The characteristics of summertime heat waves in North America are examined using reanalysis data and simulations by two general circulation models with horizontal resolution of 50 and 200 km. Several “key regions” with spatially coherent and high amplitude fluctuations in daily surface air temperature are identified. The typical synoptic features accompanying warm episodes in these regions are described. The averaged intensity, duration, and frequency of occurrence of the heat waves in various key regions, as simulated in the two models for twentieth-century climate, are in general agreement with the results based on reanalysis data.
The impact of climate change on the heat wave characteristics in various key regions is assessed by contrasting model runs based on a scenario for the twenty-first century with those for the twentieth century. Both models indicate considerable increases in the duration and frequency of heat wave episodes, and in number of heat wave days per year, during the twenty-first century. The duration and frequency statistics of the heat waves in the mid-twenty-first century, as generated by the model with 50-km resolution, can be reproduced by adding the projected warming trend to the daily temperature data for the late twentieth century, and then recomputing these statistics. The detailed evolution of the averaged intensity, duration, and frequency of the heat waves through individual decades of the twentieth and twenty-first centuries, as simulated and projected by the model with 200-km resolution, indicates that the upward trend in these heat wave measures should become apparent in the early decades of the twenty-first century.
Summertime episodes with extremely high surface air temperatures and lasting for several days or longer are often referred to as “heat waves.” They are associated with distinctive signatures in the ambient atmospheric circulation and precipitation patterns and are of strong interest to weather forecasters and research meteorologists. Projected increases in the occurrence of extreme heat wave episodes incur huge socioeconomic costs (IPCC 2012). It is estimated that an average of 1000 deaths per year can be attributed to heat waves occurring in the United States (Changnon et al. 1996). The heat wave events in the 1980–2003 era are known to have inflicted agricultural and industrial damages ranging from billions to tens of billions of U.S. dollars per episode (Kunkel et al. 1999b; Ross and Lott 2003). The physical processes contributing to the initiation and maintenance of the heat waves in different geographical locations, as well as the variations in the severity, longevity, and frequency of these extreme events in the twentieth and twenty-first centuries, are therefore research topics of strong societal relevance.
Heat waves are observed in many parts of the world. In the present study, we shall focus on the characteristics of this phenomenon over the North American continent. Within this chosen domain, the region that has received the most attention is the Great Plains of the United States. The essential meteorological features accompanying the prominent heat waves occurring in this general area in the summers of 1952, 1980, 1995, and 1999 are documented by Klein (1952), Namias (1982), Kunkel et al. (1996), and Palecki et al. (2001), respectively. The typical patterns of the sea level pressure, 500-mb height, and lower-tropospheric thickness fields associated with heat wave activity over the same region throughout the 1946–76 period are also analyzed by Chang and Wallace (1987). In addition to the Great Plains region, heat waves also affect other sectors of North America. The factors contributing to the hot and dry episode in the summer of 1998 over Oklahoma and Texas are examined by Hong and Kalnay (2002) using modeling tools. Prolonged periods of warm temperature anomalies are noted in the south-central states centered in Arkansas (Choi and Meentemeyer 2002). The severe 2006 heat wave over California and Nevada is studied by Gershunov et al. (2009).
Some efforts are devoted to the detection of secular trends in the characteristics of the U.S. heat waves based on historical weather records. The review articles by Kunkel et al. (1999a) and Easterling et al. (2000a,b) report that the temperature variability over the United States in the twentieth century is dominated by the large warm and dry anomalies in the 1930s and 1950s, to the extent that the heat wave occurrences do not exhibit any noticeable trend in the 1931–97 period, despite the overall warming over the western, midwestern, and northeastern parts of the country in that era (e.g., see Karl et al. 1996). However, analysis of station data for the more recent 1949–95 period by Gaffen and Ross (1998) indicates significant positive trends in the frequency of heat waves over most parts of the United States, especially in the eastern and western states. This finding is corroborated by the study of DeGaetano and Allen (2002), who show increasing occurrences of extreme temperature exceedances across the United States during the 1960–96 era, with the largest trends being observed at urban locations.
The characteristics of extreme high temperature events are also studied by subjecting general circulation models (GCMs) to present-day climatic conditions (e.g., Hunt 2007) and by comparing such control integrations to those conducted under various projected climate scenarios in the future. The assessment of these results by Easterling et al. (2000b) indicates that a number of models project more occurrences of heat waves toward the end of the twenty-first century. The model experiments examined by Meehl and Tebaldi (2004) illustrate that heat waves in the Chicago area will be more intense, more frequent, and longer lasting in the warmer climates during the latter half of the twenty-first century. Diffenbaugh et al. (2005) analyze the output from a regional climate model of the North American region with 25-km resolution, and similarly note strong positive trends in the projected frequency and duration of extreme warm events toward the twenty-first century.
The aforecited observational and modeling studies indicate that the synoptic environment of the heat waves in North America as well as their historical and future trends exhibit a strong geographical dependence. In the present study, we shall make joint use of GCM outputs and reanalysis datasets to perform a comprehensive survey of the representative ambient flow patterns associated with the heat wave episodes in different regions over North America. To delineate the regional details of heat wave characteristics, we shall devote our primary attention to the results from a high-resolution (~50-km) GCM developed at the Geophysical Fluid Dynamics Laboratory (GFDL). We shall augment the findings based on this model by presenting some corresponding results from another GFDL GCM with a lower resolution (~200 km).
