We conducted the Lagrangian transport simulations for this study using two models. MPTRAC has been developed recently to support analyses of atmospheric transport processes in the free troposphere and stratosphere. MPTRAC features a modular structure for different geophysical processes. Most importantly, the advection module of MPTRAC solves the trajectory equation for atmospheric air parcels based on given wind fields from ERA5, ERA-Interim, or other meteorological data sets. Kinematic trajectories are calculated using pressure as the vertical coordinate. Another module is available to simulate diffusion and subgrid-scale wind fluctuations by adding stochastic perturbations to the trajectories, following the approach of . Additional modules can simulate sedimentation (i.e., gravitational settling) or the decay of mass assigned to the air parcels. MPTRAC is particularly suited for large-scale simulations on supercomputers due to its Message Passing Interface (MPI)/Open Multi-Processing (OpenMP) hybrid parallelization. Among its first applications, MPTRAC was used to perform Lagrangian transport simulations of the dispersion of volcanic plumes and to estimate sulfur dioxide emission rates for these events . presented an intercomparison of meteorological analyses and an evaluation of MPTRAC trajectory calculations with super-pressure balloon observations for the Antarctic lower stratosphere. evaluated trajectory errors of different numerical integration schemes diagnosed with the MPTRAC advection module driven by high-resolution ECMWF operational analyses and forecasts.

In this study, we also applied the Chemical Lagrangian Model of the Stratosphere (CLaMS) trajectory module to calculate kinematic forward trajectories. CLaMS performs the fully Lagrangian, non diffusive, three-dimensional advection of an ensemble of air parcels . Combined with additional modules to represent mixing of air masses, CLaMS is well suited for reproducing atmospheric transport barriers, such as the edge of the polar vortex and the Asian summer monsoon anticyclone . The trajectories of air parcels are calculated using the classical 4th-order Runge–Kutta method with a 600 s time step for simulations based on ERA-Interim and 240 s for simulations based on ERA5. The same time steps were used for MPTRAC, applying the midpoint method to solve the trajectory equation. Sensitivity tests showed that the time steps are small enough so that truncation errors do not contribute significantly to the simulation results. Like MPTRAC, the CLaMS trajectory module employs pressure (interpolated from the ECMWF hybrid vertical coordinate) as the vertical coordinate along with vertical velocity, ω=dp/dt, as provided by ECMWF to calculate kinematic trajectories. Alternatively, the CLaMS trajectory module can be used to calculate diabatic trajectories. Although diabatic trajectories have known advantages for the upper troposphere and stratosphere e.g.,, they are rarely used for the lower and middle troposphere. A comparison of diabatic and kinematic trajectory calculations is beyond the scope of our present work, which focuses exclusively on kinematic forward trajectories.

In this section, we analyze the impact of the diffusion and subgrid-scale wind fluctuation parameterizations in MPTRAC on the Lagrangian transport simulations. Quantifying the impact of diffusion and subgrid-scale wind fluctuations is particularly helpful, because it provides us with a reference for assessing the impact of other effects on the Lagrangian transport simulations. For example, comparing the deviations between ERA5 and ERA-Interim simulations to the deviations due to diffusion and subgrid-scale wind fluctuations allows us to assess, whether the differences found between the meteorological data sets can be considered significant or not. This approach is similar to the concept of significance rating by means of the “meteorological complexity factor” of . Unfortunately, a difficulty arises from the fact that the strength of dispersion modeled with the approach of depends on the particular meteorological data set . Tests showed that the spread of particles in terms of AHTDs and AVTDs with respect to trajectories calculated without diffusion and subgrid-scale wind fluctuations modeled with ERA5 is about a factor of 2 lower compared with ERA-Interim. However, ERA5 provides a higher spatiotemporal resolution and potentially bears lower uncertainty on the subgrid scales. Hence, we selected diffusion and subgrid-scale wind fluctuation simulations based on ERA5 as a reference for further comparisons. ERA5 data provide a stricter measure of significance in our assessment, as trajectories based on ERA5 have a lower spread than those based on ERA-Interim.

