Corresponding author: E. P. Olaguer, Houston Advanced Research Center, 4800 Research Forest Dr., The Woodlands, TX 77381, USA. (email@example.com)
 During the 2006 Second Texas Air Quality Study (TexAQS II) field study, ambient mixing ratios of formaldehyde (HCHO) up to 52 ppbv were observed at Lynchburg Ferry in the Houston Ship Channel on the morning of 27 September 2006. These elevated mixing ratios coincided with a flare event during a sequential planned shutdown of a petrochemical facility ~8 km from the monitoring site. An adjoint version of the Houston Advanced Research Center (HARC) neighborhood air quality model was used to perform 4-D variational inverse modeling of industrial emissions of HCHO and other ozone precursors based on Lynchburg Ferry observations. The simulation employed a horizontal domain size and grid resolution of 8 km × 8 km and 400 m, and was conducted for a 1.5 h period (8–9:30 A.M.) during which the highest HCHO concentrations were recorded. The event emissions of ethene and propene computed by the inverse model are consistent with the largest estimated emissions for the facility in question derived from the Solar Occultation Flux technique during TexAQS II. Moreover, the computed peak flare emissions of HCHO during the shutdown event were around 282 kg/h, which is less than but comparable in magnitude to the largest area-wide total (primary plus secondary) formaldehyde flux from the Houston Ship Channel measured by Differential Optical Absorption Spectroscopy during TexAQS II. The estimated flare event emissions of primary formaldehyde are roughly 50 times larger than HCHO emissions from flares used in routine operations, as inferred from remote sensing and/or real-time in situ measurements during the 2009 SHARP campaign.
 A controversial hypothesis explored during the 2006 Second Texas Air Quality Study (TexAQS II) and 2009 Study of Houston Atmospheric Radical Precursors (SHARP) was the possible existence of large, uncounted emissions of the radical precursor, formaldehyde (HCHO), from flares and other industrial combustion sources in the Houston region. Olaguer et al.  discussed the origin of this hypothesis, and the evidence in its favor at the time of writing, which included research-grade measurements made in the vicinity of the Houston Ship Channel during TexAQS II.
 Figure 1 presents 10 min Hantzsch florescence measurements of HCHO performed by Eom et al.  from midnight to noon on Wednesday, 27 September 2006 (toward the close of TexAQS II). The observations were conducted at Lynchburg Ferry (LF) and Haden Rd. (HRM-3), two Ship Channel monitoring stations located approximately 12 km apart (see Figure 2). Although there appears to be some correlation between the two sets of measurements, there is nonetheless a large difference in amplitude between them. In particular, there are several transient peaks in the LF observations that are not at all evident in the corresponding data at HRM-3, especially before sunrise. These peaks may indicate the contribution of primary HCHO from some industrial source near LF, as opposed to a broad plume of secondary HCHO.
Zhang et al.  used the Community Multi-scale Air Quality Model to simulate a two-week episode (28 August to 12 September 2006) in the Houston metropolitan area during TexAQS II, based on the 2005 National Emission Inventory supplemented by a special hourly point source inventory developed by the Texas Commission on Environmental Quality (TCEQ) for the summer of 2006. That model under-predicted HCHO concentrations at LF, a result which may be due to unreported industrial emissions of HCHO.
Parrish et al.  disagreed that there is any persuasive evidence in favor of primary formaldehyde. They analyzed TexAQS II air trajectories and suggested the possibility that the elevated HCHO concentrations at LF on the morning of 27 September 2006 may have been due to overnight recirculation of air from the Ship Channel to the Gulf of Mexico and back, with accompanying secondary production of formaldehyde from primary VOCs. Although this is one possible explanation for the coincidence of the LF and HRM-3 peaks around 9:30 A.M., we propose an even simpler alternative. The period from 9:00 to 10:00 A.M. is near the beginning of the work day, and is therefore a likely period for emissions from batch processes by widely separated, though formally uncoordinated industrial facilities.
