The Ensemble Kalman filter (EnKF; ) is a sequential data assimilation method in which uncertainties in the model state are represented by an ensemble of simulations, which is updated using observations. In this study, we use the Local Ensemble Transform Kalman Filter (LETKF), a localized formulation of the EnKF that updates the model state by combining the ensemble forecast with observations within a defined spatial neighborhood. The LOTOS-EUROS LETKF v3.0.7 applied here has previously been used in studies of particulate matter , NO2 , and NH3 . The formulation is described in , and the implementation used here follows . Compared with the standard Ensemble Kalman Filter, the LETKF is more computationally efficient and performs the analysis on a per-grid-cell basis using only nearby observations, which are determined using a specified spatial localization length (discussed in further detail in Sect. ).

In the present application, the LETKF uses an augmented state vector, 1X=(c,β), where c denotes the three-dimensional trace-gas concentration fields and β denotes one or more two-dimensional emission perturbation fields for the optimized species. The primary objective of the filter is to estimate β, which defines multiplicative per-grid-cell scaling factors applied to the prior emissions. The perturbed emissions are computed as 2E=max⁡0,Ebase⋅β, where Ebase is the prior emission field. This clipping ensures that the updated emissions remain non-negative and prevents non-physical emission sinks. The concentration field c is included in the augmented state because it provides the dynamical link between the emission perturbations and the observations. During the forecast step, the model propagates the concentration fields forward using emissions modified by the current β values, so that free-running simulations, or simulations in regions without recently assimilated observations, remain influenced by earlier analysis updates.

The temporal variability in the emissions is specified in the assimilation through the temporal correlation length τ (set to 3 d for NH3 based on , and 1 d for NO2), with the temporal correlation coefficient α defined as , : 3αk=e-|tk-tk-1|/τ where tk and tk-1 are successive hourly analysis times. This formulation ensures that, in the absence of new observations for an extended period, the influence of past updates diminishes and the system progressively returns toward the a priori emission state. The LETKF analysis is applied at hourly analysis times throughout the simulation period. At each analysis time tk, only the emission state corresponding to the current time step is updated; emissions from previous time steps are not retrospectively adjusted. The temporal correlation coefficient αk in Eq. () therefore does not define a multi-time assimilation window, but instead controls the persistence of emission adjustments between successive hourly analysis times.

In the main co-assimilation configuration used in this study, species-specific emission perturbation factors are optimized simultaneously for both NH3 and NO2. As a result, assimilated NO2 observations constrain the NOx emission field directly rather than allowing their signal to be attributed to NH3 emissions alone. The uncertainty in this system is represented by an ensemble of N members. In this study, N=12 was used following , who applied the same LOTOS-EUROS LETKF framework. This relatively modest ensemble size is feasible here because the analysis is strongly localized in space and the short atmospheric lifetimes of NH3 and NO2 lead to comparatively compact, local covariance structures. For the initialization of the ensemble, the emission perturbation factors are sampled from a normal distribution with a mean of 1.0 and a standard deviation of 0.5, corresponding to 50 % uncertainty around the prior emissions. The resulting emissions are then constrained through Eq. (), such that perturbation factors that would otherwise produce negative emissions instead yield zero.

The LETKF operates in two sequential steps, the forecast and the analysis. In the forecast step, the state vector ensemble Xf={x1f,x2f,…,xNf} is propagated forward in time using the model dynamics, where xif represents the ith forecast ensemble member. Each analyzed ensemble member at time tk-1 is propagated forward to tk according to : 4xif(tk)=Mk-1xia(tk-1), where the model operator Mk-1 describes the forward model simulation from tk-1 to tk, including the application of the emission perturbation factors to the prior emissions and the persistence of β between successive analysis times through the temporal correlation coefficient αk. Here, xia(tk-1) denotes the ith analyzed ensemble member at time tk-1. Once the ensemble has been propagated forward in time, the ensemble mean x‾f and forecast error covariance Pf are calculated as 5x‾f=1N∑i=1Nxif,6Pf=1N-1∑i=1Nxif-x‾fxif-x‾fT,

When new observations yobs are available, the analysis ensemble Xa is obtained by updating each ensemble member according to : 7xia=xif+PaHTR-1yobs-hxif. Here, h(xif) denotes the model-simulated equivalent of the satellite retrieval, H is the linearized observation operator, R is the observation error covariance matrix, and Pa is the analysis error covariance, which is computed from : 8Pa=PfHTR-1H+I-1Pf. The simulated satellite observations are computed following the averaging kernel formalism of and . First, the model state is interpolated to the retrieval grid using the gridding operator G: 9xr,i=Gxif. To ensure that the comparison with the satellite product is made at the same effective vertical resolution as the retrieval, the averaging kernel A is applied: 10hxif=xa+Axr,i-xa, where xa is the a priori profile used in the retrieval. In the linear approximation, the observation operator becomes: 11H=AG. The observations are assumed to satisfy 12yobs=hxtrue+v,v∼N(0,R), with R taken from the retrieval error covariance matrices of the satellite data products and represents both measurement and representativeness errors . Once the update is complete, the analyzed ensemble Xa becomes the initial condition for the next forecast step.

