We use a photochemical box model run over 3 days to represent a worsening period of ozone air quality during a stagnation event. Meteorological stagnation events under hot, sunlit conditions over urban areas typically lead to poor ozone air quality . We assume that the idealised mixing and transport represented in the box model are sufficient to represent the meteorology during anticyclonic conditions. For each of the different sensitivity tests that we perform we use different sets of pseudo-observations of ozone, HCHO, CO and NO2 (see Sect. 2.3 and examine Fig.  to see an example of the pseudo-observations relative to the true ozone state) in order to separately constrain the ozone precursor emissions with the 4D-variational data assimilation system. The ozone precursor emissions have known a priori errors. We then make a prediction of ozone using the a posteriori emissions. Within the model framework, days 1–2 represent the period over which observations are made and the assimilation is carried out and the final day represents the prediction and monitoring period. Within this final phase, we compare the ozone prediction, based upon the a posteriori emissions, to the ozone true state in order to assess the assimilation performance. We support this assessment using a range of statistics and diagnostics that shall be discussed shortly.

The use of 4D-variational data assimilation to solve the ozone precursor emission inversion problem is consistent with the current state of the art in prognostic air quality forecast modelling development. For example, the Community Multi Scale Air Quality modelling system (), the Sulfur Transport Eulerian Model (), and are all developing such assimilation capabilities. Thus, our model framework is relevant to and is reflective of the current and future direction of air quality forecasting.

In order to establish the utility of more complex air quality forecasting systems that might use 4D-variational data assimilation, our prototype forecasting system is demonstrated theoretically. Since the emission inversion problem that we explore only becomes more complex as the model state space increases and additional sources of uncertainty are introduced, a failure to show sufficiently reduced prediction error in this simplified setting would indicate that more complex systems are unlikely to fare better. Sufficient prediction model error within our framework is therefore a necessary but not sufficient condition for more complex 4D-variational data assimilation forecasting systems using air quality observations to be successful.

One other advantage of selecting a photochemical box model is that we are able to generate a Jacobian describing the model response to emission parameter perturbations, which can be used within an analytical modelling framework to conduct uncertainty analysis. It would be very difficult to produce a Jacobian within regional or global chemical transport models in a timely fashion given the size of the model state space. Therefore, we use an analytic model (derived from the photochemical box model) that is simplified relative to the full assimilation framework. This is a linear estimation technique based upon . To support our analyses we calculate the following diagnostics using this method: a posteriori ozone prediction error covariance, a posteriori emission parameter error covariance, the emission averaging kernel, and the associated degrees of freedom of signal.

The 4D-variational (4D-var) data assimilation and uncertainty analysis using the linear estimation are therefore complementary methods, and we use both techniques to achieve our aim of exploring the effect of observing characteristics on ozone prediction. In addition, we conduct a series of supporting analyses to test some of our assumptions.

A pseudo 1-D photochemical box model was built using the Kinetic Pre-Processor (KPP) . The model is not truly 1-D in the vertical because we use a parameterisation to describe variability in the boundary layer height and mixing volume. The Rosenbrock solver is used to integrate the KPP-generated ordinary differential equations required to calculate trace gas concentrations . The photochemical mechanism consists of 171 gas phase species and 524 chemical reactions simulating the degradation of hydrocarbons from C1 to C5 including isoprene and is based upon the Master Chemical Mechanism v3.1 (http://mcm.leeds.ac.uk/MCM/). In addition, the model includes dry deposition for all relevant chemical species, it contains a two-parameter photolysis scheme, and it simulates the emission of ozone precursors including NOx, CO, and VOCs.

Coastal urbanised southern California (SC) has historically been, and continues to be, an interesting area of study for air quality owing to the large-scale urbanisation and population, the resulting anthropogenic emissions, and the meteorological conditions during summertime that are favourable for the development of photochemical smog conditions. We therefore set up the box model to study conditions that are analogous to this region and environment. Consequently, we situate the box model at 33∘ N, run it from 30 June to 2 July, and use an atmospheric humidity equivalent to a volume mixing ratio of 0.0162. In addition, we use anthropogenic (NOx, CO, and VOCs) and biogenic (isoprene) emissions that result in a range of atmospheric mixing ratios typical for urbanised SC.