After a description of the model tools and reanalysis datasets in section 2, the findings of this study are presented in the succeeding sections as follows. The regions of enhanced surface temperature variability over North America in the model and observed atmospheres are documented in section 3. The relationships between the heat waves occurring in these selected regions and the corresponding changes in the ambient circulation and precipitation fields are examined in section 4. The projected secular changes in behavior of the heat waves in different regions (including intensity, duration, frequency of occurrence, and probability distribution function) from twentieth- to twenty-first-century climate settings are explored in section 5. The spatial patterns of these trends in various heat wave characteristics are described in further detail in section 6. Some conclusions and discussions of the principal results are offered in section 7.
2. Model and reanalysis datasets
Outputs from the following two GFDL models are analyzed in this study
A global coupled GCM [the Geophysical Fluid Dynamics Laboratory Climate Model version 2.1 (CM2.1); see Delworth et al. (2006) for more details] consisting of a 24-layer atmospheric model (AM2) with finite-volume dynamical core and a latitude–longitude resolution of 2° × 2.5° (see GFDL Global Atmospheric Model Development Team 2004); a 50-layer modular oceanic model (MOM4) with a 1° × 1° resolution in the extratropics and the meridional resolution increasing to 1/3° at the equator (Griffies et al. 2003); and a land model (LM2.1) designed by Milly and Shmakin (2002). Two experimental suites are performed with CM2.1. The first set is an ensemble of 100-yr runs for the climate of the twentieth century (CM2.1-C20C experiment, or C20C in short) with prescription of the observed temporal evolution of radiative forcings due to different atmospheric constituents and solar variations. Data for a three-member (five-member) ensemble are available for the 1901–60 (1961–2000) period. The second set is analogous to the C20C experiment, except that it is conducted for the twenty-first century, with radiative forcings of various trace constituents being derived from the A1B emission scenario (Nakićenović et al. 2000). Three such integrations are made for the 2001–2100 period and will hereafter be referred as the CM2.1-C21C, or C21C, runs.
A high-resolution global atmospheric GCM using a finite-volume dynamical core with a cubed-sphere grid topology (Putman and Lin 2007). Each face of the cube contains 180 × 180 grid points with grid spacing ranging from 43.5 to 61.6 km. We shall henceforth refer to this model as the C180 version. Vertical variations are represented in 32 model layers. The model retains many of the physical parameterization schemes in the AM2 version described by the GFDL Global Atmospheric Model Development Team (2004), except that the convective scheme is replaced by the treatment of Bretherton et al. (2004) for shallow convection and that a new cloud fraction diagnostic scheme assuming a subgrid-scale distribution of total water is used. This atmospheric model is coupled to a new land model (LM3), described in Donner et al. (2011, see their appendix A). More details of the numerics and physics packages incorporated in the C180 model are provided by Zhao et al. (2009). Two integrations are conducted using this model. The first experiment is a 30-yr historical run (C180-H2, or H2 in short) subjected to monthly varying sea surface temperature and sea ice boundary conditions and radiative forcings associated with various trace atmospheric constituents, as observed during the 1971–2000 period. The SST and sea ice values in this epoch are obtained from the second Hadley Centre SST dataset (HADISST2; see Rayner et al. 2006). The radiative forcings are identical to those used in the CM2.1-C20C experiment. The second integration with the C180 model is a 30-yr scenario run (C180-S2, or S2) based on SST and radiative forcings projected for the 2041–70 period. The SST conditions for this experiment are obtained by the following procedure: the SST change from 1971–2000 to 2041–70 is estimated by taking the difference between the 30-yr mean SST climatologies for these two periods, as generated in the CM2.1-C20C and CM2.1-C21C experiments, respectively. This difference is then added to the HadISST2 observations for individual years in the 1971–2000 period. The linear trend of the HadISST2 dataset within the 1971–2000 period is also replaced by the projected trend of the C21C experiment within the 2041–70 period. The prescribed SST forcing for the S2 experiment hence incorporates the constant shift in the SST climatology from the late twentieth century to the middle twenty-first century and the SST trend within the 2041–70 period (with both adjustments being projected by the CM2.1 model), while retaining the interannual SST variability as given by the HadISST2 dataset for the late twentieth century. The radiative forcings for the C180-S2 experiment are identical to those used in the CM2.1-C21C experiment (i.e., A1B scenario) for the 2041–70 period.
Some of the model results are compared with products generated by the North American Regional Reanalysis (NARR) project, as described by Mesinger et al. (2006). Archives of this dataset for the 1980–2003 period are analyzed in the present study. The horizontal resolution (32 km) of this dataset is comparable with that of the C180 model. The evidence presented in Mesinger et al. indicates that the precipitation field in the NARR dataset is in good agreement with observations. These authors also show that the fit between the observed near-surface temperature and wind fields and the NARR data is generally better than the corresponding fit with global reanalysis products with coarser spatial resolution.
3. Identification of regions with prominent and coherent variations in surface air temperature
Since most of the heat wave characteristics examined in this study are defined on the basis of the daily maximum surface air temperature, Tmax, we first evaluate the capability of the model atmosphere in reproducing the seasonal climatology of this field. The patterns of Tmax, as averaged over all days within the June–August (JJA) season in the C180-H2 experiment and the NARR dataset, are presented in Figs. 1a and 1b. The difference between these two patterns is shown in Fig. 1c. The deviation between model and reanalysis is less than 2°C in most parts of the contiguous United States. The model exhibits a warm bias over the Mississippi basin and a cold bias along the east coast and some parts of western North America. Climatological maps of observed SST conditions as applied in the H2 experiment are compared with the SST values being assimilated in the compilation of the NARR archives. These charts (not shown) indicate that the discrepancies in Tmax seen in Fig. 1c off the coasts of California and northeastern United States may be attributable to the slight differences in the SST forcing used to generate the H2 and NARR datasets.
