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Spatial interpolation of mean annual precipitations in Sardinia. A comparative analysis of several methods

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Our study attempts to test several spatial interpolation methods used for the purpose of mapping the mean annual precipitations in the island of Sardinia (Italy). The spatial modelling is based on data from 243 meteorological stations. We tested the usefullness of regression analysis, ordinary kriuging, cokriging and residual kriging. The performance of each method was assessed by crossvalidation. Our results show that better results are achieved using residual kriging with altitude as predictor.
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SPATIAL INTERPOLATION OF MEAN ANNUAL PRECIPITATIONS IN
SARDINIA. A COMPARATIVE ANALYSIS OF SEVERAL METHODS
D. Secci1, C. V. Patriche2, A. Ursu3, L. Sfîcă3
ABSTRACT:
Our study attempts to test several spatial interpolation methods used for the purpose of mapping
the mean annual precipitations in the island of Sardinia (Italy). The spatial modelling is based on
data from 243 meteorological stations. We tested the usefullness of regression analysis, ordinary
kriuging, cokriging and residual kriging. The performance of each method was assessed by
crossvalidation. Our results show that better results are achieved using residual kriging with
altitude as predictor.
Keywords: spatial interpolation, mean annual precipitations, kriging method, regresion
analysis, Sardinia.
1. INTRODUCTION
The first official rainfall measurements began in Sardinia in 1922, carried out by the
Hydrographic Institute of Sardinia. The institute, now called the Sardinian Hydrographic
Agency for Protection and Management of Water Resources, works with over 250
meteorological stations, from which 92 are automatic temperature-rainfall weather stations,
evenly distributed in the territory. The data collected through this network was used for
preparation of the first publication regarding the climate of Sardinia (Pinna, 1954). It
includes the first maps showing the spatial distribution of precipitations in Sardinia, drawn
using manuals methods (Fig. 1).
Since 1995, the Regional Department for Hydro-Meteo-Climatology has become
operational within the Regional Agency for Environmental Protection of Sardinia (ARPAS),
specialized in agro-meteorological data collection and modelling using over 50 automatic
weather stations. This department has started the processing of data through GIS softwares,
therefore publishing more accurate climatic maps. One of the latest works on the average
rainfall in Sardinia is included in The climate of Sardinia by P. A. Chessa and A. Delitala4.
where the authors used an interpolation method to derive the mean annual precipitation map
(Fig. 2). Other studies are also published periodically by this department, including periodic
summaries, monthly reports and analysis of extreme events.
2. MATERIALS AND METHODS
The island of Sardinia is situated in the central-western part of the Mediteranean Sea,
along the paralel of 40oN and the meridian of 9oE, covering a surface of about 23600km2.
The input data used in our study is represented by the mean annual precipitation values for
a 70 years period (1922-1991), recorded at 243 meteorological stations and made available
1 Università degli studi di Cagliari, Sardegna
2 Romanian Academy, Department of Iaşi, Geography Group
3 “Al. I. Cuza” University of Iaşi, Faculty of Geography and Geology, Department of Geography
68 Geographia Technica, no.1, 2010
through the courtesy of the Hydrographic Agency for Protection and Management of Water
Resources. Compared to the surface of the island, this stations network is quite dense,
therefore ensuring the accuracy and stability of our statistical spatial models. The network
of Voronoi polygons indicates that the mean surface around a station is about 97km2, the
values ranging from 18km2 to 244km2.
Fig. 1 The first mean annual
precipitations map of Sardinia drawn
using manuals methods (M. Pinna,
1954).
Fig. 2 The mean annual precipitations digital map
obtained by interpolation techniques (P. A. Chessa, A.
Delitala, http://www.sar.sardegna.it)
The spatialization methods we used belong to 2 broad categories, namely regression
analysis and kriging. Numerous studies have proved that, among the various spatialization
methods, the the ones mentioned above yields the best spatial models for climatic variables
(Dobesch et colab., 2007; Hengl, 2007; Lhotellier, 2005; Patriche, 2009). We tested the
usefullness of multiple stepwise linear regression, ordinary kriging, cokriging with altitude
as auxiliary variable and universal kriging with a locally derived 3rd order polynomial trend
surface. The perfomance of all these methods was assessed through the cross-validation.
