Evaluation of topographical and geographical effects on some climatic parameters in the Central Anatolia Region of Turkey

Authors


Abstract

A two-phase research was implemented to determine the effect of topography on climate parameters by using spatial interpolation and conventional statistical procedures in non-homogeneous topography. The primary set of climate data for the Central Anatolia Region includes monthly mean global solar radiation, sunshine duration, surface air temperature, relative humidity, wind speed and rainfall, recorded from 1976 to 2005.

In the first phase, the effect of elevation on climate parameters was evaluated. For this purpose, kriging and co-kriging geostatistical interpolation techniques were compared to determine which one of the two techniques was more successful in determining the spatial distribution of climate parameters in variable topography. The inclusion of elevation as a covariate resulted in reduction of errors on sunshine duration, temperature and wind speed. On the basis of these error values, there is a relationship between elevation and sunshine duration, temperature and wind speed.

In the second phase, multiple regression equations were developed to determine the effect of topography on annual mean values of climate factors. The highest correlation (−0.76) was found between solar radiation and latitude. The most effective factors were latitude and elevation. They alone explain 57% of the variability for sunshine duration and 56% for temperature, respectively. The multiple regression results were more significant than were the individual, pairwise correlation relationships. The mostly explained factor was temperature. Its variability was explained by latitude, elevation, aspect and slope as a ratio of 81.7%. Separate regression models for each data set and both response variables varied in their ability to explain variability in the response, with R2 values between 0.125 and 0.817. Copyright © 2010 Royal Meteorological Society

1 Introduction

Climate has an important role on population, livestock, cropping systems, and native flora and fauna. A comprehensive understanding of climate and distribution of climate parameters in time and space is essential in terms of correct and cost-effective design of many engineering structures and applications (Georgakakos, 1984; Hutchinson et al., 1996; Park and Singh, 1996). A detailed description of current climate and also resulting forecasting with great accuracy on climatic change on terrestrial ecosystems is pointed by IPCC (2001).

There are many different factors affecting the climate of a particular place across the world. The climate of a region is mainly determined by the interaction of some important natural controls such as latitude (proximity to the equator), elevation, distance from the sea (continentality), aspect, slope, ocean currents, orographic influence, heating and cooling characteristics, and air pressure. Recently, human activity has also been accepted as affecting climate (Scott, 2004).

Latitude controls the amount of solar radiation reaching to the earth surface. From a global perspective, the mean angle of the sun is highest, on average, at the equator, and decreases progressively towards the pole. This is due to two factors: (1) the angle at which the sun rays are positioned to the earth surface based on its curvature. (2) The amount of atmosphere through which the light has to travel at particular latitude. As latitude increases, the angle at which the sun rays hit the ground decreases. This leads to decreased temperatures and evaporation rates at higher latitudes. Variations in elevation can cause large variations in temperature even for locations at similar latitudes. Temperatures decrease at an average of about 6.4 °C/1000 m. Therefore, high mountain and plateau stations are much colder than low-elevation stations at the same latitude. That is why snow is often seen on top of the mountains all year round, even in tropical areas. Solar radiation turns into heat only when it is absorbed by a body of matter. Lower down in the atmosphere, the air is denser and contains more water vapour, air molecules, dust, etc. Therefore, more energy can be absorbed and turned into heat at lower elevations. Thinner air is less able to absorb and retain heat. Distance from the sea is another factor. Land can heat up or cool down much quicker than water. Therefore, coastal areas have a lower temperature range than those inland areas due to the moisture content. At the coast, winters are mild and summers are cool. In the summer, the water acts like an air conditioner to keep the air temperatures cool. The centre of continents is subject to a large range of temperatures. In the summer, temperatures can be very hot and dry, and cold in the winter. Also, water bodies provide a source of moisture for the land masses of the world. Clouds are formed when warm air from inland areas meets cool air from the sea. Slope and aspect affect the moisture and temperature of air and soil. Sun-facing slopes are warmer than those that are not. This is the reason why south-facing slopes in the Northern Hemisphere are usually warm. However, slopes facing north in the Southern Hemisphere are warmest. Surface ocean currents can transport masses of warm or cold water at great distances from their source regions, affecting temperature, precipitation and moisture conditions. The influence of ocean currents in land areas is greatest in coastal regions and decreases towards inland. Orographic influence is the lifting effect of mountain peaks or ranges on winds that pass over them. As air approaches a mountain barrier, it rises, typically producing clouds and precipitation on the windward (upwind) side of the mountains. Most of the world's wettest locations are found on the windward sides of high mountain ranges (Clarke and Wallace, 1999; Jackson, 2000; Scott, 2004). These factors are a function of location, and correct determination of spatial distribution of meteorological variables is as important as their measurements (Apaydin et al., 2004).

Until 10 years ago, the relationship between topography and climate parameters using statistical procedures have been examined by a lot of researchers. After Geographic Information Systems (GIS) and modelling have become powerful tools, spatial interpolation of climate parameters has become one of the most actual occupation for climatologist, hydrologist and environmentalist. In this article, both methods (statistical procedures and spatial interpolation) were used. The difference between kriging and co-kriging in the same climate parameters would show the effect of topography on climate. Kriging and co-kriging spatial interpolation techniques were compared to determine the influences of elevation on six climate varieties (solar radiation, sunshine duration, temperature, relative humidity, wind speed and rainfall) in the Central Anatolia Region, and regression equations were also generated to demonstrate the importance of some topographic variables on climate.

2 Background

As well as interpolation of point data was mainly performed for rainfall data, it is also used from hydrological variables to distribution of water in soil. While some of researchers (Tabios and Salas, 1985; Phillips et al., 1992; Borga and Vizzaccaro, 1997; Goovaerts, 2000; Apaydin et al., 2004) have stated that geostatistical prediction techniques provide better estimates than the conventional methods, some others have advised conventional methods such as Thiessen polygon, inverse square distance and the isohyetal method. In some situations, no differences were found between the methods (Michaud and Sorooshian, 1994; Dirks et al., 1998).

