High-resolution temperature climatology for Italy: interpolation method intercomparison



High-resolution monthly temperature climatologies for Italy are presented. They are based on a dense and quality-controlled observational dataset which includes 1484 stations and on three distinct approaches: multi-linear regression with local improvements (MLRLI), an enhanced version of the model recently used for the Greater Alpine Region, regression kriging (RK), widely used in literature and, lastly, local weighted linear regression (LWLR) of temperature versus elevation, which may be considered more suitable for the complex orography characterizing the Italian territory.

Dataset and methods used both to check the station records and to get the 1961–1990 normals used for the climatologies are discussed. Advantages and shortcomings of the three approaches are investigated and the results are compared.

All three approaches lead to quite reasonable models of station temperature normals, with lowest errors in spring and autumn and highest errors in winter. The LWLR approach shows slightly better performances than the other two, with monthly leave-one-out estimated root mean square errors ranging from 0.74 °C (April and May) to 1.03 °C (December). Further evidence in its favour is the greater reliability of local approach in modelling the behaviour of the temperature-elevation relationship in Italy's complex territory.

The comparison of the different climatologies is a very effective tool to understand the robustness of each approach. Moreover, the first two methods (MLRLI and RK) turn out to be important to tune the third one (LWLR), as they help not only to understand the relationship between temperature normals and some important physiographical variables (MLRLI) but also to study the decrease of station normals covariance with distance (RK).

1 Introduction

Datasets of monthly climatological normals of meteorological variables (or climatologies) at a high spatial resolution have proved to be of increasing importance in the recent past, and they are likely to become even more important in the near future. Indeed, they are crucial in a variety of models and decision-supporting tools in a wide spectrum of fields such as agriculture, engineering, hydrology, ecology and natural resource conservation (Daly et al., 2002; Daly, 2006), just to cite a few. In order to provide reliable estimates of monthly climatologies, even for areas with complex topography, a large, high-density dataset must be used together with interpolation techniques that allow the most realistic representation of the main factors driving the spatial gradients (Daly et al., 2008).

At present time, monthly high-resolution temperature climatologies are not available for the entire Italian territory, but only for its Northern part (Brunetti et al., 2009, 2012; Hiebl et al., 2009). At a national scale, only lower-resolution climatologies are available, such as the 30 km resolution temperature climatology delivered within the ‘Sistema Informativo Agricolo Nazionale’ (Perini et al, 2008), as well as collections of monthly station normals, such as those produced by the National Hydrographic Service in the 1960s (Servizio Idrografico, 1966), or more recently, those produced by the Italian National agency for new technologies, energy and sustainable economic development (ENEA, see Petrarca et al., 1999), and those by the Italian National Air Force (http://clima.meteoam.it/atlanteClimatico.php).

A very important contribution towards a better knowledge of the spatial distribution of air temperature over Italy has been given in the last years by SCIA (see www.scia.sinanet.apat.it), a system for the elaboration, update, and fast availability of climatological indicators set up by the ‘Istituto Superiore per la Protezione e la Ricerca Ambientale’ (ISPRA): SCIA is the basis for the yearly reports on Italian climate issued by ISPRA (ISPRA, 2011). ISPRA also produced monthly high-resolution temperature maps from 1961 to 2009 by means of regression-kriging with altitude and latitude as external variables (and also longitude for mean temperature). The underlying observational dataset, however, shows rather discontinuous records (from about 200 stations in the 1960s to about 750 in 2008) as well as an inhomogeneous spatial coverage (Fioravanti et al., 2010a, 2010b).

Within this context we developed a research programme to produce 1961–1990 monthly temperature climatologies at a 30-arc-second-resolution for the entire Italy based on a dense, quality-controlled observational dataset. The basic assumption here is that the spatial distribution of temperature normals is tightly related to the physiographical features of the Earth's surface (Daly et al., 2002, 2008; Daly, 2006). Understanding and modelling these relations guide the construction of climatologies on digital elevation models (DEMs) which can have several orders of magnitude more nodes than the available records. The relationships between meteorological and physiographical variables range over a wide spectrum of spatial scales and, if in some cases it is necessary to investigate such relations on large geographical areas, in some others it is more appropriate to investigate them only at a local scale (Vicente-Serrano et al., 2003).

This paper aims at presenting the collected dataset, discussing the advantages and disadvantages of three of the most common methods for constructing climatologies and comparing respective results. Here we explored (1) multi-linear regression with local improvements (MLRLI), recently developed in Hiebl et al. (2009); (2) regression kriging (RK), widely used in literature; and (3) local weighted linear regression (LWLR) of temperature versus elevation, that may be considered more suitable for the complex Italian orography. The latter approach is based on the PRISM (parameter-elevation regression on independent slopes model) conceptual framework. Complete documentation on PRISM is available at the WEB site of the PRISM climate group (http://www.prism.oregonstate.edu) as well as in a number of papers (Daly et al., 1994, 2001, 2002, 2008; Daly, 2006). The PRISM approach is an improvement of the geographically weighted regression (GWR) approach (Brunsdon et al, 1996), based on weights depending on the physiographical features of the Earth's surface.

After the introduction, Section 'Data' focuses on the construction of the dataset and the quality control procedures. Then, Section 'Methods' illustrates the methods and Section 'Results and discussion' discusses the results. Finally, Section 'Conclusions' presents the main conclusions.