Cross-validation is the “leave one out” validation procedure. For a certain point, it implies
the comparison of the real value with the one estimated when the point value was not
included in the analysis. The root mean square error (RMSE) of the cross-validation
procedure was further used as a synthetic quality parameter in order to assess the acuracy of
our spatial models.
A digital elevation model (DEM) with a 69x69m resolution, derived from the SRTM
global model (USGS, 2004), was used in order to obtain secondary terrain data, potentially
usefull for explaining the spatial distribution of mean annual precipitations: slope,
D. Secci et colab. / SPATIAL INTERPOLATION OF MEAN ANNUAL PRECIPITATIONS... _
69
exposition, altitudinal range within 1x1km moving windows, terrain exposure towards the
dominant winds (computed in SAGA-GIS software). We also tested the influence of the
distance from the coastline.
The spatial analysis was perfomed in ArcGIS v9.3 software, using the Geostatistical
Analyst extension for interpolation. As mentioned before, we also used SAGA-GIS v2.0.4
to derive the wind effect parameter.
3. GENERAL PLUVIOMETRIC CHARACTERISTICS OF SARDINIA
Located in the heart of the Mediterranean Sea, in the temperate climate zone, Sardinia
is characterized by a subtropical climate with rainy winters and hot dry summers. By
Köppen classfication, the island is characterized by a Mediterranean climate (group C), the
“Csa” type being characterizing most of the region. The “Csb” type is present in the
internal areas above 800-1000 m of altitude.
Generally, there can be distinguished a rainy season from October to May and a dry
season from June to September, but the dry season can be reduced to only two months in
the higher areas of the island (July and August) and can start from May to October in the
southern areas. Also, one can be observe that precipitations in Sardinia are extremely
variable, considering both their temporal variation and their intensity (G. Torre, 1977). The
temporal distribution of rainfall is related to the changes in latitude of the main pressures
systems. In May, Sardinia gets under the influence of subtropical high pressures systems,
which determine conditions of clear skies and dry weather. In September, when the band of
high pressure drops in latitude, the island is under the influence of Atlantic and
Mediterranean depressions, therefore under unstable weather conditions. The maximum
mean monthly precipitation is recorded in December and the minimum is recorded in July.
In May and in June, there is a clear North-South gradient. In this period, the latitudinal
position is more important than in other periods of the year. The spatial distribution of
precipitations is governed almost exclusively by the island’s relief and by the position in
relation to dominant atmospheric circulation. The prevailing humid and warm westerly
circulation is responsabile for most of the precipitation distribution patterns in the island,
obviously favoring the western sectors. However, low pressures systems coming from
North Africa, generate easterly winds that cause more precipitations in the eastern sector,
where the 24 hours amounts of precipitations are very high and sometimes exceptional, also
compared to all the italian national territory (Torre, 1977). This type of pressure system
occurs rarely, but it can induce flood events for two reasons: 1) air masses of this kind are
warmer than the western ones and their absolute humidity is higher; 2) the eastern sector
presents a more complex topography, characterized by hills overlooking the sea that favor
windward precipitations, which are intense and sometimes persistent.
The largest mean annual precipitation amounts are recorded on the main mountains,
located in 4 areas: Gallura in the North-East, Gennargentu in the central-eastern area,
Campeda – Montiferru – Marghine in the North-West and Iglesiente in the South-West.
The precipitation amounts are smaller in the South of the island, where the particular
topography induces foehn effects to both the western and the eastern air currents. The driest
place is Capo Carbonara, in the extreme South-East of the island, where the mean annual
precipitations value is 381.4 mm. The rainiest place is located in the North-East of the
island (Valliciola) which receives 1343,6 mm.