The diurnal emission variability in anthropogenic compounds is prescribed according to the National Atmospheric Emissions Inventory (NAEI) (http://www.naei.org.uk/emissions/) for an urbanised area (see Fig. ), and the isoprene emission variability is parameterised to correlate to solar zenith angle offset by 2 h to consider both temperature and photon flux effects . The isoprene emissions have an average daily emission of 1.7 × 1010 molecules m2 s-1 and an afternoon peak of 4.6 × 1010 molecules m2 s-1, which yields modelled isoprene mixing ratios less than 10 pptv (parts per trillion by volume) typical for this region. The diurnal variability in the isoprene emissions is separate and distinct to the anthropogenic VOCs. From now on, when we discuss VOCs we are referring to anthropogenic VOCs unless otherwise stated. The VOC speciation is defined according to NAEI and the total peak emission of carbon via VOCs (excluding isoprene) is 2.3 × 1012 carbon atoms m-2 s-1 and the average emission is 1.2 × 1012 carbon atoms m-2 s-1. These anthropogenic VOC emissions are typical for urbanised regions. Boundary layer dynamics are described with a prescribed variability in mixing height ranging from 500 to 1500 m and mixing between the boundary layer and free troposphere equivalent to a constant 10 % mass exchange per hour. In our model, the vertical extent represents the full depth of the boundary layer. Background free tropospheric concentrations of long-lived species are assumed to remain constant and are defined in Table .

The model is run under a range of photochemical conditions typical for urbanised SC. This is achieved by varying the NO emissions across nine different scenarios that span the full range of modelled ozone responses with respect to changing NOx concentration (i.e. from NOx- to VOC-limited conditions). We use the same emissions for the other species across all of these different NO emission scenarios. For the purposes of the emission inversion, we define our ozone precursor emissions in a simplified form (excluding emitted species not considered in the inversion) as

ϕi(t)=xiEi(t),i=NO,CO,VOC, where xi represents the time-independent emission scaling factors for the emitted species, i, and Ei(t) represents the emissions with a prescribed and repeating diurnal cycle for each emitted species. The emission inversion solves for xi, the time-independent emission scaling factors, which can be represented as a vector, x, for the emitted species, i, as shown by xi=xi,i=NO,CO,VOC. Further, we define the true state of the emission scaling factors as xt. The variability in ENO(t) is shown in Fig. , and this variability is represented by Ei(t)=eik(t), where k(t) is the temporal variability emission factor for all of the emitted species and ei is the time-independent emission for each species. Note then that all of the anthropogenic emissions (NO, CO, and VOCs – Ei(t)) share the same temporal variability. The variability in k(t) is shown in Fig.  as the “standard emission variability”. Table  shows the values of eNO, eCO, and eVOC used in our model simulations.

In the emission inversion calculations, we represent VOC emissions via ethene emissions. We selected ethene because it is a sufficiently reactive gas that is emitted in abundance through the course of anthropogenic activity. Thus, the adjoint sensitivities to ethene emissions are sufficiently high to allow the 4D-var system to find adequate solutions for the VOC emission parameter. Table  describes the set-up of the photochemical model for the range of different NO emission scenarios that we investigate and shows the values of k(t)‾, and, for each species, e and E(t)‾. Note that for E(t)‾ the overbar indicates the mean value of a variable.

The NO emission scalings shown in Table  are chosen to represent a wide range of photochemical conditions and given the VOC burden in the model, xNO emission scalings 0.5, 0.75 and 1.0 represent NOx-limited conditions, 1.25, 1.5 and 1.75 represent transitional conditions, and 2.0, 2.25, and 2.5 represent VOC-limited conditions. The mixing ratios of NOx that result from these different NO emission factors, and the mixing ratios of CO and HCHO that result from the CO and VOC emissions are all summarised in Table .

