Parametrizing the mixing by clear air turbulence in the chemistry climate model EMAC and its respective radiative impact

The Earth's radiation budget is found to be sensitive to changes in the upper troposphere and lower stratosphere (UTLS) chemical composition. Stratosphere-troposphere exchange is the major process that influences the UTLS chemical composition with remaining uncertainties in current climate-chemistry models. This exchange could be e.g., facilitated by clear air turbulence (CAT), as it leads to diabatic mixing of chemical tracers between stratosphere and troposphere. In this work, we examine the potential impact of vertical mixing by CAT on the UTLS chemical composition and its corresponding radiative impact by implementing a newly developed submodel parametrizing turbulent mixing in the free troposphere and stratosphere within the chemistry climate model EMAC. This submodel parametrizes the vertical mixing by CAT based on a newly introduced turbulence diagnostic Modified CAT Index (MoCATI). MoCATI shows a comparable performance with the well-established Ellrod-Knox index. Simulations are conducted with EMAC under the Quasi Chemistry transport Model (QCTM) mode to examine the sole impact of mixing, without taking the potential feedback into account. Results show that the radiatively active ozone in the UTLS is most sensitive to the vertical mixing of CAT and is significantly reduced by 10 % to 20 % by the CAT submodel. This modification is not a pure result of the physical mixing but also the chemical feedback of other tracer distributions modified by CAT. The tracer mixing through CAT also changes the atmospheric chemistry by shortening the CH₄ lifetime and changing the O₃ becoming more sensitive to NO_x. It also leads to potential surface radiative heating and radiative cooling at the top of the atmosphere. The global average radiative effect is about −0.2 W m⁻² without considering water vapour.

1 Introduction

The upper troposphere and lower stratosphere (UTLS) plays a crucial role on the Earth's radiation budget (Forster et al., 2021). Changes in the chemical composition in the UTLS could lead to changes via the radiation locally as well as at the surface. Ozone and water vapour near the tropopause are found to have more radiative influence on the surface compared to other well-mixed greenhouse gases (Riese et al., 2012; Lacis et al., 1990). Removal of ozone above the tropopause could lead to local cooling (Randel et al., 2007). The surface temperature is also highly sensitive to changing ozone concentration in the UTLS, increasing ozone in this region could increase the surface temperature (Forster and Shine, 1997; Lacis et al., 1990). Water vapour also has complex impacts on the Earth's radiation. Increasing stratospheric water vapour could lead to local cooling (Forster and Shine, 1999; Randel et al., 2007) and surface warming (Solomon et al., 2010).

Since stratosphere-troposphere exchange (STE) is one of the major processes that influence the UTLS chemical composition (Holton et al., 1995; Stohl et al., 2003), it is crucial to improve the representation of STE in the model. Previous studies show that the simulated upper tropospheric ozone budget depends on the model representation of STE (Stevenson et al., 2006). A key feature for STE is the occurrence of vertical shear, which has recently been shown to form a layer with high probability of shear occurrence near the local tropopause (Kaluza et al., 2021). Vertical shear is a key mechanism to initiate turbulence and thus mixing. Turbulent mixing in the UTLS is one of the pathways of the STE (Holton et al., 1995) and it is not represented in several state-of-the-art chemistry climate models, such as EMAC (Jöckel et al., 2016). In ECHAM5, the base model of EMAC, the turbulence scheme was designed for the surface boundary layer only; it sets a constant asymptotic mixing length in the boundary layer and simply assumes it decreases exponentially with height, approaching 1 m in the lower stratosphere (Roeckner et al., 2003), resulting in a dampening effect on the turbulence in the UTLS, which normally does not mix tracers significantly. Therefore, this study presents a parametrization of tracer mixing by clear air turbulence (CAT), which is commonly found in the UTLS and could lead to rapid mixing of the chemical composition between the troposphere and stratosphere (Dutton and Panofsky, 1970; Esler and Polvani, 2004; Traub and Lelieveld, 2003).

CAT represents the turbulence in the free atmosphere that occurs in a cloud-free region (Ellrod et al., 2003). Kelvin-Helmholtz instability, which is a result of vertical wind shear (Kunkel et al., 2019; Dutton and Panofsky, 1970; Richardson, 1920), is the major mechanism that leads to CAT formation (Watkins and Browning, 1973; Ellrod and Knapp, 1992; Dutton and Panofsky, 1970). Considering turbulence is not explicitly represented by global scale numerical models, CAT is usually forecast using diagnostics that are based on related larger-scale mechanisms. A previous study has shown that turbulence diagnostics are reliable for forecasting CAT operationally in NWP models (Sharman et al., 2006). However, each of the turbulence diagnostics has its own advantages and disadvantages. Ellrod index (TI) is one of the most commonly used CAT diagnostics in the aviation sector. It is based on the meso-scale condition that leads to CAT including vertical wind shear and deformation of the horizontal wind (Ellrod and Knapp, 1992). The Ellrod-Knox index is the improved version of the TI by introducing an additional divergence trend term (Ellrod and Knox, 2010). (Williams and Storer, 2022) confirmed that turbulence diagnostics are capable of diagnosing CAT and its response to climate change in climate models with coarser resolution. Another recent study from (Chau et al., 2025) shows that the turbulence diagnostic calculated from the grid scale wind field matches well with a detailed sub-grid scale turbulence scheme in the UTLS for a regional forecast model.

