This study provides a monsoonal link to the rapid Arctic ice melt. Each year the planetary-scale African–Asian monsoonal outflow near the tropopause carries a large anticyclonic gyre that has a longitudinal spread that occupies nearly half of the entire tropics. In recent years, the South Asian summer monsoon has experienced increased rainfall over northwestern India and Pakistan and it has also contributed to more intense local anticyclonic outflows from this region. The western lobes of these intense upper-high-pressure areas carry outflows with large heat fluxes from the monsoon belt toward central Asia and eventually to the region of the rapid ice melt of the Canadian Arctic. In this study this spectacular pathway has been defined from airflow trajectories, heat content, and heat flux anomalies. Most of these show slow increasing trends in the last 20 years. The monsoonal connection to the rapid Arctic ice melt is a new contribution of this study. This is shown from the passage of a vertical column of large positive values of the heat content anomaly that can be traced from the Asian monsoon belt to the Canadian Arctic. The heat flux along these episodic and intermittently active pathways is shown to be considerably larger than the atmospheric poleward flux across latitude circles and from the oceans. This study contrasts these thermodynamic wave trains (defining this pathway) for the more conventional dynamic wave trains.
Two time scales of Arctic ice melt have been noted in recent years: one is a somewhat slower trend in the last 20 years of ice-volume datasets and the other is a more rapid trend during the last 7 years. Examining the monsoon’s daily and climatological (time averaged) circulations, we describe the size of the monsoonal outflows of the upper-tropospheric flows for both the summer and the winter seasons, which is an impressive aspect of the general circulation. Perturbations of this mean state resulting from heavy rain events of northern India and Pakistan are shown to be associated with emanations of small-amplitude wave trains that seem to provide a major connection of the monsoon to the Arctic. In this study that connection seems to be largely into the region of the Canadian Arctic. Examining daily maps of the summer monsoon of South Asia for many years, it was noted that the monsoonal teleconnections to the regions north of Tibet was quite apparent, especially via the western flanks of the Tibetan circulation. In recent years the summer monsoon has experienced heavier rains and intense local floods over Pakistan and northern India (Houze et al. 2011; Lau and Kim 2012). According to Lau and Kim, the European block in the middle troposphere results in a transfer of cyclonic vorticity (ahead of the blocking high) toward Pakistan, assisting in the formation of a low pressure area. That low pressure draws moist air from the east (from as far as the Bay of Bengal), resulting in heavy rains and much stronger intensification of the low is noted. Our study starts after that point. It should be qualified that our study is based on case studies and hence emphasizes case histories that are indeed important. A statistical approach based on many years of data, using empirical orthogonal functions or other statistical tools may be other avenues for addressing this problem. Some very noteworthy events were seen over Pakistan during 2010 and in Uttarakand, India, in 2013. We illustrate large values of heat content anomaly along a corridor that connects the monsoon to the Arctic. Parcel trajectories in three dimensions and the transport of heat content anomaly and Hovmöller diagrams confirm the pathway derived from the heat content anomalies. Of major importance are the heat flux and the convergence of flux of heat along this pathway. Those are compared with the meridional flux across latitude circles and with the best available estimates of the oceanic heat transports that impact the recent rapid melt of the Arctic ice. There are two types of atmospheric wave trains. One, typical of the middle latitudes, is known for the wave energy fluxes [see Blackmon et al. (1984a,b), Lim and Wallace (1991), Chang (1993), and many others]. The other is typically a tropical wave train that carries large-heat-content anomalies from the tropics into the higher latitudes. The latter is the topic of this paper. Traditionally the first type of wave train carries wave energy that is identified by the kinetic energy (υ2/2), whereas the latter is identified by the temporal anomalies of gz + CpT + Lq (where g = 9.8 m s−2, z is geopotential height, Cp is specific heat at constant pressure, T is atmospheric temperature, L is latent heat of vaporization, and q is specific humidity)—the moist static energy. In the formal derivation of the moist static energy equation (Krishnamurti et al. 2013), it was shown that gz + CpT + Lq is roughly two orders of magnitude larger than υ2/2 and the latter is usually neglected in heat budget studies (Riehl and Malkus 1958). Thus, wave trains carrying large-heat-content anomalies are of much interest where heat transports are encountered.
This is an observational study at this stage. This study does not go into issues of wave energy fluxes for the following reason. It is noted in this study that wave trains excited by Pakistan heavy rain events, presented here, carry a small meridional amplitude and are fast moving (roughly 30° longitude per day) and make it the Canadian Arctic in around 4 days. The phase speed of individual synoptic waves is only on the order of 5°–7° longitude per day whereas the westerly winds north of the highs and south of the lows are faster than the waves and move roughly 15°–17° longitude per day. The winds along the pathway of the heat content physically carry out heat transports from the western flanks of the Tibetan Plateau to the Canadian Arctic in a matter of 6–7 days. There are clearly some fluctuations in the amount of heat flux along these pathways since there are sources and sinks of a local nature along this pathway; this should be expected. It is this aspect of the heat flux that is addressed in this paper. This monsoonal–Arctic pathway, related to the Pakistan rains, is not undulating with large amplitudes. The amplitude of these southern waves is much smaller in comparison to the northern waves of the summer season. This path may have been determined by a Rossby waveguide of the kind explained by Hoskins and Ambrizzi (1993), where the stationary wavenumber K has a localized maximum and Rossby waves are refracted into regions of larger K. In the present study the heat flux is directly computed (thus including compressional warming within ducts via sinking). It should be noted that the study of Hoskins and Ambrizzi refers to a winter season, whereas the present study addresses the summer monsoon period. The computations are based on 6-hourly reanalysis data. Implicitly detailed fluxes along the small amplitude pathway are what have been accomplished here. Full computations of energy dispersion would clearly be needed in the context of the winter monsoon where larger-amplitude wave trains, toward the Antarctic, are encountered. The wave trains that we illustrate in our study are thermodynamic in character as opposed to dynamic wave trains. The former carries two-order-of-magnitude-larger energy from gz + CpT + Lq, the moist static energy, as contrasted with the dynamical counterparts that are usually tagged by the wave energy fluxes (i.e., their eddy kinetic energy).
