This study uses two data products, namely CAMSRA and CAMSFC, that have been produced by the ECMWF in the framework of the CAMS. These datasets focusing on surface ozone are introduced in the following subsections. An overview of the main differences and similarities between both products is given in Table 1. For more details on other aspects, the reader is referred to the references.

Surface-based measurements of ozone were extracted from the Tehran air quality control portal, which is publicly available, for 21 stations. A couple of the stations contain no data records, and the data sparsity at the stations differs from year to year. Hourly time series of surface ozone for other cities are not accessible to the public and were obtained from the Iranian Environmental Protection Organization for 54 air quality monitoring stations. We added the Geophysics station, which is located at the Geophysics Institute, University of Tehran, in Tehran. This station measures surface ozone along with several other variables such as air temperature, nitrogen oxide, wind, total ozone column, etc. Most of the air quality monitoring stations in Iran are installed in the cities, as they are aimed for the public health report. There is no information about stations' type or availability of the data at background sites. To have a common quality, the validity of the data was checked by performing a few statistical tests, such as (1) range test: verifies if the values are within the acceptable range limits (Zahumenský, 2004; Taylor and Loescher, 2013); (2) constant value test: checks the required variability among successive values (Zahumenský, 2004); and (3) discontinuity test: identifies suspicious data points before and ahead of the discontinuities (Zurbenko et al., 1996; Gerharz et al., 2011). We use the stations containing data for the year 2020, where more than 50 % of the data are available for each month. Table A1 lists the names and geographical locations of the stations, of which the first 22 are ordered based on the stations' latitudes. In Table A1, there is a number along with the stations' names, and hereafter the stations are referred to using these numbers. To include more stations in the analysis, we consider five more stations in Table A1, i.e., from 23 to 27, for which only 1 or 2 months of 2020 contain less than 50 % of data (see Fig. A1). The distribution of the stations is shown in Fig. 1, which covers three large cities (Tehran, Shiraz, and Tabriz) and six small cities (Birjand, Gilan, Hamedan, Zanjan, Markazi, and Yazd). Hereafter, the observation datasets and observed ozone time series are called OBS and O3OBS, respectively.

Both reanalysis and forecast datasets were co-located with OBS through temporal and spatial interpolations. OBS data are available in hourly resolution, in contrast to the CAMS datasets that are available in 3-hourly intervals. To match the frequency of the CAMS outputs with OBS, 3-hourly observed values are considered in such a way that at least two hourly values are available; otherwise, it renders the value as missing.

The presence of various scales of motion, which are caused by several physical and chemical processes, in the time series of O3 can complicate the analysis and interpretation of data. As an example, short-term and fast fluctuations in the O3 time series are majorly attributed to chemical processes such as NO titration, whereas long-term and seasonal variations are mainly related to solar radiation, long-range transport, and stratosphere–troposphere exchange (Monks, 2000). Scale analysis is a method by which the time series can be separated into different temporal terms. Here, the time series of O3 is decomposed into three different spectral components, namely short (period less than 2 d), medium (period of 2–21 d), and long (period longer than 21 d) terms, by applying the Kolmogorov–Zurbenko (KZ) technique (Rao et al., 1997). The KZ technique is essentially a low-pass filter that consists of repeated moving averages. Its use has been demonstrated in earlier studies (Hogrefe et al., 2000; Kang et al., 2013; Seo et al., 2014). A detailed discussion of the KZ filter along with a comparison with other separation techniques can be found in Eskridge et al. (1997) and Loneck and Zurbenko (2020). The KZ technique requires two input parameters, KZ (m and k), where m is the window size for filtering and k is the number of iterations. Since the values that have been commonly used for m and k in the literature may not be applicable for 3-hourly data, we selected them based on the criteria suggested in Yang and Zurbenko (2010): 1m×k≤p. The KZ technique filters out all periods that are less than p, i.e., the number of filtered time intervals. Therefore, three components of interest in this study are estimated as follows: 2S=O-KZ(5,5)3M=KZ(5,5)-KZ(35,5)4L=KZ(35,5), where O refers to the original time series and S, M, and L indicate the short, medium, and long terms, respectively. Here, the units of O and the spectral terms are in nmol mol-1. As expected from Eq. (1), KZ(5, 5) filters all periods less than 11.2 time steps. This corresponds to 33.54 h, or 1.4 d, as the data are recorded at intervals of 3 h. The same holds for KZ(35, 5), which filters all periods less than 9.8 d. Hence, the S refers to the short-scale fluctuations, which are done in less than 1.4 d. Similarly, M refers to synoptic-scale events with timescales ranging from 1.4 to 9.8 d. The variations with timescales of more than 9.8 d are represented in the L term.

