2.1.1 Step 1: sectorial total emission calculations

Total annual emissions (F_X in kg yr⁻¹) per sector and species (X=CO₂, CO, NO_x, SO₂) are calculated as a function of the economic activity and an emission factor (adapted from Raupach et al., 2007):

where A is the amount of activity (which is often given in EUR when GDP or industrial productivity is used as proxy) and E is the primary energy consumption (petajoule, PJ). R_X is the emission ratio needed to calculate emissions of co-emitted species X from the CO₂ emissions (kg kg⁻¹), which is specific for each economic sector ($R_{{\mathrm{CO}}_{\mathrm{2}}}$ is always 1, others are illustrated in Fig. 2). In this equation the term $F_{{\mathrm{CO}}_{\mathrm{2}}}/E$ is the CO₂ emission factor (EF), i.e. the amount of CO₂ emitted per amount of energy consumed. The term E∕A can be seen as a measure of energy efficiency, in which technological development plays an important role (Nakicenovic et al., 2000).

Figure 2Emission ratios of CO∕CO₂ (R_CO), NO_x∕CO₂ ($R_{{\mathrm{NO}}_x}$), and SO₂∕CO₂ ($R_{{\mathrm{SO}}_{\mathrm{2}}}$) for specific source sectors based on the Dutch Pollution Release and Transfer Register (Netherlands PRTR, 2014). Units are in parts per billion per parts per million (ppb ppm⁻¹). A value of 10 on the y axis thus implies that for each 1000 mol of CO₂ 10 mol of the auxiliary tracer is emitted.

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The information needed in Eq. (1) comes from various inventories and national information sources. For example, changes in annual activity can be approximated based on national statistics such as the GDP (gross domestic product), which can be a proxy for industrial activity. Or A can be based on environmental data such as the annual degree day sum based on the outside temperature, as proxy for the need for household heating in a particular year. These proxies for A are known globally, which is why we use Eq. (1) instead of directly using energy consumption data (E). For local studies, more specific activity data could be used, e.g. vehicle kilometres driven as a predictor for road traffic emissions. The second term in Eq. (1) (E∕A, the energy efficiency) can be estimated from activity data and energy consumption statistics, such as those available from the International Energy Agency or data from national statistics agencies. Even if E is not directly available for a country, an estimate can be made based on a country with a comparable level of development and climatology. Note that this term can show a large trend in the case of technological development. The last terms in Eq. (1) (F∕E and R_X, the emission factors) are the most uncertain ones, because the emission factor is dependent on the fuel mix and the energy efficiency, which itself can vary with environmental conditions (e.g. a cold engine on a winter day burns less efficiently). It can therefore differ significantly between countries. Emission factor values that are generally valid can be gathered from the Intergovernmental Panel on Climate Change (IPCC) or the European Environmental Agency (EEA), while country-specific values are typically less easily accessible. For our study area, we have access to both EEA data and to Netherlands-specific numbers, as well as Rijnmond-specific values (Netherlands PRTR, 2014). See Appendix A for a full overview of the data used.

2.1.2 Step 2: temporal profiles and parameterizing activity

The second step is to disaggregate the annual emissions to hourly emissions by calculating time profiles, such that Eq. (1) becomes “dynamic”:

where T_t is the hourly time factor and F is in kilograms per year (kg yr⁻¹). Averaged over a year the value of T_t is 1.0, so that it only alters the temporal evolution and not the total emissions. Energy use is often specifically linked to an activity (A in Eq. 1) and Eq. (2) on which temporal information is more readily available than on the resulting emissions. Therefore, T_t can be calculated in two ways: (1) by directly using temporally explicit activity data or (2) by parameterizing temporal variations from environmental and/or economic conditions. When activity data are available, the first option is preferable. However, in data-sparse regions the second option might be necessary to implement, which is still an improvement compared to long-term average profiles as commonly used as we will discuss next for several sectors represented in our emission model. Appendix B provides an overview of the data that are used per sector.

Non-industrial combustion is dominated by household natural gas consumption to heat houses, for cooking, and for warm water supply. A Dutch energy provider has a dataset publicly available from about 80 smart meters for the year 2013 with hourly gas consumption (Liander, 2018). It clearly shows a seasonal cycle but also more small-term variations (daily data are shown in Fig. 3). We also see higher gas consumption in the beginning of the year, when the first 3 months of 2013 had some long, cold spells.

