ARTICLE IN PRESS

Atmospheric Environment 41 (2007) 3082–3094 www.elsevier.com/locate/atmosenv

Ensemble-based data assimilation and targeted observation of a chemical tracer in a sea breeze model

Amy L. Stuarta,Ã, Altug Aksoyb, Fuqing Zhangc, John W. Nielsen-Gammonc

aDepartments of Environmental and Occupational Health and Civil and Environmental Engineering, University of South Florida, 13201 Bruce B. Downs Boulevard, MDC-56, Tampa, FL 33612-3805, USA bNational Center for Atmospheric Research, Boulder, CO, USA cDepartment of Atmospheric Sciences, Texas A&M University, College Station, TX, USA

Received 5 June 2006; received in revised form 25 September 2006; accepted 28 November 2006

Abstract

We study the use of ensemble-based Kalman filtering of chemical observations for constraining forecast uncertainties and for selecting targeted observations. Using a coupled model of two-dimensional sea breeze dynamics and chemical tracer transport, we perform three numerical experiments. First, we investigate the chemical tracer forecast uncertainties associated with meteorological initial condition and forcing error. We find that the ensemble variance and error builds during the transition between land and sea breeze phases of the circulation. Second, we investigate the effects on the forecast variance and error of assimilating tracer concentration observations extracted from a truth simulation for a network of surface locations. We find that assimilation reduces the variance and error in both the observed variable (chemical tracer concentrations) and unobserved meteorological variables (vorticity and buoyancy). Finally, we investigate the potential value to the forecast of targeted observations. We calculate an observation impact factor that maximizes the total decrease in model uncertainty summed over all state variables. We find that locations of optimal targeted observations remain similar before and after assimilation of regular network observations. r 2006 Elsevier Ltd. All rights reserved.

Keywords: Air quality modeling; Data assimilation; Ensemble modeling; Adaptive observations

1. Introduction nificant uncertainties (Seigneur, 2005). The com- plexity comes in large part from three areas. First, Significant strides in understanding and mitigat- air pollution involves numerous nonlinear physical ing air pollution have been achieved over the past and chemical processes, many of which are not well several decades (Seinfeld, 2004). Despite this pro- understood. Second, the characteristic spatial and gress, modeling and prediction of air pollution and time scales of these processes span many orders of its effects remains difficult and is prone to sig- magnitude. Due to poor understanding of some processes and the computational cost of resolving all processes at the appropriate scale, many ÃCorresponding author. Tel.: +1 813 974 6632; fax: +1 813 974 4986. processes are parameterized in models. These para- E-mail address: [email protected] (A.L. Stuart). meterizations are, by nature, only approximations,

