Spatial interpolation of sunshine duration in Slovenia

Transcription

1 Meteorol. Appl. 13, (2006) Spatial interpolation of sunshine duration in Slovenia doi: /s Mojca Dolinar Environmental Agency of the Republic of Slovenia, Meteorological Office, Vojkova 1 b, 1000 Ljubljana, Slovenia m.dolinar@gov.si The objective of the present study is the calculation of the spatial distribution of sunshine duration in the territory of Slovenia. Four maps at 1 km resolution were prepared to present the spatial distribution of sunshine duration for winter, spring, summer and autumn. The values on all four maps are 30-year mean seasonal sunshine duration, calculated from measurements from 43 meteorological stations in the period The seasonal presentation was chosen due to the high inter-seasonal variability in spatial distribution of sunshine duration. The values on the maps were calculated on a mathematical horizon, to avoid the influence of geographical, urban and vegetation distortions. The interpolation model is a combination of a multivariate regression model, residual kriging and simple mathematical models. Geographical variables (altitude, latitude and longitude) are used in models to explain the spatial variability of sunshine duration. For each season, regionalisation is performed based on sunshine duration data, derived geographical data and radio-sounding data. The interpolation models are developed for each region separately and afterwards the calculated layers are merged using GIS techniques. Keywords: sunshine duration, spatial interpolation, climatological maps, Digital Terrain Model, kriging, GIS, Slovenia Received 12 August 2005, revised 18 July Introduction Solar energy has great potential as a renewable energy resource and demand for detailed solar energy climatology is growing rapidly (Medved et al. 2001). Sunshine duration is one of the indicators and is an input variable in the calculation of solar energy potential, since solar energy measurements are too sparse to permit the calculation of a detailed solar energy climatology. In Slovenia only one station has solar energy measurements spanning 30 years, but there are 43 stations with sunshine duration measurements within the reference period (Ovsenik-Jeglič 2004). This is the main reason for calculating the spatial distribution of seasonal sunshine duration on a mathematical horizon. The seasonal maps are used afterwards for calculating the sunshine duration on the actual horizon on the decadal scale, taking into consideration the topographical influences. A simple model is built on the decadal scale to calculate the solar energy received at the surface using the sunshine duration. The dependence of sunshine duration on altitude is strong, but varies from month to month (Hočevar et al. 1982). In the winter and autumn months there are more sunshine hours in regions with higher elevation on account of fog and low cloud persisting in valleys and basins. On the other hand, in the late spring and summer months, there is more sunshine on the plains due to more pronounced convection in and near mountainous regions. Because of this, regionalisation is performed and an interpolation model developed for every region and season separately. Geographic Information Systems (GIS) provide scientists with a range of tools, which are important in many environmental sciences including climatology (Dobesch et al. 2001). In the present study, GIS functionalities are used for the derivation of complex terrain variables, regionalisation, developing interpolation models, merging the spatialisation results of different regions into the final map and, finally, for the presentation and cartographic production of digital results. The advantage of digital maps, constructed by GIS, is the simplicity of their use as an input in different models (e.g. computation of solar energy potential, different environmental sciences models). 2. Data Two basic types of data are used to calculate the spatial distribution of sunshine duration: climate data geographical data 375

2 Mojca Dolinar Figure 1. Relief map of Slovenia showing the spatial distribution of meteorological stations which measured sunshine duration in the period Figure 2. The distribution (relative frequency) of Slovenian terrain (Digital Terrain Model with resolution 100 m) ( the stations with sunshine duration measurements ( ) according to the altitude. )andof In the reference period , sunshine duration was measured continuously at 19 stations. Additionally, there are 24 stations with observations spanning at least five years. The missing data for these 24 stations were supplied using interpolation on a daily basis. When available, direct and global radiation measurements were used and sunshine duration calculated using longterm monthly factors. Otherwise, explanatory variables such as sunshine duration at the nearest station and cloudiness at the station and nearest station were used, and sunshine duration was calculated from correlations 376 between described variables. The spatial distribution of observational stations is presented in Figure 1. The distribution of the stations according to altitude is relatively consistent with the altitude distribution of the topography of Slovenia, shown in Figure 2, with the highest station being Kredarica (2514 m). To determine the border between basins (with fog and low cloud) and highlands in autumn and winter, and the average base of convective clouds in mountainous regions in spring and summer months, radio-sounding

