We have implemented the stratospheric ozone model described by , the BMS ozone scheme, within the ECMWF Integrated Forecasting System (IFS).

The scheme represents the effects of stratospheric ozone sources and sinks following a linear approach, so that a CTM or GCM can simulate the time evolution of ozone by including an advected tracer for which the local concentration f (i.e. the local net ozone chemical production minus loss) evolves in time according to the following equation: 1∂f∂t=c0+c1(f-f¯)+c2(T-T¯)+c3(cO3-cO3¯), where the coefficients ci (i=0,1,2,3) are tendencies derived from the full-chemistry CTM runs, and the terms f¯, T¯ and cO3¯ are climatological reference values (in this case obtained from the full-chemistry output fields) for the ozone concentration f, temperature T and partial column of ozone above the considered location cO3. The coefficients ci and the climatological terms are provided as a function of latitude, pressure and month. For complete details on the calculation methodology and CTM runs leading to this ozone model, see . A full discussion on the differences between this new ozone model and the default CD scheme used by the ECMWF operational system can also be found in . For convenience, we also briefly describe here the main differences regarding, most importantly, the treatment of heterogeneous chemistry but also differences in the photochemical model runs to derive the schemes, meteorological forcing fields and resolution. For completeness, we include here below the equation of the default CD scheme. The time evolution of the ozone concentration in the default ECMWF CD scheme is based on the expression 2∂f∂t=c0+c1(f-f¯)+c2(T-T¯)+c3(cO3-cO3¯)+c4(ClEQ)2f, where the tendency coefficients ci (i=0,1,2,3) include only gas-phase chemistry effects, making it necessary to add the fifth term and the corresponding coefficient c4 to account for ozone destruction related to heterogenous chemistry processes. ClEQ is the equivalent chlorine content of the stratosphere and varies from year to year. This fifth term is only active when temperature falls below 195 K in daytime for latitudes polewards of 45∘, and the coefficient c4 is calculated with different methods and approximations from the rest of the coefficients, reducing the consistency of the approach. Conceptually, this kind of term is too restrictive with respect to the current understanding of heterogeneous processes. For instance, in reality the temperature threshold for the formation of polar stratospheric clouds (PSCs) actually depends on altitude and trace gas concentrations (e.g. ). Another shortcoming in the heterogeneous approach in Eq. () is that it assumes chlorine activation and O3 destruction by sunlight take place at the same time. Actually, the activation of air masses takes place during the polar night inside the polar vortex, when temperature is low enough (e.g. ). Later, when spring sunlight returns to polar latitudes, the processed air is able to destroy ozone. However, the destruction can also happen during winter if activated air masses reach lower latitudes (e.g. by filamentation or vortex break-up) and are exposed to sunlight. This latter kind of process is completely missed by a localised simple temperature threshold term like the one in the default ECMWF scheme.

The treatment of heterogeneous chemistry is one fundamental difference in the new (BMS) scheme, which includes stratospheric ozone chemistry processes, both gas-phase and heterogeneous chemistry, in a consistent embedded way for all locations using only the first four linear coefficients ci (i=0,1,2,3). Unlike previous stratospheric ozone linear schemes, the BMS scheme is the first one to include heterogeneous chemistry effects and gas-phase chemistry in a consistent, implicit way in all terms of Eq. (). Since the BMS scheme coefficients are obtained taking into account all heterogenous chemistry included by the CTM, heterogeneous chemistry is embedded in all the terms in Eq. () and not restricted to limited regions and times as in the CD scheme. This new approach was shown to be very beneficial for the representation of ozone at high latitudes .

In addition, the coefficients for the new scheme have been derived from a 3D full-chemistry model, in contrast to the default ozone scheme used by ECMWF, which is based on a 2D photochemical model. This provides additional information on spatial variability of the chemical tendencies represented by the coefficients. To derive the chemical tendencies, the box model used to derive the coefficients for the BMS scheme was initialised from a 3D SLIMCAT full-chemistry reference run forced by ERA-40 meteorological fields, corresponding to year 2000, while the 2D model used to derive the CD coefficients was run from output from the climate model ARPEGE (Action de Recherche Petite Echelle Grande Echelle) averaged for the period 1990–2000 . Deriving coefficients from one representative meteorological year does not limit the performance of the BMS model. compared two versions of the scheme, one was based on a representative year with cold winter conditions (year 2000), and another version was based on a year with mild winter conditions (year 2004). Their results demonstrated that when the coefficients are derived from years with more extreme conditions (cold winters), the scheme is able to realistically capture ozone distributions for both cold and mild conditions.

