510 Journal of the Meteorological Society of Japan Vol. 61, No. 4

Transcription

1 510 Journal of the Meteorological Society of Japan Vol. 61, No. 4 General Circulation of Air Parcels and Transport Characteristics Derived from a Hemispheric GCM Part 2. Very Long-Term Motions of Air Parcels in the Troposphere and Stratosphere By Hideji Kida Meteorological Research Institute, Tsukuba, Ibaraki 305, Japan (Manuscript received 29 September 1982 in revised form 20 June 1983) Abstract A Lagrangian-type description of transport mechanisms of tracers in the stratosphere and troposphere is presented on the basis of trajectory analysis of a large number of marked air parcels using a hemispheric GCM. It is demonstrated that the transport of the lower stratospheric air is due both to slow advective general circulation and to large-scale quasihorizontal eddy diffusion, while the transports within the troposphere are highly diffusive both in the horizontal and vertical directions. The present simulation shows that the tropospheric air parcels are well mixed within one month throughout the troposphere by quasihorizontal mixing due to cyclones and vertical mixing due to small-scale convection. It is also shown that the stratospheric air can be supplied mainly from the tropical tropopause. Only the bottom layer (below *100mb) of the extratropical stratosphere may be intruded by tropospheric air parcels through the subtropical tropopause gap. However, such intrusion can hardly affect the levels above the bottom layer. In this paper, the age of the stratospheric air is analyzed; the age of an air parcel is defined as the length of time elapsed since it entered the stratosphere. The results show that the tropical stratosphere consists of `new' air parcels, which is thought to retain properties of the tropospheric air, while the polar stratosphere involves relatively `old' air parcels which have long-term residence in the stratosphere. This interpretation may be useful to understand major features of distributions of tracers originating either the surface or the stratosphere. 1, Introduction Major features of global distributions of nearly conservative tracers can be explained only by taking transport processes into account. We have two ways to describe transport mechanisms; one is the budget analysis based on Eulerian framework and the other is the Lagrangian analysis, i.e., the trajectory analysis of air parcels. In order to answer the question what motions are essential to transport of a tracer, the Lagrangian analysis is a straightforward method. Moreover, the method does not include a mistakable problem known as the non-transport theorem that eddy transport and mean transport due to eddyinduced mean motion are both large but completely cancel each other in the Eulerian framework. Thus, we shall consider transport mechanisms of tracers from the Lagrangian viewpoints. Despite such advantage of the Lagrangian analysis, few studies have been conducted on the general circulation of air parcels so far. We will shortly review some studies conducted from the Lagrangian viewpoints. From the trajectory analysis of tropospheric air parcels on isentropic surfaces in middle latitudes, Palmen (1951) proposed a Lagrangian-type general circulation model in which large scale horizontal mixing in the extra-tropical region and meridional cellular advection (i.e., the Hadley cell) in the tropical region are considered to be major modes of large-scale motions to transport air parcels in the troposphere. As to the stratosphere, Brewer (1949) and Dobson (1956) hypothesized a men-