To ensure computational efficiency and avoid spurious correlations, the LETKF applies spatial and temporal localization in a per-grid-cell approach following . In contrast to approaches that apply covariance localization directly to the background error covariance matrix, the LETKF implementation used here applies localization in observation space by selecting and weighting nearby observations for each local analysis. As a result, the localization length in this framework should be interpreted as application-specific and is not expected to match the much larger values used in numerical weather prediction studies such as , where the analyzed variables exhibit broader synoptic-scale spatial correlations. The temporal localization was described in the previous section, and is applied using Eq. (). For the spatial localization, the simulated observations are first computed for all ensemble members, and then for the given grid cell to be analyzed, all observations (both simulated and real) within 3.5ρ distance are gathered, with ρ being the specified localization length (in units of km). The analysis is then performed using the collected observations, with the contribution of each observation to the local analysis decreasing smoothly with distance from the analyzed grid cell. In the present implementation, this distance weighting is represented using a Gaussian decay function: 13w(Δd)=exp⁡-Δd22ρ2, where Δd is the distance (in km) between the observation and the model grid point. Thus, observations closest to the analyzed grid cell have the largest influence, while the contribution of more distant observations decreases smoothly with distance. This is consistent with the localized observation-space LETKF framework described by , although the functional form shown here corresponds to the implementation used in the present study. In this study, the spatial correlation lengths are chosen to be consistent with the horizontal representativeness of the corresponding satellite retrievals and are therefore guided by the mean footprint sizes. This also reflects the relatively local emission-concentration relationships of short-lived reactive gases such as NH3 and NO2. Using a localization length much larger than the footprint would allow a single observation to influence the analysis over spatial scales that are not resolved by the measurement, potentially producing spurious long-range increments and unrealistically smooth updates. To ensure spatial consistency between the retrieval resolution and its influence in the LETKF, we use ρ=15 km for CrIS and IASI NH3 and a smaller ρ=5 km for TROPOMI NO2, reflecting the higher spatial resolution of the latter.

In this section, a short summary of the most important model inputs and configuration parameters are provided. For a more detailed description of the LOTOS-EUROS model we direct the reader to . The LETKF v3.0.7 is coupled to version 2.2.009 of the LOTOS-EUROS model. An initial long simulation covering the period of 2018–2022 was performed on a domain that covers the majority of Europe (15° W–35° E; 35–70° N) with a resolution of approximately 25km×25km, and the output from this run was utilized as boundary conditions for the assimilation run which was performed on a domain covering most of North-western Europe (2–16° E; 47–56° N) with a resolution of 7km×7km. The model is driven by meteorological fields obtained from the ECMWF short-term forecast model at a 3-hourly temporal resolution which is then interpolated to an hourly frequency within the model. The simulations were conducted using 12 vertical levels, extending from the ground to about 10 km above the earth's surface, matching the vertical layer structure of the ECMWF meteorology dataset.

The base emission dataset used in the model simulations combines the European-scale CAMS-REG-v5.1 inventory with higher-resolution national inventories for the Netherlands (Emissieregistratie; ER) and Germany (Gridding Emission Tool for ArcGIS; GRETA). This combined CAMS GRETA-ER emissions dataset was developed within the National Kennisprogramma Stikstof (NKS) funded by the Dutch Ministry of Agriculture, Fisheries, Food Security and Nature (LVVN). The base emission dataset was compiled using the corresponding inventory year where available; for years after 2019, the 2019 emission totals were used as the baseline because 2019 was the most recent year available in the harmonized CAMS-GrETa-ER emissions dataset, and these emissions were then adjusted dynamically according to meteorological conditions. As a result, year-to-year variations in the base emissions remain relatively small and primarily reflect meteorological influences rather than structural changes in activity or policy. Temporally, the emissions are distributed using hourly time factors specific to aggregated source categories. For agricultural NH3 emissions, a meteorologically dependent parameterization is applied that accounts for weather-driven shifts in fertilizer application timing, following the approach of . Emissions are also vertically distributed according to sector-specific release heights, which is particularly relevant for industrial and power-generation sources where average stack heights determine the initial plume elevation.

The model output for all major nitrogen species consists of simulated concentrations (surface, and all vertical layers) and wet and dry deposition, as well as concentrations matched at the footprints of all satellite products (i.e. IASI, CrIS, TROPOMI). To match the model with the satellite footprints, and for the ingestion of these observations in the LETKF, the CAMS Satellite Operator (CSO) is used. CSO (https://ci.tno.nl/gitlab/cams/cso, last access: 6 July 2026) is an open-access tool developed at the Netherlands Organisation for Applied Scientific Research (TNO) and implemented to facilitate fast intercomparisons between modelled and satellite concentrations. The tool consists of two entities: a pre-processor to download, select, and convert satellite observations into a common format, accompanied by post-processing tools to aggregate and visualize the data; and a source code that can be used within regional air quality modelling and assimilation systems such as LOTOS-EUROS. The CSO module is able to read the files created by the pre-processor, simulate satellite observations using model variables, and apply observational operators where applicable.

The IASI instruments onboard the MetOp-A, -B, and -C satellites are in sun-synchronous orbits, with Equator crossing times at approximately 09:30 and 21:30 LT . Although the three platforms fly in the same local-time orbit, they are phased along that orbit and therefore do not acquire measurements simultaneously over the same ground location; the temporal separation between the platforms is on the order of 45 min. The data products of IASI-A, -B, and -C span the periods October 2007–October 2021 (IASI-A), March 2013 onward (IASI-B), and September 2019 onward (IASI-C), with the latter two instruments still operational. Each of the three IASI instruments has an observational swath width exceeding 2000 km, with a pixel footprint of approximately 12 km in diameter at nadir, increasing to around ∼20km×40km at the swath edges. In this study, we utilize the most recent IASI product, the Artificial Neural Network for IASI (ANNI)v4 , which is an updated version of the earlier IASI-NNv2 and LUT products .