Figure  provides an illustrative example of the impacts of parameterized diffusion and subgrid-scale wind fluctuations on the Lagrangian transport simulations. The figure shows ERA5 10-day forward trajectories with and without diffusion and subgrid-scale wind fluctuations for a single seed in the midlatitude lower stratosphere in Northern Hemisphere winter. A more detailed analysis showed that the dispersion of the ERA5 trajectory set seen in this particular example is mostly due to a combination of vertical displacements owing to the use of a constant vertical diffusivity Dz=0.1m2s-1 in the stratosphere and vertical shear of the resolved horizontal winds. Note that the resulting horizontal and vertical distributions of the particle positions became non-Gaussian. For comparison, the ERA-Interim trajectory without diffusion and subgrid-scale wind fluctuations is also shown. In this example, we found particularly good agreement between the positions of the ERA5 and ERA-Interim trajectories without diffusion and subgrid-scale wind fluctuations at all times (AHTD ≤250 km and AVTD ≤600 m, Fig. a and b). The ERA5 trajectory set with diffusion and subgrid-scale wind fluctuations shows a large spread that typically exceeds the differences between the ERA5 and ERA-Interim trajectories without diffusion and subgrid-scale wind fluctuations. The spatial differences between the reference trajectories without diffusion and subgrid-scale wind fluctuations can therefore be attributed to the meteorological complexity of the situation rather than to significant differences between the ERA5 and ERA-Interim data set in this case.

Figure  also shows differences of meteorological variables sampled along the trajectories. Starting from an initial temperature bias of 0.9 K between ERA-Interim and ERA5, temperature deviations mostly remain below 2.5 K along the trajectories (Fig. c). The ERA5 trajectory reveals larger temperature variability than the ERA-Interim trajectory, owing to the better spatiotemporal resolution of the ERA5 data possibly providing an improved representation of small-scale features. Significant differences are observed for water vapor volume mixing ratios, which remain nearly constant at 4.6 ppmv for ERA5, but vary between 4.3 and 4.55 ppmv for ERA-Interim (Fig. d). The differences between ERA5 and ERA-Interim water vapor volume mixing ratios exceed the spread of the ERA5 trajectory set. Considering that this is a stratospheric trajectory, the nearly constant water volume mixing ratio for ERA5 looks more realistic. Increased water vapor volume mixing ratios in ERA5 are promising, as ERA-Interim was previously found to have a cold and dry bias in the UT/LS region . Similar to the characteristics of water vapor, potential temperature along the trajectory remains nearly constant at 485 K for ERA5 compared with variations between 460 and 500 K for ERA-Interim (Fig. e). Again, the simulation result for ERA5 looks more realistic, considering that potential temperature is typically an excellent dynamical tracer in the stratosphere. Potential vorticity shows larger variations than potential temperature in this particular example, remaining mostly in the range between 20 and 30 PVU for both ERA5 and ERA-Interim (Fig. f). As potential temperature is nearly constant in this case, the variability in potential vorticity is due to variability in relative vorticity as calculated from the horizontal winds and variability in absolute vorticity due to the particles being dispersed to different latitudes.