Wave trains have drawn increasing attention in the literature in the last 20 years. Other relevant studies on Arctic ice melt related issues have been addressed by Ogi et al. (2008), Rigor and Wallace (2004), Fang and Wallace (1994), and many others (Hoskins et al. 1977). Simmons and Hoskins (1979) used a dry idealized numerical model to study unstable barotropic Rossby waves. They found that new waves develop downstream of old waves in the upper troposphere and upstream at lower levels. Hoskins and Karoly (1981) provided a further analysis of this phenomenon using a spherical geometry for such waves traversing in a slowly varying medium. In Krishnamurti et al. (2000), a numerical simulation, using a coupled atmosphere–ocean global model, the Pacific–North America pattern was illustrated. It was shown that all of the downstream waves were baroclinic with substantial vertical motions and weather; those wave elements were not simple external barotropic Rossby waves in terms of amplitude and phase speeds, and the pattern of the wave train did not quite follow a great-circle route. Wave trains excited by the winter monsoon have been addressed by Krishnamurti et al. (1999), where they noted that downstream amplification in these Southern Hemispheric waves that cross the entire southern Pacific Ocean often lead to very large-amplitude waves over South America. Very cold air entering tropical latitudes damaged coffee crops over Brazil. It was also noted that the wave train was composed of slow-moving long waves (zonal wavenumbers 1–3) and faster-moving shorter waves (wavenumbers greater than 4). Wave trains are also seen in the belt of tropical easterlies (of the upper troposphere). Some 30 examples of typhoons making landfall over Vietnam were discussed in that study. The typhoon landfall resulted in a pressure rise over Southeast Asia and in the formation of a monsoon depression over the Bay of Bengal (Krishnamurti et al. 1977). In the year 2000, several papers covering nearly an entire issue of Weather magazine (2000) were devoted to a major heavy rain and flood event over England. Krishnamurti et al. (2003) discussed the antecedents of this event as a downstream amplification of a wave train that originated in southern Siberia. A cold dome of air over Siberia stagnated for a week prior to intensification. The arrival of a frontal wave from central Europe disrupted the cold dome and caused its collapse, resulting in the emanation of a wave train. That wave train crossed parts of Russia, all of the Pacific Ocean, all of North America, and all of the Atlantic Ocean as it showed a major downstream amplification over western Europe, resulting in severe weather over England. A striking example of a wave train excited by the impact of a typhoon over the western Pacific on the subtropical jet stream resulted in a downstream amplifying wave across the Pacific Ocean (Archambault et al. 2013). Archambault et al. (2013) presented results from an examination of as many as 292 cases of tropical cyclones that resulted in downstream responses as extratropical waves. They illustrated the impact of a typhoon near Japan on the subtropical westerly jet that resulted in the excitation of a wave train that amplified over the United States, resulting in a large number of tornadoes. The phase velocity in the extratropics, for the individual highs and lows, is generally on the order of 5°–7° longitude per day. The wave train’s motion is that of a group velocity is generally as large as 30° longitude per day. The zonal wind often moves faster than the single lows and highs and carries a speed of around 17° longitude per day. Wave-train dynamics is addressed by Grams et al. (2011), Hoerling (1992), Chang and Orlanski (1994), and many others. Wang et al. (2005) addressed the steady-state response of monsoonal heat sources. This theoretical problem was solved by these authors using a direct matrix inversion to portray the extratropical wave response using barotropic dynamics as the frame of reference. This study suggests a relative insensitivity on the location of the tropical forcing (i.e., communication of wave energy from the easterlies to the northern westerly belt). The Pakistan heavy rain region does not need to face the issue of trapping of wave energy flux across the critical latitude between easterlies and westerlies since it is located in the westerly belt.
In an enlightening study on teleconnections to northern extratropics through a southern conveyor, Wang et al. (2005) showed that by introducing a Rossby wave source in the tropical easterlies, the southerlies from the tropics can in fact excite a wave train that eventually moves eastward toward the Canadian longitudes (their Fig. 2b, p. 4060). They also noted that a stronger southerly flow favors a stronger extratropical response. This theoretical modeling study is important for the findings of our study. Another important, and related, study is that of Ding et al. (2011), where they noted that Indian monsoon rainfall anomalies a summer after ENSO events can lead to circumglobal telecommunication patterns over the Northern Hemisphere extratropics and can be seen in the 200-hPa height fields. These studies provide a useful background for our findings. Other relevant and important studies on Arctic ice melt related issues have been performed by Ogi et al. (2008), Rigor and Wallace (2004), and Fang and Wallace (1994). These above references were important for the motivation of our study.
Rodwell and Hoskins (1996) have provided a link between the South Asian monsoon and the descent of air over Sahara–Mediterranean and the Aral Sea regions. This was a modeling study where a remote diabatic heating of the Asian monsoon region induces a Rossby wave that shows a descent over some of these desert regions. That study has relevance to the findings of our study.
2. Current decline of the Arctic ice volume
The decline on the decadal time scale of the Arctic sea ice volume in recent years has been noted by Kwok et al. (2004) and Rothrock et al. (2008). From an examination of the data on ice volume of the last 33 years (Fig. 1), a rapid decline of the ice volume is apparent. However, another time scale of a more rapid Arctic ice decline is noted since 2005 (Schweiger et al. 2011). The ice melt datasets suggest two time scales: a slower decreasing trend during the last 20 years and a faster decreasing trend during the last 7 years. This study addresses the later. Using satellite-based ice-area coverage, a 9% decline per decade in the areal coverage between 1978 and 2000 was reported by Comiso (2002). The datasets over the Canadian basin of the Arctic, especially the area of the Beaufort and Chukchi Seas, showed a record minimum of ice-cover extent in September 2007 that reached values 24% lower than the corresponding satellite estimates of 2005 (Giles et al. 2008).
The polar research group of National Snow and Ice Data Center (NSIDC) has mapped (Fig. 2) this decline using daily and monthly sea ice concentration derived from Scanning Multichannel Microwave Radiometer (SMMR) and Special Sensor Microwave Imager (SSM/I) brightness temperature (Stroeve et al. 2012) based on National Aeronautics and Space Administration (NASA) Team Sea Ice Algorithm (Cavalieri et al. 1996; Meier et al. 2006). The geographical distributions clearly show the rapid decline of the Arctic ice, especially over the Beaufort and the Chukchi Seas. Screen and Simmonds (2013a,b) and Screen et al. (2013a,b) have addressed issues related to the Arctic ice melt. In summary, the ice-volume datasets of Fig. 1 suggest two time scales of decline; the recent decline is the topic of this study. During this recent period, we have noted several heavy rain episodes that relate to the emanation of thermodynamically active wave trains that transport large quantities of heat from the monsoon belt toward the Canadian Arctic. These are seen from various data displays that are presented in this paper, and that is the topic of this study.
