A Lagrangian description on the troposphere-to-stratosphere transport changes associated with the stratospheric water drop around the year 2000

The sudden decrease in stratospheric water vapor at around the year 2000 to 2001 is relatively well accepted in spite of the difficulty to quantify the long-term variations. This stepwise change is studied by examining the entry value of water to the stratosphere ([H2O]e) and some Lagrangian diagnostics of dehydration taking place in the tropical tropopause layer (TTL). The analysis is made using the backward kinematic trajectories initialized every ∼ 10 days from January 1997 to December 2002 at 400 K potential temperature surface in the tropics. The [H2O]e is estimated by the ensemble mean value of the water saturation mixing ratio (SMR) at the Lagrangian cold point (LCP) where SMR becomes minimum (SMRmin) in the TTL before reaching the 400 K surface. The drop in [H2O]e is identified to have occurred in September 2000. The horizontal projection of September trajectories, tightly trapped by anticyclonic circulation around the Tibetan high, shows eastward expansion since the year 2000. Associated changes are measured by three-dimensional bins, each having the dimension of 10 longitude by 10 latitude within the TTL. The probability distribution of LCPs shows an appreciable change exhibiting a composite pattern of two components: (i) the dipole structure consisting of the decrease over the Bay of Bengal and Malay Peninsula and the increase over the northern subtropical western Pacific and (ii) the patterns of the decrease over the equatorial western Pacific and the increase over the central Pacific that are almost symmetric with respect to the Equator. The SMRmin shows a general decrease in the tropics with some enhancement in the central Pacific. The expectation values, defined by the multiple of the probability of LCP events and the ensemble mean values of SMRmin, are calculated on each bin for both periods prior and posterior to the drop. These values are the spatial projection of [H2O]e on an individual bin. The results indicate that the drop is brought about by the decrease in water transport borne by the air parcels that have experienced the LCP over the Bay of Bengal and the western tropical Pacific. The former is related to the eastward expansion of the anticyclonic circulation around the weakened Tibetan high, while the latter would be linked to the eastward expansion of western tropical warm water to the central Pacific. This oceanic surface forcing may be responsible also for the modulation of dehydration efficiency in the successive northern winter. The drop in September 2000 and the sustained low values thereafter of [H2O]e are thus interpreted as being driven by the changes in thermal forcing from the continental and oceanic bottom boundaries.