The transport deviations of individual trajectories depend strongly on the meteorological situation. In order to obtain statistically meaningful results, we averaged over large numbers of trajectories; i.e., 106 particles distributed globally in the free troposphere and stratosphere. As an example, Fig.  shows the transport deviations due to diffusion and subgrid-scale wind fluctuations in different height ranges for 10-day forward trajectories started on 1 July 2017. The AHTDs grow steadily over time, indicating that this behavior is statistically robust, with maximum values of 1400 km for the troposphere and UT/LS region (2–16 km), 1100 km for the middle and upper stratosphere (32–48 km), and 500 km for the lower and middle stratosphere (16–32 km) after 10 days (Fig. a). Except for an initial phase of about 0.5–1 day, where individual horizontal trajectory lengths are rather short, the RHTDs also grow steadily over time. After about 3 to 4 days, the RHTDs consistently decrease with increasing altitude, showing the reduced impacts of diffusion and subgrid-scale wind fluctuations with height. RHTD maxima after 10 days decrease from 14 % in the troposphere to 4 % in the upper stratosphere (Fig. b). AVTDs also grow steadily over time, but initially exhibit a distinct scaling behavior of AVTD∝t in the stratosphere (Fig. c). We attribute this to the approach of used to simulate diffusion in MPTRAC, as this approach applies a constant vertical diffusivity of Dz=0.1m2s-1 in the stratosphere following. Later in the simulation, an exponential regime characteristic of chaotic dispersion and a linear regime due to large eddy dispersion are observed. As vertical trajectory lengths are initially rather short, RVTDs tend to be largest in the beginning (up to 74 % after 6 h in the lower and middle stratosphere), but converge towards much smaller values of 6 %–10 % after 10 days at all heights (Fig. d).

Figure  illustrates seasonal and latitudinal variations of the transport deviations due to parameterized diffusion and subgrid-scale wind fluctuations. It shows AHTDs and RHTDs after 10 days for each of the 24 simulations during the year 2017 for the Northern Hemisphere and Southern Hemisphere extratropics. In the AHTDs we found a strong annual cycle with wintertime maxima in the middle and upper stratosphere and peak-to-peak variations in the range from 200 to 2200 km (Fig. a, c). This seasonal cycle is plausible, considering that the wintertime stratosphere is generally more disturbed and affected by planetary wave activity in the vicinity of the polar vortex relative to the summertime stratosphere. Weaker annual cycles are present in the lower and middle stratosphere (wintertime maxima, AHTDs of 300–800 km in both hemispheres) and the UT/LS region (summertime maxima, AHTDs of 800–1300 km at 90–20∘S and 1100–1600 km at 20–90∘N). In the extratropical troposphere the AHTDs due to diffusion and subgrid-scale wind fluctuations are generally large (1500–1900 km in both hemispheres), but no annual cycle is evident. Annual cycles are also present in the RHTDs (Fig. b, d), but the peak-to-peak variations are different compared with the AHTDs. We found that the annual cycles in the RHTDs are more pronounced in the troposphere (RHTDs of 10 %–16 %) and UT/LS region (5 %–12 %) and less pronounced in the lower and middle stratosphere (4 %–7 %) and the middle and upper stratosphere (2 %–9 %). A direct influence of specific meteorological conditions can be seen in the strong variations of the AHTDs in the Southern Hemisphere extratropical stratosphere from August to October 2017 (Fig. c), which coincides with a strong sudden stratospheric warming and associated weakening of the zonal winds in September 2017.

Figure  provides a statistical summary of the transport deviations between the ERA-5 and ERA-Interim trajectories for the year 2017, showing the existence of significant differences between these two data sets. Figure  shows the median as well as the peak-to-peak range (minimum to maximum) of individual transport deviations during the course of the year. As mentioned earlier, transport deviations are shown separately for four height ranges, as well as globally, for the Northern Hemisphere extratropics, the Southern Hemisphere extratropics, and the tropics. Large peak-to-peak ranges are associated with the presence of seasonal cycles in the data (see Sect.  and Fig. ). Transport deviations due to parameterized diffusion and subgrid-scale wind fluctuations are shown for reference in Fig. . We decided to analyze the transport deviations after both 1 and 10 days. The transport deviations after 1 day are most indicative of the specific differences between ERA5 and ERA-Interim in this case. Transport deviations after 10 days can be thought of as “global errors”, which accumulate individual local errors over time. The 10-day transport deviations are typically strongly affected by the individual atmospheric conditions, e.g., as particles enter chaotic regions and are dispersed by divergent flows.