CAT is expected to become more frequent and intense under climate change because of the more sheared atmosphere (Williams, 2017). The vertical wind shear at 250 hPa in the North Atlantic region has increased by 15 % between 1979 and 2017 (Lee et al., 2019). Several studies show that the strength of CAT will be stronger in the North Atlantic and East Asia under different climate change scenarios (Williams and Joshi, 2013; Smith et al., 2023; Hu et al., 2021). Therefore, there is a necessity to study how CAT could potentially change the atmosphere. Previous studies have examined the sensitivity of the vertical mixing in a Lagrangian approach, concluding that water vapour and ozone are most sensitive to vertical mixing and lead to a significant impact on the radiation budget (Riese et al., 2012). The main objective of this study is to examine the potential impact of vertical turbulent mixing by CAT on the UTLS chemistry and radiation in an Eulerian approach. For this purpose, we introduce a new EMAC submodel to parametrize the CAT-induced vertical mixing of tracers in the UTLS. In order to examine the sole impact of CAT but not its feedback, the simulations are conducted in a Quasi Chemistry transport Model (QCTM) mode (Deckert et al., 2011) to ensure identical model dynamics independent of the chemical composition.

This paper consists of three further sections after the introduction: Sect. 2 introduces the EMAC model configuration and the newly developed CAT submodel. Section 3 presents the results and discusses the CAT submodel in terms of redistributing chemical composition and radiative impact. Section 4 summarises the findings and draws conclusions with a future outlook.

2 Method

2.1 EMAC Model Description

EMAC (ECHAM/MESSy Atmospheric Chemistry; Jöckel et al., 2006; Jöckel et al., 2010) is a state-of-the-art chemistry climate model that allows flexible model configuration via different submodels. It combines the general circulation model ECHAM5 (Roeckner et al., 2003) with the Modular Earth Submodel System (MESSy; Jöckel et al., 2005) which allows users to include different physical and chemical processes via a namelist interface. EMAC is also able to operate in quasi chemistry-transport model mode (QCTM; Deckert et al., 2011), which allows decoupling between chemistry and dynamics in the model, suppressing the feedback between chemistry and dynamics to better quantify the signal from a particular process. For our study, EMAC is operated in T42L90MA resolution (Giorgetta et al., 2006). It is a configuration designed for the middle atmosphere with a horizontal resolution of T42 (approximately 2.8° × 2.8°) and 90 vertical hybrid pressure levels up to 0.01 hPa. The vertical resolution in the UTLS is approximately 400 to 500 m.

2.2 Experimental setup

Two simulations: QCTM-MIX and QCTM-NOMIX are performed in this work. Two decadal simulations with gas-phase chemistry are performed using the EMAC-QCTM to examine the long-term impact of the CAT submodel without the dynamical feedback from chemistry. Both simulations are performed with the perpetual year of 2014 for 10 years, prescribing the emission, sea surface temperature and sea ice concentration of 2014 repetitively. The chemistry setup is adapted from the RC1-base-07 of Jöckel et al. (2016), which is the Ref-C1 of the CCMI (Eyring et al., 2013), a free-running historical hindcast. The emissions are prescribed by the CCMI-2022 Ref-D1 (Plummer et al., 2021), which is a historical hindcast. The sea surface temperature and sea ice concentration are prescribed by the AMIP-II data set (Taylor et al., 2000), the monthly means computed from model output, which agree with the observations. Both simulations are initialized with the ERA-Interim reanalysis data (Dee et al., 2011).

QCTM-NOMIX with the CAT submodel disabled is used as a reference simulation, while the QCTM-MIX enables the CAT submodel to examine the impact of the CAT tracer mixing. The details for the CAT submodel are discussed in Sect. 2.3.

2.2.1 Radiation (RAD) submodel of EMAC

In EMAC, the radiation scheme (RAD) is a re-implementation of the ECHAM5/ECHAM6 radiation codes with more flexibility (Dietmüller et al., 2016). It calculates the radiation depending on radiatively active tracers, including CO₂, CH₄, O₃, N₂O, CFC-11 and CFC-12. It also requires input parameters like water vapour, cloud cover, clear-sky index, cloud optical properties, aerosol optical properties, and orbital parameters provided by the model. RAD allows for both online and offline radiation calculations, i.e., using either prognostic variables (tracers) or external data sources for the radiatively active species. To run EMAC in the QCTM mode, climatological values or distributions of the radiatively active gases are utilised for the radiation calculation to decouple the feedback between the gases and the radiation scheme. Water vapour also needs to be decoupled from the chemistry to prevent inconsistency in model dynamics. Therefore, the mixing scheme of the new submodel CAT (Sect. 2.3) does not include water vapour at this stage. RAD also provides an option to calculate the radiative disturbances from different sets of radiatively active gases by calling the radiation routine multiple times within one model time step. The temperature feedback will be provided by the first call. This option provides an opportunity to examine the pure radiative impact of the CAT mixing without dynamical feedback within EMAC-QCTM. In both simulations, a total of six calls are set. For the first call, which provides the temperature feedback of the model, prescribed values for the radiatively active gases are used. For the second call, the radiation calculation uses all the online interactive chemistry output provided by EMAC. To isolate the individual contribution of each gas, four additional radiation calls are set. In each call, only the specified gas uses the online output from the model, the other gases remain unchanged using the prescribed values. Detailed information about the applied values and the dataset is given in Table 1. The prescribed values for CO₂, CH₄, N₂O, CFC-11 and CFC-12 are provided by the Global Monitoring Laboratory of NOAA. The prescribed O₃ is taken from the climatology of (Paul et al., 1998).