1352-2310/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2006.11.046 ARTICLE IN PRESS A.L. Stuart et al. / Atmospheric Environment 41 (2007) 3082–3094 3083 and hence have errors and uncertainties associated short-term monitoring, for specific management and with them. Finally, uncertainties in the initial and research purposes. Recently, interest has escalated boundary conditions lead to uncertain predictions in observation targeting for response to air pollu- of air quality. The chaotic nature of the meteor- tion hazards that result from emergency releases. ological system governing underlying atmospheric In the weather forecasting field, there has been transport (Lorenz, 1963) can often cause even small significant research on adaptive location of targeted uncertainties to grow substantially in time. observations using techniques originating with data Due to the uncertain nature of the prediction of assimilation (Emanuel et al., 1995; Emanuel and air pollution hazards (whether due to routine Langland, 1998; Lorenz and Emanuel, 1998; Berli- emissions or emergency releases), simulation tech- ner et al., 1999) that could be applied to air quality niques combining deterministic modeling with network design. statistical methods (i.e. Monte Carlo methods) have Although data assimilation is used operationally sometimes been used to determine air pollution for meteorological modeling and prediction, its use hazard probabilities and to explore the sensitivity of for air quality modeling is less developed. None- predictions to underlying input and model uncer- theless, it has been found to be useful as an inverse tainties (e.g. Boybeyi et al., 1995; Stuart et al., 1996; modeling technique for diagnosing pollutant emis- Bergin et al., 1999; Dabberdt and Miller, 2000; Sax sion source locations and strengths (i.e. parameter and Isakov, 2003; Zhang et al., 2006). One such estimation) (Chang et al., 1997; Elbern et al., 2000; statistical technique that has significant promise Mendoza-Dominguez and Russell, 2001) and for for improving air quality modeling and prediction identifying locations (in time and space) for field is four-dimensional data assimilation (FDDA). observation networks and adaptive observations FDDA combines observational data, knowledge (Daescu and Carmichael, 2003). Much of this of the physical and chemical system behavior (as previous work has focused on variational data represented in predictive models), and information assimilation techniques (three-dimensional and on the uncertainty in both the observed data and the four-dimensional variational assimilation, 3DVAR model representation over space and time (Kalnay, and 4DVAR). 2003). By integrating this information, data assim- Ensemble-based Kalman filtering is an alternative ilation can provide a more accurate description of data assimilation approach that is undergoing the system state (i.e., multidimensional information significant investigation for many environmental on wind speed, wind direction, temperature, and modeling applications (Evensen, 2003). Advantages chemical concentration) and its expected evolution include lower computational costs than extended in time. Data assimilation can also be used to Kalman filtering and explicit calculation of the constrain errors associated with the uncertain model nonlinear evolution of background covariances parameterizations and to determine parameter through the ensemble forecast. Explicit calculation values, through on-line optimization of the para- of covariance eliminates the assumption of statio- meters used (‘‘parameter estimation’’) (e.g., Navon, narity of covariances used in 3DVAR, and alleviates 1998). the need for the development of tangent linear and In addition to improving model predictions, data adjoint models of the dynamics used in extended assimilation research has led to the development of Kalman filtering and 4DVAR (Tippett et al., 2003; tools such as adjoint models for the selection and Kalnay, 2003). Heemink and collaborators have design of observational networks and targeted investigated ensemble-based Kalman filtering and observations, as it provides a mechanism for on- other Kalman filtering techniques for prediction of line optimization of this selection (Morss et al., ozone concentrations over Europe with two- and 2001). Existing long-term air quality observational three-dimensional chemical transport models that networks are generally fixed in space and have very are decoupled (calculated off-line) from the under- sparse spatial and temporal resolution. The sparse lying meteorological dynamics simulation (Hanea resolution is due to the number of variables that et al., 2004; Heemink and Segers, 2002). Their work need to be observed (several meteorological vari- indicates improvement in model predictions with ables and up to hundreds of toxic chemical filtering, and demonstrates the feasibility of Kalman pollutants) and large equipment and operational filtering techniques for modeling air quality. expenses. In addition to long-term fixed locations, Here, we study the utility of ensemble-based targeted observational locations are often used for Kalman filtering in the context of a two-dimensional ARTICLE IN PRESS 3084 A.L. Stuart et al. / Atmospheric Environment 41 (2007) 3082–3094 sea breeze model in which chemical tracer transport The model spatial domain represents the cross- is directly coupled to the underlying nonlinear shore horizontal distance and the vertical above- meteorological dynamics. The sea breeze circulation ground altitude. The coast is located at horizontal is an important weather pattern affecting coastal domain center. The force that drives the sea breeze areas. Since many cities are located near coasts, these circulation is modeled as an explicit volume buoy- circulations have important impacts on the forma- ancy source that represents the differential heating tion and transport of urban air pollution. In the over land and sea. The source function varies United States, two of the most polluted cities, horizontally as an arc tangent with the inflection Houston and Los Angeles, are located on coastlines point at the coast-line, decays exponentially with for which sea breeze circulations affect air quality. vertical distance from the ground, and varies For example, observational and modeling studies sinusoidally in time but with added stochastic noise. (Banta et al., 2005; Bao et al., 2005; Zhang et al., Free slip and thermal insulation are assumed at 2006) have found that the sea breeze circulation was the vertical domain boundaries, and zero flux is a significant contributing factor to high ozone events assumed at the horizontal boundaries. The forecast in Houston during the Texas 2000 Air Quality Study, domain size is 500 km horizontally and 3 km as polluted air was recirculated over emissions vertically. Rayleigh-damping sponge layers are sources. used beyond the sides and top of the forecast Section 2 of this manuscript describes the sea domain, to lessen the effects of the boundaries on breeze model, the chemical tracer algorithm, and the the forecast domain. The horizontal and vertical ensemble-based Kalman filter technique used. Section sponge layers are 300 and 2 km thick, respectively. 3 describes and discusses our numerical experiments. Grid spacing is 4 km horizontally and 50 m vertically. Section 4 provides conclusions and implications. Hence, the model resolves the mesoscale features of the sea breeze circulation and marginally resolves 2. Model description the nonlinear frontal structure associated with the sea breeze. 2.1. The sea breeze model 2.2. The chemical tracer model A detailed description of the sea breeze model can be found in Aksoy et al. (2005). For the purposes of To simulate tracer concentrations, the following this paper, we note that the meteorological model tracer transport equation has been coupled with the equations are two-dimensional, nonlinear, hydro- sea breeze meteorological dynamics model: static, non-rotating, and incompressible. Perturba- @A @A @A @2A tion buoyancy (b) and vorticity (Z) are the prognostic þ u þ w ¼ kA þ S, (4) @t @x @z @z2 variables, as described by the following equations: where A is the tracer concentration, kA is the @Z @Z @Z @b @2Z vertical dispersion coefficient, and S is a source þ u þ w þ ¼ k (1) @t @x @z @x Z @z2 term. The numerical solution is accomplished with and the scheme consistent with that used for meteor- ological dynamics (as described in Aksoy et al., @b @b @b @2b 2005, 2006). All spatial derivatives are discretized þ u þ w þ N2w ¼ k þ Q,(2) @t @x @z b @z2 using second order central differences. Dispersion terms are discretized in time with the trapezoidal where kZ and kb are the vertical dispersion coeffi- cients, Q is a buoyancy source term, N is the method (resulting in an overall Crank–Nicolson Brunt–Vaisala frequency, x and z are the horizontal scheme) and advection terms are discretized in time (coastline normal) and vertical domain variables, and with the leap frog method. Lagged-in-time numer- t is time. The horizontal and vertical wind speeds, u ical horizontal dispersion and an Asselin time filter and w, are diagnosed from the vorticity through the (Asselin, 1972) are used to increase the stability stream function, c, with the following definitional of the simulations. Boundary conditions for the equations: tracer concentrations are implemented to ensure no diffusive or advective flux at all boundaries. Source 2 @ c @c @c terms can include externally set grid-cell-average Z ¼ ; u ¼ ; and w ¼ .(3) @z2 @z @x tracer sources and lower boundary flux sources. ARTICLE IN PRESS A.L. Stuart et al. / Atmospheric Environment 41 (2007) 3082–3094 3085

