Temperature variability and trends have been extensively investigated. Results from the huge body of studies indicate that significant warming took place over the last century (e.g. Jones et al., 1986; Vinnikov et al., 1990; Crowley and Lowery, 2000; IPCC, 2001, 2007; Mann and Jones, 2003; Soon et al., 2004; Moberg et al., 2005). Furthermore, climate model experiments and multiple observational datasets suggest that the warming observed in the ocean, at the surface and in the troposphere is consistent with anthropogenic greenhouse forcing of the climate system (Mears and Wentz, 2005; Barnett et al., 2005a, 2005b; Santer et al., 2005; Sherwood et al., 2005; IPCC, 2007; Santer et al., 2008).
Recent study also shows that atmospheric moisture content has increased in the past decades (Wentz and Schabel, 2000; Held and Soden, 2006; Santer et al., 2007; Wentz et al., 2007). Although positive trends in moisture content are consistent with positive trends in temperature, relatively few studies have focused on a simultaneous analysis that integrates temperature and moisture. Steadman (1979, 1984) derived a scale of apparent temperature, which expresses the combined effects of air temperature, vapour pressure, wind and solar radiation. Using observed temperature and humidity datasets over the 1961–1995 period, Gaffen and Ross (1999) found upward trends in apparent temperature over the United States. More recent studies focus on moist enthalpy (or, alternatively, equivalent temperature), which combines both air temperature and humidity in a single variable, to assess surface heating trends. Results from such studies suggest that the utilisation of temperature as a monitor of climate change may not provide a complete evaluation of the heat storage changes to the earth system (Pielke, 2003), and that temperature, by itself, is an incomplete characterisation of surface air heat content (Pielke et al., 2004; Davey et al., 2006).
At a global scale, Ribera et al. (2004) used the NCEP/NCAR re-analysis temperature to study the relationships between equivalent temperature and modes of climate variability. The expression for moist enthalpy (Pielke et al., 2004) is
where Cp is the specific heat of air at constant pressure, T is the air temperature, Lv is the latent heat of vapourisation and q is the specific humidity. Following the Priestley–Taylor method, Lv (J/kg) is estimated with the temperature function:
Such an estimate allows accounting for the variation of Lv with temperature, instead of assigning its approximate value at 30 °C that has been used in previous studies. H is in units of Joule and must be scaled into degree units in order to obtain equivalent temperature for easy comparison to air temperature
where Lv is in units of Joules per kilogram and Cp is in units of Joules per kilogram per degree K. As q is dimensionless (i.e. kg per kg), the ratio has units of degree K.
The motivation for the current study is to explore atmospheric heating as reflected in changes in both temperature and moisture. We focus on heating trends over the United States by comparing air temperature (T) and equivalent temperature (TE) for different time scales, at near-surface (2 m) and standard pressure levels (up to 200 mb). In addition, because land use/cover change can affect the heat and moisture budgets at the surface (e.g. changes in transpiration from vegetation and evaporation from the surface hydrology), we relate both T and TE to the normalised difference vegetation index (NDVI) and land use/cover to analyse their relationship with vegetation characteristics.
We describe the data and methods used in this study in Section 2. The results are presented in Section 3, followed by concluding remarks in Section 4.
2. Data and methods
Monthly T and specific humidity (q) at 2 m, 850 mb, 700 mb, 500 mb, 300 mb and 200 mb for the 1979–2005 period were obtained from the National Centers for Environmental Prediction (NCEP) North American Regional Reanalysis (NARR). NARR has been developed as a major improvement in both resolution (32 km, 3 h) and accuracy relative to the global NCEP/NCAR re-analysis (Mesinger et al., 2006).
After computing TE from T and q values using the method described in the previous section, we extracted monthly and seasonal subsets of the variables and derived their seasonal and monthly climatologies. Various calculations were performed on the gridded data, including: (1) mean absolute difference between T and TE, differences between each of the variables at different levels (with significance assessed using the t-test); (2) the contribution of temperature and moisture to the magnitude of TE (e.g. moisture contribution was computed as (Lvq/H)× 100); (3) gridpoint correlations; (4) trend analysis and (5) additive decomposition of time series (Cleveland et al., 1990; Makridakis et al., 1998). The last consists of decomposing the time series into three components (trend + seasonality + random) and isolating the true trend signal.