3. Planetary-scale monsoon
a. Monsoonal outflows
The sheer size of the planetary-scale African and the Asian monsoonal outflows of the upper troposphere at the 200-hPa level, near 12 km MSL, is a very impressive aspect of tropical general circulation. A 20-yr-average wind circulation (1992–2011) of this feature spans a longitudinal spread of nearly 200° during the boreal summer seasons (Fig. 3a). During the boreal summer, the South Asian outflows occur from a massive anticyclone called the Tibetan high (Rao 1976). This anticyclone resides above a warm troposphere carrying the highest temperature (−25°C) (Krishnamurti et al. 2013; Fig. 3b). At 30°N, 300-hPa, there is a large zonal asymmetry in the planetary-scale thermal field. The middle troposphere of the subtropical Pacific and Atlantic Oceans, at the 300-hPa level, carry temperatures that are nearly 10°C colder than the Tibetan region. These warm temperatures are attributed to warming from sensible heating and convection over the Tibetan Plateau and from deep monsoonal convection of the Asian monsoon (Flohn 1968). These relate to another important feature of the monsoon, which is the vertically integrated tropospheric heat content (see appendix). This monsoonal region also carries the largest reservoir of heat content (2.9 × 109 J) over the entire Northern Hemisphere (Fig. 3c). In contrast, the Arctic carries the lowest values for the vertically integrated heat content (2.5 × 109 J).
b. Episodes connecting the monsoon to the Arctic
In this study we show that large heat content anomalies exist during and after heavy rain episodes of Pakistan and northern India. In that context, individual episodes of heavy rains over northern India and Pakistan are addressed. A 6-day average of the same variables, as were shown for the climatology in Figs. 3a–c are presented in Figs. 3d–f for a Pakistan flood event covering the period from 31 July to 5 August 2010. This is a well-documented flood event (Houze et al. 2011; Saeed et al. 2011; Hong et al. 2011; Lau and Kim 2012). This flood period includes an intense local upper-tropospheric anticyclone at the 200-hPa level, near 12 km (Fig. 3d). In this heavy rain period, monsoonal air from the south of the Himalayas is carried northwestward over Pakistan and toward central Asia, and it eventually continues on to the Canadian Arctic. A westward extension of the upper-tropospheric warmest temperatures (−25°C) toward Pakistan and Arabia (Fig. 3e) and a westward spread of the largest total heat content (109 J) of the monsoonal air (Fig. 3f) are important features of this as well as other events that we have studied here. During periods of anomalously heavy rains and floods over Pakistan, the heat content anomalies amplify, as can be seen from a comparison of Figs. 3c and 3f; this feature extends toward the western flanks of the Tibetan high circulation. A telecommunication between this region of large heating and the cold Arctic region suggests a pathway through a wave train excited by this strong local heavy rainfall and the deep convection. This small-amplitude wave train carries westerlies to the north of the highs and south of the lows. In these undulating westerly winds, we have noted that they physically contribute to heat transport along the entire pathway carved by these westerlies. That is the main topic of this study. The Pakistan heavy rains seem to contribute to smaller-amplitude wave trains, whereas the heavy rains of northern India seem to excite somewhat-larger-amplitude wave trains that emanate from the heavy-rain regions and traverse the Himalayas across Tibet, northeastward toward Eurasia, and, eventually, to the Arctic latitudes.
The issue of wave trains of the midlatitude westerlies (Lau and Kim 2012) is clearly distinguishable from the more southern wave train emanating from the heavy-rain regions of Pakistan. The former carries a larger meridional amplitude and low total heat content in comparison to the southern monsoonal wave train (Fig. 3c). As a result, the heat fluxes across 60°N of the northern wave trains are much smaller in comparison to the southern one (Fig. 4).
The topic of heat transports by midlatitude waves toward the Arctic latitudes has been addressed by many authors (Peixoto and Oort 1992; Trenberth and Solomon 1994; Trenberth and Caron 2001; Trenberth and Stepaniak 2003; Fasullo and Trenberth 2008; Lau and Kim 2012). The designation of the northern and the southern pathways follows Kapsch et al. (2013). Here the authors had more specifically studied the northern midlatitude waves, which, during the boreal summer months, are active at around 45°–50°N and northward. Our study clearly shows the presence of two pathways: one to the north and the second related to the monsoon. The former carries a larger meridional amplitude, as is typical of atmospheric baroclinic waves, whereas the narrow latitudinal belt between the Himalayas and these northern waves carries a smaller (meridional) amplitude with a much larger heat content. In our current study the heat content anomaly at the 300-hPa level averaged over these 30-day periods and the vertically integrated heat content (100–1000-hPa levels), also averaged over a 30-day period, are presented in Fig. 4). Figures 4a and 4c are very similar because the orders of magnitude of the largest fluxes of Fig. 4b are smaller than those of Fig. 4a, hence the difference between Figs. 4a and 4b are almost similar to Fig. 4a over most of the regions of interest. In Fig. 4a, variations in the heat content along the pathway suggest local convergence and divergence of flux of heat arising from local heat sources and sinks (Krishnamurti et al. 2013); this is also discussed in the appendix. During the boreal summer these waves are most active between 30° and 60°N. The vertically averaged climatological heat content at 50°N is around 2.1 × 109 J (Fig. 4d), which is smaller than the corresponding value over the western Tibetan circulation near 30°N, where it is around 2.35 × 109 J (Fig. 4d). These differences can be seen in Fig. 4f. When anomalies are added to the climatological values, the total heat content of the monsoonal pathway is much larger. The important question is how different are these heat contents and heat transports along the southern pathway connecting the monsoon to Canadian Arctic as compared to those for the northern pathway? Figures 4d and 4e show the vertically integrated total heat content for the Pakistan flood and nonflood days. They both contain the same climatological component. When these are subtracted, the climatology cancels out and we see in the difference chart (Fig. 4f) the vertically integrated anomaly difference between the Pakistan flood days and nonflood days. This vertically integrated difference in the anomaly is quite similar to that of the 300-hPa-level differences shown in Fig. 4c.
The total heat content over the regions of the northern waves are generally much smaller than those of the more southern wave train that emanates from the monsoon; this is clearly seen from the variations of the total heat content in Figs. 4d and 4e. This relates to the climatology of the total heat content that drops with latitude. Thus, anomalies of even similar strength added to the climatology for the northern and the southern waves clearly make the southern one more effective for the total heat transport.
Our study distinguishes the northern wave trains, known for their contributions to wave energy fluxes (eddy kinetic energy), from the tropical counterparts that carry larger heat content (moist static energy).
Graversen et al. (2008) noted a warm-season temperature trend poleward of 75°N with a maximum around the 700-hPa level; they also noted that the anomalous advection from southern latitudes was more important in comparison to the contribution from northern waves.