2.3. The ensemble-based Kalman filtering method In this paper, we extend the work on ensemble- based Kalman filtering to consider a coupled The filtering method applied here is described in meteorological and chemical tracer model applica- detail in Aksoy et al. (2005) and Snyder and Zhang tion. For this work, tracer concentrations were (2003). The ensemble Kalman filter assimilation built into the observational and state vectors for equations are the following: assimilation calculations in order to investigate the use and optimization of concentration observa- x¯ a ¼ x¯ b þ Kðy0 Hx¯ bÞ, (5a) tions for improved meteorological and air quality predictions. K ¼ PbHT ðHPbHT þ RÞ1. (5b) Here, x¯ b is the mean forecast (background) state 3. Numerical experiments in chemical tracer vector, Pb is the forecast covariance matrix. x¯ a is the forecasting analysis mean state vector (after the assimilation update), y0 is the observation vector, R is the Using the coupled model, we performed three observational error matrix, H is an operator matrix numerical experiments. Through these, we investi- mapping model state to observational space, HT is gate (1) uncertainty in tracer concentration forecast its transpose, and K is the Kalman gain matrix. predictions, (2) effects of the assimilation of tracer Essentially, the assimilation updates the state vector concentration data on the prediction, and (3) use of variables using linear combinations of the observa- the ensemble-based Kalman filtering assimilation tions and the model forecast. The weighting factors system for observation targeting. in the linear combination (given by K) are deter- mined by the degree to which observational vari- 3.1. Ensemble forecasts of tracer concentrations ables covary with state variables (represented by Pb) and the error in the observations (represented by R) In order to understand the predictability of tracer versus the uncertainty in the forecast (also in Pb). concentrations and for benchmarking improve- Features of the ensemble-based method applied ments in the prediction due to data assimilation, it here include sequential processing of observational is important to understand the underlying uncer- data (Whitaker and Hamill, 2002), square root tainty in predicted tracer concentrations. To in- filtering (Whitaker and Hamill, 2002), and the use of vestigate this uncertainty in the coupled system, we covariance localization (Gaspari and Cohn, 1999; performed pure forecast simulations with a 50 Houtekamer and Mitchell, 2001) with a radius of member ensemble and no data assimilation. Simula- influence of 100 grid points. No covariance inflation tions were initialized at the maximum diurnal is used in the technique applied here. heating phase (local noon). Initial values of vorticity In ensemble-based Kalman filtering, Pb is forecast and buoyancy were varied among ensemble mem- directly through the evolution of ensemble member bers using the climatological scheme discussed perturbations. Here, initialization of the ensemble is above. Initial concentration profiles were not achieved through a ‘‘climatological’’ scheme, in varied. Model parameters were also not varied which initial values of vorticity and buoyancy for among ensemble members. The variability in model each ensemble member are statistically sampled results is therefore representative of uncertainty from a time series of data generated from a prior due to meteorological initial conditions and buoy- model run. A normal probability distribution that is ancy forcing (the stochastic uncertainty of heating). centered at the maximum diurnal heating phase The initial tracer concentration profile was assumed (local noon) and has a standard deviation of 8 h is to be a constant value throughout the domain used for the random sampling of initial states (more (3 105 kg m3). To simulate tracer emissions, an details are provided in Aksoy et al., 2005). This idealized lower boundary tracer source flux was also assimilation method has been used to study the applied. As shown in Fig. 1, the source flux varies nonlinearity of the sea breeze circulation and horizontally from 1010 to 106 kg m2 s1 with a the effects of assimilating buoyancy observations maximum at 28 km to the land side of the coastline. on meteorological state uncertainties (Aksoy et al., The source flux remained constant in time. (Tracer 2005, 2006). However, neither chemical tracer concentration and source values and shapes used dynamics nor chemical observations were repre- here were chosen to be simple representations of sented or considered. those observed for pollutants in the atmosphere.) ARTICLE IN PRESS 3086 A.L. Stuart et al. / Atmospheric Environment 41 (2007) 3082–3094

