Introduction
Converting temperature forecasts and observations at synoptic weather stations into a gridded dataset is widely used for ecosystem modeling studies and for model-based decision making at regional scales. Among the daily weather information issued by public weather services, minimum temperature is fundamental for preventive measures for frost damage as well as for input data for heat unit calculations, crop growth simulation, plant disease forecasting, and irrigation scheduling.
Synoptic weather stations tend to be located in populated areas and, therefore, tend to overestimate temperature across rural areas, where weather-monitoring stations are sparse. Overestimation by 2°C is common in South Korea when synoptic weather station data and distance- and elevation-based spatial interpolators are used to calculate gridded daily minimum temperature (Choi 2002; Yun et al. 2001). It is necessary to subtract the urban effect from the interpolated temperature surfaces to prepare the gridded dataset relevant to the regional application of ecosystem models. Removal of urban effects from climatic data is also a prerequisite for global-warming studies (Karl et al. 1988; Jones et al. 1989) and has been done using various methods, including classification of data sources based on the nighttime ground surface brightness seen from a satellite (Peterson et al. 1999; Hansen et al. 2001).
Based on an analysis of temperature data for 1911–85, Cho et al. (1988) found a close relationship between the warming trend and the growth of urban areas in Korea. Urban warming is often defined as the difference in temperature between a city and the surrounding rural area and is called urban heat island (UHI) intensity. The maximum UHI intensity in Korea ranges from 3.0° to 9.8°C, depending on season and geographic location (Han et al. 1993; Yoon et al. 1994; Ryoo and Moon 1995; Kim and Baik 2002). There is a clear relationship between UHI intensity and population size (Landsberg 1979). Furthermore, maximum UHI intensity at any time increases as a logarithmic function of population difference (Oke 1981). Park (1986) derived regression equations between maximum UHI intensity and the population size in Korea. The regression coefficients, that is, observed warming by a unit increase in population, showed an abrupt change at a population of 300 000 people.
These relationships can be used to predict temperature deviation at a city from the background rural temperature trend, if the city population is known. For spatial application, however, these relationships are of little use because population statistics are categorical rather than continuous in nature. Even though population itself is a continuous entity with respect to spatial distribution, the statistics are reported in a census tract unit, which is irregular in shape. There is no spatial variability in population within a city or county boundary, prohibiting realistic simulation of temperature variation within it. Urban effects simulated by the city- or county-based population show an abrupt change along the boundary, and the simulated temperature field has discontinuity. As a result, it is difficult to use population itself as a proxy variable to represent urban effects in spatial interpolation of temperature. It is necessary to find a new proxy variable for spatially explicit expression of the urban effect while utilizing existing relationships between the urban effect and population.
The objectives of this study are 1) to find a population-based proxy variable for spatial analysis of urban effects on temperature, 2) to develop an improved temperature interpolation model using the urban effect correction, and 3) to test the validity of this model in improving the accuracy of temperature estimates by existing methods.
Data and methods
A model for temperature interpolation
Much of the temperature estimation error by distance-weighted interpolators comes from the elevation difference between the unobserved point and surrounding weather stations. This error can be removed by multiplying a lapse rate by the elevation difference. The elevation difference stands for the difference between real and virtual terrain. A digital elevation model (DEM) at relevant resolution represents the real terrain, and a spatially averaged elevation surface generated by an interpolation of station elevations represents the “virtual terrain.”
The first term on the right-hand side of Eq. (1) is nothing more than the estimated temperature using the inverse-distance-squared weighting (IDSW) method. The second term within the first set of parentheses is the virtual terrain generated by the IDSW interpolation of the station elevation. The calculation within the parentheses represents the elevation difference of the site from the virtual terrain. Hence, this component defines the size of the error from the local variation in elevation and can serve as the elevation correction scheme. The calculation within the second set of parentheses indicates the difference in population, that is, the difference between real and virtual population. Here, the population means a population-based proxy variable representing the urban effect. The proxy variable P must be continuous and, hence, is expressed in a regular gridcell unit rather than a total sum of a city boundary. This component, when coupled with a proper conversion coefficient, represents the temperature estimation error caused by urban heat island effects and serves as the urban-effect correction scheme.