In this investigation, we shall devote our attention to heat wave episodes occurring in those regions in North America where the daily fluctuations in Tmax are spatially coherent and account for a substantial fraction of the domain-integrated temporal variance. An objective tool that is well suited for identifying these regions is the rotated empirical orthogonal function (REOF) analysis (e.g., see Horel 1981). This technique is applied separately to the daily Tmax data in the JJA season for the NARR dataset, the output from the 30-yr C180-H2 and C180-S2 experiments, the 1971–2000 segment of the five-member CM2.1-C20C suite, as well as the 2041–70 segment of the three-member CM2.1-C21C suite (see section 2 for details). The domain for this REOF analysis is 25°–50°N, 125°–70°W for all datasets. The analysis is performed based on a covariance matrix computed using unnormalized and area-weighted Tmax data at all available grid points within this domain. The climatological seasonal cycle is removed from the daily data for individual years.
The eight leading rotated eigenvectors, as computed based on output from the C180-H2 experiment, are presented in the left column of Fig. 2. These charts show the spatial distributions of the regression coefficients of daily Tmax versus the standardized daily time series of the temporal coefficients of individual REOF modes. The values plotted in these patterns indicate the typical amplitude of Tmax variations associated with one standard deviation of the fluctuations of the respective REOF mode. The regression maps are arranged in descending order of the fraction of domain-integrated variance explained by the individual modes.
The corresponding eigenvector patterns, as obtained on the basis of Tmax data from the 1971–2000 segment of the CM2.1-C20C experiment and the NARR archives, are displayed in the middle and right columns of Fig. 2. To facilitate comparison of the results from different datasets, NARR and C20C patterns with spatial characteristics that are similar to a given H2 pattern are shown on the same row as that H2 pattern. This arrangement entails some slight changes in the order of the NARR and C20C patterns within their respective columns. A common characteristic of all the panels in Fig. 2 is that each REOF pattern is dominated by a single extremum. Comparison of the three panels along a given row in this figure reveals that the observed geographical location and spatial scale of the extremum for the respective mode, as inferred from the NARR pattern, are well captured by the H2 and C20C experiments.
The REOF patterns in Fig. 2 offer an objective and comprehensive compilation of various regions in North America with local Tmax fluctuations contributing strongly to the domainwide variability. We shall henceforth refer to such active zones as “key regions.” The boundaries of these key regions are determined by considering those grid points with regression coefficients exceeding a certain threshold (see black contours in Fig. 2). Different thresholds are used for various key regions and datasets, so as to allow for decreasing Tmax amplitudes in higher-order REOF modes and for discrepancies in Tmax amplitudes among the three datasets. In general, these thresholds are chosen so as to define key regions with a spatial extent of approximately 10° latitude/ longitude.
Regression patterns analogous to those presented in Fig. 2 are also obtained using output from the C180-S2 and CM2.1-C21C experiments for the twenty-first century. In the latter computation, the Tmax anomalies are defined as deviations from the mean conditions for the 2041–70 era. The results of these REOF analyses (not shown) bear a strong resemblance to the charts in Fig. 2, thus implying that, despite the projected changes in the basic climatological state over North America in the coming decades, the preferred locations of extreme temperature episodes in the future are not noticeably altered from those in the twentieth century.
To ascertain that the REOF patterns in Fig. 2 represent preferred modes of variability of the Tmax field, maps are constructed showing the spatial distributions of regression coefficients of Tmax at all grid points versus Tmax at the center of each of the key regions identified in Fig. 2. The set of “teleconnection” charts thus obtained (not shown) bear a strong resemblance to the corresponding REOF patterns, even for those higher-order modes explaining a small fraction of the total variance. This favorable comparison indicates that results in Fig. 2 are not mere artifacts of the REOF technique, but offer a robust depiction of the characteristic spatial structure of the covariance of Tmax at different grid points.
4. Meteorological conditions attending temperature anomalies in various regions
a. Simultaneous regression patterns
The temporal variability of temperature in each of the key regions identified in Fig. 2 may be depicted by the daily time series of the areal average of Tmax over that region as demarcated by the black contour. Various aspects of the synoptic environment associated with prominent temperature anomalies at a given region may be highlighted by regressing selected meteorological variables against the standardized form of this reference time series for the key region of interest. In this section, we shall show such regression patterns for each of the key regions as identified in Fig. 2. The fields to be examined in this fashion include
the 500-mb height, subjected to a low-pass filter retaining fluctuations with periods longer than 10 days, using a procedure similar to that described by Blackmon (1976);
an envelope function (EF) depicting the low frequency variation of the squared amplitude of the synoptic-scale (2.5–6 day) fluctuations of 500-mb height, as computed using the procedure outlined in Nakamura and Wallace (1990); and
the unfiltered sea level pressure (SLP), precipitation, and horizontal wind vector at 10-m altitude.
To simplify the ensuing presentation, the eight key regions shown in Fig. 2 are grouped into four general areas: the Great Plains, U. S. West Coast, eastern North America, and southern United States, with each area consisting of two regions. In Figs. 3–6, the charts for each key region are displayed in a column of three panels. The top panel shows the simultaneous regression coefficients of the 500-mb height (contours) and EF (shading) versus the reference Tmax time series for the key region of interest. The middle and bottom panels show the corresponding regression patterns of SLP, precipitation, and surface wind vector. The top and middle panels are based on data generated by the C180-H2 experiment. The bottom panel is computed using NARR data.