Besides the comparison of interpolation techniques, most of the meteorological variables are mapped or analyzed by spatial interpolation techniques. Park and Singh (1996) studied rainfall variability in time and space in Korea. Monthly mean climate surfaces were developed for the African continent by Hutchinson et al. (1996) and for Australia by Hutchinson and Kesteven (1998). Prudhomme and Reed (1999) investigated a method of mapping extreme rainfall in the mountainous region of Scotland. Perry and Hollis (2005) mapped monthly climatic variables over the United Kingdom. Caramelo and Orgaz (2007) analyzed spatial and temporal variability of winter precipitation in the Duero basin.

Some studies have examined statistical relationships between the geographical variables (slope, elevation, latitude and distance from sea) or landscape variables and climatological variables. Chuan and Lockwood (1974) found that approximately 50–60% of the variance in annual precipitation was explained by gauge altitude in the Pennines. Griffiths and McSaveney (1983) have stated that the distance from the moisture source is an obvious factor. Hevesi et al. (1992) reported a significant correlation between average annual precipitation and elevation in Nevada and GB California. Basist et al. (1994) derived statistical relationships between annual precipitation and elevation, slope, exposure and valley orientation. Konrad (1995) identified relationships between the maximum precipitation and selected topographic and geographic attributes, and Konrad (1996) found that elevation explains only approximately 3% of the variance of total annual precipitation in the southern Blue Ridge Mountains. Prudhomme and Reed (1998) investigated the relationships between rainfall and topography in Scotland. Ninyerola et al. (2000) developed a multiple regression analysis between temperature and rainfall as response variables, and some geographical variables. Daly et al. (2000) introduced a regression-based model (PRISM) for precipitation and temperature. In addition, Daly et al. (2002) used PRISM and a digital elevation model (DEM) to generate repeatable estimates of annual, monthly and event-based climatic elements. Deems (2002, unpublished thesis) investigated the importance of topography in snow temperature gradients. Oettli and Camberlin (2005) made a study to discuss topographical predictors and their ability to estimate spatial rainfall distribution.

3 Site description

The study was carried out in Central Anatolia Region of Turkey (Figure 1). The region covers 13 administrative provinces (Aksaray, Ankara, Cankiri, Eskisehir, Karaman, Kayseri, Kirikkale, Kirsehir, Konya, Nevsehir, Nigde, Sivas and Yozgat). The Central Anatolian Region occupies 19% of the total area of Turkey with a 151 000 km2 area of land; it is the second largest region of Turkey after Eastern Anatolia. In order to show the effect of topography clearly, Central Anatolia Region has been selected because it has homogenous climate and is surrounded by mountains which limit the sea effect.

Figure 1.

Location of meteorological stations. This figure is available in colour online at wileyonlinelibrary.com/journal/joc

The Central Anatolian Region (also known as the Anatolian Plateau) is an area of diverse landforms. The dry, arid highlands of Anatolia lie between the two zones of folded mountains (the Taurus and the Northern Anatolian mountain ranges) and extend to the east to the point where the mountain ranges converge. The region varies from 600 to 1600 m in altitude from west to east, averaging 1070 m in elevation. It is an area of extreme heat, and virtually no rainfall is observed in summer; the Anatolian plateau continental climate is cold in winter and receives heavy, lasting snows. The two largest basins on the plateau are Konya Ovasi and the basin occupied by Tuz Golu (Salt Lake). Both are characterized by inland drainage. Wheat and barley are the most important crops, but the yields are irregular, and crops fail during years of drought. One-third of the total wheat of Turkey comes from this region (Yazici, 2002; Sahin, 2005).

There are three main climates in Turkey: Humid subtropical climate, Mediterranean climate and Continental climate. Mountains also play a role in the formation of climates in Turkey. If the mountains lay perpendicular to sea as in Aegean coasts, dominant climate along the coast line will still be dominant in inner parts. On the other hand, if the mountains lay parallel to coast line as in Black Sea and Mediterranean regions, dominant climate of the coast line will not affect the climate of inner parts. That is why, continental climate is observed in Central Anatolian Region.

The primary set of climate data for the Central Anatolia Region includes monthly mean global solar radiation, sunshine duration, surface air temperature, relative humidity, wind speed and rainfall, recorded from 1976 to 2005. All variables were measured at 74 meteorological stations (measurement length equal to or greater than 25 years), 51 stations of which were within the region (Figure 1). The Central Anatolia Region is located in the continental Mediterranean region, where annual precipitation is between 400 and 800 mm (Table I). Besides the meteorological variables, DEM data from a 1/250 000 scale digital topographic map with a resolution of 0.01° extending from 41°00′ to 36°30′N and from 29°30′ to 38°30′E was used. The DEM data were required for considering elevation as a covariate for the co-kriging methods.

Table I. Long-term averages of annual climatic elements typical for the provinces in the Central Anatolia Region (1976–2005)
StationLatitude (N)Longitude (E)Elevation (m)Temperature ( °C)Relative humidity (%)Rainfall (mm)Wind speed (m s−1)Solar radiation (cal cm−2)Sunshine duration (h)
Aksaray38.3834.0896511.958.3340.22.54372.47.5
Ankara39.9532.8889111.861.3397.51.91344.66.9
Cankiri40.6033.6275111.167.4400.60.98348.56.2
Eskisehir39.8230.5278910.665.9309.13.12287.96.7
Karaman37.1833.22102511.860.7329.12.27408.28.0
Kayseri38.7335.48109310.464.2391.81.79348.06.8
Kirikkale39.8533.5274712.563.7383.61.81345.47.0
Kirsehir39.1534.17100711.363.8382.52.82376.97.3
Konya37.8732.48103111.459.0317.72.15378.97.2
Nevsehir38.5834.67126010.459.9417.72.237.1
Nigde37.9734.68121111.059.7332.52.77455.97.6
Sivas39.7537.0212859.065.2445.71.30304.76.7
Yozgat39.8234.8012988.967.7603.12.25341.06.8

4 Methods

This study was composed of two stages. While spatial interpolation was used only in the evaluation of the effects of altitude on climate during the first stage, conventional linear regression was used at the second stage to determine the effects of altitude, latitude, distance from sea, degrees from north, aspect and slope on climate.

4.1 Interpolation of climate

Spatial interpolation may be used to estimate climate variables at non-sampled sites or to prepare irregularly scattered data to construct a contour map or contour surface, which is a two-dimensional representation of a three-dimensional surface (Collins, 1996).