2 Data

The first goal of our research was to recover a dense dataset of monthly mean temperature (T m) records for Italy and surrounding areas. We collected data from many different providers at international (NCDC-GSOD), national (Air Force, Agricultural Research Council, ISPRA, Electric Board), regional (meteorological and hydrological services, agro-meteorological services, environmental agencies, civil protection offices) and local (universities, private observatories) level. In this context, we also digitized a significant fraction of data from a collection of national records published by the former Italian Hydrological Service in the 1960s (Servizio Idrografico, 1966). Finally, we also considered a number of stations with only monthly temperature normals, even though the relative monthly series were not available. For Italy these normals were recovered from the ENEA climatological database (Petrarca et al., 1999), whereas for the surrounding countries they were recovered from the dataset set up within the ECSN HRT-GAR Project (Auer et al., 2008; see also http://www.zamg.ac.at/forschung/klimatologie/klimamodellierung/ecsn_hrt-gar/), and used to obtain a temperature climatology for the Greater Alpine Region (Hiebl et al., 2009). The normals provided by ENEA were considered only when the correspondent metadata reported more than 15 valid years and there was clear information about the period on which the normals were calculated. This check was not necessary for the ECSN HRT-GAR data set, as the records were subjected to a gap filling procedure in the 1961–1990 period. However, it has been necessary to convert the ECSN HRT-GAR normals from the Kämtz mean T m = (T7 + T14 + 2 T21)/4) to the common Italian scheme T m = (T n + T x)/2, as explained in Hiebl et al. (2009).

In spite of the wide range of data providers we considered, most of the Italian records derive from the same source, i.e. the former Italian Hydrographical Service. This institution stopped its activities at the end of the 20th century and its activities and personnel were transferred to the Italian Regions: in some cases they continued to manage the station network directly, in other cases they assigned its management to external agencies. The attribution of the Hydrographical Service competences to the Italian administrative regions generally brought new resources for the station network and data rescue activities, though at the price of a greater difficulty of collecting data for the whole national territory.

All the collected records were subjected to a quality control which consisted in checking all the sites for their position (the consistency between the declared position and the elevation was the main constraint) and correcting the coordinates, when possible, or discarding the series any time the correct position could not be identified with a reasonable confidence. This checking procedure was performed by: (1) comparing the elevation of each station site with the elevation of the closest grid point of the 30-arc-second-resolution USGS GTOPO30 digital elevation model (United States Geological Survey USGS, 1996), (2) investigating discrepancies by means of metadata and/or supporting mapping tools like Google-Earth (about 500 suspect station coordinates were analysed and approximately 200 were corrected). Additional checks concerned the stations series available from more than one source: in this case only the most reliable version was included in the final dataset (i.e. usually that with the smallest amount of missing values). The time-consuming detailed check of the data turned out to be very important. In particular it was necessary to enhance the reliability of the information concerning the station elevations, as incorrect elevation values may induce significant errors in the estimation of the temperature-elevation dependence, which is the most important relation on which our climatologies are constructed.

After data quality check, the 1961–1990 temperature monthly climatological normals have been estimated for each station site (the choice of the 1961–1990 period was suggested by the wider data availability in that 30-year time window). To overcome the problem of missing data, when the 1961–1990 period was not completely available (or not available at all), the normals were first calculated with the available data, and then re-adjusted to the 1961–1990 period by means of the database of the Italian temperature anomaly records presented by Brunetti et al. (2006). Specifically, for each location corresponding to a target station with 1961–1990 partly (or fully) missing, a complete monthly local temperature anomaly (relative to the 1961–1990 period) record was calculated using the data and the interpolation method discussed in Brunetti et al. (2006). These local records were obtained by a weighted average of neighbouring stations, the weights being the product of a radial weight (taking into account the distance) and an angular weight (taking into account the anisotropy in station spatial distribution). Then, monthly temperature normals over the same period available in the target station were calculated from this reconstructed series and subtracted to the target station normals to adjust them to the 1961–1990 span. The reconstructed local anomaly records are particularly suitable for this adjustment procedure because the database used for their calculation was subjected to a very accurate quality check and homogenization procedure, and missing values were filled (Brunetti et al., 2006).

An additional data check was performed once all station normals relative to the 1961–1990 period were obtained: all station normals were compared with those of neighbouring sites to highlight the largest discrepancies. This new check allowed us to identify and correct several data errors, and to discard unreliable records. However, in a few cases large discrepancies turned out to be caused by peculiar position of the station itself and therefore judged as correct. This effect is mostly evident in winter for some Alpine stations located in narrow west–east oriented valleys: they exhibit very low temperatures for the absence of direct solar radiation.

The spatial distribution of the 1484 stations in the final dataset is shown in Figure 1 together with the area for which climatologies were calculated, which includes 1361 stations. A total of 1231 of the stations in the dataset are located in Italy or in Swiss areas south to the main Alpine ridge, while the others are distributed in the surrounding countries. The fraction of normal values not calculated from monthly records is about 29%: most of them (263 sites), however, were taken from the ECSN HRT-GAR dataset, which was subjected to a detailed procedure in order to make all values representative of 1961–1990 T m normals (Auer et al., 2008, Hiebl et al., 2009). Moreover, a large fraction of these normals is from stations that are not included in the area of our calculated climatologies: these stations were considered to have a balanced station distribution also around the points located near the boundaries of this area.

Figure 1.

Spatial distribution of the 1484 stations in the final version of the dataset. The figure also shows the orography of the region and the area for which we calculated the climatologies: the 1361 stations included within this area (red dots) were used to evaluate the performances of the three methods; the stations outside this area (white dots) were considered just to have a balanced station distribution also around the points located in the boundaries of the domain of interest.

Figure 2 shows the vertical distribution of the 1484 stations compared to that of the grid cells of the DEM belonging to the study domain highlighted in Figure 1. The figure shows that the station distribution is rather homogeneous up to about 2000 m, with an average of around three stations per 1000 grid points.

Figure 2.

Vertical distribution of the 1484 stations compared to the GTOPO30 grid-cell elevation distribution in the domain for which we calculated the climatologies.

3 Methods

The 1961–1990 Italian monthly temperature climatologies were constructed by means of three methods: (1) MLRLI; (2) RK; (3) LWLR of temperature versus elevation. All three methods aim at reconstructing the temperature normals on the 30-arc-second-resolution GTOPO30 DEM. This DEM has a root mean square error (RMSE) of about 18 m (USGS, 1996).