1) Great Plains
The regression patterns, as constructed using the scheme described in the preceding paragraph, for the central Great Plains (based on the key region portrayed in Figs. 2a and 2c) and the nearby northern Great Plains (see key region in Figs. 2d and 2f) are presented in the left and right columns of Fig. 3, respectively. It is seen from Figs. 3b and 3e that the warm deviations of Tmax in both key regions of the C180 model atmosphere (see pink patches in these panels) are situated near a prominent low SLP anomaly, with enhanced southerly surface flows. Dry conditions prevail to the south or east of these key regions. The above spatial relationships between the simulated surface anomalies (Figs. 3b and 3e) are in good agreement with the corresponding patterns based on the NARR dataset (Figs. 3c and 3f). The gross characteristics of the regression charts for the surface variables simulated in the CM2.1-C20C experiment (not shown) bear a considerable resemblance to the corresponding results in Fig. 3, except that some of the local details generated in the higher-resolution C180 model are not as evident in the CM2.1 pattern. The above remarks on similarity among the surface patterns based on the H2, NARR, and C20C datasets are generally applicable to the results presented in the succeeding figures for other key regions (i.e., Figs. 4–6).
The meteorological signals near the surface are accompanied by organized, low-frequency circulation changes at the 500-mb level (see contours in Figs. 3a and 3d). The strong positive 500-mb height anomaly located northeast of the low SLP center is indicative of a prominent midtropospheric blocking anticyclone over that region. Also evident in the upper-air patterns are the positive height changes over the central North Pacific and North Atlantic and the negative height changes over western Canada/Gulf of Alaska and southern Greenland. This string of anomalies is suggestive of a realignment of the planetary-scale wave structure. The overall model patterns of Figs. 3a and 3d are similar to the corresponding observational result obtained by Chang and Wallace (1987, see their Fig. 3a) based on monthly mean data and reference time series of temperature at Kansas City.
The patterns of the envelope function (see shading in Figs. 3a and 3d), which provides a measure of the level of synoptic-scale activity, are closely related to the anomalous 500-mb height field (contours in Figs. 3a and 3d). Reduced transient eddy activity is discernible along zonally elongated belts situated at, or slightly to the south of, the anomalous blocking ridges; whereas an increased EF is seen on the northern flanks of these anticyclones. Particularly noteworthy are the negative anomalies of the EF (which is indicative of a stagnant circulation regime) over the regions of high Tmax and reduced precipitation (Figs. 3b and 3e).
2) West Coast
The regression patterns based on the two key regions situated near the western seaboard of North America (i.e., the Pacific Northwest and California) are displayed in Fig. 4. The key regions with high Tmax are collocated with a low SLP anomaly, with generally dry conditions (particularly for the Pacific Northwest region). The local surface circulation is characterized by easterly wind anomalies, which originate from the continental interior and are mostly directed down the slope of the Rocky Mountain Range. The SLP pattern off the Pacific coast is dominated by a high center situated to the northwest of the respective key region, with prevalent anticyclonic surface flows.
The wavelike character of the anomalous 500-mb height patterns (Figs. 4a and 4d) is similar to that described for the key regions in the Great Plains (Figs. 3a and 3d) except that the primary positive center in the present case is shifted to the western part of North America. The spatial relationships between the patterns of the EF (shading in Figs. 4a and 4d) and 500-mb height (contours in the same panels) are also analogous to those noted in the previous subsection. The negative anomaly in the EF located just to the south of the anticyclone over western North America at the 500-mb level indicates that this blocking feature tends to impede the passage of synoptic disturbances toward the Pacific Northwest/California during periods of high Tmax.
3) Eastern North America
The representative circulation and precipitation patterns accompanying hot episodes over southeastern (SE) Canada and northeastern (NE) United States are illustrated in the regression charts in Fig. 5. These key regions are straddled by a continental low SLP center to the west and a maritime high SLP center off the eastern seaboard of North America. The prevalent anomalous southerly flows over the key regions are part of the overall downgradient surface circulation pattern accompanying this pair of pressure centers. Wet (dry) conditions prevail in the vicinity of the low (high) SLP anomalies. The most prominent feature in the wavy 500-mb height pattern (contours in Fig. 5a and 5d) is the positive center over eastern North America. This center is located directly above or just to the west of the warm Tmax anomaly at the surface and is accompanied by reduced synoptic activity over the Great Lakes and the northeastern United States (see shading pattern of EF in Figs. 5a and 5d).
4) Southern United States
The regression patterns based on the key regions in Texas/Oklahoma and the central U.S. Gulf Coast are presented in Fig. 6. High temperatures in these regions occur in conjunction with a continental low SLP center to the north and are accompanied by southerly winds, with mostly continental sources, and reduced precipitation. The 500-mb height field over the United States is dominated by the anomalous ridge and reduced transient eddy activity near the Great Lakes.
b. Lagged regression patterns of 500-mb height
To examine the evolution of the midtropospheric circulation pattern with time, regression statistics are computed for various temporal lags between the low-pass filtered 500-mb height at selected reference points and the corresponding fluctuations at all other grid points. For a given key region, the reference region for this analysis is chosen to coincide with the center of the primary positive maximum appearing in the zero-lag regression chart of 500-mb height for that region. The distributions of the regression coefficients thus obtained, with the height fluctuations at various grid points leading (lagging) those at the reference grid point by 3 days, are presented in the left (right) panels of Fig. 7. The results for only one key region in each of the four broad geographical sectors considered in this section are presented in Fig. 7. The patterns for the remaining key regions that are not shown (i.e., central Great Plains, California, northeastern United States, and the central U.S. Gulf Coast) exhibit similar characteristics as their counterparts in the same geographical sector.
