Agroclimatic Atlas of Alberta: Interpolation of Climate Station Data

This document is part of the Agroclimatic Atlas of Alberta.

The maps in this 1971 to 2000 Atlas are based on data from all of the Alberta stations (Figure 5), including data from many new stations that were not available for the previous edition of the Atlas. Along with this advance, the maps in this edition have been created using more sophisticated computerized interpolation methods that remove the need to adjust the data for such problems as missing data and allow the use of all available quality controlled daily climate data.

Each station collects data specific to the station's particular location. However, the maps in the Atlas show information for the entire area of the province, as if the climate values are known for all possible locations in the province, rather than only at the station locations. Therefore, climate values need to be assigned for the locations between stations. The process of calculating estimated climate values for locations between weather stations is called interpolation.

Description of the Daily Climate Data Interpolated Over Townships

The Alberta Township Survey System is a grid network dividing the province into equal-size, square parcels of land, for purposes of administering legal land title. The grid specifies squares of land at several resolutions. Townships are approximately 10 km by 10 km in size. (The surveying was done long before Canada started using the Metric system, so the townships are precisely 6 miles by 6 miles in size.) Each township is divided into 36 sections, 1 mile by 1 mile (1.6 km by 1.6 km) in size. These in turn are divided into quarter-sections, and in residential areas these are further divided into land parcels and lots.

The townships were selected as the standard land unit for the Alberta agroclimate database because they are small enough to provide detail yet not so small that the database becomes cumbersome and redundant, and also because any location in the province is easily identified by township. Daily weather data for each day from January 1, 1901 to December 31, 2000, were interpolated to the centre point of each of the 6900 townships in Alberta. Few of the stations have complete daily records of 100 years and some have only a few years or only summer records. The interpolation for any given day in the century was based only on those stations that reported weather values for that day. The interpolation procedure is based on that of Shen et al. (2001).

This interpolation procedure used all available, reliable station data, to generate a database of 36,525 days of daily data for each of the 6900 townships, with no missing data. This database has value not only for preparing this Atlas, but also for many other research and analysis purposes, such as soil quality modeling, environmental impact modeling, and assessing agroclimatic change.

Seven basic and directly observed weather parameters have been interpolated. They are:

Original station data
The climate stations within Alberta and just beyond Alberta's borders (4° of longitude to the east and west, 4° of latitude to the north and 2° of latitude to the south) were used for interpolation. Every piece of raw data, except apparently incorrect data, was used in the interpolation.

The temperature and precipitation data cover the entire 100-year period from 1901. Collection of relative humidity data started in 1948, and collection of solar radiation data started in 1957. Determining the prevailing wind direction requires hourly data; collection of hourly data of wind speed and wind direction started in 1953.

Table 5 shows the number of stations used to construct the interpolated data set, according to climate parameters and regions. (This table does not show the total number of stations operating in each jurisdiction; additional stations operate outside the interpolation area. The total also does not represent the actual number of weather stations operating at any given time. Weather stations sometimes move to a nearby location, close or encounter program changes, resulting in double counting and a larger overall total.)

Table 5. Number of weather and climate stations used to create the interpolated data set, 1901 to 2000

Country	Province	Temperature and precipitation	Wind	Relative humidity	Solar radiation
United States		239	6	6	2
Canada	Alberta	1209	91	95	11
	British Columbia	757	166	74	7
	Saskatchewan	283	67	33	3
	Yukon, Northwest Territories, Nunavut	123	188	55	1
	Canada subtotal	2372	512	257	22
Total number of stations		2611	518	263	24

Interpolation methods and interpolation error
Many interpolation methods are available, with different strengths and weaknesses. The interpolation method used for the maps in this Atlas depended on the characteristics of the climate parameter.

Daily maximum and minimum temperatures at the midpoint of a township were obtained by a weighted average of the data from up to eight neighbouring stations. The weight of each station was inversely proportional to the distance between the station and the midpoint of the township. In this way the value assigned to the township midpoint was influenced most strongly by the stations closest to the township midpoint. This is called the inverse-distance weighting method. Other weighting schemes also exist for interpolations, to vary the relative importance of station proximity. For example, inverse-distance-square weighting further emphasizes the influence of closer stations over more distant ones by squaring all the inverse distances.