Similar to its predecessors, the IASI-ANNIv4 retrieval involves two steps. First, the hyperspectral range index (HRI) is calculated to characterize the NH3 signal strength in each spectrum . The second step utilizes a neural network trained on a large dataset of modeled data, which links the HRI to the NH3 total column. The primary improvement in this version is the addition of a column averaging kernel to facilitate comparisons with in-situ and model data, enabling the effects of the a-priori profile shape to be considered. Earlier ANNI NH3 products were evaluated in previous studies by , , , , including against ground-based FTIR observations from the Network for the Detection of Atmospheric Composition Change (NDACC). The validation of IASI NH3 against NDACC measurements by showed on average favorable correlations (R=0.80), with a mean low bias on the order of 35 %.

In the current study, we apply the recommended data quality filters, namely, with the pre-filter and post-filter set to 1, and only observations with a cloud_fraction <25 % are used.

The CrIS-1 instrument on the Suomi-NPP and CrIS-2 on NOAA-20 were launched in October 2011 and November 2017, respectively, with CrIS-Fast Physical Retrieval (CFPR) NH3 data products starting in May 2012 and March 2019. Both instruments are in sun-synchronous orbits, providing global coverage twice daily at around 13:30 and 01:30 local solar time, with overpasses within 45 min of each other. They offer observations with circular pixel footprints of approximately 14 km at nadir over a 2200 km wide swath. This study utilizes the CFPR NH3 product version 1.6.4 . The CFPR method involves a physical retrieval based on the optimal estimation method combined with a fast optimal spectral sampling forward model , minimizing the residual between measured and simulated spectra. The excellent signal-to-noise ratio (∼1600) of the CrIS instrument in the ammonia spectral region enables detection sensitivities of approximately 0.5 ppbv near the surface, or 3.5×1015 molec.cm-2 for total columns, under typical atmospheric conditions (∼50 % detection rate). Under highly favorable infrared remote sensing conditions (e.g. strong thermal contrast) the detection limit can improve to about 0.2 ppbv, corresponding to a ∼10 % detection rate . Since the last major validation study by , the product has undergone several iterations, including the addition of a cloud flag based on VIIRS data, non-detects, and a quality flag . The validation study by reported a good correlation between FTIR and satellite observations (R≈0.8) with a slight high bias (slope=1.02). For higher column concentrations, CrIS observations showed a small positive difference with the ground-based FTIR measurements around 25 %–50 %, while for lower concentrations, the bias increased to 2.5×1015 molec.cm-2 with a standard deviation of around 50 %–100 %. This study only includes observations with a quality_flag of ≥3, thereby excluding failed or lower-confidence retrievals, and with a cloud_flag equal to 0 (clear-sky scenes). Only daytime observations are assimilated. It should be noted that the CrIS-1 instrument suffered a failure of its mid-wave IR (MWIR) band from 26 March to 24 June 2019, leading to a data gap in this period .

The TROPOMI instrument, aboard the Sentinel-5 Precursor (S5P) polar-orbiting satellite, is a nadir-viewing spectrometer designed for atmospheric observations. It crosses the equator at approximately 13:30 LT. The instrument measures radiation across the ultraviolet, visible, and infrared spectral ranges, enabling the monitoring of atmospheric trace gases and aerosols . TROPOMI has a swath width of approximately 2600 km, and the NO2 product has a nadir spatial resolution of 7.2 km in the along-track direction and 3.6 km in the across-track direction, improving to 5.6km×3.6km after 6 August 2019 . The retrieval of NO2 columns follows a three-step process. First, the NO2 slant column density is calculated from the L1b spectra recorded by TROPOMI using a DOAS fitting algorithm. This slant column is then separated into stratospheric and tropospheric components through data assimilation using the TM5-MP model, which operates at a horizontal resolution of 1°×1° . Finally, slant column densities are converted to vertical column densities (VCD) by applying total and altitude-dependent air mass factors (AMFs). These AMFs are influenced by several factors, including NO2 vertical profiles obtained from TM5-MP, the satellite's viewing geometry, surface albedo, surface pressure, and characteristics of clouds and aerosols. Further details on the retrieval process can be found in and in the algorithm theoretical baseline document .

Routine validation of TROPOMI NO2 measurements against ground-based MAX-DOAS observations from 29 stations has revealed a mean bias of -28 %, increasing to -40 % in regions with heavy pollution . This bias largely stems from the TM5-MP vertical profiles, which inadequately resolve high-concentration hot-spots and show deviations in the profile shape, particularly near the surface . To address these discrepancies, the a-priori vertical profile can be updated using one derived from a higher-resolution air quality model, which has been shown to partially mitigate biases . This correction process employs TROPOMI averaging kernels and is described in detail in the TROPOMI NO2 Product User Manual .

In this study, we used the VCDs from the reprocessed TROPOMI NO2 version 2.4.0 dataset. To ensure data reliability, observations with a quality assurance value below 0.75 were excluded. This threshold effectively eliminates pixels with cloud radiance fractions exceeding 0.5, thereby reducing the impact of uncertain retrievals .