Regarding vertical resolution of the schemes, the CD scheme original number of levels is larger (60 levels) than that of the original BMS number of levels (24 levels). Both schemes are then interpolated to the same grid for each experiment in the ECMWF model, using the same interpolation method for both to ensure numerical consistency.

Despite the relatively coarse vertical resolution, as discussed, the new approach allows for more realistic interactions between parameterised ozone, radiation and temperature, and therefore better response and feedbacks to meteorological conditions, than previous ozone parameterisation approaches.

We have used the Integrated Forecasting System (IFS) of ECMWF to run forecast experiments at medium-range (10 d, where d stands for day) and long-range (seasonal) timescales. The IFS configuration in each pair of experiments (control and new) differs only in the scheme used to model stratospheric ozone and whether prognostic ozone is used or not by the radiation scheme. All other aspects of the model configuration remain identical.

In situ observations from the global network of ozone sondes have been used for the validation of the modelled ozone vertical profiles. These observations come from the networks of the World Ozone and Ultraviolet Radiation Data Centre (WOUDC, https://woudc.org/data/explore.php, last access: 21  February 2022), the Network for the Detection of Atmospheric Composition Change (NDACC), the Norwegian Institute for Air Research (NILU), the Southern Hemisphere Additional Ozonesondes (SHADOZ, e.g. ), and the National Oceanic and Atmospheric Administration (NOAA). Additional measurements from the Coordinated Airborne Studies in the Tropics (CAST) and measurements from the Match campaigns for stratospheric ozone have also been used. These ozone sonde observations provide a completely independent validation dataset as they are not assimilated by the (re)analyses used to provide the initial conditions in our model experiments. Ozone observations from these ozone sondes are highly reliable (±5%) up to altitudes of 10.0–5.0 hPa.

The global reanalysis produced by the Copernicus Atmosphere Monitoring Service (CAMS), CAMSiRA has provided additional comparisons for the ozone field in our model experiments. The ERA-Interim reanalysis has been used to validate meteorological fields from our experiments.

Figure  shows the time series of monthly averaged vertical profiles of ozone, for the period August 2012–February 2013, from two experiments in which the ozone field is freely evolving along the 1-year period, but meteorology is initialised every 10 d (i.e. medium-range 10 d meteorological forecasts). One of the experiments uses the new BMS ozone (exp001bms); the other uses the default CD ozone scheme (exp001cd). By comparing ozone concentrations from these experiments with ozone sonde measurements (Fig. , left panel), we can clearly see the improvement obtained with the new ozone scheme over the Antarctic region, both in terms of vertical distribution of ozone concentrations and in terms of time evolution of the concentrations, especially during and after the ozone hole season. The recovery of the ozone concentrations after October is also much more realistic with the new ozone model.

The distribution of differences between these model runs and the sonde observations (model - observations) are shown in Fig. . The largest differences for the BMS model run (up to 3 mPa) are found in August between 100–200 hPa and in September–October between 20–50 hPa; for all other months and regions differences are smaller (within ±1.5 mPa). However, for the CD model run positive biases (of up to 4 mPa) between 100–200 hPa persist over the first 6 months, and differences with observations are larger between 30–100 hPa from September–April (negatively biased, with differences values of up to -5 mPa).

The better performance of the new BMS scheme is mainly due to the new formulation of the heterogeneous chemistry treatment, which has been derived from realistic full chemistry at all altitudes, unlike the fifth term in Eq. () that is representative of an altitude of approximately 20 km. Moreover, the default scheme specifies a dependence on the square of the chlorine content (ClEQ)2 which is not representative of typical atmospheric conditions in the activated polar vortex (e.g. ). In the CD model run differences centred around 20 hPa are also larger than in the BMS run for March–July months.

Ozone loss in the Arctic region does not usually reach the levels found in the Antarctic. However, ozone depletion over the Arctic presents high interannual variability because of the large variations in this region's winter dynamics. Arctic winter temperature variations and vortex variability affect the formation of polar stratospheric clouds (PSCs), and thus the chemical processing that leads to ozone destruction can be largely different from year to year (e.g. ).

The occurrence of sudden stratospheric warming (SSW) events, with temperatures in the polar stratosphere experiencing very rapid increases, leads to significantly lower Arctic ozone loss than during cold Arctic years without vortex disturbances (e.g. ).