Physical model parameter values used were a mean Diurnal heating profile parameters include an wind of 0.5 m s1, Brunt–Vaisala frequency of amplitude of 7 106 ms3 and horizontal and 102 s1, and vertical eddy diffusivities of 0.75 m2 s1 vertical scales of 10 km and 500 m, respectively. for vorticity, buoyancy, and tracer concentration. Fig. 2 shows the evolution of ensemble mean winds and concentration distributions for a 36 h pure forecast. 0 and 24 h correspond to local noon and the maximum in the differential day-time heating source, 6 and 36 h (6 pm) correspond to peak temperatures over land, 9 and 33 h (9 pm) correspond to peak sea breeze winds, and 21 h (9 am) corresponds to the peak land breeze. Released tracer concentrations are largely confined to the area near the source maximum, tailing to the sea side after about 24 h. The sea-land breeze recirculation also allows concentrations to build somewhat near the surface source maximum, with advection away from the local area confined both horizontally and vertically. Fig. 3 shows the corresponding evolution of predicted uncertainty (the ensemble standard devia- tion) in tracer concentrations. We see that uncer- Fig. 1. Horizontal domain and tracer source configuration. The tainty spreads relatively quickly in the horizontal, network of seven land surface observation locations are marked by X’s. The network starts at 8 km to the land side of the with maxima migrating diurnally between the land coastline an has 40 km spacing. The solid line (and y-axis) provide and sea sides of the coast. Uncertainty is largely the tracer source flux profile. confined to the near surface, with greater vertical

