In this research, we use the Weather Research and Forecasting (WRF) model coupled with Chemistry (WRF-Chem) version 3.4.1 as a prediction model on a regional scale. It simulates the emission, transport, mixing and chemical transformation of trace gasses and aerosols simultaneously with meteorology (Grell et al., 2005). The WRF-Chem uses configuration options for various meteorological processes such as the WRF Single-Moment 6-class (WSM6) scheme for the microphysics, the Community Atmospheric Model (CAM) scheme for the radiation physics, the Monin–Obukhov scheme for the surface layer, the Noah land surface model for the land surface, the Yonsei University (YSU) scheme for the planetary boundary layer, and the Kain–Fritsch scheme for the cumulus parameterization. These are the recommended physics options for the regional climate case at 10–30 km grid size. As an advection option, the monotonic transport is applied to turbulent kinetic energy and scalars such as mixing ratios of water vapor, cloud water, rain, snow and ice and chemical species. The monotonic transport is commonly used for real-time and research applications (e.g., Chapman et al., 2009; Yang et al., 2011). Regarding the chemical mechanism, the Carbon Bond Mechanism version Z (CBM-Z) without Dimethylsulfide scheme is used for gas-phase chemistry. The CBM-Z includes the prediction of O3 and several other chemical constituents (Fast et al., 2006).

In terms of the DA system, we use an ensemble-based DA method called the Maximum Likelihood Ensemble Filter (MLEF; Zupanski, 2005; Zupanski et al., 2008). The MLEF generates the analysis solution which maximizes the likelihood of the posterior probability distribution, obtained by minimization of a cost function. The MLEF belongs to the family of deterministic ensemble filters, hence it is a hybrid between variational and ensemble DA methods. The MLEF employs a cost function derived using a Gaussian probability density function and produces both the analysis and the background error covariance (Zupanski, 2005). It is well suited for use with highly nonlinear observation operators, for a small additional computational cost of minimization using the Hessian preconditioning (Zupanski, 2005; Zupanski et al., 2007b, 2008), and has been employed in many studies including uncertainty analysis, parameter estimation and data assimilation (e.g., Zupanski and Zupanski, 2006; Zupanski et al., 2007a; Lokupitiya et al., 2008; Kim et al., 2010; Apodaca et al., 2014; Tran et al., 2014; Park et al., 2015).

The coupling between the MLEF and WRF-Chem is made through an interface module that transforms the MLEF control variables into the netcdf file of WRF-Chem, and vice versa. This interface module is a component of MLEF, and hence the WRF-Chem is not altered.

Satellite retrievals often provide estimates of chemical concentration as a total vertical column, and they cover a wide geographical range compared to other measurements (e.g., Silver et al., 2013). In our study, the total column O3 obtained by OMI is used as an observation. The OMI is a nadir-viewing near-UV/visible charge-coupled device (CCD) spectrometer aboard NASA's Aura satellite (OMI Team, 2012). The total column O3 is Level 2 data (OMTO3) based on the TOMS v8.5 algorithm, which is obtained from an orbital swath with a resolution of 13km×24km at nadir (OMI Team, 2012). It achieves global coverage in 1 day. In this experiment, we did not apply the quality flags because the first appearance of the row anomaly that affects particular viewing directions, corresponding to the rows on the CCD detectors (OMI Team, 2012) did not occur in 2005, when the TC case considered occurred (i.e., Typhoon Nabi, 2005). Therefore, we employ the OMI data without quality flags.

Figure 1 shows the total column O3 from OMI at 04:05 UTC 3 September 2005. It shows a lower concentration just inside the eyewall and elevated concentration around the eye. This distinct distribution is well described when the TC has the strongest intensity in the intensifying stages (e.g., Carsey and Willoughby, 2005). Note that OMI switches from its normal global mode to zoom-in mode, to perform spatial zoom (higher resolution) measurements, for a 24 h period about once a month. It occurs when OMI finishes its last orbital pass over Europe, and returns to global mode after 14–15 orbits or about 24 h later. During this period of zoom-in mode, OMI has no global coverage of data (OMI Team, 2012). Typhoon Nabi (2005) reached the maximum intensity on 2 September when OMI entered into the zoom-in mode. Due to the lack of O3 data in our domain on 2 September, we have alternatively chosen 3 September for the analysis of O3 properties during the maximum development of the TC case.

