Forecast error covariance structure in coupled atmosphere – chemistry data assimilation

Introduction Conclusions References


Methodology and Synoptic Case
In this research, we use the Weather Research and Forecasting (WRF) model coupled with Chemistry (WRF-Chem) as a prediction model (Grell et al., 2005).The chosen chemistry option is the Carbon-Bond Mechanism version Z (CBMZ), which simulates the emission, transport, mixing, and chemical transformation of trace gases and aerosols simultaneously with meteorology and investigates the regional-scale air quality.More details on the WRF-Chem and corresponding options used in this study are described in Appendix A.
We chose a synoptic case on 03 September 2005 related to Typhoon Nabi (2005), characterized by an increased impact on the Korean Peninsula.The experiment begins at 0000 UTC and ends at 0600 UTC on 03 September 2005.The WRF-Chem is set up with a horizontal resolution of 30 km and 28 vertical levels.Model domain is centered over the Korean Peninsula, covering an area of approximately 3900 km x 4400 km with 132 x 147 horizontal grid points.
The ensemble forecast includes 32 ensemble members with a 6-hour assimilation window.The lateral boundary conditions are provided by the National Center for Environmental Prediction (NCEP) Global Forecasting System (GFS).The control variables defined in DA (i.e., variables adjusted during DA) are the WRF-Chem prognostic variables that include dynamical variables such as winds, perturbation potential temperature, perturbation geopotential, water vapor mixing ratio and perturbation dry air mass in column, and the chemical variables such as ozone (O 3 ), nitrates (NO, NO 2 , NO 3 ) and sulfur dioxide (SO 2 ) as well.
However, in order to investigate the structure of a coupled forecast error covariance before real observations are available and even before the full DA algorithm is developed, one can consider the assimilation of a single synthetic observation located at a chosen model grid point.In particular, we define the synthetic observation as where x f is the forecast and σ o is the observation error standard deviation.Following Thepaut et al.
[1996, Eq. ( 3)], with some modifications and using (1), the analysis increment in a single synthetic observation experiment is where x a is the analysis, σ f is the forecast error standard deviation, and the subscript ijk defines the grid location of the pseudo-observation point.Equation (2) indicates that analysis increment represents the ijk-th column of the forecast error covariance scaled by standard deviations of observation error and forecast error.In our experiments the forecast error covariance is ensemble-based, as defined in Zupanski (2005) as: where the superscript T denotes the transpose, the index n refers to ensemble member, N is the total number of ensemble forecasts, m represents the nonlinear WRF-Chem model, and the subscript 0 denotes the initial time of the forecast with corresponding initial conditions x 0 and ensemble initial conditions x n 0 .In this experiment, the control initial conditions are obtained by interpolation from the NCEP GFS model, while the initial ensemble perturbations are created using the lagged forecast outputs.
Since we are interested in the coupled atmosphere-chemistry forecast error covariance, we design two experiments with: (i) synthetic temperature observation at 250 hPa located at a grid point near (132E, 23N), on the northwest side of the typhoon, and (ii) synthetic ozone observation at 250 hPa located at a grid point near the eye of the typhoon (134E, 21N).