2 August 1983 H. Kida 511 dional circulation of air parcels from the tropical essentials of the Palmen's and Brewer-Dobson's to the polar regions in order to explain the models and present the Lagrangian-type general extreme dryness and the ozone excess in the circulation of air parcels in the atmosphere. The lower stratosphere at high latitudes. Recently, analysis of the ages of the stratospheric air shows this model is partly supported by theoretical that the age increases with increasing height and studies (e.g., Dunkerton, 1978; Matsuno, 1980; latitude. This implies that the air of the tropical Holton, 1981). However, it must be noted that lower stratosphere posesses properties of the either Palmen's model for the troposphere or tropospheric air and conversely the air of the Brewer-Dobson's one for the lower stratosphere polar stratosphere is much affected by physical has not yet been confirmed by direct evidence and chemical processes in the stratosphere. mainly because of the insufficiency of data of Hence, we can easily recognize the observational wind especially in the stratosphere and tropical troposphere. Concerning mass exchange be- increase, while tracers originating the surface facts that the content of ozone shows poleward tween the stratosphere and troposphere, not a (e.g., CFMs) show poleward decrease in the few observational studies have demonstrated lower stratosphere. downward intrusion of stratospheric air parcels 2. Assumptions for incorporating the effect of into the troposphere associated with remarkable subgrid-scale vertical mixing in trajectory folding of the extra-tropical tropopause (e.g., analysis Reed and Sander, 1953; Reed and Danielsen, 1959; Staley, 1960). But, upward intrusion The computational scheme of trajectories of mechanisms of tropospheric air parcels into the marked air parcels is almost the same as that stratosphere remain to be solved, although Reihl used in Part 1. In the present paper, however, and Malkus (1959), Newell and Gould-Stewart we treat the effect of vertical mixing by subgridscale motions such as convection and turbulence. (1981) and Danielsen (1982) suggested that convective motion in the ITCZ is a mechanism to Since it is impossible to specify the subgrid-scale supply the air into the tropical stratosphere. As motion of each air parcel, we shall adopt, as above mentioned, there is no well-established a first step, fairly intuitive assumptions to calculate the movement of marked air parcels affected and complihensive model for the Lagrangian-type by such subgrid-scale motions as follows; general circulation of air parcels throughout the stratosphere and troposphere. The main purpose (i) Random vertical mixing due to active convective motion occurs in a region where grid- of this study is to derive such a model by means of numerical simulations. scale upward motion takes place in the whole Two kinds of analyses are performed in this column extending from the surface to the tropopause at one place. (ii) This vertical mixing paper. First, we calculate very long-term movements of a large number of air parcels initially makes air parcels move randomly upward or located at three selected places; the middle downward in the column within a depth of latitude-900mb, the tropics-100mb and the 2km (i.e., *1km in height from the original tropics-30mb. The results will be presented in level) in a period of 3 hours (*t). This roughly corresponds to vertical diffusion with the diffusion coefficient of_*106cm2/s, but the vertical Section 3. Second, we analyze the `age' of an air parcel in the stratosphere by defining it as the time length of residence within the stratosphere since it became a stratospheric air parcel. extension of tall convections such as tropical cumulus convection is not correctly represented The statistics of the ages are determined as a in this scheme. This is obviously a defect. According to these assumptions, the vertical dis- function of height and latitude. The properties of the ages will be discussed in Section 4. Furthermore, it must be noted that the analysis of placement (*z) of the air parcel can be calculated the age provides a computational basis necessary to evaluate the mixing ratio of a tracer as will where w is the vertical component of the gridscale motion and z' is randomly specified as discussed in detail in the forthcoming paper (Kida and Shimazaki, 1983) which aims at -1km<z'<lkm. (iii) An additional assumption is that in the tropical region, 0* to 25*, simulating distributions of CFMs on the basis of individual trajectories of marked air parcels. the upper and lower limits of vertical mixing are The obtained results clearly reproduce the taken to be 150mb and 850mb, respectively.

3 512 Journal of the Meteorological Society of Japan Vol. 61, No. 4 This assumption is artificial but needed to prevent a shortcoming that the direct application of (ii) results in unresonably rapid intrusion of tropospheric air parcels into the tropical stratosphere in the ITCZ. Therefore, marked air parcels in the tropical troposphere above the upper and below the lower limits are assumed to be transported only by the grid-scale motions. 3. Simulations of very long-term movements of air parcels 3.1 Initial positions Meridional and vertical movements of air parcels are of prime interest in the present work, although their trajectories were computed in the 3-D space. Therefore, we will treat only the distribution of instantaneous positions of marked air parcels projected onto a meridional plane. The distributions will be illustrated by dots on the plane. However, note that the concentration of dots does not properly represent the density (per volume) of the marked air parcels, because of the use of a linear scale in latitude. The initial positions of marked air parcels are set in the horizontal as follows; and where N and M are the ordered numbers used as the names of marked air parcels. *N, M and N, M are the longitude and latitude where * the parcel (N, M) is located at the initial. * and are the intervals between adjacent air parcels. Nmax and *0 will be specified for each * simulation. Mmax is always taken to be Case 1: Source in the troposphere Motions of individual air parcels will not be presented in this work; but only the time evolution of the distribution of marked air parcels will be shown. The air parcels which are initially placed at the latitude belt between 35 and 40 degrees and at a level of 900mb are treated in order to investigate transport processes in the troposphere. Fig. 1A depicts the instantaneous positions of the marked air parcels at the end of the first month. Fig. 1 The positions of the marked air parcels for Case 1; (A) is at the end of the first month, (B) the third month, (C) the ninth month and (D) the first year. Their initial positions are in the latitude belt (35*-40*) and at 900mb as symbolically marked by xxx in (A).

