Former Student, University of Calicut, India
E-mail: [email protected]
Department of Physics, St.Thomas College, Thrissur, Kerala, India
Email: [email protected]
Consultant, Kerala Sustainable Urban Development Project (KSUDP), India
Email: [email protected]
The main objective of this study was the spatial interpolation of ambient temperature for the Thrissur district of Kerala, India, through GIS technologies. At the outset, a review of spatial interpolation methods was made. Several spatial interpolation methods were tested: Inverse Distance Weighting (IDW), SPLINE and KRIGING. The first two of these – IDW and SPLINE – were chosen for the preparation of map. The dataset contained temperatures from 23 locations at different time across Thrissur district. The study identified IDW as the best spatial interpolation method to use for the creation of continuous data for air temperature. Temperature range, temperature variance, and temperature correlation with elevation, all influence the choice of interpolation technique. GIS tools enable the easy calculation and display of the area under specified thermal conditions and the display of maps for climate monitoring purposes.
Temperature is one of the most sensitive indicators of dynamical and physical processes in atmosphere. It is affected by interactions between air and land or ocean, by the radiation received from the Sun and emitted by the atmosphere and the Earth’s surface, by chemical interactions (particularly in the upper atmosphere), by changes in state of water from gas to liquid to ice and vice versa, and by upward and downward motion. Knowledge of the current temperature in all parts of the atmosphere is crucial for weather forecasting.
Atmospheric temperature data are used for monitoring inter-annual global temperature changes, for identifying correlations between atmospheric parameters and climatic behaviour and to validate global models of the atmosphere. They may also be used for computing the upper level wind structure, which, in turn, is a useful aid in the prediction of strong winds at the surface and warning of possible storm surges in the sea level around coasts.
The temperature at any particular place is influenced by a number of factors like latitude, season, altitude, proximity to ocean, time of day, wind direction and present weather conditions. The last three of these control variations in temperature over short periods.
GIS is a very important and widespread tool serving a variety of functions in many environmental sciences including meteorology and climatology (e.g. Tveito et al.2000). It captures, stores, analyses, manages and presents data that is linked to location. Technically, GIS includes mapping software and its application with remote sensing, land surveying, aerial photography, mathematics, photogrammetry, geography and tools that can be implemented with GIS software.
Interpolation is a method or mathematical function that estimates the values at locations where no measured values are available. Interpolation can be as simple as a number line. Spatial interpolation assumes the attribute data are continuous over space. It allows estimation of the attribute at any location within the data boundary. Another assumption is the attribute is spatially dependent, indicating the values closer together are more likely to be similar than the values farther apart. These assumptions allow spatial interpolation methods to be formulated. Spatial interpolation is widely used for creating continuous data when data are collected at discrete locations (i.e., at points).
Materials and Methods
Study site: The study area was Thrissur district of Kerala. The sampling sites were uniformly distributed in the study area. One of the peculiarities of study area was that the area included-Urban, midland, coastal, highland areas. So the spatial variation of temperature was notable.
Data: For this study spatial data and non spatial data were used.
Non spatial data
The temperature data used for this application was collected at twenty-three locations in the study area. These locations were sporadically distributed within the study area. Temperature was measured using scientific thermometer. It was measured at different time i.e., 8.00am, 12.00pm, 3.00pm, 5.00pm in the same day, at different locations. The temperature data was collected for two days (27-03-2010, 28-03-2010).The actual range of temperature on these days was 220C to 370C. The interpolated surfaces were created by estimating temperature from twenty-three sampled points. The created surfaces represent the temperature of the study area.
Spatial Data Set
SOI Topomap: Topographical maps prepared by Survey of India (SOI) at 1:50,000 scales were used to generate the base map of the study area. They were projected to Transverse Mercator Projection and mosaiced to get the study area.
Location Data: The exact location of sampling locations was noted with the help of GPS.
Software and devices Used
ArcGIS 9.2 software was used to analyse the spatial data. It was also used for the generation of various interpolated and thematic maps. In addition, for the purpose of obtaining exact location data, a handheld GPS was used in the study.