Introduction
Stratospheric water vapor (SWV) observed by balloon-borne hygrometers exhibits gradual increase 30 in the 1980s and 1990s (Oltmans and Hofmann, 1995;Oltmans et al., 2000) followed by a stepwise drop at around the year 2000 (Scherer et al., 2008;Fujiwara et al., 2010). Since SWV has a positive radiative forcing as a greenhouse gas (Shindell, 2001), its possible increase during the two decades could have caused enhanced surface warming by about 30 % as compared to that without taking this increase into account, while the subsequent drop could have slowed down the surface warming by 35 about 25 % from about 0.14 to 0.10 • C per decade (Solomon et al., 2010). The cause and mechanism of this stepwise change have been fluently discussed (e.g., Randel et al., 2006;Rosenlof and Reid, 2008;Bönisch et al., 2011;Fueglistaler, 2012;Fueglistaler et al., 2014;Dessler et al., 2014). While constructing a reliable long-term SWV record is still a challenge (Hegglin et al., 2014), the understanding of a possible stepwise change in SWV is required in assessing possible modulation of the 40 Brewer-Dobson circulation under global warming.
The variation of SWV is driven dynamically by the troposphere-to-stratosphere transport of water and chemically by the oxidation of methane. The dynamical control is mostly associated with the efficiency of dehydration functioning on the air mass advected in the TTL (Holton and Gettelman, 2001;Hatsushika and Yamazaki, 2003). The Lagrangian description of the transport processes in the 45 tropical troposphere to the stratosphere using trajectory calculations proved to be quite effective not only in the reproduction of SWV variations but also in the characterization of the dehydration processes in the TTL (e.g., Bonazzola and Haynes, 2004;Fueglistaler et al., 2004Dessler et al., 2014) even though the quantitative estimation of the water amount entering the stratosphere requires detailed consideration dealing with aerosols and ice particles (ice nucleation and sublimation 50 processes, supersaturation, and deposition and precipitation of ice particles) as well as the minute description of meteorological conditions (subgrid-scale variabilities, intrusion of deep convection into advected air parcels, and irreversible mixing due to breaking waves along with the ambiguity in the analysis field).
Here, we discuss the cause of the stepwise drop in SWV by making the analysis of the entry 55 mixing ratio of water to the stratosphere ([H 2 O] e ) with the aid of some Lagrangian diagnostics of TTL dehydration such as the preferred advection pathways in the TTL, the location in which water saturation mixing ratio (SMR) takes minimum along each trajectory (Lagrangian cold point; LCP) together with the minimum value (SMR min ) before entering the stratosphere (Sect. 3). The backward kinematic trajectories initialized on 400 K potential temperature surface in the tropics, similar 60 to those of , are used. The calculations cover the period from January 1997 to December 2002. The statistical features of the LCP and SMR min are analyzed for the 90 day trajectories in which the air parcels experienced LCP in the TTL (Sect. 2). The analysis is focused on the examination of the entry value of water to the stratosphere, meaning that any contribution from the recirculation within the stratosphere (ST) and the sideway entry of water to ST without 65 taking the LCP in the TTL are intentionally left out of the scope. Detailed examinations on the driving mechanism itself are left for future studies. However, such a restriction will serve to focus our investigation on some specific processes that may have led to the SWV drop in Lagrangian framework. This approach has an advantage over Eulerian description because the drop in SWV does not necessarily mean TTL cooling conveniently described in Eulerian framework. For example, it might 70 simply reflect the change in the proportion of air parcels that have passed the coldest region in the TTL. Conversely, any extreme cooling does not necessarily result in enhanced dehydration as long as the air parcels do not experience LCP event in that region. We will try to describe a hypothetical story on the cause of the stepwise drop of SWV through the discussion of the results in Sect. 4.
Conclusions are placed in Sect. 5. The method of estimating [H 2 O] e in the present study is similar to that of .
[H 2 O] e at time t is estimated as the ensemble mean value of SMR min along 90 day backward kinematic trajectories initialized at t. The backward trajectory calculations are started from uniformly 80 distributed gridpoints (every 5.0 • longitude by 1.5 • latitude) within 30 • N and S from the equator on 400 K potential temperature surface. The initializations are made on the 5th, 15th, and 25th of every month during the period since January 1997 till December 2002 relying on the European Centre For Medium-Range Weather Forecasts ERA Interim dataset (Dee et al., 2011). The number of initialization points is 2952 for a single calculation resulting in 8856 for the estimation of monthly 85 values. This number compares well with that of the reduced set of trajectories in the study on the sensitivity of number of trajectories by Bonazzola and Haynes (2004) and turned out to be enough to derive statistically significant results as can be seen later in Section 3. All meteorological variables given on 60 model levels have been interpolated to those on 91 pressure levels keeping the horizontal resolution of 0.75 • by 0.75 • longitude-latitude gridpoints prior to calculations. The time step has 90 been set to 30 minutes, similar to 36 minutes taken by Bonazzola and Haynes (2004), by applying spatiotemporal interpolations to the 6-hour interval ERA Interim dataset. As for the limitation and caution of this method, see, for example, the pioneering studies by Fueglistaler et al. (2004) and Bonazzola and Haynes (2004).