Inspection of the patterns in Fig. 7 and the upper panels of Figs. 3–6 reveals that the geographical locations of the individual maxima and minima in 500-mb height perturbations do not change appreciably with time lead or lag. However, for grid points situated west of the reference regions (see green dots), the typical amplitude of the height anomalies at 3 days prior to the reference time series (see left panels in Fig. 7) is noticeably higher than that of the signals at a 3-day lag (right panels). The regression charts for the Pacific Northwest region further indicate that the perturbations to the east of this region are stronger at a 3-day lag after the reference series (Fig. 7d) than at a 3-day lead (Fig. 7c). The cumulative evidence shown in Fig. 7 indicates the presence of successive downstream development of geographically fixed nodes and antinodes of the height field from the Pacific basin toward North America and the Atlantic. This phenomenon is previously examined using wintertime observational data by Blackmon et al. (1984), who attribute this mode of temporal evolution to two-dimensional Rossby wave dispersion on intermediate (10–30 day) time scales.
5. Projected changes in heat wave characteristics in the twenty-first century
a. Identification of heat wave episodes and documentation of the changes in their characteristics from the twentieth to twenty-first century
After demonstrating in the previous section the fidelity of the GCM tools in reproducing various observed synoptic features associated with Tmax variations in key regions, we proceed to examine the future behavior of heat wave episodes using projections based on these models. We follow a slightly modified version of the procedure of Meehl and Tebaldi (2004) to identify the heat waves occurring in the observed and modeled atmospheres. This method entails the definition of two thresholds: T1, corresponding to the 90th percentile of the daily Tmax values in the JJA season, and T2, the 75th percentile. These thresholds are computed for the areal averages of Tmax over each key region and are determined separately for each of the NARR, C180-H2, and CM2.1-C20C (1971–2000 segment) datasets. A heat wave event is defined as the string of days satisfying the following criteria:
Tmax must exceed T1 for at least three consecutive days,
averaged Tmax over the entire event must exceed T1, and
Tmax on each day of the event must exceed T2.
This procedure is applied to search for occurrences of the heat waves in the NARR dataset and each of the H2, S2, C20C (1971–2000 segment; five members), and C21C (2041–70 segment; three members) experiments. Note that the heat waves in the S2 (C21C) experiment are identified on the basis of T1 and T2 conditions determined using H2 (C20C) output. This particular treatment of the selection criteria must be kept in mind while interpreting the deviations of heat wave characteristics in the S2 experiment from those in the H2 experiment, as reported later in this paper. The search for heat waves is conducted separately for each of the coherent key regions described in Fig. 2.
For a given key region the following measures are then computed for each heat wave episode that meets the above conditions:
severity, defined as the averaged Tmax (°C) over the entire episode, and
duration, defined as the time span (days) of the episode.
Upon completion of the search through a given dataset, the mean severity and duration are evaluated by averaging these measures over all heat wave events identified in that dataset for each key region. The mean frequency of heat wave occurrence in each region is also obtained by dividing the total count of episodes by the number of years covered by the dataset in question. The averaged number of heat wave days per year is estimated by the product of mean duration and mean frequency for a given region.
It should be noted that the duration and frequency measures as described above are dependent on the specific procedure being applied. For example, consider a string of N hot days satisfying the three criteria listed at the beginning of this section. Such an occurrence would be counted as a single event with duration of N days. However, if a slightly higher threshold T2 were used, and the temperature on the Mth day falls just below this new threshold, then the same procedure would yield two separate events, with durations of M − 1 and N − M days, respectively. Such sensitivities to the analysis method and threshold should be borne in mind while interpreting the duration and frequency metrics reported in this study. Nonetheless, the number of heat wave days is a more robust measure of heat wave activity. In the above example, the number of heat wave days as estimated by using the two thresholds of T2 would be N and N − 1, respectively, with a difference of only one day. In view of these considerations, we shall devote more attention in the following discussion to the statistics for the number of heat wave days per season.
The statistical measures of the heat waves occurring in various key regions are summarized in Table 1 for the H2 and S2 datasets. These model values are to be compared with estimates derived from the NARR dataset, which are also shown in this table. In these tabulations, the key regions are grouped in pairs according to the classification scheme adopted in section 4.
For the C180 model, the averaged severity, duration, and frequency of the twentieth-century heat waves occurring in various regions are generally in good agreement with the reanalysis results, as can be inferred from the data entries under the “H2” and “NARR” columns for each of these measures in Table 1. However, notable differences between model and reanalysis are discernible in the severity of the heat waves over the Central Plains, northeastern (NE) United States, and the central U.S. Gulf Coast, where the simulated value is higher than the NARR estimate by 3°–4°C. The discrepancy over the Central Plains and central U.S. Gulf Coast is related to the warm bias in the model climatology of Tmax relative to reanalysis (see Fig. 1).
The projected change in heat wave behavior in the C180 atmosphere during the 2041–70 era may be inferred by inspecting the columns for S2, H2, and ratio of S2 versus H2 in Table 1. It is seen that the severity of the heat waves in the S2 experiment is higher than that in H2 by less than 1°C in all key regions. This finding indicates that the projected mean intensity of the heat waves, as estimated on the basis of the identification scheme adopted in the present study (see beginning of this section) does not increase appreciably from the H2 to the S2 scenario. On the contrary, much more drastic changes are discernible in the duration and frequency of the heat waves. The C180 model projects that the duration of the heat waves will increase by a factor of 1.2–1.9 with the largest changes being located in California, Texas/Oklahoma, and the central plains. The projected rise in frequency is even more substantial with most notable increases (by a factor of more than 3) over the northern plains and central U.S. Gulf Coast. The longer-lasting and more frequent heat waves lead to an increased count of heat wave days per year, with the strongest changes being projected for the northern plains, California, and Texas/Oklahoma.