Several NOx emissions scenarios are simulated to cover a wide range of photochemical conditions (xNO = 0.5–2.5). Each emission scenario is represented mathematically as a forward model, F(x,t), which represents the concentrations as a function of time-evaluated emissions, x. Depending on the scenario, either pseudo-observations of CO, NO2, O3, or HCHO are used in various combinations (see Fig.  for a representation of the ozone pseudo-observations relative to the true state for ozone). In order to derive the pseudo-observations the model true state is sampled at 3-hourly intervals in the standard scenarios (used as default unless specified) and at intervals between 1 and 24 h in scenarios characterising the impact of observing frequency on prediction error. The sampled species concentrations are then combined with an additive-noise model to generate the pseudo-observations, y, represented by y=F(x,t)+n, where n is the noise n=F(x)‾×β×ϵ, where F(x)‾ is the average species concentration (values shown in Table ), β is the noise scaling factor, and ϵ is a random number with a normalised Gaussian distribution with a standard deviation of 1 and a mean of 0. The modelled concentrations for all species and times resulting from F(x) can be represented as a vector, q, q=F(x,t) or for specific species, z, at time t as qz(x,t), qz(x,t)=F(x,t)z, where z can be O3, NO2, CO or HCHO. We define a priori emission scaling factors, xa, with specified errors relative to xt (Table  provides a summary of the values of x used for both xt and xa), which are combined with the model to yield the a priori model state, F(xa). Note that within our framework the a priori is also the initial guess.

The assimilation is started at the first iteration with the forward model using the initial guess and is thus described as F(xa) after one iteration. A cost function, which is a scalar, J(x), is then evaluated: J(x)=12((y-F(x))TSn-1(y-F(x))+12(x-xa)TSa-1(x-xa)), where Sa is the a priori constraint matrix and Sn is the observation error covariance (where the superscript T indicates the transpose). The 4D-variational data assimilation method seeks the solution for x, x^, that minimises J(x), x^=minxJ(x), such that the gradient of the cost function with respect to x is 0 if the solution x^ is equal to the true state, xt, (though this is never fully achieved): ∇xJ=KTSn-1(y-F(x^))-Sa-1(x^-xa)=0, where K is the Jacobian matrix (see Eq. ) describing the forward-model response to perturbations to the emission parameters and ∇xJ is the adjoint sensitivity , which was calculated by the Rosenbrock solver and which indicates the sensitivity of the cost function to the emission parameters. The cost function and its adjoint sensitivities are passed to the quasi-Newton L-BFGS algorithm . The L-BFGS algorithm iteratively determines the optimal state of x, x^, that minimises the difference between the model and observations subject to the a priori constraints.

Using the estimated emissions, x^, the forward model, F(x^), provides the air quality prediction of the ozone concentration, qO3(x,t), on the afternoon of the third day of the simulation during the prediction and monitoring period. The relevance of qO3(x,t) to the prediction and monitoring period is shown in Fig. .

Figure  shows how the a priori emissions, xa, relate to the true emissions xt and the a posteriori emissions, x^, after the 4D-variational data assimilation, as well as the a priori, the true and the a posteriori ozone levels (i.e. qO3(xa,t), qO3(xt,t), and qO3(x^,t), respectively). The left panel of Fig.  shows the a priori emission error for NO emissions and the right panel shows the a posteriori NO emission error. The a posteriori emission parameter error can be defined more generally as a vector x̃.

x̃=x^-xt Figure  provides an example representation of the pseudo-observation ozone prediction, qO3(x^,t), relative to the true state, qO3(xt,t), during the prediction and monitoring period on the third day. In Fig.  D represents the a posteriori ozone prediction error at time tμ (tμ is 15:00 LT on day 3 during the prediction and monitoring period), defined by D=qO3(x^,tμ)-qO3(xt,tμ). In Fig.  G represents the a priori ozone prediction error defined by G=qO3(xa,tμ)-qO3(xt,tμ). The air quality prediction error over the entire prediction and monitoring period for each of the species, z, can be defined as a vector, q̃: q̃zj=qz(x^,tj)-qz(xt,tj),j=3,6…21,24, where j is the hour of day on the third day during the prediction and monitoring period.