Geostatistical interpolation techniques (e.g. kriging and co-kriging) use the statistical properties of the measured points. Geostatistical techniques quantify the spatial autocorrelation among measured points and account for the spatial configuration of the sample points around the prediction location (Borga and Vizzaccaro, 1997; Campling et al., 2001; Johnston et al., 2001).

The first step in geostatistical interpolation is statistical data analysis to verify three data features: dependency, distribution and stationary. The data used in geostatistical analysis should be spatially dependent. As the goal of geostatistical analysis is to predict values where no data have been collected, geostatistical interpolation will work only on spatially dependent data (Intarakosit and Ramirez, 2007). Despite the independency of the data, there is no possibility to predict realistic values between them. The most important step in geostatistical interpolation is to model the spatial dependency by using semivariograms (Krivoruchko 2004.).

Distribution of input data affects success degree of geostatistical interpolation. Exploring tools such as histogram and normal quantile–quantile (QQ) plots were used to investigate the data (Intarakosit and Ramirez, 2007). The closer points on the QQ plots create a straight line and the closer distribution is normally distributed. If the data do not exhibit a normal distribution either in the histogram or the normal QQ plot, it may be necessary to transform the data to make it conform to a normal distribution before using certain kriging interpolation techniques (Johnston et al., 2001).

The last data requirement is stationary means that statistical properties do not depend on location. Therefore, the mean (expected value) of a variable in one location is equal to the mean in any other location (Intarakosit and Ramirez, 2007). Standard geostatistical models assume stationarity and rely on a variogram model to account for the spatial dependence at the observed data. In some instances, this assumption that the spatial dependence structure is constant throughout the sampling region is clearly violated. Assuming a field to be stationary is natural in some settings, especially when the spatial region of interest is relatively small (Higdon et al., 1998). Without making data stationary, it gives sensible results in many applications, but sometimes maps constructed via kriging that rely on such a biased semivariogram may be misleading (Higdon et al., 1998; Krivoruchko, 2003).

When the data are non-stationary, there are two ways to use geostatistics: (1) to make the data close to stationary by using detrending and transformation techniques and (2) to estimate heterogeneous semivariogram (Krivoruchko and Gribov, 2002).

  • (1)Transformations and trend removal are often applied to data for justifying the assumptions of normality and stationarity. Predictions using ordinary, simple and universal kriging after data transformation require back-transformation to the original data; however, Cressie (1993) has stated that this can only be done approximately (Krivoruchko and Gribov, 2002). Similarly, Goovaerts (1997) stated that when log transformation is applied to give precipitation data, a more normal distribution back-transformed values can be problematic because exponentiation tends to exaggerate any interpolation related error. So data transformation is not applied in this study.
  • (2)The second method is to estimate a heterogeneous semivariogram instead of homogeneous one; in other words, to use a moving window or kernal centred on the location to be predicted and to create a semivariogram for each local neighbourhood. The prediction at each point in the study area can be mapped sequentially as the window moves through the study area. To exhaustively map every location in the study area, semivariograms are calculated for each location to be predicted. Within each neighbourhood, the data are assumed to be locally stationary and hence the assumptions of the kriging algorithm are not violated (Krivoruchko and Gribov, 2002). Moving window method was introduced by Haas (1990) and developed and used by some researchers, e.g. Higdon et al. (1998), Sampson and Guttorp (1992), Loader and Switzer (1992), Le and Zidek (1992), Goovaerts (1997), Costa et al. (2008) and Stein et al. (1988), by dividing the study area into several parts to stratify into more homogeneous units before co-kriging (Krivoruchko and Gribov, 2002).

Advanced textbooks in geostatistics can provide the interested readers with details (Isaaks and Srivastava, 1989; Cressie, 1993; Rivoirard, 1994; Kitanidis, 1997; Chiles and Delfiner, 1999; Nielson and Wendroth, 2003).

The GIS software ArcGIS 9 is used as the main tool in the study to create base maps and database of the study areas. Exploratory Spatial Data Analysis (ESDA) tools are used to statistically explore and analyze spatial data. Visualizing the distribution of the data, looking for data trends, looking for global and local outliers, examining spatial autocorrelation and understanding the covariation among multiple data sets are useful tasks to perform on data.

Histograms, QQ plots, voronoi maps (Johnston et al., 2001) and semivariogram surfaces (clouds) were drawn for mean solar radiation, sunshine duration, temperature, relative humidity, wind speed, and rainfall was measured at 74 stations with monthly temporal scale to check distribution, spatial dependency and stationary of input data.

Histograms and QQ plots have shown that most of the parameters are normally distributed. Only rainfall on January, November and December are not normally distributed (positive skew). But these limited conditions did not affect the entire study. Spatial variation at mean and standard deviation values were mapped by using Voronoi maps (Krivoruchko and Gribov, 2002). At the last stage of statistical data analysis, summarized values of three important semivariogram values (Table II) and surfaces were obtained. Visual inspection of Voronoi maps and semivariogram surfaces for entire data set has shown that there is non-stationarity in rainfall and wind speed values. Due to the possibility of problem in back-transformation, it was decided to use moving window tool for rainfall and wind speed values to be close to stationary (ESRI, 2001; Krivoruchko and Gribov, 2002).

