TROPOMI is the single payload on the Copernicus Sentinel-5P satellite that was launched on 13 October 2017. The satellite has near-full-surface coverage on a daily basis with a local overpass time of around 13:30 . The instrument has four spectrometers; three that cover the ultraviolet–near infrared (UV-NIR) with two spectral bands at 270–500 and 675–775 nm, and there is one for the shortwave infrared (SWIR). The spatial resolution of TROPOMI varies with across-track position and is between 3.6km×7.2km (in UV-NIR) and 7.2km×7.1km (SWIR). As of 6 August 2019, the along-track sampling has been improved to 5.6 km.

The TROPOMI Aerosol Layer Height (AER_LH) algorithm was developed by the Royal Netherlands Meteorological Institute (KNMI) and utilizes the absorption in the oxygen A band of the spectrum between 759 and 770 nm . The oxygen A band is a highly structured line absorption spectrum with strongest absorption lines occurring between 760 and 761 nm. An aerosol layer aloft will decrease the photon path of the backscattered solar radiation, due to scattering by the aerosol layer, compared to backscattered radiation in a similar scene without the aerosol layer. This decreases the depths of the absorption lines in the oxygen A band of the measurements of the scene with the aerosol layer. The aerosol layer mid-height is estimated from a fit of the measurements to a simplified, single aerosol layer model simulation of the oxygen A-band reflectance, using an optimal estimation scheme, under cloud-free conditions. The final height reported is the difference between top pressure and bottom pressure of the assumed uniform scattering layer with a constant thickness of 50 hPa. The vertical data resolution is continuous, and values for the aerosol layer height (ALH) range from 1050 to 75 hPa. A more detailed description of the TROPOMI aerosol layer height product can be found in and . Due to the importance of the backscatter signal in the retrieval, which can be dominated by the surface reflectance in case of bright surfaces and thin aerosol layers, the aerosol layer height is expected to be more robust over dark surfaces such as sea and oceans .

The aerosol layer height can give insight into the height of aerosols in the free troposphere of plumes from wildfires, volcanoes and desert dust. This product could supply important information in a timely manner on aerosol location and transport of wildfire plumes for the purpose of air quality forecasting and aviation safety.

There are two versions available for the TROPOMI aerosol layer height; the near-real-time (NRTI) product is available approximately 3 h after the satellite overpass, and the offline (OFFL) product is available approximately 2 weeks after the satellite overpass. The algorithm for the NRTI and OFFL product is the same; however, not all products needed for the retrieval are available in NRTI. Therefore, differences between the NRTI and OFFL products include the following:

In NRTI the Visible Infrared Imaging Radiometer Suite (VIIRS) cloud mask is not available, and a cloud mask is constructed from the FRESCO cloud product, brightness thresholds, and scene homogeneity.

The Multi-angle Imaging SpectroRadiometer (MISR) instrument is on NASA's Terra spacecraft that has been in orbit since 1999. MISR has nine fixed push-broom cameras and views every scene from nine different angles. Each of these cameras has four line-array charge-coupled devices (CCDs) covering spectral bands centred at 446, 558, 672, and 867 nm. Its highest spatial sampling is 275 m at all angles. This design allows it to measure the height of smoke plumes using stereoscopic techniques . The height retrieval from MISR is not impacted by bright surfaces . MISR has approximately three overpasses daily over North America at around 10:30 a.m. local time, with a swath width of approximately 360 km.