We describe all of the experiments that we perform for the uncertainty analysis (Sect.  3.1) in Table . In each experiment we test a range of different observation characteristics using different parameters. To give an example, for the CN observing scenario we test the model forecast uncertainties across the nine values of xNO (i.e. 0.5–2.5 with increments of 0.25) and for eight different levels of observing error (β=0.01–5; equivalent to 1, 5, 10, 25, 50, 100, 250, and 500 % relative error). Thus, we perform 72 separate tests for this experiment and for the OCN and HCN scenarios as well. However, for the experiment comparing HCN and OCN we carry out three separate tests where we scale HCHO observation noise relative to the other species. We test three different scalings: 50 % lower, the same, and 50 % higher noise.

Section 3.2 is dedicated to sensitivity studies using the full 4D-var data assimilation forecast system. In Sect. 3.2.1 we demonstrate the ability of the 4D-var data assimilation forecast system to forecast ozone when using the three observation scenarios CN, OCN, and HCN. For these experiments we use observations made at 3 h intervals and using β=0.1.

Next, in Sect. 3.2.2, we define a range of different k(t) scenarios in order to probe the emission solution and ozone forecast sensitivity to the assumed diurnal emission variability. These alternative k(t) scenarios and the standard emission variability are shown in Fig. . In each test we perform the 4D-var data assimilation forecast using the alternative k(t) scenario while still assuming that the standard emission variability is representative of the true state. We perform this test using the OCN scenario, observing at 3 h intervals and with β=0.1.

When conducting the VOC emission inversion, we represent VOC emission uncertainties as ethene emission uncertainties (rather than a more diverse range of VOCs). In Sect. 3.2.3 we test that assumption using a sensitivity analysis by assuming VOC emission errors for ethane instead of ethene. Again, we perform this test for the OCN scenario, observing at a 3 h frequency and with β=0.1.

Our results show that the variability in ozone prediction error with both photochemical regime and observing species scenario (CN, OCN and HCN) is complex and no single observed species is ideal for all photochemical conditions.

Under NOx-limited conditions ozone prediction error is strongly controlled by the a posteriori NO emission errors, and therefore observations of NO2 and ozone would be highly advantageous. Ozone provides a particularly good constraint upon NO emissions under very NOx-limited and VOC-limited conditions. The value of NO2 observations in constraining NO emissions improves as the NOx lifetime increases under the somewhat less NOx-limited conditions (xNO=1.0–1.25). Much of the troposphere is in fact highly NOx-limited outside of the most polluted areas .

Under VOC-limited conditions ozone prediction error is sensitive to both a posteriori xNO (due to the anticorrelation of ozone to NOx) and xVOC errors, and thus observations of ozone, HCHO and NO2 allow significant improvements in ozone prediction error. Assimilating ozone, therefore, allows constraints to be placed upon VOC and NO emission uncertainties. HCHO provides an excellent constraint upon reactive VOC emissions, which due to their reactivity are more relevant to air quality compared to less reactive VOCs. NO2 provides an excellent constraint upon NO emissions under VOC-limited conditions; more than under NOx-limited conditions due to the longer NOx lifetime. Despite the fact that large geographical portions of the US are NOx-limited, a disproportionately large percentage of the population lives within or is exposed to ozone arising from VOC-limited conditions due to the significant extent of urbanisation within the US. Large urbanised areas of the south-west of the US that lack significant native vegetative biomass typically have a larger VOC-limited regime that extends over the urban as well as suburban areas. In contrast, US cities in the east are located in regions with often dense vegetative biomass, e.g. Atlanta, and thus the VOC-limited region is far more geographically limited to the urban centre itself. Therefore, improving ozone predictive skill within VOC-limited conditions will not yield forecasting improvements over a wide geographical area but will yield improvements within certain regions with large populations.

Our findings with respect to the utility of NO2 and HCHO observations for constraining NOx and VOC emissions, respectively, and in turn for improving ozone estimation are broadly consistent with the findings of , who used satellite observations of NO2 and HCHO in conjunction with 4D-variational data assimilation to solve for NO2 and HCHO emissions and to improve the model's ozone estimation. One should note, however, that our work goes further by demonstrating how the efficacy of NO2 and HCHO observations varies according to photochemical regime. Similar to , we demonstrate the use of ozone in this regard. Our work offers an extension to  by considering the photochemical regime and by considering other observations simultaneously.