The Dutch National Air Quality Monitoring Network, known as the “Landelijk Meetnet Luchtkwaliteit” (LML) , is a comprehensive ground-based measurement network designed to monitor air quality across the Netherlands. Operated by Rijksinstituut voor Volksgezondheid en Milieu (RIVM), the LML network consists of a large number of monitoring stations distributed across urban, suburban, and rural areas. These stations continuously collect data on various air pollutants, including PM10, PM2.5, NO2, NH3, O3, sulfur dioxide (SO2), carbon monoxide (CO), and volatile organic compounds (VOCs).

The network provides real-time data, which is crucial for assessing the air quality in different regions and understanding the impact of pollution on public health and the environment. LML stations employ state-of-the-art sensors and analytical techniques to ensure high data accuracy and consistency, enabling authorities to monitor trends, detect exceedances of air quality standards, and develop policy interventions when necessary. NH3 measurements are made using the miniDOAS, an active instrument that utilizes the differential optical absorption spectroscopy (DOAS) measurement technique. These instruments have an NH3 detection limit of roughly 0.25 µgm-3 and an estimated precision of 0.1 µgm-3 for hourly averaged observations , however, no measurement uncertainties are provided in the dataset.

Data from the LML are publicly accessible (http://www.luchtmeetnet.nl, last access: 6 July 2026), allowing citizens, researchers, and policymakers to track air quality levels in near real-time. This transparency helps raise awareness about air pollution issues and supports efforts toward improving air quality across the country. The LML network is also integrated with broader European air quality initiatives, contributing to the wider understanding of transboundary pollution and climate change mitigation efforts. The LML NH3 measurements were previously applied to study long-term trends in the Netherlands by .

Ten LML sites were selected in total for the comparisons with the model simulations, and the coordinates, details, and species measured for each of these sites are provided in Table . The locations of the sites within the Netherlands are shown on a map in Fig. . Six of the chosen LML sites provide hourly NH3 surface concentration measurements; De Zilk-Vogelaarsdreef, Valthermond-Noorderdiep, Vredepeel-Vredeweg, Wekerom-Riemterdijk, Wieringerwerf-Medeblikkerweg, and Zegveld-Oude Meije. These sites were selected because they provided hourly NH3 measurements over a long period (>1 year). In addition to the NH3 measurements, wet deposition measurements of dissolved ammonium (NH4+) concentrations in precipitation are made periodically (i.e. at irregular intervals) at Biest Houtakker-Biestsestraat, De Bilt-Wilheminalaan, Philippine-Stelleweg, Speuld-Garderenseweg, Valthermond-Noorderdiep, Vredepeel-Vredeweg, and Wieringerwerf-Medemblikkerweg. Wet deposition is also measured at the De Zilk-Vogelaarsdreef site, which serves as a European Monitoring and Evaluation Programme (EMEP) location where dissolved ammonium is monitored on a daily basis. The observed NH4+ measurements were paired with the model output and converted to monthly mean fluxes using the corresponding measured and modeled precipitation amounts. The modeled and observed precipitation agreed well on average, though some transient mismatches occurred. To minimize the influence of transient precipitation mismatches on the wet-deposition comparison, a relatively strict filter was applied: cases where the mean absolute deviation of the measured and modeled precipitation differed by more than 1σ were excluded, as were measurements with very low precipitation (<0.1 mm). Sensitivity tests with looser thresholds (2σ and 3σ) led to poorer agreement and increased spread in the deposition comparison, so the 1σ filter was adopted for the final wet-deposition evaluation.

The NH3 measurement sites occasionally experience local-scale enhancement events (i.e. nearby manure dumping events), which are not spatially representative of the model resolution. For 2020 onward, official flags are provided in the LML dataset to enable the filtering of such events, but for the years prior to this no such information is available. As a result, additional filtering was manually applied, and any hourly NH3 observations with concentrations exceeding 100 µgm-3 are removed and excluded from the comparisons.

The “Measuring Ammonia in Nature” (MAN) network was established in 2005 to monitor atmospheric ammonia concentrations in nature reserve areas across the Netherlands, with a particular focus on nitrogen-sensitive Natura 2000 areas . The network provides essential data for assessing national ammonia concentration trends, validating air quality models, and analyzing regional variability.

The network employs commercial Gradko passive ammonia samplers, which are cost-effective, easy to deploy, and well-suited for large-scale monitoring . These samplers are calibrated monthly using active ammonia sampling devices within the LML network . Local volunteers, often conservation wardens, handle the monthly exchange of samplers, ensuring consistent data collection across diverse habitats.

Currently, the MAN network includes over 300 sampling sites across the Netherlands. The ammonia concentration data gathered by the network facilitates the identification of spatial concentration patterns and regional anomalies throughout the country. Note that in comparison to LML, the MAN samplers are typically placed in nature areas and away from source regions.

The MAN network's data plays a critical role in assessing the effectiveness of environmental policies aimed at reducing nitrogen emissions and in analyzing long-term trends in nitrogen deposition. The network can detect annual trends as low as 3 % over extended time series, making it a valuable tool for air quality management and biodiversity conservation in nitrogen-sensitive areas .

To reduce meteorological influences on the passive samplers, the MAN network is calibrated against high-performance reference instruments for NH3 at six locations in the Netherlands (see ). The calibration process is detailed in . The uncertainty in the MAN measurements consists of two components: the measurement uncertainty and the calibration uncertainty. The random uncertainty is approximately 0.9 µgm-3 for a single monthly value and 0.32 µgm-3 for annual averages. The systematic uncertainty is estimated at 28 % for monthly values and 10 % for annual averages .