An operational MISR cloud top product is available; however, the operational algorithm uses fixed parameters that are applied to all scenes equally . Instead, the plume height used here is not a standard product of MISR, and we used the visualization and analysis program called the MISR INteractive eXplorer (MINX) tool to retrieve the plume heights . This tool takes advantage of wind-direction information inherent in smoke plumes from active fires in order to determine plume heights and wind speeds at higher resolution and with greater accuracy than provided by the standard-operational MISR product . MINX is an interactive visualization and analysis program written in IDL and designed to make MISR data more accessible to science users. Its principal use is to retrieve heights and motion for aerosol plumes and clouds using stereoscopic methods. Within MINX, each plume has to be processed individually and plume shapes have to be digitized manually. Moderate Resolution Imaging Spectroradiometer (MODIS) brightness temperature anomalies are used to help locate the fire plumes, and plume heights are retrieved for smoke plumes close to the fire hotspots. The red-band data have a higher horizontal resolution (275 m); however, where contrast is poor within plume features and between the plume and the surface, blue-band retrievals provide better results at 1.1 km resolution . In this study, we used the blue-band results with “good” and “fair” quality flags. Further details can be found in . Limitations of the MISR instrument include the following: (1) the narrow MISR swath limits the frequency of global coverage; thus many smoke plumes can be missed; (2) the overpass time of around 10:30 LT precedes the daytime peak in fire activity.

The MODIS thermal anomaly product (MOD14) is used here to locate the wildfires. We searched for clusters of thermal anomalies with a confidence of at least 75 % and a minimum summed fire radiative power (FRP) (within a 5 km radius) of at least 1000. These locations were then used to search for plumes using the MINX package. There are currently two MODIS instruments in space, on NASA's Terra and Aqua satellites. Daytime measurements of Terra and Aqua are around 10:30 and 13:30 local time, respectively. For the MINX analysis, we utilized the thermal anomalies from MODIS Terra. Note that fires can potentially be missed for several reasons, including when there is cloud cover, when it is under thick smoke plumes and if the FRP signal is too low (e.g. small fires).

CALIOP, part of the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite that was launched in 2006, is a two-wavelength (532 and 1064 nm) polarization-sensitive lidar. CALIOP can provide high-resolution vertical profiles of aerosols and clouds, as well as their optical properties . It is an active satellite instrument, sensing pulses of light at 532 and 1064 nm. The backscattered return is measured through a 1 m telescope that measures the intensities at 1064 nm and two orientations at 532 nm (parallel and perpendicular to the polarization plane of the transmitted beam). The vertical resolution of the cloud and aerosol profiles is between 120 and 360 m, and the footprint is 90 m. CALIOP can detect even very thin aerosol layers with an aerosol optical thickness of 0.01 with sufficient averaging . CALIOP has approximately three overpasses at 01:30 and 13:30 local time over North America and has a very narrow swath width of just a hundred metres. In this study, we use the daytime aerosol layer product v4 (Layer_Top_Altitude and Layer_Base_Altitude) , which provides the top and base height of aerosol layers detected (between the surface and 30 km), averaged over 5 km along the 100 m wide swath and filter out all aerosol plumes except those containing smoke or polluted dust . While CALIOP has excellent vertical resolution and has the ability to resolve the layer heights of multiple plumes in a single profile, its swath width is very narrow and has a 16 d global coverage.

We also make use of the satellite-derived plume heights to evaluate the modelled plume heights from an experimental version of ECCC's FireWork biomass burning air quality forecast modelling system. The core of the FireWork system is the Global Environmental Multiscale–Modelling Air-quality and Chemistry (GEM-MACH) coupled meteorology and chemical transport model. GEM-MACH contains a detailed representation of atmospheric chemistry, including emissions, dispersion, and removal processes of 42 gaseous and eight particle species, which reside within the physics module of the Global Environmental Multiscale (GEM) weather forecast model . The operational version of the model has a horizontal resolution of 10km×10km for the North American domain and 80 vertical levels (from the surface to approximately 0.1 hPa) on a hybrid pressure grid. The forecast system produces air quality forecast conditions for 48 h and is initialized every 12 h at 00:00 and 12:00 UTC.