Figure 3Daily time profiles for households (a) and glasshouses (b). Solid red lines are based on true activity data, whereas dashed black lines are parameterizations based on the degree day function.

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The use of energy for household heating is connected to the outside temperature. Previous studies have therefore used the concept of heating degree days to describe the temporal variability in emissions from households (Mues et al., 2014; Terrenoire et al., 2015). This method weighs all daily mean temperatures below a certain temperature threshold (here 18 ^∘C, as suggested by Mues et al., 2014) and assigns emissions to these days accordingly. Besides heating, gas consumption is related to warm water supply and cooking, which is largely independent of the outside temperature. Therefore, a constant offset is assumed of 20 %, similar to Mues et al. (2014). More details can be found in Appendix B.

We compared the heating degree day method using observed temperature data from the Royal Netherlands Meteorological Institute (KNMI) with gas consumption data on a daily basis (Fig. 3). The degree day function follows the gas consumption data very well, including the higher consumption at the start of the year, reaching an R² of 0.90 (N=365). The gas consumption of consumers also has a diurnal pattern with peaks in the early morning and late afternoon. Therefore, a diurnal profile can be estimated based on typical working hours, for which we used profiles from Denier van der Gon et al. (2011). For hourly data, R² is 0.80 (N=8760, not shown).

For the energy consumption of glasshouses, there is no true activity data available. Instead, we use modelled daily energy consumption for a typical Dutch glasshouse cultivating tomatoes (courtesy of Bas Knoll, TNO) as the “truth” (activity data). This time profile is calculated for typical meteorological conditions, such that the order of magnitude and the peaks are representative for an average year. There is almost no energy consumption during the summer, which indicates that there is no constant offset. So, we use the heating degree day function with no constant offset to determine the time factors. Moreover, we use a lower temperature threshold of 15 ^∘C to get a better fit with the observed energy consumption. During summer several days show a peak in the relative gas consumption, suggesting that the average temperature has dropped below the threshold. The estimated function compares well with the activity data (Fig. 3) with an R² of 0.85 (N=365). The diurnal cycle of glasshouse emissions is likely to be different from that of household emissions. Yet we lack data to establish a diurnal cycle. We therefore use the same diurnal profile as for households, although this is likely to be incorrect.

Power plants can use different fuels such as hard coal, natural gas, or biomass. In the Netherlands coal-fired and gas-fired power plants account for 80 %–85 % of the total energy production. The remainder comes mainly from wind energy (5 %–6 %) and biomass burning (5 %–6 %). Power generation data are reported by the European Network of Transmission System Operators for Electricity (ENTSO-E), which has detailed data available for the whole of Europe (Hirth et al., 2018). Coal-fired power plants are currently the main source of energy, and their electricity generation is relatively stable compared to other sources. This sector does, however, show a seasonal cycle with less energy production during the summer months. Gas-fired power plants have a larger temporal variability as they are mainly used as back-up for peak hours, depending also on the amount of renewable energy that is available.

We use the degree day function to estimate the time profiles of both coal- and gas-fired power plants. Linear regression analysis shows that the coal-fired power generation is correlated with degree days (R²=0.17). In this case we use a large constant offset of 80 % and a threshold of 25 ^∘C, which were chosen to best match the actual power generation data. The offset is much larger than for households because there is always a basic energy demand from industry. In contrast, the gas-fired power plants are (negatively) correlated with the wind speed (R²=0.13) and incoming solar radiation (R²=0.10), which may indicate a higher need for gas-fired power generation in the absence of renewable sources. Therefore, we replace the temperature in the degree day function with the multiplication of wind speed (threshold of 10 m s⁻¹) and incoming solar radiation (threshold of 150 J cm⁻²). A constant offset of 10 % is assumed.

The diurnal cycles for power plants can be based on socio-economic factors. For example, the energy demand peaks early in the morning when people get ready to go to work and at the end of the afternoon when they get home. We find this pattern in the actual power generation data, with coal-fired power plants being less variable during the day than gas-fired power plants. The fixed profile from the European MACC-III emission inventory (Denier van der Gon et al., 2011; Kuenen et al., 2014) matches reasonably well with gas-fired power plant profiles, but it is less applicable for coal-fired power plants (Fig. 4). Overall, the estimated profiles for gas-fired power plants (daily or hourly data) have an R² of 0.31 or 0.32 (N=366 or 8784) when compared to the activity data. For coal-fired power plants, this R² is 0.17 or 0.21 (N=366 or 8784).