Paul et al. (1998)Paul et al. (1998)Paul et al. (1998)Paul et al. (1998)

Table 1 Summary of the performed radiation calls and the applied values [mol/mol] for the active tracers

2.3 New MESSy submodel CAT for clear air turbulence mixing

This section introduces the newly developed submodel CAT of MESSy. The new CAT submodel is developed to parametrize the vertical mixing of tracers caused by clear air turbulence in the UTLS. It allows vertical mixing of tracers based on a 2-layer mixing algorithm between 500 to 70 hPa, considering that CAT occurs most frequently in the UTLS (Dutton and Panofsky, 1970). At pressure levels below 70 hPa, vertical tracer mixing by turbulence is strongly suppressed due to the strong static stability. At pressures higher than 500 hPa, deep tropopause fold intrusions might occur and lead to tracer mixing; however, such structures are usually not represented well in a typical EMAC setup with a coarse horizontal resolution (e.g. T42 and T63). Therefore, the CAT parametrization is switched off for pressure lower than 70 hPa and higher than 500 hPa, considering the limited computational resources and to avoid overlap with the boundary layer parametrization scheme. The mixing scheme of CAT follows a typical K-theory for turbulence fluxes and uses a turbulence diagnostic (CAT Index) to serve as a mixing coefficient and provides two options for now: the Ellrod-Knox index (Ellrod and Knox, 2010) and a newly introduced Modified CAT Index (MoCATI) specifically modified for tracer mixing. The Ellrod-Knox index is a widely tested and used turbulence diagnostic, which is based on the grid scale wind field data including deformation (DEF), vertical wind shear (VWS), and divergence trend (DVT):

$$\begin{array}{}\text{(1)}& \begin{array}{rl}\text{Ellrod-Knox index}& =\underset{\text{DEF}}{\underbrace{{\left[{\left({\displaystyle \frac{\partial u}{\partial x}}-{\displaystyle \frac{\partial v}{\partial y}}\right)}^{\mathrm{2}}+{\left({\displaystyle \frac{\partial v}{\partial x}}+{\displaystyle \frac{\partial u}{\partial y}}\right)}^{\mathrm{2}}\right]}^{\frac{\mathrm{1}}{\mathrm{2}}}}}\\ & \cdot \underset{\text{VWS}}{\underbrace{{\left({\left|{\displaystyle \frac{\partial u}{\partial z}}\right|}^{\mathrm{2}}+{\left|{\displaystyle \frac{\partial v}{\partial z}}\right|}^{\mathrm{2}}\right)}^{\frac{\mathrm{1}}{\mathrm{2}}}}}\\ & +\underset{\text{DVT}}{\underbrace{C\left[{\left({\displaystyle \frac{\partial u}{\partial x}}+{\displaystyle \frac{\partial v}{\partial y}}\right)}_{h\mathrm{2}}-{\left({\displaystyle \frac{\partial u}{\partial x}}+{\displaystyle \frac{\partial v}{\partial y}}\right)}_{h\mathrm{1}}\right]}}\end{array}\end{array}$$

The subscripts h1 and h2 represent the selected time interval for the divergence trend. C is a weighting constant to prevent the divergence trend term from dominating the whole Ellord-Knox index.

MoCATI is developed on top of the Ellrod-Knox index. It is a modification of the Ellrod-Knox index including static stability to moderate the mixing of tracer under stable conditions:

$$\begin{array}{}\text{(2)}& \text{MoCATI}={\displaystyle \frac{N_{\text{lim}}^{\mathrm{2}}-N^{\mathrm{2}}}{N_{\text{lim}}^{\mathrm{2}}}}\cdot \text{Ellrod-Knox index}\end{array}$$

The N² is the moist Brunt-Väisälä frequency calculated by the equivalent potential temperature and $N_{\text{lim}}^{\mathrm{2}}$ is a limitation threshold to modify the whole stability term, considering that a stable environment will suppress the formation of turbulence. In addition, the mixing will be switched off above the $N_{\text{lim}}^{\mathrm{2}}$. In order to demonstrate that the stability modification of MoCATI preserves the utility of the original Ellrod-Knox index, statistical tests and frequency distribution analysis are performed. MoCATI shows a comparable performance with the Ellrod-Knox index; details can be found in the Supplement Sect. S1.

Figure 1 Schematic of the tracer mixing algorithm of the CAT submodel. F represents the flux of mixing and n represents the model vertical level.