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The meridional projections of the backward trajectories extracted from those initialized on 15 January 1999 are shown in Fig. 1. The top and bottom diagrams are the same except that pressure (top) and potential temperature (bottom) are taken as the ordinate. The asterisks in red indicate the location of the LCP while those in green are the termination point of trajectory calculations (90 days before initialization at the longest). In case the backward extension of the trajectories hit the surface 100 of the earth, the calculations are terminated at that point, and those portions of the trajectories immediately before the surface collision are used for the analysis. The migration of air parcels depicted in the trajectories is roughly categorized into three major branches: quasi-isentropic advection in the TTL and the lower stratosphere (LS), vertical displacement in the troposphere due to diabatic motion resolvable in grid-scale velocity field, and quasi-isentropic migration in the troposphere. We 105 can see many air parcels are traced back to the troposphere representing the tropical troposphere-tostratosphere transport (TST), while some portion of the trajectories remain in the LS and/or reach the tropical 400 K surface by taking the sideways without making excursions in the TTL. All non-TST trajectories are removed from the following analysis to focus our discussion on the modulation of For the sake of clarity, the TST particles in the present study are defined as a subset of those 110 particles traceable down to 340 K having recorded LCP in the TTL. For the application of this LCP condition to our trajectories, we introduce the Lagrangian definition of the TTL to assure internal consistency of the analysis.
The motion of air parcels ascending in the tropical troposphere is characterized by rapid convective up-lift that accompanies latitudinal migration associated with the seasonal displacement of the Inter-115 Tropical Convergence Zone. Up in the TTL, on the other hand, the diabatic ascent is driven by radiative heating, in which the seasonal migration with respect to latitude is much smaller than that in the troposphere because the dynamical field generated by the thermal forcing at the bottom boundary retains relatively high symmetry with respect to the equator. By translating these features into the characteristics of trajectories, we derive a definition of the TTL in a Lagrangian fashion. 120 Figure 2 on the top illustrates the vertical distribution of the proportion of trajectories categorized on a daily basis as "fast" ascending air parcels. The required rate for the fast ascent is empirically set to more than 0.2 K in potential temperature within 1 time step (30 min), that is, the condition for θ K isentrope is met if the air parcel crosses θ K surface from below θ − 0.1 K to above θ + 0.1 K in 30 min. We can see that the proportion of the fast diabatic ascent thus defined takes maximum 125 at around 340 K in the troposphere and minimum at around 355 K. The proportion of such "fast" air parcels reduces above the level of main outflow and rapidly goes to near zero toward the level of zero net radiative heating in the TTL. Above this level, the air parcels are diabatically lifted up by radiative heating and further pumped-up by dissipating planetary waves in the midlatitude stratosphere (Holton et al., 1995). The alternation of the primary forcing that drives diabatic ascent 130 is also seen from the bottom panel of Fig. 2, which shows the seasonal migration of the latitudinal position of the trajectories traceable to down below 340 K averaged for (blue) January, (green) April, (yellow) July, and (red) October. The altitude of the kink at around 355 K suggests that the influence of tropical convective motion almost ceases at this level and the diabatic forcing gradually shifts to radiative heating in the TTL and above.

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The diagnostic features depicted in Fig. 2 agree that the bottom of the TTL would be most properly defined at 355 K potential temperature level for our study. In the following analysis, we make use of TST trajectories defined by the air parcels that have ascended from the lower troposphere below 340 K isentrope experiencing the LCP in the TTL, which is defined by the layer between the isentropic levels 355 and 400 K within 30 • N and S from the equator.

The drop in [H 2 O] e
The calculations are made on a monthly basis using the three initialization days (5th, 15th and 25th of each month) at a time. The following description refers to a specific month omitting the suffix for time. Let start by assuming that the minimum saturation mixing ratio along i-th TST trajectory 145 (i = 1, · · · , N TST ) is denoted by SMR min i . The entry value of water to the stratosphere [H 2 O] e is defined as the ensemble mean value of SMR min as in :

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The shift in the circulation pattern of air parcels is not enough to characterize the modification of dehydration efficiency in the TTL. To quantify the change in the LCP distribution associated with the modal shift seen in Fig. 4, the numbers of LCPs are counted by every 10 • longitude-latitude bin in the tropics. The probabilities of LCPs are estimated for each bin by dividing the LCP counts by the total number of TST trajectories.

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Let assume that i-th TST trajectory (i = 1, · · · , N TST ) takes minimum saturation mixing ratio (SMR min i ) at bin j (j = 1, · · · , M ), that is, the Lagrangian cold point (LCP) for i-th TST trajectory is found at bin j. If we denote the number of LCP events at bin j as N (LCP ∈ j), Because some trajectories do not satisfy the TST condition in general, N TST ≤ N , where N is the 190 total number of initialization points used for the calculation. The probability of LCP events at bin j, so that the normalization condition

Statistical change in the SMR min
The increase of the LCP events in some bins does not necessarily mean enhanced dehydration over 220 there. The next step is to examine the change in the SMR min . This corresponds to focus on the change in "the temperature effect" of Bonazzola and Haynes (2004). Simultaneous with counting the LCP events, the values of SMR at the time of each LCP event (SMR min ) have been summed-up to calculate the average for each bin. The ensemble mean value of SMR min at bin j, SMR(LCP∈ j), where LCP∈j ∑ i indicates the sum with respect to the subset of TST trajectories that take LCP at bin j. We can see that the averages of SMR min in the tropics are roughly smaller in the eastern than in the western hemisphere accompanying a broad minimum of about 3.5 to 3.7 ppmv over the maritime 230 continent during the period prior to the drop ( Fig. 6(a)). The values show general decrease in the tropics with some enhanced drop in the central Pacific reaching less than 3.0 ppmv in the period posterior to the drop ( Fig. 6(b)). The gross features correspond well to the horizontal distribution of the LCP-averaged SMR of July/August 2001 estimated by Fueglistaler et al. (2004). The difference between the two periods ( Fig. 6(c)), together with the statistical significance ( Fig. 6(d)), confirms the 235 pronounced decrease of SMR min in the central Pacific after 2000. On the other hand, the change of SMR min associated with the east-west dipole structure is not so remarkable in terms of the difference of SMR min , although the tendency is the same.