The same DEM was used to assign to each station the physiographical variables necessary for MLRLI and (partially) for LWLR and not available from metadata (only longitude, latitude and elevation were available for each station). In particular, for each grid cell of the DEM, we calculated the slope steepness [or simply slope (sl)] and orientation [or more simply facet (fc)], and the crossed distance from the sea (dsea), obtained by minimizing the sum of the cell-sea horizontal distance plus all vertical gradients crossed by the cell-sea segment. Slope and facet were calculated also from a smoothed version of the DEM (Msl and Mfc in the following) which allows better investigating the effect of large-scale topographic barriers on the spatial temperature distribution. This smoothed DEM was obtained by considering for each cell a weighted average of the elevations of the surrounding cells: it was calculated considering a 35 × 35 grid-cell box in which weights decrease with distance from the centre according to a Gaussian function, with value equal to 0.5 at a distance of 15 km. This combination of box width and weights decreasing rate is a compromise to obtain Mfc maps with strong gradients almost only across the main ridges of the Alps and the Apennines and to avoid extending the influence of the orographic reliefs into the surrounding plain areas. Moreover, other grid-cell variables were defined according to soil morphology and land cover. The physiographical variables of the closest grid cell to each station were then assigned to the station itself.

3.1 Multi-linear regression with local improvements (MLRLI)

The first step of this method (Hiebl et al., 2009) consists in applying, for each month, a multi-linear regression (MLR) of temperature versus elevation (h), latitude (φ) and longitude (λ) to the entire station normal data set:

display math(1)

The monthly residuals (ε) from the MLR are then subjected to further analyses aimed at identifying the most significant relations with additional geographical and physiographical variables: step by step, improvement terms are added to the MLR equation and after each step temperature residuals from this new equation are considered. The final result is an equation expressing temperature as a function of the various variables F(h, λ, φ, dsea,....). This equation can be finally applied to each grid cell of a DEM to construct, for each month, a high-resolution temperature climatology.

Amongst the possible improvements, we considered some of those taken into account in the frame of the ECSN HRT-GAR Project (Hiebl et al., 2009) and additional new effects which are also discussed in Brunetti et al. (2009; 2012) and Spinoni (2010).

The effects producing relevant improvements to the temperature estimation are: (1) sea effect; (2) lake effect; (3) Po-Plain continentality effect; (4) facet effect for both the non-smoothed and the smoothed DEM; (5) summit/valley effect; (6) urban heat island effect. They are briefly discussed below.

3.1.1 Sea effect ( ΔT sea )

The sea effect accounts for the sea water mitigation effect. It was modelled by attributing to the grid cells with dsea ≤ 1.3 km the average residual (math formula) of the corresponding non-Po-Plain stations (see Section 'Po-Plain continentality effect ( ΔT Po Plain )' and Figure 3) having dsea ≤ 1.3 km. At Italian latitudes this distance is smaller than the distance between two non-adjacent grid cells. It was also imposed that this effect vanishes when dsea ≥ 15 km. This was obtained by setting:

display math(2)
Figure 3.

Classification of the grid cells affected by Po Plain (red), urban (orange) and sea/lake (blue) effects; the orange cells are superimposed to the other ones; purple corresponds to cells affected by both Po Plain and sea/lake effects.

with dsea in km and math formula in ° C.

Both range and form of sea effect have been defined according to the analysis of scatter plots of temperature residuals versus dsea.

3.1.2. Lake effect ( ΔT lake )

The lake effect is similar to, but less prominent than, the sea effect and it was taken into account using a similar approach. In this case, however, the number of stations was too small to study the decrease of the effect with the distance from the lake (dlake); for this reason we attributed to the grid cells with dlake ≤ 1.3 km the average residual of the corresponding non-Po-Plain stations within this distance from the lakes and half of this value to grid cells with 1.3 ≤ dlake ≤ 2.6 (km). As in other cases, our choices were based on the analyses of scatter plots of temperature residuals versus dlake.

The distance of each grid cell and station from the closest lake was estimated by means of the GLC2000 land cover grid (European Commission, Joint Research Centre, 2003) considering the ‘inland water’ classified cells. The same land cover was used to identify the areas used to estimate urban heat island effect as discussed below (see Section 'Facet Effect ( ΔT facet ; ΔT macro - facet )' and Figure 3).

3.1.3. Po-Plain continentality effect ( ΔT Po Plain )

During winter months the Po Plain is affected by a cold-air pool effect causing lower than normal temperatures and temperature inversion conditions. In summer months, on the contrary, the Po Plain is affected by higher than normal temperatures. The Po-Plain continentality effect was modelled by the average residual (math formula) of all Po-Plain classified stations not affected by sea and urban effects.

display math(3)

where ppl is a binary variable, set equal to 1 for all Po-Plain grid cells and equal to 0 otherwise.

The Po Plain was identified in a few subsequent steps. First a rough contour including this area was defined by means of GIS techniques; then the minimum elevation corresponding to each longitude (Po Plain has west–east orientation) was determined and the points with elevation exceeding 300 m over this minimum were excluded. Finally, the points for which at least 20 of the surrounding 120 grid cells (i.e. those in a 11 × 11 cell box about the point) are more than 50 m higher were also excluded; this condition excludes valleys surrounding the Po-Plain area. Figure 3 shows the area identified by means of all these constraints.

3.1.4. Facet Effect ( ΔT facet ; ΔT macro - facet )

We estimated a facet effect and a macro-facet effect. The former accounts for the effect of exposition to solar radiation, while the latter is aimed to investigate the effect of large-scale topographic barriers (e.g. the Alpine and Apennines ridges) on the spatial temperature distribution.

