Ground-level ozone is a secondary air pollutant which is harmful for humans and ecosystems. Besides chemical destruction, a large fraction of it is removed by dry deposition which accounts for about 20 % of the total O3 loss . The process description of dry deposition considers boundary-layer meteorology (e.g. turbulence), chemical properties of the trace gases and surface types. In most global models, dry deposition of trace gases is parameterized using the “resistance in series” analogy by . The largest deposition rates of ozone occur over dense vegetation where it mainly follows two pathways: through leaf openings (stomata) and to leaf waxes (cuticle) . Thereby, stomatal uptake is commonly parameterized following the empirical multiplicative approach by which uses a predefined minimum resistance and multiple environmental response factors like in , and . More advanced formulations often used by land surface models are based on the CO2 assimilation by plants during photosynthesis . Both approaches rely on the choice and constraints of ecosystem-dependent parameters and have different advantages . A further role in coupling stomata to ecosystems is played by stomatal optimization models, whereas optimal stomatal activity with a maximum amount of carbon gain and a minimum loss of water is calculated based on ecophysiological processes e.g.. Of particular interest are stomatal optimization models which, based on ecophysiological processes, maximize carbon gain while minimizing water loss. According to , these models are promising in representing stomatal behaviour and improving carbon cycle modelling. Non-stomatal deposition has been less investigated by now; therefore, most models use predefined constant resistances or scale it with leaf area index e.g., while some apply an explicit parameterization based on the observational findings of enhance cuticular uptake under leaf surface wetness .

The different parameterizations of the (surface) resistances cause main model uncertainties in computing dry deposition fluxes of trace gases, which depend on the response to hydroclimate and land-type-specific properties . Thereby, it has been shown that the original Wesely-based parameterization generally captures well the seasonal and diurnal cycles of dry deposition velocity, whereas model–observation discrepancy at seasonal scales arises from biased land type and leaf area index input data . stated that discrepancies of up to 8 ppb in ground-level ozone arise from different parameterizations.

The current dry deposition scheme of EMAC uses six surface types, where the parameterized processes represent the forest canopy as a whole (big-leaf approach). Thereby, the uptake over vegetation relies on stomatal deposition as the only pathway determined by the photosynthetically active radiation . According to and , the stomatal uptake in parameterizations often lacks the dependence on meteorological and environmental variables (leaf area index, temperature, vapour pressure deficit). Moreover, several studies (e.g. ) found the contribution of an additional process to dry deposition at the leaf covering of plants. firstly derived a parameterization from field studies which establishes the important link of this process to meteorology. In general, findings by , and highlight the importance of considering the dry deposition–meteorology dependence in global models. Such an extension would realistically enhance the sensitivity of dry deposition to climate variability and would result in a more accurate prediction of ground-level ozone.

Given the importance of ozone as a major tropospheric oxidant, air pollutant and greenhouse gas, an accurate representation of dry deposition is desirable . Additionally, the significance of a realistic representation of land–atmosphere feedbacks rises in light of the changing Earth's climate with the projected increase of extreme events' frequency and intensity .

Here, we present a revision of the existing Wesely-based dry deposition scheme in the Modular Earth Submodel System (MESSy), which has a very simplified representation of vegetation and soil. The modifications are done by well-established findings about the controls of stomatal and cuticular uptake of trace gases. The calculation of stomatal deposition fluxes is extended by including the vegetation density, two meteorological adjustment factors and an improved soil moisture availability function for plant stomata following the multiplicative algorithm by . For the first time in MESSy, a parameterization for cuticular dry deposition dependent on important meteorological and environmental variables is implemented explicitly . In Sect. , a description of the model setup and the simulations is provided, whereas especially the transition to the new vertical exchange scheme is described in detail. Subsequently, the new VERTEX scheme is evaluated. In Sect. , the impact of the changes on ozone dry deposition is evaluated on daily and seasonal scales by comparison with measurements at four different sites. Here, advantages, uncertainties and missing processes in the revised scheme are identified. Next, the global impact on ground-level ozone is assessed by separating the effect of the different implemented parameterizations. Then, Sect.  provides a description of the uncertainties in modelling stomatal conductance and Sect.  comprises an investigation of the sensitivity to model resolution. Section  summarizes the main findings and the remaining process and model uncertainties which form the basis for the provided recommendations. Section  describes planned future developments.