The experimental GEM-MACH system was used as part of an ensemble of models contributing to the Fire Influence on Regional to Global Environments and Air Quality (FIREX-AQ) experiment at a resolution of 2.5 km – here, the same system was used at 10 km resolution to simulate forest fire emissions, transformation, and transport for the summer of 2018 (1 June to 31 August 2018), with an internal model physics time step of 7.5 min, and output provided every hour. The outputs for the simulations included PM2.5 fields and estimates of the aerosol optical depth at a variety of wavelengths calculated internally using an online Mie lookup table . Differences between the operational and experimental version of GEM-MACH can be found in Table S1 in the Supplement.

Near-real-time fire hotspot information is obtained from the three satellite sensors MODIS, the Advanced Very High Resolution Radiometer (AVHRR) and VIIRS processed through the Canadian Wildland Fire Information System operated by the Canadian Forest Service, Natural Resources Canada http://cwfis.cfs.nrcan.gc.ca, last access: 1 October 2019;. Hourly fire emissions and smoke plume injection heights were estimated with the CFFEPS module at individual hotspot locations. Fire plume injection height in GEM-MACH is parameterized in the CFFEPS module with hourly modelled meteorology as detailed in . The injection height is determined based on the balance of estimated plume buoyancy and the modelled environmental lapse rate at the fire location. Total heat flux from fire is determined from modelled fuel consumed per area and the heat of combustion of dry wood fuel . The fraction of energy that enters the plume for convection is further parameterized based on thermodynamic energy balance, accounting for heat lost to fuel, moisture, radiation, conduction and incomplete combustion. The hourly plume injection height is determined based on the dry adiabatic equilibrium of the buoyant plume and the modelled environmental lapse rate at fire location. Further details describing the implementation of the GEM-MACH wildfire component within the model can be found in e.g. , , and .

Previous work with CFFEPSv2.03 showed a substantial improvement in forecast skill for daily maximum values of particulate matter, NO2 and PM2.5 relative to the previous ECCC operational forecast, which employed a much simpler Briggs plume rise approach for forest fire emissions plume rise. Here, we investigate how the particulate mass and plume injection height calculated with GEM-MACH and from CFFEPSv4.0 and transported downwind over a short period of time by GEM-MACH near fire hotspot locations compares to satellite-derived plume heights. In order to allow a direct comparison between satellite-derived plume heights and those predicted by GEM-MACH/CFFEPSv4.0, the hourly modelled PM2.5 concentrations were interpolated temporally to the satellite overpass times. Only plumes due to fires are investigated; we subtracted the model run without fire emissions from the run with fire emissions to remove PM2.5 contributions from non-fire sources.

In order to simulate the layer height retrieved by MISR using aerosol profiles from GEM-MACH, we rely on the concept that MISR's layer height is defined as the layer contributing the most to the reflective contrast relative to the surrounding air . Thus, to determine the MISR-equivalent plume layer height from the GEM-MACH profiles, we simply calculate the dI/dNz weighting function, where I is the 672 nm monochromatic radiance at the top of the atmosphere for a viewing zenith angle of 26∘. Nz is the GEM-MACH aerosol number density at altitude z, and the weighting function is calculated numerically by perturbing layers of the profile independently and determining the radiance difference relative to the unperturbed case. The PM2.5 aerosol number density vertical profile is obtained from GEM-MACH for these smoke cases. The number density is obtained from the fine-mode mass density profile of the model, assuming a typical mass of a fine-mode particle of 1.55×10-9 µg based on a particle density of 1.35 gcm-3 and assuming spherical particles with a radius of 130 nm. These approximations used here may not necessarily reflect GEM-MACH's predictions for particulate mass, radius or density, but those assumptions have been used to reflect that smoke particles tend to be small and to make the interpretation of the results less complicated by using the same assumptions for each simulated case. The retrieved layer heights will not depend on a multitude of aerosol properties. The VECTOR radiative transfer (RT) model is used , and aerosol scattering is simulated using Mie theory. For the Mie calculations, a gamma distribution is used for the aerosol size distribution (Eq. 2.56 of ) with an effective radius of 130 nm, an effective variance of 130 nm, and a size range of 0.01 to 260 nm. The complex refractive index, 1.68+0.36i, is appropriate for external mixed black carbon at 99 % relative humidity (which is expected near the fire source) . Note that this might not reflect the true aerosol size distribution of a fire smoke plume. However, the approximation can be used since the retrieved layer contributing the most to the reflective contrast does not depend on the exact size distribution used. We have also estimated the plume height assuming organic carbon (OC) with a refractive index of 1.36+0.001i (at RH=99 %) and found negligible differences between the plume heights obtained assuming BC and OC refractive indices for most cases (see Figs. S1 and S2 in the Supplement). The surface albedo provided in the TROPOMI layer height product is used for each different scene (for MISR and TROPOMI), and five orders of scattering were computed. For the MISR and the TROPOMI OSSE (MISR-OSSE and TROPOMI-OSSE; see below), it is critical to have fine layering in the radiative transfer model simulations that serve as the pseudo-observations in order to properly capture the shape of GEM-MACH aerosol profile. For MISR simulations using VECTOR, 100 m layering was used in the lowest 20 km of the atmosphere, and, thus, the GEM-MACH aerosol profiles were interpolated to 100 m layers.