Converting population from a categorical to a continuous variable
We obtained a land cover map of the Korean peninsula at a 30-m grid spacing from the Environmental Mapping Service of the Ministry of Environment (see online at http://www.me.go.kr). In their work, scenes from Landsat Thematic Mapper in 1990 were used to classify the land cover into seven features, including “urban” and “built up” areas. After the initial unsupervised classification, training sets were chosen by referring to topographic maps, aerial photos, other thematic maps, and field surveys. A maximum likelihood classifier was used for supervised land cover classification. The urban and built-up class includes residential areas, commercial and industrial areas, transportation structures, and sports and recreational facilities. A polygon-featured map of city and county boundaries of South Korea was overlaid on the land cover map, and the number of urban pixels falling within each city or county was counted (Fig. 1). Population data for all the cities and counties in 1990 were obtained from the National Statistics Office (see online at http://www.nso.go.kr). By dividing the population of a city or a county by the number of urban pixels within its boundary, the population per unit urban pixel was calculated for each city and county and named “urban population density” (unit: persons per 900 square meters). An attribute table consisting of the urban population-density values was produced and spatially joined with corresponding polygons representing cities and counties. The city and county boundary map now consists of polygons with the attribute of an urban population-density value unique to each polygon. The polygons were again overlaid on the land cover map and urban pixels falling within a same polygon boundary were multiplied by the urban population density unique to that polygon. A digital map consisting of the same grid cells as the land cover map was created, but each grid cell now has population information instead of land cover information. This map shows the spatial pattern of population distribution, even within an individual city, and the number of people living in each land unit, excluding natural landscapes such as parks, water bodies, and mountains. For ease of data handling, we aggregated a block of nine pixels into a new unit (90-m resolution) and named the grid map consisting of such grid cells the “digital population model” (DPM). Each grid cell has the population sum of the nine 30-m pixels (unit: persons per 8100 square meters) as its attribute and is georeferenced for further spatial analysis.
Derivation of the coefficient Π
Urban effects on temperature observed at a given grid cell might be created by the population of surrounding cells as well as the gridcell population itself. To find the radial extent that best explains the urban effect on observed temperature, several DPMs smoothed at different radii were tested for their relationship to temperature variations. First, we calculated the spatial sum of all DPM values within a radius of 0.5, 1.5, 2.5, 3.5, and 5.0 km, respectively, and substituted these aggregated values for original cell values. Next, grid cells corresponding to the locations of a random selection of 25 out of 56 synoptic weather stations operated by the Korea Meteorological Administration (KMA) were extracted from the five smoothed DPMs, and the values were assumed to be the “real population.” These real population data at 25 station locations were spatially interpolated to generate “virtual population” surfaces with different smoothings. The remaining 31 station locations were identified on the virtual population surfaces and on the original DPM, and corresponding values were read to obtain the population difference.
Climatological normals of daily minimum temperature for each month at 56 stations were collected from the KMA climate data archive for 1971–2000. With the data from 25 randomly selected stations, an interpolation scheme using the IDSW and a lapse-rate correction was performed to generate the temperature surfaces over South Korea at a 250-m grid spacing.
Daily lapse-rate values were calculated using a periodic function (Yun 2003). A so-called mountain slope lapse rate (MSLR) was calculated for each day based on a time-dependent formula. The formula was derived from empirical relationships between the station elevation and the observed daily minimum temperature at 63 locations in South Korea. Because temperature deviation between any two stations at different altitudes consists of the portions from geographical variability (latitude, proximity to water bodies, aspect of the slope, etc.) and weather variability (solar radiation, cloud amount, etc.) as well as the portion from the elevation difference, extraction of the “signal” contributed by the elevation effect alone from “noise” caused by other factors is necessary to delineate meaningful relationships between the temperature and elevation. A set of variables best explaining the spatial variation of the minimum temperature on a given date was selected by a stepwise regression analysis. Latitude, longitude, distance from the nearest coastline, and elevation of stations were among the most frequently selected. Because the partial regression coefficient of each variable in the regression model represents the amount of temperature change with respect to a step change in the corresponding variable, the partial regression coefficients of the elevation variable in the models should be close to the MSLR. A periodic pattern was detected when the coefficient values were plotted against the corresponding dates, and the absolute value of MSLR (°C m−1) was estimated by 0.006 95 + 0.0013 cos[0.0172(I − 30)] for daily minimum temperature, where I is the day of year.
Estimated temperature values at the grid cells corresponding to the remaining 31 station locations were extracted from the interpolated surface and compared with the observed data. Estimation error was regressed to the logarithm of population differences at five different smoothings. If the population difference was negative, that is, the virtual population was less than the actual population (DPM), the location was removed from the analysis. There were two such cases with the 0.5-km radius and one such case with the 1.5-km radius. Linear-regression equations for each month were obtained for the five smoothings. Hence, the regression coefficient or the slope of the equation with the highest coefficient of determination (r2) can be regarded as Π. The procedures are described by a flow chart in Fig. 2.