The most important result of this analysis is that the transport deviations between ERA5 and ERA-Interim are substantially larger than the transport deviations due to diffusion and subgrid-scale wind fluctuations. After 1 day the transport deviations between ERA5 and ERA-Interim are up to an order of magnitude larger than the transport deviations due to diffusion and subgrid-scale wind fluctuations. After 10 days the differences are still larger by a factor of 2–3. This indicates that there are considerable differences between Lagrangian transport simulations based on ERA5 and those based on ERA-Interim at all latitudes and in all height ranges considered here. Globally, the medians of the horizontal transport deviations at different height levels are in the range of 100–250 km (Fig. a) or 14 %–25 % (Fig. c) after 1 day and 1400–3500 km (Fig. b) or 16 %–35 % (Fig. d) after 10 days. The medians of the vertical transport deviations are in the range of 0.17–0.37 km (Fig. e) or 38 %–50 % (Fig. g) after 1 day and 0.5–1.4 km (Fig. f) or 14 %–19 % (Fig. h) after 10 days. The spatial differences between ERA5 and ERA-Interim trajectories are typically largest in the troposphere and in the middle to upper stratosphere, whereas ERA5 and ERA-Interim tend to agree best in the UT/LS region and the lower to middle stratosphere. A notable exception is the maximum in AVTD found in the UT/LS region in the tropics (Fig. e, f). In general, transport deviations in the middle and high latitudes of both hemispheres compare well to each other, but are distinctly different from those in the tropics. In particular, RHTDs in the tropics are larger than those in the extratropics (Figs. c, d). The largest peak-to-peak variations are mostly found in the middle and upper stratosphere (e.g., Fig. a, b), which indicates that annual cycles in the wind fields at these altitudes are represented differently in ERA5 and ERA-Interim.

One reason explaining the large differences between ERA5 and ERA-Interim in the troposphere and the tropical UT/LS region may be an improved representation of convective updrafts and other small-scale features due to the better spatial resolution of the ERA5 data (cf. Fig. ). To further assess the effect of convective updrafts and other types of vertical motion, we analyzed the total vertical displacements of particles seeded in the height range of 2–8 km along the 10-day trajectories. Figure  shows a two-dimensional histogram of the positive vertical displacements for June to August 2017 for the ERA5 trajectories, as well as the relative differences of this histogram with respect to ERA-Interim. Overall, the distribution of vertical displacements for the ERA5 trajectories looks realistic (Fig. a), as we would expect to find stronger updrafts associated with convection near the ITCZ and downdrafts or weaker updrafts in the subtropics due to the Hadley cells. A closer inspection of the relative differences (Fig. b) indicates that strong updrafts are found more frequently (up to 50 %) in ERA5 compared with ERA-Interim in the extratropics. Stronger updrafts in ERA5 are associated with significantly larger vertical velocities (Fig. c). However, for the tropics the analysis shows that the number of strong updrafts is reduced (down to -20 %) in ERA5. This discrepancy may be due to the fact that the areas in which strong tropical updrafts occur are more confined in ERA5 compared with ERA-Interim (compare Fig. c and d), such that fewer particles are affected by these updrafts. Convective properties are quite different in ERA5, which displays much more intermittency than ERA-Interim.

In this section, we discuss the differences in meteorological variables and dynamical tracers sampled along the ERA5 and ERA-Interim trajectories. For temperature, we analyzed the mean absolute deviation (MAD). Specific humidity, potential temperature, and potential vorticity exhibit strong variations with height; therefore, these factors are compared using the mean relative deviation (MRD). The height ranges and latitude bands for the analysis are the same as those used in the previous analysis and the analysis covers the same global simulations for the year 2017. The results of the statistical analysis are presented in Fig. . Overall, this analysis confirms the key finding of Sect. : there are substantial differences between Lagrangian transport simulations using ERA5 and those using ERA-Interim data. The deviations of the meteorological variables and dynamical tracers between ERA5 and ERA-Interim are significantly larger than those caused by parameterized diffusion and subgrid-scale wind fluctuations in all cases.