Rappenglück et al.  analyzed composite diurnal variations of ambient HCHO measured during TexAQS II at LF, HRM-3, and the University of Houston Moody Tower, the last of which is an urban nonindustrial site southwest of the Ship Channel. They found that at both LF and HRM-3, HCHO concentrations typically peaked after 9:00 A.M. but before noon, with a second more intense peak occurring in the afternoon at HRM-3, but not at LF. By contrast, the Moody Tower site did not exhibit any composite peaks between 9:00 A.M. and noon, except when the wind was blowing from the Ship Channel.
 During the period in which prolonged high concentrations of HCHO were observed at LF, there was a reported flare event during a sequential planned shutdown of a major petrochemical facility approximately 8 km from the monitoring site. We identified this event using the Air Research Information Infrastructure [Olaguer et al., 2011; Buzcu-Guven and Olaguer, 2011], a Web portal for Houston air quality data available at www.airhoustontx.org. We were not able to identify any other industrial facilities within appropriate range of LF that also reported an ongoing upset, maintenance, start-up, or shutdown event that could plausibly release a large plume of formaldehyde on 27 September 2006. We will refer to the petrochemical facility of interest as PF rather than by its real name.
 The official report submitted by PF to the TCEQ described the sequential planned shutdown as lasting 18 days. During the shutdown, PF estimated emissions of 16 species from three flares that operate in tandem as an olefins flare system (OFS). Emissions of CO and NOx were also reported for a fourth flare, which we will ignore due to their much smaller magnitude. Only total event emissions were reported by PF, with variability indicated by the number of block hours (22) during which the TCEQ permit limits for the OFS were thought to have been exceeded based on monitored flows to the OFS, estimates of destruction and removal efficiency (DRE, typically 98% or 99%), and standard emission factors for products of incomplete combustion (PICs). As has been customary in regulatory settings, flare emissions of HCHO were not reported.
 A recent spate of studies has called into question traditional estimates of DRE and PICs for industrial flares [Castineira and Edgar, 2006, 2008a, 2008b; Allen and Torres, 2011; Torres et al., 2012a; Wood et al., 2012; Knighton et al., 2012]. Low flare destruction efficiencies have been observed even under some conditions when standard estimation methods would have predicted 98% or 99% DRE [Al-Fadhli et al., 2011]. Factors that may result in low values of DRE include high cross-wind speed, overuse of steam assist or aeration, and low heating values of waste gases. Moreover, formaldehyde has been definitively identified as a significant component of flare PICs, with typical HCHO-to-CO molar ratios of 4% to 8% [Wood et al., 2012; Knighton et al., 2012]. In addition, Knighton et al.  found that the maximum fraction of carbon attributable to HCHO in flare plumes occurs when DRE is about 70%.
 We hypothesize that on 27 September 2006 the PF OFS had an unrecognized emissions variability that manifested itself in elevated downwind concentrations of HCHO at the LF site, particularly as the ambient wind speed increased after 8:00 A.M. We will use inverse modeling as circumstantial evidence to estimate the likely level of emissions of HCHO and other ozone precursors from PF that would be needed to explain the observations. In addition, we will determine to what extent long-range transport may also account for the HCHO peak at LF. Finally, we will discuss our findings in the context of current industrial permitting practice, and their implications for building future emission inventories for atmospheric science applications.
2 The HARC Air Quality Model
 The HARC neighborhood air quality model that we will use for this study has been documented in three previous publications [Olaguer, 2011, 2012a, 2012b]. It is a 3-D Eulerian chemical transport model designed for horizontal domains up to about 12 km × 12 km and horizontal resolutions as fine as 100 m. The major features of the HARC model are summarized in Table 1.
Table 1. HARC Model Features
Spatial domain (this study)
8 km × 8 km horizontal
900 m vertical
Resolution (this study)
400 m horizontal
50 m vertical
30 s temporal
Piecewise Parabolic Method
Positive definite zero-flux outflow at boundaries
Uniform horizontal wind
Zero gradient (Neumann) boundary conditions
Uniform horizontal eddy diffusion coefficient
Semi-implicit (Crank-Nicholson) scheme
Zero-flux boundary condition
Vertical diffusion coefficient specified from similarity theory
47 gas-phase reactions
Parameterized clear sky photolysis rates
Chemical equilibrium assumed for HOx and other radicals
Euler Backward Iterative (EBI) scheme for NO, NO2, and O3
Noniterative backward Euler scheme for longer lived species
Deposition velocities (cm/s) specified for NO (3 × 10–9), NO2 (0.35), O3 (0.6), HONO (0.3), and HCHO (0.4)
 The HARC transport model, as applied here, includes advection by a horizontally uniform wind and separate treatments of horizontal and vertical turbulent diffusion. The horizontal diffusion coefficient is assumed to be uniform throughout the model domain. The vertical diffusion coefficient varies with height and can be specified for three stability classes (stable, unstable, and neutral) based on similarity theory. The details of the vertical diffusivity parameterization are further discussed in section 4.3.