To simulate the layer height retrieval from TROPOMI, we used MODTRAN 5.2 and references therein to take advantage of the correlated-k option for simulating radiances in an absorption band, namely the oxygen A band (∼762 nm). The correlated-k absorption parameter data are specified at 1 cm-1 (∼0.06 nm at 760 nm) resolution. The terrain height for the MODTRAN modelling is obtained from GEM-MACH for each scene. The radiance is convolved with a triangular slit function with a full width at half maximum of 0.5 nm to account for the TROPOMI spectral resolution in channel 6 , which covers the O2 A band. The discrete ordinates method is used to simulate the radiative transfer with eight streams. The solar zenith angle and viewing nadir angle of each scene are taken into account (as was done for MISR-OSSE). MODTRAN expects an aerosol extinction profile as an input rather than an aerosol number density profile. This conversion involves scaling the number density profile determined in Sect.  such that the aerosol optical depth simulated by MODTRAN is equal to the aerosol optical depth simulated for MISR. The A-band absorption depth is used as the observable in the retrieval and is computed using the following ratio: (I762.95+I760.75)/(I768.94+I768.82+I759.01), where the subscripted numbers are the wavelength (in nanometres) at which spectral radiances are simulated. The numerator is the sum of the radiance at two wavelengths for which O2 is strongly absorbing, and the denominator contains three wavelengths in the continuum (i.e. minimal absorption). The retrieval method is iterative and seeks to match the observed absorption depth with the forward modelled one by solely varying the layer height during the retrieval. The observations involve using the GEM-MACH aerosol profile, whereas for the forward model simulations during the retrieval, the profile shape is not known, and we assume that the aerosol layer has a vertical extent of 500 m with no aerosol outside this 500 m layer. Note that TROPOMI operational algorithm uses spectral fitting to retrieve AER_LH, whereas a simple ratio has been used here, similar to . The reported layer height is the middle of this layer.

