Lagrangian trajectories are frequently used to trace air parcels from the troposphere to the stratosphere through the tropical tropopause layer (TTL), and the coldest temperatures of these trajectories have been used to reconstruct water vapor variability in the lower stratosphere, where water vapor's radiative impact on Earth's surface is strongest. As such, the ability of these trajectories to accurately capture temperatures encountered by parcels in the TTL is crucial to water vapor reconstructions and calculations of water vapor's radiative forcing. A potential source of error for trajectory calculations is the resolution of the input data. Here, we explore how improving the spatial and temporal resolution of model input data impacts the temperatures measured by Lagrangian trajectories that cross the TTL during boreal winter using ERA5 reanalysis data. We do so by comparing the temperature distribution of trajectories computed with data downsampled in either space or time to those computed with ERA5's maximum resolution. We find that improvements in temporal resolution from 6 to 3 and 1 h lower the cold point temperature distribution, with the mean cold point temperature decreasing from 185.9 to 185.0 and 184.5 K for reverse trajectories initialized at the end of February for each year from 2010 to 2019, while improvements to vertical resolution from that of MERRA2 data (the GEOS5 model grid) to full ERA5 resolution also lower the distribution but are of secondary importance, and improvements in horizontal resolution from 1

The composition of air entering the middle atmosphere through the tropical tropopause layer (TTL) is an important control on the composition of air throughout the stratosphere. This idea was proposed by Alan Brewer in 1949 to explain his observations of a dry mid-latitude stratosphere: the coldest region that mid-latitude air may have encountered is near the tropical tropopause (Fig.

The January 2017 zonal mean tropical tropopause temperature for ERA5 and MERRA2 reanalysis data. Note the increased number of model layers near the coldest temperatures for the ERA5 data. A plot of the reduced resolution ERA5 data used in this paper is shown in Fig. S1.

This two-dimensional description accurately describes the meridional movement of air in the stratosphere, but it does not capture zonal variability in the circulation or in troposphere-to-stratosphere transport (TST). A seasonally varying zonal structure for TST was proposed by

Lagrangian trajectory models have also been used to show that the coldest temperature of trajectories that transit the TTL are predominantly encountered over the tropical West Pacific, and that entry into the stratosphere occurs at least 20 d later and thousands of kilometers away

Another important consideration for Lagrangian trajectory models is whether the input vertical velocities are diabatic or kinematic. Previous work has shown that kinematic trajectories are more dispersive than diabatic trajectories

The stratospheric water vapor values calculated from the temperature history of the aforementioned Lagrangian trajectory studies are in good agreement with satellite observations, but it is not inconceivable that these values are right due to compensating errors. The undersampling of the temperature field due to insufficient spatial or temporal resolution is bound to produce warm (moist) biases in the cold point temperature distribution, while an underestimation of the fraction of air originating in the troposphere due to unrealistic trajectory paths would decrease the mass of air recently undergoing dehydration and produce an additional moist bias. Therefore, improving the models' representation of how air parcels transit the TTL by increasing the temporal resolution of input data could eliminate this moist bias and decrease the water vapor concentration calculated from Lagrangian trajectory models. This would imply that an additional source of water vapor is needed to match the observed values. Previous work has suggested that ice lofting could potentially inject a significant amount of water into the lower stratosphere

With the release of ECMWF’s (European Center for Medium-range Weather Forecasts) updated ERA5

We use ECMWF’s Lagrangian analysis tool LAGRANTO version 2

By default, LAGRANTO integrates trajectories 12 times per input data time step (e.g., every 5 min for 1 h data or 30 min for 6 h data). To test the sensitivity of trajectories to the length of the integration time step, we ran a set of integrations with 1 h data and a 30 min time step and a set with 6 h data and a 5 min time step. The results are nearly identical to the integrations run with LAGRANTO’s default time steps (Fig. S2), so we ran trajectories with the default setting, and we obtained outputs once per hour regardless of the input data frequency.

Summary of the LAGRANTO runs used to test the sensitivity of trajectory cold points to input data resolution. All runs are with ERA5 data

We test how LAGRANTO observes the TTL cold point using a range of spatial and temporal resolutions as described in Table 1. The figures presented in Sect. 3 contain data from DJF 2017, which are close to the averages of all years; throughout the text we note when we are quoting either 2017 data or averages from 2010–2019. All data were obtained at 1 h, 0.25

For each configuration listed in Table

We determined that the integration length was sufficient for this study based on the convergence of the cold point temperature and height distributions by the end of the runs (Fig. S4). The fraction of trajectories traced to the troposphere also asymptotes for the 6 h trajectories by day 90, but the fraction for the 1 h trajectories does not reach an asymptote within the integration. Therefore, we cannot comment here on the fraction of trajectories at 400 K that ultimately ascend from the troposphere, but we are still confident in these trajectories' representation of the cold point based on Fig. S4. We do introduce a bias in the observed cold points towards the TTL conditions in late January and early February by initializing at the end of February, although trajectories still need to be run through December to trace them to the troposphere. As we will discuss in Sect. 3, this bias differs for each set of trajectories and needs to be considered when comparing trajectory cold points.