For the TC case, we choose Typhoon Nabi (2005), which lasted several days from 29 August 2005 until 8 September 2005. Nabi moved westward after its formation and passed near Saipan on 31 August as an intensifying TC, transformed to a super typhoon on 1 September, and reached its peak with winds of 175 kmh-1 (10 min average) on 2 September. It became weak while turning to the north and striking Kyushu on 6 September. Nabi turned to the northeast after passing by South Korea, and transformed to an extratropical cyclone passing over Hokkaido on 8 September.

In general the DA is composed of two components – prediction and analysis. A meaningful cycling of DA is inherently related to the prediction component, as every new cycle begins from the forecast guess from the previous cycle. The analysis component of DA is also important, as it provides the impact of observations on the analysis produced by DA. In the current research, we focus on the analysis component of DA, as the first step towards the eventual DA system for OMI observations.

Conducting the DA cycling with several cycles can make DA more powerful. Although one can potentially have four cycles with a 6-h assimilation window in a day, the infrequent availability of OMI observations over the model domain allows only one DA cycle per day. Therefore, we only perform the first DA cycle, which has the strongest impact among the cycles. It is our view that this single cycle DA experiment is sufficient to illustrate the effect of coupled meteorology–chemistry DA.

We focused on a single DA cycle from 00:00 to 06:00 UTC 3 September 2005, which is one of the strongest periods of the typhoon lifetime. We conduct the experiment with 32 ensembles and 6 h assimilation window. Note that the OMI observations have an approximate frequency of once per day over the typhoon and the surrounding geographical area. Therefore, adding more DA cycles would not be beneficial since no additional data are available. In the future we plan to add a capability to assimilate other observations, such as meteorological observations and all-sky infrared radiances from a geostationary satellite.

The initial and lateral boundary conditions for meteorological states are provided by the National Centers for Environmental Prediction (NCEP) Global Forecasting System (GFS), while those for chemical variables are obtained from the Model for Ozone and Related chemical Tracers (MOZART) chemistry global model of the National Center for Atmospheric Research (NCAR)/Atmospheric Chemistry Division (ACD). The WRF-Chem is set up with a horizontal resolution of 30 km and 51 vertical levels with the bottom at the ground and the top at 10 hPa using a terrain-following hydrostatic pressure coordinate (Skamarock et al., 2008).

The model domain is centered over the Korean Peninsula, covering an area of approximately 3900km×4400km with 132×147 horizontal grid points. The control variables defined in the coupled meteorology–chemistry DA are the WRF-Chem prognostic variables that contain meteorological variables such as winds, perturbation potential temperature, perturbation geopotential, water vapor mixing ratio and perturbation dry air mass in a column, and the chemical variables such as ozone (O3), nitrates (NO, NO2, NO3), and sulfur dioxide (SO2). The experiments consist of (i) the forecast (without DA) which is useful to understand the synoptic situation and background error covariance, and (ii) the analysis (with DA) which is useful to understand the assimilation impact.

We define the observation operator transforming the WRF-Chem O3 forecast to the total column O3 observation. It contains the calculation of total column O3 with unit conversion and bi-linear interpolation, that is; (1) to transform the physical units of O3 from the model-produced concentrations in parts-per-million-volume (ppmv) units to the OMI data in Dobson Units (DU), and (2) to transform the O3 amount from the model grid levels to vertically integrated value at the observation location. Mathematically, the operator can be written as h(x)=hi(hc(hu(x))), where x denotes an input model variable (e.g., concentration), and hi represents the horizontal interpolation operator, hc the vertical column integration and hu the unit transformation from ppmv to DU. The unit transformation for ozone, hu, is given by hu(x)=A×10-8Δpg×md×x, where A=6.02252×1023 is the Avogadro number, Δp is the vertical increment of pressure in the layer (hPa), g is the gravity constant, and md is the molecular weight of dry air (kg mol-1). The vertical column integration, hc, is hc(s)=∑k=1Ksk, where sk is the ozone in DU at layer k, and K denotes the number of vertical layers. Finally the bi-linear horizontal interpolation, hi, is hi(r)=∑i=1Iwiri, where ri is the vertically integrated ozone at grid point i, wi is the bi-linear observation weight at grid point i, and I denotes the number of grid points used in the interpolation (I=4 in our case). After combining Eqs. ()–() into Eq. (), the observation operator for OMI observations becomes h(x)=∑i=1Iwi∑k=1KA×10-8(Δp)kg×md×xki.