The facet effect was modelled binning the station residuals into 36 exposition intervals 10° wide and fitting the corresponding values by means of the first two harmonics of a Fourier series. The same method was used for both the smoothed and the non-smoothed DEM. In the first case we considered all the stations with macro-slope variable (Msl) ≥ 5 m km−1, while in the second we set the slope variable (sl) threshold to 10 m km−1. With these fits we got, for any grid cell, the facet effect ΔT facet(fc,sl) and the macro-facet effect ΔT macro - facet(Mfc,Msl), where fc and Mfc are the facet and macro-facet variables (i.e. the slope orientation in the original and smoothed DEM, respectively).

3.1.5. Summit/valley effect ( ΔT summit - valley )

This effect was introduced to take into account the cold-air pool effect of the valleys and the higher exposition to solar radiation of summits and ridges. The summit/valley effect was modelled considering all non-Po-Plain classified station residuals and a new variable named sv (standing for summit-valley). It was defined determining for each point (λ,φ) the fraction of the 120 surrounding points (i.e. as above, the grid points belonging to a 11 × 11-cell box centred on the grid point under examination) that satisfy the condition h(λ,φ) − h(λ + i · Δλ, φ + j · Δφ) > 50 m (with h indicating the grid-point elevation and i and j running from −5 to +5 grid steps). This variable adequately discriminates valleys from summits and ridge areas: valleys, in fact, tend to present sv values which are very close to 0 (the minimum of sv), whereas areas on mountain ridges or on the top of hills or mountains tend to have sv values close to 1. The sv parameter identifies not only the largest valleys but also minor valleys not covered by an adequate number of stations or without stations at all.

The effect was modelled according to

display math(4)

where a 0 (b 0) and a 1 (b 1) are the coefficients of the linear fit between the station residuals ε and sv for sv < 0.25 (>0.75), math formula is the average of the residuals of the stations with 0.25 < sv < 0.75 and sva and svb are the values of sv in which the first and last interpolating lines cross the line math formula.

As for the other effects, in this case we also developed the model plotting the station residuals versus the considered variable.

3.1.6. Urban heat island effect ( ΔT uhi )

Urban heat island effect causes higher temperature if compared to rural locations. This effect was modelled simply by averaging the residuals of the urban-classified stations (math formula):

display math(5)

where lc is a land-cover variable obtained from the GLC2000 land cover grid. Figure 3 shows the grid points with lc corresponding to urban areas.

Once all the above effects have been included in the model, the final result is an equation which estimates the temperature normal of each grid cell as a function of the previous variables. That is,

display math(6)

where the only independent variables are λ and φ, whereas all other variables are obtained from them by means of the GTOPO30 DEM and the GLG2000 land cover grid.

3.2. Regression kriging (RK)

An alternative approach to the step-wise local improvements (LI) to the MLR estimations of temperature normals is to consider, for each grid cell, a distance-weighted average of the station residuals, with weights calculated by means of a kriging-based approach (Hengl, 2009). The combination of regression techniques and kriging is named RK or residual kriging, and is widely used to construct climatologies (Tveito et al., 2008; Perčec Tadič, 2010).

The MLR residual (ε) of each grid point (λ,φ) is estimated by

display math(7)

where k is the vector of the kriging weights (ki ) for the grid point (λ,φ), ε is the vector of station residuals and n is the number of stations.

For RK, as for MLRLI, all analyses have been performed on a monthly basis. The first step consists in the definition of the variogram that describes the spatial covariance of the station data. In our case the variogram was determined by (1) considering all station pairs within 300 km and clustering them according to station distance, binned into 10 km intervals; (2) calculating, for each distance interval, the semivariance of the differences of temperature residuals of all station pairs within the interval and (3) fitting semivariance versus distance by means of a chosen theoretical variogram.

The exponential variogram turned out to be the most suitable for our application. As an example Figure 4 shows distance interval semivariances versus distance for January together with the corresponding fitted exponential variogram.

Figure 4.

January variogram (nugget parameter: 0.78 °C; sill parameter: 2.35 °C; range parameter: 25 km).

The exponential variogram models the dependence of semivariance (γ) on distance (r), by means of the following relation:

display math(8)

It assumes that semivariance tends to C 0 (the nugget parameter) for r → 0, which means that spatial coherence cannot completely explain station temperature residuals. As r increases, the semivariance tends to C 0 + C 1 (the sill parameter), which means that for large distances (e.g. r > 3R) there is no more spatial coherence between station temperature residuals. The semivariance therefore approximates the global variance of the station residuals. The range parameter (R) was defined as 1/3 of the minimum distance with semivariance equal to at least 95% of the average semivariance of the intervals from that with maximum semivariance to the last within 300 km. The parameters C 0 and C 1 were determined by a fit of the theoretical variogram to the binned semivariances. This fit was performed using a weighted linear interpolation of γ versus (1 − er/R ) (Hengl, 2009), with weights given by the ratios between the number of station pairs within each distance interval and the corresponding average distance.

R ranges from 25 km in the period December–February to 45–50 km in the period May–October. C 0 ranges from about 0.4 (°C2) in the period March–July to about 0.8 (°C2) in the period December–January. C 1 ranges from about 0.3–0.5 (°C2) in the periods March–May and September–October to about 1.5–1.6 (°C2) in the period December–January.

The theoretical variogram was then used to obtain the covariance (C) versus the distance (C(r) = C1 ·er/R , (r > 0)) and the covariance matrix C, expressing the covariance of any pair of stations. The vector of kriging weights (k) for the grid point (λ,φ) was then obtained as

display math(9)

where c0 (λ,φ) is the vector expressing the covariances of the grid cell (λ,φ) with all the station positions.

The temperature of each grid cell is therefore estimated by RK as

display math(10)

where m 0, m 1, m 2 and m 3 are the previously determined MLR parameters (Equation (1)).

3.3. Local weighted linear regression of temperature versus elevation (LWLR)

An alternative approach to a global MLR with local improvements and RK is to explicitly evaluate the relationship between temperature and elevation at a local level, as it can vary appreciably over a wide and complex territory as Italy. It is then interesting to evaluate this relationship separately for each grid cell, giving more importance to the nearby stations, especially to those having topographic characteristics similar to those of the grid cell itself.