Table II. Variogram parameter values
Climate parametersMethodKrigingCo-kriging
  MajorPartial sillNuggetMajorPartial sillNugget
HumidityOrdinary5.64–8.366.96–67.09.35–18.26.88–8.366.96–67.09.35–18.2
 Simple1.36–4.670.69–23.511.2–27.12.27–3.290.34–23.711.6–26.9
 Universal5.64–8.366.96–67.09.35–18.26.88–8.366.96–67.09.35–18.2
 Disjunctive4.67–8.370.69–67.216.86–18.32.53–8.190.34–67.316.23–18.3
PrecipitationOrdinary4.88–8.3641.0–993.18.23–294.15.94–8.3644.0–10887.20–327.8
 Simple1.73–4.0614.1–355.323.6–628.41.89–3.8814.6–310.321.3–673.4
 Universal4.88–8.3641.0–993.18.23–294.15.94–8.3644.0–10887.20–327.8
 Disjunctive1.59–4.0314.2–993.127.7–297.02.10–3.8716.1–108826.7–327.9
Sunshine durationOrdinary4.46–7.970.28–0.990.06–0.215.36–7.970.30–1.050.05–0.23
 Simple2.37–6.080.11–0.430.06–0.392.36–3.210.12–0.450.11–0.38
 Universal4.46–7.970.28–0.990.06–0.215.36–7.970.30–1.050.05–0.23
 Disjunctive2.55–3.260.27–0.760.16–0.662.72–3.240.27–0.750.17–0.66
Solar radiationOrdinary3.85–6.03493.1–933.8322.4–3672.66.58–6.91641.2–876.4562.2–2188
 Simple3.02–3.53342.5–522.3299.9–3672.72.87–3.13425.0–557.0484.9–2051
 Universal3.85–6.03493.1–933.8322.4–3672.66.58–6.91641.2–876.4562.2–2188
 Disjunctive3.53–6.03344.0–932.4302.4–3672.63.01–3.24405.5–542.2504.4–2065
TemperatureOrdinary5.05–7.982.40–9.401.62–2.066.01–7.762.54–9.561.70–2.18
 Simple1.56–3.740.31–1.962.91–5.121.54–2.480.69–2.842.42–4.24
 Universal5.05–7.982.40–9.401.62–2.066.01–7.762.54–9.561.70–2.18
 Disjunctive1.37–3.730.37–9.421.52–2.072.40–3.350.68–9.462.48–2.86
WindOrdinary1.73–8.360.07–0.280.25–0.558.36–8.360.00–0.280.02–0.60
 Simple1.28–1.770.03–0.130.33–0.622.03–2.390.01–0.120.36–0.66
 Universal1.73–8.360.07–0.280.25–0.558.36–8.360.00–0.280.38–0.60
 Disjunctive1.28–1.900.05–0.220.72–0.890.56–3.070.01–0.130.81–0.94

4.2 Kriging

Kriging is a method of interpolation named after the South African mining engineer D. G. Krige who developed the technique in an attempt to predict ore reserves more accurately. Over the past several decades, kriging technique has become a fundamental tool in the field of geostatistics (Caruso and Quarta, 1998).

In the kriging technique, values for weights are measured from the surrounding known locations to predict values at unmeasured locations. The closest measured values usually have the most influence. However, the kriging weights for the surrounding measured points are more sophisticated. Kriging weights are derived from a semivariogram that was developed from the observation of the spatial structure of the data. To create a continuous surface or map of the phenomenon, predictions are made for locations in the study area based on the semivariogram and the spatial arrangement of measured values of the surrounding location (Collins, 1996; Johnston et al., 2001). Four different kriging types were used in this study.

Simple, ordinary and universal kriging predictors are all linear predictors, meaning that prediction at any location is obtained as a weighted average of neighbouring data. All assumes normal distribution of data, but make different assumptions about the mean value of the variable under study: simple kriging requires a known mean value as input to the model, while ordinary kriging assumes a constant, but unknown mean, and estimates the mean value as a constant in the searching neighbourhood. Universal kriging assumes a varying mean over space. This type of model is appropriate when there are strong trends or gradients in the measurements. Disjunctive kriging uses a linear combination of functions of the data, rather than just the original data values themselves (Krivoruchko, 2004; Tatalovich, 2005).

Geostatistical Analyst extension is used to create different kriging prediction maps. The extension enables to visualize the adjusting of the interpolation methods and parameters and to see a preview of the surface in real time as the changes are made in the wizard. The extension quantifies the statistical significance of the model and the model can be changed by refining the parameters. It also provides with comparative tools for choosing the best interpolated surface for the data. These tools are provided so that the user can quantify the predictions based on one relative to another. By visually analyzing the prediction errors of the different models, the optimal model can be used.

Prior to the geostatistical estimation, it is required to choose a model that enables to compute a variogram value for any possible sampling interval. The most commonly used models are spherical, exponential and Gaussian (Isaaks and Srivastava, 1989). Spherical model was used in this study due to appropriateness for the data.

Kriging can use all input data. However, there are several reasons for using nearby data to make predictions. First, the uncertainties in semivariogram estimation and measurement make it possible for interpolation with a large number of neighbours to produce a larger prediction error than interpolation with a relatively small number of neighbours. Second, use of local neighbourhood leads to the requirement that the mean value should be the same only in the local neighbourhood and not for the entire data domain. Therefore, it is a common practice to specify a research neighbourhood that limits the number and the configuration of the points to be used in the predictions. Used software provided many options for selecting the neighbourhood window. The shape of the research neighbourhood ellipse, the points within and outside the shape, the number of angular sectors, and the minimum and maximum number of points in each sector were adjusted repeatedly (ESRI, 2001; Krivoruchko, 2004). By using ‘Show Research Direction’ option, Nugget, Partial sill, Range (Figure 2), Angle Direction, Angle Tolerance, Bandwidth, Lag Size, and Number of Lags values were adjusted interactively to determine the local direction (Krivoruchko and Gribov, 2002; Krivoruchko, 2004).

Figure 2.

Nugget, Partial sill and Range values in a semivariogram (Krivoruchko, 2004)

4.3 Co-kriging

In general, the estimates of kriging are derived using only the sample values of one variable. However, a data set will often contain not only the limited primary (prediction) variable of interest, but also one or more secondary variables (covariates). These secondary variables were spatially cross-correlated with the primary variable, can contain useful information about the primary variable and usually sampled more intensely than the primary variable. This information can be included within the estimation process via co-kriging which is a form of kriging. It seems reasonable that the addition of the cross-correlated information contained in the secondary variable should help to further reduce the variance of the estimation error. In addition, the inclusion of correlated data can also ensure the ‘coherence’ of the estimates (Krivoruchko, 2004; Yalcin, 2005).

Four different co-kriging types (Ordinary, CKO; Simple, CKS; Universal, CKU; Disjunctive, CKD) similar to kriging were also used in this study. Co-kriging is most effective when the covariate is highly correlated with the prediction variable. To apply co-kriging, one needs to model the relationship between the prediction variable and a co-variable. This is done by fitting a model through the cross-variogram. Estimation of the cross-variogram is carried out similar to estimation of the semivariogram (Collins, 1996; Hartkamp et al., 1999).

The difference between kriging and co-kriging in the same type will show the effect of topography on climate. The value of the first phase of this paper lies in the use of elevation as a source of auxiliary information for climatological variables.