We chose to analyze the boreal winter because the Brewer–Dobson circulation (BDC) and the correlation between TTL temperatures and lower stratospheric water vapor are both strongest during this season

Following the method of

To explore the well-documented vertical dispersion of kinematic trajectories, we run a set of 20 d reverse trajectories on a global 0.5

To look more closely at trajectory dispersion in the deep tropics, we follow the height of reverse trajectories initialized above and below the TTL transport barrier (interpolated onto 400 and 340 K isentropes) over the course of 90 d integrations. With increased dispersion, we expect both a larger fraction of trajectories to more quickly cross the TTL and a larger fraction of trajectories to be traced upwards into the stratosphere.

Panels

Figure

A major source of these errors is the undersampling of the wind field by lower-resolution trajectories. As we will discuss in Sect. 3.1.2, the decreased temporal sampling of the wind field results in excess dispersion in the lower stratosphere and TTL, which causes trajectories to undersample spatial temperature variability by crossing the TTL before reaching regions with lower temperatures and/or by skipping over the coldest point along a trajectory's path. We can approximate the resulting warm bias by reweighting the lower-resolution trajectories' cold point temperatures with the spatial distribution of the 1 h trajectories. This removes “edge” cold points, which are located outside of the horizontal range of the 1 h trajectories and therefore get a weight of 0 in this redistribution. Previous work with 6 h temporal resolution noted the importance of these edge cold points in determining the mean cold point

Excess dispersion also drives a warm bias by reducing trajectories' residence time in the TTL, thereby reducing the temporal temperature variability to which the trajectories are exposed. We quantify the trajectories' TTL residence time as the mean 340 K-to-400 K transit time, which decreases for DJF 2017 from 62 d for the 1 h trajectories to 56 and 47 d for the 3 and 6 h trajectories, respectively. The mean cold point-to-400 K transit time also decreases from 37 to 32 and 26 d. Figure

We estimate the warm biases associated with the trajectories' decreased residence time by weighting the temperature (blue line) in Fig.

The daily running mean zonal minimum temperature averaged between 15

The remaining cold point temperature error is caused by the undersampling of the temperature field's temporal variability. We isolate this bias by subsampling the mean cold point temperature from the output of the 1 h trajectories every 3 and 6 h. Doing so removes the effects of the decreased transit times and shifted spatial distributions (i.e., removes the edge points) of the lower-resolution trajectories by taking these directly from the 1 h trajectories. The cold point temperatures from the 3 and 6 h trajectories would be identical to this if the temporal resolution of the temperature was the only source of the warm bias, while differences between the two result from the decreased resolution of the wind field, as discussed above. The mean cold point temperatures from subsampling every third and sixth hour are 185.0 and 185.3 K, so 0.2 and 0.5 K of the 3 and 6 h trajectories' warm bias can be explained by this output subsampling.

In summary, there are three drivers of the warm cold point temperature bias for trajectories with decreased temporal resolution: (1) the spatial extent of trajectories' sampling within the TTL (i.e., the inclusion of warm edge points), (2) the time at which trajectories encounter their cold point, and (3) the frequency of temperature sampling in time. As we state above, the warm bias that we calculate from the decreased residence time is only an estimate, plus it may be double counted in the warm bias of the edge points. (If excess dispersion drives both of these, then it is possible that the trajectories at these points are warmer, partly because they do not sample a full range of temporal temperature variability at their given location.) Therefore, these impacts cannot necessarily be summed up linearly to reconstruct the total warm bias: for the 3 h trajectories, each of these effects have an estimated warm bias of about 0.2 K, which would be summed up to greater than the total warm bias of 0.4 K, while the respective values of 0.3, 0.4, and 0.5 K for the 6 h trajectories are summed up to the total warm bias of 1.2 K. These values are also specific to DJF 2017, and their relative importance depends on the variability of the temperature and wind fields during the period of integration; regardless, we demonstrate that there is potential for each of these three effects to impact Lagrangian studies of the cold point.