Ozone loss in the Arctic region is largely dependent on the number of consecutive cold days during winter and therefore on dynamics and the occurrence of SSWs. The Arctic winter 2015/16 saw anomalous polar vortex behaviour. Polar stratospheric vortex winds were stronger than usual since early winter, and then in mid-winter a minor SSW took place, followed by a major warming in late winter (e.g. ). During the minor warming in February 2016, PSCs were seen over northern England mid-latitude locations; the closest ozonesonde station is the Irish station of Valentia (52∘ N, 10∘ W).

To take into account feedbacks between ozone and dynamics during this event we ran two experiments: one with the new BMS ozone scheme interactive with radiation and one using the default ozone configuration in which the radiation sees a climatological ozone field. Monthly averaged profiles of differences (model - observations) at Valentia station in January and February 2016 show that both experiments underestimate the maximum of the ozone profile, but differences between forecast ozone and observations are smaller when using the new BMS ozone scheme interactive with radiation than using the default ozone configuration, at all pressure levels except around 150 hPa (Fig. ).

Similar differences are also seen for Arctic stations. Arctic ozone profiles corresponding to day 10 in the forecast runs are shown in Fig.  together with the corresponding ozonesonde observations for February 2016. Although both model runs overestimate the concentration values, and underestimate the altitude, of the ozone maximum compared to the ozonesonde profiles, the model run with the new BMS scheme results in concentrations closer to observations; the percentage differences (forecast - observed) are up to 10 % smaller with the new ozone, except at 250 hPa.

SSW events like this one in winter 2015/16 are good case studies to assess the new stratospheric ozone scheme. Important feedbacks between ozone and dynamics take place in this type of events: the occurrence of a SSW reduces the amount of ozone loss over the Arctic; therefore, more ozone is available to absorb UV radiation, which contributes to a further increase of temperature in the region.

Past versions of the operational ECMWF forecast model reproduced SSW events overall weaker (colder) than observed (e.g. ); although not the only factor, this is consistent with the fact that by using an ozone climatology in the radiation scheme, past model versions could not fully reproduce the feedbacks between stratospheric ozone and rapid temperature increases that take place during SSWs. A realistic scheme for prognostic stratospheric ozone is therefore able to contribute to a better reproduction of SSW events and their feedbacks within the model.

The mean error in the temperature field is shown in Fig.  for two forecast model experiments in which the prognostic ozone has been made interactive with the radiation scheme. Both experiments are 10 d forecast covering the period August 2012–July 2013. The only difference between the configuration of the two experiments is in the prognostic ozone model: one of them uses the CD ozone, and the other one uses the new BMS ozone. In the stratosphere (above 100 hPa), the new ozone clearly reduces the model temperature bias by up to 1 K. Smaller improvements can also be seen for lower levels in the extratropics (Fig. ). The tropical region at 100 hPa is the only region in which the use of the new ozone scheme increases the temperature mean error. This is most probably attributable to the negative bias in tropical ozone exhibited by the BMS scheme. Although the negative ozone bias is found above 100 hPa, it means that more UV can reach lower altitudes (less ozone above), therefore less ozone below (more dissociation by UV); and with less ozone there is also a decrease in local temperature, leading to the larger negative temperature bias over the tropics at 100 hPa shown in Fig. . For tropospheric levels there is an overall improvement in the temperature mean error, although not everywhere for all lead times, but results for the troposphere are not statistically significant.

To display the statistical significance of these results, the differences in normalised error change in the temperature field, and corresponding significance 95 % bars, are shown in Fig. . The improvement in the model error in the stratosphere above 100 hPa is clearly evident and statistically significant with the new ozone. For altitudes below 100 hPa, it shows small increases in model error with the new scheme, but these are not statistically significant, except in the tropical upper troposphere and lower stratosphere (UTLS). Interpreting results in the tropical UTLS is not straightforward due to the many interplaying factors in this region, but the negative concentration bias exhibited at higher altitudes over the tropics is most probably playing a role.

In summary, the new scheme, therefore, improves the temperature behaviour in the stratosphere without degrading the temperature field in the troposphere; the only atmospheric region where there is some degradation in the temperature field is the tropical LS, and this is at least partly due to a known bias in the new ozone scheme.

A similar comparison can be performed between the forecast experiment using the prognostic BMS ozone interactive with radiation and the default ECMWF operational configuration in which the radiation scheme uses an ozone climatology. Figure  shows the mean error in temperature for these two experiments, and Fig.  shows the corresponding differences in normalised error change with the 95 % significance bars. These results show a similar pattern to those from the comparison of the two prognostic schemes; i.e. the BMS scheme provides an improved temperature field in the stratosphere compared to the default climatology, with the exception of the tropical region at 50 hPa and the NH extratropics at the same 50 hPa level. The new ozone also provides mean error improvements for the troposphere outside the tropics, although results are only marginally statistically significant or not significant. Note also that differences in the troposphere are 1 order of magnitude smaller than in the stratosphere. In the tropical troposphere a small degradation can be found, which unlike in the comparison of both schemes now becomes statistically significant. This is related to the fact that ozone linear models are not designed for tropospheric use, and in the troposphere the use of a realistic climatology could be considered a good alternative for numerical weather prediction (NWP) purposes.