4.4 Cross-validation

Cross-validation is a technique that allows for comparison of estimated and true (measured) values by using only the information available in sample data set. In a cross-validation procedure, the sample value at a particular location is temporarily discarded from the sample data set; the value at the same location is then estimated by using the remaining samples. This procedure is repeated for all available samples (Isaaks and Srivastava, 1989).

If the selected geostatistical model describes a good structure of spatial autocorrelation, the difference between the estimated and observed values must be minimum; otherwise, the model is rejected and the process is repeated (Sotter et al., 2003). In general, for making a good geostatistical analysis, it is necessary to make an iterative process to obtain good results.

The adequacy and validity of the developed geostatistical surface were tested satisfactorily by cross-validation. Interpolated and actual values are compared, and the model that yields the most accurate predictions is retained. The most appropriate variogram was chosen based on the lowest error value by trial and error procedure (Ahmadi and Sedghamiz, 2007).

The calculated statistics serve as diagnostics that indicate whether the model and its associated parameter values are reasonable (ESRI, 2001). Finally, the results of each interpolation method were examined visually and statistically (Collins, 1996).

4.5 Comparison of kriging and co-kriging results

Deviations of the actual values from the predicted ones have been treated as errors, and four different means of these errors have been calculated: mean error (ME) is as an indication of the degree of bias; mean absolute error (MAE) stands for a measure of the extent of the deviations from the estimate; mean relative error (MRE), with its sign ignored, reveals the error gap in between the measured mean and the estimate; and root mean square error (RMSE) provides a measure that takes outliers into account.

4.6 Regression modelling

Stepwise multiple linear regression models were used to quantify the relationships between the topographic variables and annual mean meteorological data in the spatially distributed data set and to demonstrate the relative importance of the terrain variables in determining spatial patterns of meteorological data.

The data set used in this study contains four recorded (Yearly mean temperature, relative humidity, precipitation, wind velocity, solar radiation, sunshine duration), one measured (latitude, elevation, distance from sea, degrees from North, aspect) and one derived (Slope, mean values of elevation, aspect and slope within radius of 2.5, 5 and 10 km) variable.

4.7 Comparison of regression and kriging interpolations

While the method in Section 4.2 was used to obtain kriging maps, for regression maps, initially, regression equations were obtained by using the method specified in Section 4.6 as defined by Ninyerola et al. (2000) and regression estimation values for entire area were obtained based on these equations. Then, the difference between the kriging and regression estimation is determined at measurement point.

5 Results and discussion

At first step, Kriging and co-kriging estimation errors were compared to show the effect of elevation on interpolation of climate. In this way, it can be concluded that altitude has an effect on factors where co-kriging provided better results. For each meteorological variable, monthly prediction maps were generated through eight interpolation methods. Predicted temperature maps and pairwise scatter plots of measured and interpolated values for April are given in Figure 3 as an example for showing differences between the methods clearly. Detailed statistics of the measured and calculated monthly data from 1976 to 2005 are given in Table III. Statistics in this table are number of data, mean, minimum value, maximum value, coefficient of correlation, ME, MAE, MRE and RMSE. In earlier studies, generally, MAE, MRE and RMSE were used to determine which method was the best. Therefore, these error values given in Table III are comparatively given in Table IV. An upward arrow symbol is used for the ones having lower error values than subtypes, downward arrow for higher ones and a dot for equal ones. Obtained results may be interpreted for each meteorological variable given below.

Figure 3.

Interpolated temperature maps for April obtained by different interpolation methods. This figure is available in colour online at wileyonlinelibrary.com/journal/joc

Table III. Summary statistics for the interpolation of observed climate data (1976–2005) (lowest MAE, MRE and RMSE values are shown in boldface and the highest values are in italic font)
Climate parametersStatisticMeasuredKOKSKUKDCKOCKSCKUCKD
HumidityNumber612612612612612612612612612
 Mean62.9763.0263.0463.0263.0863.0062.8063.0062.92
 Min42.046.847.246.847.246.846.346.847.2
 Max82.578.878.778.878.978.778.178.778.5
 CC 0.92740.92860.92740.92930.92700.92030.92700.9222
 ME 0.0500.0680.0500.1100.027− 0.1800.027− 0.054
 RMSE 3.4693.4473.4693.4313.4783.6303.4783.587
 MAE 2.7552.7552.7552.7282.7642.9372.7642.898
 MRE 0.0460.0460.0460.0450.0460.0490.0460.048
PrecipitationNumber612612612612612612612612612
 Mean414.89456.60450.70456.60446.53457.26451.56457.26446.19
 Min284.59355.1376.4355.1333.0365.1381.0365.1348.9
 Max757.13626.5567.0626.5529.0595.9538.7595.9515.2
 CC 0.87590.86850.87590.85780.87450.86050.87450.8447
 ME 2.4262.4122.4261.9992.5232.3012.5232.345
 RMSE 9.4819.5499.4819.7769.5499.7809.54910.275
 MAE 6.3466.3536.3466.3436.4026.5926.4026.782
 MRE 0.2060.2080.2060.2010.2090.2200.2090.222
Sunshine durationNumber528528528528528528528528528
 Mean7.057.017.007.017.007.017.037.017.02
 Min1.82.22.32.22.32.22.32.22.3
 Max12.812.112.012.112.012.112.212.112.0
 CC 0.99010.99060.99010.99060.99010.98950.99010.9899
 ME − 0.047− 0.047− 0.047− 0.049− 0.044− 0.026− 0.044− 0.030
 RMSE 0.4210.4110.4210.4100.4210.4310.4210.424
 MAE 0.3090.3040.3090.3020.3090.3200.3090.313
 MRE 0.0530.0520.0530.0520.0530.0550.0530.053
Solar radiationNumber396396396396396396396396396
 Mean366.44367.99366.80367.99366.76368.15367.82368.15366.77
 Min100.4121.5122.0121.5124.6123.3122.2123.3125.2
 Max704.6604.2586.8604.2607.1601.9598.4601.9595.5
 CC 0.95050.94820.95050.94770.95080.94830.95080.9478
 ME 1.5510.3601.5510.3201.7031.3801.7030.332
 RMSE 47.56448.54947.56448.78347.37848.55147.37848.720
 MAE 36.33136.82836.33136.98036.13437.06036.13436.892
 MRE 0.1070.1090.1070.1090.1060.1090.1060.109
TemperatureNumber612612612612612612612612612
 Mean10.5110.9810.9910.9810.9710.9810.7810.9810.91
 Min− 5.8− 3.3− 2.1− 3.3− 2.6− 3.4− 3.4− 3.4− 3.7
 Max24.825.023.425.023.424.923.424.923.3
 CC 0.98560.98760.98560.98760.98600.99040.98600.9907
 ME 0.4700.4830.4700.4640.4670.2740.4670.402
 RMSE 1.4611.3781.4611.3671.4421.1681.4421.187
 MAE 1.1101.0571.1101.0551.0980.9241.0980.931
 MRE 0.6260.6090.6260.6220.6120.5720.6120.496
WindNumber612612612612612612612612612
 Mean2.212.092.072.092.072.102.112.102.09
 Min0.51.11.51.11.41.31.41.31.5
 Max4.52.72.72.72.72.73.02.72.9
 CC 0.33210.36190.33210.36570.30330.38340.30330.3761
 ME − 0.114− 0.137− 0.114− 0.136− 0.108− 0.100− 0.108− 0.120
 RMSE 0.7100.7050.7100.7030.7160.6920.7160.697
 MAE 0.5380.5350.5380.5350.5360.5230.5360.525
 MRE 0.2960.2920.2960.2920.2970.2910.2970.289
Table IV. Comparison of kriging and co-kriging methods via error values
ParametersErrorKOKSKUKDCKOCKSCKUCKD
HumidityRMSEequation imageequation imageequation imageequation image
 MAEequation imageequation imageequation imageequation image
 MREequation imageequation image
PrecipitationRMSEequation imageequation imageequation imageequation image
 MAEequation imageequation imageequation imageequation image
 MREequation imageequation imageequation imageequation image
Sunshine durationRMSEequation imageequation image
 MAEequation imageequation image
 MREequation imageequation image
Solar radiationRMSEequation imageequation imageequation imageequation image
 MAEequation imageequation imageequation imageequation image
 MREequation imageequation image
TemperatureRMSEequation imageequation imageequation imageequation image
 MAEequation imageequation imageequation imageequation image
 MREequation imageequation imageequation imageequation image
WindRMSEequation imageequation imageequation imageequation image
 MAEequation imageequation imageequation imageequation image
 MREequation imageequation imageequation imageequation image