Note that the statements above regarding the need to constrain NO and VOC emissions under NOx- and VOC-limited conditions, respectively, are consistent with expectations since ozone is more sensitive to both sets of emission uncertainties under the respective conditions. Further, the use of ozone to constrain either NOx or VOC emissions in either of the respective photochemical regimes is fully consistent with existing theory relating to ozone control strategies  and our understanding of factors controlling ozone on regional and continental scales . This was one motivation for us to explore this problem.

There is one further advantage to observations of ozone and HCHO made under VOC-limited conditions. Often, plumes of NOx-polluted and VOC-limited air can be exported from regions that are VOC limited into areas that are NOx limited, and this can lead to significant temporal variability in the photochemical regime in the regions surrounding an urban centre. Therefore, observations of HCHO and ozone in addition to NO2 observations could help to understand such events and in turn reduce ozone prediction errors.

We have indirectly performed a sensitivity test to see if CO observations affect ozone a posteriori prediction errors. We can address their potential impact within the OCN scenario by examining the Jacobian matrix (see Fig. ). This shows that ozone is relatively insensitive to perturbations in CO emissions and, therefore, also to a posteriori CO emission uncertainties. In fact, it appears that only the β=5.0 noise scenario has sufficiently large a posteriori CO emission error to cause significant a posteriori ozone prediction error (about 5 ppbv). The Jacobian predicts perturbations in CO associated with such emission error to be over 700 ppbv. Such large changes in CO mixing ratios can occur in reality in urban areas from the influence of wildfires. For instance, CO mixing ratios were as high as 10 ppmv during the summer of 2010 as a direct result of the rare and extreme fire events occurring in Russia that summer . Episodic perturbations of only ∼ 700 ppbv are therefore more likely to result from the more frequent and less severe wildfire events that occur within Europe on an annual basis.

We now make some broad conclusions regarding the observation uncertainties. Both the OCN and standard HCN scenarios achieve a posteriori ozone prediction errors of 2.4–6.1 and 1.9–6.3 ppbv, respectively, when absolute errors equivalent to 33 % of the average over polluted regions were used. Even though the OCN and HCN scenarios compared favourably to one another in terms of their a posteriori ozone prediction errors, when we considered more realistic observational noise on the HCHO observations, the performance of the HCN scenario was degraded to 2.2–6.9 ppbv (33 % noise level). In comparison, for the same noise level, the CN scenario achieved ozone prediction errors of 2.5–8.4 ppbv. Only when the noise level was reduced to 25 % were the OCN and HCN scenarios able to achieve ozone prediction errors of 5 ppbv or less. At 10 % noise, ozone prediction errors of less than 2.5 ppbv were consistently attained for both OCN and HCN. This strongly points towards there being a good payoff in forecast accuracy with reducing observation error. Further work in a 3-D framework would be required in order to determine how these ozone forecast errors translate into the context of real air quality forecasting. For instance, it might be possible to calculate the probability of detection or false-alarm rate statistics in a similar way to the work carried out by .

Connecting this to real instrument profiles and real observations, and how these might perform in a real assimilation system, is beyond the scope of this study. The furthest we can take this point is to note that the resulting prediction uncertainties for a particular observation noise scenario are optimistic and represent the lowest error that could be expected. This is because of reduced complexity in our model's representation of its spatial domain and its meteorology and because of the way we represented the errors in our observations, which in reality would be more complex.