In this section, the modelled plume heights, derived using five simple methods, and the simulated plume height, using modelled profiles with the MISR (Sect. ) and TROPOMI (Sect. ) retrieval methods, are compared. In Sect.  and , we described methods based on remote sensing for plume height estimation using modelled aerosol profiles. These simulations are, however, time consuming and therefore not practical for the model–satellite comparison as thousands of aerosol profiles would have to be simulated. Instead, several simpler methods are considered to define plume heights from model output, which can be used to compare the modelled output to satellite observations in the subsequent section. These methods define plume height as (1) the altitude of the model layer of the maximum PM2.5 concentration (shown as down-pointing red triangles in Fig. ); (2) the altitude of the highest model layer that exceeds PM2.5 concentration of 10 µgm-3 (shown as blue down-pointing triangles in Fig. ); (3) the altitude of the highest model layer that exceeds 10 % of the maximum PM2.5 concentration (this definition has previously been used in ; shown as black dots in Fig. ); (4) the average height between methods (1) and (2) (shown as right-pointing cyan triangles in Fig. ); and (5) a PM2.5 concentration weighted average of model layer heights (shown as left-pointing magenta triangles in Fig. ). The results of this simulated plume height comparison are shown in Fig.  with the reference 1:1 line shown as a black dash. These results show that the methodology in which the top layer of the plume is that exceeds 10 µgm-3, method (2), is closest to the MISR simulated plume heights (Fig. a) with a mean difference (± standard error) of -98 m (±181 m). Method (3) overestimates the plume height consistently for all plumes. Methods (1), (2), (4), and (5) are very close for many aerosol profiles, but for profiles containing multiple plumes, methods (2), (4), and (5) underestimate the MISR-simulated plume height. For the TROPOMI-OSSE (Fig. b), simulated plume heights with method (4) are the closest with a mean difference of 37±90 m, and except two profiles, the differences are all less than 200 m. For simple plumes with one strong aerosol peak (Fig. d–h), method (2) is close to the simulated TROPOMI-OSSE plume height but tends to overestimate the plume height of more complicated plumes with multiple aerosol layers, while methods (1) and (5) tend to underestimate the TROPOMI-OSSE plume height. Using method (3), with plume height as the altitude of the highest model layer that exceeds 10 % of the maximum PM2.5 concentration, overestimates the plume height for all plumes. Lastly, the simulated plume heights using the MISR and the TROPOMI approaches are compared over different AOD simulated using the VECTOR RT model (Fig. c). Overall, the plume heights estimated using the five different simple methods are consistent with the satellite retrievals for most plumes; however, there are cases in which the TROPOMI-OSSE plume heights are lower in comparison to the MISR-OSSE plume heights. We have found these to be unrelated to the AOD of the plume. The average mean difference (± standard deviation) between the simulated aerosol layer heights between MISR and TROPOMI is 0.52±0.84 km. This difference can be attributed purely to the different observation/retrieval methods of the aerosol layer height between the two instruments.

The differences between the MISR-OSSE and TROPOMI-OSSE plume heights were further investigated, and Fig. d–l show examples of the profiles used, along with the retrieved plume heights. Profiles for which the MISR-OSSE and TROPOMI-OSSE plume heights agree well are displayed in Fig. d–h, and all show one single dominant plume. Profiles that result in differences between MISR-OSSE and TROPOMI-OSSE are more complicated profiles consisting of multiple aerosol layers (Fig. i–l). In these cases, MISR observes the altitude of the upper plume, whereas the A-band method used for TROPOMI (and EPIC) retrieves an optical centroid altitude . Note that retrieving a single layer height can be difficult particularly when the volume enclosing the plume takes the shape of a column or when there are multiple plumes at different altitudes due to either multiple source locations (i.e. points of origin) or shifts in the wind direction or atmospheric stability during the course of emissions. Large differences between TROPOMI and MISR might be an indicator that multiple plumes are present.