For comparison with the LETKF simulations, all available MAN data from the period 2018–2022 was used, comprising a total of 309 standard sites, and 6 additional MAN calibration sensors located at LML measurement sites. While not all sites provide uninterrupted time series over the full period, the large number of sites and monthly measurements ensures statistically robust results.

To accurately assess the impact of the assimilation of the satellite observations, and to evaluate whether the optimized concentration fields represent more realistic estimates of the true spatio-temporal distribution of NH3, it is important to compare the results against an independent dataset. The surface concentrations from the base and optimized model runs were compared against ground-based surface observations from six sites in the LML network that were described in Sect. . These sites were selected because they provide hourly NH3 surface concentration measurements and have significant time-series (i.e. >1 year) of data. As the primary focus of this study is NH3, detailed discussion of the corresponding NO2 assimilation results is beyond the scope of the present study. These results will be presented separately in a forthcoming paper to allow for a more comprehensive treatment.

A correlation plot of the monthly temporal comparison is shown in Fig. , and a corresponding plot of the spatial means (i.e. all sites averaged for a given month) is provided in Fig. . These two summary views are shown separately to distinguish temporal agreement at individual sites from agreement in the spatial pattern across the Dutch monitoring network. They provide compact statistical summaries, while complementary temporal and spatial context is given by the diurnal-cycle analysis and the mapped concentration fields shown elsewhere in the manuscript. All linear regressions were performed using an ordinary least squares fitting approach. Uncertainty estimates are reported for the statistical quantities shown in the model–observation scatter-plot comparisons. Unless otherwise stated, uncertainties correspond to one standard error. For the mean bias, μ, the uncertainty was estimated as sd/N, where sd is the sample standard deviation of the model–observation differences and N is the number of paired data points. For the standard deviation of the differences, σ, the standard error was approximated as σ/2(N-1), assuming normally distributed differences. For the Pearson correlation coefficient, R, uncertainties were estimated using the Fisher transformation, with standard error 1/N-3 in Fisher-z space and then transformed back to correlation space. Uncertainties in linear regression slopes were estimated from the ordinary least-squares covariance matrix. These uncertainty estimates assume independent paired samples and should therefore be interpreted as approximate, particularly for comparisons involving repeated monthly values across sites. For changes between the base and optimized simulations, statistical robustness was assessed using paired bootstrap resampling of the matched observation, base-model, and optimized-model triplets; changes were considered statistically significant when the 95 % bootstrap confidence interval did not include zero. The main surface NH3 comparison statistics are summarized in Table , while the full surface-concentration uncertainty estimates and bootstrap confidence intervals are provided in Appendix Tables  and . Corresponding uncertainty estimates and bootstrap confidence intervals for the wet deposition comparisons are provided in Appendix Tables  and . Uncertainty estimates for the 2020 satellite-subset sensitivity experiments are provided in Appendix Table .

Not all LML sites provided data for all months, leading to a total of 346 data points compared with the expected 360 in Fig. . For the LML temporal comparison, the assimilation produces a statistically robust reduction in mean bias and a significant improvement in the regression slope, while the already high temporal correlation remains statistically similar before and after assimilation. The bias decreases from -1.97±0.21 to -0.97±0.21 µgm-3, and paired bootstrap resampling indicates that this change is significant at the 95 % level (Δμ=+0.99 µgm-3, 95 %CI: +0.74–+1.25 µgm-3). The regression slope increases from 0.790±0.028 to 0.909±0.031, also representing a statistically significant improvement (Δslope=+0.118, 95 %CI: +0.062–+0.173). In contrast, the change in correlation from R=0.836 [0.801, 0.865] to R=0.846 [0.813, 0.874] is not statistically significant (ΔR=+0.015, 95 %CI: -0.012–+0.040). For the monthly spatial means shown in Fig. , the assimilation again produces a statistically significant reduction in mean bias, from -2.04±0.36 to -1.05±0.31 µgm-3 (Δμ=+0.99 µgm-3, 95 %CI: +0.54–+1.44 µgm-3). The Pearson correlation and regression slope also increase, from R=0.765 [0.635, 0.853] to R=0.837 [0.740, 0.900] and from 0.787±0.087 to 0.895±0.077, respectively. However, paired bootstrap confidence intervals for these changes include zero (ΔR=+0.071, 95 %CI: -0.002–+0.146; Δslope=+0.110, 95 %CI: -0.028–+0.236), so these increases should be interpreted as suggestive rather than statistically significant at the 95 % level. The LML comparison therefore indicates that the most robust improvement is the reduction of systematic underestimation, with additional but weaker evidence for improved spatial agreement.

A Taylor diagram illustrating the measurement-model comparisons for the base and optimized simulations at each individual LML site is shown in Fig. . In general, the correlations between the measured and modeled surface NH3 concentrations are higher for the optimized run at all LML sites except Wekerom-Riemterdijk, with the clearest increases seen at Zegveld Oude-Meije and Valthermond-Noorderdiep. The correlation shows a small improvement at Vredepeel-Vredeweg and this was accompanied by a substantial reduction in the bias from -3.10 to 0.20 µgm-3, but a large increase in the relative standard deviation is also seen that is driven by an apparent larger number of short-term enhancement events being captured in the modeled time-series in the optimized simulation (shown in Appendix Fig. ). The mean over all sites displays a small improvement in the correlation, but also a small increase in the standard deviation (also shown earlier in Fig. ).