4 August 1983 H. Kida 513 In this figure, we see that the air parcels According to the results, we see no distinct difference among the distributions of marked air originated near the surface are greatly dispersed throughout the whole extra-tropical troposphere parcels at the three different stages and also from within one month. In the tropical troposphere Fig. 1 A, at least in the extra-tropical region. it is seen that an equatorward movement of This means that the time needed for air parcels marked air parcels only in the lowest layer originating from 900mb at middle latitudes to where the trade wind prevails. The head of the disperse throughout the troposphere is *one equatorward flow has not yet reached the region month, this roughly corresponding to that estimated by Palmen (1951). On the other hand, of upward motion (the ITCZ) in this period. This speed of the equatorward flow may be gradual change of the distribution of air parcels slower compared with that in the actual atmosphere because the simulated zonal-mean meri- steady upward motion takes place. Most of air has proceeded at the tropics where extensive and dional circulation of the Hadley cell seems to parcels which have reached the uppermost troposphere moves poleward to the subtropical region be by a factor of *2 slower than the observed one (as shown in Part 1). where the subtropical jet stream exists. Fig. 1 A shows that the air parcels in the It is noteworthy that some of marked air extra-tropical region are significantly diffused parcels have intruded into the stratosphere crossing the tropical tropopause. Interestingly, such both in the horizontal and vertical directions. It is due both to large-scale quasi-horizontal motion is the primary mechanism for the tropospheric air to enter the stratosphere above eddy diffusion associated with extra-tropical cyclones and to the vertical mixing by the subgridscale motions. On the other hand, advective the subtropics is another route for the tropical 100mb. The major tropopause gap existing * in transports dominant in the tropics except for tropospheric air to enter the extratropical stratosphere. In the latter case, however, the air par- vertical mixing in the ITCZ. It must be noted, however, that there remains a possibility that cels can hardly ascend further to higher levels this result somewhat depends on the GCM used; owing to the overall downward motion in the namely, the model Hadley cell is almost zonally symmetric, but the actual one has remark- return to the troposphere in a relatively short extra-tropical stratosphere and eventually they able longitudinal variation. The difference arises time. Hence, it may be said that the stratosphere mainly from the use of a zonally constant prescribed heating and partly from the equatorial has come there across the tropical tropopause. above *100mb is composed of air parcels which lateral boundary which tends to surpress the In the above simulation, the effect of subgridscale vertical mixing has been taken into ac- development of tropical large-scale disturbances. If the actual Hadley cell is inseparable from count. Without this effect, the movement of air tropical large-scale eddies such as easterly waves parcels would be quasi-horizontal. This is because the large-scale motion is approximately and equatorial waves, horizontal diffusion would be more important in the transport mechanisms adiabatic. In other words, the vertical mixing in the tropics. However, according to studies on of air parcels can hardly occur between two interhemispheric exchange of tracers (e.g., Czeplak and Junge, 1974), the magnitude of the peratures. In fact, another expermient conducted material surfaces having different potential tem- horizontal eddy diffusion coefficient seems to be with no subgrid-scale vertical mixing has shown by a factor of several to ten smaller in the that the time needed for air parcels to be mixed tropics than at middle latitudes. This implies up in the whole troposphere is a few times longer that air mass is not effectively exchange across than that shown in Fig. 1. From this result, it the equator. Consequently, it may be considered can be said that the subgrid-scale vertical motion that the present calculation well simulates trans- plays an important role not only in the vertical port processes in the tropics, though the model fairly exaggerates the advective transport. In Figs.1B-1D, the results obtained by the further integration are shown at each end of the third, sixth and twelveth months. The calculation was performed using the 30 day basic data set repeatedly as mentioned in Part 1. mixing but also in the horizontal mixing through a cooperative effect with the large-scale motions. In the ITCZ, the subgrid-scale vertical mixing dominates the grid-scale upward motion in transports. Namely, the vertical transport process is diffusive rather than advective there. On the contrary, air parcels slowly descend in the sub-

5 514 Journal of the Meteorological Society of Japan Vol. 61, No. 4 tropical region. In this case, the subgrid-scale vertical mixing does not take place because the atmosphere is extremely stable. Thus, in the subtropical region, the vertical transport becomes advective rather than diffusive. 3.3 Case 2: Source at the tropical tropopause The previous simulation has clearly shown that the stratospheric air consists of air parcels which intrude into the stratosphere across the tropical tropopause. Based on this result, a further simulation has been carried out to gain insight into the movements of air parcels after their intrusions. How do they move within the stratosphere? And eventually where do they leave the stratosphere and return to the troposphere? For this purpose, a large number of air parcels are marked which are located at the latitude belt between 2.5* and 7.5* and at the 100mb level, i.e., the place of the tropical tropopuase. The locations of individual marked air parcels are set by using (3,1). The number of them is Fig. 2A shows the instantaneous locations of the marked air parcels at the sixth month, and the others of Fig. 2 depict sequential change for a period of five years at one year interval. In Fig. 2A, it is clearly shown that most of the air parcels spread to higher latitudes in this period, while a certain number of the air parcels continue to stay in the tropical region. The distribution indicates that quasi-horizontal diffusion is remarkable especially in the extra-tropical Fig. 2 The positions of the marked air parcels for Case 2; (A) is at the end of sixth month. (B) to (F) are displayed at one year interval. The initial positions are marked by xxx in (A).

