The impact of temperature vertical structure on 1 trajectory modeling of stratospheric water vapour 2

Lagrangian trajectories driven by reanalysis meteorological fields are frequently used to 13 study water vapour (H 2 O) in the stratosphere, in which the tropical cold - point 14 temperatures regulate H 2 O amount enterin g the stratosphere. Therefore, the accuracy of 15 temperatures in the tropical tropopause layer (TTL) is of great importance for 16 understanding stratospheric H 2 O abundances . Currently, most reanalyses, such as the 17 NASA MERRA (Modern Era Retrospective-Analysis for Research and Applications), 18 only provide temperatures with ~1.2 km vertical resolution in the TTL , which has been 19 argued misses finer vertical structure in the tropopause and therefore introduce 20 uncertainties in our understanding of stratospheric H 2 O. In this paper, we quantify this 21 uncertainty by comparing the Lagrangian trajectory prediction of H 2 O using MERRA 22 temperatures on standard model levels ( traj.MER-T ), to those using GPS temperatures in 23


Trajectory Model and Temperatures Used 35
Stratospheric water vapour (H 2 O) and its feedback play an important role in regulating 36 the global radiation budget and the climate system (e.g., Holton et al., 1995;Randel et al., 37 2006;Solomon et al., 2010;Dessler et al., 2013). It has been known since Brewer's 38 seminal work on stratospheric circulation that tropical tropopause temperature is the main 39 driver of stratospheric H 2 O concentration (Brewer, 1949). As parcels approach and pass 40 through the cold-point tropopause -the altitude at which air temperature is the coldest, 41 condensation occurs and ice falls out, thereby regulating the parcel's H 2 O concentration 42 to local saturation level (e.g., Fueglistaler et al., 2009, and references therein). This is the 43 dehydration process. The role of tropopause temperature variation in tropical dehydration 44 is most apparent in the annual variation in tropical stratospheric H 2 O, also known as the 45 "tape recorder" (Mote et al., 1996). 46 When air crosses the tropical tropopause layer (TTL), it experiences multiple 48 dehydrations due to encounter of lower temperatures, and the final stratospheric H 2 O 49 mixing ratio is established after air passing through the coldest temperature along its path, 50 which sets the strong relation between cold-point tropopause and the entry level H 2 O 51 (e.g., Holton and Gettelman, 2001;Randel et al., 2004Randel et al., , 2006. 52 53 The details of the transport and dehydration process can be understood by performing 54 Lagrangian trajectory simulations, which track the temperature history of a large number 55 of individual parcels. Unlike modeling chemical tracers that depends strongly on the 56 transport imposed (Ploeger et al., 2011;Wang et al., 2014), the simulation of H 2 O is 57 primarily constrained by tropopause temperatures. Dehydration thus primarily depends 58 on the air parcel temperature history, and stratospheric H 2 O simulations ultimately 59 require accurate analyses of temperatures particularly in the tropopause (e.g., Mote et al., 60 1996;Fueglistaler et al., 2005Fueglistaler et al., , 2009Liu et al., 2010;Schoeberl and Dessler, 2011;61 Schoeberl et al., 201261 Schoeberl et al., , 2013. 62

63
In this paper, we use a forward, domain-filling trajectory model to study the detailed 64 dehydration behavior of the humidity of air parcels entering the tropical lower 65 stratosphere. Previous analyses have demonstrated that this model can accurately 66 simulate many aspects of the observed stratospheric H 2 O (Schoeberl and Dessler, 2011;67 Schoeberl et al., 201267 Schoeberl et al., , 2013. Despite the good agreements with observations, there are 68 clear areas of uncertainties from, for instance the accuracy of circulation fields 69 atmosphere (Kursinski et al., 1997). 162 163 The GPS radio occultation (RO) technique makes the data accuracy independent of 164 platforms. That makes the biases among different RO payloads could be as low as 0.2 K 165 in the tropopause and stratosphere (Ho et al., 2009). Therefore, to compensate the 166 relatively lower horizontal resolution (relative to that of reanalysis), we include GPS RO 167 from all platforms. This include the Constellation Observing System for Meteorology, 168 Satellite-A (MetOp-A), the Satellite de Aplicaciones Cientifico-C (SACC) satellite (Hajj 173 et al., 2004), and the TerraSAR-X (TerraSAR-X). There are ~2000-3500 profiles per day, 174 mostly from COSMIC, with ~700-1100 profiles of these in the tropics. 175 176 Each day, GPS temperature profiles are binned to 200-m vertical resolution. Horizontally, 177 we grid data into 2.5x1.25 (longitude by latitude) grids with 2-D Gaussian function 178 weighting. This gridded dataset has been successfully used in diagnosing many detailed 179 features of tropopause inversion layer (Gettelman and Wang, 2015 finer vertical structure induced by waves (refer Fig. 3 in Kim and Alexander, 2013). The 218 trajectory simulation using this temperature dataset is denoted as traj.MER-Twave. 219 220 Note that we only considered the vertical structure issue, since it is by far a limiting 221 factor in representing waves in the TTL. A large portion of TTL wave spectrum has 222 horizontal and temporal scales much larger and longer than reanalysis resolution, 223 therefore, temperature behaves almost linearly in-between model horizontal and temporal 224 resolution. However, temperature does not behave linearly in vertical space due to the 225 fact that a significant portion of TTL waves have vertical wavelengths shorter than ~4 km 226 (see Figure S4 in supporting information of Kim and Alexander, 2015), which could 227 make wave-induced disturbances less represented by the ~1.2 km vertical resolution in 228 reanalyses. 229