Figure 4Daily time profiles for gas-fired (a) and coal-fired (b) power plants. Solid red lines are based on true activity data, whereas dashed black lines are parameterizations based on observed temperature (coal) and wind speed and radiation (gas). Average diurnal cycle for gas-fired (c) and coal-fired (d) power plants. Solid red lines are based on true activity data, whereas dashed black lines are fixed profiles from the MACC inventory (Denier van der Gon et al., 2011; Kuenen et al., 2014). Shading gives the 1σ variability of the diurnal cycle based on activity data.

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The constant offset of 80 % for coal-fired power plants is mainly caused by the energy demand of the industry and other semi-continuous processes. Taking into account seasonal variations in these processes could improve the timing of coal-fired power plant activities, probably increasing the power generation in winter relative to the summer holiday period. Moreover, the renewable energy supply is probably better modelled when taking into account a larger domain, since the energy supply is not just local. With a better prediction of the amount of renewables, we could improve the timing of the gas-fired power plant emissions, which mostly function as a back-up for renewable energy.

The industrial sector consists of a wide range of activities of which some are semi-continuous and only interrupted by maintenance stops, while others follow working hours. This makes it very difficult to predict the temporal variability, especially for the overall sector. Since the largest CO₂ emissions are related to refineries and heavy industry, we will focus on these activities. We find a seasonal cycle in the reported industrial activity, with a small decline during the summer and Christmas holidays. However, the variations are very small (max 1 %). Therefore, we assume constant emissions.

Road transport emissions can vary between different road and vehicle types (Mues et al., 2014), but they are also strongly dependent on environmental, socio-economic, and driving conditions (such as the amount of stops, free-flow versus stagnant conditions, and engine temperature). Traffic count data are often used to create average time profiles for road traffic emissions; although, with traffic counts we are unable to account for environmental and driving conditions. Traffic counts for the Netherlands are made available by the Nationale Databank Wegverkeersgegevens (NDW), and similar data are available in many developed countries. We differentiate between two vehicle types (passenger cars + motorcycles (hereafter referred to as cars) and light-duty + heavy-duty vehicles (hereafter referred to as HDVs)) and three road types (highway, main road, urban road). We selected all available locations for 2014 within or close to Rotterdam that distinguish three to five vehicle lengths and filtered for a minimum data coverage of 75 %. This leaves us with 25 highway, 6 main road, and 13 urban road locations. From these data, we make average time profiles (daily, weekly, and monthly) per road and vehicle type, as is often done to disaggregate road traffic emissions. Note that this method excludes any spatial variations (e.g. highways leading towards the city vs. the beach), except for differentiating between road types.

Generally, HDVs show a larger spread due to the low counts during the weekend (Fig. 5). Car counts on weekdays show morning and evening rush hours, and they go down in between. In contrast, HDV counts peak throughout the day and only go down after the evening rush hour. Moreover, the diurnal cycles are different during the weekend than on weekdays. These patterns can be explained from socio-economic factors. Current time profiles are often based on cars and are unable to correctly represent the temporal variability of HDVs. This also affects the spatial distribution of emissions; therefore, we create average diurnal, weekly, and seasonal profiles separately for cars and HDVs for different road types and considering the day of the week. The comparison of true traffic counts and averaged traffic counts results in R² values between 0.83 and 0.95 for hourly data for the whole year (N between 2665 and 6471 because of gaps in the traffic count data).

Figure 5Time profiles of passenger cars (a) and heavy-duty vehicles (b) road transport on highways for 10 randomly chosen days in March. Solid red lines are based on true activity data, whereas dashed black lines are parameterizations based on averaged traffic counts for Rotterdam.

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Shipping emissions are dependent on the type of fuel used and whether ships apply slow steaming. Additionally, during loading and unloading, ships still emit CO₂ and other pollutants, even though they are not moving. Such information is currently not available, so instead we use information about the arrival and departure of ships in the port of Rotterdam to make a time series of ship movements. Note that this only applies to large vessels that transport goods and passengers and that the time profile will look different for recreational shipping. However, large ships account for approximately 80 % of the total shipping emissions in the area of interest. Since we lack information about other types of shipping movements, we will only account for large ships in the time profiles.

