Ontario is Canada’s most populous province and second largest province in total area. It is home to the nation’s most populous city, Toronto and the nation’s capital, Ottawa. The total area of Ontario is 1.1 × 106 km2, of which 85.3% is land and 14.7% is water (http://en.wikipedia.org/wiki/Ontario). Two-thirds of Ontario is covered by the Canadian Shield, which contains Precambrian rocks that are over 570 million years old. The rest Ontario in the north are the Hudson Bay Lowlands, consisting of swamp, meadow and forest. The landscape of Ontario is characterized by forests. Sixty-six per cent of Ontario is classified as forested land, totaling 0.7 × 106 km2, which accounts for about 2% of the world’s forests. (http://www.ontario.ca/government/about-ontario). The climate in Ontario is humid continental in the south and subarctic in the north. The large bodies of water within the province have a moderating effect on climate, making summer and winter temperatures less extreme and the difference between day and night temperatures smaller. During the past decades, climate change has brought many impacts upon human societies around the world, including Ontario. The Ontario government has conducted many researches and programs to help people adapt to the effects that are already being experienced, as well as the future effects of climate change (Baldwin et al. 2000).
Data collection & project procedures
Two sets of datasets were employed in this study. The primary dataset, 25 km regional climate modeling (RCM) data over the province of Ontario, was obtained from the website (http://env.uregina.ca/moe/). This RCM result dataset over the province of Ontario was generated by a well-established Providing Regional Climates for Impacts Studies (PRECIS) model. In this study, the annual mean temperature would be taken into consideration and this dataset would be processed as the source dataset that to be interpolated through the three interpolation methods in ArcGIS.
The secondary dataset, daily 10 km gridded climate dataset for Canada 1961-2003, was obtained from the website (http://www.agr.gc.ca/nlwis-snite/index_e.cfm). It was provided by Agriculture and Agri-Food Canada, Government of Canada. The Daily 10 km Gridded Climate dataset for Canada south of 60° north contained the coordinates of locations as well as the associated daily maximum temperature, minimum temperature, and precipitation data. In this dataset, the desired climate information for 10 km was stored in a number of individual files and the climate information was offered by daily data. Therefore, pretreatments of this dataset was necessary for obtaining the climate data that contained annual temperature information in one file. The desired 10 km annual mean temperature dataset could be obtained based on the data of maximum and minimum temperature.The primary dataset was based on the period of 1979 to 2009 while the secondary dataset was based on the period of 1961 to 2003. Therefore, we considered the period of 1979 to 2003 as our study period and the 25 years mean temperature would be studied. The flowchart of this project was given in Figure 7. It showed the detailed procedures of this study.
Spatial interpolation methods in a GIS
The following is a brief introduction of the interpolation methods available in ArcGis desktop 10.
Inverse Distance Weighting (IDW)
Inverse distance weighting (IDW) is an interpolation method that interpolated estimates are made based on values at nearby locations weighted by distance from the interpolation location. IDW works under a basic assumption that nearby points ought to be more closely related to the value of interpolated location than distant points (Naoum and Tsanis 2004). In IDW method, estimation at interpolated location is a weighted linear combination, with the weights λι being inversely proportional to the square distance between sampled location μι and the point of estimate μ (Van der Heijden and Haberlandt 2010):
Spline interpolation consist of the approximation of a function by means of series of polynomials over nearby intervals with continuous derivatives at the end-point of the intervals (Naoum and Tsanis 2004). Smoothing spline interpolation enables the variance of the residuals over the dataset being controlled. The interpolation estimates are calculated by an iterative algorithm. In spline interpolation, the interpolated surface must precisely pass through the data points; meanwhile, the surface must have minimum curvature (Naoum and Tsanis 2004). ArcGIS provides two types of spine interpolation methods which are regularized type and tension type.
Kriging is based on regionalized variable theory that provides optimal interpolation estimates at given coordinate locations. It involves an interactive investigation into the spatial behavior of the phenomenon before outputting the interpolation surface. In the regionalized variable theory, it assumes that the spatial variation is statistically homogeneous through the surface, which means the same pattern of variation can be captured at all locations on the surface. The hypothesis of spatial homogeneity is the basis of the regionalized variable theory (Naoum and Tsanis 2004).