We therefore developed a methodology for evaluating the temperature of each grid cell of the DEM by means of a ‘local’ temperature-versus-elevation relation. Specifically we used a weighted linear regression (Taylor, 1997) of the data from nearby stations to predict the temperature at the grid cell (λ, φ) as a function of its elevation h. That is,

display math(11)

where a(λ,φ) and b(λ,φ) are the local regression coefficients.

Here, for any grid cell, only a cluster of stations is considered and greater weights are given to the stations with elevation and topographic position similar to that of the grid cell that is being considered. Specifically, a minimum number of 15 stations is required (and a maximum of 35 is used) to evaluate the temperature/elevation regression. If less than 15 stations are available the temperature normal of the grid cell is not estimated (this never happened in the considered domain). The stations selected for the regression are the 35 stations with the highest weights among those within 200 km from the given grid cell. Instead of progressively increasing the search range until a sufficient number of stations is available, we consider a very large search range (200 km) and chose only the stations with the highest weights. This is because the radial distance from the grid cell is not always the leading discriminant.

The weight of the ith station involved in the linear regression yielding the estimation of the temperature of the point (λ,φ) is the product of the following weighting factors:

display math(12)

All the weighting factors (position, height, distance from the sea, slope steepness and slope orientation) are based on Gaussian functions of the form:

display math(13)

where var is the specific geographical variable which is being considered, math formula the absolute value of the difference between the value of this variable at the grid-cell point (λ,φ) and that at the ith station location and cvar a coefficient which regulates the decrease of the weighting function with increasing math formula. In the case of facet the difference math formula is defined as

display math(14)

For an easier interpretation of the weighting factors, the coefficients cvar can also be expressed in terms of the value math formula which gives a weighting factor equal to 0.5:

display math(15)

The selection of the most appropriate math formula values to be used in the weighting factors was performed iteratively, for each month of the year, by searching for the value that gives, for any variable, the lowest possible error at station locations (see the next section for an extended discussion of the calculation of the errors at station locations). Detailed below are our choices of math formula:

3.3.1. Distance

The math formula varies from month to month, with the smallest decay distances corresponding to winter months (33 km in December) and the largest ones to late spring/early summer months (58 km in May).

3.3.2. Elevation

display math(16)

where h is the elevation of the grid point (λ,φ). This choice guarantees a steeper decrease of the elevation weight at the foothills to capture the thermal inversion in winter months, and a more gradual decrease at high elevations to avoid underweighting of the stations in the reconstruction of higher and isolated grid cells.

3.3.3. Sea distance

display math(17)

where dsea is the distance from the sea of the grid point (λ,φ). Here a sharper decrease is imposed close to the sea, whereas at greater distances a more gradual decay is used.

3.3.4. Slope steepness and orientation

display math(18)
display math(19)

Figure 5 shows an example of the application of the method to two grid points about 15 km from each other and with different characteristics in terms of exposition and sea influence. As it is evident from Figure 5(a) and (b), the stations involved in the linear fit evaluation are not those closest to the grid cell, neither is their distribution around the grid-cell isotropic, although it is significantly influenced by the topographic parameters. To provide the reader with an example about the differences in station choice between a weighted and an unweighted method (with the distance from the grid cell as the only discriminant) Figure 5 shows a circle which includes the stations that would be selected using the latter method. The two sets of 35 stations involved for the temperature evaluation of the two grid cells indicated in Figure 5(a) and (b) have 2/3 of stations (23 out of 35) in common, but they contribute in a different way to the weighted linear fit (see Figure 5(c) and (d), where the circle size is proportional to the corresponding station weight, producing significantly different lapse rates (Figure 5(c) and (d)).

Figure 5.

Example of local weighted linear regression for two grid points a few kilometres from each other and with different characteristics in terms of exposition and sea influence. Coloured dots in panels (a) and (b) show the locations of the stations involved in the regression fits of the two grid cells ((a) lon = 10.00°E, lat = 44.30°N, h = 472 m; (b) lon = 10.12°E, lat = 44.41°N, h = 850 m), the colours indicate the weights of the stations; the circle indicate a distance of 50 km from the grid cell. Panels (c) and (d) show the weighted regression fits for the same two grid cells; station weights are represented by the size of the corresponding points in the scatter plots. The regression parameters correspond to −6.94 °C km−1 (c) and −5.01 °C km−1 (d).

4. Results and discussion

4.1 Model-data comparison: estimated and observed station normals

The methods discussed above were evaluated individually in terms of their ability to estimate observed temperature normals at station level. Specifically, the 1961–1990 normals of monthly temperatures were estimated by each method for the 1361 stations shown in Figure 1, and then compared with the observed values. In all cases we used a leave-one-out approach that implies the removal of the station whose monthly normals were being reconstructed, to avoid ‘self-influence’ of the station data under consideration. Only a minor exception to this approach was made for RK due to computational time reasons. Here, the kriging weight of the station to be reconstructed was simply set to 0 and weights of the remaining stations properly re-normalized, while the MLR coefficients and the covariance matrix were obtained from the full station data set.

The results of the comparison between estimated and observed station normals are given month-by-month in Table 1, where the accuracy of each method is measured by the mean error (bias), the mean absolute error (MAE), and the RMSE.

Table 1. Accuracy of the monthly climatologies obtained with the three methods
  1. The accuracy was quantified by comparing the estimated station normals with the observed ones by means of mean error (BIAS), mean absolute error (MAE) and root mean square error (RMSE). All the estimations were performed with the leave-one-out approach.−0.040.771.01

The three methods show a very small bias, with values within ±0.05 °C in any month. This indicates that none of these methods is seriously affected by systematic errors, at least globally, i.e. when the mean bias over all the stations is taken. On the other hand, the MAE and RMSE turned out to be smaller for LWLR (with monthly averages of 0.65 and 0.84 °C, respectively) than for RK (0.69 and 0.88 °C, respectively) and MLRLI (0.80 and 1.01 °C, respectively).

