MIRA2 is a remote sensing microwave radiometer operated as a guest instrument at the Swedish Institute of space physics in Kiruna (67.84° N, 20.41° E, 425 m a.s.l.). MIRA2 is a heterodyne radiometer with a Schottky-diode mixer with a system noise temperature Tsys of about 1250 K (Single Side Band). The mixer is cryogenically cooled down to about 70 K by a two-stage He refrigerator. Measurements are obtained pointing North at an elevation angle between 7 and 55° depending on the tropospheric conditions. MIRA2 covers the frequency range 268 to 281 GHz, deploying an acousto-optical spectrometer with 2048 channels and a Fast-Fourier-Transform spectrometer (FFTS) with 8224 channels and 1.0 and 1.5 GHz bandwidth, respectively. With the FFTS bandwidth and 180 kHz frequency resolution a vertical profile between about 16 and 54 km can be retrieved, with a vertical resolution of about 8 km at best . In the above mentioned frequency range, observation of HNO3, N2O, ClO and O3 is possible. In this study, we use measurements of the ozone emission line centered at 273.05 GHz, the strongest spectral feature within the available frequency range. Although N2O is of central importance for the ozone loss analysis described in Sect. , its emission signature in the MIRA2 spectral range is too weak to be distinguished from the measurement residuals (i.e., the instrument noise). Consequently, due to these instrumental limitations, MIRA2 has been operated exclusively in continuous ozone observation mode.

The Microwave Limb Sounder (MLS) aboard the Aura satellite is a microwave radiometer that measures a wide range of atmospheric trace gases over altitudes of approximately 5–120 km. It succeeds the MLS instrument on the Upper Atmosphere Research Satellite (UARS). Owing to extensive validation and continuous improvements in retrieval algorithms, MLS observations are widely regarded as a reliable reference dataset .

The limb-sounding geometry yields a vertical resolution for ozone retrievals of about 2.5–7 km (full width at half maximum, FWHM) covering the altitude range of 5–120 km, and an effective horizontal resolution of approximately 300 km. MLS provides near-global coverage every three days. These characteristics must be considered in the analysis (see Sect.  for spatial screening and Sect.  for the application of MIRA2 averaging kernels).

In this study, we deploy Level 2 (v5.0) O3 products from MLS for the comparison between MIRA2 and MLS (Sect. ), as well as MLS Level 2 (v5.0) ClO and N2O products for the quantification of ozone loss and for the interpretation of the ozone depletion observed with MIRA2 (Sect. ).

Ozone measurements were collected with MIRA2 between 1 October 2019 and 30 April 2020 at the Swedish Institute of Space Physics in Kiruna, Sweden, targeting the ozone emission line centered at 273.05 GHz . For the analysis and estimation of ozone loss from MIRA2 observations, it is essential to ensure that MIRA2 measurements occur within the polar vortex, which also holds for coincident measurements by MLS. In contrast to satellite measurements, ground-based measurements, such as those obtained from MIRA2, are limited to a fixed geographical location. As the polar vortex evolves in both position and shape over the course of the winter, observations at a given site may sample air passing over it, with the site located inside the vortex, within the vortex edge region, or outside the vortex altogether. This variability introduces intermittent influence from mixing processes, particularly in the vortex edge region, where ozone-rich air from lower latitudes can be advected into the measurement region .

Consequently, time series from ground-based instruments may consist of a combination of vortex and extra-vortex conditions. To ensure that measurements used for ozone loss determination represent air masses within the polar vortex, ECMWF reanalysis data are used to identify whether MIRA2 observations were obtained inside the vortex. Further details on the data selection are given in Sect. .

The Atmospheric Radiative Transfer Simulator (ARTS) is an open-source software package written primarily in C++ that enables detailed simulation of radiative transfer through planetary atmospheres. ARTS includes a comprehensive line-by-line radiative transfer model and provides tools for forward modelling as well as atmospheric retrieval applications.

In this work, ARTS and its Python interface, pyARTS (v2.6.18), are used to simulate the microwave emission spectra observed by MIRA2 and to retrieve the vertical volume mixing ratio (VMR) profile of ozone from measurements conducted during the winter 2019–2020 campaign.