Two types of trend calculations were made for both temperature and equivalent temperature: (1) simple linear trend estimates (linear least square regression) and corresponding p-values (at 0.05 and 0.01 significance levels) displayed in spatial distribution maps and (2) time series of linear trends using 10-year running windows, i.e. linear trends are computed for the first 10 years, and the window moves to the next 10 years at a monthly time step. As a result of this procedure which highlights long-term patterns, the trends time series were presented for the period December 1983 to January 1998. Trend calculations were performed on anomalies obtained from cosine-weighted spatially averaged time series.
The NDVI dataset from the Joint Institute for the Study of the Atmosphere and Ocean (JISAO, http://jisao.washington.edu/data_sets) was used to quantify the relationships between NDVI, T and TE. NDVI is commonly used to investigate the effects of vegetation greenness and biomass density on near-surface energy partitioning and temperature (Sellers, 1985). It is derived from the radiance values of the visible (VIS) and near-infrared (NIR) channels: NDVI = (NIR − VIS)/(NIR + VIS). Because of a number of limitations, NDVI, like other spectral vegetation indices, is not a perfect measure of vegetation biomass and greenness. However, it has the ability to distinguish vegetated areas from other land cover types and to survey vegetation dynamics. Analyses included: (1) correlation of the time series at a seasonal timescale using the Pearson product-moment method (Rodgers and Nicewander, 1988; Stigler, 1989); (2) gridpoint correlation of monthly T and TE with NDVI and subsequent comparison of the spatial patterns; (3) assignment of gridpoint correlation values to each vegetation type using Geographic Information Systems (GIS) overlay techniques and summary statistics of the resulting correlation coefficients for each set and (4) for each gridpoint, calculation of the mean difference between T and TE; summary statistics of the resulting difference values are computed for each land cover type.
For the gridpoint correlation, T and TE were regridded to the coarser NDVI 1° increment. The monthly NDVI dataset spans the period July 1981 to September 2001 and as a result, T and TE subsets were accordingly created. Over this study period, the monthly values of each T and TE gridpoint have been correlated to the corresponding monthly values of NDVI to generate spatial patterns of correlation.
Two land cover datasets were used to relate both T and TE to vegetation characteristics: (1) the classification derived from AVHRR (Hansen et al., 2000) and (2) the National Land Cover Database (NLCD) 1992–2001 Retrofit Land Cover Change (Homer et al., 2007). The AVHRR classification is a 1 km grid spacing data that originates from the Global Land Cover Facility (University of Maryland). It consists of 14 land cover types for North America (12 represented over the Continental United States, including the 9 vegetation classes used in this study); the dataset includes red, infrared and thermal bands in addition to the NDVI and has a length of record of 14 years (1981–1994), providing the ability to test the stability of classification algorithms (Hansen et al., 2000). The NLCD dataset (30-m increment) consists of unchanged pixels between the two dates and changed pixels that are labelled with a ‘from-to’ land cover change value. In this study, only unchanged land cover types (9 classes out of 87) are considered, the remainder (78 change classes) being addressed in a subsequent study.
The GIS software ArcGIS (http://www.esri.com) was used to interpolate gridded surfaces of T and TE values, and their correlation with NDVI. The data were linked to the land cover information using the Zonal Statistics method, which generates summary statistics of gridded surfaces values for each land cover type.
The monthly climatology of T, TE and q at the 2-m level (1979–2005) is shown in Figure 1. T and TE exhibit identical temporal patterns, but TE values are larger. During the winter and early spring months with low humidity, differences between the two variables are small. As humidity increases from late spring to early fall, differences become much larger, especially during summer months (up to 22.74 °C in July).
Overall, most of the magnitude of TE is expressed by T, with q contributing a small proportion (Figure 2). The maximum contribution of moisture occurs during the summer months (11.01% in July). This distribution is consistent with the patterns shown in Figure 1.