4. Pathways and structure
Three-dimensional trajectories (Krishnamurti and Bounoua 1996) were constructed and are addressed next. These make use of the global reanalysis datasets from Kalnay et al. (1996). For the construction of trajectories, the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) algorithm of National Oceanic and Atmospheric Administration (NOAA) is utilized here. Six-hourly wind components (u, υ, and w) for a 10-day period, subsequent to several major rainfall events over northwestern India and Pakistan, were used. Figure 5a shows that a parcel originating on the western lobes of the Tibetan circulation, at the 300-hPa level (near 9 km MSL), passes over Eurasia and makes it to the Canadian Arctic in about 5–6 days. The red and the blue lines are forward and backward trajectories covering this region of interest. This trajectory was derived for the flood event of Pakistan during 30 July–8 August 2010. This trajectory highlights the parcel motions from the monsoon to the Arctic. Figure 5b illustrates the pressure levels for the trajectories for the forward trajectory. It should be noted that parcels are sensitive to the time and point of origin; these reflect the general behavior of trajectories over this region. For this case study, the starting point of the trajectory was selected at the 314-hPa level over western Pakistan at 1200 UTC 30 July 2010. The yellow tick marks for this trajectory have an interval of 1 day. After day 6, a faster descent of this parcel was noted. This is a 10-day forward trajectory. There are some smaller-scale up-and-down motions of the trajectory during its traverse that is to be expected in case studies, since there are local heat sources and sinks along any such long pathway. These are not time-averaged climatological trajectories. A swath of such wind trajectories emanating from the western lobes of the monsoonal upper-tropospheric anticyclone are illustrated in Fig. 5c. The selected starting point for these trajectories lies between 9 and 12 km MSL. These are sample trajectories during various flood events of Pakistan during the years 2007, 2008, 2011, and 2012. This swath shows that most trajectories make it to the Canadian Arctic in a matter of 1 week from the monsoon belt. The lateral spread of this swath of trajectories, based on this sample, is around 1500 km. The horizontal component of trajectories show parcel motions, starting from the west of the Tibetan plateau, traversing over Kazakhstan, northwestern parts of China (including the Gobi and Taklamakan Deserts), southern and eastern parts of Russia, and northwestern Canada.
Figure 6a for the Pakistan flood event of 18–23 August 2007 shows a forward trajectory starting from the western flanks of the Tibetan Circulation at 300-hPa level. Figure 6b shows a 6-day average (covering a period following the start of the heavy rains of a Pakistan event) of the heat content anomaly at the 300-hPa level for 18–23 August 2007. In Fig. 6c the vertical mean of the heat content anomaly for the same period and Fig. 6d the vertical average of the heat content transport for the same period are shown. These are four similar fields, connecting the monsoon to the Canadian Arctic, that were examined in this study. They all show such a link. The trajectories originating at the 300-hPa level (Fig. 6a), the pathway as seen from the maximum value of the heat content at the 300-hPa level (Fig. 6b), the maximum value of the vertically integrated heat content (Fig. 6c), and the vertically integrated transport vector Fig. 6d show some differences in their respective locations because of what they are meant to emphasize. That is to be expected since they are all different quantities with different dimensions. The trajectory has dimensions of distance covered over a period of time (unit of velocity), the heat content has dimensions of velocity squared, and the heat transport has dimensions of velocity cubed, hence their portrayal cannot be expected to be identical; that they are as close to each other as they are is important. The trajectory is simply drawn from a carefully selected initial location, given the known spread of an ensemble of trajectories; this particular trajectory should not necessarily coincide with lines of maximum heat transport. This should be kept in perspective while interpreting Fig. 6. We have examined the reanalysis data to generate such fields since the start of the boreal summer of 2007 and noted the similarity of trajectories, heat content anomalies, and heat transport vectors that bear such a robust link. These comparisons show that these four ways of looking at the link between the monsoon and the Canadian Arctic ice melt region are indeed quite similar for these heavy rain/flood events and this link is indeed quite robust. In this section we have shown results of computations for forward trajectory and for a swath of trajectories, starting from the heavy rain area of Pakistan. These suggest the strong monsoonal link to the region of the Arctic ice melt. The vertical tubes of the heat content anomaly physically carry heat, since that is their signature. As they traverse from west to east, they arrive at a new longitude, bringing larger heat content from the west to the east along the pathway. Climatological winds do transport some heat along these pathways but those values are similar to values outside the wave duct (where the heat content is one order of magnitude smaller); that is how we define the lateral extent of this thermodynamical wave train.
b. Vertical motions along the pathway
The time-averaged vertical motions, for a week following the Pakistan flood event of the 2010 summer season, are shown in Fig. 7a. These are based on reanalysis data (Kalnay et al. 1996). A rising lobe of air is found at the 500-hPa level (near 5.5-km altitude) over the active parts of the monsoon and over the eastern Tibetan Plateau. To its north, there is a sinking lobe of air; a line of maximum sinking motion is shown by the red line over the northern Chinese desert region (the Gobi and the Taklamakan Deserts) and then extends toward Alaska and the Canadian Arctic. A narrow belt of sinking air essentially follows the entire pathway from the monsoon to the Canadian Arctic. Several vertical profiles of the vertical velocity of the descending air along this entire pathway are included in Fig. 7b. The red line in Fig. 7a is not a trajectory—it is a hand-drawn line that follows a belt of maximum downward motion; this belt resembles the pathway of heat content anomaly [shown in Fig. 10b(6)]. The vertical motions, shown in Fig. 7a, is a time mean at the 500-hPa level covering the period of a Pakistan rain event during July–August 2010. Several vertical profiles of vertical motions are shown are shown for five selected points along the red line of maximum vertical motion. All these show tropospheric descending motions with a mean amplitude of roughly 0.04 Pa s−1. All profiles show a descent over the entire troposphere. In particular, it should be noted that air descends from the 700-hPa level (near 3 km), which is close to the level of maximum heat content anomaly, to Earth’s surface in a matter of 3–4 days. This descending air warms by adiabatic compression along the belt around 45°N, 60°–100°E as it moves to the Arctic latitudes.
c. Vertical structure of the heat content anomaly
The vertical structure of the heat content anomaly is like a vertical column of large positive values that can roughly be followed from the monsoon to the Canadian Arctic. Figure 8a shows the passage of such a vertical structure of the heat flux anomaly (where climatology is removed) along selected points of the pathway from the monsoon belt to the Canadian Arctic. This illustration is for the Pakistan heavy rain and flood event of August 2010. The different panels of this illustration clearly show the monsoonal heat flux anomaly making its way northward along the pathway from Tibet to the Canadian Arctic in roughly 5–6 days.