5.1 Relative humidity

While measured mean monthly relative humidity was 62.97%, predicted values were between 63.02 and 63.08% for types of kriging and 62.8 and 63.00% for types of co-kriging (Table III). These values proved by spatial interpolation were very close to the measured values for humidity predictions. KD method produced the lowest error and the highest correlation values in relative humidity. On the contrary, CKS produced the highest error and the lowest correlation values. As it can be seen from the Table IV, co-kriging methods have produced higher errors than kriging methods in 10 of 12 error measures. The remaining two error values were the same. In this case, a positive relationship was not found between change in altitude and humidity.

5.2 Precipitation

While measured mean yearly precipitation was 414.89 mm, predicted values were all higher than the measured (minimum mean 446.19 and maximum mean 457.26 mm); in addition, the coefficient of correlation values were between 0.8447 and 0.8759. KO and KU had the lowest RMSE and the highest coefficient of correlation (CC) values in precipitation (Table III). Lowest MAE and MRE values were produced by KD. The highest error and the lowest correlation values were produced by CKD. None of the methods used elevation as the ancillary information could produce better results for precipitation (Table IV).

5.3 Sunshine duration

In this study, sunshine duration had the highest coefficient of correlation values, which were between 0.9895 and 0.9906 (Table III). KS and KD had the lowest error and the highest CC values in sunshine duration, whereas CKS had the highest error and the lowest CC values. Like humidity and precipitation, different types of co-kriging techniques gave poor results compared with different types of kriging. As seen in Table IV, ordinary and universal types have yielded equal error values.

5.4 Solar radiation

While mean predicted values were very close to the measured values, minimum predicted values were 20% higher than the minimum measured values. CC values were approximately 0.95. Lowest error values were produced by CKO and CKU. They also had the highest CC values. The highest RMSE and MRE values were produced by KD. The inclusion of elevation as a covariate resulted in better predictions. CKO and CKU gave better results than all of the kriging types.

5.5 Temperature

All mean values predicted by using these methods were higher than the mean measured values for temperature. CC values were very high and close to each other (0.9860 to 0.9907). CKS had the lowest MAE and RMSE; CKD had the lowest MRE and the highest CC value. The highest error values were produced by KO and KU methods. The positive effect of using elevation as ancillary information has been clearly seen in interpolation of temperature. All 12 error values in co-kriging types were lower than those in the same kriging types (Table IV).

5.6 Wind speed

While measured mean monthly wind speed was 2.21 m s−1, predicted values ranged between between 2.07 and 2.11 m s−1. Wind speed had the lowest coefficient of correlation values in this study, which were between 0.3033 and 0.3834. While CKD produced lowest MRE value, CKS gave the best results for wind speed. The highest error values were sparse KO, KU, CKO and CKU methods.

5.7 Evaluation of methods

For temperature estimations, all of co-kriging error values (i.e. MAE, MRE and RMSE values for CKO, CKS, CKU and CKD) were smaller than those of kriging (Tables III and IV). The error values decreased when elevation was used as the ancillary information in co-kriging methods. A similar situation occurred for solar radiation and wind speed values, but to a lesser extent. Minimum error values were produced when different types of kriging were used for interpolation of humidity, precipitation and sunshine duration. No significant correlation was found between elevation and sunshine duration, relative humidity and rainfall when the results of kriging and co-kriging methods were compared. Comparison of the error values in Table IV clearly shows the success situation between kriging and co-kriging methods, i.e. all error values predicted by kriging methods for interpolation of precipitation are lower than those predicted by co-kriging. For predictions involving temperature, the situation is opposite.

Although four subtypes of kriging were used in this study, KO, KS and KU gave the lowest MRE, MAE or RMSE values for precipitation and sunshine duration for six times, but they gave the highest error values for eight times for solar radiation, temperature and wind speed. KD gave the lowest error value for nine times for humidity, precipitation and sunshine duration. CKO and CKU produced the lowest error value for only solar radiation, and they produced the highest error value only for interpolation of wind speed. The lowest error values were produced by CKS and CKD for temperature and wind speed, but the error values for humidity, precipitation and sunshine duration were not the lowest.