The medians of the global MADs of temperature are in the range of 0.7–3.0 K after 1 day and 2–13 K after 10 days (Fig. a, b), with the smallest values found in the lower and middle stratosphere and the largest values found in the troposphere. Temperature MADs in the extratropics are quite similar to global values. In contrast, temperature MADs in the tropics are largest in the UT/LS region, which correlates with particularly large AVTDs in this region (see Fig. e, f). For specific humidity we found median global MRDs of 29 % in the troposphere, 26 % in the UT/LS region, and ≤4 % in the stratosphere after 1 day (Fig. c). After 10 days, the MRDs increase to 85 % in the troposphere and 45 % in the UT/LS region, but still remain below 5 % in the stratosphere (Fig. d). The large differences between the ERA5 and ERA-Interim specific humidities in the troposphere and UT/LS region are associated with large variability of specific humidity itself in these regions. The stratosphere is very dry and exhibits much lower variations in specific humidity compared with the troposphere. However, the small stratospheric differences reported here are significant in comparison to those arising from diffusion and subgrid-scale wind fluctuations (see also Fig. d). As for temperature, the largest relative differences between ERA5 and ERA-Interim specific humidity are found in the troposphere in the extratropics and in the UT/LS region in the tropics, and can be traced back to the respective AVTDs.

Turning to the dynamical tracers, global median MRDs of potential temperature are in the range of 0.4 %–1.6 % after 1 day and 1.4 %–5.2 % after 10 days (Fig. e, f). MRDs of potential temperature mostly increase with height, in particular in the stratosphere. This is partially related to the exponential increase of potential temperature with height, which is not entirely suppressed by analyzing relative rather than absolute deviations. For the second dynamical tracer, potential vorticity, we found much larger deviations between ERA5 and ERA-Interim (Fig. g and h). Global median MRDs in potential vorticity after 1 day are about 50 % in the troposphere and UT/LS region and around 16 %–24 % in the stratosphere. MRDs in all four altitude ranges further increase to 20 %–80 % after 10 days. The largest MRDs are found in the tropics, which might be due to the fact that values of potential vorticity in this region are small when compared with those in the extratropics. Overall, the rather large deviations of potential vorticity between ERA5 and ERA-Interim were surprising. Additional tests showed that these differences are comparable when we use the CLaMS model instead of the MPTRAC model for this analysis, and that they are much larger than differences between the two models (see Sect. ). A possible reason for the large relative deviations is that ERA5 exhibits more fine structure in the potential vorticity fields than ERA-Interim, because of its better resolution (cf. Fig. e, f). Differences in vertical dispersion may also play a role, given the relatively large vertical gradient of potential vorticity around the tropopause.

In addition to MADs and MRDs, which measure variability between the ERA5 and ERA-Interim tracer data along the trajectories, we also analyzed for biases, which measure the systematic differences between the means of the distributions. The results of this statistical analysis are presented in Fig. . Overall, the biases are notably smaller than the MADs or MRDs, typically by a factor of 2 or more. However, in nearly all cases the biases are larger than the systematic differences introduced by parameterized diffusion and subgrid-scale wind fluctuations. Global temperature biases of ERA5 minus ERA-Interim are in the range of -0.2 to 1.3 K, with the largest positive biases being found in the mid to upper stratosphere after 1 day (Fig. a) and in the troposphere after 10 days (Fig. b). This bias along the trajectories is partly due to direct biases between ERA5 and ERA-Interim temperature data (Figs. d, d). Global relative biases of specific humidity remain in the range of -18 % to 6 % after 10 days (Fig. d). Significantly smaller specific humidities of ERA5 compared to ERA-Interim in the UT/LS region after only 1 day seem noteworthy (Fig. c), as they can be attributed to direct biases between the data sets in this region (Figs. e, e). Being correlated with temperature biases, global relative biases of potential temperature remain in the range of -0.4 % in the troposphere to 0.9 % in the mid to upper stratosphere after 10 days (Fig. f). Global relative biases of potential vorticity are in the range of -4 % to 8 % after 10 days (Fig. h). A systematic, yet unexplained difference in potential vorticity between the Southern Hemisphere and Northern Hemisphere extratropics was already evident in the troposphere and UT/LS region after 1 day (Fig. g).