As the stationary Rossby wave pattern forms, the wave train’s group velocity generally carries a speed of around 30° longitude per day. The individual synoptic-scale waves travel slowly at a phase speed of around 7° longitude per day. The zonal winds around the lows and the highs average between around 15° and 17° longitude per day (roughly 20 m s−1 at the 300-hPa level). During the heavy rain and flood events over Pakistan, the meridional amplitude of the individual waves was not very large, but the winds around the lows and highs often physically transport heat at a fast rate along the entire pathway from the western flanks of the Tibetan high to the Canadian Arctic. To demonstrate this, an animation of the heat flux anomaly along the pathway was prepared based on the 6-hourly reanalysis datasets (see the online supplemental material). That animation utilized 29 analysis files at time intervals 6 h apart. The interpolations were done for every 3 min using a multiple-weighted interpolation scheme. Here, each interpolated field utilizes the inverse of the time interval between that time and the 29 known times as the 29 weights. These weights are normalized to a sum of 1.0. This weighted interpolation sees all 29 files for each interpolated point and does not require a large matrix inversion, as is necessary for high-order polynomial based interpolations. The animation shows a clear passage of a vertical tube of positive heat flux anomaly from the monsoon to the Arctic. The rate of propagation is close to that of the vertically averaged upper-tropospheric zonal wind along the pathway, which is around 20 m s−1. The robustness of the direct transports by the winds is portrayed by this animation.
Hovmöller diagrams were constructed for all cases they show rather similar features. Figure 8b shows a space–time (S–t) Hovmöller diagram of the heat content anomaly for the Pakistan heavy rain and flood case of 2010. Here, S follows the maxima of the heat content along the pathway. This clearly shows the passage of the heat content anomaly from roughly 80°E to 170°W. This is also confirmed by Fig. 8a and by the animation presented in the online supplemental material. We did have the benefit of additional days of data for the construction of the Hovmöller diagram (Fig. 8b), which suggested farther motion of the heat content anomalies than is reflected in the previous diagram (Fig. 8a), which only covers the period through 5 August 2010 and shows the passage of the vertical tubes of the heat content anomaly that were used for constructing the animation.
d. Additional examples
A single-day’s upper-tropospheric flow field (Fig. 9) for a Pakistan heavy rain event shows a locally strong anticyclone above these rains. These episodic events build a route for the poleward transport of heat from the western flanks of locally intense upper-tropospheric anticyclones.
The rainfall histories of Pakistan daily average rainfall (mm day−1), over a domain covering 32°–35°N, 70°–73°E are shown in Fig. 10a for the Pakistan heavy rain and flood years 2005–12. The ordinate in Fig. 10a denotes averaged rain over this domain and the abscissa denotes dates from 1 June to 31 August for each year. The dates and duration of the rain events studied here are marked by horizontal arrows near the top of each panel. The selection of specific dates depends on many factors—the prevailing circulations of these periods of heavy rains resulted in the excitation of strong wave trains; those are studied in this paper. The datasets for rainfall came from the NASA Tropical Rainfall Measuring Mission (TRMM) archives. Although wave trains emanating from Pakistan were noted during all of these years, Fig. 10b includes the most prominent of these waves. Figure 11 shows a composite of the vertically integrated heat content anomaly averaged over all eight events (107 J kg−1). This is an important illustration of this study, as it clearly shows a pathway of the large heat content anomaly that extends from the western lobes of the Tibetan circulation toward the Canadian Arctic. Heat content anomalies of the northern latitudes can be seen in this illustration. However, the total heat content of the northern stream are much lower compared to that of the lower-latitude stream because of the large gradient of the climatological heat content that was shown in Fig. 3c.
The pathway from the monsoon to the Arctic is also illustrated by the vectors of the transport of the heat content anomaly that emanate from the monsoonal circulation, specifically from south of the Himalayas, and are traced to the Arctic; see Fig. 12a. Houze et al. (2007, 2011) noted that monsoonal clouds often extend to 16 km in the vertical. This vector field shows the instantaneous direction of heat transport, which is the same as that of a local wind vector and with a magnitude that is the product of the wind speed and the heat content.
It should be noted that the central axis of the pathway of the heat content anomaly in Fig. 10b at 300 hPa is somewhat different from the heat transport vectors at 300 hPa in Fig. 12a (the blue arrows are drawn here along the longest vectors). That difference has to be expected since these two are somewhat different quantities having respective dimensions of velocity squared and velocity cubed.
The heat transport by the anomalies along the pathway is the product of the wind component along S and the local value of the heat content anomaly (coordinate S is along the pathway and N is normal to it; N = 0 is located where the maximum value of the heat content anomaly of the pathway, for a given S, resides). The heat flux is a double integral of this product, laterally covering the wave duct and vertically from Earth surface to the top of the atmosphere. The width of the wave duct, at any location S, N is defined by two outer values of the heat content anomaly that are one order of magnitude smaller than the maximum value which is defined to be located at N = 0. The total heat flux is the sum of the transport of the heat content anomaly plus that by the climatology. These locations of the vertically integrated heat fluxes are illustrated in Fig. 12b. The vectors point toward the direction the local heat transport and the magnitude of the heat transport (J kg−1) is shown by colored shading. Also shown, at selected vertical walls and selected longitudes along this pathway, are the total heat fluxes (petawatts; 1 PW = 1015 watts). This is further shown in Table 1. A southern stream of heat transport can be seen from these vectors emanating from south of the Himalayas; they show a 5-day-averaged (subsequent to each Pakistan flood events) direction of transport around the western Himalayas toward central Asia, China, and southern Russia before making it to the Canadian Arctic. In this context the animation (shown in the online supplemental material) also conveys an important message: the heat content anomaly (Fig. 10b), at the 300-hPa level, roughly 9 km MSL, is a good level for illustrating the passage of heat content and the heat content anomalies. The heat content’s signal at the 300-hPa level carries a good signature for the total heat content. That same level can also be used for labeling the heat content anomaly since it varies little with height (Fig. 7) [see also Krishnamurti et al. (2013)]. For that reason, this vertical level is being used here to illustrate the pathway of the vertically integrated heat content anomaly. These weekly averages suggest that, in a matter of roughly a week, large positive anomalies show a passage from the monsoon circulation to the Arctic.
The latitudinal falloff in the value of the total vertically integrated heat content is very important for a distinction of the southern wave train near 35°N with northern wave trains near 55°N. If one looks at the climatological values of the vertically integrated heat content of Fig. 3c, those values at 35°N, 73°E (close to the heavy rain area of Pakistan) are around 2.72 × 109 J. The corresponding numbers for the northern wave train at around 55°N, 73°E (close to the waves of the midlatitude polar jet stream) are around 2.61 × 109 J. At these two locations (Fig. 3c), the vertically integrated heat content anomalies are two orders of magnitude smaller (i.e., around 2.5 × 107 and 1.5 × 107 J, respectively). The base value from climatology distinguishes a large difference in the total heat content for the southern and the northern wave trains. Ultimately the total heat transport, which utilizes the total heat content, is what matters in distinguishing between these two wave trains.