For the latter method we also studied the error reduction when the residuals are subjected to an additional interpolation method (see Spinoni (2010) for more details on this approach). We used both inverse distance weighting (IDW, with weights given by distance and elevation differences) and kriging, again with the leave-one-out approach; we obtained MLRLI errors slightly smaller than RK errors, although still larger than those of LWLR (results not shown).

We also analysed monthly LWLR residuals in order to check whether we could further reduce errors by applying a spatial interpolation method such as IDW or kriging. We considered the same distance intervals used for the kriging variograms and plotted the semivariance of the temperature residual differences versus distance: these plots (not shown) highlight that the LWLR station residuals do not depend on distance; therefore, it is useless to subject them to spatial interpolation methods such as IDW or kriging.

We additionally tested the importance of station weighting in LWLR by performing an ordinary regression with the closest stations and all weights set equal to 1. In this case the errors turned out to be equal to those of RK, with monthly average MAE and RMSE of 0.69 and 0.88 °C, respectively.

We then tested whether the three methods produce systematic errors at a local level when selected station clusters are considered. To this end, we evaluated the station bias separately for different 1° latitude belts, including (1) all the stations, (2) only those stations with elevation above 800 m a.s.l. Figures 6 and 7 report the bias distribution in January and July, for case (1) and (2) respectively. Figure 6 clearly shows that at some latitude belts MLRLI is affected by a large bias during winter, especially in Southern Italy (positive bias), and to a lesser extent in the Northern part of Central Italy (negative bias). Errors are generally smaller in summer, even though MLRLI again shows the largest errors. Figure 7 (case 2) proves that the large winter bias of MLRLI in the southernmost part of Italy mainly concerns high-elevation stations. For these stations also RK shows a marked bias, whereas the LWLR errors remain small at any latitude belt. Also in this case the differences between competing methods are smaller in summer than winter, and MLRLI again exhibits the lowest performance.

Figure 6.

January and July box-plots of the errors of the three methods, clustering the stations within 1° latitude belts. All stations are considered here. The boxes range from the lowest quartile to the highest one and are centred on the median; whiskers represent the minimum and the maximum errors.

Figure 7.

As in Figure 6, but for stations with an elevation above 800 m a.s.l. only.

The difficulty of MLRLI (and partially RK) in correctly estimating temperature normals of the high-elevation stations in Southern Italy is even more apparent from Figure 8 which shows for any month a bias distribution restricted only to stations with elevation ≥800 m a.s.l. and latitude ≤40°N.

Figure 8.

Monthly box-plot of the errors of the three methods from stations with latitude <40°N and elevation >800 m a.s.l. The boxes range from the lower to the higher quartiles and are centred on the median; whiskers represent the minimum and the maximum errors.

Further insights into limitations of a global MLR involving all stations—at the base of both MLRLI and RK—can be gained by comparing the full MLR results with those of an additional MLR restricted to those stations located at a latitude below 44°N. The regression coefficients relative to each independent variable are listed month-by-month in Table 2, for (a) the full MLR and (b) the restricted MLR as above. Here, elevation coefficients (lapse rates) are markedly different, especially during winter. This discrepancy can be explained by the strong influence that Alpine stations have on the full MLR: they are the bulk of mountain stations and cover a wider altitude range than the Apennine stations. The contribution of the Alpine stations, in particular, leads to weaker than observed lapse rates during winter in large parts of Italy, thereby producing the MLRLI positive bias at high-elevation stations in Southern Italy (Figures 6-8). Hence, the lapse rates estimated by MLR over all stations do not reflect the real temperature-elevation relationship across the entire region. Actually, both local improvements and RK after the initial MLR yield a more realistic spatial distribution of the lapse rates (especially for kriging), albeit these subsequent re-adjustments cannot completely remove the above bias.

Table 2. Coefficients obtained applying the temperature versus elevation-latitude-longitude MLR to (a) all the 1484 stations of the area and (b) only to the 572 stations with latitude <44°N


(°C 100 m−1)


(°C degree−1)


(°C degree−1)



(°C 100 m−1)


(°C degree−1)


(°C degree−1)

1 −0.440−1.15−0.17 −0.628−0.82−0.14
2 −0.514−0.91−0.15 −0.636−0.66−0.13
3 −0.573−0.64−0.11 −0.599−0.49−0.06
4 −0.611−0.43−0.03 −0.567−0.330.02
5 −0.606−0.370.04 −0.521−0.300.09
6 −0.607−0.460.01 −0.516−0.370.07
7 −0.600−0.59−0.05 −0.497−0.390.02
8 −0.592−0.66−0.03 −0.515−0.460.01
9 −0.566−0.67−0.03 −0.561−0.53−0.02
10 −0.514−0.79−0.07 −0.597−0.64−0.09
11 −0.477−1.02−0.07 −0.608−0.79−0.07
12 −0.435−1.20−0.15 −0.618−0.86−0.11

Similar discrepancies between global and restricted MLR appear in the latitude coefficients as seen in Table 2(a) and (b), and underline the fact that temperature dependence from latitude is also poorly captured by a global, linear approach. The increase of temperature along the north-to-south direction is, in fact, strongly emphasized by the Alps and the northern parts of the Apennines. These west-to-east-oriented orographic barriers cause important climatic discontinuities with strong north-to-south temperature gradients within rather small distances; the Alpine temperature discontinuity is more important in summer, whilst the Apennine one is mainly evident in winter.