Direct validation of trajectory calculations can be performed by means of comparison to balloon observations e.g.,. However, this type of validation is limited by the sparse spatial and temporal coverage of the balloon data. In this study, we followed the approach of and conducted a systematic global assessment of our trajectory calculations with respect to the conservation of dynamical tracers along trajectories, including specific humidity, potential temperature, and potential vorticity. We performed this analysis for both ERA5 and ERA-Interim to assess whether tracer conservation has improved in ERA5. The results are summarized in Fig. .

Conservation of specific humidity applies unless the parcel is affected by condensation, evaporation, chemical reactions, or mixing . In the free troposphere, specific humidity can be considered to be a dynamical tracer on short timescales, such as a few hours to a day. In the stratosphere, even longer timescales apply. In our simulations, we found global RTCEs of specific humidity of about 30 % in the troposphere and 20 % in the UT/LS region after 1 day (Fig. a). These results compare well to those reported by , who found a specific humidity RTCE of about 35 % after 24 h for three-dimensional tropospheric trajectories calculated using ECMWF meteorological data. Stratospheric values of the RTCE are very low (≤2 %), due to better conservation and the weak spatiotemporal variability of specific humidity itself in this region. RTCEs of specific humidity exhibit some variations with latitude, in particular in the troposphere and in the UT/LS region. The largest conservation errors are in the troposphere in the extratropics, whereas these errors maximize in the UT/LS in the tropics. RTCEs in tropospheric specific humidity are quite similar between ERA5 and ERA-Interim. After 10 days RTCEs in the troposphere exceed 100 % (Fig. b), at which point we may confidently say that conservation of specific humidity no longer applies. Tracer conservation errors in the UT/LS region rise to 30 % in the extratropics and 100 % in the tropics after 10 days, although stratospheric RTCE values remain well below 5 %.

Potential temperature and potential vorticity are conserved in reversible adiabatic processes and will not change in the absence of heating, cooling, evaporation, condensation, or mixing e.g.,. Our analysis of tracer conservation for potential temperature revealed major improvements when the new ERA5 products are used in place of ERA-Interim throughout the stratosphere and UT/LS. Global median RTCEs of potential temperature after 1 day are in the range of 0.4 %–1.6 % for ERA-Interim, but as low as 0.2 %–0.6 % for ERA5 (Fig. c). After 10 days, RTCE values increase to 1.9 %–6.2 % for ERA-Interim and 1.8 %–4.5 % for ERA5 (Fig. d). RTCEs for potential temperature are quite similar among the different latitude bands. Following , Fig.  further illustrates the improvements in consistency and tracer conservation of potential temperatures for ERA5. The figure shows the dispersion of 10-day trajectories from seeds at potential temperature levels ranging from 400 to 1200 K for simulations initialized on 1 July 2017. The results for both data sets reveal downwelling of air in the Southern Hemisphere polar vortex and upwelling over the ITCZ. However, much larger dispersion or “scattering” of the final positions of the trajectories is found in the simulations based on ERA-Interim relative to those based on ERA5, especially above the 800 K isentropic surface. Possible reasons for improved conservation of potential temperatures in simulations based on ERA5 compared to those based on ERA-Interim may be improved internal consistency of the ECMWF forecast model or between the model and observations as well as shorter analysis intervals, leading in turn to smaller assimilation increments in temperature.