The techniques assessed here include the deterministic interpolation methods of SPLINE and IDW and the stochastic method of KRIGING in an effort to retain actual temperature measurement in a final surface. Each method selected requires that the exact data values for the sample points are included in the final output surface.
These spatial interpolation methods have various decision parameters. The descriptions below include the options and values used in the different modules of ArcGIS. For display purposes, all images are grouped to nine classes. The images show the colder values in lighter colours with the warmest values in the darkest colour. The selected techniques, SPLINE, IDW and KRIGING, are not all of the interpolation methods, nor are they a comprehensive review of the ArcGIS Geostatistical extension. ArcGIS was employed as the software for this study, although the techniques are available in other software products as well.
Inverse Distance Weighting (IDW): Inverse Distance Weighting (IDW) is based on the assumption that the nearby values contribute more to the interpolated values than distant observations. In other words, for this method, influence of a known data point is inversely related to the distance from the unknown location that is being estimated. The advantage of IDW is that it is intuitive and efficient. This interpolation works best with evenly distributed points. Similar to the SPLINE functions, IDW is sensitive to outliers. Furthermore, unevenly distributed data clusters results in introduced errors.
SPLINE: The SPLINE method can be thought of as fitting a rubber-sheeted surface through the known points using a mathematical function. In ArcGIS, the SPLINE interpolation is a Radial Basis Function (RBF). These functions allow analysts to decide between smooth curves or tight straight edges between measured points. Advantages of splining functions are that they can generate sufficiently accurate surfaces from only a few sampled points and they retain small features. A disadvantage is that they may have different minimum and maximum values than the data set and the functions are sensitive to outliers due to the inclusion of the original data values at the sample points. This is true for all exact interpolators, which are commonly used in GIS, but can present more serious problems for SPLINE since it operates best for gently varying surfaces, i.e. those having a low variance.
KRIGING: Similar to IDW, KRIGING uses a weighting, which assigns more influence to the nearest data points in the interpolation of values for unknown locations. KRIGING, however, is not deterministic but extends the proximity weighting approach of IDW to include random components where exact point location is not known by the function. KRIGING depends on spatial and statistical relationships to calculate the surface. The two-step process of KRIGING begins with semivariance estimations and then performs the interpolation. Some advantages of this method are the incorporation of variable interdependence and the available error surface output. A disadvantage is that it requires substantially more computing and modelling time and KRIGING requires more input from the user.
Analysis of results
Each interpolation technique was compared on the basis of bias, mean absolute error (MAE), and mean squared error (MSE). Cross validation techniques are used to choose the best semivariogram model from among candidate models (spherical, exponential, or Guassian). In addition, cross validation techniques are used to select the search radius which minimise the KRIGING variance. Summary statistics rather than analysis of variance (ANOVA) were used to determine if any interpolation method was significantly better than the methods tested on the basis of bias, MAE, and MSE. The reason for this choice was that hypothesis testing using ANOVA assumes that the means compared are drawn from populations with a common variance. As this analysis provides a comparison across different temporal scales and geographic regions, the assumption of a common variance is not valid. Data attribute s were also investigated to determine whether data variance, data correlation with elevation, or lapse rate significantly affect interpolation. Because these spatial metrics are easy to calculate, they can be determined prior to interpolation to determine which method may be most appropriate.
Results and Discussion
Spatial data were used for the generation of various maps which show spatial features of the study area and certain interpolation analysis were conducted using the output. The interpolated surfaces were created by estimating temperature from twenty-three sampled points. The created surfaces represent the temperature of the study area.
The study identified IDW as the best method for interpolating surfaces, followed by IDW and KRIGING then SPLINE. Nevertheless, as illustrated in Figure 1 none of the interpolation methods did a reasonable job of estimating the actual temperatures because the variation in temperature with 23 sample points is too small to assess temperature over study area. It is also true that only having twenty-three points to interpolate across that area is also a significant limitation because there are little differences in temperatures between the climate stations. It is impossible, however, to increase the sample size of either because we are constrained by the number samples.