Concerning the temporal sampling of observations, there is a strong sensitivity of ozone prediction error to observation removal in the daytime, particularly in the afternoon, and therefore observations made during the day present greater returns in terms of improved forecasting ability. The NOx-limited regimes favour observations made throughout the day with increased observing density close to 15:00 LT The VOC-limited regimes favour a greater concentration of observations within the afternoon even up to 18:00 LT in the most VOC-limited cases. These differing results for the two different photochemical regimes are consistent with existing knowledge about photochemistry and NOx lifetime. The main underlying factors controlling this are the changing time at which ozone peaks and the time of day that emissions occur that contribute to that peak. Under VOC-limited conditions ozone peaks later in the day due to the reduced ozone lifetime and the slower recovery of HOx radicals (suppressed by NOx) that occurs after the night-time period. The NOx-limited scenarios also show a smaller peak in the morning. This smaller peak is present due to the observations of ozone and NO2 during the morning rush hour that better allow NOx emissions to be constrained. The presence of the smaller peak also indicates that peak afternoon ozone concentrations are sensitive to the morning rush hour emissions of NOx; this is possible due to the longer ozone lifetime present under NOx-limited conditions.

We demonstrate that the ozone prediction error is sensitive to the frequency of observation. We show that ozone prediction errors vary between negligible values and up to 12.5 ppbv as the observing frequency varies between once per hour to once per day, respectively. The ozone prediction error is maximised within either the NOx-limited or VOC-limited regimes. We find very similar levels of ozone prediction error for the scenarios that observe once every hour and every 3 h (1.8–3.2 ppbv compared to 2.2–4.8 ppbv, respectively), and we also find that ozone prediction errors greater than 5 ppbv only emerge for observing scenarios using a frequency of 6 h or more. The fact that our forecasting system performs best using observations made at a frequency of 3 h or less highlights the temporal sampling advantage posed by the ground observation network relative to observing systems with lower observing frequency, i.e. a satellite in LEO configuration.

It is likely that there is an effect on ozone prediction error due to the interaction between observing frequency and observing time. Figure  implies that observing scenarios measuring at the same frequency could yield different prediction errors due to when they actually sampled during the diurnal cycle. However, in each test we made at a particular observing frequency, the observations were made at a fixed specific set of times, and so our work does not address this issue. We do think that this is relevant to evaluating different types of observing scenario, and we would therefore like to explore this problem in a future paper.

Aside from the relevance of these results to air quality forecasting and research in general, we believe these results are also relevant for emission and flux estimation via inversion methodologies. Our prototype framework is very similar to other work using 4D-variational data assimilation methodologies and chemistry transport models that have focused on emission inversion. Much of the emission inversion performance shown in this study is driven by the photochemistry, and it is reasonable to suppose that some of our results are relevant to future work conducted using 4D-variational data assimilation in emission inversion studies. Note too that Kalman filter methods can also be used in this application and we should expect that the performance of this method will be similarly affected by photochemistry. From this premise, we recommend that emission inversion studies for NOx utilise both observations of NO2 and ozone since ozone observations add information to the xNO estimation under both strongly positively and negatively NOx-limited conditions and NO2 observations constrain emission parameter uncertainties the most under the more VOC-limited conditions. Thus, these two observations are complementary to each other. Likewise, for emission inversions of VOCs, we recommend observations of HCHO and ozone since HCHO observations can constrain VOC emission uncertainties under a wide variety of photochemical conditions and ozone can constrain VOC emission uncertainties under VOC-limited conditions.

Previous studies have shown that NO2 and HCHO  observations can constrain NOx and VOC emissions, respectively. Although one could have inferred that combining ozone observations with either NO2 or HCHO observations would be beneficial, we have shown that it could be highly advantageous, which is consistent with .

It should be noted that the conclusions regarding VOC emission inversion are sensitive to our choice of representing VOC emission uncertainties with ethene. The success of the VOC emission inversion is significantly limited by solving for ethane instead of ethene emission uncertainties. This is due to the lack of impact on secondary chemical species such as HCHO. This is one reason why previous emission inversion modelling studies have focused on constraining reactive VOCs like isoprene .