 An adjoint version of the transport component of the HARC model was developed by Olaguer  to demonstrate a new method for performing computer-aided tomography scans using differential optical absorption spectroscopy. The method is based on inverse estimation of the horizontal turbulent diffusion coefficient and local emissions based on remote sensing measurements over multiple intersecting light paths. The forward version of the transport model with optimized turbulence and emission parameters is then used to reconstruct pollution plumes within the remotely scanned domain.
Olaguer [2012a] developed a chemical mechanism customized for near-source applications based on 47 gas-phase reactions (see Table 2). The mechanism was successfully tested against observations from the TexAQS II Radical and Aerosol Measurement Project [Lefer et al., 2010; Chen et al., 2010]. It was also compared against the SAPRC and CB05 chemical mechanisms using the U. S. Environmental Protection Agency's (USEPA) OZIPR model for scenarios involving rapid short-term ozone production from olefins. Olaguer [2012a] used the new chemical mechanism in the HARC model to assess the likely near-source ozone impacts of upstream oil and gas activities, primarily emissions from natural gas flares and large compressor engines.
Olaguer [2012b] tested the performance of the forward chemical transport model against downwind monitoring measurements for two historical emission events in the Houston Ship Channel. He found that improving the horizontal resolution in the HARC model from 1 km to 200 m resulted in narrower, more intense ozone plumes from large olefin flares, in better agreement with observations. The ozone plumes were also much more sensitive to primary formaldehyde when finer resolution was employed. The conclusions of Olaguer [2012b] mitigated the findings of Al-Fadhli et al. , who generated a relatively weak ozone response from primary HCHO in industrial flares using a regional air quality model at 1 km resolution.
3 Inverse Modeling Method
 For this investigation, we developed an adjoint of the full chemical transport model that can be used for inverse modeling of emissions based on in situ observations of chemically reactive species and the 4-D variational (4Dvar) data assimilation technique [Zou et al., 1997; Sandu et al., 2005]. The 4Dvar method minimizes a cost function J, defined as the weighted least squares distance between the 4-D spatial and temporal predictions of a forward model and observations over an assimilation window or time period.
 If C(x, t) is the vector of the concentrations of n transported species at position vector x and time t, then the forward evolution of the concentration of the ith transported species is given by the equation
where u is the wind vector, K the diffusion tensor, f the net chemical generation rate, and E the emission rate. From the tangent linear approximation to equation (1), one can derive λ, the vector of adjoint values corresponding to C, which are the Lagrange multipliers by which the constraint of the physical model is enforced. The adjoint values can also be interpreted as the sensitivity of the cost function to the forward model concentration predictions. The continuous (as opposed to the discrete) adjoint is governed by the equation
where φ is a forcing term related to the deviation of the model predictions from the observations. The term in brackets, that is the transpose of the chemical Jacobian matrix multiplied by the adjoint vector, is the chemical adjoint. The mathematical details of the chemical adjoint are provided in the online auxiliary material, which also includes a performance evaluation based on comparison of adjoint sensitivities to finite difference sensitivities computed using the forward model, as in Hakami et al.  and Henze et al. .
 The minus sign on the left hand side of equation (2) denotes backward integration in time. Let the time step be denoted by k. Moreover, let Ck be the vector of predicted concentrations at time step k, λk the corresponding adjoint vector, the vector of observed concentrations, and Rk the measurement error covariance. The adjoint condition at final time step N is given by
while for k = N − 1, … 0:
 The first term on the right hand side of equation (4) is the discrete implementation of the continuous advection, diffusion, and chemical adjoint terms in equation (2). The observational forcing terms on the right hand sides of equations ((3)) and ((4)), on the other hand, are the discrete equivalent of the term φ in the continuous adjoint, and are assumed to be zero when no observations are available.