The zonal variance of potential temperature displacement for 1 and 6 h trajectories run for 20 d with starting heights between 310 and 420 K. Contours are at every 100 K

Figure

The variance above 380 K diverges for the two temporal resolutions shown in Fig.

The distribution of trajectories' potential temperature for 1 (black) and 6 h (red) runs initialized on the interpolated 340 K and 400 K isentropes after 1, 40, and 80 d. Different

Figure

The impact of temporal resolution on vertical transport in the lower stratosphere and TTL is revealed by the differences in the 1 and 6 h distributions for the 400 K trajectories. After 40 d, only 7 % of 1 h trajectories have gone below 340 K, while 22 % of 6 h trajectories have done so by this time. After 80 d, the fraction of trajectories traced to the troposphere is similar for the 6 and 1 h resolutions (47 % and 43 %), but their distributions throughout the stratosphere are different. The 1 h trajectories are confined to the lower stratosphere, while the 6 h trajectories have a long tail that extends up to 800 K, which reflects excess dispersion rather than a realistic representation of stratospheric circulation. These results together imply that the excess dispersion resulting from insufficient temporal resolution causes lower stratospheric trajectories to be traced artificially from both above and below, thereby failing to resolve either the TTL transport barrier or the slow ascent of air in the lower stratosphere. The backwards Lagrangian trajectory studies discussed above completed integrations for at least 3 months, with some going for as long as 1 year

As mentioned in Sect. 3.1.1, the average cold point-to-400 K transit time is reduced when the temporal resolution is reduced from 1 to 6 h as a result of dispersion in the TTL. The 6 h trajectories' cold point-to-400 K transit time is consistent with the 22.4 d transit time during DJF that was found by

Panels

The enhanced vertical resolution of the ERA5 dataset provides an opportunity to improve the accuracy of Lagrangian trajectories by increasing the sampling of both the temperature and wind fields. As Fig.

Figure

As is discussed in Sect. 3.1, decreased sampling of the wind field can result in excess trajectory dispersion, which can alter the spatial and temporal distributions of the cold point. The edge points that result from this dispersion have a mean temperature of 188.0 K, while the colocated cold points have a mean temperature of 185.6 K. Therefore, removing the edge points would eliminate 0.2 K (about 20 %) of the warm bias. As was the case with changes to the input data's temporal resolution, reweighting the cold points' spatial distribution within the colocated regions to match that of the full resolution trajectories has a negligible impact on the mean cold point temperature. Quantifying the impact of dispersion on the temporal temperature variability sampled by these trajectories is complicated here by the different initial model setup required by the 72-level trajectories. These trajectories need an average of 12 d to reach 400 K from their 75 hPa starting height, and they are therefore able to experience the negative temperature excursion seen around day 65 in Fig.

Temperature profiles of the DJF 2017 mean trajectory cold points measured by full (137-level) resolution and 72-level vertical resolution trajectories (solid lines), and the ERA5 time-averaged JF 2017 zonal minimum cold point temperature taken from the full grid (dashed black line) and the 72-level vertical grid (dashed green line). The left axis is exact pressure from ERA5, and the right axis is the potential temperature calculated at those pressure levels with the DJF 2017 zonal mean temperature.

The remaining trajectory cold point warm bias can be explained by the undersampling of the temperature profile near the cold point. This is reflected by the PDFs of cold point pressure in Fig.

The trajectory cold point temperature profiles in Fig.

Panels

As mentioned in Sect. 2.1, we found that our trajectory calculations were not impacted by improving the horizontal resolution of the input data from 1.0

Although the warm biases resulting from decreased resolution are small, we can decompose the warm biases into effects associated with undersampling of the wind and temperature fields.
As discussed in Sect. 3.1, undersampling of the wind field can result in excess dispersion that alters trajectories' paths and reduces their residence time in the TTL. The mean 340 K-to-400 K transit times for 0.25, 0.5, and 1.0

The remaining warm bias comes from undersampling of the spatial temperature variability. We compare the tropical cold temperatures for different spatial resolutions in the following way: for each latitude between 15

Studies that use the cold point of Lagrangian trajectories to reconstruct water vapor in the lower stratosphere

Due to the nonlinear relationship between temperature and water vapor mixing ratio, the shifted temperature distribution for the lower temporal resolution data results in a larger increase in water vapor than the increase calculated from the mean cold point temperature (positive water vapor anomalies from the warm tail of the temperature distribution are greater than negative water vapor anomalies from the cold tail). For example, the DJF 2017 1 and 6 h saturation water vapor concentrations are 1.51 and 1.82 ppmv when calculated with the mean cold point temperatures, while these concentrations are 1.59 and 1.95 ppmv when calculated with the full cold point temperature distributions. This means that the lower-resolution trajectories' edge points have an outsized role in the moist bias: in DJF 2017 they comprise 11 % of the 6 h cold points but drive 20 % of the trajectories' moist bias.

