The Polar SWIFT model is a fast scheme for calculating the
chemistry of stratospheric ozone depletion in polar winter. It is intended
for use in global climate models (GCMs) and Earth system models (ESMs) to
enable the simulation of mutual interactions between the ozone layer and
climate. To date, climate models often use prescribed ozone fields, since a
full stratospheric chemistry scheme is computationally very expensive. Polar
SWIFT is based on a set of coupled differential equations, which simulate the
polar vortex-averaged mixing ratios of the key species involved in polar
ozone depletion on a given vertical level. These species are O

List of equations used in the original and new Polar SWIFT version.
Terms A to L are specified in Table

The importance of interactions between climate change and the ozone layer has
long been recognized

Polar SWIFT simulates the evolution of the polar vortex-averaged mixing
ratios of six key species that are involved in polar ozone depletion by
solving a set of coupled differential equations for these species on a given
vertical level

Polar SWIFT is driven by time series of two external input parameters. The
first is the fraction of the polar vortex area that is cold enough to allow
for the formation of polar stratospheric clouds (fractional area of PSCs,
abbreviated FAP) and the second is the 24 h average of the fraction
of the polar vortex that is exposed to sunlight (fractional area of sunlight,
abbreviated FAS). A system of four differential equations is formulated that
describes the chemical rate of change of the prognostic variables as a
function of FAP, FAS and the mixing ratios of the species only (the term for
HNO

Since only a single value per vertical level and species is used in Polar SWIFT, which is constant over the polar vortex, and since the model is able to use a large time step of typically 1 day and a simple integration scheme, it is possible to calculate the ozone evolution of a complete winter in a few seconds.

The original system of equations is shown in Tables

Other fast ozone schemes developed for climate models, such as the Cariolle
scheme

The latest version of the Cariolle scheme

In Sect.

List of the terms used in the differential equations in the original
and new Polar SWIFT version.

The original formulation of the system of differential equations is revised
based on results of the Lagrangian Chemistry and Transport Model ATLAS. A
detailed description of the model can be found in

Vortex-averaged mixing ratios of all model species and vortex-averaged
reaction rates of all modeled reactions are used to identify the important
processes involved in polar ozone depletion, and to identify the relevant
reactions, their relative importance and their time evolution. Results are
based on two model runs for the southern hemispheric winters 2006 and 2011
(1 May to 30 November) and two model runs for the northern hemispheric
winters 2004/2005 (15 November to 31 March) and 2009/2010 (1 December to 31 March).
The identification of the most important processes and reactions is discussed
in a companion paper

Fit coefficients.

Details of the model setup are described in

Fitted parameters for the differential equations from
Tables

The fitting procedure for the original model version was based on fitting the
time series of species mixing ratios of a complete Polar SWIFT model run to
satellite observations at a given vertical level. This approach has several disadvantages:

The fit is nonlinear, since the solution of the differential equations depends nonlinearly on the fit parameters. This requires a nonlinear fitting algorithm, which may only find a local and not a global minimum for the residuum of the fit.

In addition, the fitting procedure is iterative and is computationally more expensive than a linear fit. Every iteration of the fitting procedure requires a complete run of the Polar SWIFT model.

Transport effects are implicitly included. The rate of change of the
satellite data at a given level is the sum of the chemical rate of change and
the rate of change by transport. Hence, the fit parameters include a
transport effect. This effect is most pronounced for O

Satellite data of the species that are fitted have to be available. For
species like ClONO

To simplify the fit further, we split the left-hand side into a sum of the
rates of change that are caused by single chemical reactions

The time series of the northern hemispheric runs and of the southern hemispheric runs are concatenated and fitted at the same time to obtain one set of fit parameters valid for both hemispheres. This is done because the physical and chemical foundations are the same in both hemispheres and the same parameterizations can be used. Since the conditions in the Northern and Southern hemispheres cover a wide range of temperatures, this approach ensures that the model does respond correctly to changes in temperature, e.g., temperature trends caused by climate change.

The vortex-averaged mixing ratios of the species

The air parcels of ATLAS that are inside the vortex are vertically binned
into bins centered at the five pressure levels of Polar SWIFT to obtain the
mixing ratios

Usually, it is easy to find a parameterization for the rate of a specified
reaction or the mixing ratios of a chemical equilibrium if only looking at a
given location inside the vortex (i.e., a reaction

However, we will see in the following that it is not possible in all cases to transform the original expression for the chemical reaction at a single location to an equivalent expression that only uses vortex averages. We use expressions that are empirically derived in these cases. Here, the quality of the approximation is assessed by the goodness of fit for the wide range of climate conditions observed in the training data set.

The 24 h averaged fraction of the polar vortex in sunlight (FAS) and the fraction of the polar vortex below the formation temperature of polar stratospheric clouds (FAP) are calculated from the same ERA Interim data that is used for running the ATLAS model for consistency.