 In this work, we make use of observations at a single monitoring site to drive the adjoint model, and because information on species gradients is lacking, we do not optimize the horizontal turbulent diffusion coefficient as did Olaguer . Moreover, we optimize the emissions of several species simultaneously by defining a single event emissions adjustment factor α, such that the emission magnitude Ei for a given set of species is a linear combination of the routine emissions εi, which are kept constant within the assimilation window, and the initial estimate for the PF event emissions denoted by Si
 In other words, we will determine the uniform factor by which the event emissions of a set of species from the PF OFS must be increased to account for the observations at LF. While it is possible to separately optimize the emissions of individual species, a more computationally efficient approach was adopted in view of the coarse temporal resolution of available measurements at LF for species other than HCHO (see section 4.5).
 The cost function to be minimized is as follows:
where the superscript b refers to the prior (or background) estimate of an optimized parameter, and Q and B are the error covariances corresponding to α (the event emissions adjustment factor) and C0 (the transported species initial conditions), respectively.
 The optimized values of the emissions adjustment factor and of the initial conditions can be obtained from the adjoint values as follows:
 An important quantity in the minimization of the cost function is its Hessian with respect to the optimized parameter P (that is, either α or C0), which we approximate by the following linearized expression, as in Olaguer :
where G is the prior estimate of the error covariance of the parameter P. The inverse of the Hessian is then the updated estimate for the error covariance.
 The inversion of the Hessian for the initial conditions is facilitated by assuming a block diagonal structure, with an upper block corresponding to all levels above the surface (where no measurements are made), and a lower block corresponding to the surface. The upper block is assumed to be purely diagonal and constant, while the lower block is a full matrix that is inverted using singular value decomposition. This technique enables us to update the error covariance of the initial conditions without enormous storage requirements or problems with ill conditioning.
 To optimize the model parameters, the forward model is run for the entire assimilation window, using the initial estimates for the parameters and their error covariances. At the end of the forward run, an adjoint final condition is computed from equation (3) and used as input to the adjoint model, which is then run backward in time. After each forward-backward iteration, the values for the parameters and their error covariances are adjusted using equations ((7)) through ((9)). Multiple iterations are performed until the cost function converges to some minimum value.
 Note that in equation (9), there appears the sensitivity of the final concentration to the optimized parameter P. As in Olaguer , this quantity is computed from adjacent iterations in which only the parameter in question is varied, while the other parameter is held constant. The parameters are alternately treated in this manner using successive iteration pairs.
4 Model Inputs
4.1 Model Domain and Resolution
 In this study, we employed a horizontal domain size of 8 km × 8 km with 400 m grid resolution. The vertical domain size and grid resolution, on the other hand, were 900 and 50 m, respectively, sufficient to resolve the midmorning boundary layer. The model time step was set at 30 s. The simulation was conducted for a 1.5 h period (8–9:30 A.M., 27 September 2006) during which the highest HCHO concentrations were recorded at LF. Figure 2 shows the location of the LF monitor site relative to the PF OFS in the model grid. The length of the assimilation window was chosen to enable the PF OFS to have sufficient influence on simulated LF ambient concentrations at prevailing wind speeds. The event emissions inferred from the inverse model should be considered time averages over this assimilation window.
 Regular emissions were assigned to industrial point sources within the model domain based on 2006 annual average emissions reported to the TCEQ. Link-based, traffic emissions of NOx, HCHO, CO and 1,3-butadiene averaged over the assimilation window were obtained from a simulation of mobile source air toxics performed by the Houston-Galveston Area Council (G. Lubertino, personal communication, 2012) for the year 2009 using the Motor Vehicle Emission Simulator, commonly referred to as the MOVES model [USEPA, 2012]. Regular point source and traffic emissions were unaltered by the inverse model, which was only applied to event emissions from the PF OFS. The flare release height, including the effect of plume rise, was set at 75 m.
