72 COST Action 719 Final report
the applications dominating at the start of the Action were concentrating on developing
national climate maps, showing e.g. 1961-90 or 1971-2000 mean monthly, seasonal or annual
values of selected climate elements. The development of applying spatial interpolation
methods with GIS has accelerated during the Action period, and now applications describing
the spatial distribution of climate elements at daily scales and even synoptic scales are
implemented in several NMSs in Europe.
In this chapter, different applications of spatialisation methods within meteorology and
climatology are presented. All the examples were prepared by scientists and experts
participating in COST Action719, and give a relatively complete overview of the
spatialisation principles currently applied in Europe. The applications include a wide range of
elements at spatial and temporal scales. No single method is applied, or one suitable that
could be applied everywhere in Europe. However, as pointed out by Obled et al. (1982), most
spatial interpolation methods can mathematically be brought down to basically the same
principles. Therefore most of the applications follow these principles in order to meet the
assumptions and criteria required by the methods.
The climatic conditions vary dramatically across Europe, and information needed about
weather and climate as well. The applications developed in Europe will therefore vary from
region to region, reflecting the local/regional climatic conditions, and the relevant information
about weather and climate. The choice of a spatialisation method is subject to the
characteristics of the weather element that should be described. Some elements, like
temperature describe continuous fields, while others, like the occurrence of precipitation can
be described as a discrete binary feature. Such difference in the “nature” of the elements will
lead to a variety of challenges when developing a robust spatialisation method.
These facts are reflected in the examples presented in the next chapters. Different approaches
for describing various weather elements at relevant scales are presented. The use of external
predictors with scale and validation procedures is emphasized, since these are critical factors
for success in applying spatialisation operationally in a sound and robust way.
The next chapters proceed with applications for describing “pure” climate elements like
temperature, precipitation, humidity, wind and radiation. Thereafter, applications deriving the
spatialized information further into advice about air-pollution and climatic indexes for biocomfort,
agriculture, hydrology etc. will be clarified.
II.3.1.1 Monthly mean temperature
Computer assisted methods for developing temperature maps are widely applied across
Europe because this is an element which highly correlates to terrain and land use
characteristics. In addition, temperature is a spatially homogenous element with a strong
seasonal and diurnal cycle, which makes it relatively easy to predict. Most applications for
establishing spatial representations of temperature rely on the principle of residual
interpolation (Figure II.3.1), or detrended interpolation (ref. Chapter II.2.3) where the
influence of different terrain characteristics in addition to a few other external parameters are
used to describe the global trend expression.
There are however a few difficulties that are still not easily solved when applying traditional
residual interpolation, e.g. the problem with temperature inversions, where the expected
decreasing temperature with altitude is reversed
II.3.1.1.1 Mapping mean temperatures.
COST Action 719 Final report 73
The first approaches using GIS and geostatistics to map temperature in the European NMSs
was made in the late 1990’s. When COST Action 719 was started in 2001, many countries
had already, or were developing their climate reference maps using GIS as a tool. In this
piloting time the applications were quite manual, which could be afforded due the relatively
few number of events (monthly, seasonal and annual mean values) to be analysed. Many
different approaches were tested, and a lot of different possible external predictors were
investigated. These investigations have been of considerable help for the further development
of automatic mapping routines applied for finer time resolutions today.
In this chapter an extensive presentation and comparison of several potential spatialisation
methods applied on Portuguese temperatures are presented. Also work carried out in Spain,
Hungary, Slovenia and for the Nordic countries will be presented.
II.3.1.1.2 Comparison of several methods for mapping mean temperatures, an example
from Portugal
Here is a comparison of the performance of several spatial interpolation methods available,
and readily integrated in a GIS for spatialisation of mean monthly air temperatures in
Portugal. The methods that were compared are:
- Inverse distance weighting - IDW;
- Spline tension - Spline;
- Ordinary kriging - KN;
- Ordinary cokriging (with altitude) - CKa;
- Ordinary cokriging (with altitude and distance to sea) - CKadl;
- Linear regression (with altitude) - Reg;
- Linear regression (with altitude) + kriging of the residuals - RegK;
- Multivariate regression (with altitude and distance to sea) + kriging of the residuals -
MRegK;
- Neural networks (using altitude and distance to sea) - NN.
For the multivariate methods the altitude and the distance to sea were used as covariables.
Such a comparative study has relevance mainly in cases where the network stations are
sparse, as mentioned in Burrough and McDonnell (2000, p. 132) and Goovaerts (1997):
“When data are abundant, most interpolation techniques give similar results. When data are
sparse, however, the assumptions made about the underlying variation that has been sampled
and the choice of method and its parameters can be critical...”
