The Sensitivity of Moisture Flux Partitioning in the Cold-Point Tropopause to External Forcing

The dryness of the stratosphere is the result of air entering through the cold tropical tropopause layer (TTL). However, our understanding of the moisture flux partitioning into water vapor and frozen hydrometeors is incomplete. This raises concerns regarding the ability of General Circulation Models to accurately predict changes in stratospheric water vapor following perturbations in the radiative budget due to volcanic aerosol or stratospheric geoengineering. We present the first results using a


10.1029/2022GL102262
2 of 8 The stratosphere is extremely dry because virtually all moisture entering it from below has to pass the tropical cold-point tropopause.This temperature minimum between the troposphere and stratosphere causes freeze drying of air on its upwards journey, restricting the vapor content entering the stratosphere (Brewer, 1949).The correlation between specific humidity entering the stratosphere and cold-point temperatures is also evident in the well known "atmospheric tape recorder" signal (Mote et al., 1996) formed by alternating bands of lower and higher specific humidity which are dictated by seasonal variations of the cold-point temperature.This correlation of cold-point temperature and specific humidity, however, does not give information on the partitioning of moisture fluxes into large-scale upwelling water vapor and small-scale processes such as convection overshooting the cold-point tropopause, in-cloud upwelling, and turbulent mixing.This adds uncertainty to estimates of the stratospheric water vapor budget as these small-scale processes have been recognized as a non negligible source of moisture (i.e., Fueglistaler et al., 2013;Dessler et al., 2016).Efforts to quantify the contribution of frozen hydrometeors often rely on an indirect quantification of the contribution of frozen moisture with the help of trajectory models.Corresponding estimates for the frozen contribution to the moisture flux can have a low bias if coarse scale wind fields are used.Reported values include Schoeberl et al. (2018) with 2% (between 18 and −30 km), Ueyama et al. (2015) with 14% (at 100 hPa), Ueyama et al. (2018) with 15% (at 100 hPa) and Smith et al. (2022) with 26-32% (entry above 18.6 km).
The large spread of estimates demonstrates the difficulties in representing small-scale processes, especially in GCM model simulations.The situation is complicated by the fact that the convective parameterizations used in the current generation of GCMs do not reproduce all essential features of convection (i.e., Arakawa, 2004;Jones & Randall, 2011;Sherwood et al., 2014).For a description of the stratospheric water vapor budget an accurate representation of thin cirrus clouds and convection overshooting the cold-point tropopause is essential, however.Additionally some shortcomings of parametrization schemes are not immediately apparent as errors in process representation often compensate for each other (Hardiman et al., 2015).Since computational resources are becoming more readily available and storm-resolving simulations are emerging, this problem can finally be alleviated by employing high resolution simulations which do not depend on convective parametrizations (i.e., Stevens et al., 2020).Several mesoscale studies confirm the hydration by overshooting convection (Behera et al., 2022;Chaboureau et al., 2007;Dauhut et al., 2018).Based on the analysis of a single storm Dauhut et al. (2015) estimate a frozen moisture contribution of 18%.Dauhut and Hohenegger (2022) report a frozen moisture contribution of 11%, which is the only estimate based on direct quantification using a global storm-resolving simulation.Additionally, Bolot and Fueglistaler (2021) presented the first global estimate based on observational data with a frozen contribution of around 18%.
Apart from unperturbed scenarios, the explicitly resolved deep convection overshooting the cold-point tropopause offers the possibility to predict the sensitivity of the TTL moisture fluxes to external forcing more reliably.The TTL sensitivity will be of special interest in a future where the TTL is affected by climate change and the potential employment of solar radiation management methods relying on sulfate aerosol in the lower stratosphere.We use this unprecedented opportunity and investigate the question how the moisture flux partitioning changes under perturbation.To address the question we set up a simulation pair consisting of a control (CTL) and perturbed simulation (PTB) in which the TTL is disturbed by introduction of a large heating source.This simulation pair allows us to address the question how the moisture fluxes into the stratosphere are partitioned between water vapor and frozen hydrometeors within one single framework.Additionally, the sensitivity experiment will shed light into changes of the flux partitioning at the cold-point tropopause under external perturbation.In order to get a clear signal we deliberately choose a strong forcing even if it may not be encountered in nature in this form.
In the following Section 2 the model experiments and the analysis methods are described.Section 3 summarizes the results of the study: first a quantification of the perturbation, followed by a description of the dependence of the water vapor content on the large-scale temperature field, and a discussion of the flux partitioning under perturbations.The results are discussed in Section 4.