Results
We show the impact of single synthetic temperature (T) and ozone (O 3 ) observations in terms of the analysis increments x a − x f impacting all control variables.As mentioned earlier, our main interest is to examine the cross-variable covariance structure between atmospheric and chemistry variables, since the cross-variable analysis impact is possible only because of the multivariate structure of the coupled ensemble forecast error covariance.
In Fig. 1 we show the impact of synthetic T observation at 250 hPa on the analysis increments of T, O 3 , nitrogen-dioxide (NO 2 ), and sulfur dioxide (SO 2 ).The analysis increment of T at 250 hPa (e.g., at the same level of synthetic T observation) shows a typical response with nearly circular isolines with the maximum of 0.4 K at the observation location (Fig. 1a).The analysis increments of O 3 , NO 2 , and SO 2 are also shown in vertical cross-sections.One can see that O 3 (Fig. 1b) and NO 2 (Fig. 1c) analyses have the largest change at the level of single T observation, while the SO 2 analysis (Fig. 1d) is mostly impacted near 700 hPa (approximately σ-level 13).This is likely a consequence of the vertical structure of O 3 and NO 2 with the largest values in the upper troposphere and the stratosphere, while SO 2 has typically the largest values in the lower troposphere (e.g., Meena et al., 2006).The strongest impact of T observation is on O 3 , with the magnitude up to 0.001 ppmv, while the magnitude is somewhat smaller for NO 2 and SO 2 .One can also infer that an increase of T will imply a decrease of O 3 , NO 2 , and SO 2 .Probably the most important implication of these results is that observations of an atmospheric variable (e.g., temperature) can change the analysis of chemical variables in a physically meaningful way.This means that even with no chemistry observations in the local area, the analysis of chemical variables can still be adjusted in agreement with standard dynamical variables of the model.On the other hand, if there are chemistry observations in the area, the chemistry analysis change introduced by atmospheric observations will act as an additional dynamical constraint to the final analysis.In Fig. 2 the impact of O 3 single observation at 250 hPa on itself and the other variables is shown.
As before, we focus on the vertical cross-section of the analysis response.The impact of O 3 observation on its own analysis shows the anticipated response with the largest magnitude at observation location, approximately 0.02 ppmv (Fig. 2a).Although smaller in magnitude, the analysis increments of NO 2 (Fig. 2b) and SO 2 (Fig. 2c) show the vertical structure with maxima in the upper and lower troposphere, respectively.It is also notable that an increase of O 3 brings about an increase of NO 2 and SO 2 , confirming the direct relationship between these variables as noticed in Fig. 1.The T analysis increment indicates that there is a cooling at the level of O 3 observation, while there is a warming above and below (Fig. 2d).
The results shown in Figs. 1 and 2 indirectly confirm that the improved stratospheric ozone distribution by DA can make a better representation of stratospheric winds, temperature and other constituents (e.g., Lahoz et al., 2007).

Conclusions
The structure of an ensemble-based coupled atmosphere-chemistry forecast error covariance was examined in the context of the WRF-Chem model.A synthetic single observation experiment was designed in order to evaluate the cross-variable components of the coupled error covariance.Our results indicate that the coupled error covariance has important cross-variable components that allow a physically meaningful adjustment of all control variables, and a much wider impact of observations (e.g., atmospheric observation on chemistry analysis, and vice versa).The analysis increments created in response to synthetic temperature and ozone observations illustrate the complexity of atmosphere-chemistry cross-correlations and the forecast error covariance structure.Given the realistic structure of ensemble forecast error covariance produced by the WRF-Chem, we anticipate the ensemble-based coupled atmosphere-chemistry data assimilation will respond similarly to assimilation of real observations.Therefore, our next step is to apply the WRF-Chem with an ensemble-based data assimilation algorithm (e.g., the maximum likelihood ensemble filter (MLEF); Zupanski, 2005) to assimilation of real chemical and atmospheric observations.To evaluate the cross-variable component of forecast error covariance, we select the simplified dynamics rather than sophisticated physical processes.Regarding the atmospheric processes, we use the recommended physics options for the regional climate case at 30 km grid size in our experiments.
As the chemical options, the Carbon Bond Mechanism version Z (CBM-Z) without Dimethylsulfide scheme is used for the gas-phase chemistry.The CBM-Z photochemical mechanism contains 55 prognostic species and 134 reactions having the lumped structure approach for condensing organic chemical species and reactions (Fast et al., 2006).It also uses a regime dependent approach based on the partitioned kinetics, such as background, anthropogenic, and biogenic submechanisms for saving the computational time (Fast et al., 2006).Furthermore, we consider the chemical tendency diagnostic for equation budget analysis.However, we did not consider the convective parameterization which can simulate the subgrid convective transport, wet scavenging, and aqueous chemistry due to simple experiment setting, even with a typhoon case.

Figure 1 .
Figure 1.The analysis increments (x a − x f ) in response to a single T observation at 250 hPa (near σ-level 24): (a) horizontal response of T at 250 hPa, and vertical responses of (b) O3, (c) NO2 and (d) SO2.In (b)-(d), the vertical axis represents the vertical σ-levels.Units are ppmv for chemical variables and K for temperature.

Figure 2 .
Figure 2. Same as in Fig. 1 but for vertical cross-section of the analysis increments (x a − x f ) in response to a single O3 observation at 250 hPa for (a) O3, (b) NO2, (c) SO2 and (d) T.