Ozone retrievals from MIRA2 measurements are performed using an inversion model based on the Optimal Estimation Method (OEM) , implemented within the pyARTS framework. This statistical approach provides an optimal estimate of the atmospheric state by combining measured spectra with a priori information, each weighted with their respective uncertainties. The forward model, implemented in ARTS, describes the relationship between the atmospheric state vector and the measured radiances. The atmospheric state deployed covers approximately 0.5–78 km in altitude, with a nominal vertical resolution of about 2 km. Averaging kernel matrices and measurement response diagnostics are calculated to quantify the vertical sensitivity and to characterize the information content of the retrieved ozone profiles.

Within the OEM framework, the retrieved state vector x^ is obtained by combining the measurement vector y with the a priori state xa and their associated covariance matrices: 1x^=xa+SaKT(KSaKT+Sϵ)-1(y-Kxa), where K is the Jacobian matrix describing the sensitivity of the measurements to changes in the atmospheric state, Sa is the a priori covariance matrix, and Sϵ represents the measurement noise covariance. Measurement noise is assumed to be Gaussian and is estimated from the observed spectra.

A priori profiles for the retrieved species are primarily derived from the COSPAR International Reference Atmosphere (CIRA-86). For ozone, a climatology based on Version 8 IMK–IAA MIPAS ozone profiles, representative of the winter season for the latitude range of Kiruna, is used to provide a realistic description of the expected ozone distribution . The MIPAS O3 profile was scaled by 75 % as this lead to stable and consistent retrievals. The a priori covariance for ozone varies with atmospheric pressure to balance the relative weighting between measurements and prior constraints. In regions with low measurement sensitivity, the retrieval is dominated by the a priori, while in regions with higher sensitivity it is primarily driven by the observed spectra.

Coincident MIRA2 and MLS measurements were identified using combined temporal and spatial coincidence criteria. MLS overpasses of the Kiruna region occur at approximately 12:00 UTC (noon), and only MIRA2 measurements acquired within ±2 h of the overpass 12:00 UTC were considered. In addition, MLS profiles were required to lie within 400 km of Kiruna. The resulting set of coincident measurements is shown in Fig.  (black).

Both datasets were subsequently filtered using retrieval quality criteria. For the MIRA2 observations, only measurements with an integration time of at least 1 h were retained to ensure a sufficient signal-to-noise ratio. Furthermore, retrievals were required to meet two conditions: (i) the residual between the fitted and observed spectra does not exceed 1 K, and (ii) the measurement response (MR) is ≥ 0.8.

The measurement response describes the fraction of information in the retrieval that is provided by the measurement rather than the a priori, and thus quantifies the sensitivity of the retrieved profile to the true atmospheric state. It is derived from the averaging kernel matrix, A, which characterizes the sensitivity of the retrieval to perturbations in the true state . The retrieved state x^ is given by 2x^=xa+A(x-xa), where x denotes the true state and xa the a priori. The measurement response at pressure level i is defined as 3MRi=∑jAij. Values of MR approaching unity indicate that the retrieved profiles are largely determined by the measurement rather than the a priori, whereas lower values indicate a stronger a priori influence. The applied threshold (MR ≥0.8), commonly used in atmospheric studies, ensures that at least 80 % of the retrieved information originates from the measurement .

For calculations of the chemically induced O3 loss, ECMWF reanalysis of potential vorticity was used to determine whether coincident MIRA2 and MLS measurements were conducted within the polar vortex. The criterion of was applied, and measurements satisfying this were classified as obtained inside the polar vortex (see ).

Moreover, for MLS data selection, recommended quality flags from the MLS Data Quality and Description (DQD) document were considered, which further constrained the dataset. To ensure that the measurements represent vortex-confined air, only observations identified as within the polar vortex in were included for O3 loss calculations (red crosses in Fig. ). Following the application of the quality control and coincidence criteria, all accepted measurements were retained for analysis. The accepted set of measurements from MIRA2 and MLS were then averaged to produce a single representative value for each day.