The heat wave measures for the C20C and C21C experiments, as performed using the CM2.1 model, are compared with each other and with the NARR results in Table 2. The deviations of the measures based on the C20C experiment from the reanalysis results are generally larger than the deviations for the C180-H2 run (see Table 1). Similar to the situation with the C180 experiments, the CM2.1 model does not project a substantial increase in severity of the heat waves from the twentieth to the twenty-first century. For most regions in the CM2.1-C21C experiment, the number of heat wave days per year is projected to increase by a factor of more than 4 (see last column of Table 2), which is generally higher than the corresponding ratios based on the C180 results (Table 1).
We have focused our attention on the impact of climate change on the temporal characteristics of the heat waves, such as duration, frequency, and number of heat wave days per year. It is also of interest to briefly consider the changes in various spatial aspects of these heat waves from the twentieth to the twenty-first century. For each key region, typical patterns of the anomalous Tmax field are constructed by averaging the data over all identified heat wave days and by using the output from the H2 and S2 experiments separately. These composite charts (not shown) indicate that the spatial extent of the heat waves in the twenty-first century is noticeably larger than that in the twentieth century. For instance, it is seen from such maps that a typical heat wave (with anomalous Tmax > 4°C) in the central or northern Great Plains region affects an area of about 10° longitude by 10° latitude in the H2 experiment, whereas a typical heat wave with the same anomalous amplitude of Tmax expands to a much larger domain of about 20° longitude by 15° latitude in the S2 experiment.
b. Relating the changes in heat wave characteristics to shifts in the mean state
Variations in the statistics of some extreme events such as heat waves are closely linked to changes in the mean conditions, as well as the nature of the “spread” of amplitudes of instantaneous fluctuations about the mean state (e.g., Schär et al. 2004; IPCC 2012). Secular changes of the temporal characteristics of the climate system may be illustrated by contrasting probability distribution functions (PDFs) for different epochs. The PDFs for daily values of Tmax averaged over individual key regions in the JJA season are presented in Fig. 8. Results are shown for the H2 (blue histograms in left panels) and S2 (red histograms) experiments and for the C20C (blue histograms in right panels) and C21C (red histograms) experiments. The vertical lines in these histograms represent the frequency (expressed in number of days per year) of areal-averaged Tmax in individual bins with a uniform width of 1°C. A key region from each of the four general geographical groups considered in sections 3–4 is chosen for this display.
The histograms in Fig. 8 indicate that, in all key regions, the PDFs for S2 (C21C) exhibit a prominent displacement toward the right on the abscissa by typically 3°–4°C relative to the PDFs for H2 (C20C). Application of a chi-squared test (e.g., see Panofsky and Brier 1958) confirms that the PDFs based on S2 (C21C) data are different from those based on H2 (C20C) data at above the 99.9% significance level for all key regions. Comparison between the blue and red histograms in a given panel in the left column of Fig. 8 suggests that, for most regions, the general shape of the PDFs based on the H2 and S2 experiments is similar to each other. In particular, the degree of “spread” of the Tmax fluctuations, and the population of extreme outliers relative to the peak of the PDFs, do not appear to experience very noticeable changes from the twentieth to the twenty-first century in the simulations using the C180 model. On the contrary, the corresponding results based on output for most key regions from the CM2.1 model indicate a noticeable broadening in the shape of the PDFs in the C21C experiment as compared to those in the C20C experiment. The above visual impressions of the PDFs generated by the C180 and CM2.1 models may be checked against the standard deviations (σ) of Tmax for each of the eight key regions and for the reanalysis and various model datasets, as shown in the left half of Table 3. For a given key region, the pair of σ values for H2 and S2, and for C20C and C21C, is subjected to a standard F test (e.g., see Panofsky and Brier 1958). Those pairs of values that are different from each other at the 99% significance level are indicated by bold type. The data entries in Table 3 confirm that the σ values for the H2 and S2 runs are not significantly different from each other in all key regions. Conversely, the σ values for the C21C dataset are significantly higher than those for the C20C dataset in six of the eight key regions.
The skewness of the Tmax data for various key regions and datasets is displayed in the right half of Table 3. The H2 (C20C) experiment reproduces the polarity of the skewness statistic in six (four) of the eight key regions based on the NARR dataset. In a large majority of the key regions, the S2 (C21C) experiment yields the same polarity of skewness as the H2 (C20C) experiment. In most cases, the magnitude of the skewness exhibits only minor changes from the H2 to S2 runs or from the C20C to C21C runs.
The results in Fig. 8 are indicative of a significant shift of the Tmax climatology from the twentieth to the twenty-first century. The spatial pattern of this shift is depicted in Fig. 9, which shows the summertime distribution of (panel a) Tmax averaged over the 30-yr span of the C180-S2 experiment, and (panel b) the deviation of this S2 climatology from that of the H2 experiment (see Fig. 1a). We shall henceforth refer to change in the climatological norm (Fig. 9b) as ΔTmax. The C180 model projects that the mean Tmax will increase by 2°–5°C in most of the continental United States and southern Canada during the period from 1971–2000 to 2041–70. The strongest warming is predicted along the northern tier of states in the United States.