Validation
As a test of the accuracy of this method, we used “cross validation” (Nalder and Wein 1998). Climatological normals of daily minimum temperature for each month at 56 stations were used for this purpose. With the data excluding one station, interpolation schemes using a simple IDSW, a lapse-rate-corrected IDSW, and the lapse-rate- and urban-effect-corrected IDSW were performed to generate temperature surfaces over South Korea at a 250-m grid spacing. A temperature value for each grid cell corresponding to the excluded weather station location was extracted from the temperature grids. For this procedure, we prepared 56 datasets, each consisting of 55 stations' data. Elevation data of 55 stations were used to generate the virtual terrain, and the lapse-rate correction was applied to the IDSW interpolated temperature surface by using the elevation difference between the virtual and the 250-m DEM.
For the urban-effect correction, population data extracted from 55 station pixels were used to generate the virtual population surfaces. The difference between virtual population and the DPM surface smoothed for relevant radial extent was calculated. Urban warming at each site was estimated by multiplying the logarithm of population difference by the slope value from the regression.
Observed and estimated data for 56 grid cells, which were excluded from the analysis, were compared to get the estimation errors for three methods: the simple IDSW, lapse-rate-corrected IDSW, and lapse-rate- and urban-effect-corrected IDSW. The entire procedure was repeated for each month.
Results
Digital population model
According to the DPM statistics, the maximum number of people living in a 90 m × 90 m land area is 510 in Korea, which is equivalent to 63 000 people per square kilometer. This value is possible in several high-density apartment complexes around Seoul. There is a slight pattern change with respect to the position and the concentration when the DPMs are smoothed with increasing extent (Fig. 3). The maximum population is 24 000 people per square kilometer if smoothed to the radial extent of 2.5 km.
Urban warming coefficient (Π)
The coefficient of determination (r2) was highest in 2.5-km smoothing radius across the seasons, when the temperature estimation errors at 31 stations were regressed to the DPMs smoothed at five different radial extents (Fig. 4a). Hence, we assigned the slopes of regression equations with 2.5-km smoothing radius to the monthly value for the urban warming coefficient Π.
Regardless of the smoothing extent, r2 values are high in summer and low in winter. That is, urban heat island effects could explain a greater portion of the estimation error in summer than in winter. This result should not be interpreted as lesser importance of the urban effect in winter. The absolute size of the estimation error is actually much larger in winter, and the portions explained by regression model could be equal to or even greater than in summer. The larger estimation error in winter may be accounted for by unknown factors other than the urban effect, such as cold-air accumulation in a lower watershed. In addition, slopes of regression coefficients are higher in winter than in summer (Fig. 4b). Assuming a 10 000 population difference, calculated warming will be 0.4°C in December and 0.02°C in July. Even though the r2 value is higher in summer, urban effect on daily minimum temperature is greater in winter.
The x-axis intercept value of the regression equation implies a threshold value that is the minimum population size that could induce urban effect and can be used as a measure of rural–urban classification. The average value is around 12 000 people and implies that at least 12 000 people must live within a radius of 2.5 km if any urban effect is going to occur (Fig. 4c). Although the overall value is comparable with the population criterion used to classify the U.S. Historical Climatology Network stations into urban or rural (Gallo and Owen 1999), there is a distinct seasonal variation with lower than 10 000 in June and July and higher than 14 000 in winter.
Validity of the model
Daily minimum temperature was estimated by our model with much less error than other existing methods (Fig. 5). Mean absolute error (MAE) ranged from 0.4°C in summer to 1.1°C in winter, and root-mean-square error (rmse) was slightly higher, with a minimum of 0.5°C in summer and a maximum of 1.4°C in the winter season. Seasonal dependency of the temperature estimation error has also been reported in existing interpolation methods (Yun et al. 2001). If we omit the urban effect in the interpolation, MAE values will increase by 0.1°–0.6°C, and rmse will increase by 0.2°–0.7°C, depending on the season. Hence, we could eliminate around 30% of the estimation error by considering the urban effect alone. This magnitude of improvement over the best existing method (the lapse-rate-corrected IDSW) is comparable with that by lapse-rate correction over a simple IDSW interpolation. That means the urban effect could be as important as the elevation effect in the estimation of daily minimum temperature in Korea.
Daily minimum temperature for January estimated by the three methods is draped over a map of South Korea for a visual comparison of spatial pattern (Fig. 6). The output from a simple IDSW interpolation shows a wide region of warm temperature (>−6°C) along the southern coastline. When elevation difference is considered by incorporating the lapse-rate correction, this warm region shrinks as mountainous areas become cooler and the cool region expands toward the coastline. With the additional urban effect correction, the warm region is further reduced and the cool region keeps expanding. However, warm spots now begin to appear in urbanized areas, making more contrast in the temperature pattern between urban and rural areas.