6 August 1983 H. Kida 515 region. As seen in the figure, the air parcels which have reached the extra-tropical region gradually descend with small vertical diffusion and large horizontal diffusion. After that, some of them leave the stratosphere and then merge with the tropospheric air. According to Fig. 2B, about half of the marked air parcels could return to the troposphere across the extra-tropical tropopause within a year. It is notable that a small part of the air parcels re-enter the stratosphere through the upward branch of the Hadley cell. Fig. 2 shows that some air parcels remain in the tropics for a very long time. They slowly ascend there at a constant rate of *5km/year. Some of them leave the tropics little by little due to poleward motions. This is natural in view of mass conservation, i.e., that the air density decreases with increasing height. The magnitude of the advective vertical motion is about one scale height per year. Therefore, the characteristic length of time needed for the stratospheric air to be completely replaced by newly intruding air parcels into the stratosphere from the troposphere is estimated to be about two years. This estimation is verified by the result that about half of marked air parcels of the tropical origin leave the stratosphere to return to the troposphere in a period of one year (Figs. 2A and 2B). However, note that the so-called residense time of an individual air parcel depends on its own history of the trajectory. The major features of the above results agree well with the Brewer-Dobson model. However, it must be noted that the poleward movements of air parcels can not be described only by the Brewer-Dobson circulation but it is greatly affected by the quasi-horizontal eddy diffusion. According to the present simulation, large-scale horizontal diffusive motion of the air parcels occurs nearly on an isentropic surface, probably because the diffusive motion is almost adiabatic for a relatively short time especially in the lower stratosphere. Consequently, diabatic heating/ cooling is considered to be important for the air parcels to move across isentropic surfaces. Thus, it can be said that the transport mechanism in the lower stratosphere is a combination of largescale quasi-horizontal eddy mixing and vertical advection. 3.4 Case 3: Source at the tropical middle stratosphere In order to investigate transport characteristics of tracers such as ozone which are produced (or injected) at the tropical middle stratosphere, air parcels were marked which initially located in the latitude belt between 2.5* and 7.5* and at the 30mb level. The present simulation may be regarded as a continuation of a part of the simulation of Case 2 since the present case corresponds to a further tracing of those air parcels which have ascended from the tropical tropopause to reach the 30mb height in the tropics. Fig. 3 shows the instantaneous positions of the marked air parcels at selected times for five years. According to the results, most of the air parcels moved nearly horizontally toward the pole during the first six months. As shown previously, overall upward and downward movements take place in the tropical and extratropical regions, respectively. It is interesting that the air parcels are certainly dispersed in the vertical direction at the subtropics. The cause of this dispersion can be attributed to the fact that quasi-horizontal eddy motions cause exchanges of air parcels between the two areas with oppositely directed vertical motions. It is important to notice that this vertical dispersion is not due to convective motions but due to a result of coupling between the advective vertical motion and horizontal eddy mixing. Such transport is likely to play a role in vertical mixing of air parcels in the stratosphere and hence could explain the discrepancy between empirically determined eddy diffusivity in 1-D chemical transport modelings and the estimations based on observations of turbulence. As previously seen, some of the air parcels remain in the tropics and continuously ascend there. But, eventually, most of them move toward the pole and then slowly descend in middle and high latitudes. According to Fig. 3C, by the end of the second year more than half of the air parcels have displaced below their initial level, and a small part of them have already reached the bottom layer of the extra-tropical stratosphere. It is found that these parcels took the route mainly through high latitudes. This suggests that tracers originating at the tropical middle stratosphere are first quasi-horizontally transported to higher latitudes and then are transported to lower levels by relatively large descending motion in high latitudes. One of the most interesting results is that in the bottom layer of the extra-tropical stratosphere there exist air parcels which have been