This study uses the ECHAM/MESSy atmospheric chemistry model. MESSy v2.54 provides a flexible infrastructure for coupling processes to build comprehensive Earth system models (ESMs) and is utilized here with the fifth-generation European Centre Hamburg general circulation model (ECHAM5; ) as an atmospheric general circulation model. The dry deposition process of gases is calculated within the submodel DDEP . This is described in Sect. . It relies on the VERTEX vertical exchange submodel (Sect. ), former E5VDIFF, which contains the calculation of stomatal uptake (Eq. ) and soil moisture stress (Eq. ). The stomatal uptake parameterization is the base for the evapotranspiration scheme in VERTEX (Appendix ) which also incorporates the soil moisture stress.

In order to advise the usage of VERTEX (with the default settings) as the default vertical exchange submodel in MESSy, the dynamics produced by both submodels are compared. Therefore, two dynamical, free-running 30-year simulations have been performed using the E5VDIFF or the VERTEX submodels, respectively. To obtain a comparable radiative imbalance at TOA (top of the atmosphere) with VERTEX, the four cloud parameters have been tuned in advance according to . The tuning factors can be found in Table . The radiative imbalance at TOA is slightly positive at present-day conditions ; here, E5VDIFF gives a negative value. The difference between the tuned VERTEX and E5VDIFF is small and within the uncertainty range of ±0.4 Wm-2.

Additionally, global mean values of surface temperature, cloud liquid water, relative humidity and planetary boundary layer height of EMAC using E5VDIFF and EMAC using VERTEX with the respective uncertainty range for the period 1979–2008 are represented in Fig. . The results for cloud liquid water and planetary boundary height show no significant differences between the VERTEX and E5VDIFF simulations since the annual mean of each falls in the confidence interval of the other. This is not always the case for surface temperature and relative humidity. However, the 30-year means of surface temperature and relative humidity simulated by E5VDIFF and VERTEX are not significantly different.

To assess the impact of the code revision/modifications on the variability of dry deposition, we compare the sensitivity simulations DEF, REV, REV-fTfVPD, REV-fws and REV-NNTR (see Table , all at T106L31 resolution) with dry deposition measurements at four field sites (listed in Table ). The chosen data sets are the best available of ozone dry deposition (flux data and ozone mixing ratio or velocity data) with the required temporal resolution and coverage of diverse biomes of the world. The analysis is aimed at covering the recent decade, which includes the most extreme drought and heat events (where the stomatal stress factors are aimed). For the reason of uniqueness and importance of atmospheric processes in a remote and pristine forest like the Amazon, we included measurements from, among others, the Amazon Tall Tower Observatory (ATTO). Ozone dry deposition fluxes were measured with the eddy covariance and gradient method (Ontario). From these data, deposition velocities were calculated by the means of ozone concentration data. The eddy covariance technique determines a turbulent flux by the covariance of the measured vertical velocity and the gas concentration. Due to the stochastic nature of turbulence, these measurements have an uncertainty of 10 % to 20 % under typical observation conditions . For the gradient method used at the Borden forest research station, the dry deposition flux was estimated from concentration gradients below and above the canopy and the eddy diffusivity according to the Monin–Obukhov similarity theory. The estimated dry deposition velocities (Vd) show an uncertainty of ≈ 20 %, which is due to the assigned canopy, the inherent limitations of the algorithm and the measurement uncertainties in concentrations. However, results are in good agreement with other eddy covariance measurements .

Given the importance of dry deposition for ground-level ozone and the uncertainty of dry deposition parameterizations in models , the global impact of the implemented code changes is assessed in this section. The global (boreal) summer mean distributions of deposition velocity and ground-level mixing ratio for O3 shown in Fig. a–b are generally in the same range as reported for global models (e.g. ). However, like most global models, EMAC overestimates tropospheric ozone in comparison to satellite observations . Applying the revised dry deposition scheme increases the mean summer Vd by up to 0.5 cms-1 (Fig. a). The highest fraction of this increase arises from the inclusion of cuticular uptake at wet surfaces (Vcut,w) (Fig. b). The effect is large over the most northern continental regions (Fig. d) and even more pronounced where LAI is high like in Scandinavia and eastern Canada (for LAI distribution, see Fig. a). Additionally, the uptake at dry surfaces (Vcut,d) is enhanced with up to 0.3 cms-1 higher dry deposition velocity (Fig. c). This is because the default scheme applies a very high constant resistance for this process.