In total, we found 115 fire plumes for which the MISR layer height retrieval was of good (87) to fair (29) quality and which were captured by both MISR and TROPOMI between June and August 2018 in North America. Most of the plumes were located in western Canada and the western US where fire activity was high to extreme for the year. There were few plumes in eastern Canada, in the provinces of Ontario and Quebec, or in the states of Wyoming and Colorado in the central US. Due to the differences in sensor spatial resolution, each plume spanned many pixels, on the order of a several hundred for MISR and a dozen for TROPOMI. For the comparison, we investigated the maximum plume heights and the mean plume heights within those fire plumes. An example is shown in Fig.  for two fires (the fire hotspot is shown as red dots) in central British Columbia on 6 August 2018 at approximately 53∘ N, 126∘ W. The plume height pixels from MISR, TROPOMI and GEM-MACH are overlaid on the VIIRS true colour visible imagery showing the smoke plume (obtained from NASA Worldview; https://worldview.earthdata.nasa.gov/, last access: 25 March 2020). For MISR a plume has to be digitally outlined in MINX (dashed red line in Fig. ), this plume polygon was also used to define the spatial extent of the same smoke plume for TROPOMI. As MISR overpasses a location approximately 2 h earlier than TROPOMI, MISR, and TROPOMI do not observe the fires at exactly the same time. Forest fire emissions typically follow a diurnal cycle with a decrease in emissions and intensity during the night and increase throughout the day until the late afternoon; hence the plume might be expected to grow between the two overpass times. To account for plume growth from atmospheric dispersion over this time, the plume shape derived for the MISR analysis was increased spatially in size by 0.15∘ in longitude and latitude for TROPOMI (see dashed navy line in Fig. ). All pixels within this slightly enlarged plume outline were assumed to belong to the same fire plume, and the mean and the maximum of those observations were calculated for comparison with MISR. The enlarged polygon is used as a guidance on which pixels from TROPOMI belong to the same plume that is outlined in MINX; there is no manual input or outlining required for the TROPOMI algorithm. If the enlarged polygon is too large or the plume does not cover the whole area, the mean will not be affected as the TROPOMI plume heights are set to a fill value (and masked) if no plume has been detected or retrieval did not pass the quality control. Since the resolution of the MISR pixels is around 1km×1km and of much finer resolution than that of TROPOMI (5km×7km), greater variability and extremes in plume heights are expected from MISR, with significantly higher sampling of pixel within the same plume, as spatial smoothing of layer height is limited. To correct the impact of sensor resolution on the maximum plume height derived from a cluster of pixels in a given plume, the MISR pixels were averaged and binned on a 0.05∘ × 0.05∘ grid to approximately match the TROPOMI resolution.

The results of the comparison between the TROPOMI- and MISR-derived plume heights for 155 identified collocated fire plumes from both sensors in North America are shown in Fig. . The average maximum plume heights above ground level for the 2018 fires in North America are, on average, 2 km (ranging between 0.4 and 5.5 km) and 1.6 km (ranging between 0.01 and 8.4 km) for MISR and TROPOMI, respectively. The mean plume heights (above ground level) from the 155 fire plumes are on average 1.4 km (ranging between 0.3 and 3.2 km for MISR) and 0.8 km (ranging between 0.01 and 2.8 km for TROPOMI). Overall, TROPOMI's maximum and mean plume height is on average 0.59±1.3 km and is 0.55±0.74 km lower than the plume height derived from MISR, respectively, when horizontal resolution impacts have been removed by averaging, as noted above. The mean difference found for the TROPOMI and MISR observed plume heights is similar to those found for the simulated plume heights of the OSSE. The maximum plume heights from all smoke plumes are similar; however, they have a large spread (σ=1.3 km) and only a moderate correlation (R=0.44), even when taking the difference in resolution into account by binning the data. This is expected, and in fact the results are reasonable, since the maximum plume height will only contain the observations of a single TROPOMI pixel and there is a time difference between 0.5 and 3 h between the TROPOMI and MISR overpass in which plume heights can change significantly. The average plume heights, a more aggregated quantity, have a better correlation with a correlation coefficient, R, with R=0.61, and slope of best fit, s, with s=0.8, and TROPOMI biased low. This low bias of the TROPOMI observations of plume heights is expected based on the retrieval technique (see Sect. ), where MISR observes the top plume height and TROPOMI observes an average plume height when multiple layers of aerosols are present. Furthermore, despite the spatial adjustment of expanding the sampling footprint of the MISR plume, the 0.5–3 h earlier overpass time of MISR is likely sampling plume heights earlier in the day when the planetary boundary layer (PBL) is not fully established and of lower fire intensity. TROPOMI plume height observations are, therefore, expected to be slightly higher compared to MISR because of general increases in fire intensity in the afternoon enhancing plume advection. However, the differences between the satellite observations and the differences of the OSSE simulated plume heights based on the satellite retrieval algorithm (Sect. ) are similar; no increasing plume height is apparent from this TROPOMI and MISR dataset.