We collected ship movements for 1 month (daily data) and an average diurnal profile. The diurnal cycle shows a peak throughout the day, which corresponds well with the HDV road transport emission patterns on highways. The reason for this is that HDV road transport is related to shipping movements, as HDVs take care of part of the goods transported further inland after the goods have arrived by ship. We also find a clear weekly pattern with less ship movements during the weekend, although the decrease is less than for HDV road transport. This is likely because large ships, such as entering the port of Rotterdam, continue travelling during the weekend. Therefore, the weekly pattern resembles more that of car road transport on highways. Thus, we can estimate ship movements by using the temporal profiles of HDVs and cars on highways. This method is specifically tested for Rotterdam and different patterns might be visible elsewhere. We also use HDV patterns for the seasonal variability, and final parameterized and reported activity in this method reach an R² value of 0.89 for a period of 18 d with hourly data (N=432) as shown in Fig. 6.

Figure 6Daily time profiles for shipping. Solid red line is based on true activity data, whereas dashed black line is a parameterization based on traffic counts of heavy-duty vehicles (diurnal cycle) and cars (day-to-day variations) on highways.

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2.1.3 Step 3: spatial disaggregation

National total sectorial emissions need to be distributed into spatially explicit emissions for our study domain. The spatial disaggregation of emissions has already received attention from inventory builders. Existing emission inventories can be used to describe the spatial disaggregation, if available for the region at high resolution. Therefore, no extra effort is put into the spatial disaggregation, and the spatial patterns from the Dutch Emission Registration have been adopted (Netherlands PRTR, 2014).

In absence of a high-resolution inventory, simple default proxies for the spatial distribution can be used, such as population density (e.g. Gridded Population of the World, GPW) and the presence of roads or waterways (e.g. OpenStreetMap). Generally, these proxies are also used by inventory builders but are often updated to take into account local circumstances. For example, main roads and urban roads are busiest in densely populated areas, and we can assume emissions on main and urban roads are correlated with population density. Highways are used for transport between cities; therefore, emissions take place outside densely populated areas as well. Nevertheless, highway transport is usually to and from densely populated areas, such that most emissions will take place close to cities. We can therefore relate these emissions with the population density in the area of interest (in this case Rijnmond) relative to the rest of the country, which places the same amount of the country-level emissions in our case study domain as the gridded inventory. Additionally, the location of large power plants or industrial plants is often known (for example from E-PRTR, Pollutant Release and Transfer Register), which can be used directly.

Although such information allows us to possibly construct a detailed fossil fuel model in data-sparse regions in the future, in this study we focus first on the more easily implementable and less-developed parameterization of temporal activity in different sectors (step 2) to assess whether this approach is promising enough for future extension.

2.1.4 Step 4: uncertainty analysis

The emission model we have constructed in steps 1–3 contains several parameters per source sector: activity, emission factor, spatial proxy, and time profile. For the analysis, we only consider the emission factors and time profiles, as we assume activity data and the spatial distribution to be (a) well known for our study area and (b) be mostly unobservable from the network of only seven sites which is used here to evaluate our approach (see Sect. 2.2.3). Although the spatial distribution is actually a large source of uncertainty, we aim at optimizing parameter values that are valid for the entire case study area, and for simplicity we ignore the spatially variable uncertainties. Nevertheless, it is possible to incorporate spatial uncertainties in this methodology as well, as illustrated by Super et al. (2020).

As input for step 1 in the dynamic emission model, we use generalized parameters which we take from the IPCC, EEA, and other organizations. These databases also provide an uncertainty range, which we use in a final step to create a covariance matrix. The covariance matrix describes the Gaussian uncertainty of these parameters (diagonal values) and error correlations between parameters (off-diagonal values). From the covariance matrix we create an ensemble of parameters (N=500) that represents their joint distributions, and we use them to calculate an ensemble of emissions. In this Monte Carlo simulation, we transform some Gaussian parameters into log-normal distributions to account for non-negativity or to account for distributions with a very long tail (mainly emission ratios, which can become high in specific cases where no emission reduction measures are taken). Appendix A summarizes the used parameter values and uncertainties (including the shape of the distributions) and shows an example of the covariance matrix. This method is a first step towards a better quantification of parameter uncertainties and error correlations, and additional effort has already been made to improve this method (Super et al., 2020).

In a final step, we select the most important parameters, which are either very uncertain or have a large impact on the total emissions. This leaves us with the 44 parameters that we optimize in a set of data assimilation experiments, described next. In Sect. 3.1 we report uncertainties in per cent (1σ) for normal distributions (CO₂) or as a 90 % confidence interval (CI) for log-normal distribution (co-emitted species).