A schematic of the tracer mixing algorithm is shown in Fig. 1. The flux of the mixing between level n and level n+1 depends on the mixing ratio (χ) and the CAT index at the boundary of both layers. The flux from level n to n+1 can be express as:

$$\begin{array}{}\text{(3)}& F_{n\to n+\mathrm{1}}=\mathit{\chi }\cdot {\text{CAT Index}}_{\text{boundary}}\end{array}$$

The CAT index at the boundary can be calculated by:

$$\begin{array}{}\text{(4)}& {\mathrm{\text{CAT Index}}}_{\text{boundary}}={\displaystyle \frac{{\text{CAT Index}}_n+{\text{CAT Index}}_{n+\mathrm{1}}}{\mathrm{2}}}\cdot {\displaystyle \frac{\mathrm{\Delta }t}{t_{\text{norm}}}}\end{array}$$

The Δt is the time step length and the t_norm is a time normalization factor. The whole term is used to moderate the strength of mixing.

The CAT submodel allows changes in different parameters via a simple namelist. An example namelist can be found in the electronic supplement. The values used in this study are summarized in Table 2. The constant C in the DVT of the Ellrod-Knox index is selected according to our sensitivity analysis on the frequency distribution (Fig. S3). We found that the suggested values of 0.1 from (Ellrod and Knox, 2010) and 0.01 from Lee et al. (2020) lead to either too strong or too weak DVT compared to the VWS and DEF. The time interval of DVT (nhours) is selected based on (Ellrod and Knox, 2010) and the limitation threshold ($N_{\text{lim}}^{\mathrm{2}}$) is selected based on (Chau et al., 2025). The t_norm which moderates the strength of tracer mixing is an empirical value that shown to improve the ozone representation in EMAC (Fig. 2b) against observations (SWOOSH).

Ellrod and Knox (2010)Chau et al. (2025)

Table 2 Used values of the namelist parameters.

2.3.1 Limitations of the CAT approach

Despite the improvements shown in Sect. 3.1, several limitations regarding the current CAT mixing scheme should be noted. The current approach of the CAT mixing scheme assumes the tracer mixing flux is linearly proportional to the magnitude of the CAT index, while the mapping functions between the turbulence strength and turbulence diagnostics are only piecewise linear (Sharman et al., 2006). It should also be noted that this parametrization is specifically tuned for the EMAC model under T42L90MA resolution, which is one of the most widely used resolutions, especially for long-term climatic studies including the stratosphere. For example, the namelist parameter C in the DVT is resolution-dependent and t_norm is an empirical value as well. Application of the CAT submodel to other model setups of EMAC or other climate models will require retuning. Also, water vapour is not treated as a chemical tracer in EMAC but as a thermodynamic quantity (specific humidity) and is therefore excluded in the current version of CAT in order to maintain identical model dynamics for comparison between the simulations under QCTM mode.

Figure 2 Cross section of the annual ozone zonal mean difference for (a) QCTM-NOMIX minus SWOOSH, (b) QCTM-MIX minus SWOOSH, and (c) QCTM-MIX-ENI minus SWOOSH. The contour lines represent the mixing ratio of O₃ in ppmv of the respective QCTM simulation. The black solid line indicates the PV tropopause in the extratropics and lapse rate tropopause in the tropics.

3 Results and Discussion

3.1 Comparison of simulated O₃ with SWOOSH observations

In order to examine the performance of the new CAT submodel, a comparison between both simulations and the satellite-based database SWOOSH (Davis et al., 2016) is conducted. Figure 2a and b show the annual mean difference of ozone between both simulations and the SWOOSH. By applying the CAT submodel, the overestimated ozone over the polar regions in the stratosphere is significantly reduced. The vertical mixing by CAT in QCTM-MIX reduces the ozone significantly between 75 to 175 hPa compared to QCTM-NOMIX, the details are discussed further in Sect. 3.2. A previous study from (Righi et al., 2015) shows that EMAC underestimates the ozone hole in Antarctica, causing a warm bias in the southern hemispheric stratosphere. QCTM-MIX shows a better consistency with SWOOSH in this region for ozone. As will be described later, Fig. 8 shows the annual mean difference in the net radiation between both simulations. The local cooling caused by the changes in ozone in this region might partly resolve the warm bias in this region. An extra simulation (QCTM-MIX-ENI) is conducted to show the necessity of the stability modification of MoCATI by using simply the Ellrod-Knox index as the mixing coefficient (the other model setup is identical). Figure 2c shows the annual mean difference of ozone between QCTM-MIX-ENI and SWOOSH. Without the stability modification, ozone is “overmixed” and leads to underestimation in many regions, especially the Northern Hemisphere and the tropics. In order to evaluate whether CAT could improve the representation of ozone climatologically in EMAC, we calculated the normalized root mean square error (RMSE) of all 3 simulations (Table 3). QCTM-MIX shows the lowest normalized RMSE in most of the region except for the Southern Hemisphere. QCTM-MIX-ENI shows the lowest RMSE in the Southern Hemisphere, but shows a larger RMSE in other regions compared to QCTM-NOMIX. These results indicate that QCTM-MIX shows an improvement in all regions compared to QCTM-NOMIX, while QCTM-MIX-ENI improves the most in the Southern Hemisphere, but worsens the representation in other regions compared to QCTM-NOMIX. These results show that with the new mixing parametrization of tracers based on the static stability correction on the Ellrod-Knox index (MoCATI), the representation of ozone in the EMAC model is improved compared to SWOOSH in a climatological sense.

Table 3 Root mean square error between simulation and SWOOSH normalized with SWOOSH for global, Northern Hemisphere (NH), Southern Hemisphere (SH) and the tropics. Bold font represents the lowest RMSE.