5.8 Regression equations

Initially, it is helpful to explore the relationship between the annual mean meteorological and topographic variables on an individual basis. Pairwise scatter plots of individual predictor variables versus each response variable were examined. Summary statistics (minimum, mean and maximum values) of used topographical and response variables are given in Table V. To examine the detailed relationships between topography and climate parameters, three of the predictor variables (elevation, aspect and slope) were expanded. These three variables were measured or determined for the point where meteorological measurements were done. But some of the climatological variables may be affected by the local topographical conditions. To show local influences, besides point values, mean elevation, aspect and slope values within radius of 2.5, 5 and 10 km were also used. Determined predictor variables for the provinces (as example) in the Central Anatolia Region by GIS are given in Table VI. Correlation matrix of correlation coefficients for predictor and response variables used in the development of the regression models are given in Table VII. High correlations were found between latitude and solar radiation; elevation and temperature; and slope and precipitation. The highest correlation value of − 0.76 was found between solar radiation and latitude. The second highest was between temperature and all kind of elevations (Elev, elev25, elev50 and elev100). The third highest was between precipitation and slope25–slope50. Interestingly, while slope25 has a value of 0.52, slope has a value of only 0.34. The values of other correlation coefficients were lower than 0.5.

Table V. Summary statistics for spatial and climatic attributes of the stations: variables, descriptions, minimum, maximum and mean values. [Correction added on 4 November 2010 after original online publication: the descriptions for Elev25, Elev50, Elev100, Aspect25, Aspect50, Aspect100, Slope25, Slope50 and Slope100 have been amended.]
VariableDescriptionMinimumMaximumMean
LatitudeLatitude (degrees)36.9840.9239.05
ElevElevation (m)65015521077
Elev25Mean elevation within the radius of 2.5 km727.101619.721116.04
Elev50Mean elevation within the radius of 5 km765.121695.421144.75
Elev100Mean elevation within the radius of 10 km805.501802.161184.26
DisSeaDistance from sea (km)85.91291.70183.03
DfNorthDegrees from north (degrees)2.22180.0090.09
AspectAspect (degrees)3.29356.04174.94
Aspect25Mean aspect within the radius of 2.5 km47.79288.12176.77
Aspect50Mean aspect within the radius of 5 km57.67255.66172.28
Aspect100Mean aspect within the radius of 10 km94.33232.94174.78
SlopeSlope angle (degrees)0.077.151.92
Slope25Mean slope within the radius of 2.5 km0.097.192.31
Slope50Mean slope within the radius of 5 km0.096.782.48
Slope100Mean slope within the radius of 10 km0.126.962.75
TmYearly mean temperature ( °C)6.6813.0110.48
HmYearly mean relative humidity (%)55.3169.6062.96
PmYearly mean precipitation (mm)284.64757.08414.84
WmYearly mean wind velocity (m s−1)0.723.902.21
SRmYearly mean solar radiation (cal cm−2)256.79455.95365.87
SDmYearly mean sunshine duration (h)5.988.047.05
Table VI. Determined predictor variables for the provinces in the Central Anatolia Region
StationLatitude (N)Elev. (m)DisSea (km)DfNorth (km)Aspect (degrees)Slope (degrees)
Aksaray38.389651961653452.06
Ankara39.95891201330.67
Cankiri40.60751153762560.92
Eskisehir39.8278911945450.07
Karaman37.1810251851453250.93
Kayseri38.7310932091553350.29
Kirikkale39.8574723421821.59
Kirsehir39.151007273512312.66
Konya37.87103118651510.10
Nevsehir38.58126020113132.32
Nigde37.9712111321651651.62
Sivas39.7512851521801801.04
Yozgat39.8212982161223020.65
Table VII. Correlation matrix of correlation coefficients for predictor and response variables (bold values indicate coefficients of 0.5 or greater)
 LatitudeElevElev25Elev50Elev100DisSeaDfNorth
Hm0.380.00− 0.010.000.02− 0.10− 0.16
Pm− 0.010.400.430.470.47− 0.16− 0.13
SDm− 0.440.130.160.150.130.230.24
SRm0.760.150.180.140.070.200.09
Tm− 0.110.750.710.710.720.020.03
Wm− 0.130.330.310.300.260.22− 0.16
 AspectAspect25Aspect50Aspect100SlopeSlope25Slope50Slope100
Hm−0.090.040.140.21−0.35−0.21−0.23−0.20
Pm0.01−0.09−0.15−0.110.340.520.510.44
SDm0.150.010.110.250.130.010.060.01
SRm0.05−0.02−0.03−0.110.06−0.06−0.11−0.22
Tm0.09−0.04−0.09−0.130.060.040.01−0.05
Wm−0.35−0.20−0.17−0.050.270.230.210.16

The regression technique used was stepwise multiple regression. However, attention was paid to avoid the appearance of highly mutually correlated variables in the predictor terms. Only variables that exhibited a low correlation between predictor variables (Pearson Correlation Coefficient < 0.5) were used in the same regression model. The preferred equations and the percentages of variance in the meteorological variables explained by different topographical variables (R2) are presented in Table VIII. All the variables are significant at a 1% or 5% level.

Table VIII. The preferred equations and the percentages of variance in the meteorological variables explained by different topographical variables (A: regression equation which has the maximum coefficient of determination with only one factor; B: statistically preferred equation; C: regression equation with all 15 factors but statistically not significant)
VariableDescriptionR2Equation and significance level (*, 0.01; **, 0.05)
HA14.2%Hm = 15.7 + 1.21 Latitude *
 B36.8%Hm = − 6.8 + 1.80 Latitude − 0.0204 DisSea + 0.00538 Elev100 − 1.21 Slope100 **
 C48.8% 
PA25.9%Pm = 349.0 + 27.5 Slope25 *
 B32.3%Pm = 220 + 20.7 Slope25 + 0.122 Elev100 *
 C24.7% 
SDA57.0%SDm = 18.5 − 0.294 Latitude *
 B63.9%SDm = 19.6 − 0.321 Latitude + 0.00155 DisSea − 0.000313 Elev *
 C77.3% 
SRA19.7%SRm = 1213 − 21.7 Latitude *
 B47.5%SRm = 1227 − 27.0 Latitude + 0.441 DisSea + 0.181 DfNorth + 0.373 Aspect100 + 12.1 Slope100 *
 C65.3% 
TA56.0%Tm = 15.7 − 0.00479 Elev *
 B81.7%Tm = 43.2 − 0.669 Latitude − 0.00643 Elev − 0.000107 Aspect + 0.226 Slope *
 C89.8% 
WA12.5%Wm = 2.55 − 0.00199 Aspect **
 B34.9%Wm = 0.425 + 0.00483 DisSea + 0.00228 DfNorth − 0.00279 Aspect + 0.000720 Elev25 + 0.139 Slope100 *
 C46.4% 