Statistical change in the expectation values
While the differences of SMR min appear smaller over the Bay of Bengal and Malay Peninsula than   (Fig. 7(a)). The contribution from this core area remains dominant during the posterior period ( Fig. 7(b)). While the reduction of [H 2 O] e cannot be 260 free from the general cooling (lowering of SMR(LCP∈ j)) in posterior years over most of the tropics (Fig. 6), it is interesting to note the increase of E(LCP ∈ j) despite the decrease in SMR(LCP∈ j) over the central Pacific. This is because the increase of P (LCP ∈ j) more than compensate for the decrease of SMR(LCP∈ j) over there. In this sense, it is not appropriate to attribute the cooling over  (Fig. 4).

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This modal shift appears as decreases in the probability distribution of the LCP over the Bay of Bengal and the western tropical Pacific (Fig. 5). The SMR averaged on the occasion of LCP events (SMR min ) shows general decrease with some enhancement in the central Pacific (Fig. 6). These from the equatorial ocean. The regional contribution to [H 2 O] e , quantified by E(LCP ∈ j), shows distinct decrease in two regions; one over the Bay of Bengal and the other over the equator in the western tropical Pacific (Fig. 7(c)). The former will be related to the weakening of Tibetan high, while the latter may imply the modulation of the Matsuno-Gill pattern (Matsuno, 1966;Gill, 1980), although these will not be independent between each other. The results indicate that the drop is 320 brought about by a response of the TTL circulation to the modulated forcing both from the continental summer monsoon and the equatorial ocean. It is thus quite interesting to take a brief look at the changes in the TTL meteorological fields in Eulerian framework before concluding this study. with additional heating to the subtropical Northern Hemisphere (Matsuno, 1966;Gill, 1980). The 335 difference ( Fig. 9(e)) indicates substantial cooling in the northern subtropics at around 150 • E and the central Pacific. The latter corresponds to the findings of Rosenlof and Reid (2008)  Kelvin wave response to underlying convective heating (Hatsushika and Yamazaki, 2003). Thus the notion by Rosenlof and Reid (2008) suggests that the SWV drop in 2000 is driven by some dynamical process that accompanies the generation of Matsuno-Gill pattern. This is consistent with the recognize the dipole structure, that is, the paired increase and decrease, in E(LCP ∈ j) over the equatorial Pacific (Fig. 7). The modified pathway of TTL trajectories, resulted in the reduction of LCP probabilities over the Bay of Bengal and the western tropical Pacific (Fig. 5), is quite important.
The study by Young et al. (2012), discussing the changes in the Brewer-Dobson circulation during the period 1979 to 2005 by referring to the out-of-phase temperature relationship between the trop-uniform component exhibiting the out-of-phase relationship between the tropics and the extratropics in 100 hPa temperature difference (Fig. 9) (Randel et al., 2006) through wave-driven pumping (Holton et al., 1995). Actually the analysis of dynamical fields such as eddy heat flux and EP-flux by Fueglistaler (2012) (Plumb and Bell, 1982;Hasebe, 1994). What is interesting here is 380 that the enhanced upward motion is found in September and October 2000 blocking the downward propagation of easterlies. The limitation from our use of Eulerian vertical velocity, rather than TEM residual velocity, will be minimal as we focus our discussion in the tropics. Actually the anomalies in the equatorial upwelling at 78 hPa estimated by Rosenlof and Reid (2008) show similar results. In addition, the sustained low values of [H 2 O] e after September 2000 need some mechanism that lasts longer than the seasonal time scale, since the modulation of Tibetan high cannot explain the reduction continuing to the successive months in northern winter (Fig. 3). Figure 12 is the same as Fig. 7 except that the January projection is illustrated. We can see, in addi-405 tion to the values generally lower than those in September, the larger values are found in the western tropical Pacific (Fig. 12(a), (b)), indicating the January values of [H 2 O] e are controlled by those over the western Pacific. This is consistent with the picture having been presented in numerical simulations (Hatsushika and Yamazaki, 2003). The difference between the two periods ( Fig. 12(c)) shows decrease over Indonesia and increase over the central Pacific during the period posterior to the drop.