Figure 3 Annual zonal mean O₃, CH₄, CO₂ and N₂O profile of QCTM-NOMIX (first column), absolute difference between both simulations(centre column), and relative percentage difference (right column). The black solid line indicates the PV tropopause in the extratropics and lapse rate tropopause in the tropics.

3.2 Difference in tracer distributions

Figure 3 shows the annual zonal mean mixing ratio and difference of O₃, CH₄, CO₂ and N₂O between QCTM-MIX and QCTM-NOMIX to assess the potential impact of tracers by the mixing algorithm of CAT. These major radiatively active gases were selected for the analysis to illustrate the different responses to CAT between spatially variable gases and well-mixed gases. As a result of enabling CAT, the O₃ in the UTLS is significantly reduced, especially in the vicinity of the tropopause with a 10 % to 20 % decrease (except below the tropical tropopause). The changes between 100 to 50 hPa at the extratropics could also be attributed to changes of the tracer gradient by the enhanced vertical mixing at the tropics which leads to enhanced horizontal advection through the shallow branch of the Brewer-Dobson circulation. CAT also changed the O₃ by changing the chemistry (Fig. 4a, b) in the upper stratosphere (above 50 hPa), causing up to 3 % increase, and transport downward across the tropopause to the troposphere with maximum of 9 % increase in the tropical upper troposphere and Southern Hemisphere. In terms of the mixing ratio, the largest absolute difference is located at around 75 hPa in the extratropical region, with up to 320 ppbv reduction of O₃. For CH₄, CAT leads to a significant increase in the UTLS up to 2.5 % or 40 ppbv and a slight loss in the troposphere. The two gases exhibit an opposite behaviour with O₃ decreasing and CH₄ increasing in the UTLS since the O₃ mixing ratio is higher in the UTLS than in the troposphere whereas the CH₄ mixing ratio is higher in the troposphere. O₃ also has a more significant change compared to CH4 due to the steeper gradient. The changes in both gases are stronger in the Southern Hemisphere, potentially due to the stronger jet streams and fewer mountains, leading to a stronger vertical wind gradient and resulting in a higher CAT Index_boundary as in Fig. A1 . For CO₂, since it is well-mixed with a long atmospheric lifetime, the effect of mixing is comparatively weak, given the resulting low vertical gradient. In contrast to this, the effect of CAT mixing on the N₂O mixing ratio is slightly stronger, similar to CH₄, but with a more homogeneous effect on both hemispheres.

Figure 4 Annual zonal mean difference (MIX – NOMIX) of O₃ chemical production and chemical loss: (a) total production, (b) total loss, (c) loss by bromine, (d) loss by chlorine, (e) loss by hydrogen species, (f) loss by nitrogen species, (g) loss by atomic oxygen and (h) loss by peroxy radicals. The black solid line indicates the PV tropopause in the extratropics and lapse rate tropopause in the tropics.

To examine whether the differences in the tracer distribution are attributed solely to the mixing of CAT or also influenced by the chemical feedback of other mixed tracers, we analyzed the chemical production and loss terms of ozone as well. The chemistry submodel MECCA (Sander et al., 2011) used in EMAC provided diagnostic output for some of the chemical species. Figure 4 shows the difference (MIX minus NOMIX) in ozone production, total loss and loss by species. With CAT mixing, the production of ozone (Fig. 4a) is reduced and the loss is enhanced (Fig. 4b) at the tropical tropopause, whereas the extra-tropical lower stratosphere (LS) shows an inverse behaviour. These results indicate that the reduction of ozone (Fig. 3) at the tropical tropopause is enhanced by the chemical feedback, whereas the physical mixing is offset by the chemical feedback in the extra-tropical LS.

The chemical loss of ozone (Fig. 4b) is enhanced below the tropical tropopause after including the CAT mixing parametrization. It is mainly contributed by HO_x (Fig. 4e) and O(¹D) (Fig. 4g). Fig. 4g shows the difference in the chemical loss by atomic oxygen. This shows the loss of ozone by removing O(¹D) from the odd oxygen: ozone is photolysed to form O(¹D) via Reaction (R1), O(¹D) is then consumed with H₂O to form OH (Reaction R2). This also partly explains the increase of OH in Fig. S2c in the supplement.

$$\begin{array}{}\text{(R1)}& {\displaystyle }{\mathrm{O}}_{\mathrm{3}}->\left[h\mathit{\nu }\right]\mathrm{O}{(}^{\mathrm{1}}D)+{\mathrm{O}}_{\mathrm{2}}\text{(R2)}& {\displaystyle }\mathrm{O}{(}^{\mathrm{1}}D)+{\mathrm{H}}_{\mathrm{2}}\mathrm{O}->\mathrm{2}\mathrm{OH}\end{array}$$

Figure 4e shows the changes in the chemical loss by HO_x. This illustrates the increasing loss of ozone at the tropical tropopause due to the OH $/$ HO_x catalytic cycle. Ozone is destroyed by Equations R3 and R4 with OH $/$ HO_x as a catalyst. This cycle is enhanced due to the increasing HO_x concentration (Fig. S2f in the Supplement).