The season of highly 24 hours rainfalls corresponds, for most of Sardinia, with the
rainfall season. The probability of high amounts of precipitations increases once the
eastward extention of Azores high-pressure cell collapses, especially in the west part of the
70 Geographia Technica, no.1, 2010
Mediterranean basin, with a sudden drop in pressure that occurs during the second half of
October (Barry, Chorley, 2003). The synoptic conditions of reaching maximum 24-hour
precipitations can be synthetised in the 3 following main types:
1) Cut-off lows. Under anticyclonic conditions over the continent, cut-off lows can be
splitted from the circumpolar vortex in altitude and remain isolated over eastern Europe
from which they are being triggered clockwise over western mediteranean. Here, the steep
temperature contrast between the warm waters of the Mediterranean Sea and the cold air in
altitude leads to a very unstable troposphere. Convective cells extends over Italy and
western Mediterrana, including Sardinia, where high amounts of precipitations can occur
upon the whole island, but especially upon the easterly slopes of mountain ranges. In the
later stages of cut-off evolution a weak cyclone can appear on the sea level (Fig. 3). In this
manner are measured the absolute maximum 24 h precipitations over Sardinia (for instance,
in such conditions, from 11 to 15 of November 1999 the weather station of Muravera
situated on the East coast gathered 461,6 mm, Decimommanu on the South 537,4 mm, but
just 19 mm at Sindia on the west sector).
Fig. 3. Weak cyclone at ground level, enhanced by
cut-off low in western Mediterrana on November
12, 1999
Fig. 4. Genoa cyclone developing after atlantic
mP air invasion on January 5, 2003
2) Genoa type cyclones. The potential for high amounts of precipitation grows in
Sardinia because of its position in the center of the western Mediterranean basin, in the near
proximity of the most important region of cyclogenesis from subtropical latitude – The Gulf
of Genoa. Within the rainy season, the often invasions of cold atlantic air (mP) above the
warmer waters of Genoa gulf leads to cyclogenesis in this area, Sardinia being positioned in
winter on the so called Mediteranean front (Fig. 4). There is an average of 60 cyclones per
year that develop in this region (Meteorological Office, 1962). In this situation,
precipitations in Sardinia are generated primarly from multiconvective cells that move from
South-West to North-East in the warm sector of the cyclone centered in the Genoa Gulf.
Thus, the highest 24 h precipitation amounts are generally recorded in the South-West of
the island and along the South-West orientated slopes of the mountain ranges. Also, the
eastward movement of the cyclone leads to the passage of the cold front over Sardinia
determining considerable amounts of precipitation in the North-West of the island (122.7
mm between 7 and 9 of January 2003 at Sindia weather station in the West of the isle and
17.2 mm in the same period at Tortoli weather station on the east coast). This is the
dominant cause for precipitation occurring when cyclonic conditions over the continent
D. Secci et colab. / SPATIAL INTERPOLATION OF MEAN ANNUAL PRECIPITATIONS... _
71
prevail, the Azores maximum being driven over the Atlantic or even eradicated by the
Icelandic low.
3) Warm season convection. In the warm season, especially under anticyclonical
conditions, the contrasting warming of the island and of the sea around determines the
convective mixing of the two air masses, leading to appreciable amounts of precipitation
over island, especially in the mountain area (for instance 47,4 mm at Colonia Penale
Sarcidano and 40.4 mm at Sadali on 23 August, 1997).
4. SPATIAL MODELS OF MEAN ANNUAL PRECIPITATIONS
Regression analysis is a global spatialization method, which uses all the data from the
region of interest and correlates it with different quantitative terrain aspects in order to
derive a single prediction equation for the dependent variable. This approach has the
advantage of explaining the spatial distribution of the analysed parameter through the
predictors integrated in the regression equation. The main disadvantage is that the
regression model does not keep the values of the predictand in the known points. Moreover,
because it is a global spatialization method, the regression is uncapable of rendering spatial
anomalies, which are important for precipitations. These limitations could be minimized by
using a local regression approach, such as the Geographically Weighted Regression – GWR
(Fotheringham et al., 2002). Also, one must pay great attention in choosing the right
predictors, which may be statistically significant, but may also have a contribution to the
overall degree of explanation of the model too small for them to be regarded as real
predictors.
In our case, from all the tested terrain aspects, the terrain altitude proved to be the only
certain predictor for the mean annual precipitations, explaining 53% of its spatial
distribution. The other variables, though some of them statistically significant, did not
contribute with more than a few percents to the overall degree of explanation.