74 COST Action 719 Final report
Figure II.3.1 Schematization of the processes (Lhotellier R., 2005)
DEM Topographic or environmental variables
slope
spect
tangential curvature
plan curvature
profile curvature
potential radiation
Layers of topographic variables
Measured temperature
at the station
elevation
Assignment of the variables to the
co-ordinates of the stations
Stepwise regression
temperature / environmental variables
Regression model mapping by
GIS
Keeping residuals
Interpolation of residuals using
kriging
Residuals mapping (GIS)
+
=
Temperature layer
Maps and results comparison
Validation
Sample 1
Sample 2
Climatic Stations
latitude
longitude
Sufficient for annual or monthly
temperature
Daily temperature : add weather type
Filtering topographic and environmental
grids
PCA (possibly)
………
Add new topographic and environmental
variables (slope-aspect factor…)
COST Action 719 Final report 75
II.3.1.1.3 Data and methodology
The data used in this study are the mean air temperature values for the 1961-90 period from
98 climatological stations: 89 in Mainland Portugal and 9 in Spain. By using temperature
values from Spain the problems of extrapolation along the border was reduced.
The auxiliary geographical information such as altitude and distance to sea has been produced
in GIS, using the digital elevation model - GTOPO30 for altitude and measuring the closest
distance to the coast line.
II.3.1.1.4 Validation and comparison of the interpolation
For the interoplations 84 stations were used, while the remaining 14 stations were used for an
independent validation. In this way the problems of using cross-validation were suppressed.
This comparison of the methods guarantees the independence of the validation data from the
interpolated data, which the cross-validation does not fulfil.
Three measures were used for the comparison:
- Difference between observed and estimated values (estimation error);
- Correlation coefficients between observed and estimated values;
- Visual analysis of the prediction maps.
Tables II.3.1 and II.3.2 showing the mean square error and the correlation coefficient between
measured and estimated values reveal that the univariate methods present higher error values
than those using auxiliary information such as altitude and distance to sea. The linear
regression of temperature with altitude has always the highest errors except in March and
April, because this covariable explains almost all the variance of the temperature in these
months. The inclusion of the residuals in the predictions increases their accuracy the
estimations.
Table II.3.3 shows the “best” monthly methods in terms of mean square error and correlation
coefficient. As can be seen, residual kriging with altitude, incorporating distance to sea or not,
presents the lowest errors. Only in January and November the ordinary cokriging (covariable
altitude) gives better results.
The neural networks - NN presents the second lowest error in July. This method, despite the
lack of training cases (84 stations), has similar but poorer results than residual kriging. In
general, the multilayer perceptron with two hidden layers was the network type with more
reliable learning results, and it was used in the majority of the months. It must be mentioned
that the residuals of the NN were not interpolated; probably the method would present better
performance if used that way.
Table II.3.1 Mean square error between measured and predicted values. Underlined –
Highest errors; Italic – Lowest errors
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Ann
IDW 0.72 0.85 1.08 1.09 1.02 1.12 1.48 1.27 1.25 1.02 0.95 0.91 0.84
Spline 0.71 0.79 0.85 1.09 0.99 1.21 1.47 1.32 1.30 0.83 0.99 0.83 0.99
KN 0.74 0.87 1.12 1.05 0.92 1.09 1.30 1.18 1.12 0.96 0.94 0.84 0.80
Cka 0.23 0.37 0.61 0.41 0.35 0.49 0.64 0.59 0.51 0.38 0.29 0.75 0.49
CKadl 0.38 0.56 0.74 0.51 0.55 0.48 0.57 0.44 0.47 0.82 0.46 0.49 0.46
Reg 1.79 0.89 0.60 0.51 1.10 2.18 4.08 4.30 2.29 1.00 1.21 1.67 0.98
RegK 0.62 0.36 0.29 0.18 0.13 0.30 0.66 0.59 0.49 0.21 0.56 0.63 0.20
MRegK 0.36 0.55 0.27 0.20 0.14 0.19 0.43 0.42 0.39 0.23 0.42 0.43 0.20
RN 0.44 0.51 0.47 0.88 0.95 0.44 0.55 0.68 0.83 1.00 0.65 0.76 0.35
76 COST Action 719 Final report
Table II.3.2 Correlation coefficient between measured and predicted values. Underlined –
Lowest correlation values; Italic – Highest correlation values
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Ann
IDW 0.94 0.93 0.91 0.91 0.91 0.90 0.87 0.89 0.89 0.91 0.92 0.92 0.92
Spline 0.94 0.94 0.93 0.91 0.91 0.89 0.87 0.89 0.88 0.93 0.92 0.93 0.90
KN 0.94 0.93 0.91 0.92 0.92 0.90 0.89 0.90 0.91 0.92 0.93 0.93 0.92
Cka 0.98 0.97 0.96 0.98 0.97 0.95 0.94 0.95 0.96 0.98 0.98 0.93 0.95
CKadl 0.97 0.95 0.94 0.96 0.95 0.96 0.95 0.96 0.97 0.93 0.96 0.96 0.96
Reg 0.86 0.94 0.95 0.96 0.89 0.78 0.58 0.57 0.78 0.91 0.91 0.87 0.90
RegK 0.96 0.98 0.98 0.99 0.99 0.97 0.94 0.95 0.96 0.98 0.97 0.96 0.98
MRegK 0.98 0.98 0.98 0.99 0.99 0.98 0.96 0.96 0.97 0.98 0.97 0.97 0.98
RN 0.97 0.96 0.97 0.96 0.96 0.97 0.95 0.95 0.95 0.90 0.96 0.94 0.97
Table II.3.3 Lowest monthly mean square error and correlation coefficient between observed
and predicted values.