 The chemical species whose event emissions were optimized include CO, HCHO, and the highly reactive olefins: ethene, propene, 1,3-butadiene, and 1- and 2-butenes. We did not include NOx in this set, as the uncertainties in industrial point source emissions of NOx are considered much less than those of VOCs [Parrish et al., 2009]. Combustion emissions of CO, on the other hand, are subject to uncertainties in combustion efficiency (CE) similar to those for DRE. We maintained a constant HCHO-to-CO molar ratio of 8% in OFS emissions, roughly consistent with observations from the 2010 TCEQ Flare Study documented by Allen and Torres  and Torres et al. [2012a], and with a lower DRE in the flare as indicated by the unusually high ambient HCHO concentrations at LF. This enforced ratio allowed us to derive an initial estimate for HCHO emissions from the OFS, despite the fact that they were unreported. The initial estimate for event emissions of CO and olefins was set equal to the reported average hourly emissions from the OFS during the entire shutdown. The initial estimates for the OFS event emissions are summarized in Table 3.
Table 3. Initial Estimates for Event Emissions
Event Emissions (kg/h)
Nitric Oxide (NO)
Nitrogen Dioxide (NO2)
Carbon Monoxide (CO)
 The meteorological inputs to the HARC model are summarized in Table 4. All meteorological input parameters were assumed to be horizontally uniform. For this study, the wind speed and direction were assumed to be vertically uniform. Although it is possible to model the turning of the wind in a baroclinic Ekman layer above a Monin-Obukhov layer, as was done by Wilson and Flesch , the assumption of vertical uniformity is a good approximation throughout most of the atmospheric boundary layer for moderate-to-strong convective instability, with vertical shear confined largely to the surface layer (for which transport effects are important only in the immediate vicinity of sources) and to an upper transition layer where geostrophic adjustment mainly takes place [Garratt and Wyngaard, 1982]. Moreover, wind profiler data from La Porte Airport near the Ship Channel showed relatively little variation of the measured wind with height through most of the boundary layer during the time period of interest.
Table 4. Model Meteorological Conditions
 Because Houston terrain is relatively flat, the effects of orography on pollutant mixing were not considered. The influence of building geometry on wind flow was likewise ignored, because this study is not primarily concerned with air quality impacts near industrial fence lines.
 Resultant horizontal wind speed and direction, surface air temperature, and relative humidity were obtained from CAMS 35, the regulatory monitoring station closest to the PF OFS and the only nearby site for which relative humidity measurements were available. Boundary layer height was specified from a database of day-specific TexAQS II meteorological measurements maintained by the Texas State Climatologist. The surface pressure was set at 1 atm, while the temperature lapse rate was assumed to be super-adiabatic and uniform at 12°C/km. No vertical wind beyond turbulent eddies was accounted for in the model. As in Olaguer [2012a, 2012b], the vertical diffusion coefficient was computed using the formula of McRae et al.  for unstable stratification, with a Monin-Obukhov length of −100 m and a friction velocity equal to 1/3 of the horizontal wind speed. The horizontal diffusion coefficient was set at 50 m2/s, a typical value used in air dispersion models [see Byun and Ching, 1999, p. 7–43].
 Table 5 compares hourly wind measurements at CAMS 35 and LF. The latter station is adjacent to water, hence more likely influenced by land-sea thermal contrasts than the former, which is inland and to the south of the model domain (see Figure 2). We therefore judged that the CAMS 35 wind data were more representative of meteorological conditions along the flare plume trajectory than the wind data from LF. Within the assimilation window, the resultant wind speed at LF is somewhat higher than at CAMS 35, while the resultant wind direction is slightly more southerly. Despite these differences, the assumption of a uniform horizontal wind in the model is altogether not an unreasonable one for the time period being simulated.
Table 5. Hourly Wind Measurements at CAMS 35 (C35) and Lynchburg Ferry (LF)
4.4 Boundary and Initial Conditions
 Chemical species boundary conditions for regional air quality models are usually adopted from coarser resolution global models. For a neighborhood scale model, it is tempting to resort to the analogous strategy of specifying boundary conditions from a regional model, preferably one with a horizontal resolution of about 4 km in the Houston Ship Channel area. However, the accuracy of regional models in the vicinity of the large industrial sources in the Ship Channel is suspect, as demonstrated by the Community Multi-scale Air Quality Model modeling study of Zhang et al. . It is therefore more reasonable to specify chemical boundary conditions for the neighborhood-scale model directly from available observations.