To bridge the spatial scaling issue between coarse resolution CAMS datasets and local-scale measured data, statistical downscaling (SD) methods have been developed (Wilby and Wigley, 1997). SD refers to the use of statistical-based techniques to determine a relationship between global-scale models' outputs and observed small-scale (local) variables (Wilby et al., 2004; Wilby and Dawson, 2013). There are numerous SD methods, such as linear regression (Sachindra et al., 2013; Beecham et al., 2014), stochastic weather generators (Wilks, 1999; Kilsby et al., 2007; Semenov and Stratonovitch, 2010), and artificial neural networks (Tripathi et al., 2006; Ahmed et al., 2015; Sachindra et al., 2018; Sebbar et al., 2023), to name a few. In this study, a deep learning method known as the LSTM network was used to analyze the complex relationship between O3 and its precursors. LSTM is a modified version of a recurrent neural network designed to handle long-term (and short-term) dependencies in sequential data (Hochreiter and Schmidhuber, 1997). LSTM contains memory cells that can hold (and store) information for a long time, thus making them suitable for time series analysis. The standard LSTM consists of three gates: input, forget, and output gates for controlling the movement of information. We use Keras, a high-level neural network Python library (“Keras: the Python Deep Learning library”; Chollet et al., 2015; https://keras.io, last access: 15 May 2014) to build and train the LSTM model. This model requires a specific configuration and tuning to work effectively with the datasets. A range of control values for several hyperparameters (Table A2) were tested by multiple trial-and-error tests. The most effective hyperparameters (Table A5) were selected using the random search optimization method.

To prepare the LSTM inputs, several meteorological variables (Table A3) were obtained from the CAMSRA and CAMSFC datasets. To prevent overfitting of the model, a cross-validation LASSO regression was performed to identify the potential predictors at each station. The lagged O3 (from OBS) was also considered as one of the model inputs, since the concentration of O3 is not only affected by meteorological factors but also by the influence of the O3 levels in the past. A partial autocorrection function was utilized to estimate the correlation between observed O3 at time T and earlier time steps. For most of the stations, the autocorrelation coefficients decrease after a time lag of 24 h within a confidence interval of 95 %. So, the O3OBS at times T-1,…, and T-8, were also considered predictors at each station. Selected predictors and observed O3 were decomposed using Eqs. (2)–(4).

In order to provide the final output, i.e., downscaled O3, the LSTM architecture was trained on the decomposed datasets. The data records were divided into 65 % for the training subset and 35 % for the validation subset. The best model was chosen based on the R2 (coefficient of determination) score and mean square error (MSE). The selected model was applied to all data records to provide a downscaled output. All these procedures were applied to each station separately and are illustrated in Fig. 2.

We use the mean square error (MSE) as a metric to evaluate the models' performance. The MSE is defined as the squared mean of the difference between modeled (xm) and observed (xo) variables.

This metric can be modified to include all relevant model evaluation indicators, i.e., bias, variance, and correlation, as (Murphy, 1988; Solazzo and Galmarini, 2016) 5MSE=(x‾m-x‾o)2+(σm-rσo)2+σo2(1-r2), where σm and σo refer to the standard deviation of the modeled and observed data, respectively, and r is the coefficient of correlation between the observed and assimilated datasets. In Eq. (5), the first term (hereafter E1) shows the deviation between average modeled (x‾m) and measured (x‾o) datasets and refers to the model accuracy. The second term (hereafter E2) contains the variance error, i.e., the discrepancy in amplitude or phase between the variability in the modeled and observed values, that determines the precision of the model. Also, the third part (hereafter E3) refers to unsystematic errors related to the associativity between observed and assimilated datasets. In other words, the E2 indicates an explained error, which reveals the variance error arising from the variability in the modeled variables that are not observed in measurements. That could arise from overfitting associated with complex chemical processes in the model or imbalance among coupled components. The E3 represents an unexplained error, reflecting the lack of observed variability in the modeled data. That refers to the variabilities which are not captured by the models, even though those variabilities exist in the observations. The E3 can arise from random and non-representative errors caused by sub-scales and non-resolvable processes in the observations, or from a deficiency in the model in capturing meso-scale phenomena. Due to the spectral decomposition of the data, the S and M components have zero mean fluctuations. Hence, the E1 term in Eq. (5) is zero, and only the E2 and E3 terms are analyzed below.