Concerning the stomatal deposition, the impacts of three different stress factors are considered. First, over relatively dry soil, i.e. where soil moisture exceeds 35 % of field capacity (wilting point of plants), the soil moisture stress is reduced by the modified parameterization. Neglecting the plants' wilting point as the lower limit for soil moisture stress on stomata weakens the dependency on field capacity. Thus, dry deposition is enhanced by up to 0.32 cms-1, as illustrated in Fig. a. Second, the inclusion of temperature and (third) VPD adjustment factors, indeed, leads to a spatially varying impact of ±0.27 cms-1 change in Vd (Fig. b). In humid and cold temperate regions, like Siberia and Canada, no temperature stress appears and the VPD adjustment factor increases the stomatal uptake. In the eastern US, Kazakhstan and central Amazon during boreal summer, stomata are stressed by temperature and VPD. This effect is overpredicted by the model, as the humidity over the Amazon forest is probably too low in the model (see Fig. ). The stress factors are shown in Fig. c and d.

However, the overall decrease in ozone concentration dampens the impact of the change in dry deposition flux. In total, the changes by the revised dry deposition scheme increase the multiyear mean (2010–2015) loss of ozone by dry deposition from 946 to 1001 Tgyr-1 . Accordingly, (boreal) summer ground-level ozone over land is reduced by up to 12 ppb (24 %), peaking over Scandinavia, Asia, central Africa and eastern Canada (Fig. b). In the Northern Hemisphere, also the zonal mean of the tropospheric ozone mixing ratio show a noticeable reduction far from the ground compared to the default scheme (Fig. a). This has the potential to reduce the positive bias of tropospheric ozone on the Northern Hemisphere (20 %) reported by . However, besides ozone, also other atmospheric tracer gases are affected by the change in dry deposition. The global annual dry deposition flux of odd oxygen (Ox)

Ox≡O+O3+NO2+2NO3+3N2O5+HNO3+HNO4+BrO+HOBr+BrNO2+2BrNO3+PAN

Dry deposition is a highly uncertain term in modelling ozone pollution . Its representation is generally limited by a lack of measurements and process understanding but also to a large extent driven by the quality of land cover information . Although the dry deposition scheme by is commonly used in global and regional models (e.g. MOZART, GEOS-Chem), the approach has some constraints . The disadvantage of the big-leaf approach used in MESSy is that a vertical variation of leaf properties, affecting, for instance, the attenuation of solar radiation, is not considered e.g.. Regarding stomatal uptake, we neglect the mesophyll resistance as reactions inside the leaf are commonly assumed to not limit stomatal ozone uptake, whereas, besides mostly supporting laboratory studies e.g., a few contradicting findings exist e.g.. The here-used empirical multiplicative algorithm by for stomatal modelling has one general drawback concerning that the environmental responses to stomata are treated clearly in contrast to experimental evidence . However, Jarvis-type models have been shown to be able to compete with the semi-mechanistic Anet-gs models which link stomatal uptake to the CO2 assimilation during plant photosynthesis . The critics in state that the Jarvis model cannot capture the afternoon depression of ozone dry deposition is due to the original used VPD stress factor which has been replaced here by a mechanistic one based on the optimized exchange of CO2 and water by plants . Furthermore, a larger set of land cover types is expected to improve the vegetation-dependent variation of dry deposition. The parameters used to model dry deposition of stomata, cuticle and soil are biome dependent and using generalized ones like for the input cuticular resistance can lead to differences in dry deposition . Exemplary discrepancies for the stomatal conductance calculated with different parameter sets are shown in Fig.  as the summer mean of 2010. Thereby, the temperature stress factor has been calculated as in Eq. () using the obtained surface temperature by EMAC (Fig. a, c) and applied to the model (DEFAULT) stomatal conductance (Eq. ) with two different parameter sets for coniferous and mixed forest by

Used parameters: Tmin=0 ∘C, Topt=18 ∘C, Tmax⁡=36 ∘C.