3 Spatial interpolation of sunshine duration in Slovenia data were used. The cloud base heights and the cold air pool heights were calculated from temperature and humidity profiles. The continuous time series of radio-sounding measurements above Ljubljana (every morning at 0600 UTC) was also available. In the case of missing data, radio-soundings from Zagreb (Croatia) or Udine (Italy) were used. Ljubljana is situated in the large Ljubljana basin, and temperature and humidity profiles from Ljubljana radio-soundings are representative for all larger basins within the territory of Slovenia. Smaller basins are not considered in the present study. Terrain variables are very important in the regionalisation and interpolation process (Petkovšek 1980). Longitude, latitude, altitude and other terrain variables of the observation stations were collected from the metadata base of the Environmental Agency of the Republic of Slovenia (EARS). For all other areas of Slovenia, the geographical variables were derived from Digital Terrain Models (DTM) of Slovenia with 100 m or 25 m resolution. For the terrain outside Slovenian territory, the GTOPO (Global 30 Arc-Second Elevation Data Set) ( gtopo30.asp, 1996) dataset was used. 3. Methods The spatial distribution of average seasonal sunshine duration was calculated using objective interpolation methods (Isaaks & Srivastava 1989; Daley 1991; Cressie 1993). A seasonal presentation was selected owing to the high inter-seasonal variability in the spatial distribution of sunshine duration (Hočevar et. al. 1982; Ovsenik- Jeglič 2004), which would otherwise not be obvious on a yearly basis. Measured sunshine duration is not always representative of larger regions, especially where there are different obstacles in the vicinity of the measuring point (Hočevar et al. 1982). If the measurements are obtained from stations in a narrow valley or basin, they cannot be extrapolated to a wider region. In order to avoid the influence of these smaller terrain features, as well as those of urban and vegetation obstacles, and to ensure that only the spatial variability of sunshine duration due to climatic influences is presented, the measured sunshine duration was corrected by extrapolating on an hourly basis the sunshine duration values for the time when the measuring site was in shadow due to obstacles on the horizon. From the obstacle listing of the station and the astronomical position of the Sun, the duration of the artificial shadow was calculated. On the basis of artificial shadow duration and sunshine duration at nearby stations during the time of artificial shadow, the daily sunshine duration values were recalculated to the mathematical horizon. Since sunshine duration does not have very pronounced spatial variability, corrected values are representative of a wider region. The average distance between 43 measuring points is 27 km, which is enough to detect weather-influenced spatial variability of sunshine duration. In the first step, regionalisation was performed on the basis of seasonal sunshine duration values, geographical values and vertical profiles of temperature and humidity, separately for each season. Basins, valleys and large plains are derived from DTMs (at 100 m and 25 m resolutions) using GIS modelling (Hrvatin & Perko 2002) and radio-sounding data to determine the relative height (border) between the terrain structures (basins and highland). Spatial interpolation methodology proved to be very important in the correct calculation of spatial distribution of sunshine duration. There is a wide variety of spatial interpolation methods (Tveito & Schöner 2002; Ustrnul & Czekierda 2005), which are classified according to whether they are deterministic or stochastic. Deterministic methods use a mathematical and physical background to explain the spatial variability of selected meteorological variables, while stochastic methods usually apply probability theory and the concept of randomness in the spatial process. Interpolation models were developed separately for each region and season and are combinations of the following deterministic and stochastic approaches: multivariate regression model, residual kriging and simple mathematical models. In the case of a small number of stations in a region, when the stochastic approach is not appropriate, residual kriging was substituted by the Inverse Distance Weighting (IDW) method. With exploratory data analysis, explanatory variables for multivariate linear regression were chosen. In the majority of cases, elevation explains most of the variation in sunshine duration, although sometimes longitude and latitude are also chosen as explanatory variables. A cross-validation method (Isaaks & Srivastava 1989; Cressie 1993) was used to validate the models and spatial interpolation results. A complete description of the geostatistical methods can be found in Isaaks & Srivastava (1989) and Cressie (1993) or in other geostatistical literature. The notion of variogram models is taken from Cressie (1993). To ensure spatial continuity on a region s border, the closest stations to the border outside the region were also considered in the interpolation procedure for the region. The spatial distribution of seasonal sunshine duration for the whole territory of Slovenia was finally derived by merging the results from the separate regions. The merging procedure is based on common GIS techniques, using inverse distance weights in buffer zones on the region s borders. The width of the buffer zones was specified on the basis of radio-sounding and geographical data. The values of seasonal sunshine duration were calculated on a 100 m resolution grid in order to take into account high spatial variability of geographical variables. In the final step, 377