Fig. 2. Evolution of predicted mean winds (arrows) and tracer concentrations (contours) for a pure forecast simulation. The domain shown is the forecast model domain (without numerical sponge layers) of 500 km (horizontal) by 3 km (vertical). ARTICLE IN PRESS A.L. Stuart et al. / Atmospheric Environment 41 (2007) 3082–3094 3087

Fig. 3. Evolution of the predicted tracer concentration uncertainties (ensemble standard deviation) for the pure forecast simulation. error growth occurring at times and locations near values of vorticity and buoyancy were not varied the peak sea breeze front. This correlation in timing among ensemble errors. (Hence, in this simulation and location with the sea breeze front is similar to the only source of error is the stochastic buoyancy that observed by Aksoy et al. (2005) for uncertainty forcing.) Comparing the long simulations with and in vorticity. The similar behavior of concentration without uncertainty in the initial meteorological uncertainty is consistent with our experimental set-up conditions, we see that at earlier times, the total in which meteorological initial conditions and for- error is dominated by initial condition error, which cing are the sources of forecast uncertainty. largely propagates out of the domain after a few Fig. 4 provides the evolution of the domain days. Nonetheless, the error due to stochastic averaged ensemble uncertainty for all prognostic buoyancy forcing grows in time. Aksoy et al. state variables (vorticity, buoyancy, and concentra- (2005) discuss the meteorological error growth tion) for this 36 h simulation. (Here, we will discuss characteristics of this representation of a chaotic the pure forecast predictions.) We see that although forced dissipative system. there are short periods of error growth, the meteorological variable errors are damped with 3.2. Assimilation of concentration observations overall time during this period. Strong error growth is apparent for the chemical prediction. However, To investigate the effect of assimilating concen- concentration errors also eventually decay overall tration observations on meteorological and tracer with time, with a maximum at about 30 h. The predictions, we performed a second experiment chemical prediction errors appear to grow during using ensemble-based Kalman filtering data assim- the transition from the peak land to peak sea breeze, ilation. A 50 member ensemble was also used here. from about 0 to 9 h and from 21 to 30 h. Results are An arbitrarily chosen 51st member was used to also shown for two longer (12 days) ensemble represent the true evolution of the state and for forecast simulations: one case with the same set-up extraction of observations. Concentration values as the 36 h run, and one case for which the initial were extracted for a network of seven land surface ARTICLE IN PRESS 3088 A.L. Stuart et al. / Atmospheric Environment 41 (2007) 3082–3094

Fig. 4. Domain averaged ensemble root mean squared errors (rmse) with respect to the truth simulation and standard deviations (stdev) in model prognostic variables. Plots (a–c) provide trends for the 36 h forecast and analysis simulations. Plots (d–f) provide trends for two long-term (12 days) forecast simulations. The gray lines are for a case with the same set-up as the 36 h case (but with slight differences due to the forcing stochasticity). The black lines are for a case with no ensemble variability in the initial conditions.

locations (see Fig. 1). These truth values were heights and slightly less horizontal spread. The stochastically perturbed to create observations, analysis mean is a significantly better representation assuming a Gaussian distribution of errors with of the truth than the pure forecast for both winds standard deviation of 1 107 kg m3. The observa- and concentrations. It captures the stronger vertical tions were assimilated into the predicted state every circulation and predicts concentrations fields that 3 h. Note that only concentration observations and are very similar to the truth. In the pure forecast no meteorological observations were used in the ensemble mean, the circulation wind speeds are analysis. Ensemble member initialization, model significantly damped, with more horizontal and less set-up, and physical parameters used in this simula- vertical concentration spread. tion were as described above for the forecast. Domain averaged ensemble uncertainty and Figs. 5 and 6 show the evolution of winds and mean error for analysis predictions of all prognostic concentration distributions for the truth and mean state variables are compared with the pure forecast analysis forecast, respectively. In the truth simula- prediction in Fig. 4(a–c). Assimilation of concentra- tion, a strong vertical circulation during the sea tion observations is clearly effective at constraining breeze portion of the diurnal cycle is present. This the meteorological errors, as well as the concentration results in advection of peak concentrations to higher errors. Hence, the filter is effective for both the ARTICLE IN PRESS A.L. Stuart et al. / Atmospheric Environment 41 (2007) 3082–3094 3089