The rest of this paper focuses on the evaluation of meteorological impacts for experiments using the new BMS prognostic ozone compared to the control experiments using the default climatology configuration. It is worth noting that the ECMWF operational model has gone through version updates after our study, and the ozone climatology has been updated following . Although beyond the scope of this paper, comparison of biases for the currently operational default configuration should be a matter of future investigation.

The winter stratospheric variability in the NH high latitudes is dominated by the occurrence of sudden stratospheric warmings (SSWs); since these SSW events can lead to surface cold outbreaks over NH midlatitudes (e.g. ), it is important for the forecast model of an NWP system to simulate them as realistically as possible.

During the SSW that took place in early February 2016, temperature anomalies reached maximum values on 7 February 2016 between 5 and 20 hPa (e.g. ). Two medium-range forecast experiments are used to assess the role of the new ozone model in this SSW event: one using the new BMS ozone interactive with radiation and one using the default model configuration in which the radiation scheme sees an ozone climatology. These experiments cover the period 15 December 2015–14 February 2016; to compare them we show some of the diagnostics used by .

Figure  shows that, with the new prognostic ozone scheme, temperature at 5 hPa becomes warmer over the Eastern Arctic region (up to 20 K warmer) compared to the default model configuration (Fig. a, b, d), bringing it closer to the operational analysis (Fig. c). We have compared t+240 h in the forecast experiments, from the 28 January forecast, against the corresponding operational analysis for the 7 February to allow for the maximum ozone response. The improvement seen at 5 hPa is also seen at lower altitude levels (figure not shown).

For these two experiments we have also examined the impact on the wind field. Figure  shows the change in RMSE for the vector wind velocity for different lead times, averaged over the experiment duration. The improvement in wind errors when BMS ozone is used consistently increases with lead time and is transferred from the stratosphere down to the troposphere for high latitudes from day 6. By day 10 in the forecast the error reduction in the wind field is statistically significant in the troposphere.

During SSW events, when both temperature and ozone distributions change rapidly in the stratosphere, a climatology-based ozone field cannot pass information to the radiation code that resembles the actual atmospheric situation; therefore, the model misses the potential source of tropospheric predictability that comes from the downward propagation of the stratospheric signal.

We have performed two seasonal experiments with start dates in May and November, covering the period 1981–2010, using a horizontal resolution of T255, 91 vertical levels and three ensemble members. The control experiment uses the MACC ozone climatology inside the radiation code, while the BMS experiment uses the new prognostic ozone interactive with the radiation code. Temperature differences with respect to ERA-Interim for these two experiments are shown in Fig. , averaged over DJF (upper panels) and MAM (lower panels).

There is a clear improvement around 50 hPa when using the new ozone scheme for both seasons and all latitudes, especially over the SH middle and high latitudes. In these SH regions the BMS prognostic ozone reduces differences by up to 4.0 K. Also for levels above 20 hPa differences with respect to ERA-Interim are reduced, especially in the summer hemisphere, by more than 1.0 K during DJF and MAM. These results have shown that a prognostic ozone field contributes to more realistic temperatures in the SH stratosphere than a climatology, also for the seasons following the Antarctic ozone hole months.

Figure  shows the zonal averaged differences in zonal wind between the two experiments for the SON season to assess the impact on wind circulation during the ozone hole season (differences for other seasons were smaller or not statistically significant). The new ozone experiment shows stronger zonal winds over the Antarctic vortex edge latitudes between 20–400 hPa, which is physically linked to the lower concentrations of ozone simulated by the new scheme over this region compared to the default climatology. When comparing to ERA-Interim (figure not shown), the control run was negatively biased over this region compared to the reanalysis (up to 2 ms-1); this bias appears reduced in the BMS run. The strengthening of winds in the BMS run is also in overall agreement with findings in .

Seasonal experiments performed under the Seasonal-to-decadal climate Prediction for the improvement of European Climate Services (SPECS) EU project also showed improvements in the equatorial winds and the quasi-biennial oscillation (QBO) signal when the new BMS prognostic ozone was made interactive with radiation .