The regression equation infers a vertical pluviometric gradient of 44.6mm/100m,
starting from a mean precipitation value of 598mm/year at sea level (Fig. 8). The latter
aspect is a limitation of the method, as there are many stations dispaying precipitation
values lower than this threshold. The mean difference between the real and the predicted
values (RMSE) is 115.6mm/year (116.7mm/year for the cross-validation chart). To sum up,
the altitude is a real and important predictor, but the altitude in its self is not enough to
obtain an acurate spatial model of mean annual precipitations.
Opposite to regression, kriging is a local interpolation approach, based on the spatial
autocorrelation of the analysed parameter. The main advantages of using kriging are the its
capability of rendering spatial anomalies and the fact that the values in the known points are
presearved. The main disadvantage is the fact that the spatial distribution is not actually
explained e.g. the method does not infer an altitudinal gradient.
There are many types of kriging analysis. Three of them were tested in our study,
namely the ordinary kriging, cokriging and universal kriging. The fourth method, that of
residual kriging (regression kriging) is a mixt approach and it will be discussed later.
Ordinary kriging is the simplest approach. It does not take into account any terrain
aspects, the interpolation being based only on the values associated to the points. The
outcome of this method is shown in Fig. 5. We may notice that the spatial variation of
precipitations is quite smooth and we can broadly differetiate the moutainous area from the
lowlands. This method has the highest RMSE value (120.2mm/year).
72 Geographia Technica, no.1, 2010
Fig. 5. Mean annual precipitations map obtained
by ordinary kriging (RMSE=120.2mm/year) Fig. 6. Mean annual precipitations map obtained by
cokriging (RMSE=103.1mm/year)
Fig. 7 Mean annual precipitations map obtained
by universal kriging (RMSE=104.3mm/year)
Fig. 8 Mean annual precipitations map obtained by
altitude regression: P=598.3+0.446·H
(RMSE=116.7mm/year)
D. Secci et colab. / SPATIAL INTERPOLATION OF MEAN ANNUAL PRECIPITATIONS... _
73
Fig. 9. The residual kriging approach and the resulting mean annual precipitations map
(RMSE=86.2mm/year)
74 Geographia Technica, no.1, 2010
Cokriging with altitude as auxiliary variable slightly improves the spatial model, the
RMSE of the cross-validation chart being 103.1mm/year. We may notice that the terrain
relief is better accounted for (Fig. 6).
Universal kriging is a three-stages approach. During the first stage, a polynomial trend
surface is extracted from the data, then the differencies from this surface (residuals) are
interpolated, generally by ordinary kriging and finally the trend surface and the residuals
are added up, resulting the spatial distribution. Our analysis found that better results could
be obtained using a 3rd order polynomial locally derived trend surface (Fig. 7). The RMSE
is similar to the one of previous method (104.3mm/year), but the precipitations field
displays more variation and also some unrealistic values (e.g. the minimum raster value is
148mm/year, while the minimum station value is 381.4mm/year).
Residual kriging (regression-kriging) is a mixt approach, combining regression and
kriging in a single method. This integration eliminates the disadvatages of both these
methods. Therefore, such an approach is able to both explain the spatial distribution by
means of the predictors integrated in the regression equation and to render spatial
anomalies. The method operates in a manner similar to the universal kriging, but instead of
using polynomial trend surfaces, it uses the spatial model achieved by regression. In our
case, the residuals from the altitude-precipitations model were interpolated by ordinary
kriging, then the altitudinal and the residuals models were added up in order to obtain the
final precipitation map (Fig. 9). Judging by the RMSE of the cross-validation chart
(86.2mm/year), this approach seems better than the previous ones
5. CONCLUSIONS AND PERSPECTIVES
Our study shows that, from all the spatialization methods we tested, the residual
kriging (regression-kriging) approach seem to yield better results, the method displaying
the minimum RMSE value for the cross-validation procedure. Our intention is to extend our
analysis to the mean monthly precipitations. Further reasearch will focus on deriving new
predictors to improve the regression model, on testing other spatialization method, such as
the GWR (Fotheringham et al., 2002).