5. Recent trends in temperatures, heat content, and precipitation
Global warming is a possible likely cause of the decline of the Arctic ice. Although the intention of the study is not to solve the problem of global warming and the Arctic ice melt, this section is very relevant for the readers who will be contributing to this problem. In this section, linear trends of the surface air temperatures and the heat content anomaly over the monsoon belt and along the pathway that was discussed in the previous section are provided. The India Meteorological Department (Srivastava and Guhathakurta 2012) provided records for the maximum surface air temperatures over India for its surface meteorological network of stations. Figure 13a illustrates recent (2005–10) record-breaking temperatures. That spread of recent record temperatures covers a good part of India. In some locations, especially over central and northwestern India, the maximum values are as high as 50°C (122°F). Such increasing trends of surface air temperature were recently reported by Kothawale and Rupa Kumar (2005).
The trends in the heat content over India and along the pathway are illustrated in (Figs. 13b–g). The average surface air temperatures over India (domain 0°–30°N, 65°–90°E) and the total vertically integrated heat content over India, as well as along the pathway connecting the monsoon to the Arctic, all show slow increasing trends from the past two decades of datasets. Year 2007 in Fig. 13b shows an increasing trend for the average surface air temperatures over India of 0.15 K decade−1. The trend of the total heat content over India (Figs. 13b and 13c) for the months of June–August (the monsoon months) and for May (premonsoon) also show increasing trends on the order of 5 × 106 and 4 × 106 J decade−1, respectively. During the premonsoon month of May when heavy rains and evaporation are lacking, sensible heat fluxes from the warm Earth’s surface play a major role, and the trends in the sensible heating are reflected in surface air temperatures. However, for the wet monsoon months of June–August the total heat content, including latent heating, is more important. The trends of the total heat content along composited pathway from the western lobes of the Tibetan circulation (25°–35°N, 70°–100°E) to central Asia (50°–70°N, 150°E–180°) and to the Arctic (75°–85°N, 180°–165°W) were also calculated and are also provided (Figs. 13e–g). These all show a slow increasing trend for the vertically integrated heat content along the pathway. These trends are respectively 8 × 104 J, 7.5 × 104, and 4 × 104 J decade−1. All of the trends displayed in Fig. 13 had been subjected to the statistical t test, and the results show that they are all significant at the 90% confidence level.
The warm-temperature records for 110 years, over all of India, are best portrayed by histograms showing the year-by-year variations of the surface air temperature anomalies (Srivastava and Guhathakurta 2012). The anomalies are with respect to 30-yr-average values (1961–90). Figures 14a–e respectively show these anomalies for the annual mean, winter season (January and February), premonsoon (March–May), monsoon (June–September), and postmonsoon (October–December). The large recent increasing positive trends of surface air temperatures stand out in all of these figures. These are very striking features suggesting a global change in recent years. Major rain-producing disturbances of recent years seem to be able to convey this excess heat of the monsoon via extreme rainfall events to the massive Tibetan circulation, which is the outflow layer of the monsoon. That was a motivation for carrying out this study.
The rainfall distribution for one of these flood events is illustrated in Fig. 15; this illustration shows the 6-day-averaged rains over Pakistan from 31 July to 5 August 2010. This is contrasted with the TRMM-based climatological rainfall distribution covering the years 1998–2012. The flood event, as expected, carries much higher rainfall over Pakistan compared to climatology. This is quite similar to other events that were examined. Chaudhary (1994) and Singh and Sontakke (1996) noted increasing trends in the rainfall over northwestern India in the 1990s. This is also noted from the recent 15-yr rainfall estimates from the TRMM satellite. Figure 15c illustrates the increasing trends of summer monsoon rains over northern India and Pakistan, respectively, for the years 1998–2012. The linear trend is statistically significant at the 99% level based on a chi-squared test.
This section simply strengthens the possible link of the monsoon to the rapid Arctic ice melt from formal computations of linear trends of the surface air temperatures over the monsoon belt and also the heat content anomaly along the pathway that was discussed in the previous section.
6. Uttarakhand rain event
One example of a monsoon-to-Arctic heat content pathway carved by a heavy rain event over northern India is included here. During 15–18 June 2013, a major rain event occurred over Uttarakhand, a province in the foothills of the Himalayas. This was a record-breaking rain event—the total rains for that week were around 322 mm; this resulted in massive floods, landslides, and the destruction of life and property (Ramachandran 2013). Using the NCEP operational analysis datasets, this event was studied using near-real-time datasets. The results were quite similar to those we had seen for other events of heavy rains and floods over Pakistan. With Himalayas to the north, the upper-tropospheric flows experienced southerly flows from a locally intense Tibetan high that conveyed mass directly northeastward over the tallest mountains on Earth. The 300- and 200-hPa levels are above Mount Everest; clouds from this heavy rain event streamed northeastward. The heat content anomaly for the 300-hPa levels (Fig. 16) shows a pathway with large positive values for the heat content anomaly that stretches from northern India to Eurasia and on to the Canadian Arctic. The vertical structure of the heat content anomaly for this event is shown in Fig. 17. The nine panels show a steady 6-day progression of the heat content anomaly from northern India to the Canadian Arctic. These results are still preliminary but appear very promising because it became possible to predict this heavy rain event along with the emanating wave train from the monsoon belt to the Canadian Arctic with a very-high-resolution global model. These results will be reported in a subsequent paper.
7. Heat fluxes along the pathway from the monsoon to the Arctic
Table 1 shows the total atmospheric heat fluxes (PW) across different reference segments along the pathway. The magnitudes of the transport of heat content anomalies along the pathway connecting the monsoon to the Arctic are as large as 5–10 PW. These are much higher values compared to meridional transport of heat across entire latitude circles where the average poleward transport of heat flux at 40°, 50°, and 60°N are 0.8, 0.82, and 0.25 PW, respectively, during 1992–2011. These computations were carried out in detail, following Oort (1977). In these computations, the width of the pathway is determined for a composite of cases of intense rains over northern India and Pakistan during the last 8 years. Table 1 includes the averaged values of the heat transports along the pathway for the last 8 years and the mean of the net convergence (calculated from these averages) of fluxes of heat along this pathway belt. The Gobi Desert, around 45°N, 90°–110°E, resides along this pathway. This pathway also follows a region where the surface air temperatures have increased by as much as 5°C in the last 6 years (Zhang et al. 2012). A large heat flux convergence shown in the last column of Table 1 has values of 0.23 × 10−3 PW K m−1 over this region of this surface temperature warming. The pathway then moves north of Alaska over the Chukchi and Beaufort Seas and the Canadian Arctic where the convergence of flux of heat attains values of around 2.68 × 10−3 PW K m−1. This region of large convergence values of heat flux is nearly the same region as that shown in Fig. 2 for the rapid Arctic ice melt.