 As a simplification, we specify uniform inflow boundary conditions for each transported species, rather than separate boundary conditions for each edge of the model domain. Inflow boundary conditions are summarized in Table 6, and were in most cases obtained from the CAMS 35 monitoring station, including automated gas chromatograph (auto-GC) measurements of hydrocarbons. For CO, nitrous acid (HONO), HCHO, and organic nitrate (RNO3), boundary conditions were set equal to typical mixing ratios observed at Moody Tower during TexAQS II Radical and Aerosol Measurement Project for the same time of day. The adopted HCHO boundary condition is also similar to the HCHO concentration over nonindustrialized urban areas of Houston simulated by Zhang et al. . The OH reactivity of organic species not explicitly resolved by the chemical mechanism was set at 5 s–1, as in Olaguer [2012a].
Table 6. Model Boundary Conditions
Nitric Oxide (NO)
Nitrogen Dioxide (NO2)
Nitrous Acid (HONO)
Carbon Monoxide (CO)
Organic Nitrate (RNO3)
 The first estimates of initial concentrations for the assimilation window (8–9:30 A.M.) were derived from a single forward model run for the time period, 7–8:00 A.M., assuming initial conditions at 7:00 A.M. uniformly equal to the boundary conditions, and higher traffic emissions than for the assimilation window. The assimilation window initial conditions were then updated by the inverse model, along with the event emissions from the PF OFS.
4.5 Adjoint Model Inputs
 The initial estimates for the optimized parameters and their error covariances are summarized in Table 7, along with the assumed LF measurement error, which is independent of species and time.
Table 7. Initial Estimates for Adjoint Model Parameters
I is the identity matrix with dimension equal to the number of model grid cells.
Event emissions adjustment factor (α)
Concentration initial conditions ()
LF measurement root-mean-square error ()
 Time-interpolated HCHO concentrations derived from the 10 min average measurements by Eom et al.  at LF were used as input to the adjoint model. In addition, chemiluminescence, UV photometer, and auto-GC measurements of NOx, O3, and highly reactive olefins at the LF site were used to drive the adjoint model. (No CO measurements were available at this site.) Only hourly average measurements were available for species other than HCHO, so that their ambient concentrations at LF were considered uniform within two distinct time periods: 8–9:00 A.M., and 9–9:30 A.M. The LF concentration inputs to the adjoint model are summarized in Table 8.
Table 8. LF Measurements Used to Drive Adjoint Model
 Table 9 shows optimized values of the event emissions adjustment factor, α, and its error covariance derived from the inverse model for the control simulation, in which event emissions and initial conditions were optimized. Note that the inverse model attributes 500 times the amount of primary formaldehyde to the PF OFS compared to the initial estimate of the event emissions. This corresponds to optimized HCHO event emissions of 282 kg/h, roughly 50 times larger than HCHO emissions from routine flares inferred from remote sensing and/or real-time in situ measurements during the 2009 SHARP campaign [Wood et al., 2012].
Table 9. Inverse Model Results From Control Run
The factor α applies only to the chemical species CO, HCHO, ethene, propene, 1,3-butadiene, and 1- and 2-butenes.
adjustment factor (α)
 The event emissions computed by the inverse model are quite reasonable, even with a 500-fold increase over the initial estimate. If we include reported and unadjusted event emissions of 6 lb/h of non-olefin VOCs (the use of English system units here is for the sake of comparison to Texas permit data), the control simulation implies total VOC event emissions of 4291 lb/h, which is still under the TCEQ permit limit of 5105 lb/h for the OFS. The inferred event emissions of CO, on the other hand, are roughly 25 times larger than the TCEQ permit limit of 287 lb/h for the OFS. However, the combination of transience in flare operating conditions and significantly lower CE than assumed in standard permit calculations (due in part to stronger cross-winds after 8 am) could account for this possible exceedance.