Since the LML data are provided at an hourly frequency, the impact of assimilation on the diurnal cycles of NH3 in the model can also be investigated at each site. The mean diurnal cycles from the observations, the base model simulation, and the optimized simulation calculated over the 2018–2022 period are shown in Fig. . The box-and-whisker representation is used to show not only the central tendency of the diurnal cycle, but also the spread of the hourly concentration distributions at each site. In most cases, the mean differences in the diurnal cycles showed improvement relative to the observations in the optimized run in comparison to the base simulation even though only morning and afternoon satellite overpasses were used. This is partly because the effect of the assimilation persists between overpass times through the forecast step and temporal persistence of the emission adjustments, allowing the updated state to influence concentrations beyond the observation times themselves. From Fig.  it can be seen that in the base simulation, the diurnal cycles are in many cases largely underestimated relative to the surface observations, however after the assimilation of the satellite observations a much closer agreement between the measurements and the model is found. At Wekerom-Riemterdijk and Wieringerwerf-Medemblikkerweg the mean differences increased from -2.03 to -2.70 and -2.83 to -2.92 µgm-3, respectively. At all other LML sites a decrease in the mean difference of the diurnal cycles was observed in the optimized run relative to the base run. The correlations in the mean diurnal cycles remain largely the same, with the exception of Wieringerwerf-Medemblikkerweg where a moderate improvement from R=0.72 to R=0.77 is found. However, the diurnal cycle at Wieringerwerf-Medemblikkerweg appears to be substantially underestimated in both the base model and the optimized simulation. These underestimations are likely related to local-scale NH3 enhancements from the nearby farmlands in the Wieringermeer polder being poorly captured by the model, coupled with complex local meteorological conditions due to the proximity of the site to the IJselmeer and the North Sea which is roughly 15–20 km away.

Although the assimilation of satellite observations improves the representation of NH3 diurnal cycles relative to measurements at several LML sites, particularly with respect to systematic biases, it does not fully reproduce the observed variability. A fundamental limitation of Kalman filter–based approaches is that, although emissions are adjusted, there can be a temporal lag associated with the transport of concentrations from source regions to the measurement locations, which is strongly modulated by local meteorological conditions. Furthermore, when the underlying diurnal cycle in the model is misrepresented, assimilation at only two main satellite overpass times may be insufficient to correct these deficiencies. An additional challenge is that NH3 emissions originate from diverse sources such as livestock housing, manure application, and industry, each with distinct diurnal patterns, whereas the present assimilation setup applies a single total emission adjustment per species and grid cell, without distinguishing among source types that may have different underlying diurnal emission profiles. Overall, at sites located in regions of intensive agricultural activity such as Valthermond, Vredepeel, and Zegveld where midday enhancements are more likely to be captured by satellite observations, the influence of the assimilation on the diurnal cycles is more pronounced.

While these comparisons demonstrate clear improvements after assimilation, several further limitations should be acknowledged. First, the six LML sites provide only sparse coverage of the Netherlands and may not fully represent the strong spatial heterogeneity of NH3 concentrations across the entire country, particularly in regions with intensive agricultural emissions. Second, the model–observation comparison involves a scale mismatch: the LML instruments measure point concentrations, while the LOTOS-EUROS model output represents grid-cell averages at 7km×7km resolution, which can potentially introduce representativity errors. In addition, the ground-based measurements themselves are not perfect and subject to calibration uncertainties and potential interferences. Lastly, because the statistics are based on monthly averages, the analysis does not explicitly resolve short-term (daily to synoptic) variability. Consequently, part of the observed agreement may reflect the influence of meteorological variability in addition to the direct effects of the assimilation. Taken together, the LML comparisons suggest that the assimilation generally improves the agreement of the model with independent ground-based observations, particularly through a robust reduction in systematic underestimation, with weaker but positive evidence for improved spatial agreement. At the same time, the analysis also underlines the limitations of both the observational dataset and the comparison methodology, which should be taken into account when interpreting the results.

To investigate the impact of the co-assimilation and the choice of satellites on the final optimized model state, assimilation runs were repeated for the year of 2020 using subsets of the satellite data products. These runs were: IASI only, CrIS only, and CrIS and IASI (without TROPOMI NO2), and the comparisons against the hourly LML NH3 observations were then repeated.

The temporal means for each of the four assimilation runs vs. the LML observations are shown in Fig. . From Fig. , it can be seen that relative to the other assimilation runs, the assimilation performed using IASI, CrIS and TROPOMI yields the lowest overall bias (0.1 µgm-3) relative to the LML observations while maintaining a relatively strong correlation of R=0.88. The simulation performed with IASI and CrIS without the assimilation of TROPOMI NO2 yields a higher correlation of R=0.90, but displays a higher bias of 0.7 µgm-3, a higher standard deviation, and a poorer regression slope. The simulations using only CrIS and only IASI display relatively higher mean biases of 1.4 and -1.1 µgm-3, respectively. For comparison purposes, the temporal mean comparison for the base (unoptimized) simulation for 2020 is shown in the Appendix in panel a of Fig. . Each of the simulations performed with assimilation show an improvement over the unoptimized base model run, which displays a correlation of R=0.82 and a mean bias of -1.9 µgm-3 relative to the LML observations.