7 516 Journal of the Meteorological Society of Japan Vol. 61, No. 4 transported equatorward from higher latitudes despite that their origin was the tropics. This equatorward movement is due to quasi-horizontal eddy diffusion, and the effect increases with decreasing height. This is presumably because the eddy mixing is caused mainly by the activity of the upward extended part of the tropospheric cyclones. It should be noted again that in the bottom layer most of the air parcels are transported toward the equator from higher latitudes. Therefore, in middle and subtropical latitudes the bottom layer of the stratosphere could contain tracers which have characteristics of tropical origin but was transported from higher latitudes. In this case we must be careful not to interpret that the tracers have been carried directly from the tropical middle stratosphere. Unfortunately, the behaviors of the used GCM is not realistic for the upper stratosphere because of both assumptions of the lateral boundary imposed at the equator and no seasonal change in diabatic forcing. However, when we concern only with the annually averaged transport, the present simulation may be relevant in containing the poleward motion in the upper stratosphere, provided that the cross-equatorial motion observed there in solstice has no contribution to the annually averaged net transport of mass. Anyway, the air density is very small in the upper stratosphere, so that the role played by that layer upon transports in the lower stratosphere is supposed to be small in magni- Fig. 3 The positions of the marked air parcels for Case 3; (A) is at the end of sixth month. (B) to (F) are displayed at one year interval. The initial positions are marked by xxx in (A).

8 August 1983 H. Kida 517 tulle. Mt. El Chichon injected a large amount of dust into the middle stratosphere over the tropics on April 4, The volcanic cloud spread into the high latitude by the end of the year and its column amount shows a latitudinal profile with two peaks; at the equator and pole (e.g., Pollack, 1983). This fact supports our results as shown in Figs. 3(b) and 3(c) when mass density on the meridional section is taken into account, although the tropical peak in the model may be somewhat influenced by the lateral boundary condition there. 4. Statistics of the ages of air parcels in the stratosphere 4.1 Definition o f the age As shown in the previous simulations, the main part of the stratospheric air (above *100 mb) consists of air parcels entering the stratosphere across the tropical tropopause. Most of the air parcels tend to move poleward owing to the mean meridional flow as well as to the large-scale eddy diffusion and return to the troposphere passing through the bottom layer of the extra-tropical stratosphere. Since the largescale eddy diffusion is significantly strong, the movements of individual air parcels are not so simple but scattered around the mean advective flow. The influence of the random eddy motions upon the movements of air parcels has been shown in the fact that some air parcels continue to remain in the tropical region for a long time, while the major part of the air parcels with the same origin follow the average motion toward the pole. It is notable that in the extratropical region a small part of the air parcels can may move equatorward, i.e., in the opposite direction of the mean poleward flow in the lower stratosphere. Let us consider the histories or the experiences of various air parcels within the stratosphere. For instance, what route has an air parcel taken to arrive at the place where it is after leaving the tropical tropopause? If only a stationary mean circulation is responsible to the movements of air parcels, the question could be easily answered. The past position of an air parcel could be completely determined by tracing back in the opposite direction along the streamline. In the presence of eddy diffusion, however, it becomes imposible to know the individual history of air parcels deterministically. Therefore, the history of an air parcel in the stratosphere must be described in a statistical form. In order to describe the history of the stratospheric air parcels, we will employ the following method. First, consider a rectangular domain in the meridional plane bounded by two latitudes and two heights as shown in Fig. 4. Hence this is a torus in the 3-D space. Such a tours will be referred to as `box' hereafter. We assume that the meridional cross sectional area of a box is small compared with the whole stratosphere, but a box can contain a large number of air parcels as a 3-dimensional torus. Undoubtedly, each of air parcels existing in a box has its own history to become a constituent of the box. Therefore, the time elapsed till the air parcel arrives at the box is different from one to another. We will define the length of time elapsed since the concerned air parcel entered the stratosphere as the `age' of the air parcel. For instance, consider the box A in Fig. 4 which is located at the tropics. Most of the air parcels in the box A may be those which have Distribution of Elapsed Time Fig. 4 A conceptual explanation for the spectrum of the age.