 The inferred event emissions of ethene and propene in the control case are 551 kg/h and 767 kg/h respectively, compared to 2006 annual mean emissions for the entire PF of 5.2 kg/h ethene and 10.8 kg/h propene. During TexAQS II, Mellqvist et al.  performed infrared remote sensing measurements of Houston Ship Channel emissions of VOCs using the solar occultation flux (SOF) method. Their measurements for the geographic sector with emissions dominated by PF are displayed in Table 10. The total PF emissions of ethene and propene computed by the inverse model are consistent with the largest of these measurements. Moreover, the inferred event emissions of HCHO (282 kg/h) are less than but comparable in magnitude to the largest area-wide total (primary plus secondary) formaldehyde flux from the Houston Ship Channel (481 kg/h on 31 August 2006) measured by differential optical absorption spectroscopy during TexAQS II [Rivera et al., 2010].
Table 10. Ethene and Propene Emissions Obtained by Mellqvist et al.  From SOF Measurements in the Sector: 29.700°N–29.800°N, 95.154°W– 95.103°W
Start-Stop Time (LST)
30 Aug 2006
30 Aug 2006
13 Sep 2006
19 Sep 2006
19 Sep 2006
19 Sep 2006
25 Sep 2006
 Figure 3 compares the HCHO initial conditions for the assimilation window inferred by the inverse model at the surface to the final surface concentrations predicted by the forward model with optimized parameters in the control case. The inverse model predicts a build-up of HCHO concentration near the PF OFS prior to the assimilation time period, consistent with the prolonged duration of the flare emission event and the downward mixing of the elevated flare plume by atmospheric turbulence before 8:00 A.M. LST.
 Figure 4 displays initial and final HCHO mixing ratios at the surface for a second model experiment, in which the event emissions were maintained at the PF-reported values without any adjustment, but the mixing ratio boundary conditions for formaldehyde and olefins were optimized in addition to the transported species initial conditions. For this purpose, α, Q, S, and E in equations ((6)) and ((7)) were replaced by the vector of species inflow mixing ratios, its error covariance matrix (initially estimated at 10 ppb2I), unity, and the species inflow mixing ratio respectively. Note that the absence of a strong primary HCHO source in the optimized boundary condition experiment results in a relatively uniform distribution of final concentration.
 Figure 5 shows model-predicted HCHO mixing ratios at LF for both the control run and the optimized boundary condition experiment versus corresponding measurements from the Hantzsch instrument of Eom et al. . The deviation between the two model experiments is only apparent in the last 40 min of the simulation, reflecting their similar optimized initial conditions (see Figures 3a and 4a) and transport times to the receptor from either the emission source or the upwind edge of the model domain.
 Table 11 compares the inflow mixing ratios inferred from the optimized boundary condition experiment with those specified in the control case. The model preferentially increases the inflow mixing ratios of olefins roughly in the order of their ozone incremental reactivity [Carter, 1994], with ethene being the least reactive of these species (see http://www.arb.ca.gov/consprod/regs/2012/4mirtable50411.pdf). Ozone incremental reactivity is in turn correlated with secondary formaldehyde formation.
Table 11. Inflow Mixing Ratios for the Control and Optimized Boundary Condition (BC) Experiments
Mixing Ratio (ppb)
 The control run produced better HCHO performance statistics based on the LF observations than the optimized boundary condition experiment. The mean normalized bias and mean normalized error associated with the control run were 2.31% and 11.4%, respectively, whereas the corresponding values for the optimized boundary condition experiment were −6.76% and 14.01%, respectively. Moreover, inflow mixing ratios of higher olefins (>C3) considerably larger than detected by local auto-GC measurements were inferred from the optimized boundary condition experiment. For HCHO, the maximum observed mixing ratio at the HRM-3 station to the west of LF was 31.5 ppb, well below the inflow mixing ratio of 52.5 ppb computed by the inverse model without enhanced event emissions. Such high concentrations would likely be dissipated by boundary layer turbulence over large distances. This demonstrates that the LF observations are unlikely to be explained by transport of secondary HCHO from outside the model domain. Note that the simulated HCHO concentrations at LF in the control case include secondary HCHO due to local olefin emissions already comparable to the largest SOF measurements in the relevant geographical sector during TexAQS II, and at a source location that maximizes local secondary formation of HCHO arriving at the LF receptor site.