We found much larger tracer conservation errors for potential vorticity than for potential temperature. Global median RTCEs are in the range of 48 %–54 % in the troposphere, 44 %–48 % in the UT/LS region, and 8 %–18 % in the stratosphere after 1 day (Fig. e). The stratospheric values compare well to estimates of relative potential vorticity changes calculated for balloon trajectories by , whereas the tropospheric values are about 10–20 percentage points larger than those reported by . After 10 days the RTCEs increased to 90 %–100 %, 60 %–70 %, and 20 %–50 %, respectively, in the same three height ranges (Fig. f). We found that tracer conservation is similar or slightly improved when using ERA5 data in the stratosphere, but it is weaker in the troposphere and UT/LS region. Following , we conducted several tests to check whether RTCEs can be improved by excluding trajectories for which potential vorticity conservation is not likely to be applicable. We excluded trajectories entering levels below 1 km altitude above the surface, to avoid turbulent and unstable conditions in the planetary boundary layer. We also excluded trajectories with relative humidities larger than 90 %, as condensation or evaporation may cause diabatic temperature changes in such cases. However, these tests did not yield any substantial changes in our RTCE results. The increase in tropospheric RTCEs of potential vorticity between ERA-Interim and ERA5 might be due to the higher spatiotemporal resolution in ERA5, which allows for finer structures in the potential vorticity fields relative to ERA-Interim (see Sect. ). The small improvements in stratospheric RTCEs are likely related to the improved conservation of potential temperature along trajectories.

As spatial and temporal resolution is a key factor in the trade-off between accuracy and computational time of Lagrangian transport simulations , our study covers a number of downsampling experiments using ERA5 data. The process of downsampling or decimation to reduce the sampling rate of a signal typically consists of two steps e.g.,. The first step is to apply a low-pass filter to the original data to avoid aliasing of high-frequency features. Here, we applied smoothing with triangular weights in space and time to achieve this effect. The second step is to subsample the smoothed data on the reduced grid. For example, to downsample ERA5 data from hourly to 2-hourly time intervals, we averaged data of {t-1h,t,t+1h} for a given time t with weighting factors of {0.25,0.5,0.25} and kept the smoothed data only at a 2-hourly interval. Sensitivity tests showed that this approach including low-pass filtering may significantly reduce aliasing errors and improve simulation results.

We conducted four downsampling experiments with the ERA5 data, in which we reduced (I) the number of synoptic time steps nt by a factor of 2, (II) the number of vertical levels nlev by a factor of 2, (III) the numbers of longitudes nlon and latitudes nlat by a factor of 2, and (IV) nt by a factor of 6, nlev by a factor of 2, and nlon and nlat by a factor of 3. Experiment IV was set up to achieve a spatiotemporal sampling similar to ERA-Interim. In order to enable a fair comparison, in experiment IV the low-pass filtering in the temporal domain was switched off and only subsampling was applied, as both ERA5 and ERA-Interim winds are instantaneous values rather than time-integrated quantities. We quantified the differences of the Lagrangian transport simulations using the downsampled and the full-resolution ERA5 data by calculating transport deviations after 1 day, as these are most sensitive to the specific uncertainties and less dependent on the individual meteorological conditions and flow conditions . Figures  and show the results of these four experiments.

Considering the downscaling experiments I–III (Fig. ), it was found that the impacts of downsampling of the ERA5 data are comparable to the impacts of parameterized diffusion and subgrid-scale wind fluctuations in most cases. The impacts of downsampling generally tend to be strongest in the troposphere, where transport deviations due to downsampling exceed those by diffusion and subgrid-scale wind fluctuations by up to a factor of 3. In the UT/LS region the horizontal transport deviations exceed those by diffusion and subgrid-scale wind fluctuations by up to a factor of 2 (Fig. a, b), whereas the vertical transport deviations are smaller by up to a factor of 2 (Fig. c, d). For the stratosphere the experiments suggest that we can downsample from hourly to 2-hourly data or that we can reduce the horizontal sampling by a factor of 2×2 without any significant impact compared to diffusion and subgrid-scale wind fluctuations. This may reflect the reduced sensitivity of the stratosphere to downsampling in the horizontal direction and in time, as the stratosphere is dynamically more stable and has a redder spectrum of motion than the troposphere. The number of vertical levels nlev should not be reduced in the stratosphere, because the vertical sampling even of the high-resolution ERA5 data is relatively coarse at stratospheric levels (see Fig. ).