We have implemented the stratospheric ozone model by (also known as the BMS model) in the ECMWF system, compared its performance to that of the default ozone used by ECMWF, and assessed its impacts on meteorological fields at medium-range and seasonal timescales.

The BMS scheme is the first stratospheric ozone linear model that consistently accounts for heterogeneous chemistry (e.g. ozone destruction due to polar stratospheric clouds), instead of using a separate ad hoc term, providing a more realistic link with temperature and radiation. The new approach is in better agreement with the current scientific knowledge of chemical and physical processes that affect stratospheric ozone than approaches adopted by previous linear ozone models ().

The present study is, to the best of our knowledge, the first time that the impacts of a stratospheric ozone model are assessed at different NWP timescales to evaluate its performance towards its implementation in a seamless model system. We have shown that the new scheme provides significantly better ozone distribution and variability in the ECMWF model than the currently default ozone configuration, showing particularly good agreement with observations over the high southern latitudes and the ozone hole season, even during the unusual atmospheric conditions of the 2002 Antarctic vortex split.

When used interactively with radiation in the ECMWF model, the BMS ozone scheme reduces stratospheric temperature biases both for medium-range and seasonal timescales, compared to the default ECMWF model configuration in which the radiation scheme uses an ozone climatology, and improves temperature and wind fields during Arctic SSWs.

We have also shown that the BMS ozone improves the NAO signal in seasonal model runs, therefore contributing to a more realistic stratosphere–troposphere coupling in the model. The interannual variability and seasonality of the SH polar vortex is also improved when using the BMS ozone model in runs performed with the ECMWF seasonal system (SEAS5), compared to the default SEAS5 configuration which uses an ozone climatology. All this demonstrates that the BMS scheme is realistically linked to temperature and dynamics and therefore well prepared to adapt and feed back to rapid changes in meteorology. The same adaptability cannot be achieved with an ozone climatology in the radiation scheme.

Our results also provide evidence for the need of a realistic prognostic stratospheric ozone field in ESMs for these models to perform more accurately at different timescales. The realistic stratospheric concentration values obtained with the BMS scheme, as well as its high adaptability to both usual and unusual meteorological conditions at different timescales together with its low computational cost, make the BMS scheme an excellent option to model stratospheric ozone within ESMs. The BMS scheme is able to model stratospheric ozone with a degree of complexity that provides realistic stratospheric ozone distributions, of comparable quality to the ozone field from world-leading full-chemistry models, while keeping low computational costs suitable for resolution and production times required for weather forecasting (both at medium-range and seasonal timescales). Future work should also investigate the performance of the BMS scheme within other global models and exploit its benefits for different ESMs applications beyond medium-range NWP and seasonal prediction into climate timescales.

Next, we briefly discuss ongoing further developments of the BMS model version we have used here and how they are expected to improve the results obtained with the current version. We also provide a summary of benefits that the implementation of a realistic prognostic stratospheric ozone brings to seamless Earth system models, from medium-range NWP forecasts to seasonal prediction and reanalysis production.

To tackle the tropical bias exhibited in model runs with the BMS scheme, tested the use of a different climatology reference based on observations, and although results improved over the tropics (Fig. 7 in their paper), concentrations over high latitudes were degraded by the different climatology. More recent versions of the parent full-chemistry CTM have solved the tropical bias issue and can now be used to derive a new version of the climatology terms that would not suffer from this tropical negative bias. To reduce differences with observations at high latitudes, the scheme could use coefficients that are provided twice a month, instead of just on the 15th of each month, which allow us to simulate more realistic loss rates for the sunlight levels found in the polar early spring. As a further method to improve the simulation of ozone distributions, unlike the default CD scheme, the BMS scheme coefficients could be provided in a 3D grid, instead of 2D averaged values, to also account for intrinsic longitudinal variations in ozone chemistry. Following the method by a newer version of the parent CTM can be used to compute a more advanced version of the BMS ozone scheme. This newly derived version can be obtained at higher horizontal and vertical resolution, and the tendencies can be computed with CTM runs driven by more accurate meteorology, e.g. from ERA-5 reanalysis fields. Solar effects are now also part of the latest CTM version; thus, solar variability effects can also be incorporated in the linear ozone model by deriving tendencies corresponding to solar maxima and solar minima conditions. The production of this new version of the BMS scheme is now part of ongoing work. As additional future developments the ozone scheme can also include higher-order terms to take into account second-order nonlinear effects, as well as links to other main stratospheric species like chlorofluorocarbons (CFCs) and CH4 .