The above discussion then suggests that the reason for larger errors in MLRLI (and partially RK) than in LWLR mainly lies in the assumption that the same relations of temperature with elevation, latitude and longitude hold over the entire study area. In fact, in both MLRLI and RK the effect of these variables is estimated globally by means of a unique MLR computed over all the station temperature normals. In previous studies (Hiebl et al., 2009; 2011), the limitations of a unique MLR over complex regions were overcome by splitting the area of interest into smaller, more homogeneous sub-domains and performing a separate MLR for each of them. A drawback of this approach, however, is the frequent artificial discontinuities arising at the boundaries of nearby sub-domains. On the other hand, LWLR here proposed estimates temperature with a local approach using at most 35 stations and avoids these boundary discontinuities.

A final remark concerns the role of major local improvements to MLR in special station clusters, e.g. sea and Po-Plain stations. In the case of the Po-plain effect, restricting the error analysis only to those stations to which local improvement was tailored, both MLRLI and LWLR present a very low bias, on the contrary, RK is affected by an important positive bias in winter (Figure 9(b)). In the case of sea effect, no bias is found for MLRLI, whereas a negative winter bias affects both RK and LWLR (Figure 9(a)), while in summer RK is positively biased and LWLR is almost unbiased. A deeper analysis, however, shows that even though MLRLI is unbiased, it exhibits larger MAEs and RMSEs than the other two methods, and LWLR again performs best in any month (Figure 9(a) and (b)). This is because MLRLI well captures the modelled effect only on average and overlooks its variability from point-to-point. For instance, coastal effects of the Adriatic and Ligurian Seas are modelled by MLRLI in the same way without taking into account the different geographic features of the two regions.

Figure 9.

Monthly average errors of the three methods from (a) coastal (stations within the first 1.3 km from the sea) and (b) Po-Plain stations. Filled symbols indicate RMSE, empty symbols indicate BIAS.

In view of the above results LWLR exhibits the best performances at the station level, if we consider both the entire study area and smaller clusters of stations, especially during winter months when the complex orography of the Italian territory strongly influences mean temperatures and gradients. Therefore, since LWLR convincingly reproduces local variations of temperature with elevation, it stands out as the most suitable approach for producing Italian climatologies on a high-resolution grid, as discussed in detail below.

4.2 High-resolution climatologies

A detailed comparison between the climatologies produced with the three methods is illustrated in Figure 10(a)–(d) for January and July. Here, the differences between monthly normals are reported (MLRLI minus LWLR and RK minus LWLR), rather than their absolute values, to emphasize even small discrepancies.

Figure 10.

Differences between MLRLI (RK) and LWLR climatologies for January (a) and (b) and July (c) and (d).

The most pronounced differences appear in the MLRLI-LWLR comparison, where the MLRLI difficulties previously detected in the estimates of station normals are distinctly reflected at the grid-point level. Noteworthy is the large positive difference observed in January (Figure 10(a)) between MLRLI and LWLR climatologies of high elevation grid points in southern Italy, with values that exceed 3 °C and peak at the highest mountains (e.g. Mount Etna).

As seen in Figure 10(b), similar discrepancies, though with smaller values, also appear in the January comparison between RK and LWLR. The RK and MLRLI overestimations at these grid points have their common root in the large error affecting MLR elevation coefficients during winter in Southern Italy, which causes a relevant positive bias at high-elevation sites, as discussed in the previous section (Table 2).

Remarkable winter differences also concern the Po-Plain basin (Figure 10(a) where, as previously discussed (Figure 9), it turned out that LWLR estimates the station normals in a more accurate way than MLRLI does (LWLR has lower RMSE than MLRLI). Indeed, in the latter case a single monthly correction to MLR coefficients for the whole Po-Plain basin hardly captures the complexity of the continentality effect of this area. This can be seen, for instance, in the north-eastern part of the Po-Plain basin (to the north of the Venice lagoon) where the MLRLI grid-point estimates of temperature normals appear to be overly corrected (i.e. negatively biased) by the Po-Plain local improvement. Instead, MLRLI estimations suffer from a positive bias in the area South to the Po river, where a larger correction would be required to account for thermal inversion effects. Likewise, MLRLI normals appear to be under-corrected in the western part of the basin, and especially in some areas not classified as Po-Plain points on the basis of the elevation criteria (Figure 3) but nonetheless affected by the cold air pool which characterizes the Po Plain in winter.

It can be seen again in Figure 10(a) that the MLRLI normals in the coastal areas are either positively or negatively biased with respect to LWLR, where the detailed effect of the sea, especially during winter, is not well described by a global regression performed over the Italian coastal stations altogether.

The unsatisfactory representation of the latitude effects provided by MLR and, in particular, the overestimation of the north-to-south temperature gradient (significantly affected by the temperature discontinuity across the northern part of the Apennines), as discussed in the previous section (Table 2), is clearly reflected in winter climatologies (Figure 10(a)) in the cold biased MLRLI normals of the northern part of Central Italy and the warm biased MLRLI normals of the southernmost part of the country. These biases persist to a lesser degree during summer (Figure 10(c)), when MLRLI-LWLR discrepancies are generally less marked. During summer the MLRLI normals show a warm bias in the northern part of the Alps (Switzerland and Austria), induced by the poor MLR representation of the Alpine temperature gradient (also in this case there is an important discontinuity due to a geographic barrier).

As with the RK-LWLR comparison (Figure 10(b) and (d)), the most pronounced discrepancies can be found again in winter climatologies. Besides the above-discussed high-elevation warm bias in Southern Italy, RK normals are up to 3 °C colder than LWLR normals in the North-Eastern Alps. In this area the valleys are characterized by a very strong thermal inversion during winter, which is not well accounted for by the MLR performed over the full station data set. Hence, the corresponding stations normals have strong negative residuals which are extended to the surrounding points (regardless of their elevation) by kriging. Note that excluding the highest-elevation stations from LWLR, resulting normals of high-elevation grid points in the above region get colder and the RK-LWRL differences gradually reduce. That is, a potentially negative bias in LWRL vanishes with increasing availability of high-elevation data, whereas RK is less sensitive and its bias persists.