Two different FAP parameters are used in the new version of the Polar SWIFT
model, which are called FAP and FAP

For FAS, the area below a solar zenith angle of 90

In the next sections, we present the new differential equations for the four
prognostic variables of the model (HCl, ClONO

The equation for HCl is changed from

Vortex-averaged mixing ratio of Cl

Term

The vortex average of the photolysis coefficient

Fit of term

Term

That is, a formulation of term

A very good fit for term

The sum

Vortex-averaged mixing ratio of ClO for the Arctic winter 2004/2005,
the Antarctic winter 2006, the Arctic winter 2009/2010 and the Antarctic
winter 011 at 54 hPa. Vortex average (solid blue) and parameterization for
the mixing ratio by

Vortex-averaged mixing ratio of OH for the Arctic winter 2004/2005,
the Antarctic winter 2006, the Arctic winter 2009/2010 and the Antarctic
winter 2011 at 54 hPa. Vortex average (solid blue) and parameterization for
the mixing ratio by FAS

Term

Fit of term

Production and loss processes of HO

Term

Term

Normalized pseudo first-order rate coefficients as a function of HCl
mixing ratio for the heterogeneous reactions ClONO

Fit of term

For heterogeneous reactions on NAT, reaction rates are not proportional to
HCl; i.e., the change of HCl is given by

Term

The new term

HOCl

Term

Fit of term

Fit of term

A reaction not included in the original model that affects the redistribution
of HCl and ClONO

Fit of term

The equation for ClONO

Term

See explanation in Sect.

Term

The change in the total amount of HNO

Normalized pseudo first-order rate coefficient of ClONO

Fit of term

The partitioning between HNO

Fit of term

The rate of change of ozone is given by

The ClO dimer cycle alone would lead to a quadratic dependence on ClO
in the sunlit part of the vortex, since the reaction

The fact that most of the ClO

The amount of Br

Term

Fit of term

The species mixing ratios simulated by the Polar SWIFT model are compared to corresponding measurements of the MLS satellite instrument and to simulations by the full stratospheric scheme of the ATLAS model for validation. Polar SWIFT is implemented into the ATLAS model for the validation runs and uses the transport and mixing scheme of the ATLAS model, while the detailed stratospheric chemistry scheme of the ATLAS model is replaced by the simplified Polar SWIFT model. Runs are driven by ECMWF ERA Interim reanalysis data. This approach is needed to obtain results from Polar SWIFT that can be compared to measured data.

Polar SWIFT is implemented in ATLAS by adding the rate of change of ozone
calculated by Polar SWIFT for a given layer to the ozone value of every air
parcel inside the vortex and inside this layer. Note that this means that the
ozone field does still vary across the vortex. The same is done for the other
species HCl, ClONO

Simulations of the Arctic winters 1979/1980–2013/2014 and the Antarctic winters 1980–2014 are conducted. The simulated interannual variability of ozone is compared to the observed interannual variability derived from MLS satellite data for the years 2005 to 2014.

For every winter and hemisphere, a new run is started, which is initialized
with species mixing ratios from the same MLS and ATLAS climatologies that are
used for the re-initialization described above (i.e., the same starting
conditions in every year). Runs start on 1 November and end on 31 March in
the Northern Hemisphere and start on 1 May and end on 30 November in the
Southern Hemisphere. The long-term change in the chlorine loading of the
stratosphere is considered by multiplying the Cl

Interannual variability of vortex-averaged ozone mixing ratios in
Arctic winter at 46 hPa for Polar SWIFT (blue) and MLS (red), on the last
day before vortex breakup. The date differs for different years due to
different dates of vortex breakup; see
Table

Interannual variability of vortex-averaged ozone mixing ratios in Antarctic spring at 46 hPa on 1 October for Polar SWIFT (blue) and MLS (red).

Figure

Dates of vortex breakup for
Fig.

Time evolution of vortex means of O

Same as Fig.

Figure

This study presents an update of the Polar SWIFT model for fast calculation of stratospheric ozone depletion in polar winter. The update includes a revised formulation of the system of differential equations, a new training method based on model results of the ATLAS Chemistry and Transport Model and an extension from a single level to the vertical range in which polar ozone depletion is observed.

The model is validated by comparison to MLS satellite data and the full
stratospheric chemistry scheme of the ATLAS model. It is shown that Polar
SWIFT is able to successfully simulate the interannual variability and the
seasonal change of ozone mixing ratios in the Northern and Southern
hemispheres (Figs.

Polar SWIFT was specifically developed to enable interactions between climate and the ozone layer in climate models. So far, climate models often use prescribed ozone fields, since a detailed calculation of ozone chemistry is computationally very expensive. The computational effort needed is significantly reduced when using the Polar SWIFT model. The computing time for a complete winter simulated by Polar SWIFT is on the order of a fraction of a second on a single processor core, while the computational effort for the detailed chemistry model of ATLAS is on the order of several days per winter on 50 cores on current machines.

Polar SWIFT models the response of ozone to temperature changes and changes
in the chlorine loading well, since care has been taken to represent the
underlying chemical and physical processes in the model equations. This is
also shown in Figs.

The source code is available on the AWIForge repository
(

The authors declare that they have no conflict of interest.

This work was supported by the BMBF under the FAST-O3 project in the MiKliP framework programme (FKZ 01LP1137A) and in the MiKliP II programme (FKZ 01LP1517E). This research has received funding from the European Community's Seventh Framework Programme (FP7/2007–2013) under grant agreement no. 603557 (StratoClim). We thank ECMWF for providing reanalysis data. The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association. Edited by: Fiona O'Connor Reviewed by: two anonymous referees