Model Setup
We use the atmosphere model of the Icosahedral Nonhydrostatic Weather and Climate Model (ICON) (Crueger et al., 2018;Giorgetta et al., 2018) and an approximately isotropic horizontal grid of 10 km.At this resolution the model can explicitly resolve deep convection and no convective parametrization is employed (Hohenegger et al., 2020;Vergara-Temprado et al., 2020).The model encompasses 90 vertical levels up to the model top at 75 km.The sponge layer reaches down to 44 km with continuously decreasing impact.We use the sapphire physics setup (Hohenegger et al., 2022) with the PSrad radiation parametrization (Pincus & Stevens, 2013) and the one moment "three category ice scheme" (an updated version of Baldauf et al., 2011), which considers six water categories: water vapor, cloud water, rain, cloud ice, graupel and snow.

Experiments
Two experiments are investigated: an unperturbed run (CTL) and a run perturbed by the introduction of an additional heating source in the TTL and stratosphere up to a height of 30 km (PTB).In PTB the SSTs are fixed to those of the control run.Both CTL and PTB are run with all boundary conditions fixed to conditions for 1 January 2020.In PTB the additional heating source is realized by adding sulfate aerosol represented by monthly means of height and latitude dependent optical properties for all radiation bands of the model.The corresponding forcing fields were generated offline with the Easy Volcanic Aerosol (EVA) forcing generator (Toohey et al., 2016).EVA simulations were performed for an hypothetical equatorial volcanic eruption with a stratospheric emission of 20 Tg S. This corresponds to twice the sulfur amount emitted by the Mt.Pinatubo eruption.With the objective to generate a large tropopause perturbation the month with the highest near infrared extinction was selected and set constant throughout the simulations.The peak of the Gaussian shaped extinction profile is located at a height of 21.5 km, latitudinally the forcing is centered around the equator.Extinction values in the [20,20]°N region are relatively homogeneous, but decline rapidly toward the poles.Our analysis is based on a 60 days average after 150 days of spin-up both for CTL and PTB each.

Budget Calculations
In order to investigate the different contributions to the moisture fluxes in the TTL a budget analysis is performed.The changes in specific moisture content q i with i ∈ {frozen, non-frozen} are described by the continuity equation where the first three terms on the right hand side of the equation describe the advective transport of the specific moisture q i through the atmosphere of density ρ with the velocities u, v or w, the fourth term the flux due to the sedimentation velocity w sedi,i , the fifth term the parameterized component of turbulent mixing with diffusion constant D, and σ i accounts for the sources and sinks of moisture due to microphysical conversion processes between frozen and non-frozen phases.For our budget calculations we use the vertical flux terms due to advection, sedimentation and turbulent mixing.
Special care is taken to ensure mass conservation within the analysis.We circumvent issues arising from the mixing of variables calculated in different subsequent calculation steps, by adding advection and sedimentation fluxes, as well as the microphysical tendencies, as output streams to ICON allowing for a direct online calculation.The quality of our analysis also depends on the handling of the Courant-Friedrichs-Lewy criterion (CFL, Courant et al., 1928) and the choice of model surface on which the analysis is performed.Violations of the CFL criterion are prevented in the model by velocity damping.This damping, however, may create or delete tracer mass in extreme cases.To prevent this the time step is reduced to a quarter of the default time step for the used resolution.This reduces the distance which can be traveled by air parcels within one time step and thus the probability to pass through multiple grid cells within one integration step.All calculations are performed on the native grid to ensure a closed budget.

Choice of Reference Height
The moisture budget calculation is carried out on the original native grid.For the calculation of the moisture flux the time and spatial average of the total fluxes in the area between [−30,30]°N is computed and then evaluated at the height level nearest to the correspondingly averaged cold-point tropopause height.The latter is defined here as the lowest temperature between troposphere and stratosphere on height levels of around 500-700 m spacing in the TTL.Any reference to the tropopause in the text hereafter consequently refers to the average cold-point tropopause.Although this vertical resolution will not allow for a replication of radio-sounding measurements (Gettelman & Forster, 2002), we chose it as Dauhut and Hohenegger (2022) showed that it is possible to compute a moisture budget at this grid spacing.