9 518 Journal of the Meteorological Society of Japan Vol. 61, No. 4 been lifted up by the mean ascending motion there, so that the ages of them must be almost the same. On the other hand, the box B which is located at middle latitudes may contain air parcels having various ages; some air parcels may have taken the nearest way to reach the box B by the horizontal eddy diffusion and others may have taken other routes once reaching much higher levels by the mean upward motion. In this case, the distribution of the ages of the air parcels is supposed to be broad, while in the box A the distribution must have a narrow peak. 4.2 Determination of the age distributions (age spectra) As explained above, if we consider a fixed box in the stratosphere, the box contains many air parcels having various histories and various ages, so that the age of the air in the box cannot be uniquely determined. It seems more appropreate to treat the distribution function n(*), of ages of the air parcels in the box, where n is the number of air parcels whose age is *. For simplicity's sake, we shall call this function age spectrum hereafter. For determining n(*), the simplest and most straightforward method is to compute ages of all air parcels existing in the box by tracing them backward until they return to the troposphere passing across the tropical tropopause. However, this method is not economical in computation, if we want to calculate n(*) for many boxes in order to obtain the age spectrum distribution in the whole stratosphere. Fortunately, we can determine n(*) simply from the time series of the number of marked air parcels counted at a fixed place as explained below. Let us consider an experiment to trace marked air parcels, similar to the present experiment except that air parcels are marked continuously at the entrance to the stratosphere (tropical tropopause), and the mark carries information about the entry time. If such an experiment has been done we can obtain the number of air parcels, N(t, t0) which are existing in the specified box at a given time t and have an entry time t0. Then the age spectrum is readily found to be As seen above, N is generally a function of t, and the spectrum may change depending upon the observation time t. However, if the circulation is (statistically) stationary, N does not depend on the choice of the initial time, i.e., the following relation holds for any T. This relation ensures that n(*) given by (4.1) is independent from t. Applying the above relation to (4.1) with a time shift *, we now have Thus it is possible to obtain the age spectrum by counting the number of air parcels (in the box) which have the same enntry time as a function of observation time (or arrival time), instead of counting the number of air parcels at the same observation time as a function of entry time. The above described procedure is rather easily applied to the present experiment. Namely, we can obtain n(*), simply by obtaining the time series of the number of the marked air parcels contained in the box under consideration. Note that all the marked air parcels have the same entry time. In principle, the size of the boxes must be infinitismal. But, since the number of marked air parcels is not infinite, we will deal with fairly large boxes. The two sides of the rectangle were taken to be 5 degrees and 1km. The number of marked air parcels was This is ten times larger than those treated in the previous simulations. The initial positions of them were the same as those in Case 2. This means that in the present analysis the origin of the stratospheric air is assumed to be the tropical tropopause. Since rapid horizontal dispersion of marked air parcels occurs in the initial stage, the present simulation may be considered to be nearly equivalent to that they are initially placed in a latitude belt wider than the 2.5*-7.5* belt. In this sense, we should say that the source of the stratospheric air is not narrow but wide area over the tropics. It must be noted that some part of the air in the bottom layer of the extratropical stratosphere may be supplied from the tropical troposphere passing through the major tropopause gap in the subtropics. Therefore, we must be cautious in the ages of the air in the bottom stratosphere. 4.3 Results Using the five year records of trajectories of marked air parcels, the spectra of the ages have been determined for selected boxes. The results are shown in Figs In this analysis, the

10 August 1983 H. Kida 519 number of the air parcels was counted at one month interval. Fig. 5 describes the age spectra for boxes at 5*-10* latitude and at several selected levels. This shows a remarkable feature that all the peaks are sharp except for the lowest box placed within the troposphere. As expected before, these sharp peaks are formed by a group of air parcels which have entered the stratosphere at the same time. Conversely, this sharpness implies that the age of an air parcel can be well defined. Such property is contrasting to that in middle latitudes as will be described later. Because of the low resolutions of the spatial and time increments, most of the air parcels forming the sharp peak continue to stay in the Fig. 5 The spectra of the ages for the tropics. Note that the shaded part is due to those which have once entered the troposphere and, after a long time, re-entered the stratosphere or remained in the troposphere. box for a certain time until they leave the box across its upper boundary. During the time while the collective air parcels are passing the boundary, they are divided into the two adjacent boxes. This effect tends to make the peak apparently broader. According to the results, the pretty sharp peak continuously move upward at a speed of *5km per year in the tropics. It is interesting to see characteristics of the age spectrum below the tropical tropopause (the bottom diagram of Fig. 5) which are quite different from those seen in the stratosphere. The spectrum rises at the end of the first year and gradually increase until 1.5 year and, after that, it attains a nearly * constant level. There is no peak for the whole time. This implies that the gradual increase is caused by a balance between gradual downward intrusion of the marked air parcels into the troposphere and considerably rapid mixing within the troposphere. Eventually, after years, most of marked air parcels located at the tropical tropopause at the initial time have left the stratosphere. As a result, the tropospheric air has a constant mixing ratio of the marked air parcels and the spectrum becomes almost constant after the second year, implying that the characteristic length of time for marked air parcels to stay in the stratosphere is years. This value is consistent with the estimation of the residence time previously made from the speed of the vertical mean motion. In the spectra there are a few minor peaks in the tail of longer ages. These peaks and also the tail itself are formed mainly by two causes. One is numerical noise originated from the insufficiency of the number of marked air parcels and the other is the manifestation of the real physical process that some of the marked air parcels have re-entered the stratosphere across the tropical tropopause after they stayed in the troposphere for a certain period. This part of air parcels should be excluded from the present analysis. Therefore, the part to be excluded are shaded in the spectra. The tails of the spectra become nearly constant. This implies that a state of complete mixing of the marked air parcels is realized. In this case the number of the marked air parcels should be proportional to the air density. This appears correct in our results shown in Fig. 5. In Fig. 6, we shall look into the features of the ages at middle latitudes. In this region, the