A formal computation of heat flux for the northern pathway was also carried out following latitude circles for 50° and 60°N for several summer seasons covering each of the years 2005–11 by excluding the Pakistan flood days. Those fluxes were on the order of 0.15–0.2 PW. The southern pathway fluxes, shown in Table 1, are on the order of 5–10 PW. It is not possible to directly translate the heat fluxes or the convergence of fluxes of heat to any measurable Artic ice melt; that is beyond the scope of this study. It is shown that the monsoonal pathway of this study carries much larger heat transports compared to fluxes across latitude circles such as 60°N. The episodic nature of monsoonal wave train–related heat fluxes and the monthly-averaged normal fluxes across latitude circles are compared here. Further work, more in the nature of a sharp, well-coordinated field experiment, is needed to get much deeper insights on budgets from atmosphere, ocean, and ice measurements.
8. On oceanic contributions to the heat flux
The main oceanic heat flux into the Arctic Ocean is carried by the Norwegian Current from the North Atlantic and the Bering Strait throughflow from the North Pacific. The former is determined from an 11-yr-long record (1995–2005) from moored temperature and current meters at the Svinoy Section (62°N) across the Norwegian Current (Orvik and Skagseth 2005). They estimate the mean volume flux to be 4.2 Sv (1 Sv = 106 m3 s−1) with anomalies in the range of −0.46–0.63 Sv and the overall mean heat flux to be 0.133 PW with anomalies in the range of −0.016–0.0146 PW. For the 11-yr period, they find a minor downtrend in the volume flux but no significant decrease in heat flux; in particular, there is no increase in heat flux in spite of the observed 1°C increase in temperature. They noted that this striking temperature increase appears to be independent of variations in flow. Similarly, the Bering Strait fluxes of volume and heat from the North Pacific into the Arctic are obtained (Woodgate et al. 2012) from instruments on moorings placed across the 85-km-wide, 50-m-deep strait. Again, an 11-yr-long record (2001–11) of hourly temperature and current meter data has been obtained. In the 11-yr period the volume flux showed a 50% increase from 0.7 to 1.1 Sv with a corresponding increase in heat flux. The annual heat flux for the year 2011 was 5 × 1020 J yr−1 or an average rate of 0.016 PW. Their analysis shows that the increasing trend in volume flux is largely (two-thirds) explained by the increased pressure head from the North Pacific. About 50% of the increased heat flux is related to ocean warming: years with warmer lower-layer temperatures and not necessarily higher SSTs are seen to have larger heat flux. In summary, the total oceanic heat flux (the sum of Pacific and Atlantic fluxes) into the Arctic Ocean is 0.149 PW.
The ice-volume trend (Schweiger et al. 2011) obtained from Pan-Arctic Ice Ocean Modeling and Assimilation System (PIOMAS) gives −2.8 × 103 km3 decade−1 carries an uncertainty of ±1.0 × 103 km3 decade−1. Using a latent heat appropriate for average salinities of ice and seawater, this rate of melting would require an excess of heating rate over cooling rate, averaged over a decade, of 0.0019 PW. The net radiative cooling of the Arctic north of 60°N during the summer months is around 0.2 PW, which is close to the latitudinal tropospheric transport.
9. Similar features during the winter monsoon
The monsoonal link to the polar ice seems to extend to the Antarctic during the boreal winter months when similar heavy rain and flood events over northeastern Australia and Indonesia are encountered. The monsoonal outflow at the 200-hPa level of the winter monsoon is a very massive circulation feature of the troposphere, as shown in Fig. 18 (Krishnamurti et al. 2013). The streamlines of the monsoonal outflows above the heavy monsoon rain area are counterclockwise over the upper local anticyclone and continue around a massive clockwise high in the Northern Hemisphere; this circulation returns to the south across the Pacific Ocean toward South America. A heavy rain and heavy flood event over Indonesia, during January 2013, resulted in major loss of property and life. Three recent examples of Indonesian heavy rains and related heat content anomalies (Fig. 19) and their vertical structures are shown in Figs. 20–22. These show that a winter monsoonal connection to the general region of the Wilkins Island of the Antarctic Peninsula is a distinct possibility. These wave trains, seen from the 6-day-averaged heat content anomaly datasets at the 300-hPa level are quite similar to the northern counterparts that we have discussed in this study. These also exhibit the passage of the vertical tubelike structures (shown by double dashed vertical lines) of heat content anomalies—covering the periods 2–7 February 2002, 17–22 January 2006, and 3–8 January 2012—originating from the general region of heavy winter monsoon rain areas to the Wilkins Island. An examination of reanalysis datasets of the last 30 years, during episodes of heavy rains around the regions of Indonesia, suggest that such thermodynamical wave trains are worthy of further investigation.
The similarity of the features of the heat content pathway of the two hemispheres suggests that further investigation on the links of the monsoon and the polar ice regions of the two hemispheres may be important.
10. Concluding remarks
The main conclusions of this study are as follows.
The most important contribution is the time-mean chart of the vertically integrated heat transport anomalies, covering 8 years of Pakistan flood events of the summer season. This includes the mean of eight events. This is a vector transport of the heat content (Fig. 9); this shows vectors emanating from south of the Himalayas, going around the western flanks of the Tibetan anticyclone through central Asia, China, southern Russia, and on toward the Canadian Arctic. The magnitude of these vectors is a measure of the heat that the vectors are transporting. That heat transport is around 4.0 PW over the western flanks of the Tibetan high. Table 1 shows the heat transports along the pathway suggested by these vectors. That value varies from 4.0–9.52 to 7.84–2.81 PW along different longitudes of this pathway. Local heat sources and sinks do modify the heat content, as should be expected in any atmospheric problem.
Related to the above, the first finding was the heat content anomaly (Fig. 11) that has a vertically stretched, somewhat barotropic shape (see the animation in the online supplement and Fig. 8a). This was a consistent shape that was noted for all major rainfall events of the Pakistan floods, as well as those of northwestern India. The heat content, as seen in the upper-troposphere (300-hPa level), shows a small-meridional-amplitude, wave train–like structure. The initial speed of the wave train is around 30° longitude per day. The zonal winds within this wave train, after the wave train acquires a near stationary character for nearly a week, are around 17° longitude per day. Swaths of parcel trajectories show that parcels of air originating from the western flanks of the Tibetan circulation travel to the region of the Canadian Arctic in around 5 days. These parcels show a slow descent along the entire pathway for the first 3–4 days and a somewhat faster descent in the last period.