Spatial patterns of the mean differences between T and TE at various levels are displayed in Figure 3. At 2 m (and to a lesser extent at 850 mb), there is a sharp contrast between the eastern and western United States. Differences are larger in the Midwest and along the coastal Carolinas (up to 8 °C) and decrease westward (below 2 °C over the mountainous regions). These patterns are consistent with the temperature and moisture distribution: on average, q values are much larger in the eastern part of the country (Figure 4) and contribute to larger values of TE. In contrast, both T and q are low over most of the Rockies and as a result, there are small differences between T and TE. As shown in Figure 3, differences between T and TE decrease with altitude (average difference of 4.91 °C at 2 m, 3.67 °C at 850 mb) and become small at 500 and 200 mb (0.63 and 0.02 °C, respectively, not shown). This trend appears clearly in Figure 5, which shows the interannual variations of T, TE and q. The time series depict a contrast between near-surface (2 m) and upper air T and TE: the near-surface differences are statistically significant at 5% significance level, in contrast with the 200 mb level (not shown) which shows minor differences between T and TE. The varying amount of q as a function of altitude is a key factor of the surface/upper-level contrast between T and TE because nearly half the total water vapour in the air is found within the lowest 1.5 km layer (Ross et al., 2002; Seidel, 2002).
T and TE exhibit an increasing (decreasing) trend at 2 m (200 mb) and are both positively correlated with q: at the 2-m level, there is a stronger (weaker) relationship between TE (T) and q with a correlation coefficient at 0.80 (0.51). At 200 mb, the coefficient is 0.75 for both Tversusq and TEversusq.
Decadal anomaly trends at different levels (Figure 6) indicate a statistically significant warming of both T and TE, with values generally decreasing from near-surface (T, 0.31 °C/decade; TE, 0.52 °C/decade) to 300 mb (T, 0.15 °C/decade; TE, 0.16 °C/decade). At 200 mb, there is a decreasing trend for both variables (−0.23 °C/decade for both T and TE). This gradual decrease upward is disrupted at the 700 mb level, which records larger increase than the level below (850 mb) for both T and TE. The reason for this pattern is not clear. As depicted in Figure 6, trend differences between T and TE are larger at 2 m (0.21 °C/decade) and decrease upward. At 200 mb, there is very little trend difference (0.003 °C/decade). In summary, there is an increasing trend for both T and TE up to 300 mb, with the largest increases observed near the surface. Above the 300-mb level, there is a decreasing trend for both variables.
The near-surface long-term trends (Figure 7(a)) show that T and TE are closely related, with the exception of a period of abrupt decreasing trend in the early 1990s. During this period, T trends are much cooler than TE trends. Temperature records worldwide experienced a decrease following the eruption of Mount Pinatubo on June 1991 (Parker et al., 1996). However, at the same time, there is a substantial increase of q trends that helps to maintain TE trends at a much higher level than T trends [a positive trend in water vapour has been observed over the global oceans as well (Santer et al., 2007)]. As a result, this period records the largest differences between the two variables (up to 0.67 °C/decade in the early 1990s). Overall, TE shows more increase than T (a 0.9 °C/decade difference) over the study period. The long-term trends at 500 mb (Figure 7(b)) show the same patterns as the 2-m trends, although with less decrease. The 500 mb analysis confirms that the magnitude of the q trend contributes to the magnitude of differences between T and TE trends: largest increases in q trends (e.g. early 1990s) correspond to the largest differences between TE and T.
The 2-m seasonal anomaly trends (Table I) show that most of the increase for both T and TE has occurred during winter (0.71 °C/decade and 0.98 °C/decade, respectively), whereas the trends reach their lowest values in summer (0.03 and 0.24 °C/decade, respectively). Seasonal anomaly trends of q (not shown) follow the same temporal patterns: the increasing trend in q from spring to summer (0.0011 kg/kg/decade to 0.014 kg/kg/decade) compensates the summer decreasing T trend and helps maintain a larger TE trend.
Table I. Seasonal anomaly trends for temperature and (equivalent temperature)
Units are in °C/10 years. Trend values in bold are significant at the 5% level.
− 0.24 (−0.24)
− 0.18 (−0.18)
− 0.05 (−0.06)
From the 2-m level to 700 mb, the largest increases in both T and TE occur during winter. Above 700 mb, most of the increase takes place in fall. At 200 mb, the strongest decrease takes place in winter (in contrast with the 2-m level) and there is no substantial difference between T and TE trends for all seasons. This similarity between T and TE at 300–200 mb is a consistent pattern.