In view of the notable similarities between the shape of the PDFs as well as higher-moment statistics generated by the H2 and S2 experiments (Fig. 8 and Table 3), it is of interest to assess the degree to which the change in various heat wave statistics from the H2 to the S2 experiment, as documented in Table 1, can be attributed to ΔTmax. For each key region the areal average of ΔTmax is computed for each calendar month of the summer season (i.e., June, July, and August). This constant temperature shift for a given key region and calendar month is then added to the daily output of Tmax from the H2 experiment. We shall refer to the new dataset generated by this procedure as S2*. The heat wave identification scheme outlined in section 5a is applied to this new dataset by using the T1 and T2 thresholds obtained from the H2 experiment. Various statistical measures of the heat wave episodes satisfying the selection criteria are then computed. The results of this analysis are inserted in Table 1 in the columns labeled as S2*. The ratios of values based on S2* data versus those based on H2 data are also listed in additional columns in this table. In a large majority of the cases considered here, the statistics derived from the S2* dataset match well with those produced by the S2 experiment. The close correspondence between these two sets of results signifies that the change in heat wave intensity, duration, frequency, and number of heat wave days per year from the twentieth to twenty-first century, as projected by the C180 model, may largely be attributed to the shift in the climatological norm of Tmax in these two periods. This finding implies that the change in various heat wave statistics in a future climatic state can be estimated by simply adding the mean temperature change (i.e., ΔTmax) to the daily data for the control climate (as simulated in the S1 experiment). This “short-cut” is much less computationally intensive than the full model integration for the future climate state of interest (such as the S2 experiment examined here). The simplified approach would be particularly advantageous if several future climate scenarios (with a range of values for ΔTmax) are to be evaluated, as is typical in impact studies on public health and economic planning.
c. Evolution of heat wave characteristics in the twentieth and twenty-first centuries
We proceed to examine the detailed evolution of various measures of heat wave activity through the entire course of the 1901–2100 period, by making use of output from the century-long integrations of the C20C and C21C experiments with the CM2.1 model. For a given decade the heat waves in each key region are identified by submitting the daily time series of Tmax from three members of the appropriate CM2.1 experiment to the testing procedure described in section 5a. The T1 and T2 criteria based on the 1971–2000 segment of the C20C experiment are used in this procedure. The averaged severity, duration, frequency, and number of heat wave days per year within that decade are then computed. These calculations are repeated for all 20 decades in the twentieth and twenty-first centuries. The results thus obtained are displayed in Fig. 10, with each row describing the two key regions within a certain geographical group (as represented by blue and red curves).
A large majority of the time series in Fig. 10 exhibit relatively modest variations within the twentieth century, but very prominent upward trends in the twenty-first century. Largest values of these measures are attained toward the end of the twenty-first century. In many cases the steepening of the positive slope of the time series is projected to occur in the early decades of the twenty-first century. By the end of the twenty-first century the CM2.1 model projects that the averaged heat wave in the central Great Plains, California, and the southern U.S. states will last longer than 30 days; and many key regions will have 50–60 heat wave days per year.
6. Detailed spatial distributions of heat wave measures in present and future climates
The eight key regions considered in the previous section cover only a fraction of the North American landmass. For the sake of completeness, it is worthwhile to document the twentieth and twenty-first -century heat wave characteristics at all regions of this continent. The heat wave identification process in section 5a is applied to the daily Tmax time series at every grid point in various reanalysis and model datasets, using the T1 and T2 thresholds as determined for the grid point in question. The averaged severity, duration, and frequency of the heat wave events, as well as the number of heat wave days per year, are then obtained at each grid point.
The overall spatial patterns of the severity of the heat waves based on the H2 experiment and NARR data (not shown) are in agreement with each other. The pattern for heat wave severity in the S2 experiment (also not shown) does not show any notable departures from that in the H2 run. Projected rises in severity from twentieth to twenty-first century are limited to less than 1°C at most grid points.
The spatial patterns for averaged duration, frequency, and number of heat wave days per year are shown in Fig. 11 for NARR data (first row) and output from the experiments of C180-H2 (second row) and C180-S2 (third row). The ratios of heat wave measures in S2 versus those in H2 are depicted in the fourth row.
The C180 model reproduces the gross regional characteristics of the heat wave measures as inferred from NARR data (first and second rows in Fig. 11). Striking positive changes in the heat wave measures are evident in the S2 experiment (third row in Fig. 11) in relation to the corresponding H2 values. Specifically, the averaged heat wave duration in Texas, the western mountain states, as well as the southeastern portion of the United States is projected to lengthen by a factor of 1.5 or more (Fig. 11d). A 3.5- to 4.5-fold increase in the frequency of heat wave events in the northern plains, the eastern slope of the Rocky Mountain Range, and the Mississippi basin is projected for 2041–70 (Fig. 11h). The number of heat wave days per year is projected to increase by a factor of more than 5 at many grid points in the western states (Fig. 11l).
The consistency between the charts in Fig. 11 and the corresponding measures for various key regions (Table 1) is checked by comparing the areal average of the gridpoint data in Fig. 11 over a given key region (not shown) with the corresponding heat wave measure listed in Table 1. It is verified that the results based on these two complementary approaches; that is, the areal average of measures determined at individual grid points versus measures based on areal average of Tmax, are in good agreement with each other.
7. Summary and discussion
The model and reanalysis results presented in section 4 indicate that high temperature in the key regions are accompanied by anomalous surface wind vectors that are oriented either from low to high latitudes or from the warm continental interior to the coastal zones or from higher to lower terrains. The advective or adiabatic processes associated with these flow configurations are conducive to positive tendencies of the local temperature. The increased temperature and thickness of the air column over the key regions are accompanied by a prominent positive anomaly in 500-mb height near these regions. This midtropospheric anomaly is embedded in a planetary-scale wave train with distant centers over the North Pacific and North Atlantic basins. The evolution of the strengths of these centers with time is reminiscent of Rossby wave dispersion, with successive downstream development from west to east. The anticyclonic circulation associated with the 500-mb blocking ridge over the key regions impedes the passage of synoptic-scale disturbances through those regions. The diminished level of eddy activity in these regions (as inferred from the negative anomalies of the envelope function) portrays a stagnant flow environment conducive to persistence of the local warm and dry conditions.