Lower MSE Method Highest r
observed vs estimated Method
Jan 0.23 CKa 0.98 CKa
Feb 0.36 RegK 0.98 RegK
Mar 0.27 MRegK 0.98 RegK
Apr 0.18 RegK 0.99 MRegK
May 0.13 RegK 0.99 MRegK
Jun 0.19 MRegK 0.98 MRegK
Jul 0.43 MRegK 0.96 MRegK
Aug 0.42 MRegK 0.96 MRegK
Sep 0.39 MRegK 0.97 CKadl
Oct 0.21 RegK 0.98 RegK
Nov 0.29 CKa 0.98 Cka
Dec 0.43 MRegK 0.97 MRegK
Annual 0.20 MRegK 0.98 MRegK
Table II.3.4 Mean monthly square errors by altitude class of the stations.
Stations
(altitude) IDW Spline KN Cka Ckadl Reg RegK MRegK RN
200 m 0.37 0.37 0.30 0.37 0.28 1.43 0.39 0.38 0.58
> 200 m 1.99 1.91 1.97 0.59 0.88 2.30 0.45 0.28 0.84
All 1.06 1.03 1.01 0.47 0.54 1.80 0.42 0.34 0.69
These findings confirm that an “…easy way to account for both elevation and spatial
correlation is to interpolate the regression residuals using geostatistics…” (Goovaerts, P.,
2000, p.128) The residual kriging outperforms cokriging in this comparison, despite the
greater complexity in modelling and computer requirements of the latter. Considering only
univariate methods, the kriging technique presents lower errors than IDW or spline, which do
not take into account the pattern of spatial dependencies in temperature data.
Including geographical variables in the estimation produced more reliable maps with lower
prediction errors. Despite this, when the variable fluctuates smoothly, mainly in the lowest
altitudes, the kriging error is smaller than for higher elevations and complex terrain. At some
validation stations (Figure II.3.2 and Table II.3.4) the mean monthly square error is even the
smallest among all the studied methods.
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Figure II.3.3 shows three examples of the test predictions. As can be seen, the ordinary
kriging map does not capture local variations like the other two. The cokriging and neural
network maps take into account altitude and distance to sea and, in this way, present more
fine details, especially in the latter case. Visual comparative analysis of the maps
complements the validation results and is often used for this work.
Considering the above results, residual kriging was chosen to produce the final maps of mean
air temperature (examples of January and July in Figure II.3.4) using trend parameters for
altitude and distance to sea. This method presents the lowest errors in half of the months.
Figure II.3.2 Mean monthly square error in each validation station (also represented the
altitude and the distance to sea on the secondary Y axis), and map with validation stations.
Figure II.3.3 Mean annual air temperature (1961-90) test predictions.
78 COST Action 719 Final report
January July
Figure II.3.4 Mean annual air temperature (1961-90) final monthly prediction maps
(January and July), with residual kriging of multivariate regression (using altitude and
distance to sea).
The spatial pattern of temperature reveals the simultaneous effect of three main factors:
latitude, distance to sea and altitude. The relative importance of these factors varies monthly;
in the coldest months the temperature increases from North to South, but in summer the
spatial pattern is mainly dominated by the strong gradient in the coastal regions. The highest
temperatures in this season occur in the inland. Throughout the year, temperature decreases,
more or less, with increase in altitude and minimum values occur always in the highest
mountains.
In a comparative study as presented above it is a valuable approach to test several
interpolation methods, especially when the maps are obtained from a relatively sparse sample.
When the main variable has a high correlation with other variables that are densely sampled,
the predictions can be much improved if auxiliary information on the process of estimation is
included. Mean air temperature in Portugal is well correlated with altitude and shows also
some relation with distance to sea, and the method showing best results was residual kriging,
applying altitude and distance to sea plus kriging to describe the global trend. This method
exhibits very good performance, with correlation coefficients between measured and
predicted values close to 1. Other multivariate methods, like cokriging and neural networks
did not present such good results.
The univariate methods present inferior global results. Even so, for some validation stations,
kriging happens to be the method with lowest errors; this occurs mainly in low altitude
stations where the temperature values vary smoothly, although in complex terrain the errors
are high and globally the performance decreases. Among the univariate methods kriging
outperforms the IDW or the spline for the whole country.
II.3.1.1.5 Spain