2.2.1 Observation operator

The observation operator translates the 44 parameters in the emission model first into emissions (through Eqs. 1 and 2) and then into atmospheric mole fractions. The transport modelling consists of two parts. The first part, the Weather Research and Forecasting-Stochastic Time-Inverted Lagrangian Transport model (WRF-STILT; Nehrkorn et al., 2010) is used for surface emissions that are representative of large areas (i.e. not a point source). STILT is a Lagrangian particle dispersion model that describes the footprint of a single measurement by dispersing particles back in time (Gerbig et al., 2003; Lin et al., 2003). With this footprint the surface influence of emissions on a single observation can be described. An advantage of this method is that it allows for the precalculation of linear atmospheric transport, which makes this part of the observation operator less computationally demanding than running an ensemble of a full atmospheric transport model (like WRF with chemistry). The total domain covered with WRF-STILT is 77 km×88 km (Fig. 1) and includes most of the Randstad.

The second part of the transport modelling is a plume model. In a previous study we have shown that point source (stack) emissions should be modelled with a plume model to better represent the limited dimensions of the stack plume (Super et al., 2017a). Similarly, Vogel et al. (2013) have shown that the surface influence calculated by STILT can lead to large model errors for stack emissions. Therefore, we include the OPS (Operational Priority Substances, short-term version) plume model in our framework to model the transport and dispersion of stack emissions (Van Jaarsveld, 2004; Sauter et al., 2016). OPS provides hourly concentrations at predefined receptor points, which represent our measurement sites. We apply the OPS model only to point source emissions within the Rijnmond area, as we found in a previous study that a plume model only has an added value less than 10–15 km downwind from the stack (Super et al., 2017a). Point sources at more than 10–15 km from the observation site can be sufficiently represented with a Eulerian model. The OPS model input includes detailed information about the exact stack height and heat content of the plume. For more details on WRF-STILT and OPS, see Appendix C.

In addition to the fossil fuel contribution we also include background mole fractions for CO₂ and CO. NO_x and SO₂ are short-lived species; therefore, the variations in the background are relatively small compared to the fossil fuel signals. The CO₂ background is taken from the 3-D mole fractions of CarbonTracker Europe (Peters et al., 2010) and also accounts for biogenic fluxes. The resolution of these CO₂ fields is $\mathrm{1}{}^{\circ }\times \mathrm{1}{}^{\circ }$, and we select the grid box that is situated over Rotterdam. The 3-hourly data are linearly interpolated to get hourly background mole fractions that are added to the fossil fuel signals calculated by the transport models. We use the strong wintertime correlation between CO₂ and CO mole fractions (r=0.73) to calculate CO background conditions from the CO₂ background. This is not very accurate, but for the purpose of this OSSE it provides us with a decent estimate of the variability in background mole fractions.

2.2.2 State vector

We populated the state vector with a selection of the most important parameters of the emission model, based on their impact on the total emission uncertainty described in the results (Sect. 3.1). However, we hypothesize that emission model parameters that are not part of the state vector are nevertheless uncertain and may affect the results. Therefore, we include a total of 44 scaling factors in our state vector (x^b), and each scaling factor is linearly related to a parameter from the emission model. The uncertainty in these parameters (covariance matrix P) is derived from the Monte Carlo simulations described in Sect. 2.1, with the spread in the emission model parameter values provided by the same databases of the IPCC and EEA. These uncertainty values can also be found in Appendix A.

For this study, we selected an arbitrary 2-week period in January 2014 (6–20 January). Note that during the summer the importance of source sectors might be different, e.g. there will be less heating from households. Nevertheless, this period is sufficient to test the applicability of our DA system. We loop over the 14 d in our study period, resulting in one posterior state vector for each day. We initialize our state vector for every new day using the posterior values and posterior uncertainties from the previous day. Because the footprints we generated extend backwards for 6 h, the state vector for each day is effectively only constrained by the observations from that same day, and hence we did not use a Kalman-smoother approach in this work in contrast to other CTDAS applications.

Although this is a data-rich region, we use generic values for the prior emission model parameters which we take from the IPCC, EEA, and other organizations (Appendix A). These values are typically valid for a large region (e.g. Europe) and not necessarily the best estimate for our regional case study. The reason that we use these values is that they can provide a first estimate of the emissions in data-scarce regions where inverse modelling might add most to our knowledge. With this set-up we can examine how well we can constrain the true emissions starting with this generic, and widely available, information.