Fig. 5. Evolution of winds and tracer concentrations for the truth simulation.

Fig. 6. Evolution of analysis mean winds and tracer concentrations. ARTICLE IN PRESS 3090 A.L. Stuart et al. / Atmospheric Environment 41 (2007) 3082–3094 observed variable (concentration) and the unob- reduces to served variables (vorticity and buoyancy). To investigate the robustness of our assimilation XM 1 XM G ¼ ðs2 s2Þ ¼ cov2 x ; x , results, several additional ensemble simulation b a i 2 2 i y0 sx þ sy cases were also performed. We investigated the i¼1 y0 0 i¼1 sensitivity of the assimilation results to the interval (7) between analyses, the radius of influence, the observational spacing, the observational error, and where M is the size of the state vector (the number the observational variables assimilated. Simulations of state variables times the number of domain grid 2 were also performed with a distinct initial vertically points), s is the variance, xi is a state vector varying concentration profile. Fig. 7 shows results variable, xy0 is the state variable corresponding to of several sensitivity cases. The error in predicted the observation (or Hx), and cov is the covariance. variables is somewhat sensitive to all the filter We refer to G as the observational impact factor. parameters, particularly at early times. However, Here, we have applied it to calculate values of the in all cases the assimilation significantly reduced impact factor for assimilation of individual tracer the uncertainty in the forecast. Sensitivity simula- concentration observations, in order to investigate tions with single observed variables other than implications for the location of optimal chemical concentration (i.e. buoyancy alone or vorticity observations. alone) indicate that concentration is a somewhat Fig. 8 shows the spatial and temporal evolution less effective observed variable than the meteoro- of the observation impact factor fields over the logical variables for improving the forecast of simulation period. Values are shown every 6 h after meteorological variables. Simulations with both the assimilation of concentration observations from concentration and a meteorological variable ob- the fixed network (and all prior network analyses). served, performed better overall than any single Maximum values indicate locations where addi- observed variable. tional observations of tracer concentration are predicted to lead to greatest improvement (over all 3.3. Observation targeting prognostic model variables) in the model prediction. The figure indicates optimal locations for observa- The ensemble-based Kalman filter provides a tions that change with time. The most valuable mechanism for optimizing the spatial and temporal observations are generally located primarily on the location of fixed observational networks and land side of the domain and closer to the surface targeted observations. Hamill and Snyder (2002) (i.e., close to the source maximum), though com- developed a method to select observation locations plicated structures are apparent. When a sea breeze based on maximizing the improvement (decrease in front is present, observations near the front appear uncertainty) in model fields that would result due to most critical, while at other times, preferred an assimilation cycle and applied it to a weather locations are more broadly distributed. The value forecasting application. In this optimization meth- of assimilating observations also changes signifi- od, the norm used for total decrease in model cantly with time, decreasing overall (see the uncertainty is the sum over all state variables of the logarithmic scale). We note that this optimization individual differences in variances, or the trace of method, represented by Eqs. (6) and (7), values the PbPa, where Pa is the post-analysis background variance of all state variables equally, regardless of error covariance matrix. PbPa can be written as the differences in magnitude between variables. To (Hamill and Snyder, 2002) investigate impacts of this valuation, we also b a b T b T 1 b calculated impact factors for each state variable P P ¼ P H ðHP H þ RÞ HP . (6) separately (not shown). Although the impact factor To investigate the potential use of Hamill and magnitudes change for each variable, the shape of Snyder’s method in the context of chemical ob- the impact factor fields (and hence predicted servational network design and air quality forecast locations of optimal observations), remains very improvement, we have applied their development similar. to our system. Using post-processing, we calculate The above impact factor was calculated after the the effect of a single observation (yo) located at a assimilation cycle using the regular network ob- model grid point. For this case, the trace of PbPa servations. Hence, it provides optimal locations for ARTICLE IN PRESS A.L. Stuart et al. / Atmospheric Environment 41 (2007) 3082–3094 3091