A similar plot of the spatial means for each of the assimilation runs vs. the LML surface observations is provided in Fig. . It can be seen that again from Fig. a, the assimilation performed using IASI, CrIS, and TROPOMI leads to the lowest overall bias (0.1 µgm-3) of the four simulations and a relatively strong correlation of R=0.90. In comparison, the assimilation run using IASI and CrIS observations but not TROPOMI has a slightly higher correlation (R=0.93), but a higher bias of 0.7 µgm-3 and a poorer slope of regression (1.163 vs. 0.977 from the IASI, CrIS and TROPOMI assimilation). The assimilation runs performed using CrIS only and IASI only (shown in panels c and d of Fig. , respectively) have the same or poorer correlations than the IASI, CrIS and TROPOMI run, and relatively larger biases of 1.4 and -1.1 µgm-3 for the CrIS-only and IASI-only runs, respectively. As was the case for the temporal mean comparisons, each of the optimized runs shows better agreement with the observations than the unoptimized simulation (panel b of Fig. ), which had a weaker correlation of R=0.66 and a mean bias of -1.9 µgm-3 for 2020. Uncertainty estimates for the statistics reported in Figs. and , together with the corresponding 2020 base-model comparison in Appendix Fig. , are provided in Appendix Table . Because these experiments are intended as a sensitivity analysis rather than a formal pairwise model-selection test, we report uncertainty estimates for each run but do not assess all pairwise differences between satellite configurations.

These comparisons highlight that the choice of satellite datasets used for assimilation is impactful, and that using just IASI or CrIS for the optimization may lead to greater biases than using a combined assimilation approach. Although assimilating a combination of CrIS and IASI observations leads to an improvement over just a single subset of the satellite data, the inclusion of TROPOMI NO2 in the optimization aids in reducing the overall biases while still maintaining a strong correlation, particularly in comparison to the un-optimized LOTOS-EUROS simulation. The added value of assimilating NO2 is that it helps to constrain the availability of HNO3 through the NO2–OH oxidation pathway, which in turn directly regulates the partitioning of NH3 into ammonium nitrate, an important sink of NH3 . In this way, the NO2 observations provide an indirect but important constraint on the fate of NH3, thereby improving the consistency of the coupled reactive nitrogen system in the model. Overall, the subset experiments indicate that the multi-satellite configuration including IASI, CrIS, and TROPOMI provides the best balance between low bias, strong correlation, and physically consistent reactive-nitrogen constraints, although the sensitivity experiments are not treated here as a formal pairwise model-selection test.

To evaluate the impact of the assimilation on the deposition of NHx within the Netherlands, comparisons were performed against dissolved NH4+ concentrations measured in precipitation. These measurements are made at irregular intervals at several LML sites, and for the comparisons, these observations were paired with the modeled deposition interpolated to a daily frequency and converted to wet deposition fluxes (in kgNha-1yr-1) using the measured precipitation amounts.

Figure  shows the comparison of the measured and modeled monthly temporal means of NH4+ wet deposition flux before and after assimilation. The baseline simulation displays a moderate correlation with the observations, increasing from R=0.510 [0.410, 0.598] to R=0.560 [0.466, 0.641] after assimilation. Paired bootstrap resampling indicates that this increase is statistically significant, although modest in magnitude (ΔR=+0.044, 95 %CI: +0.019–+0.071). The mean bias is reduced from -1.00±0.28 to -0.80±0.25 kgNha-1yr-1, and this reduction is also statistically significant (Δμ=+0.21 kgNha-1yr-1, 95 %CI: +0.07–+0.34 kgNha-1yr-1). The spread of the model–observation differences decreases significantly from 4.40±0.20 to 3.90±0.18 kgNha-1yr-1 (Δσ=-0.51 kgNha-1yr-1, 95 %CI: -0.81–-0.21 kgNha-1yr-1). The regression slope remains statistically similar before and after assimilation (Δslope=-0.009, 95 %CI: -0.068–+0.046). The scatter plot also shows a particularly large overestimation in the modeled deposition flux for several LML sites in the spring months of 2018 and 2020, which is reduced after assimilation, while there is a general underestimation during much of the remainder of the year. A similar pattern of springtime overestimation and late-year underestimation was found in the wet deposition comparisons in the earlier LOTOS-EUROS LETKF assimilation study by , who attributed this behavior to a potential overestimation of springtime NH3 emissions and underestimation later in the year.

A scatterplot of the monthly spatial means is shown in Fig. . For this comparison, the correlation increases from R=0.578 [0.380, 0.725] to R=0.684 [0.520, 0.799], and paired bootstrap resampling indicates that this increase is significant at the 95 % level (ΔR=+0.104, 95 %CI: +0.057–+0.166). The spread of the model–observation differences is also significantly reduced, from 3.04±0.28 to 2.38±0.22 kgNha-1yr-1 (Δσ=-0.62 kgNha-1yr-1, 95 %CI: -1.08–-0.20 kgNha-1yr-1). The mean bias is reduced from -1.15±0.39 to -0.91±0.31 kgNha-1yr-1, although this change is not statistically significant at the 95 % level.

Overall, the wet deposition evaluation provides a complementary downstream consistency check. The optimized simulation shows statistically significant improvements in the correlation, mean bias, and spread of the monthly temporal-mean comparison, as well as in the correlation and spread of the monthly spatial-mean comparison. The monthly spatial mean bias is also reduced, although this change is not statistically significant at the 95 % level. These results indicate that the assimilation improves several aspects of the modeled deposition field, but that wet deposition remains a less direct and less sensitive validation constraint than the surface NH3 concentration networks.