One major challenge in this study is to attribute the mismatch between the observed and modelled mole fractions to a specific sector, as a CO₂ observation alone provides no details on the origin of the CO₂. Therefore, we include three tracers (CO, NO_x, and SO₂) that are co-emitted with CO₂ during fossil fuel combustion in a ratio (referred to as R_CO, $R_{{\mathrm{NO}}_x}$, and $R_{{\mathrm{SO}}_{\mathrm{2}}}$) that is specific for each source sector (Fig. 2). Their (pseudo-)observations can inform us about the source of the mismatch, but through their emission ratio to CO₂ they also constrain the magnitude of CO₂ emissions in the emission model. The ratios R_CO, $R_{{\mathrm{NO}}_x}$, and $R_{{\mathrm{SO}}_{\mathrm{2}}}$ used for this conversion to CO₂ emissions is not fixed: for each of the co-emitted species we included them in the state vector. This recognizes that emission ratios are highly variable and uncertain but play an important role in source attribution.

2.2.3 Pseudo-observations

In this work we create observing system simulation experiments (OSSEs), which use pseudo-observations instead of true observations. The advantage of using pseudo-observations is that we can accurately examine the abilities of our new approach without having to account yet for (often dominant) atmospheric transport errors. This approach represents an ideal situation with relatively few sources of error compared to a study using real observations, which makes it useful to study the potential of this new system to optimize emission model parameters.

The pseudo-observations used to optimize the emission model parameters are created using the same observation operator as described above. The emission model is used to create realistic emissions with a high spatio-temporal resolution. Yet in contrast to the prior state vector, we use specific local (Dutch) values for the emission model parameters. These parameters are considered to be the truth and are therefore not scaled (scaling factors are 1.0). We found that these local parameter values are always within the uncertainty range of the general (prior) values, so that the true solution is part of the distribution explored within the prior state vector. This is confirmed in an experiment with a small model–data mismatch and no noise in the background, which reproduces the true parameters very well (not shown).

The resulting emissions are used in combination with the background mole fractions and transport calculated by WRF-STILT and the OPS model to create pseudo-observations at the locations shown in Fig. 1. For the pseudo-observations, the original background time series are used, whereas in the inversion random noise is added to the background mole fractions with a standard deviation of 2 ppm for CO₂. We assume no contribution from biogenic CO₂ to the excess CO₂ over the background, which means that any biogenic contribution to CO₂ within our footprint is the same as in the inflow from outside our domain, which is thus cancelling in the subtraction of the background CO₂. An error in biogenic fluxes is therefore attributed to the fossil fuel emissions, which represents a typical case where biogenic and fossil fuel signals are hard to distinguish from each other and from the background. Biogenic fluxes can be significant, even in urban areas, and therefore add significant uncertainty to the fossil fuel flux estimates (Fischer et al., 2017; Sargent et al., 2018).

One simulated time series is illustrated in Fig. 7. The monitoring network consists of seven sites that are scattered over the city of Rotterdam and the port. All sites exist in the national CO₂ or air quality measurement networks, although not all species used in the inversion are observed at all locations. We only use the daytime (12:00–16:00 LT, local time) observations to constrain our emissions, resulting in a total of 1960 observations. This is normally done to favour well-mixed conditions when simulated transport is more reliable, and we want to mimic this limitation. We assume all instruments have an inlet at 10m above ground level. In reality this is lower for several sites, but during the well-mixed daytime conditions the difference is minimal. Representing atmospheric transport around in-city sites can be very challenging; therefore, the use of elevated sites or a transport model that can represent transport in complex terrain in more detail is recommended when true observations are used.

The covariance matrix R describes the observation error. It accounts for errors related to instrumentation but also representativeness errors due to model transport, interpolation, and parameterization used in the emission model. Although in principle such errors can be excluded in an OSSE, we prefer to use realistic estimates of these errors to allow for the random errors that we applied to the prescribed boundary inflow, as well as to account for parameters in the emission model that are not optimized even though they contained uncertainty in the pseudo-data creation. We base the R matrix on the calculated errors in the background and atmospheric transport and variability caused by parameters that are not part of the state vector from the uncertainty analysis, and we end up with variances of 2.5 ppm (CO₂), 8 ppb (CO), 3 ppb (NO_x), and 1 ppb (SO₂).