A spatial entropy analysis of temperature trends in the United States



[1] The United States Historical Climatology Network (USHCN) temperature database shows a significant upward trend over the past half century. In this investigation, we calculate the spatial entropy (dissimilarity or disorder) associated with the temperature trends of 1,221 stations in the fully adjusted USHCN. We find that over the network, the spatial entropy levels are significantly and positively related to the observed temperature trends suggesting that stations most unlike their neighbors in terms of temperature change tend to have a higher temperature trend than their neighbors. These results suggest that the USHCN contains some questionable warming signals at some stations, despite the many attempts to quantitatively control for these contaminants.

1. Introduction

[2] The United States Historical Climatology Network (USHCN) dataset has emerged as one of the most widely used and highly respected databases available for regional-scale analyses. There are multiple versions of the USHCN available depending on adjustments made for station moves, instrument changes, urbanization, and/or time of observation biases. These adjustments can produce highly statistically significant changes to the underlying trends at many of the USHCN stations [Hansen et al., 2001; Balling and Idso, 2002], and overall, the adjustments have created additional warming in the time series. Obviously, given the nature of the greenhouse debate, these adjustments are a matter on considerable debate in the climate change community [e.g., Balling and Idso, 2002; Vose et al., 2003].

[3] In this investigation, we use spatial entropy to estimate disorder in the pattern of temperature change values across the 1, 221 stations in the USHCN, and we examine the relationship between station entropy and the magnitude of the temperature change at that station. If no biases exist in the record, there should be no significant relationship between spatial entropy and the temperature trends. However, if a positive relationship exists, implying that stations most unlike their neighbors tend to warm faster than their neighbors, one could conclude that the network still contains unproven warming signals possibly related to lingering urbanization effects.

2. United States Temperature Dataset

[4] We used the United States Historical Climatology Network [Karl et al., 1990] annual time series from 1,221 largely rural and small-town stations across the conterminous United States for the period 1951–2000. The raw temperature records in this dataset had been adjusted for time of observation biasing [Karl et al., 1986], changes from mercurial to electronic sensing equipment [Quayle et al., 1991], instrument adjustments [Karl and Williams, 1987], an interpolation scheme for estimating missing data from nearby highly correlated station records, and a regression-based adjustment to account for urbanization near the station [Karl et al., 1988]. We found that only 671 of the 61,050 annual values (50 years for 1,221 stations) were missing in the dataset. A nearest neighbor analysis revealed that the distribution of the stations was random to somewhat uniform and significantly different from clustered.

3. Analyses and Results

[5] We used simple linear regression analysis to determine the change in temperature for each station over the 1951–2000 study period. The mean linear change in temperature for the 1,221 stations over the 50-year period was +0.26°C with a range from −1.34°C at Oberlin, Ohio to +1.40°C at Healdsburg, California; we did not interpolate the trend values to a grid. A Voronoi map [Voronoi, 1908] of the temperature change values (Figure 1) shows considerable spatial variability in the array with warming being most pronounced in the western United States and the least warming (or even cooling) in the southern Great Plains. The Voronoi map begin with the construction of polygons formed around each station with the criterion that every location in the polygon is closer to the station in that polygon than any station outside the polygon. There is no smoothing in the construction of Figure 1.

Figure 1.

Linear change in temperature (°C) over the 1951–2000 time period (the dots inside each polygon represent the location of the station).

[6] Our main interest in this study was to evaluate the relationship between spatial entropy and the temperature change values. The spatial entropy [Shannon, 1948] is a measure of disorder or dissimilarity in the pattern and is calculated as - Σ(pi log2pi) where pi is proportion of polygons (polygon of interest and four surrounding polygons selected with the criterion that their stations are closest to the station in the polygon of interest) that are assigned to each class based on five classes for all data using a natural grouping of temperature change values. Entropy for each station ranges from 0.0 where all five polygons are in the same class to 2.32 when all five classes are represented in the five polygons. With five classes and four surrounding polygons, there are only seven possible spatial entropy values including 0.00, 0.71, 0.97, 1.37, 1.52. 1.92, and 2.32. As seen in Figure 2, the entropy values show much more spatial variability than the temperature change values and they tend to be higher in the West than in the East.

Figure 2.

Spatial entropy associated with temperature change values over the 1951–2000 time period.

[7] The issue at hand is whether or not the change in temperature values are related to the levels of spatial entropy. As seen in Figure 3, there is an increase in temperature change with an increase in entropy class. Furthermore, a simple regression analysis showed a significant (ρ = 0.00) relationship between the variables with a 0.06°C increase in temperature change for every one unit of increase in spatial entropy. Stepwise multiple regression analyses were conducted with latitude, latitude squared, longitude, longitude squared, and elevation as other potential independent variables in explaining spatial variance in the temperature change values. Even with longitude squared and latitude squared in the multiple regression equation, thereby controlling for some underlying spatial variance in the data, the 0.06°C increase in temperature change for every one unit of increase in spatial entropy remained highly significant (ρ = 0.00). Although statistically significant, the 0.06°C value is still relatively small given the mean warming of 0.26°C observed across the network over the 50-year time period.

Figure 3.

Bar chart of temperature change by spatial entropy levels; the numbers above each bar represent the number of stations with that level of entropy. Standard errors for these mean values tend to be small and near 0.02°C.

4. Conclusion

[8] Our results show that within the conterminous United States, stations with temperature changes most unlike their four neighbors tend to have significantly higher temperature changes than their neighbors. While the developers of the United States Historical Climatology Network (USHCN) have made substantial efforts to eliminate effects of time of observation biases, changes in measuring equipment, station relocations, and urbanization, our results suggest that the adjusted records continue to contain any number of contaminants that increase the temperature trend (warm) at some stations. As seen here and elsewhere [e.g., Easterling et al., 1996], the effect is relatively small in computing trends on the regional scale.