The baseline and optimized simulations were also evaluated against monthly MAN NH3 surface observations from a total of 315 sites (309 standard sites, and 6 MAN instruments located at LML sites) across the Netherlands for 2018–2022. Figure  shows the mean observed and modeled NH3 concentrations, along with their differences. The baseline simulation exhibits a clear spatial bias, underestimation along the western coast and overestimation in the east, while the optimized run amplifies this pattern, consistent with the emission and concentration increases in the southern and eastern Netherlands. No comparable bias pattern was observed for the hourly LML sites or the CrIS and IASI total column comparisons.

Figure  compares monthly spatial means across all MAN sites, and for comparison purposes, the LML and MAN statistics are summarized together in Table . The assimilation substantially improves the spatial correlation, from R=0.791 [0.672, 0.870] to R=0.892 [0.824, 0.934]. Paired bootstrap resampling confirms that this increase is statistically significant (ΔR=+0.100, 95 %CI: +0.036–+0.178). However, the improved spatial correlation is accompanied by a statistically significant increase in the positive mean bias, from +1.22±0.37 to +2.43±0.34 µgm-3 (Δμ=+1.22 µgm-3, 95 %CI: +0.71–+1.73 µgm-3), and by an increase in the regression slope from 1.385±0.141 to 1.651±0.110 (Δslope=+0.270, 95 %CI: +0.033–+0.515). The change in the spread of the model–observation differences is not statistically significant (Δσ=-0.17 µgm-3, 95 %CI: -0.82–+0.49 µgm-3).

These results indicate that the LETKF-optimized simulation better captures the large-scale spatial variability sampled by the MAN network, but that this improved spatial coherence does not correspond to an overall reduction in model error for the full MAN dataset. Instead, the optimized simulation increases the positive offset relative to MAN observations. This contrasts with the LML surface NH3 comparison, where the assimilation significantly reduced the negative bias and brought the regression slope closer to unity. The different behavior of the full MAN network is consistent with the representativeness interpretation discussed above: many MAN sites are located in Natura 2000 areas, often in sheltered or forested environments where local NH3 concentrations are lower than the surrounding landscape-scale concentrations represented by the 7km×7km model grid and by the satellite footprints used in the assimilation. Supporting visual comparisons using individual-site MAN monthly values and national monthly mean time series (Appendix Figs.  and ) show a similar qualitative pattern to the full MAN-network comparison, with the optimized run better reproducing broad interannual variability but maintaining a high bias, particularly during the summer months of 2020 and 2022, the years with the strongest emission adjustments (see Fig. ).

To further assess the spatial representativity of the MAN network and to enable a more direct comparison with the LML results, we also evaluated the six MAN calibration sensors co-located with LML sites against the base and optimized LETKF simulations. These six sensors are not part of the standard MAN dataset, but are used for the monthly calibration of the remaining 309 MAN sites, as described by . A spatial-mean scatterplot for these six sensors is provided in Appendix Fig. B3, and the associated statistics are summarized in Table . In contrast to the full MAN network, the co-located MAN sensors show behavior consistent with the LML analysis. The mean bias is significantly reduced from -2.42±0.46 to -0.99±0.41 µgm-3 after assimilation (Δμ=+1.42 µgm-3, 95 %CI: +0.85–+2.01 µgm-3). The spatial correlation also improves significantly from R=0.662 [0.490, 0.784] to R=0.761 [0.629, 0.851] (ΔR=+0.098, 95 %CI: +0.011–+0.191), and the regression slope increases from 0.666±0.099 to 0.831±0.093 (Δslope=+0.167, 95 %CI: +0.012–+0.325). The spread of the model–observation differences decreases from 3.57±0.33 to 3.15±0.29 µgm-3, although this change is not statistically significant. The much better agreement obtained for the co-located MAN calibration sensors indicates that the broader positive bias in the full MAN network is dominated primarily by representativeness differences rather than by a uniform model overestimation across all MAN locations. In other words, when the MAN comparison is restricted to more open, regionally representative sites similar to the LML locations, the optimized simulation shows statistically robust improvements in bias, slope, and spatial correlation. Part of this contrast may stem from measurement uncertainties in the passive Gradko samplers, but representativeness effects are expected to dominate. The LML stations and the satellite footprints sample air masses that are more representative of the broader agricultural landscape, whereas most MAN sites are located within Natura 2000 areas, frequently in or near forested environments where canopy shielding and strong local heterogeneity depress NH3 concentrations relative to the surrounding terrain. These sheltered conditions are highly localized and not captured by the coarse spatial scales of the regional model (7km×7km) or the 12–14 km nadir footprint of the satellite retrievals. As a result, the MAN measurements at these locations tend to reflect sub-grid processes rather than the landscape-average conditions that the model and satellite products are designed to represent. Remaining differences may also relate to how canopy deposition or near-surface mixing is expressed at these fine spatial scales, rather than broad model biases.

Overall, the MAN comparisons reaffirm that the LETKF enhances the spatial coherence of the NH3 fields and performs consistently when evaluated against regionally representative measurements such as the LML sites. The discrepancies observed at many MAN locations primarily reflect representativeness limitations inherent in comparing coarse-scale model and satellite products with low-temporal-resolution passive samplers situated in highly heterogeneous environments. Reducing these mismatches will likely require finer-scale process representation and more explicit treatment of land-cover–dependent effects in future assimilation studies.