Accurate reconstructions of water vapor also require the fraction of lower stratospheric air that has recently undergone dehydration at the cold point, which we cannot definitively comment on due to the insufficient length of our runs. We note, however, that the fraction is subject to the errors associated with the enhanced dispersion discussed in Sect. 3.1.2. This fraction will be too high for integrations using low-resolution data for runs shorter than 90 d because of the enhanced dispersion, and it will likely be too low for longer runs due to the unrealistic portion of trajectories traced to the upper stratosphere (see upper levels in Fig.

The water vapor concentrations that would be obtained from assuming full dehydration at the cold point experienced by 1 h trajectories would be too low compared to observations, so other processes must be acting to hydrate the stratosphere. These could include microphysical (ice nucleation, particle growth, and aggregation) or advective (ice lofting, overshoot convection) processes, or a combination of the two. For example, the timescale of ice particle formation and sedimentation may be longer than the length of time that air is exposed to the absolute minimum temperature along its path. In this case, the details of how fast ice particles form based on the availability of condensation nuclei and how fast they fall due to gravitational settling, which depends on their size distribution, will determine how much water is removed from the air and how much ice re-evaporates as the air encounters warmer temperatures and ascends.
This has been explored previously

Lagrangian trajectories' representation of the path of air through the TTL is degraded when the vertical and/or temporal resolution of the trajectory input data is decreased, but it is not significantly impacted by improvements to the horizontal resolution of the input data beyond 1.0

This impact is largest for changes to temporal resolution: lowering the instantaneous input data from 1 to 3 or 6 h resolution increases the mean cold point temperature for DJF 2010–2019 trajectories from 184.5 to 185.0 and 185.9 K. For the decrease in vertical resolution from 137 to 72 levels, the DJF 2017 mean cold point increases by 1.0 K, and the decrease in horizontal resolution from 0.25 to 0.5 and 1.0

The variance of displacement for trajectories initialized in the tropical lower stratosphere increases by 1 order of magnitude when the temporal resolution of the input data drops from 6 to 1 h, though the difference between 6 and 3 h is greater than the difference between 3 and 1 h, so future improvements could be small. This is consistent with

The warm biases and excess dispersion of lower-resolution trajectories will impact lower stratospheric water vapor reconstructions. The water vapor concentrations calculated based on saturation with respect to ice at the cold point using 3 and 6 h trajectories are 0.13 and 0.41 ppmv higher than the water vapor concentration calculated with 1 h data. The 72-level vertical resolution trajectories have a moist bias of 0.24 ppmv relative to the 137-level trajectories, and the 0.5 and 1.0

Here, we have shown that the statistics obtained from Lagrangian trajectories run across the TTL are sensitive to the temporal and spatial resolution of their input data. Although we cannot evaluate the trajectories calculated with 1 h data relative to the ground truth, it is clear from this work that lower stratospheric trajectories run with 3 and 6 h data are impacted by excess dispersion in the TTL, and their frequency of temperature sampling causes an additional warm bias. Similarly, input data with the full ERA5 137-level vertical grid smooth out the distribution of trajectories' cold point heights and cool their cold point temperature distribution, but it remains possible that additional vertical levels could further improve the trajectories' representation of troposphere-to-stratosphere transport through the TTL. Future studies of this region should consider these results when selecting input data, although work still needs to be done to compare trajectories run with 1 h kinematic vertical velocities to those run with diabatic vertical velocities. Of course, the highest temporal and spatial resolution would minimize error if storage and computing resources are not an issue, but reducing the horizontal resolution to 1.0

The ERA5 hourly data on native model levels from 2010 to 2019 used in this paper can be accessed through Copernicus Climate Change Service (C3S),

The supplement related to this article is available online at:

SB acquired the ERA5 data and LAGRANTO code, ran trajectories, did post-processing and calculations, and wrote the paper. ML contributed to ideation, interpretation of results, and editing of the paper.

The contact author has declared that neither of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Thanks to Bill Randel for helpful conversations, Michael Sprenger and Stephan Fueglistaler for help with calculating and interpreting trajectories, and Alison Ming and 2 anonymous reviewers for helpful feedback.

This research has been supported by the Faculty of Arts and Sciences (grant no. HSGRP award 343327).

This paper was edited by Rolf Müller and reviewed by Alison Ming and two anonymous referees.