$$\begin{array}{}\text{(R3)}& {\displaystyle }\mathrm{OH}+{\mathrm{O}}_{\mathrm{3}}\to {\mathrm{HO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{2}}\text{(R4)}& {\displaystyle }\begin{array}{rl}{\mathrm{HO}}_{\mathrm{2}}+& {\mathrm{O}}_{\mathrm{3}}\to \mathrm{OH}+\mathrm{2}{\mathrm{O}}_{\mathrm{2}}\\ & \stackrel{\mathrm{‾}}{\text{Net}:\mathrm{2}{\mathrm{O}}_{\mathrm{3}}\to \mathrm{3}{\mathrm{O}}_{\mathrm{2}}}\end{array}\end{array}$$

Mixing by CAT also reduces the chemical loss of ozone (Fig. 4b) at the extra-tropical LS (∼ 100 to 50 hPa). Around half of the reduction is due to the reduction of HO_x (Fig. S2f) and NO_x (Fig. S2l and o) in the corresponding region. The reduction of HO_x in the extra-tropics LS and NO_x reduction in the UTLS decelerate the HO_x cycle and NO_x-related cycle. Halogens are responsible for the remaining reduction, especially in the Southern Hemisphere. The vertical mixing evened out the high concentrations at the poles, decelerating the catalytic cycle.

In addition, the change of the chemical regime of ozone is analyzed using the HCHO $/$ NO₂ ratio (Formaldehyde to NO₂ ratio; FNR) and a novel diagnostic ${\mathit{\alpha }}_{{\mathrm{CH}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{2}}}$ developed by Nussbaumer et al. (2022). FNR is a commonly used indicator that develops from the principle that formation of tropospheric ozone requires volatile organic compounds (VOCs) and NO_x as its precursors (Acdan et al., 2023; Jin et al., 2020; Jiang et al., 2025). HCHO and NO₂ serve as the proxies of the VOCs and NO_x respectively, considering their similar chemical lifetime could better show competition between species (Tonnesen and Dennis, 2000). The lower FNR indicates VOC sensitivity, while the higher FNR indicates NO_x sensitivity. The ${\mathit{\alpha }}_{{\mathrm{CH}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{2}}}$ represents the fraction of CH₃O₂ forming HCHO via NO and OH relative to the competing pathway that forms CH₃OOH via HO₂ which could be used to identify the HCHO production pathways. It could also be used to study ozone sensitivity (Nussbaumer et al., 2024). It is based on the concept that the formation of HCHO from CH₃O₂ with NO leads to O₃ production, while the formation of CH₃OOH from CH₃O₂ with HO₂ leads to termination of the HO_x cycle which decelerates the ozone production. The reaction of CH₃O₂ with OH that forms HCHO, which generally only plays a minor role, will not contribute to O₃ formation and therefore will be neglected when studying ozone sensitivity. It can therefore be calculated as shown in Eq. (5):

$$\begin{array}{}\text{(5)}& {\mathit{\alpha }}_{{\mathrm{CH}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{2}}}={\displaystyle \frac{k_{{\mathrm{CH}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{2}}+\mathrm{NO}}\times \left[\mathrm{NO}\right]}{k_{{\mathrm{CH}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{2}}+\mathrm{NO}}\times \left[\mathrm{NO}\right]+k_{{\mathrm{CH}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{2}}+{\mathrm{HO}}_{\mathrm{2}}}\times \left[{\mathrm{HO}}_{\mathrm{2}}\right]}}\end{array}$$

Nussbaumer et al. (2023) shows that both the FNR and ${\mathit{\alpha }}_{{\mathrm{CH}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{2}}}$ are good indicators for the ozone chemical regime in the upper troposphere. Fig. 5 shows the 10-year climatology of the ${\mathit{\alpha }}_{{\mathrm{CH}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{2}}}$. CAT leads to slight changes in ${\mathit{\alpha }}_{{\mathrm{CH}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{2}}}$ in different altitudes. The difference of ${\mathit{\alpha }}_{{\mathrm{CH}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{2}}}$ (Fig. 5a) shows a bi-modal distribution at the upper troposphere (∼ 200 hPa) and the lower troposphere (∼ 800 hPa). The Southern Hemisphere exhibits a larger decrease with a maximum of 3 %. The difference even reaches up to 6 % during the JJA season in the southern polar region (not shown). The decreasing ${\mathit{\alpha }}_{{\mathrm{CH}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{2}}}$ indicates the decrease of NO and increase of HO₂, which is consistent with Fig. S2l and f and the O₃ is relatively more sensitive to NO_x (less sensitive to VOCs) than without the CAT mixing. Fig. 6 shows the 10-year climatology for the FNR. The Southern Hemisphere depicts a more substantial absolute increase in FNR in the lower troposphere(∼ 800 hPa), while the upper troposphere (∼ 200 hPa) shows a percentage increase up to 26 %. The changes above 200 hPa are neglected since the stratospheric ozone chemistry is significantly different than the troposphere. It shows consistent results with the ${\mathit{\alpha }}_{{\mathrm{CH}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{2}}}$, the increasing FNR indicates the O₃ chemical regime is becoming relatively more NO_x sensitive (less VOCs sensitive). Both the FNR and ${\mathit{\alpha }}_{{\mathrm{CH}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{2}}}$ show that the CAT mixing in the UTLS also affects the tropospheric chemistry.