Due to the higher vertical resolution of the O3 retrievals from MLS (see Sect. ), a direct comparison with MIRA2 profiles is not meaningful. The MIRA2 retrievals exhibit a coarser vertical resolution, approximately 10–17 km, as illustrated in Fig. a. To ensure a consistent comparison, the MLS altitude resolution is therefore degraded using the averaging kernels from the MIRA2 retrievals. This procedure effectively smooths the MLS profiles to the vertical sensitivity and information content of MIRA2, enabling a physically meaningful comparison between the two datasets . The smoothing procedure is expressed in Eq. (), where xd denotes the degraded profile, xa and A represent the a priori profile and averaging kernel from MIRA2, and xh is the high-resolution MLS profile 4xd=xa+Axh-xa. For each comparison, the averaging kernel is selected by minimizing the temporal mismatch between coincident MLS and MIRA2 observations. Since the two datasets are defined on different pressure grids with different vertical sampling, the MLS profiles are first linearly interpolated in log-pressure space onto the MIRA2 retrieval grid, ensuring consistency between xa, A, and xh . The effect of the interpolation and smoothing on the MLS profiles is illustrated in Fig. a, which shows the retrieved MIRA2 profile (black) alongside the original (blue) and smoothed (red) MLS profiles from a coincident measurement on 6 April 2020.

The vertical resolution, shown in Fig. b (black), is determined from the full width at half maximum (FWHM) of the averaging kernel rows , seen in Fig. c. The vertical representativeness of the retrieval is further characterized by the kernel offset (Fig. b, red), which quantifies the displacement between the nominal retrieval pressure level and the effective altitude from which measurement information predominantly originates. Small offsets indicate that the retrieved state is representative of the specified pressure level, whereas larger offsets imply substantial contributions from adjacent atmospheric layers. Where the measurement response (MR) exceeds 0.8 , the offset is generally small, indicating that the retrieval is primarily constrained by the measurements and that the information is associated with approximately the correct pressure level. At lower MR values, the offset increases, reflecting a greater influence of the a priori constraints and a reduced vertical fidelity of the retrieval.

The cross-comparison and analysis of the retrieved profiles from MIRA2 are performed on the native retrieval grid (i.e. in pressure coordinates) in order to avoid interpolation artifacts and to ensure consistency with the original measurement sensitivity. Retaining the native grid is particularly advantageous for intercomparisons, as it preserves the vertical resolution and averaging kernel characteristics of the retrieval.

In contrast the ozone loss estimation is performed on isentropic surfaces of potential temperature, θ, as has been done in previous studies of Arctic winter 2020 ozone depletion . We adopt isentropic surfaces of θ because they allow repeated measurements to be compared while minimizing the influence of diabatic processes . By definition, the potential temperature accounts for the surrounding atmospheric temperature, as shown for dry air in Eq. (), where T is the atmospheric temperature, p0 and p are the reference ground-level pressure and the local atmospheric pressure, respectively, R is the specific gas constant of dry air, and cp is the specific heat capacity of dry air 5θ=Tp0pR/cp. This implies that observed changes in an air parcel along an isentropic surface are primarily due to adiabatic motion. Consequently, temporal changes observed at a constant isentropic surface more reliably reflect dynamical and chemical processes. This distinction is particularly important when estimating chemical ozone losses, as it allows us to separate changes in O3 caused by vertical transport from those due to chemical reactions. Furthermore, the use of potential temperature as a vertical coordinate aligns our methodology with prior studies of the Arctic winter 2020, mentioned earlier in this section, facilitating direct comparison of results.

While potential temperature, θ, is provided for all MLS data products via the Derived Meteorological Products (DMP) dataset, in which the meteorological fields are derived from MERRA-2 . However, for MIRA2 observations the potential temperature is calculated using Eq. (). For this calculation, we employ the same temperature and pressure profiles from ECMWF that are used in the retrieval process, as described in Sect. . Subsequently, all MLS and MIRA2 data are interpolated onto a common potential temperature grid, enabling direct comparison between the datasets and facilitating ozone loss calculations on fixed isentropic surfaces.

Chemical ozone loss was quantified using the tracer–tracer correlation method , which exploits the compact relationship between ozone (O3) and the long-lived tracer nitrous oxide (N2O) in the winter stratosphere. Because N2O is largely unaffected by chemical processes on seasonal timescales, its variability is primarily governed by transport and mixing. As a result, N2O can be used as a proxy for dynamical variability in O3. By establishing a reference relationship between O3 and N2O under conditions largely unaffected by chemical ozone depletion, the expected ozone abundance in the absence of chemical ozone loss, commonly referred to as passive ozone, can be estimated from observed N2O.