Fig. 7. Sensitivity of the rmse of the model prognostic variables. For observations of buoyancy and vorticity, observational errors of 1 103 and 1 104 were used, respectively. ARTICLE IN PRESS 3092 A.L. Stuart et al. / Atmospheric Environment 41 (2007) 3082–3094

Fig. 8. Observational impact factor fields at analysis times after the assimilation of concentration observations from the fixed network (and all prior network analyses).

targeted observations additional to the regular 4. Conclusions network. However, the calculation also requires information on observation values at the analysis We study the impact of ensemble-based Kalman times. For real-time forecasting, network observa- filter assimilation of chemical tracer concentration tions for a given analysis time are unavailable a observations on improving the prediction of both priori. Additionally, impact factor values are only a chemical and meteorological model variables for an function of state covariance and observational idealized sea breeze circulation. We also investigate variance (error) information, which is often avail- the potential utility of an optimization technique able before the analysis update. Fig. 9 shows impact based on the Kalman filtering equations for design factor fields at analysis times but prior to the of fixed air quality observational networks and assimilation of concentration observations from the targeted observations. By comparing the truth fixed network compared with those after assimila- simulation with ensemble forecasts, both with and tion. Substantially, similar structures are apparent without assimilation of concentration data, we find in the normalized impact factor fields both before that ensemble-based Kalman filtering assimilation and after analysis of the regular network observa- of concentrations observations effectively improved tions. This demonstrates the potential usefulness of the forecast of both the observed variable (concen- this norm for locating promising adaptive observa- tration) and the unobserved meteorological vari- tions in a predictive mode, without a priori ables. This suggests considerable potential value in information on regular network observation values using the plethora of air pollution data available or even observation locations. However, further from regulatory air quality monitoring networks for work is needed to test the success of this strategy improving skill in meteorological forecasts (even for through addition of targeted observations at the purposes unrelated to air pollution), when meteor- selected locations. ological and chemical models are routinely coupled. ARTICLE IN PRESS A.L. Stuart et al. / Atmospheric Environment 41 (2007) 3082–3094 3093

Fig. 9. Normalized observational impact factor fields before (left side of each pair) and after (right side) observation assimilation from the fixed network. Impact factor values have been normalized by dividing by the maximum value in the given field.

We also demonstrate the potential of the impact of chemical observations and suggest directions factor derived from ensemble-based Kalman filter- regarding targeted observation planning. However, ing for selection of observation locations. we must note that realistic systems affecting air With this work, we advance understanding of the quality are very complex and have many sources of use of ensemble-based Kalman filter data assimila- error (notably emissions data and model represen- tion of chemical observations with a nonlinear, two- tation) that we have not investigated here. Further dimensional model in which dynamics and chemical significant work is needed to understand the tracer transport are coupled. The context of our applicability of these results for a variety of realistic experiments is a chaotic force dissipative dynamic dynamic systems and complex coupled models. system, a sea breeze circulation. Such circulations are important for many municipalities with difficult Acknowledgments air quality problems, but there has been little work in the past on using ensemble-based data assimila- This work was supported in part by the Texas tion for improving predictions for such systems. Environmental Research Consortium Project No. We focus here on studying the effects when the H24-2003 and the Environmental Protection uncertainty in the forecast is driven by meteorolo- Agency Cooperative Agreement No. R-83037701. gical initial condition error. The results of our We would also like to acknowledge the services idealized modeling study suggest the potential value provided by Research Computing at USF. ARTICLE IN PRESS 3094 A.L. Stuart et al. / Atmospheric Environment 41 (2007) 3082–3094

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