Figure 5 Vertical profile of the 10-year climatology of ${\mathit{\alpha }}_{{\mathrm{CH}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{2}}}$ in different regions: (a) absolute difference (MIX – NOMIX), (b) percentage difference, (c) profiles. The solid lines indicates profiles of MIX, the dashed lines indicate profiles of NOMIX. The different colors denote respective latitude bands.

Figure 6 Vertical profile of the 10-year climatology of the HCHO $/$ NO₂ ratio (FNR) in different regions: (a) absolute difference (MIX – NOMIX), (b) percentage difference, (c) profiles. The solid lines indicate profiles of MIX, the dashed lines indicate profiles of NOMIX. The different colors denote respective latitude bands.

Figure 7 Vertical profile of the 10-year climatology of CH₄ lifetime (year) in different regions: (a) absolute difference (MIX – NOMIX), (b) percentage difference, (c) profiles. The solid lines indicate profiles of MIX, the dashed lines indicate profiles of NOMIX. The different colors denote respective latitude bands.

Furthermore, the chemical lifetime of CH₄ has been analyzed as well. Fig. 7 shows the climatology of the methane lifetime. CAT mixing leads to a significant reduction of the CH₄ lifetime in the UTLS region, the tropics experienced a 15-year (∼ 8 %) decrease. The global atmospheric lifetime of CH₄ also shortened from 7.31 years to 7.24 years. It is mainly due to the change in OH distribution by CAT. Fig. S2c shows that the OH increases mainly in the lower stratosphere with 10 % of increase at the tropical tropopause which coincides with the lifetime profile in Fig. 7. Considering the extremely short atmospheric lifetime of OH, the changes are unlikely to be a direct result of the CAT mixing on OH. It must be a result of either the changes in the OH precursors or sinks. One of the possible pathways is that the increasing OH by O(¹D) leads to a more efficient CH₄ oxidation, which produces more HCHO and HO₂ (based on the lower ${\mathit{\alpha }}_{{\mathrm{CH}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{2}}}$). Photolysis of HCHO and HO₂ recycling then generates OH, establishing a HO_x–CH₄–HCHO feedback cycle.

To conclude, the CAT mixing clearly modifies the chemical regime of the O₃ budget, shifting the O₃ to become relatively sensitive to NO_x, as well as reducing the atmospheric lifetime of CH₄ by increasing OH.

Figure 8 Annual zonal mean difference of net radiation fluxes for different radiation calls between two simulatioins: (a) RAD02, (b) RAD03 (O₃), (c) RAD04 (CO₂), (d) RAD05 (CH₄), and (e) RAD06 (N₂O). The numerical values given are differences of the global mean TOA radiation. The black solid line indicates the PV tropopause in the extratropics and lapse rate tropopause in the tropics.

Figure 9 Annual mean difference of net radiation fluxes [mW m⁻²] at the TOA for (a) RAD02, (c) RAD03, (e) RAD04, (g) RAD05, and (i) RAD06; and at the surface for (b) RAD02, (d) RAD03, (f) RAD04, (h) RAD05, and (j) RAD06.

3.3 Impact on radiation

The simulation results show that the CAT mixing of tracers leads to a radiative cooling on the global mean radiation fluxes at the top-of-the-atmosphere (TOA) of about 208.9 mW m⁻² without taking water vapour into account. It is mainly induced by the change in ozone (−210.5 mW m⁻²). The other major greenhouse gases like CO₂, CH₄ and N₂O have a comparably small impact which either leads to a radiative cooling or heating effect at the TOA. The changes of the annual mean net radiation fluxes of different radiation calls are shown in Figs. 8 and Fig. 9. Each radiation call represents a different greenhouse gas scenario; a summary of the radiation calls is given in Table 1. Figure 8 illustrates the annual zonal mean difference of the net radiation fluxes. In general, CAT mixing leads to cooling above the tropopause and heating in the troposphere (Fig. 8a). It is mainly contributed by ozone (Fig. 8b), with almost identical behaviour as in Fig. 8a. The loss of ozone in the UTLS shown in Fig. 3b, leads to local and TOA radiative cooling as well as heating in the troposphere. CO₂ and CH₄ show mainly an opposite response compared to ozone, while CO₂ has a stronger radiative heating in the Northern Hemisphere, potentially because of anthropogenic activities. N₂O shows a heating effect in almost all altitudes, except for the tropical lower troposphere. Figure 9 shows the annual mean difference of the net radiation fluxes at the TOA and surface. CAT leads to radiative cooling at the TOA and heating at the surface, mainly contributed by ozone. It is more pronounced along the storm tracks, where strong jet stream and associated wind shear favour turbulent mixing in the UTLS. At the TOA, CO₂ leads to cooling in the Southern Hemisphere and heating in the Northern Hemisphere, while the surface shows an inverse behaviour. CH₄ warms the tropics at the TOA, but cools at the surface. Changes in N₂O result in heating at the TOA and the surface, except for the tropics.

Overall, CAT mixing leads to cooling in the Earth's radiation budget, mainly contributed by O₃, which is a greenhouse gas with spatial variability and also strongly active in the shortwave spectrum. In contrast, well-mixed greenhouse gases like CO₂, CH₄ and N₂O are rather insensitive to CAT mixing, with global mean TOA radiative effects of −0.2, 0.13 and 1.62 mW m⁻² respectively.