4 Mojca Dolinar (Hočevar et al. 1982), sunshine duration decreases with altitude as shown in Figure 3. Larger variability in sunshine duration in lower regions could be explained by variability in latitude: southern parts of the country receive more Sun as shown in Figure 4. Regression analysis shows that altitude and latitude could explain 55% of sunshine duration (SD) variability: SD = altitude latitude, R 2 = 55% (1) Figure 3. Sunshine duration dependence on altitude for summer months (June, July, August). Straight line indicates statistically significant linear dependence of sunshine duration on altitude. the values were averaged out in a 1 km resolution grid, which is a consistent resolution regarding spatial density of measurements, their spatial representativeness and model output errors. 4. Results 4.1. Summer In summer the effect of altitude on sunshine duration is uniform over the whole country and there is no region where the sunshine duration gradient differs significantly from the rest of the country (Figure 3). Due to more pronounced convection in the mountains using residual kriging with the linear variogram model γ (r), depending only on distance between two points (r) (Cressie 1993): using residual kriging. The spherical variogram model γ (r), depending only on distance between two points (r) (Cressie 1993): 0 r = 0 ( γ (r) = r ( ) ) r 2 0 < r r 2 > (2) A radius of influence of 55 km was chosen because the highest correlation coefficient between observed and modelled values was obtained in this area during the cross-validation procedure. Strong correlation between sunshine duration and altitude is reflected in the final map of summer sunshine duration shown in Figure 4. The longest sunshine Figure 4. Map of sunshine duration (hr) in summer months ( ). 378

5 Spatial interpolation of sunshine duration in Slovenia Figure 5. Sunshine duration (SD) dependence on altitude for autumn months (September, October, November) for separate regions: coastal region and inland exposed region, both with indicated statistically significant linear dependence of SD on altitude and inland basin region. duration is limited to the coastal region, while the shortest is found in high mountains Autumn Fog is a frequent phenomenon in the autumn months (from nine to 15 days on average; Petkovšek 1969), and is mostly related to basins and other concave terrain features. Because of the relatively warm sea, fog is not frequent in the coastal region. The influence of fog on sunshine duration is evident in different regions, which can be clearly defined according to sunshine duration data shown in Figure 5: coastal regions with no fog have a negative sunshine duration gradient with altitude, while inland there is a positive gradient in sunshine duration with altitude. The High Dinara Edge (see Figure 1), which acts as a natural barrier to maritime influences, defines the border between the coastal and inland regions. Inland basin locations differ significantly from wind exposed locations and sunshine duration for basin locations could not be explained by altitude variability. As a consequence, the inland region is split into two subregions: the exposed region and the basin region as illustrated in Figure 6. Regionalisation is performed using GIS modelling on the 25 m DTM. Basins are defined according to altitude variability, relative altitude and average inversion depth (from radio-sounding data). Only altitude is included in the regression model for coastal and inland exposed regions, while for inland basin regions there are no geographical variables that can adequately explain the variability in sunshine duration (SD) the correlation coefficient between SD and altitude is only The regression models for coastal and inland exposed regions, respectively, are: Inland exposed region: SD = altitude, R 2 = 36% (3) Coastal region: SD = altitude, R 2 = 52% (4) Owing to the small number of measuring points (eight in the inland basin region and ten in the coastal region), the IDW method is used to interpolate residuals in coastal and inland exposed regions and sunshine duration in inland basin regions. The final map of autumn sunshine duration (Figure 7) distinguishes the two regions but the influence of the basins is a little wider and is not isolated strictly on basin regions (the border between basins and exposed regions is continuous and smooth, also due to variability in inversions and low cloud-base height). Similarly as in the summer, the longest sunshine duration is limited to the coastal region while the shortest is detected in the basins. Figure 6. Characteristic regions according to sunshine duration in autumn (September, October, November). 379

6 Mojca Dolinar Figure 7. Map of sunshine duration (hr) in autumn months ( ). variability could be explained with the regression model: Coastal region: SD = altitude, R 2 = 66% (5) Figure 8. Sunshine duration (SD) dependence on altitude for winter months (December, January, February) for separate regions: Inland region and Coastal region, showing statistically significant linear dependence of SD on altitude Winter Regionalisation based on sunshine duration values in winter is easily achieved, since two regions (coastal and inland) become evident when sunshine duration is drawn against altitude, as shown in Figure 8. Figure 9 shows the coastal region with a gradual positive sunshine duration gradient and the inland region with a more pronounced gradient. In the coastal region the correlation between sunshine duration (SD) and altitude is strong. The additional geographical variables do not significantly improve the regression model. Some 66% of sunshine duration 380 using residual kriging with the linear variogram model γ (r), depending only on distance between two points (r) (Cressie 1993): 0 r = 0 ( ) γ (r) = r r A radius of influence of 40 km was chosen because the highest correlation coefficient between observed and modelled values was obtained in this area during the cross-validation procedure. In the inland region the interpolation model is similar to that in the coastal region. A statistically significant regression model explains 79% of sunshine duration variability: Inland region: (6) SD = altitude, R 2 = 79% (7) using residual kriging with the exponential variogram model γ (r), depending only on distance between two