Concerning CO, all of the observing scenarios (CN, OCN, and HCN) performed equally well at constraining CO emission uncertainties since all these scenarios included observations of CO. The Jacobian for CO with respect to CO emission perturbations shown in Fig.  clearly shows a strong sensitivity of CO to changes in its own emissions. On the other hand, Fig.  shows much lower sensitivity of CO to the emissions of NO or VOCs. These results are fully consistent with expectations due to the relatively low reactivity of CO and its potential to produce ozone on short timescales and of the lack of a strong chemical connection between NOx levels and resulting CO concentrations. In the latter case, there is a link due to the way that NOx can perturb OH, but due to the relative unreactivity of CO this leads to only weak sensitivity in the Jacobian. Consistent with this, there have already been several studies that use observations of CO to constrain CO emissions .

In the supporting sensitivity analysis probing emission solution sensitivity to diurnal emission variability we demonstrate that emission inversions are potentially highly sensitive to the assumed variability in the emissions and that even perfect observations would lead to such errors. In our system such emission inversion errors would be hard to characterise in the absence of any information regarding the true state of the emissions variability. We recommend that such uncertainties should be considered and characterised in emissions inversion studies. Currently diurnal emission variabilities are determined in the process of building bottom-up emission inventories. Although our prototype assimilation system can only currently solve for time-independent scaling factors, it could be modified to solve for time-dependent scaling factors and the diurnal emissions variability. Future assimilation forecasting systems should also possess this ability to solve for time-dependent emission scaling factors. Observations that adequately capture the diurnal variability in pollutants will be essential to making this leap from time-independent solutions to time-dependent solutions.

In the previous sections we have motivated the potential utility of surface or boundary layer ozone, CO, NO2, and HCHO observations either in the context of improving ozone forecasting or for emission inversions. Ground station networks that implicitly sample boundary layer air are already in place across the American and European continents. However, only one of the current generation of LEO satellite instruments (MOPITT) possesses a reliable means of attaining unique instrument sensitivity to the boundary layer for these gases . If full advantage is to be taken of future GEO stationary satellite instruments' (GEO-CAPE/TEMPO, GEMS, and Sentinel-4) simultaneous potential for excellent coverage and temporal sampling, with the aim of fully contributing to state of the art ozone air quality forecasting, then attaining sensitivity to the boundary layer is essential and should be a high-priority aim.

The heightened importance of observations made during the morning and mid- to late afternoon raises the question of whether making more targeted observations, for instance during the morning and evening rush hours, would be able to support ozone forecasting even further. There are various observing systems that would be able to provide this capability, such as several combined LEO missions or ground stations or a GEO mission with increased temporal sampling capability during those periods. Investigating these questions in the future would be of interest to us and the broader scientific community.

Our forecasting system is better able to improve the ozone prediction using observations made during the day as opposed to the night. In the context of satellites, and remembering that our idealised case ignores the effects of transport, this indicates that instruments capable of observing during the night, such as those observing in the TIR, do not offer a significant advantage over instruments restricted to making measurements during the daytime. Of course, if the effects of transported pollution were to be considered, such as the night-time mixing of ozone between the boundary layer and free troposphere, then making observations during the night could offer additional utility by improving the estimated contribution to the pollution made by this process. For instance, this could provide advance warning of the trajectory of a pollution plume. Therefore, a limitation of this work is that we are not able to explore such effects using a model with only idealised meteorology.

Our forecasting system (and the emission inversion) performs best using observations made at a frequency of 3 h or less. This highlights the temporal sampling advantage posed by satellites in a GEO configuration as opposed to those in LEO. Currently, the proposed observing frequencies for the future GEO missions  and the current ground monitoring network are at least 1 h. LEO satellites, on the other hand, cannot attain high-frequency sampling without a large number of satellites being employed . In isolation, a single LEO satellite with a sampling frequency of between 1 and 16 days is perhaps inadequate for the purpose of constraining precursor emissions on the regional scale or for supporting air quality forecasting. Another consideration is that observing frequencies of 3 h or more might not be adequate for studying the diurnal cycle of pollutants and for forecasting systems that use 3D-var, for instance, to update ozone concentrations. Note that the nature of our framework for performing these tests (i.e. a box model using only idealised meteorology) places limitations on our conclusions such that the performance of the higher-frequency observing scenarios (3 h or less) may be too optimistic. Thus, observing at 3 h may be insufficient to constrain ozone precursor emissions.