Three different regression equations were obtained for each climate variables. First equation has maximum coefficient of determination with only one factor (A in the description column in Table VIII). Second equation has maximum coefficient of determination, with the selection of optimum number of predictor variables (description B). Third equation contains all the factors, but the values are statistically not significant (description C). These equations were given to determine the highest effects of topographical factors on climate factors.

The results of multiple regressions were generally similar to the correlation results mentioned above. However, linear combinations of multiple terrain variables showed more significant relationships to the meteorological data than did the individual correlations (Table VIII). The regression relationship obtained for solar radiation, sunshine duration and temperature data has rich explanatory capability (R2 of 0.475–0.817). The elevation and the latitude factors are quite effective in the spatial distribution. The regression relationships developed did not explain the majority of the variability in humidity, wind speed and precipitation data. Regression graphs and equations which have maximum coefficient of determination with only one factor are given in Figure 4.

Figure 4.

Regression equation that has the maximum coefficient of determination with only one factor. This figure is available in colour online at wileyonlinelibrary.com/journal/joc

On the basis of regression equations, latitude has the most influence on relative humidity. Latitude explains 14.2% of the variability for relative humidity (Table VIII). There is a positive correlation between latitude and relative humidity (Figure 4(a)). Statistically, 36.8% of the variability for relative humidity was related to topography (Table VIII).

Mean slope within a radius of 2.5 km can explain 27.4% of the variability for precipitation. There is a high positive (0.52) correlation between slope and precipitation. Elev100, Slope25 and DfNorth have the most influence (37.2%) on precipitation.

Latitude is the most effective factor for interpolation of climate. It explains 57% of the variability for sunshine duration alone. But they have negative correlation (Figure 4(c)). Latitude, DisSea and Elev together explain 63.9% of the variability for sunshine duration.

Similar to sunshine duration, latitude can also explain 19.7% of the variability for solar radiation. It was found that latitude has the most but negative influence on solar radiation (Cc: − 0.76). Latitude, DisSea, DfNorth, Aspect100 and Slope100 together can explain 47.5% of the variation for solar radiation.

It was found that the most effective variable for interpolation of temperature is elevation. It explains 56% of the variability with high negative correlation coefficient (−0.75). Temperature is the most explained meteorological parameter based on topography. Latitude, Elev, Aspect and Slope explain 81.7% of the variation for prediction of temperature.

Aspect has an influence of 12.5% on wind speed alone. The correlation between wind speed and aspect (Cc:− 0.35) is not good, and resulted in the lowest R2 in the study. Besides Aspect, DisSea, DfNorth, Elev25, and Slope100 explain 34.9% of the variability for prediction of wind speed.

R2 values of equations ranged from 0.125 to 0.817; thus, even the best regression leaves approximately one-fifth of the variability in the data unexplained. Latitude and elevation were included in several models, but did not always have the same sign for the coefficients. This would seem to indicate that the terrain variable in these instances, while has an important influence, also has a different effect on meteorological data depending on the behaviour of other controlling factors.

5.9 Comparison of regression and kriging interpolations

While kriging and co-krigging methods were compared in the first part of the study, regression equations were obtained in the second part. Finally, kriging interpolation maps were compared with maps obtained by regression interpolation with residual correction (Ninyerola et al., 2000). It was seen that light–dark colour distributions were within the same regions in regression and kriging maps for relative humidity given in Figure 5. While Latitude and DisSea variables in regression equation in equation B of Table VIII changed gradually, effect of changes in altitude and slope of the region (Figure 1) can be clearly seen in Figure 5. While there was a gradual variation in kriging map, there were sharp and sudden variations in regression map. The reason for this was linear effect of slope and altitude over precipitation in regression equation. As seen from the precipitation map, up to 725 mm precipitation in southwest corner of both maps decreased to 300 mm at the centre of the region and increased again at north–northeast side. Solar radiation and sunshine duration maps are very similar to each other and decreases from south to north of the region. Temperature has the highest difference between regression maps and kriging maps. While there was a distinctive decrease from west to east in kriging map, regression map was not able to distinctively reflect variations in topography. Variation of colours for wind speed was also similar in both methods, and regression map has yielded more sensitive results for spatial differences.

Figure 5.

Comparison of regression interpolation with residual correction and kriging. This figure is available in colour online at wileyonlinelibrary.com/journal/joc

6 Conclusion

Climate has many immeasurable effects on human life. It is the most important factor composing and affecting vegetable and animal production which is the main food source of humans. It also determines living conditions and standards. While climate affects these, there are also some factors affecting the climate. As the values such as elevation, latitude, distance from sea, aspect and slope of any two points over the world cannot be expected to be exactly the same, the effect of these factors on climate and the determination of positional change of climate elements gain importance.

Based on the results of this study, the inclusion of elevation as a covariate lowered the errors, particularly for interpolation of temperature, wind speed and solar radiation.

Additionally, this study aimed to determine the effect of local factors on six different climate parameters (solar radiation, sunshine duration, temperature, relative humidity, wind speed and rainfall). Multiple regression equations were developed to determine affect of geography for annual mean values of climate factors. The regression relationships obtained for solar radiation, sunshine duration and temperature data have rich explanatory capability but did not explain the majority of the variability in the humidity, wind speed and precipitation data. The regression results implied that the Latitude, Elevation, Slope, DisSea, DFNorth and Aspect variables, while important to the spatial variability of meteorological parameters as evidenced by the regression models, could only explain a portion of the overall variability in the spatial patterns of meteorological parameters.

Ancillary