7 Spatial interpolation of sunshine duration in Slovenia Figure 9. Characteristic regions according to sunshine duration in winter (December, January, February). Figure 10. Map of sunshine duration (hr) in winter months ( ). points (r) (Cressie 1993): 0 ( ( r = 0 γ (r) = exp r )) 2 r (8) A radius of influence of 30 km was chosen because the highest correlation coefficient between observed and modelled values was obtained in this area during the cross-validation procedure. In winter, higher regions have more sunshine hours, while in the lowlands and on the coast there are significantly fewer sunshine hours due to frequent fog occurrence (Figure 10). The area of lowest sunshine hours is located in inland basins, similar to the situation in autumn Spring Figure 11 shows that the gradient of sunshine duration with altitude in the lowland region is much higher than 381

8 Mojca Dolinar Regression models are calculated separately for each region. In the lowland region the gradient in sunshine duration (SD) and altitude is high. An additional geographical variable does not significantly improve the regression model. Some 50% of the sunshine duration variability could be explained with regression model: Lowland region: SD = altitude, R 2 = 50% (9) Figure 11. Sunshine duration (SD) dependence on altitude for spring months (March, April, May) for separate regions: Mountainous region and Inland region, both with indicated statistically significant linear dependence of SD on altitude. in the mountains. In both regions sunshine duration decreases with altitude. In terms of correlation of sunshine duration with altitude, the two regions can be clearly defined in spring, as shown in Figure 12. High variability in sunshine duration in the spring months is apparent. In March, fog is a frequent phenomenon in the coastal region (the long-term average is 5.1 days of fog; Petkovšek 1969), while in April and May convective clouds develop mostly in the mountainous regions (HMZ 1991). Both phenomena smooth the spatial variability of sunshine duration for the whole spring period. As a consequence of convection, a steep gradient in sunshine duration occurs in the m altitude zone, which is in agreement with vertical profiles of temperature and humidity. using residual kriging with spherical variogram model γ (r), depending only on distance between two points (r) (Cressie 1993): 0 r = 0 ( γ (r) = r ( ) ) r 2 0 < r r 2 > (10) A radius of influence of 35 km was chosen because the highest correlation coefficient between observed and modelled values was obtained in this area during the cross-validation procedure. In the mountainous region the interpolation model is similar to that in the lowland region. The statistically significant regression model explained 78% of sunshine duration variability: Mountainous region: SD = altitude, R 2 = 78% (11) Figure 12. Characteristic regions according to sunshine duration in spring (March, April, May). 382

9 Spatial interpolation of sunshine duration in Slovenia Figure 13. Map of sunshine duration (hr) in spring months ( ). using the IDW method since there are too few data to use a stochastic approach. The final spatial distribution of sunshine duration in spring, shown in Figure 13, appears to be quite smooth, with the highest values of sunshine duration in the coastal region and the lowlands of eastern Slovenia, and with lowest values in the mountains. All four seasonal maps show the typical spatial distribution of sunshine duration in each season and are further used as masks in modelling the spatial distribution of sunshine duration on the monthly and decadal scales. Comparison of all four maps shows a significant difference in the spatial distribution of sunshine duration from season to season, suggesting that the lapse rate could even be inverted. 5. Conclusions The present study shows that there is no universal method for calculating the spatial distribution of a single meteorological variable. A multiple-methods approach could improve the final results significantly, particularly if additional information such as geographical variables (DTM) and radio-sounding data were included in the present study. Regionalisation proves to be very efficient, despite the fact that merging results from different regions is a challenging task. General knowledge of the behaviour of weather variables is essential for regionalisation, but without additional data any objective regionalisation is impossible. GIS functionality proves to be very useful, especially for deriving different complex terrain data, for regionalisation and for merging data. Residual kriging seems to be the best method for spatial interpolation of sunshine duration, but in regions with a very small number of measurements it is substituted by a simple IDW method. References Cressie, N. A. C. (1993) Statistics for Spatial Data. New York: John Wiley & Sons, 900 pp. Daley, R. (1991) Atmospheric Data Analysis. Cambridge: Cambridge University Press, 457 pp. Dobesch, H., Tveito, O. E. & Bessemoulin, P. (2001) Final Report Project no. 5 in the framework of the climatological projects in the application area of ECSN Geographic Information Systems in Climatological Application. Oslo- Vienna. HMZ (1991) Sunshine duration in the period , Climatography of Slovenia. Hydrometeorological Institute of Slovenia, Ljubljana, Slovenia. Hočevar, A., Kajfež-Bogataj, L., Petkovšek, Z., Pristov, J., Rakovec, J., Roškar, J. & Zupančič, B. (1982) Solar Radiation in Slovenia. Biotechnical Faculty, Ljubljana, Slovenija (in Slovenian). Hrvatin, M. & Perko, D. (2002) Determination of surface curvature by digital elevation model and its application in geomorphology: GIS in Slovenia ZRC-SAZU, Ljubljana: (in Slovenian). 383

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