Figure 8 shows the 2-m level geographical distribution of decadal T and TE anomaly trends over the United States. Although the spatial patterns of T and TE trends agree in that they both show areas of statistically significant increase over the eastern United States (around the Great Lakes and upper Midwest) and areas of decrease over the Rockies, TE trends are much larger in magnitude (0.45 °C/decade in average) and affect larger areas (e.g. over 1.2 °C/decade in southern Texas). The trends are significant at the 5% significance level over most of the eastern (both T and TE) and southern United States (T only), and along the western coast (both T and TE). Such distribution patterns suggest that there is a close relationship between TE and q: areas where q trends increase significantly (not shown) tend to correspond to areas where TE trends are large (e.g. southern Texas and eastern coast). But T also is a key-driver of TE as shown by the similar distribution patterns of both variables over the Midwest. At 200 mb (Figure 8(b)), the spatial patterns and magnitude of both T and TE are almost identical (about 0.23 °C/decade in average). There is a generalised decrease for both variables, mainly over the central and northwestern United States. The trends are significant at the 5% level over the whole the United States, with the exception of spots over the northeast and southwest.
3.3. T and TE in relation to vegetation properties
To investigate T and TE with respect to vegetation properties at the 2-m level, we examine their time series correlation with NDVI and associate the resulting coefficients with vegetation types.
The land surface has been—and is still—experiencing various changes that alter its climate, both through surface reflectivity (albedo) and through the surface hydrologic cycle (Pielke et al., 2002). Changes in surface moisture and energy fluxes trigger local and regional climate responses which can be of a similar magnitude to that projected for future greenhouse gas concentrations (Feddema et al., 2005; Diffenbaugh 2005a, 2005b). For instance, vegetation affects the surface energy budget through transpiration (e.g. release of latent heat). Numerical studies have shown that using scenarios with different vegetation covers leads to significant climatic changes (e.g. Bonan, 1997; Bounoua et al., 2000). The relationships between NDVI and climate factors have been investigated in numerous studies (e.g. Townshend and Justice, 1986; Wang et al., 2003; Sarkar and Kafatos, 2004; Carlson, 2008; Niyogi et al., 2010).
The correlation of T and TE with NDVI at a seasonal time scale (Figure 9) reveals that the highest correlations (r > 0.72) occur in winter with almost no differences between T and TE. NDVI is less correlated with T and TE during the spring season but the values remain relatively close (0.49 and 0.55, respectively). The lowest correlations with NDVI but largest differences between T and TE are observed during the growing season: while T is negatively correlated with NDVI (−0.31), TE exhibits a positive relationship (0.49). The differences are statistically significant at the 5% level. It is likely that increased biomass and vegetation transpiration play a role in these differences. The negative correlation between T and NDVI is consistent with findings that point to a cooling of T in the northern latitudes during the growing season, because of the seasonal increase in biomass and greenness and a reduced Bowen ratio (Bounoua et al., 2000).
Distribution patterns of gridpoint correlation coefficients between NDVI and the two variables (T and TE; Figure 10) show a zonal contrast between relatively larger positive values over the northern United States (for both T and TE) and a swath of negative correlation coefficients along the Mexican border and southern California (T only). Correlation coefficients averaged over the United States show that TE is better correlated to NDVI than T (0.43 and 0.25, respectively).
The correlation between NDVI and T or TE varies with vegetation type. It is worth acknowledging that our analysis summarises correlation coefficients for land cover types that extend over broad geographic areas, and the large-scale climate may vary within each or some of them. Therefore, averaging over land cover types may partly occult finer scale climatic variations.
Figure 11 shows correlation coefficients for NDVI versusT and NDVI versusTE averaged as a function of vegetation types derived from AVHRR land cover classification. NDVI and TE are more correlated over deciduous broadleaf forests, croplands and grasslands (0.56, 0.52 and 0.49 respectively). This stronger TE–NDVI relationship may be in part explained by increased vegetation greenness (especially during the growing season) which, of course, is associated with larger transpiration. This relationship is consistent with the summer patterns displayed in Figure 9. While most of near-surface moisture over agricultural land is because of transpiration and/or the physical evaporation from irrigated areas, deciduous broadleaf forests are characterised by a high evaporative fraction because of a relatively high leaf area index (Baldocchi, 2005; Bonan, 2008). The largest correlations between NDVI and T are found in evergreen needleleaf forests, mixed forests and woodlands (0.46, 0.39 and 0.33, respectively). Over drier areas (e.g. shrublands), NDVI is weakly correlated with both T and TE. The differences between T and TE are statistically significant (5% significance level) over croplands, deciduous broadleaf forests and grasslands. Moreover, over these vegetation types with relatively high transpiration rates, NDVI versusTE exhibits smaller standard deviations (e.g. 0.15 and 0.19 over croplands and deciduous broadleaf forests) than NDVI versusT (0.32 and 0.25, respectively), indicating that the correlation coefficients for TE did not vary much and remained relatively high. Apart from one notable exception for which NDVI versusT displays a smaller value (evergreen needleleaf forest), the larger standard deviations for NDVI versusT suggest that the relationships between NDVI and T are less pronounced than the ones with TE.