Quantifying the Perturbation
Figure 1 shows the inner tropical (potential) temperature and lapse rate profiles of the Control (CTL, blue) and Perturbed (PTB, red) simulations.The heating starts to take effect at a height of around 12.5 km, but is most prominent in the TTL and lower stratosphere.Table 1 summarizes the changes in the physical parameters of CTL and PTB relevant for this study: The cold-point tropopause height is shifted downwards by (1.1 ± 0.6) km.The corresponding uncertainty in the cold-point height is the upper limit for the error made if the average cold-point were located one model level lower or higher than calculated.The mean and lowest 10th percentile of cold-point tropopause temperature rise by 8.9 and 9.2 K, respectively.The increases in saturation specific humidity caused by the elevated cold-point temperatures enhance the specific humidity values at the cold-point by more than 200%.To put these values in context, both the changes in cold-point temperature and specific humidity are between three and four times larger than the amplitudes of their seasonal variations at the cold-point tropopause (i.e., Seidel et al., 2001).

Water Vapor Distribution at the Cold-Point Tropopause
Figure 2 visualizes the average water vapor at the cold-point for CTL (blue) and PTB (red) in relation to the temperature dependent saturation water vapor mixing ratio as implemented in ICON (Doms et al., 2021).In PTB the average water vapor is about three times higher than in CTL due to the cold-point warming.Nevertheless, the large-scale picture of the dependence of the average water vapor on the cold-point temperature remains unchanged.
In line with previous studies, the model results show that the vapor at the cold point scales well with an equivalent frost point temperature.The water vapor at the cold point is dictated by the lowest temperatures in the inner tropics (Fueglistaler & Haynes, 2005;Oman et al., 2008).Here the 10th percentile of cold-point temperatures in the [−5,5]°N region describes the vapor values for CTL and PTB.For PTB, the estimate using the 10th percentile of cold-point temperatures slightly exceeds (+10%) the model's water vapor mixing ratio.This discrepancy may be explained by an increase in the horizontal velocities at the cold-point tropopause (+14%) and enhanced variability of the cold-point temperatures (±4%).Nevertheless, the correlation between saturation water vapor mixing ratio and the 10th percentile of cold-point temperatures remains a good indicator to estimate the average water vapor at the cold-point, also for the perturbed case.It is only shifted according to the 9 K ΔT of cold-point warming (compare Table 1).The 10th percentile of cold-point temperatures in Control and Perturbed can consequently be seen as the equivalent frost point temperature of the TTL in this simulation.

Change in Flux Partitioning
Figure 3 shows the contribution from water vapor and frozen hydrometeors to the total flux for CTL (blue) and PTB (red) (The plot shows unrounded values, the calculated percentage changes therefore deviate slightly from those calculated based on the values reported in the text.).A first inspection of the CTL data reveals that the frozen moisture flux of 0.0006 kg m −2 year −1 contributes with around 20%, a value which is well within the spread of values reported in previous studies (e.g., Dauhut et al., 2015;Dauhut & Hohenegger, 2022;Schoeberl et al., 2018;Smith et al., 2022;Ueyama et al., 2015Ueyama et al., , 2018)).The leading order term however is the water vapor flux of 0.0021 kg m −2 year −1 contributing around 80% to the total flux.The computed water vapor values and water vapor fluxes at the cold point are also consistent with observations in January (Fueglistaler et al., 2009;Sioris et al., 2016).In PTB the water vapor flux is enhanced to 0.0081 kg m −2 year −1 by a factor of four.However, the flux of frozen hydrometeors is increased  by almost the same factor to 0.0023 kg m −2 year −1 .This means that the partitioning into fluxes of water vapor and frozen hydrometeors remains virtually unchanged despite the strong perturbation of the TTL in the PTB experiment.