The study also found evidence that certain priori data characteristics influence choice of spatial interpolation technique. Temperature range, temperature variance and temperature correlation with elevation all influence the choice of interpolation technique.
Spatial scale also impacts interpolation. In addition, the relative spatial density and distribution of sampling stations may influence the choice of interpolation technique. These conclusions concur with MacEachren and Davidson (1987) who concluded that data measurement accuracy, data density, data distribution, and spatial variability had the greatest influence on interpolation accuracy.
Overall, polynomial regression was most representative of the original data and had the lowest MAE value of methods ranked. For all cases tested, KRIGING had lower MAE values when the data were anisotropic. When the data were isotropic, optimal inverse distance performed better than KRIGING based on MAE. Large temperature variances and temperature ranges tended to increase interpolator MAE. Higher correlations between temperature and elevation tended to favour polynomial regression over other interpolation techniques. The effects of landscape complexity did not directly affect the choice of spatial interpolator. Data attributes, however, change with landscape complexity. The high land area of Thrissur had greater landscape complexity than other Regions. As a result of this increased landscape complexity, the highland had greater temperature variances and observed temperature ranges across all temporal scales.
In general, the results indicate that increased variance and data range result in decreased interpolator accuracy as indicated by higher MAE values. The results also indicate that interpolation techniques which use ancillary elevation information to predict temperature benefit from higher correlations between elevation and temperature. Of data attributes investigated, correlation between elevation and temperature and data temperature variance had strong influences of predictor performance Temporal scale affects the choice of spatial interpolator as temperature range, temperature variance, and temperature correlation with elevation, all change with temporal scale.
Range, variance, and correlation are important attributes to consider when selecting a spatial interpolator. Where temporal scales are short, preliminary data analyses are especially important to determine the suitability of a particular interpolation technique. The larger MAE values of daily minimum and maximum temperature interpolation can be attributed to higher temperature ranges and variances.
Results from the interpolation of everyday’s maximum and minimum temperature indicate that increasing temperature variance affects interpolator performance negatively. Increased correlations between elevation and temperature had a positive effect on interpolator performance. Temperature range did not seem to affect interpolator performance. Results for Region 2 daily maximum and minimum temperature differed from Region 1 results in that temperature range had a negative effect on interpolator performance. As the temperature range increased, MAE values across all interpolators increased significantly. The effects of temperature variance and correlation between elevation and temperature were the same as for Region 1. As temperature variance increased, MAE values across all interpolators increased. As correlations between elevation and temperature increases, MAE values dropped significantly for those interpolation methods which used elevation as ancillary information.
This study has shown that IDW is most likely to produce the best estimation of a continuous surface of air temperature. Nevertheless, the study presented here illustrate s that regardless of the approach taken these interpolation methods do not adequately address the temperature variability inherent in an urban setting. As a result, it is critical that additional factors, unique to the urban environment be incorporated into spatial interpolation methods for a more realistic representation of this area. Consequently, an estimated surface of temperature based on IDW can be used as input into a more complex spatio-temporal integration model (STIM) to generate a better representation of temperature. The present study confirms that the application of GIS techniques is a useful and promising tool for constructing climate maps at different scales. There are several spatialisation methods suitable for the construction of climatic maps. However, residual KRIGING seems to be adequate for the spatial interpolation of air temperature in Poland and Central Europe. Its verification and map presentation confirm that application of this method provides relatively precise images of the particular temperature characteristics. A mesoscale approach is possible when DTM as well as relatively dense meteorological data are available. Of course, the full verification must be done with the use of both minimum and maximum temperature values. However, present knowledge of the microscale temperature differentiation in mountainous areas suggests that one should be sceptical about the application of this method in such areas. Some other additional geographical predictor variables, such as slope and aspect, land-use or soil type should be taken into consideration. Furthermore, a universal method with the same parameters for the entire area is not appropriate; rather, the new parameters must be calculated independently for much smaller regions.
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