Discussion
The primary purpose of interpolating synoptic temperature observations is to determine accurate climatic characteristics of underpopulated areas such as forests and croplands. Daily minimum temperature, in particular, has enormous value because it is coupled with phenology as well as the physiology of crops and trees. Observations or timely forecasts of daily minimum temperature can be valuable information for operational agriculture and forest management. Much effort has been devoted to improving spatial temperature estimation by considering the elevation effect, especially in topographically complex environments. There is an abundance of tools and data for diverse spatial- and temporal-scale applications. But still, much remains to be explained and solved for better temperature estimation at operational levels. Land cover difference, sun–slope geometry, and cold-air drainage are a few among those factors.
This study was initiated with the postulation of the urban effect as another possibility for reducing the estimation error and suggests a simple but robust method to incorporate the urban effect into the existing interpolation scheme. The degree of urbanization may be quantitatively explained by diverse statistics, including land cover–land use change, construction activities, automobile registration, energy consumption, and so on. We selected “population” of the city in which the climatological station resides, because population implies most of the activities related to urbanization. To overcome the spatially discontinuous nature of the population statistics, we introduced a new proxy variable that we call digital population model, based on high-resolution land cover information along with the population statistics. Because the urbanization implies both population trends and settlement patterns, the influence of urbanization on the observed temperature has been extensively studied by using combined population statistics and land use–and cover information (Peterson et al. 1999; Gallo et al. 1999; Gallo and Owen 1999; Hansen et al. 2001). Our method could be another way of integration, but it provides a tool readily applicable to spatial analysis of urban effects on temperature seldom found among other studies.
Though it has been tested only in South Korea, the approach based on the DPM concept can be applied to other countries or regions experiencing rapid urbanization and industrialization. Because of overlapping of the rapid urbanization–industrialization period with the establishment of the weather observation network in Korea, historical temperature data are influenced by the urban heat island effect. Our method could be used to correct historical data, and the corrected data might be used to restore climatological normals for rural areas. Depending on the data period, we may prepare multiple sets of climatological normals for climate-change studies on the regional scale. Because a true climatic change is a statistically significant difference between two normals, at least two sets of gridded temperature data are necessary for climate-change studies. Regional evaluation of climatic impacts on agricultural or forest ecosystems will be possible with these datasets.
Acknowledgments
This work was supported by Grant R01-1999-000-00175-0 from the Basic Research Program of the Korea Science and Engineering Foundation. We thank the three anonymous reviewers for their helpful comments.
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(a) Urbanized areas with a 30 m × 30 m pixel spacing extracted from the land cover classification map, (b) the number of urban pixels falling within each administrative boundary, (c) the urban pixel–based population density (persons per 900 square meters), and (d) the locations of synoptic weather stations
Citation: Journal of Applied Meteorology 42, 12; 10.1175/1520-0450(2003)042<1711:UCTIAO>2.0.CO;2
Selection procedure for the optimum regression equation of the urban heat island based on the digital population model.
Citation: Journal of Applied Meteorology 42, 12; 10.1175/1520-0450(2003)042<1711:UCTIAO>2.0.CO;2
(a) Population distribution pattern simulated by the 90-m DPM for the Seoul metropolitan area. Also shown are the DPM surfaces smoothed for the radial extent of (b) 500 m and (c) 1.5, (d) 2.5, (e) 3.5, and (f) 5 km
Citation: Journal of Applied Meteorology 42, 12; 10.1175/1520-0450(2003)042<1711:UCTIAO>2.0.CO;2
(a) Seasonal variation in the coefficient of determination (r2) for the regression equations with different smoothing. The (b) slope of regression coefficient and the (c) x-axis intercept for the regression equation with the 2.5-km smoothing radius
Citation: Journal of Applied Meteorology 42, 12; 10.1175/1520-0450(2003)042<1711:UCTIAO>2.0.CO;2
Seasonal change in (a) MAE and (b) rmse of the estimated temperature by the DPM-based urban heat island effect model. Results of existing methods (a simple IDSW and the elevation-effect-corrected IDSW) are shown for comparison
Citation: Journal of Applied Meteorology 42, 12; 10.1175/1520-0450(2003)042<1711:UCTIAO>2.0.CO;2
Daily minimum temperature normals of Jan (1971–2000) estimated by (a) a simple IDSW, (b) the elevation-effect-corrected IDSW, and (c) the population-effect-corrected IDSW. (d) Synoptic station locations with the topography are also presented for easy detection of the warm- and cool-region migration
Citation: Journal of Applied Meteorology 42, 12; 10.1175/1520-0450(2003)042<1711:UCTIAO>2.0.CO;2