The reference O3–N2O relationship was derived from coincident MIRA2 O3 and MLS N2O observations between 400 and 600 K potential temperature on 9 December 2019. This date was selected because it precedes the period of substantial chemical ozone depletion investigated in this study, thus representing the dynamical state of the early winter stratosphere. Figure  shows the observations used to derive the reference relationship. A fourth-degree polynomial with coefficients, ai, was fitted to the data using orthogonal distance regression (ODR), 6f(x)=∑i=04aixi, where x denotes MLS N2O observations and f(x) represents the corresponding passive ozone abundance. ODR was chosen because it accounts for measurement uncertainties in both variables. To improve numerical stability during parameter estimation, both MLS N2O observations (x) and MIRA2 O3 observations (y), as well as their associated uncertainties (σx and σy), were normalized using the sample mean (x‾ and y‾) and standard deviation (sx and sy) which is provided in Appendix  (Table ), 7xn=x-x‾sx,8yn=y-y‾sy,9σxn=σxsx,10σyn=σysy, The fitted polynomial, with coefficients ai given in Appendix  (Table ), describes the passive ozone VMR, O3P, as a function of the N2O VMR. Passive ozone was therefore obtained by evaluating Eq. () at the observed MLS N2O values. Chemical ozone loss was then calculated as the difference between the measured ozone abundance, O_3M, and the passive ozone estimate, 11ΔO3=O3M-O3P, where O_3M denotes MIRA2 O3 observations and O_3P denotes the corresponding passive ozone abundance inferred from the reference O3–N2O relationship. Deviations from the reference relationship are therefore interpreted as chemically induced ozone loss.

The regression also provides the covariance matrix of the fitted parameters, Sf. The uncertainty of the fitted polynomial was estimated by propagating Sf using the Jacobian of Eq. (), 12J(x)=1xx2x3x4, such that, 13sf=J(x)SfJ(x)T, where sf denotes the propagated uncertainty of the fitted reference function. The observations used in the regression, together with the fitted polynomial and its associated uncertainty, are shown in Fig. .

The reference relationship was assumed to remain valid throughout the 2019/2020 winter season. This assumption is justified because the O3–N2O correlation evolves only slowly in the absence of substantial chemical ozone loss, whereas the analysis period considered here spans only a few months. However, the relationship is not expected to remain stationary on interannual timescales. Long-term changes in stratospheric ozone would for example modify the N2O–O3 correlation. Consequently, the reference function should be derived separately for each winter season and should not be assumed to remain valid over periods of several years.

Comparisons over the full measurement period focus on four representative pressure levels (1, 10, 56, and 74 hPa; Fig. ), selected where MIRA2 exhibits sufficient measurement response (MR). No distinction is made between air masses inside or outside the polar vortex; all coincident measurements are included to assess the robustness of the spatiotemporal coincidence criteria and the consistency of retrievals in mixed air masses. Figure  shows generally good agreement across all levels, with MLS typically falling within the ±σ range of MIRA2. At 56 hPa (Fig. c), MIRA2 slightly overestimates O3, whereas at 1 and 10 hPa (Fig. a–b), a temporal shift is visible: early in the period, MIRA2 underestimates O3, while later it overestimates. The agreement is best at 74 hPa (Fig. d). Overall, retrievals contain sufficient information content throughout the period.

To further quantify the agreement between the two data sets, we applied a modified Bland–Altman analysis (Appendix ) that accounts for the varying uncertainty of individual measurements. Figure  shows the weighted differences (MIRA2 − MLS) as a function of MLS O3, with the weighted mean bias (d‾w) and the limits of agreement (d‾w±1.96sw) indicated. The Bland–Altman analysis supports the general agreement in Fig. . At 1 and 10 hPa, mean differences are small (Table ), and the majority of points lies within the 95 % limits of agreement (±1.96sw). This provides a quantitative measure of overall agreement across the dataset. Temporal shifts are evident: MIRA2 underestimates O3 before 15 February 2020 and overestimates it afterward. At 10 hPa, a weak magnitude-dependent bias appears, with higher MLS values being slightly overestimated by MIRA2. This could stem from a priori influence at 1 and 10 hPa, as a consequence of our approach of using a fixed O3 a priori not adjusted over the measurement period. At 56 and 74 hPa, larger differences occur, likely due to interpolating MLS onto MIRA2's pressure grid and smoothing with the averaging kernel. Nevertheless, the majority of observations remains within the weighted limits of agreement, demonstrating overall consistency with MLS across the measurement period. Correlation analysis (Appendix ) further supports the comparison, with linear correlation coefficients exceeding r>0.7 at all pressure levels (Table ). Taken together, these results demonstrate that MIRA2 retrievals are internally consistent and in good agreement with MLS, providing a robust basis for subsequent ozone loss calculations.