We examined the impact of CAT on tracers and their associated radiative effects. Overall, CAT leads to an increase in outgoing LW radiation at the TOA, corresponding to a cooling effect. It is mainly driven by ozone. The other major greenhouse gases, such as CO₂, CH₄, and N₂O which lead to changes in radiation of TOA are comparatively insensitive to CAT considering they are well-mixed in the atmosphere. A previous study by Riese et al. (2012) shows similar results on the sensitivity of the greenhouse gases by mixing, where water vapour and ozone are notably more sensitive than CH₄ and N₂O. However, due to differences in the mixing parametrization, it resulted in an opposite radiative impact. That study uses the Chemical Lagrangian Model of the Stratosphere (CLaMS) with a mixing algorithm based on atmospheric deformation (McKenna et al., 2002a, b; Konopka et al., 2004). This mixing scheme merges air parcels when they fall below the minimum separation distance. This deformation-induced mixing is a good approximation for stirring and quasi-isentropic mixing in the stably stratified stratosphere. Some more recent studies (Pommrich et al., 2014; Konopka et al., 2019) show that in the previous version of CLaMS which (Riese et al., 2012) were using, the vertical transport within the troposphere is underestimated. This causes the mixing by CLaMS to be mainly attributed to quasi-horizontal isentropic transport which dominates between tropical upper troposphere and extra-tropical lower stratosphere and within the stratosphere, which only reflects part of the potential mixing in the UTLS. The new CAT submodel, on the other hand, parametrizes the mixing by turbulence, a diabatic process that allows exchange across the tropopause. It includes not only the deformation but also vertical wind shear, divergence, and static stability. Also, the CLaMS chemistry is relatively simple compared to EMAC, as well as in describing small-scale dynamics. The mixing scheme of CAT is in turn, more sensitive to vertical mixing, while CLaMS is more sensitive to the isentropic (quasi-horizontal) mixing.

4 Conclusion and Outlook

This study presents a new submodel for parametrizing vertical tracer mixing in the UTLS by Clear Air Turbulence (CAT), developed for the chemistry climate model EMAC, considering the dampening characteristics of the ECHAM5 turbulence scheme above the planetary boundary layer. The CAT mixing scheme is based on a two-layer mixing algorithm and the newly developed turbulence diagnostic MoCATI, which is a modification of the well-known Ellrod-Knox index by introducing static stability into the calculation. We conducted statistical tests and the relative frequency distribution of MoCATI and Ellrod-Knox index. The new index shows a comparable performance as the Ellrod-Knox index.

We performed two simulations (MIX and NOMIX) using the EMAC model in a QCTM configuration to examine the impact of CAT mixing parametrization on tracer distribution and its corresponding radiative impact. CAT leads to significant impacts on the non well-mixed gases like ozone in the UTLS. The changes are contributed by both the physical mixing and the chemical feedback from other tracers. O₃ is significantly reduced in the UTLS and increases in the free troposphere as well as in the mid-stratosphere. The reduction in the tropics is a result of both the physical mixing and chemical feedback from other mixed tracers like odd oxygen and HO_x while the extratropical physical mixing is offset by the chemical feedback not only from odd oxygen and HO_x, but also from halogen species. Other major greenhouse gases including CO₂, CH₄ and N₂O are relatively insensitive to CAT considering their well-mixed characteristics and weak gradients particularly in the UTLS. It also shows that the CAT in the UTLS can change the chemical regime of O₃ not only in the UTLS region, but also in the lower troposphere, by shifting to a relatively more NO_x sensitive (less VOCs sensitive) environment. Methane lifetimes are also found to be shortened from 7.31 years to 7.24 years (especially at the stratosphere with a 15-year difference) because of the more effective HO_x catalytic cycle. CAT mixing also reduces the ozone bias at the polar mid-stratosphere by comparing the results with SWOOSH.

Simulations show that CAT could lead to surface radiative heating and radiative cooling at the TOA. The TOA is expected to be 0.2W/m² cooler without considering water vapour. It is mostly contributed by ozone since water vapour is not taken into account in the QCTM mode. Other major greenhouse gases show negligible impacts on the radiation budget. Considering the strengthening trend of CAT under climate change, the cooling effect of CAT mixing on tracers could potentially partially offset the warmer climate.

Even though water vapour is not taken into account in the current version of CAT to obtain consistent dynamics in the QCTM mode, it is planned to also consider the potential radiative impact of water vapour by extending the CAT submodel and including the mixing of water vapour and temperature. The water vapour is expected to increase in the UTLS considering its gradient. The moist tropospheric air will be expected to be mixed upward with the dry stratospheric air and may significantly change the radiative budget of the atmosphere. The CAT submodel also has the option to include or combine more turbulence diagnostics (e.g. Graphical Turbulence Guidance from Sharman et al., 2006) in the future, considering the pros and cons of each diagnostic on representing turbulence formed by different mechanisms. However, potential recalibration would be required.

Appendix A

Figure A1 Annual zonal mean of the CAT Index_boundary (MoCATI). The black solid line indicates the PV tropopause in the extratropics and lapse rate tropopause in the tropics.