The analysis on the projected trends in heat wave characteristics in the twenty-first century (sections 5–6) reveals minor changes in the heat wave severity as defined by our procedure, but notable lengthening of the averaged duration of these events, and substantial fractional increases in the frequency of occurrence and number of heat wave days per year. Results on the PDFs and various statistical moments of Tmax reveal salient modifications of the climatological mean in the H2 and S2 experiments, whereas changes in the overall shape of the PDFs and the higher statistical moments are less evident. It is demonstrated that most of the increases in heat wave duration, frequency, and number of heat wave days per year from H2 to S2 may be accounted for by the shift in the climatological norm (ΔTmax) in the key region of interest. This finding indicates that, in lieu of detailed model simulation of individual heat wave events in future climatic settings, the changes in various heat wave measures could be estimated by adding ΔTmax to the daily data in the control experiment and then recomputing the heat wave metrics (see entries for S2* in Table 1). This methodology is a convenient alternative to the much more detailed model simulation of individual heat wave events in future climate states (as is done in the S2 experiment), and would facilitate the assessment of heat wave characteristics under a broad range of anticipated climate settings. Our study concludes with the documentation of further temporal and spatial details of the changes in various heat wave measures. In the temporal dimension, the variations of these measures in individual decades throughout the twentieth and twenty-first centuries are reported using simulations with a lower-resolution model. In the spatial dimension, the changes of these measures are analyzed at every grid point by using output from a model with higher resolution.
The heat wave phenomenon is evidently linked to myriad dynamical and thermodynamical processes in the atmosphere, as well as their interactions with hydrological changes at the underlying land surfaces. Advances in our understanding of the heat waves in twentieth- and twenty-first-century climate settings entail more in-depth investigations of the physical mechanisms contributing to such extreme events, including feedbacks among the wind circulation in both the boundary layer and free atmosphere, cloud formation and associated radiative forcings, convection and condensational heating, and transfers of heat and moisture at the air–land interface. The evidence presented herein suggests that the CM2.1 and C180 models are capable of replicating the essential climatological and synoptic aspects of the observed heat waves in various North American regions. More detailed diagnoses of the output from these models will broaden our knowledge of the role of the aforementioned processes in various stages of heat wave development, as well as the impacts of projected climate changes on these processes. To assess the robustness of the findings based on the GFDL models, the results reported in this study should also be compared with those derived from other models with distinct physical parameterizations.
It is well known that the impacts of high-Tmax events on mortality and public health would be much greater when the humidity and nighttime temperature are also much above normal (e.g., Robinson 2001). In our investigation, the heat wave episodes are identified on the basis of Tmax only. Regression plots similar to those in the lower panels of Figs. 3–6, but for the near-surface relative humidity and daily minimum temperature fields (not shown), indicate that positive Tmax anomalies at various key regions are coincident with above-normal daily minimum temperature during nighttime hours, but with below-normal humidity. It would be of interest to extend the scope of our study by considering high “heat stress” episodes with strong positive anomalies in both temperature and humidity. Such analyses would address more directly the impacts of extreme weather events on human society.
In the present study, we have focused our attention on the heat waves occurring within the conventional summer season, that is, June–August (JJA). We have also examined the number of heat wave days in individual calendar months from April through October. The results (not shown) indicate that, for all key regions, almost all heat wave days fall within the JJA season in the H2 experiment, whereas only a small fraction (typically less than 10% of the yearly total) of the heat wave days can be identified in May or September in the S2 experiment. Hence the incorporation of the heat wave days in the latter “shoulder” months would not change the total annual counts appreciably.
The present study is primarily concerned with heat waves in North America. It is well known that such extreme events also affect the weather and climate in other parts of the globe, including Europe, Asia, the tropical zone, and the Southern Hemisphere. Further study is needed to delineate the temporal and spatial characteristics that are unique to the heat waves occurring in each of these regions, as well as features and processes that are common to heat waves in several regions. The methodology employed in our study (including identification of coherent regions, regression analysis of various meteorological fields, computation of heat wave measures in twentieth- and twenty-first-century climates) could readily be adapted for applications to any region of interest beyond North America.
Both C180 and CM2.1 models project substantial increases in the duration (by a factor of 1.2–2.2), frequency (by a factor of 2.2–3.8), and number of heat wave days per year (by a factor of 2.9–5.1) in various North American key regions in the mid-twenty-first century as compared to the end of the twentieth century. Changes of such proportions will exert severe stress on human livelihood and the natural environment in the affected regions. The strong socioeconomic and ecological implications of these projections warrant a vigorous and thorough evaluation of the robustness of the findings presented herein. Such assessments would entail alternative analyses of the model output using different criteria for defining the heat waves and various heat wave characteristics, as well as examination of climate change experiments performed by other modeling centers.
We thank our colleagues at GFDL for providing the output from various experiments with the C180 and CM2.1 models. We are indebted to Isaac Held, Tom Knutson, Bruce Wyman, and Ming Zhao for their perceptive comments on an earlier version of this manuscript. We have also benefited from discussions with Tony Broccoli, Isaac Held, John Lanzante, and Paul Loikith in the course of this study.