Discussion
We used ICON, a strom-resolving global model, to study the sensitivity of the moisture flux partitioning in the TTL to external forcing.The base simulation is in line with previously published data on moisture flux partitioning in non-frozen and frozen contributions.Our 20% contribution is in agreement with the 18% frozen contribution found in the observational based study by Bolot and Fueglistaler (2021).ICON was used by Dauhut and Hohenegger (2022) as well, their estimates are 11%, when only considering the deepest convection, and 29%, when considering all hydrometeors.The calculations are not directly comparable, though, for three reasons.First, they rely on a higher horizontal resolution and a slightly different physics package.Second, their analysis is based on tendencies calculated offline.Third, they indirectly inferred the frozen moisture contribution, rather than directly calculating fluxes online as in our study.Our result also falls into the range of 2%-32% frozen moisture contribution reported in GCM studies (Schoeberl et al., 2018;Smith et al., 2022;Ueyama et al., 2015Ueyama et al., , 2018)).
The analysis shows that in response to the strong tropopause perturbation, the moisture flux partitioning remains almost constant-even for a very strong perturbation with an average increase of cold-point temperatures by over 8 K.The constant share of frozen moisture to the total moisture entering the stratosphere underlines the character of the TTL as a layer which is set by a balance between radiative-dynamically induced temperature changes in the stratosphere and temperature changes due to convective-radiative-dynamical process from the troposphere (Fueglistaler et al., 2009).
The result of roughly constant partitioning may surprise at first, but is consistent with a trajectory model based climate change study (Smith et al., 2022), where ice content was explicitly tracked.Observational based studies analyzing the annual cycle (Fueglistaler et al., 2013;Liu et al., 2010) also found a constant frozen hydrometeor contribution, which can calculated from the offset between observed and modeled water vapor values.Here the frozen moisture flux is calculated directly.The agreement on the constant partitioning despite the different analysis method indicates that the robustness of the moisture flux partitioning in the TTL is not exclusive to a perturbation in form of an heating layer, as in our volcanic or geoengineering scenarios, but has also holds for other disturbances such as seasonal variations and climate change.
The constant partitioning of moisture fluxes into frozen and non-frozen states of matter demonstrates that the large-scale temperature field determines both moisture fluxes entering the stratosphere for these various perturbations.Frozen and non-frozen moisture follows the Clausius Clapeyron scaling.Consequently, the total flux can be thought of as a water vapor flux controlled by an equivalent frost point temperature, whereas the flux of frozen hydrometeors is given by an additional constant temperature offset ΔT.Based on a 12% increase of specific humidity per Kelvin in the cold-point region (C. A. Kroll et al., 2021), this offset gives an estimate of the constant relative contribution of frozen moisture to the total budget.
The contribution of frozen moisture to the total stratospheric moisture budget is still largely uncertain, especially in the current generation of GCMs.The agreement on the constant partitioning between our direct quantification in a storm-resolving framework and the indirect quantification in a framework relying on convective parametrization in a GCM (Smith et al., 2022) is therefore encouraging.
In summary, the result of the analysis shows that the moisture flux partitioning at the cold-point tropopause is robust, even under large perturbations.The explicitly resolved deep convection in our numerical model increases the confidence that this result is not a model artifact.The actual numbers presented in this study may be model specific and sensitive to the choice of microphysical parametrization (Hu et al., 2021;Lamraoui et al., 2023;van Zanten et al., 2011).Further constraints of the contribution of frozen moisture to the total flux based on observations are needed and may be complemented by simulations with even higher resolution.

Figure 1 .
Figure 1.Left panel: temperature (solid line) and potential temperature profile (θ, dashed line).Right panel: lapse rate profile for temperature.An average over the inner tropical region between [−5,5]°N is taken for both plots.Control is shown in blue, Perturbed in red.The dotted line indicates the height of the cold-point tropopause.The gray lines indicate the height levels.

Figure 2 .
Figure 2. Two-months average water vapor mixing ratio at the mean cold-point height for CTL (blue) and PTB (red) in the inner tropics between [−5,5]°N, marked by horizontal dashed lines.The average water vapor values are compared against the expected saturation water vapor mixing ratio at the mean cold-point temperature and the 10th percentile of cold-point temperatures for CTL and PTB, marked with arrows.The solid curves mark the saturation mixing ratio above ice as function of temperature at the cold-point pressure as implemented in ICON (COSMO, Doms et al., 2021) for CTL and PTB.

Figure 3 .
Figure 3. Two-month average of the moisture fluxes at the average cold-point tropopause in the region between [−30,30]°N.The contribution of water vapor and frozen hydrometeors is shown along with the total.The control simulation is shown in blue, the perturbed simulations in red.Above the bars the corresponding share of the total moisture flux is shown.