In these processes, the most demanding part of the observation operator is bias correction of total column O3 observations. Although we use the reference pressure at the model top as 10 hPa, which is the highest value we could use in the current model version, there are still considerable amounts of O3 in the stratosphere that could not be included in the calculation of the model guess (e.g., background). Since this creates a negative bias in the mean observation error, we introduce a multiplicative bias correction ε to preserve positive-definiteness of the bias-corrected guess (Apodaca et al., 2014) as hB(x)=ε×h(x), where x is the model state vector. With the multiplicative bias correction in Eq. (), we can make a new cost function in unbiased form as J(x)=12(x-xb)TPf-1(x-xb)+12[y-hB(x)]TR-1[y-hB(x)], where xb is the prior (background) state, y is the observation vector, and the superscript T means a transpose. Here, h is the nonlinear observation operator, Pf is the background (forecast) error covariance matrix in the ensemble subspace, and R is the observation error covariance matrix. Equation () is the cost function used in DA, provided ε can be estimated. The optimal value of parameter ε is obtained by implicitly assuming lognormal probability density function errors for a multiplicative bias correction in Eq. () (e.g., Apodaca et al., 2014) as ε=ε0exp⁡1N∑i=1Nlog⁡yiε0h(x)i1+r0w0, where ε0 is a guess parameter value and N is the number of observations. The empirical weighting values are set to r0=w0=0.5 which implies having the same confidence in observations and the guess. We assume the starting value of the bias to be ε0=y‾h(x)‾  where  y‾=1N∑i=1Nyi,h(x)‾=1N∑i=1Nh(x)i. Equation () is calculated once in every DA cycle.

In general, observations show that SO2 has larger concentrations in the troposphere while O3 and NO2 have larger concentrations in the stratosphere (e.g., Meena et al., 2006). However, in East Asia, especially in eastern China, there is a significant tropospheric NO2 concentration because of the industrialized and urbanized part of China (Richter et al., 2005; Ohara et al., 2007). Regarding the meteorological variables, temperature and water vapor have higher values in the troposphere, while wind has larger speed near the tropopause. To consider these characteristics, we focused on two pressure levels: (i) 850 hPa (lower troposphere) and (ii) 200 hPa (upper troposphere/lower stratosphere; UTLS). The WRF-Chem forecast is in general agreement with the observed synoptic situation, which is not shown in this paper.

The background error covariance represents the background state uncertainty (e.g., Buehner, 2005; Zupanski and Zupanski, 2007; Kim et al., 2010). These are estimated by taking the difference between the ensemble perturbation forecasts (total of 32) and the control forecast in the ensemble system (Zupanski, 2005; Zhang et al., 2013). In our study, the ensemble WRF-Chem-MLEF estimates the background error covariance defined in Zupanski (2005) as Pf=Pf1/2Pf1/2T,Pf1/2=p1f⋯pNf,pnf=m(xn0)-m(x0) where the index n is an ensemble member, N is the total number of ensemble forecasts, m is the WRF-Chem model, and the subscript 0 denotes the initial time of the forecast with corresponding initial conditions x0 (i.e., control forecast) and ensemble initial conditions xn0 (i.e., ensemble forecasts). In this experiment, the initial ensemble perturbations are generated by using the lagged forecast outputs (Zhang et al., 2013).

Being calculated from the WRF-Chem ensemble forecast, the flow-dependent background error covariance is defined for meteorological and chemical variables, which allows chemistry observations to impact meteorological variables in DA. In Zhang et al. (2013), a larger background state uncertainty was found in the storm region. Our results also identify the larger background state uncertainty near the TC, similar to Kim et al. (2010). Figure 2 shows the standard deviation (SD) of background error covariance for chemical variables. O3 in particular (Fig. 2a and d, respectively) shows a large background state uncertainty near the TC, with the maximum of 0.024 ppmv at 200 hPa (Fig. 2d). The background state uncertainties of NO2 and SO2 at 200 hPa (Fig. 2e and f, respectively) are located near the TC, characterized by small magnitude and weak influence on tropospheric pollution. On the other hand, the background state uncertainties of NO2 and SO2 at 850 hPa (Fig. 2b and c, respectively) have more impact on central eastern China, implying no visible (or obvious) impact of the low-level NO2 and SO2 on the TC.

The SD of background error covariance for meteorological variables appear to be more related to the TC structure (see Fig. 3). In particular, wind (Fig. 3a and d, respectively) shows a larger background state uncertainty near the TC at both pressure level, especially in the eye region at 850 hPa (Fig. 3a). Temperature (Fig. 3b and e) also shows a larger background state uncertainty near the TC, especially at 200 hPa (Fig. 3d). Regarding the water vapor mixing ratio (Fig. 3c and f, respectively), there is a larger background state uncertainty in the eye region at both pressure levels. Larger background state uncertainty potentially implies a stronger analysis correction, provided that total column O3 observations are available.