The simulation of dry deposition depends on meteorology including boundary layer processes, radiation (cloud distribution and reflectivity) and ozone chemistry as well as on input fields like vegetation density (LAI) . Model horizontal resolution inherently affects the amplitude and distribution of (regridded) surface processes and the artificial dilution of ozone precursors that are emitted. This aspect is investigated here by analysing simulations at three different spatial resolutions: 2.8∘ × 2.8∘, 1.9∘ × 1.9∘ and 1.1∘ × 1.1∘ (REST42, REST63, and REV (T106) in Table ).

In Fig. a, the resolution dependency is shown for the annual dry deposition flux of ozone on different continental regions. The annual dry deposition fluxes differ by up to 40 Tgyr-1 globally between the different resolutions, with highest dry deposition at high resolution (T106). For the Northern Hemisphere (and consequently globally), this difference is driven by the higher annual mean ground-level ozone compared to the lower resolutions (Fig. c). However, this effect cannot be disentangled from the effect of decreased dry deposition velocity on ground-level ozone. Globally, increasing differences in O3 are anti-correlated with relative humidity as shown in Fig. a (ρ=-0.8). The impact of humidity on ozone chemistry is considered to be relatively weak , but showed for the US that only dry deposition establishes the observed anti-correlation between ozone and relative humidity. A dominating positive correlation of the dry deposition flux with the velocity only occurs on the Southern Hemisphere extratropics (SH_exT), which is highest between T63 and T106 (Fig. c). This can be attributed to discrepancies in stomatal deposition (Fig. d) driven by differences in humidity which might be caused by different moisture cycles and transpiration.

Dry deposition to the Earth's surface is a key process for the representation of ground-level ozone in global models. Its parameterizations constitutes a relevant part of the model uncertainty . Revising the dry deposition scheme of EMAC leads to an improved representation of surface ozone in regions with a positive model ozone bias (e.g. Europe). The highest increase in ozone dry deposition is due to the implementation of cuticular uptake whose contribution is important especially during night over moist surfaces. The extension of the stomatal uptake with temperature and VPD adjustment factors accounts for the desired link of plant activity to hydroclimate as recommended by . Especially in drought-stressed regions (e.g. citrus orchards), the dependence on vapour pressure deficit leads to a realistic depression of stomatal uptake at noon. Also the dependence of dry deposition on soil moisture has been modified since the current representation of soil moisture in the model is not satisfactory. Specifically, the model simulates a too-dry soil for the Amazon basin, causing stomatal closure and thus an underestimation of dry deposition (Sect. ). We have indications that the dry bias is a consequence of meteorological nudging in EMAC and also the missing representation of organized convection in the tropics . The sensitivity of the vegetation to droughts is comparably high in the Amazon region because the model soil cannot hold water in the catchment for a realistic time period and exhibits a memory effect . Deeper root zones or buffering of the soil moisture below the root zone would improve the water holding capacity . With an improved representation of soil moisture, the more realistic parameterization of the soil moisture stress on stomatal uptake could be re-enabled. In general, the inclusion of the strong link between dry deposition and meteorology reveals some limitations of the dry deposition scheme associated with the inaccurate representation of local meteorology. The results also indicate that an improved representation of important non-stomatal dry deposition like in-canopy reactions of ozone with volatile organic compounds (e.g. citrus orchards; Sect. ) would lower the positive model–observation discrepancy. This can be achieved with the inclusion of further BVOCs and an explicit parameterization of the transport dynamics in the boundary layer in model simulations . Explicit field measurements could foster further process understanding, which is required for a detailed process description within the models, especially over tropical rainforests. The seasonal variability of the simulated dry deposition velocity could be further improved by using as model input the time series of vegetation cover from imaging products which also capture land use changes and vegetation trend that are known to impact dry deposition significantly .

The representation of gaseous dry deposition in MESSy will be further improved by using the MODIS time series of LAI which captures multi-annual vegetation changes. As the next step of dry deposition modelling in MESSy, a biome-dependent dry deposition model coupled to CO2 assimilation (White et al., 2004) will be applied. Biome-dependent vegetation cover information, required for this scheme, is then provided by global input data which, however, represent only the annual cycle of vegetation. Coupling MESSy to the recently available dynamic vegetation model LPJ-GUESS, which provides detailed vegetation information with the temporal variability required for a climate model, could be a further improvement. By now, the one-way coupling of LPJ-GUESS as a MESSy submodel is only in the initial evaluation phase of the coupling with the atmospheric model (Forrest et al., 2020).