Downsampling experiment IV (Fig. ) is intended to separate the impact of improved spatiotemporal resolution from the impacts of other improvements from ERA-Interim to ERA5, such as modified physical parameterizations in the forecast model or improved data assimilation procedures and observations. For this reason, transport deviations between the downsampled and full-resolution ERA5 data are compared to transport deviations between ERA5 and ERA-Interim and not with diffusion and subgrid-scale wind fluctuations in Fig. . In this experiment we found that transport deviations between simulations based on downsampled and full-resolution ERA5 data are mostly smaller than the deviations between ERA-Interim and ERA5. This indicates that the transport deviations between ERA-Interim and ERA5 as discussed in Sect.  are due to both improved resolution in ERA5 as well as other improvements in the forecast model and data assimilation scheme, and cannot be attributed to a single cause. Vertical transport deviations in the stratosphere are an exception, as the deviations due to downsampling became larger than the deviations between ERA-Interim and ERA5. Aliasing effects play a strong role in this case, as the vertical transport deviations in the stratosphere are reduced by a factor of 3–4 if low-pass filtering is taken into account. Other transport deviations are less affected by temporal low-pass filtering. In summary, using downsampled ERA5 data should generally not be considered to be equivalent to using ERA-Interim data for Lagrangian transport simulations.

Finally, we conducted a comparison of Lagrangian transport simulations using two different models, CLaMS and MPTRAC. This allows us (i) to check the consistency of the model results and (ii) to assess the readiness of both models for operating with the comprehensive ERA5 data set. The necessary adjustments to the codes and workflows for both models to make use of ERA5 data are described in Appendix . In this comparison, we focus on global transport deviations as well as differences in meteorological variables and dynamical tracers between CLaMS and MPTRAC after 1 day of integration at different height ranges. All simulations for the year 2017 are included. The results are shown in Fig. .

Overall, the model comparison revealed excellent agreement between CLaMS and MPTRAC kinematic trajectory calculations using ERA5 data. Transport deviations between the models are significantly smaller than those due to parameterized diffusion and subgrid-scale wind fluctuations in the MPTRAC model in most cases (Fig. a–d). The only notable exception is horizontal transport deviations in the middle and upper stratosphere (Fig. a), which are similar to or slightly exceed the deviations due to diffusion and subgrid-scale wind fluctuations. We tested whether these differences are due to the different vertical interpolation schemes applied in the models, with CLaMS using logarithmic interpolation and MPTRAC using linear interpolation with respect to pressure, but found that this only has a marginal impact. Furthermore, the results are robust against changes in the time step applied in the MPTRAC model. Nevertheless, the global AHTDs (RHTDs) between CLaMS and MPTRAC are less than 9 km (1.5 %) from the troposphere to the middle stratosphere and less than 30 km (2.3 %) in the middle and upper stratosphere at all latitudes. The global AVTDs (RVTDs) are less than 40 m (6 %) at all heights.

In most cases, transport deviations between CLaMS and MPTRAC do not lead to large deviations in meteorological variables or dynamical tracers sampled along the trajectories (Fig. e to h). Temperature MADs are less than 0.25 K, specific humidity MRDs are below 2.2 %, and potential temperature MRDs are less than 2.0 %. Larger differences (up to 12 %–13 %) were found for potential vorticity in the troposphere and UT/LS region. This may reflect the fact that numerical calculations of potential vorticity are particularly sensitive to fine-scale structure and variability in the horizontal wind field in this part of the atmosphere (see Sect. ). In the stratosphere, differences in potential vorticity between CLaMS and MPTRAC simulations are comparable to or smaller than transport deviations due to diffusion and subgrid-scale wind fluctuations.