Acknowledgment – The authors would like to thank the Sardinian Hydrographic
Agency for Protection and Management of Water Resources for providing the
meteorological data on which our study is based.
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It is now widely accepted that rivers modify their erosion rates in response to variable rock uplift rates, resulting in changes in channel slope that propagate upstream through time. Therefore, present-day river morphology may contain a record of tectonic history. The simple stream power incision model can, in principle, be used to quantify past uplift rates over a variety of spatial and temporal scales. Nonetheless, the erosional model's exponents of area and slope (m and n respectively) and ‘bedrock erodibility’ (k) remain poorly constrained. In this paper, we will use a geologically and geomorphically well constrained Plio-Pleistocene volcanic landscape in central Sardinia, Italy, to calibrate the stream power erosion equation and to investigate the slip rate of faults that have been seismically quiescent in the historic past. By analysing digital elevation models, geological maps and Landsat imagery, we have identified the geomorphic expression of several volcanic features (eruption centres and basaltic lava flows) and three normal faults with 6 to 8 km fault traces within the outcrop. Downstream, river longitudinal profiles show a similar transient response to relative base level fall, probably as a result of relief inversion at the edge of the volcanic outcrop. From measurements of incision, local slope and upstream catchment area across eight different rivers, we calculate n ≈ 1, m = 0.50 ± 0.02 and, using a landscape age from literature of 2.7 Ma, bedrock erodibility k = 0.10 ± 0.04 m(1−2m) Myr⁻¹. There are also knickpoints on rivers upstream of two normal faults, and we used numerical inverse modelling of the longitudinal profiles to predict the slip rate of these faults since 2.7 Ma. The results from the inverse model show that the erosional parameter values derived in this study can produce theoretical longitudinal profiles that closely resemble observed river profiles upstream of the faults. The lowest misfit theoretical longitudinal profiles were generated by a model of temporally discontinuous footwall uplift with consistently low throw rates (<0.1 mm yr⁻¹). The predicted footwall uplift history is similar for the two faults, both showing periods of fault slip and no fault movement since 2.7 Ma.
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Geographically weighted regression (GWR) is an important local technique for exploring spatial heterogeneity in data relationships. In fitting with Tobler's first law of geography, each local regression of GWR is estimated with data whose influence decays with distance, distances that are commonly defined as straight line or Euclidean. However, the complexity of our real world ensures that the scope of possible distance metrics is far larger than the traditional Euclidean choice. Thus in this article, the GWR model is investigated by applying it with alternative, non-Euclidean distance (non-ED) metrics. Here we use as a case study, a London house price data set coupled with hedonic independent variables, where GWR models are calibrated with Euclidean distance (ED), road network distance and travel time metrics. The results indicate that GWR calibrated with a non-Euclidean metric can not only improve model fit, but also provide additional and useful insights into the nature of varying relationships within the house price data set.
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Most of climatic parameters are measured at point locations, in climatological stations of an often unequal density network. However, many applications need climatic values at any point of the studied field. This PhD thesis proposes an evaluation of the uncertainty level for spatialization of temperatures in mountainous areas and a demonstration of the scale/method relation, then a quantification of the benefits of each method according to the scale of concerned applications. The subject thus includes, firstly, some developments of spatialization methods for temperatures, explaining spatial variations of temperatures: which factors work, make change the temperatures, and in which proportions? The realization of models, at various scales, is accompanied by an interpolation (reconstitution of the thermal fields by application of the previously computed models). This research includes a work on geographical information systems, and spatial variables extracted from them: land cover, relief, slope, aspect, radiation, etc), as well as a frequent use of statistical methods (univariate regressions, multivariate regressions, variance analysis, principal component analysis, etc.) Simulations are the final step, once spatializations are finished and validations are carried out. Geographical data are mainly provided by the SEIGAD laboratory and the French National Geographical Institute, weather knowledge and data come from Météo-France (daily minimum and maximum temperatures, weather types, SAFRAN model...)
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The Author, working out the pluviometrical series for 1 to 24 hours, locates the parameters of the curves of annual excedens series for each station and for the two areas: the western area and the eastern area. Besides, considering the monthly and seasonal frequencies, he shows up the evolution of the precipitations in Sardinia.
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