This study does not directly address the specific melt of Arctic ice, the monsoonal link, and the large heat transports compared to those across latitude circle 60°N or into the Arctic belt from oceanic transports. To specifically address the Arctic ice melt from monsoon heavy rain events and related heat transports would require a very well-coordinated field experiment where simultaneous interdisciplinary measurements covering periods of a season may be required.
It is beyond the scope of this paper to directly relate global warming to Pakistan floods and then to the pathway and to obtain precise measures of Arctic ice melt (see Fig. 23). This study simply illustrates features such as the vertically integrated heat transport (Fig. 12b) a week after the heavy rain events of Pakistan. Those are also clearly supported by the Hovmöller diagram (Fig. 8b), showing the passage of vertical tubes of heat content from the western lobes of the Tibetan circulation to the Canadian Arctic. The data sample size from five such rain events covers a small period for any reliable lag correlations between rains over Pakistan and the heat transports, a week later, to the Canadian Arctic. An attempt at computing correlations showed values between 0.1 and 0.3 for the different cases. We can clearly see that a larger sample size is required for improving such correlations.
Figure 23 illustrates the weekly changes in the ice melt datasets for the Canadian Arctic during several recent years. This illustration from the National Snow and Ice Data Center monthly archive (19 September 2012) compares yearly ice melt of a specific location with respect to total sea ice area. The figure shows a time series of total sea ice area for different years (Fig. 23a) as a function of dates within those years, whereas Fig. 23b emphasizes the extent of sea ice within the Western Parry Channel route of the Northwest Passage of Canada. From Fig. 23b, a different pattern of ice loss in the sea routes between 2007 and 2012 has been obtained, which highlights that sometimes regional melting of ice has greater importance than total extent. It calls for much further detailed work to relate these types of available sea ice datasets to meteorological fields such as heat transports.
Ongoing and future work related to the issues addressed here are in modeling. In a forthcoming paper we will address two aspects of modeling, where a single very-high-resolution global model is used to predict an extreme rain event of the monsoon and the ensuing thermodynamic wave train from the monsoon belt to the Canadian Arctic. The second area of modeling entails the use of datasets from multimodels for 1-week forecasts that show the passage of the wave train from the monsoon belt to the Canadian Arctic after an extreme rainfall event. In this context it is worth mentioning that some degree of success in the simulation of such wave trains has already been seen from the postprocessing of forecasts from European Centre for Medium-Range Weather Forecasts subsequent to individual episodes of heavy rains over Pakistan.
This work is supported by three research grants to The Florida State University: NASA Grant NNX13AQ40G, NSF Grant AGS-1047282, and by Ministry of Earth Sciences, Government of India MM/SERP/FSU-USA/2013/INT-8/002. We wish to convey our special thanks to Dr. Robert Ross, Professor John Ahlquist, and Ms. Darleen Oosterhof of Florida State University for providing editorial comments and corrections.
Vertically Integrated Tropospheric Heat Content
The heat content (where g = 9.8 m s−2, z is geopotential height, Cp is specific heat at constant pressure, T is atmospheric temperature, L is latent heat of vaporization, and q is specific humidity) is expressed in joules per unit mass of the atmosphere. Heat sources and sinks modify the values of the heat content continually in the atmosphere .The heat content anomaly is defined as the departure of the daily heat content from a long-term mean; in this study a recent 20-yr average for the long-term mean of has been used. The value of and its long-term mean vary in the three space dimensions. These results are very robust and can be followed very easily from reanalysis data archives where all one needs to compute in sequence are (i) the climatology fields of the heat content in three dimensions , (ii) the same daily fields for a major rain and flood event over northwestern India or Pakistan, and (iii) the difference of (i) and (ii) to construct the fields of the heat content anomaly.
A derivation of the equation for the time rate of change of the heat content can be seen in many text books (e.g., Krishnamurti et al. 2013, 300–302). This equation simply states that the local time rate of change of the heat content is equated to the horizontal and vertical convergence of fluxes of the heat content and the heat sources and sinks. The latter arise from air–sea and land–atmosphere interactions, the radiative transfer processes, condensation, and evaporation. It is not straightforward to relate local changes in the heat content to local precipitation simply because there can be varying amounts of divergence of fluxes of heat in the horizontal direction. The vertical partitioning of the heat content into its three components (gZ, CpT, and Lq) can also be rather complex, especially in the region of heavy rains. Here the vertical coordinate is important. Along the vertical, a decrease of Lq for saturated ascending parcels of air does not simply translate into warming temperatures; a substantial part of the buoyant air simply elevates that parcel to transform into potential energy. The potential energy for the eastern part of the Tibetan high comes from latent heating Lq in these heavy rain episodes. In saturated moist adiabatic ascent, the three components (gZ, CpT, and Lq) form a nonlinear triad. The nonlinearity comes from the Clausius–Clapeyron equation that dictates the nonlinear relationship among vapor pressure, saturation specific humidity, pressure, and temperature. The governing mutual energy exchanges among gZ, CpT, and Lq are complex (Krishnamurti et al. 2013). To relate precipitation to temperature or to heat content in open systems is not simple because of contributions to the potential energy and the lateral divergence of fluxes.
The complete heat budget at every location is not presented in this study, except to note that there are convergence and divergence of fluxes of heat over vertical columns that vary along the pathway (see Fig. 12b and Table 1). These computations have addressed the transports of the heat content (total heat) from the start of a Pakistan flood event and traced them all the way geographically to the Canadian Arctic. The implied heat sources and sinks can be easily computed as residuals from the last column of Table 1, where the net convergence and divergence of fluxes are presented. Table 1 (mean of all events) shows that 4.0 PW of heat leaving the Pakistan flood region consistently maintains a large value of heat flux along the entire pathway as it arrives over the Canadian region of Arctic ice melt with a value of 2.81 PW. Local heat sources and sinks do modify these fluxes and, in an open domain, there are also divergences of flux of heat normal to the pathway.
The transport of heat content anomaly is obtained from the product of a wind and the heat content anomaly at any (horizontal and vertical) location of the atmosphere. Both poleward and pathway transports are considered here; they call for meridional winds and for winds along the pathway. The total transports are integrals across a wall whose horizontal size is determined either by the length of a latitude circle (at any latitude) or by the width of a pathway under consideration. In the vertical, for this transport across a wall, we include vertical integrations from Earth’s surface to the 100-hPa level, which is roughly 16 km. Datasets are obtained from the reanalysis (Kalnay et al. (1996). The transport of heat across latitude circles 40°, 50°, and 60°N are on the order of 1 PW or less, whereas the transports along the active pathway, connecting the monsoon to the Arctic, are on the order of 5–10 PW.
Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/JAS-D-14-0004.s1.