For the calculation of chemically induced ozone loss, we adopt potential temperature as the vertical coordinate, as described in Sect. . This choice facilitates direct comparison with previous studies of ozone depletion during winter 2019/2020 . We focus our analysis on the 475 K isentropic surface (50–60 hPa), selected based on two considerations. First, MIRA2 retrievals exhibit strongest measurement response above 475 K. Second, previous studies report maximum ozone loss near 460 K . The 475 K level therefore represents a compromise between capturing near-maximum depletion and ensuring sufficient measurement sensitivity for a robust retrieval.

Figure a shows coincident daily mean ClO volume mixing ratios from MLS , while Fig. b (black line) presents the corresponding O3 time series at 475 K from MIRA2. The red dots in Fig. b show the passive ozone (O3P) obtained from the tracer function described in Sect.  for instances when MIRA2 measurements we obtained inside the polar vortex. The red squares in Fig.  show periods when the polar vortex was located over Kiruna. Due to the limited number of observations within the polar vortex, loss rates cannot be derived conclusively, neither is the period of peak loss according to the model (mid-March; ) fully captured.

This limited sampling reflects a fundamental constraint of ground-based measurement at a fixed location: loosening the vortex edge criteria could introduce extra-vortex air masses into the analysis, where mixing with ozone-rich mid-latitude air would bias the derived loss toward smaller values. The selected threshold therefore represents a deliberate trade-off between sampling frequency and the representativeness of the retrieved chemical ozone loss. Nevertheless, the dataset allows estimation of cumulative ozone loss over the winter and identification of the seasonal O3 minimum. While the temporal sampling does not fully exhibit the entire period of chemical loss, the tracer-based framework still allows following the cumulative ozone depletion, making the derived loss estimate less sensitive to data gaps in direct observations.

The temporal evolution of O3 observed by MIRA2 (black line; Fig. b) shows reduced O3 volume mixing ratio for observations within the polar vortex. This is visible already in January but most pronounced in late February and early April 2020, with the lowest O3 observed in April 2020. MLS observations of ClO over the Kiruna area in that time period display high chlorine activation in the area, mainly in January and February, marking periods of high chemically induced ozone depletion. During intervals of observations inside the polar vortex (indicated by the red squares) increasing differences between MIRA2 ozone measurements and the passive ozone tracer values can be seen. Lowest ozone VMR has been measured by MIRA2 in early and mid April when chlorine activation no longer prevailed but other ozone depleting processes according to still counterbalance the re-formation of ozone. The cumulative ozone loss shown in Fig.  (ΔO3) is finally calculated using Eq. (), in which the observed ozone is separated into a transport-driven component and a chemically induced loss term. While the transport-driven term, O3P (green dots; Fig. b), is derived from the passive tracer reference function described in Sect. , the difference is interpreted as chemically induced ozone depletion.

Figure  illustrates a persistent decrease in ozone from late winter into early spring, with steeper decline from late February to April 2020. This pattern is consistent with intensified halogen-induced catalytic destruction of ozone in March 2020 reported in . The cumulative chemically induced ozone loss observed by MIRA2 reaches 2.14±0.90 ppmv at 475 K from December 2019 until the first half of April 2020. The shaded area in Fig. reflects the propagated retrieval uncertainty in MIRA2 ozone observations, including measurement noise and smoothing effects.

Previous studies report maximum chemical O3 losses of up to 2.8 ppmv below 460 K (red star in Fig. ) , while near-complete depletion and minimum values of 2.5 ppmv at 54 hPa (blue star in Fig. ) are reported by . We find that these reported peak losses are in good agreement and fall well within the estimated retrieval uncertainties of the MIRA2 results. This supports the reliability of the measurements obtained with MIRA2 and of the current retrieval. It also demonstrates that, despite the limited temporal sampling within the polar vortex, the combined use of our observations with MLS measurements enables robust characterization of both the magnitude and the seasonal evolution of Arctic ozone depletion.