11 520 Journal of the Meteorological Society of Japan Vol. 61, No. 4 Fig. 6 The same with Fig. 5 except for middle latitudes. Fig. 7 The same with Fig. 5 except for the polar region. age spectra are not so sharp as those in the tropical region and have long wings outside the main peaks. This implies that the trajectories of the air parcels are significantly affected by eddy diffusion and the air in the lower stratosphere is a mixture of old and new stratospheric air parcels. The brodening tendency of the spectrum increases with increasing altitude, because the higher the location of the box, the larger the number of possible routes for air parcels to reach the place. At the level of 16-17km, the major features of the spectrum are almost the same as those at higher levels, although in the tropical case this level belongs to the upper troposphere. It is noteworthy that the bottom layer of the extra-tropical stratosphere contains many air parcels with ages shorter than half year. Fig. 7 describes the age spectra of the polar stratospheric air. In the polar region the spectra having any peaks are limited to levels below 20km. Generally, the spectrum tends * to be extremely broad and almost flat. This suggests that the polar stratosphere is composed of relatively old stratospheric air parcels. We shall examine the route of those air parcels which reach the higher levels in the polar region. We remind that there are some air parcels trapped in the tropical region for a very long time. According to the present simulation these air parcels ascend there at a speed of 5km per year. Hence, the length of time * needed for an air parcel to attain the middle level of the polar stratosphere becomes *2.5 years or more. Some air parcels may take a zigzag route. In this case, they need a longer time to attain there. However, it must be reminded that in the actual upper stratosphere there exists the interhemispheric meridional circulation with a significant speed, which trans-

12 August 1983 H. Kida 521 ports the equatorial air parcels to the polar region within a period shorter than that shown by the present simulation. Therefore, it remains to be solved whether the obtained extreme flatness of the spectrum is the case or not. It is also noted that the peak age gradually shifts to older side with increasing altitude. This suggests that the peak (i.e., the characteristic age of the air) is controlled mainly by means ascending motion in the tropical region. 5. Summary The very long-term motions of air parcels have been analyzed using a simulated general circulation of the atmosphere with a wholehemispheric model. The results show that the meridional movements of tropospheric air parcels are driven mainly by the synoptic-scale cyclones in the extra-tropical region and by the Hadley circulation in the tropics. The vertical diffusion due to the subgrid-scale convections contributes greatly to mixing in the vertical direction and further it significantly stimulates large-scale horizontal mixing of air parcels. It has been shown that the characteristic time scale of the diffusion equilibrium is less than one month for the troposphere except for the tropical region. The present simulation has confirmed the reality of the Brewer-Dobson's idea for the stratospheric transport. Namely, tropospheric air parcels enter the stratosphere mainly across the tropical tropopause. Within the lower stratosphere most of those air parcels move toward the pole and gradually descend in the extratropical region and eventually return to the troposphere. However, some fraction of the air parcels remain in the tropics for a long time and continue to ascend to the upper stratosphere there. In addition to this Brewer-Dobson circulation, large-scale eddy diffusion is remarkable in the horizontal motion of air parcels. Such eddy diffusion seems to be much effective than the meridional advection. Based on these results, a schematic model is displayed in Fig. 8. In the present analysis the effect of the subgrid-scale vertical mixing was not incorporated for the stratosphere. In spite of this, significant vertical diffusion of air parcels occured in the model lower stratosphere. That vertical diffusion can be attributed mainly to a coupling between the B-D circulation and horizontal eddy diffusion; namely, the air parcel moving along Fig. 8 (Upper); A schematic model for major modes of transport mechanisms in the atmosphere. The thick solid lines show advective motion. The solid and broken arrows stand for large-scale quasi-horizontal diffusion and small-scale vertical diffusion, respectively. The thick broken lines are approximate tropopauses. (Lower); A schematic representation for trajectories of individual air parcels. a streamline of the B-D circulation can be transferred to another streamline by eddy diffusion. It suggests that the vertical diffusions of any tracers in the stratosphere can take place even if there is no explicit mechanism of the vertical diffusive adiabatic motions such as turbulence or waves with large-amplitude. On the other hand, in the troposphere the explicit vertical diffusion is very large due both to the large-scale slanting motions associated with cyclones and to the small-scale vertical convections. Accordingly, those vertical diffusive transport plays an important role in vertical mixing within the troposphere. In order to interpret the overall features of