Daily precipitation can be very localized and highly spatially variable, particularly in the summer, when localized convective storms are the source of most precipitation events. Even for the areas with high station density like central and southern Alberta, one station may observe precipitation while a close neighbouring station observes none. The inverse-distance method results in too many days with precipitation in a month and too little precipitation for a given day, and so leads to falsely small spatial and temporal variations in the interpolated township data of precipitation.

To avoid this problem and to preserve the localized and highly spatially variable characteristics of precipitation, the hybrid interpolation method was used. The steps of this method are:

The method preserves both the monthly precipitation totals and the number of days with precipitation (the precipitation frequency).

Few Alberta stations measure solar radiation, relative humidity, wind speed and wind direction. Therefore, these parameters are interpolated using the nearest neighbour method described above, which is better suited to sparse data. The climate value assigned to a township for a given day was the value observed that day at the station nearest to the midpoint of the township. This method is equivalent to the Thiessen polygon method described by Bootsma and Ballard (1999).

The assessment of the prevailing wind direction requires hourly data, which began to be collected in Alberta in 1953. The seasonal prevailing wind directions and average wind speeds are calculated for each station, and then township values are interpolated from these seasonal station values, using the nearest neighbour method.

The reliability of the interpolated data on townships has been tested for maximum temperature, minimum temperature, and precipitation. The test is done by pretending the absence of the data from a station with a long and continuous record of observations, like the Edmonton International Airport station. Then the daily climate values of the station location are obtained by interpolation. The difference between the observed values and the interpolated values indicates the reliability of the interpolated township data. This method of testing reliability is called cross-validation in statistics. Five stations with long, continuous records in the period from 1971 to 2000 were selected as the cross-validation stations, giving a full representation from the south to the north. Table 6 gives the information for the five stations.

Table 6. Stations selected for cross-validation

When interpolating from stations onto midpoints of townships for daily data, the root mean square errors, which measure the difference between the interpolated and the true observed values, are in the following range: maximum temperature, 1.3 to 3.4°C; minimum temperature, 1.4 to 3.4°C; and precipitation, 2.4 to 3.4 mm.

The cross-validation method has also helped to select the best method of interpolation since many interpolation methods exist. For temperature and precipitation, the method used here has less error than the methods of simple nearest neighbour assignment, inverse-distance-square weighting, or kriging (see Matheron, 1963).

Relative humidity, radiation and hourly wind data are collected at very few stations. Cross-validation requires deletion of a station, resulting in a significant change of the original observational network for these three parameters. Thus, the cross-validation studies were not carried out in the error assessment for relative humidity, radiation, and wind.

Cartographic Display

The interpolation procedures described above assigned values to whole townships. The maps in this Atlas were based on measures derived from these values. However, to avoid the blocky appearance of townships on the maps and to remove small anomalies, several smoothing procedures were applied. These techniques were applied to the derived measures only and used strictly for cartographic display; the underlying interpolated values were not affected in the Alberta agroclimate database.

Parameters for which values were assigned by the nearest neighbour method were re-interpolated to present a more continuous appearance. Centres were calculated for regions of equal value and assigned the value of the particular region they represented. The values for each township were then re-interpolated from these centres using the inverse-distance method. Parameters originally assigned by the inverse-distance or hybrid methods did not require this procedure.

For all parameters, a 1000-m grid was imposed on each township polygon and each cell of the grid assigned the interpolated value of the township in which it fell. The grid was then smoothed by applying a 50-cell by 50-cell mean filter. For each cell, this filter assigned the mean value of all the cells in a 50-km window.

To reduce the final digital file size, polygons were created by merging grid cells, which fell into the same legend class. Polygon boundaries were generalized to eliminate the blocky appearance.

The wind direction that is most characteristic of a season is not always the most frequently occurring wind direction, nor the vector mean direction. In some cases, the second or third most common wind direction recorded at a specific station is characteristic of the season at the provincial scale shown here. Therefore the placement of arrows to show characteristic wind direction was based on expert knowledge, as well as prevailing wind data. Arrows showing seasonal characteristic wind direction were placed at the locations of specific stations, and other arrows were added between stations to give a visual sense of dominant airflow patterns.

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