 Finally, Table 12 displays the LF mixing ratios predicted by the control run and optimized boundary condition experiment at the end of the assimilation window for the chemical species of Table 8. For comparison, Table 10 also displays corresponding measurements, mostly averages for the time period 9:00–10:00 A.M., except for HCHO, in which case the averaging time is about 10 min. While the control run does very well in predicting the final concentrations of 1,3-butadiene and 2-butene, the other species have larger mixing ratios than indicated by the measurements, although these discrepancies may not be as large as they appear when one takes into account the time averaging of observations for species other than HCHO. The use of a uniform adjustment factor for HCHO and highly reactive olefins may partly account for some of the larger discrepancies between the control run predictions and the LF observations, so that some of the emissions may have been scaled up too much compared to others. Compared to the control run, the optimized boundary condition experiment results in a much higher ozone concentration at LF as a result of the enhanced inflow of the most reactive olefins.
Table 12. Species Mixing Ratios at LF at End of Assimilation Window
Mixing Ratio (ppb)
Nitric Oxide (NO)
Nitrogen Dioxide (NO2)
 Not increasing the event emissions of NOx species over the reported values seems reasonable in light of our results. Torres et al. [2012b] analyzed NOx emissions from the 2010 TCEQ Flare Study and found that under low flow conditions, with low heating value gases, the ratio of the inferred NOx emission factor to the standard EPA AP-42 emission factor was at most 120%. The highest ratios occurred for air-assisted flares operating at high CE, while the lowest ratios (down to 10%) occurred for steam-assisted flares operating at low CE. The fact that the forward model over-predicts the ambient concentration of NOx at LF based on the reported NOx emissions from the OFS suggests that the flare CE was indeed lower than assumed in standard estimates, corroborating the higher emissions of HCHO and CO derived from the inverse model.
 The results of our numerical experiment suggest that standard permit calculations may yield inaccurate results for both the speciation and quantity of chemically reactive species released by petrochemical facilities during emission events. Such events are common occurrences in the Houston Ship Channel and other industrialized areas of the U.S. Gulf Coast. They are typically associated with process upsets or planned maintenance, start-ups and shutdowns, and are known to release hundreds, thousands, and on occasion, tens of thousands of pounds of highly reactive olefins [Webster et al., 2007; McCoy et al., 2010]. Thus, industrial point source emission inventories used in atmospheric science applications should be regarded with a healthy skepticism when interpreting ambient observations in the vicinity of large transient sources.
 Among the chemical species that must be afforded greater care in the construction of emission inventories is formaldehyde, primary emissions of which have long been ignored or underestimated. In many cases, olefin emission events are associated with large flare releases, which recent observational studies have shown to include significant emissions of formaldehyde due to incomplete combustion. Inverse modeling based on LF observations of reactive species demonstrates that unreported flare emissions of HCHO during a sequential shutdown of a major facility may have been roughly 50 times the level only recently attributed to flares used in routine operations based on measurements during the 2009 SHARP campaign.
 Although our attribution of HCHO observed at LF specifically to PF OFS emissions is based on strong circumstantial evidence, it should not be regarded as definitive, because our analysis does not rule out unreported emission events at other nearby industrial sites or substantial HCHO emissions from barges and other maritime traffic in the immediate vicinity of the LF monitoring station. However, the results of this study considerably weaken the claim that long range transport of secondary HCHO is a dominant factor compared to local emissions of primary HCHO and olefins in explaining the very high ambient concentrations of HCHO observed at LF on 27 September 2006.
 I would like to acknowledge Zachary Vernon of HARC for his help in the processing of point source and mobile emissions using Geographical Information System software. I would also like to thank Graciela Lubertino of the Houston Galveston Area Council for providing traffic emissions output from the MOVES model, and Prof. Purnendu Dasgupta of the University of Texas at Arlington for providing access to formaldehyde measurements at Lynchburg Ferry. This work was supported by the U.S. Department of the Interior, Fish and Wildlife Service, Coastal Impact Assistance Program through Harris County, Texas.