Finally, absolute values of gridded monthly normals for LWLR are represented in Figures 11 and 12 for January and July respectively, which represent the coldest and warmest period of the year. Figure 13 shows the LWLR climatology for the yearly average temperature.

Figure 11.

January LWLR climatology.

Figure 12.

July LWLR climatology.

Figure 13.

Yearly LWLR climatology.

4.3. LWLR prediction interval

Besides a better performance in terms of station errors, LWLR has the additional advantage of estimating a prediction interval for any grid point of the considered domain. This estimation was performed as in Daly et al. (2008). The procedure consists in estimating the variance of the temperature (T) of a grid point at elevation h new as

display math(20)

where MSE is the mean square error of the observed station temperatures compared to those obtained with the regression model.

This estimation takes into account both the variation in the possible location of the expected temperature for a given elevation (math formula) and the variation of the individual station temperatures around the regression line (MSE). The former term depends on the regression coefficient errors, the second depends on the fact that the temperature versus elevation linear regression on which LWLR is based describes only a part of the variability of the station temperature normals.

Expressing math formula in terms of MSE, station weights [wi , as defined in Equation (12)] and station elevations (hi ), we get:

display math(21)

where i ranges over the stations involved in the grid-point reconstruction.

The problem of defining a prediction interval (with confidence α) for the grid point with elevation h new can easily be solved considering the interval:

display math(22)

where t is the value of a Student distribution with df degrees of freedom corresponding to cumulative probability (1 − α)/2. As in Daly et al. (2008) df was simply identified with the number of stations considered in the regression even though this assumption may have some problems which are discussed in detail by Daly et al. (2008).

In order to get prediction intervals easily comparable with the station leave-one-out RMSE, we selected α = 0.68; so, we called these intervals PI68. Their half widths, calculated for the grid points closest to the stations, turn out to be in excellent agreement with the leave-one-out station RMSE (Table 1), with monthly differences generally within 1% and with the average of the monthly differences within 0.1%.

Figure 14 shows the LWLR PI68 half widths for January and July. As expected from the results in Table 1 (LWLR RMSEs), winter months are those with the largest PI68. In winter the area with the largest confidence intervals is located in the Ligurian Alps: this area has very strong temperature gradients within rather short distances, with extremely mild conditions on the southern slopes facing the Ligurian Sea, and rather continental climate on the northern slopes. Therefore, in this area, the exposition plays a very important role, and stations at the same elevation but with different expositions can have very strong temperature differences. Other areas with rather large errors are located in the central and eastern part of the Alpine region: they probably reflect the difficulty in performing the fit in presence of stations located in very cold valleys. In summer, the area with highest errors is in Calabria: these rather large errors are due to the short distance of the Apennine chain from the sea. Here the results are affected by rather cool stations at the lowest elevations (the coastal stations are mitigated by the sea) which cause significant deviation from linear behaviour in the station temperature-elevation regression.

Figure 14.

LWLR prediction interval half width (a) January and (b) July.

Naturally, all the previous problems would greatly benefit from an increase of the density of the station network. This density, in fact, turns out to be the most important issue for LWLR. So, although MLRLI (and partially also RK) can also be used with a rather poor station network, LWLR, instead, requires a dense station network in all the parts of the study domain.

5 Conclusions

Monthly 30-arc-second-resolution temperature climatologies for the 1961–1990 period were derived for the entire Italy, based on a dense, quality controlled station network.

Three distinct approaches were used, i.e. (1) MLRLI, recently applied to a large Alpine Region which also includes Northern Italy (Hiebl et al., 2011); (2) RK, widely used in literature; and (3) LWLR of temperature versus elevation, considered more suitable for the complex orography characterizing the Italian territory.

All three approaches turned out to capture station temperature normals quite reasonably, with lowest errors in spring and autumn and highest errors in winter. LWLR showed slightly better performance than the other methods, with leave-one-out-estimated RMSEs ranging from 0.74 °C (April and May) to 1.03 °C (December). The better performance of LWLR was even more evident when selected station clusters were considered, giving evidence of a greater reliability of local approach in capturing the behaviour of the temperature–elevation relationship in a complex territory such as Italy. An additional advantage of LWLR is that it permits the estimation of a prediction interval for any grid point of the considered domain.

An important strength of MLRLI is its robustness in terms of station availability and station errors. It is due to the fact that both MLR and the main local improvements consider a very large number of stations which could be strongly reduced without producing significant effects. On the other hand, the most important point in favour of RK is its simplicity: it allows obtaining the final climatologies using only standard and well-known procedures.

Therefore, even if in our case LWLR turned out to be the most appropriate approach, this result cannot be generalized. For other datasets and/or other regions other methods could be more adequate, either because they are simpler to use or because the station density is (globally or locally) not sufficient to apply LWLR.

Moreover, the availability of results from more than one method is very important: the comparison of the different climatologies is in fact very useful to highlight the strengths and weaknesses of each method. Additionally, each approach can benefit from the results produced with the other approaches. In our case all analyses performed to set up MLRLI and RK helped to tune LWLR, as they related temperature normals with some important physiographical variables (MLRLI) and they showed how covariance of station normals decreases with distance (RK).


This study has been carried out in the framework of the EU project ECLISE (265240). We sincerely thank all the institutions and projects whose data contributed to set up the 1961–1990 temperature database. They are: ISPRA, Italian Air Force, ENEA, the former Italian National Hydrographical Service, ENEL, CRA-CMA, the Environmental Agencies of Emilia Romagna, Liguria, Lombardia, Piemonte and Veneto, the Regional Administrations of Calabria, Marche, Puglia, Sardegna, Sicilia and Toscana, Province of Bolzano, SMI, Meteo Trentino, NOAA-NCDC, Meteo-Swiss, ZAMG, ARSO, ECSN HRT GAR Project and HISTALP Project. We also kindly acknowledge Prof. Ruth Löwenstein for the help in improving the language of the paper.