13 522 Journal of the Meteorological Society of Japan Vol. 61, No. 4 the meridional distributions of stratospheric tracers, it is very convenient to use the concept of the `age' of the air. The so-called residence time is usually defined as the average of the time needed for air parcels (or any tracers) to stay in the stratosphere. In this paper, the `age' of an air parcel is defined as the time needed for an air parcel to arrive at a place since its intrusion into the stratosphere. Thus, it is a function of place within the stratosphere. The age of an air parcel can be described in terms of the spectrum of the ages because there are many routes for air parcels to go to a place after entering the stratosphere through the tropical tropopause. Calculating the trajectories and ages of a very large number of marked air parcels, the spectrum of the ages has been determined. We may interpret the spectrum as the probability density about the age of one of air parcels contained in air mass having a finite volume. Thus, the spectrum represents the age of the air mass at a place in a statistical form. The results show that the spectrum of the ages in the tropical region has a fairly sharp peak, while in the polar region it becomes broad and its peak shifts to the older ages. This means that the age of air mass increase with increasing height and latitude. Namely, the air mass in the tropical and lowest stratosphere is relatively newer but that in the polar and higher stratosphere is relatively older. Such interpretation immediately leads to the conclusion that any conservative tracers produced in the upper stratosphere should be more abundant in the `older' stratosphere than in the `newer' stratosphere. Conversely, those which originate from the troposphere and are photochemically unstable only in the upper stratosphere tend to be trapped in the `newer' stratosphere. Acknowledgements The author gratefully acknowledges the benefit of a number of helpful discussions with Dr. T. Shimazaki and Prof. T. Matsuno. The author's thanks are extended to Prof. J. R. Holton and Dr. T. Dunkerton for their valuable comments to the first version of this paper. This work was partly supported by NASA and NRC, Washington, D.C.. The main part of the present analysis was done using the electronic computer HITAC M-200H at MRI. References Brewer, A. W., 1949: Evidence for a world circulation provided by the measurements of Helium and water vapour distribution in the stratosphere. Quart. J. Roy. Met. Soc., 75, Czeplak, G., and C. Junge, 1974: Studies of interhemispheric exchange in the troposphere by a diffusion model. In Advances in Geophysics, vol. 18B, Academic Press (New York), Dobson, G. M. B., 1956: Origin and distribution of polyatomic molecules in the atmosphere. Proc. Roy. Soc. London, A. 236, Danielsen, E. F., 1982: A dehydration mechanism for the stratosphere. Geophy. Res. Lett., 9, Dunkerton, T., 1978: On the mean meridional mass motions of the stratosphere and mesosphere. J. Atmos. Sci., 35, Holton, J. R., 1981: An advective model for twodimensional transport of stratospheric trace species. J. Geophys. Res., 86, Kida, H., 1983: General circulation of air parcels and transport characteristics derived from a hemispheric GCM. Part 1. A determination of advective mass flow in the lower stratosphere. J. Meteor. Soc. Japan, 61, and T. Shimazaki, -, 1983: In preparation. Matsuno, T., 1980: Lagrangian motion of air parcels in the stratosphere in the presence of planetary waves. Pure Appl. Geophys., 118, Newell, R. J., and S. Gould-Stewart, 1981: A stratospheric fountain? J. Atmos. Sci., 38, Palmen, E., 1951: The role of atmospheric disturbances in the general circulation. Quart. J. Roy. Met. Soc., 77, Pollack, J. B., 1983: Private communication. Reed, R. J., and F. Sanders, 1953: An investigation of the development of a mid-tropospheric frontal zone and its associated vorticity field. J. Meteor., 10, , and E. F. Danielsen, 1959: Fronts in the vicinity of the tropopause. Arch. Met. Geoph. Biokl., A. Bd. 11, H.1, Riehl, H., and J. S. Malkus, 1958: On the heat balance in the equatorial trough zone. Geophysica, 6, Staley, D. O., 1960: Evaluation of potential-vorticity change near the tropopause and the related vertical motions, vertical advection of vorticity, and transfer of radioactive debris from stratosphere and troposphere. J. Meteor., 17,

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