We assess the impact of the assimilated O3 observations using analysis increments (xa-xb), which show the correction of the background state using the observations (e.g., Buehner, 2005). It is calculated by the following variable transformation (Zhang et al., 2013; Zupanski, 2005) xa-xb=Pf1/2I+[Z(xb)]TZ(xb)-1/2ζ, where ζ is the control variable in the ensemble space; the matrix in Eq. () is equal to the inverse of the square root Hessian of the cost function in Eq. (); Z is the observation information matrix with column vectors zi=R-1/2[h(xi)-h(xb)], where the index i denotes the ensemble member.

Figure 4 shows the analysis increments (xa-xb) of chemical variables obtained by assimilating O3 observations. By comparing Figs. 2 and 4 one can notice that the O3 analysis increments are in agreement with background state uncertainties, as expected from Eq. (). At 850 hPa, the O3 analysis increment has an increase near the TC, but a decrease over China (Fig. 4a). At 200 hPa, however, there is an increase of O3 near the TC, and marginal change over China (Fig. 4d). The strong positive response has the largest value of approximately 0.024 ppmv. At 200 hPa, positive O3 analysis increments are correlated with positive NO2 (Fig. 4e) and SO2 (Fig. 4f) increments in the TC region, while no clear correlation is found in other regions. Note that NO2 and SO2 are not related to the TC at 850 hPa while the O3 analysis increments are correlated with NO2 (Fig. 4b) and SO2 (Fig. 4c), increasing in central eastern China and Korea and decreasing in northeastern China.

Figure 5 shows the analysis increments (xa-xb) of meteorological variables by O3 assimilation. Corresponding to background state uncertainties, the analysis increments of wind show significant impact on both lower and upper pressure levels. Positive O3 increments correspond to positive wind increments at 850 hPa (Fig. 5a), especially in the eye region, and to positive wind increments at 200 hPa (Fig. 5d) in the TC and in northeastern China and Korea. Regarding the temperature impact (Fig. 5b and e, respectively), the positive O3 increments generate temperature cooling near the TC and warming over northeastern China. Regarding the water vapor mixing ratio, positive O3 increments generate a reduction of water vapor mixing ratio (Fig. 5c and f, respectively) near the TC as well as in the eye region at both pressure levels. At 850 hPa, the water vapor mixing ratio is increasing with positive O3 increments over northeastern China (Fig. 5c). These results illustrate that chemical observations can impact not only the chemical variables but also the meteorological variables, due to using the ensemble-based coupled meteorology–chemistry background error covariance, as indicated by Park et al. (2015).

As a verification measure, we examine the O3 assimilation impact on the cost function and on the root mean square (RMS) error with respect to O3 observations, the same data used in the analysis. The cost function of O3 driven by Eq. () has decreased from 0.36924×104 (background) to 0.30689×104 (analysis), i.e., it is reduced by approximately 16.9 %. The RMS error, calculated as RMSa=1N∑[y-h(xa)]2,RMSb=1N∑[y-h(xb)]2, where subscripts a and b denote analysis and background, respectively, has also decreased from 0.16684×102 DU (background) to 0.15204×102 DU (analysis), i.e., by about 8.87 %. These results suggest that O3 assimilation has produced a significant improvement in the initial conditions.

In addition, the impact of total column O3 observations is also quantified in terms of the uncertainty reduction. With the Gaussian probability assumption, the information content of observations can be represented as the degrees of freedom for signal (DFS; Rodgers, 2000), ds, as ds=trI-PaPf-1, where tr is the trace function, I is the identity matrix, and Pa and Pf are the analysis and background error covariances, respectively. Here ds can also be expressed as ds=∑iλi21+λi2, where λi are the eigenvalues of the observation information matrix (e.g., Zupanski et al., 2007b). Note from Eq. () that the ds are strictly a non-negative measure: zero values indicate no impact of observations, while positive values indicate a reduction of uncertainty due to assimilation. As shown in Zupanski et al. (2007b), the estimation of Eq. () is also useful in a reduced-rank setting of ensemble DA.

Figure 6 shows the DFS of assimilated total column O3 observations. One can note that the largest values of DFS coincide with the satellite path, and thus the observations, as expected. The area with the maximum impact is near the TC location, indicating that it is the area where the total column O3 observation had the strongest impact. In agreement with the analysis increments, there exists a secondary maximum over northeastern China, and a smaller one over the Yellow Sea. Given that the DA system includes meteorological and chemical control variables, this result also indicates that O3 total column observations have a positive impact on both the meteorological and chemical components of the WRF-Chem system, especially in the TC area.