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The former is due to the combination of the decreases in both P (LCP ∈ j) and SMR(LCP∈ j), while the latter is brought about by the interplay between the increase in P (LCP ∈ j) and some decrease of SMR(LCP∈ j) (not shown). This situation is the same as what we see in September (Section 3.5).
The similarity of this pattern, that is, the decrease in the equatorial western Pacific (over Indonesia) and the increase over the central Pacific, to that of the second component of September response Bengal and the western tropical Pacific (Fig. 7).
The above speculation might end up with some proper explanation on the cause of the eastward expansion of the equatorial warm water to the central Pacific observed in 2000. In this context, it is interesting to see possible occurrence of "El Niño Modoki" characterized by the warm SST event over the central Pacific (W. J. Randel, personal communication, 2015). Actually the time series of 435 normalized ENSO Modoki index of Ashok et al. (2007) turns from prolonged negative to positive towards 2001. It is also interesting to note that the "La Niña-like condition," tied to the surface cooling of the equatorial eastern Pacific, is supposedly responsible for the recent hiatus, the pause of the global-mean surface air temperature rise (Kosaka and Xie, 2013;Watanabe et al., 2014). If proved to be true, we may have unveiled another piece of pathways the internal variability of our 440 climate system could exert on the surface cooling through SST-driven SWV fluctuations.

Conclusions
Backward kinematic trajectories, initialized on 400 K potential temperature surface in the tropics, Let the random variable, X, is the number of event occurrences in some number of trials, n. The binomial distribution can be used to calculate the probabilities for each of n + 1 possible values of 460 X (X = 0, 1, · · · , n) if the following conditions are met: (1) the probability of the event occurring does not change from trial to trial, and (2) the outcomes on each of the n trials are mutually independent. These conditions are rarely met, but real situations can be close enough to this ideal that the binomial distribution provides sufficiently accurate representations. The probability that the number of occurrence X is x among n trials, Pr(X = x), follows the binomial distribution where p is the probability of occurrence of the event.
The statistical test for the difference in the population proportion of two binomial populations, p 1 − p 2 , could be made as follows. Let the sample size and the sample proportion of the two sets being n 1 and n 2 and m 1 /n 1 and m 2 /n 2 , respectively. The test statistic, T 1 , defined by follows approximately the standard normal distribution. The statistical test for the difference between P (LCP ∈ j) in prior and posterior periods could be done by applying the two-sided tests under the null hypothesis of p 1 − p 2 = 0 at some significance level α, where p 1 and p 2 are the population proportion of LCP taking place at bin j in the posterior and prior to the drop, respectively. In our 475 case, n 1 and n 2 , and m 1 and m 2 , are N TST and N (LCP ∈ j), respectively, for posterior (suffix 1) and prior (suffix 2) periods.
Here, n 1 and n 2 , x 1 and x 2 , and s 2 1 and s 2 2 are the sample size, the sample mean, and the unbi-485 ased sample variance, respectively, of the two sets. The statistical test for the difference between SMR(LCP∈ j) in prior and posterior periods could be done by applying the two-sided tests under the null hypothesis of µ 1 − µ 2 = 0 at some significance level α. In our case, n 1 and n 2 , x 1 and x 2 , and s 2 1 and s 2 2 are N (LCP ∈ j), SMR(LCP∈ j), and the unbiased variance of SMR min at bin j, respectively, for posterior (suffix 1) and prior (suffix 2) periods. (b) Figure 2. The vertical profiles of (a) proportion of the "fast" ascending air parcels and (b) averaged ascending track diagnosed by 90 day kinematic back trajectories that extends from 400 K to the lower troposphere below 340 K potential temperature surface. The upward motion on θ K isentrope is categorized as "fast" if the air parcel crosses θ K surface from below θ − 0.1 K to above θ + 0.1 K in 30 min. Each line in (a) shows the daily proportion of trajectories at each isentropic level that correspond to "fast" ascending air parcels. The ascending tracks in (b) are color-coded on a monthly basis (January in blue, April in green, July in yellow, and October in red) to visualize the seasonal migration of the ascending latitude in the tropics.