To compare the distribution of error in modeled O3 before and after downscaling, the skill score (SS) is calculated as (Wilks, 2006) 6SS=1-MSEMSEref. Here, MSEref and MSE refer to the MSE of O3RA (or O3FC) and downscaled O3 (O3SD), respectively. The value of SS varies between 0 and 1. The value is zero once there is no preference in O3SD with respect to O3RA (or O3FC), i.e., the O3 variability is not explained by selected predictors. The value of SS is one when the MSE of O3SD is zero, which means the whole O3 variability in the LSTM model is explained by the predictors, i.e., the LSTM model is perfect.

The time series of O3 and all meteorological variables for OBS and CAMS datasets decompose into three spectral components, short (S), medium (M), and long (L), by applying the method (KZ filter) explained in Sect. 3.1. Figure 3 shows the original time series of O3OBS, O3RA, and O3FC, as well as their estimated spectral components at the first station. To clearly see the signals, we only show part of the time series, here for the summer months (June, July, and August: JJA). Looking at the original 3-hourly time series (Fig. 3a), both CAMS datasets overestimate and underestimate ozone during different periods, but it is difficult to determine any clear patterns or identify specific reasons for the model bias. The S component contains frequent fast oscillations occurring every day with regular maxima and minima (see Fig. 3b). In this figure, the amplitude of the S oscillations of the O3RA and O3FC is different from that in OBS, indicating differences in the diurnal cycle of observed and simulated ozone mixing ratios. The M term captures variability on the timescale of synoptic systems. Some episodic events are more visible in the M component than in the S component. For instance, in Fig. 3c, the M component of the OBS represents a clear signal of an episodic event in the middle of June. This episode is not well captured in CAMSRA, whereas it is captured in CAMSFC. It seems that for most of the periods, the variations in the M component in both CAMS datasets are in good agreement with those in OBS, while the amplitudes of oscillations in CAMS do not correspond well with those in OBS. The underestimation and overestimation of the amplitude (with respect to observations) in CAMSFC is less than that in CAMSRA. Compared with the S and M terms, which oscillate around zero, the mean values of the L components are not zero (see Fig. 3d). The L represents variations in the ozone mixing ratios on seasonal, semi-seasonal, and multiannual timescales. Comparing the variations in CAMSRA and CAMSFC with OBS for L shows more similarity between CAMSFC and OBS than between CAMSRA and OBS. Both models exhibit a high bias with respect to the ozone mixing ratios. Nevertheless, the decomposition of the L component is not reliable due to the limited period (1 year) of the available data, so hereafter we only assess the S and M components.

The time series for 16 relevant meteorological variables were extracted from CAMS products. To avoid model overfitting, we identified potential predictors of the variables. To decide on the importance of the variables, we used the LASSO-CV estimator. The relationships between predictors and O3OBS were estimated by performing a least absolute shrinkage and selection operator (LASSO) regression. The variables with the highest absolute LASSO coefficient (importance weight) are considered the most important. Figure 4 shows that the T2m is the most explanatory meteorological variable and NO, NO2, and O3RA are the main chemical variables for CAMSRA_S at most of the stations. The variables with high feature importance (weight >0.1) were considered for use in the LSTM modeling.