230
The wave scheme produces both positive and negative perturbations to the MERRA 231 temperature profiles, depending on the phase of waves. Overall, the change in 232 temperature induced by waves is less than 2 K (Fig. 3), although in rare cases it can reach 233 5-7 K. Importantly, however, about 80% of the changes in cold-point temperature are 234 negative, with the wave scheme lowering the average cold-point temperatures by ~0.35 235 K. It is this reduction in cold-point temperature that is responsible for the reduction in 236 exists, but the mean temperatures are more accurate. In contrast, MER-Twave has better 242 variability but not accurate mean, since it is designed to have similar variability to 243 radiosondes but with mean reserved to original MER-T. In summary, the mean 244 temperature is closer to reality in GPS than in MER-T and MER-Twave, but the 245 temperature variability is closer to reality in MER-Twave than in MER-T and GPS. In 246 addition, the MER-Twave is a general technique that could be applied to situations where 247 GPS temperatures are not available (e.g., reanalyses before 2006, climate models). 248 249

Interpolation scheme 250
In our studies, we use linear interpolation to estimate the temperature between the fixed 251 levels of temperature datasets. However, some previous analyses have used higher order 252 interpolations, such as cubic spline (e.g., Liu et al., 2010), to make assumptions about the 253 strong curvature of temperature profiles around the cold-point tropopause. In order to 254 determine which approach is superior, we sample GPS tropical temperature profiles at 255 MERRA vertical levels and then use the two interpolation schemes to reconstruct the full 256 GPS resolution. Then we compare the minimum saturation mixing ratio from the 257 recovered profiles to the minimum calculated from the full resolution GPS profiles. 258 259 Fig. 4a shows the probability distribution of the differences between the minimum 260 saturation mixing ratio in the full-resolution GPS profile and in the two interpolation 261 schemes. On average, the linear interpolation performs better (RMS difference is 0.18 262 and 0.25 ppmv for the linear and cubic spline, respectively). Fig. 4b shows the 263 corresponding probability distribution of the difference of the pressure of this minimum, 264 and the linear interpolation does better for this metric, too (RMS difference is 5.2 and 7.2 265 hPa for the linear and the cubic spline interpolation, respectively). We have also tested 266 higher order spline interpolations and find that none produce lower RMS errors than 267 linear interpolation. Overall, cubic spline interpolation tends to underestimate cold-point 268 temperature, making the implied H 2 O too dry, as noted by Liu et al., (2010). Thus, in our 269 studies we adopted linear interpolation scheme for three different trajectory runs. entering the stratosphere. We define "parcels entering the stratosphere" as parcels that 277 underwent final dehydration between 45 o N-45 o S (thus ignoring polar dehydration) and 278 that were already at altitudes higher (pressure lower) than 90 hPa for at least six months 279 since the last time they were dehydrated (FDP). This guarantees that parcels already 280 crossed the cold-point tropopause (~380 K or ~100-94 hPa) and has indeed experienced 281 the coldest temperature along its ascending paths. Averaging over 7 years minimizes the 282 effects of interannual variability. In another word, the bimodal FDP distribution from MERRA run ( Fig. 5a) could be even 316 more peaked when choosing smaller integration step in our trajectories. Two reasons that 317 we didn't choose such smaller time step: 1) the wind and temperature data are only 318 available 6-hourly or even daily (GPS) so much smaller time step introduces more 319 uncertainties with more interpolation; and 2) considering the balance between model 320 efficiency and computational resources. traj.MER-Twave dries by ~0.2-0.3 ppmv ( Fig. 7a-b), accounting for at most ~2.5% and 386 7.5% changes given typical stratospheric H 2 O abundances of ~4 ppmv, respectively. 387 However, despite the differences in H 2 O abundances, the interannual variability (residual 388 from the mean annual cycle) exhibits virtually no differences, due to the strong coupling 389 between the interannual changes of stratospheric H 2 O and tropical cold-point tropopause 390 temperatures (Fig. 8). Therefore, in terms of studying the interannual changes of 391 stratospheric H 2 O, we argue that reanalysis temperatures are more useful due to its long-392 term availability. 393 Looking at the locations of FDP, we find a bimodal distribution when using standard 395 MERRA temperatures on model levels . This is caused by the fact that the 396 cold-point tropopause is constrained to be near the two MERRA model levels (100.5 and 397 85.4 hPa) that bracket the cold-point tropopause (Fig. 5d-f). When using the temperatures 398 with finer vertical structures, the resultant FDP patterns appear to be more physically 399 reasonable (Figs. 5a-c and Fig.6). 400

401
In this paper we perform linear interpolations for all trajectory runs. Other analyses have 402 used cubic spline interpolation owing to the strong curvature of temperature profile 403 around the cold-point tropopause. We investigate the performances of both schemes using 404 GPS temperature profiles (Sect. 2.2.3) and find that while introducing new information 405 due to its assumption in the temperature profile around the tropopause, cubic spline 406 scheme tends to generate unrealistically low cold-point temperatures due to cubic fitting. 407 Therefore, the results are not necessarily realistic and on the other hand linear 408 interpolation is overall more accurate (Fig. 4). 409