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Abstract
Introduction
Methodology
Results & Discussions
Error and Uncertainty
Methodology
Data
Sources
The data used
for this project came from the
National Climate Data and Information
produced by Environment
Canada and maintained by Environment Canada. The site contains official
climate
and weather observations, normals and extremes for over 10,000 weather
station
locations across
Archived data
is available from
the mid-19th century although due to time constraints the
project
used data from the last 30 years; 1970 to 2004. The number of data
points
available per year for the study area of
A 1 Km
resolution DEM of British
Columbia was used in the temperature interpolation. This was produced by the UBC GIS
Department using separate satellite images of
Method
To obtain an understanding of the distribution of extreme minimum temperatures across British Columbia we made the assumption that altitude and location within the province would determine the minimum extreme temperature. The dry adiabatic lapse rate was applied to the temperature data to produce the minimum temperatures that would be expected if all the stations were at sea level. This allowed a prediction of the distribution of temperatures over a hypothetically flat uniform British Columbia.The Dry Adiabatic lapse rate:
T1 = T2 - 0.0098 x (y)
T1 is the recorded temperature (C)
T2 is the temperature at sea level (C)
Y is the elevation (m)
Lapse rate: 0.0098 C/m
The minimum extreme temperatures at sea level were interpolated using the geostatistical analytical
technique
Kriging; which assumes that the distance or direction between sample points reflects a
spatial correlation that can be used to explain variation in the surface. Ordinary Kriging assumes the constant
mean is unknown, a normal distributed data set and the data comes from stationary stochastic processes. The
interpolation weighting is based not only on the distance between the measured points and the prediction location,
but also on the overall spatial arrangement among the measured points. Therefore Kriging uses the data twice: the
first time to estimate the spatial autocorrelation of the data and the second to make the predictions of the unknown
values.
Kriging is most appropriate when you know there is a spatially correlated distance or directional bias in the
data. In this case it is that areas to the North and away from the ocean and to the east will reveal lower temperatures.
Kriging fits a mathematical function to a specified number of points, or all points within a specified radius,
to determine the output value for each location and weights the surrounding measured values to derive a prediction for
an unmeasured location. The general formula for both interpolators is formed as a weighted sum of the data:
Z(si) is the measured value at the ith location;
£fi is an unknown weight for the measured value at the ith location;
s0 is the prediction location;
N is the number of measured values.
The Kriging technique produces a contour-map of BC representing the prediction of extreme minimum temperature
at sea level with the location of isotherms in two dimensional space. This is done for each year. The contour maps are
exported as a raster layer with a resolution of 4.5km, this is a large resolution but due to the size of the study area
and number of data points this is acceptable. To predict the extreme minimum temperatures for each year the elevation
is taken into account. The Dry Anabatic Rate is used in reverse using the 1 km Digital Elevation Model of British Columbia
in a raster calculation, increasing the resolution. This final raster map uses the interpolated data distribution on an
uniform surface and to predict a spatial distribution of minimum temperature for each year using elevation as a variable
factor.