Table 2 lists selected predictors for both components of CAMSRA at each station. At station 1, 12 variables, namely T, V, U10m, V10m, MSLP, SP, T2m, SH, W, CO, NO2, and O3RA, are identified as the potential predictors of the S component, while four variables, i.e., U10m, W, SO2, and O3RA, are selected for the M term. Some of the selected predictors are common between the S and M components. A few meteorological variables, such as T2m, SP, MSLP, W, and U10m (or V10m), appear for the S component at most of the stations. These variables reflect the information about temperature, pressure, and vertical velocity. Temperature is one of the key meteorological factors influencing the S term variability in O3 through its effect on biogenic emissions, photochemical kinetics reaction rate, and anthropogenic emissions. Stable anticyclones and sunny conditions promote O3 formation and accumulation. Zonal and meridional winds at 10 m are important for the dispersion of ozone precursors at local scales. For most of the stations, the S term is affected by pollutant species such as O3RA, NO, and NO2, of which NO and NO2 are recognized as potential drivers of O3 levels. Selection of total cloud cover (TCC) and fraction of cloud cover (FCC) for the M component at most stations indicates that cloud covers are mostly associated with synoptic systems (e.g., occurrence of high pressure systems associated with clear-sky conditions) and O3 variability on this scale. The M component at a few stations, e.g., 4, 6, 9, and 13, shows weak associations with the parameters, so no variables are selected for them. This situation often happens for the M component and suggests the role of other factors (not included in the predictors). There are a few stations where O3RA (O3FC) is not selected as an important variable, which is related to the small (weak) associations between O3RA (O3FC) and O3OBS. For instance, SH is selected as the main factor effecting the M term at station 23, i.e., Rasht. This station is located between the mountains (Alborz) and coast (Caspian Sea), with a local rainy environment and a humid subtropical climate. That is similar to the western Mediterranean regions, where a lack of strong synoptic advection, combined with the orographic characteristics and the land–sea breezes, favors episodes of high ozone levels over this region (Millaìn et al., 2000; Velchev et al., 2011; Wentworth et al., 2015). Similar to CAMSRA, for CAMSFC the number of selected parameters for the S is larger than that for the M (see Table A4). In CAMSFC, boundary layer height (BLH) and V10m (or U10m) appear as dominant meteorological drivers affecting the S component. Stable boundary layer height causes the accumulation of ozone and its precursors during night or under light (weak) winds conditions. Moreover, ozone in residual layers can be transported over long distances with prevailing winds. In the morning, trapped ozone can be entrained downward into the mixed layer (Stull, 1988; Zhang and Rao, 1999). The M term is mostly associated with O3FC.

The LSTM model was trained and validated with the datasets, as explained in Sect. 3.2. We tuned hyperparameters, which allow the learning algorithm to run until the error from the model, i.e., the loss function, has been sufficiently minimized. As there are no given values to set these numbers, the optimum values were obtained by multiple trial-and-error tests (see Table A5). The best model was selected based on the MSE and R2 (coefficient of determination) score, which indicates the amount of explained variance by the LSTM model. Figure 5 shows the R2 of the selected model for all data series at each station. For most of the datasets, the R2 is larger than 0.5, indicating that more than 50 % of the O3 variance is explained by the LSTM. The R2 for the M component is larger than that for the S term, despite the smaller number of predictors for the M. This might reflect that the M component is easier to be modeled due to less complexity. In this figure, the R2 of the M is around 0.9 for all stations, whereas it varies for the S term. The R2 value of the S at the stations over the city of Tehran is within the same range of 0.7–0.8. Both CAMSRA and CAMSFC show the R2 to be less than 0.5 for the S term at a few stations, namely 22 (Yazd), 24 (Zanjan), and 25 (Markazi). A possible reason for that could be the peculiar characteristics of short-term ozone variability at these sites or their geographical locations. Model-to-model differences in R2 are more pronounced in the S, which is likely due to the different emission inventories used in the models.

Figure 6 shows the box plots of MSE and different terms of MSE, i.e., E2 and E3, for both components of O3SD. For the sake of simplicity, descriptions of the results are mostly based on the mean values. Nevertheless, the values of the indicators at each station are shown as a scatter point next to the box plots. From Fig. 6a, it turns out that the mean MSE (shown with red squares) of O3 for the S component is larger than that for the M component for both models. That could arise from the uncertainties in O3 precursor emissions affecting modeled local photochemistry and likely S variability. The largest value of the MSE is associated with the O3SD of the stations located in the city of Tehran. That can be associated with the uncertainties in CAMS emission inventories, which may have a larger impact in cities with high anthropogenic emission sources. The stations in the northern part of the city (e.g., stations 4–9) show a larger MSE than the stations in the southern part (e.g., stations 10, 11, 14–17, and 19). That can be associated with the deficiency in the emission inventories in capturing the local emission changes within urban areas. The large value of MSE is also found for the S term at the stations located in Shiraz and Tabriz, which are known as big and highly populated cities with numerous local anthropogenic emission sources (thermal power plants, oil refinery, cars, etc.). Station 2 in Tabriz shows less MSE than stations 1 and 3, which are located in the industrialized part of the city. That can be associated with the uncertainties in the spatial variations in the emission inventories used in CAMS. Although the CAMS anthropogenic emission inventories account for emissions from different sectors, such as transportation, residential and energy sectors, as well as biogenic fluxes, they have a temporal and spatial allocation with a monthly spatial grid resolution of 0.1° × 0.1°. Low values of the MSE for CAMSRA_S and CAMSFC_S are attributed to stations 22 (Yazd), 20 (Hamedan), and 24 (Zanjan). Similar to R2, the lowest MSE belongs to the Yazd station, which contains fewer local emission sources than other cities such as Tehran, Tabriz, and Shiraz.

