is easy to implement and the
geostatistical approach allows an interpolation error to be provided, which can be introduced into crop
models for future sensitivity studies, thus giving more realistic ranges for yield estimation.
ACKNOWLEDGEMENTS
The authors thank Me´te´o France who provided the climatic data, Cedric Armand, David Mabit, Sylvain
Delabrosse (statistics students) for their help in the data processing, and Denis Allard (INRA Biometrie)
for his helpful comments on this manuscript. The study was funded in part by the ECLAT project of the
Environment Ministry and ECOSPACE from the INRA. Thanks are also due to the reviewers for their
useful comments which allowed us to clarify this paper.
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 365 – 378 (1999)
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D. COURAULT AND P. MONESTIEZ
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Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 365 – 378 (1999)