The mean differences between TE and T as a function of land cover types that did not change between 1992 and 2001 (Figure 12) show a contrast between moist and drier areas. The largest differences are found in croplands (6.9 °C), wetlands (6.7 °C), forests (6.5 °C), urban areas (6.05 °C) and open water (6 °C). Barren areas and grasslands/shrublands exhibit the lowest differences (2.7 °C and 4.5 °C respectively). The most statistically reliable differences (with the smallest confidence intervals at the 5% significance level) are found in larger samples: grasslands/shrublands (36% of land cover areas that did not change), forests (26%) and croplands (24%). These results suggest that various land cover types influence moisture availability in the lower atmosphere and that TE is larger in areas with higher physical evaporation and transpiration rates. Betts et al. (1996) and Holt et al. (2006) demonstrated that local-scale moisture fluxes into the atmosphere can significantly impact the atmospheric thermodynamic structure, modify boundary layer settings and contribute to heavy rainfall, and that short- and medium-range forecasts produce much better predictions when such factors are included in land surface parameterisation.
The TE is strongly driven by T, which accounts for about 90% of its magnitude. This can be seen in various time-series in which both T and TE exhibit similar fluctuation patterns. However, despite its small contribution to the magnitude of TE, the moisture component induces larger trends of TE relative to T. The differences between the two variables can be explained by the fact that the moisture component of TE is strongly influenced by atmospheric near-surface moisture (e.g. from vegetation transpiration and soil moisture evaporation). Indeed, our analysis has shown that at the 2-m level, there is a stronger relationship between TE and q (r = 0.8) than T and q (r = 0.51), but this large difference decreases upward and disappears at 300–200 mb. In contrast to pronounced temporal and spatial differences at the near-surface levels, this similarity between T and TE at 300–200 mb is a consistent pattern: (1) the differences between the two variables averaged over the study period are large at the 2-m level but very small at 200 mb; (2) T and TE time series present statistically significant differences at the 2-m level but minor differences at 200 mb; (3) the decadal anomaly trend differences are large at the 2-m level (up to 0.21 °C/decade) but very small at 200 mb (−0.003 °C/decade).
Our results suggest that land cover types influence both moisture availability and temperature in the lower atmosphere, and that TE is larger in areas with higher evaporation and transpiration rates. During summer, TE exhibits positive (though relatively moderate) correlation with NDVI, while T–NDVI correlation remains negative. This relationship suggests that TE is more correlated to biomass increase, vegetation transpiration and other surface moisture characteristics. Moreover, correlation coefficients averaged over the United States depict a stronger relationship between TE and NDVI, especially over vegetation types that are characterised by a high transpiration rate (e.g. deciduous broadleaf forests and croplands). Using TE to assess tropospheric heating trends is not only an efficient way to investigate the vertical structure of the combined effects of temperature and moisture, but it may also help obtain an improved estimate of the impacts of surface properties on heating trends.
Although the calculation of TE has been performed by combining sensible (CpT) heat and moisture (Lvq), the emphasis in terms of moisture has been put on q only. For a better diagnosis of TE, subsequent studies should additionally focus on: (1) the surface energy budget, as soil moisture and other flux measurements combined with q can help to better explain the magnitude and variability of TE at 2 m; (2) the effects of atmospheric circulation on the variability of q and resulting TE and (3) fingerprint studies that aim to determine the contribution of anthropogenic influences on TE magnitude and variability (e.g. Santer et al., 2007).
We thank Alan K. Betts for providing supporting documents. We would also like to thank Dallas Staley for her outstanding contribution in editing and finalising the paper, and Dr Kapo Coulibali for providing R scripts. The study benefited from the DOE ARM Program (08ER64674; Dr Rick Petty and Dr Kiran Alapaty), and in parts from NASA Terrestrial Hydrology Program (Dr Jared Entin), and NSF CAREER-0847472 (Liming Zhou and Jay Fein). R. A. Pielke Sr. received support to complete this study from the University of Colorado at Boulder (CIRES/ATOC).