Figure 6b shows the explained error (E2) in CAMSRA and CAMSFC for both components. E2 is a model-related error, and a possible source for this can be a misrepresentation of short- and meso-scale phenomena in models. The small values of E2 reflect the low contributions of E2 to the MSE and the noticeable improvement in the O3SD (via downscaling procedures). The major portions of the MSE are associated with the unexplained errors (E3) for both components (see Fig. 6c). The E3 for the S component is larger than that for M, as expected from the variance in these components. The S variability is associated with the effect of daytime photochemical production and downward transport of O3 rich from upper levels, combined with O3 loss by depositions (in the surface layer). A large value of E3 for the S component can arise from the CAMS' deficiency in resolving the meso-scale phenomena such as local winds, NO titration, deposition rates, and their influences on O3 variability. Assessing the element of E3 (see the third term of Eq. 5) shows that large variances in observations (σo) or small correlations (r) cause the large E3 and consequently the large MSE. Figure A2a shows the correlation between the models and observation datasets for both components. This figure shows that M contains a larger correlation (r>0.9) than S in both models. A high value of correlation between two terms can be attributed to the larger covariance of two terms or less variance in each term. Figure A2b shows the covariance between models and observations. As can be seen in this figure, the mean value of covariance for the S components is larger than for the M components. So, the smaller correlation of the S in comparison with that of the M is attributed to the larger variance in S (Fig. A2c). In other words, the better model performance (i.e., smaller E3 and MSE) for the M is not associated with the larger covariance of the M component. That is attributed to less variance in M than in S (see Figs. 3 and A2c).

In order to examine the effect of the CAMS products and lagged O3 (from actual observations) on the LSTM model, we exclude the measured lagged ozone from the predictors of the LSTM model (hereafter LSTMno_lag). The R2 of the LSTMno_lag is shown in Fig. A3. Overall, the R2 of the LSTMno_lag is less than that of the LSTM. This suggests that the LSTMno_lag may carry the risk of not including all important predictors (e.g., lagged ozone) in the model. This feature is more noticeable in the M term than the S term, i.e., the R2 of the S component is less affected by removing the lagged O3. That reflects the CAMS products, which explain more of the S variance than that of the M term. In other words, most of the variance in the M term in the LSTM is explained by the lagged O3 (not by the CAMS products). That could be a reason for the better performance (less MSE) of the M than the S. Figure A4a shows the MSE of the LSTMno_lag. In this figure, the MSE of the datasets increases by 2 times with respect to that of the LSTM. The higher values of the MSE in the LSTMno_lag are attributed to the removal of the observed lagged O3 from the model. Although the R2 of the LSTMno_lag for the S is larger than that for the M term, the MSE of the S is higher than that of the M term. This is similar to the MSE of the LSTM, which is related to the higher variance in S than M. Similar to the LSTM, in LSTMno_lag, the low values of MSE are seen for the S component of O3 at stations 22 (Yazd), 20 (Hamedan), and 24 (Zanjan).

The skill scores (SS) of the downscaled models O3SD with respect to the O3RA and O3FC for all datasets are shown in Fig. 7. In Fig. 7a, the mean value of the SS for three datasets, namely CAMSRA_S, CAMSRA_M, and CAMSFC_M, is larger than 0.9. This reflects that the downscaling procedure (LSTM) improves the accuracy of the results in the three mentioned datasets. The lower value of the SS for CAMSFC_S can be attributed to the higher skill of the reference dataset, i.e., O3FC, or less accuracy of the LSTM model. The SS of the LSTMno_lag for CAMSRA_S shows the same high accuracy as that in the LSTM, whereas for other datasets the mean SS declines to less than 0.8 (see Fig. 7b). There is a large difference between the SS of the LSTM and LSTMno_lag for the M component, which shows the importance of the lagged O3 for modeling of the M term. Larger values of SS for CAMSRA than that for CAMSFC reflect a better performance of O3FC over Iran. That is also shown in Fig. A7a, in which the MSE of CAMSFC_S is less than that of CAMSRA_S.