The regional distribution of the different plume heights are illustrated in a map over locations of fire hotspots during the analysis period (see Fig. d). Table  summarizes the different plume heights found by MISR in comparison to TROPOMI. The average plume heights for the maximum and mean plume height within each of the 115 plumes are shown for fires in different types of biomes as classified by the International Geosphere-Biosphere Programme (IGBP). For the comparison with MISR, enough observations within our dataset were only found for evergreen fires. To be able to do a quantitative regional comparison for additional vegetation types, more smoke plume observations are required.

For the comparison between CALIOP and TROPOMI, only CALIOP plume heights over North America are retained; filtered out (with Feature_Classification_Flags) were the ones categorized as clean marine, dust, polluted continental and clean continental plumes. Thus, only plume heights containing smoke or polluted dust were selected (we found that fire plume aerosols are classed as either smoke or polluted dust). The maximum and mean of the TROPOMI aerosol layer height within ±0.15∘ (∼15 km) of the CALIOP observations were compared. Similar to we use the top and plume base from the CALIOP L2 product (aerosol layer product v4), which are on a horizontal resolution of 5 km, similar to that of TROPOMI, and thus no additional corrections to the sampling footprint were carried out. Note that the CALIOP data are averaged to 5 km, however along a narrow swath (∼100 m), differences could arise due to the different sampling. On average there is a small overpass difference between these two sensors varying between -1 and 2 h (CALIOP–TROPOMI overpass) for this dataset, so the forest fire plume height comparisons may also be affected by plume evolution between overpasses. Unlike TROPOMI, which provides one plume height at each sampling pixel, the active lidar on CALIOP provides a detailed plume profile, some with multiple layers of aerosol in a profile. Here, we define the thickness of the plume as the difference between plume top and plume base; CALIOP's mid-layer height (average between plume top and base) are compared to TROPOMI's aerosol mid-layer heights. We further found that very high plumes (>8 km) observed by CALIOP were not captured by TROPOMI, likely because they are optically quite thin, and those have been removed from the comparison. Sometimes multiple layers of aerosols can occur in a CALIOP profile. We investigated additional CALIOP plume height interpretations to find the most representative layer height for the comparison to TROPOMI. They are (1) the CALIOP top layer height, (2) the average of all CALIOP-identified aerosol layers and (3) the thickest (geometrical thickness) CALIOP aerosol layer. Overall, we found that the first of these definitions is not appropriate for the TROPOMI comparison as the top aerosol layer in CALIOP can be a very thin plume in the upper troposphere/lower stratosphere that is not captured by TROPOMI. The second methodology comparing the CALIOP average of all aerosol plumes to TROPOMI was sometimes also biased by very low concentration layers of CALIOP aerosol at high elevations. The third methodology was not affected by the issues for the other two methods; using comparing the CALIOP geometrically thickest aerosol layer with the TROPOMI aerosol layer height seems the most applicable for the plume height comparison between those two different satellite instruments.

Figure  summarizes the CALIOP–TROPOMI plume height comparison for (a) geometrically thick plumes (> 1.5 km), (b) geometrically thin plumes, (c) a histogram of the differences, (d) how the statistics of the comparison change for different plume thickness filters and (e) how the statistics of the comparison change for different surface albedo. The results show that the difference between the plume height observed by TROPOMI and CALIOP depends significantly on the thickness of the plume (as derived from CALIOP). Thicker plumes seem to be better captured by TROPOMI, and the thicker the plume the smaller the difference between the CALIOP and TROPOMI plume height. TROPOMI was biased low, on average by 2.1 km, in comparison to CALIOP for thin smoke plumes (thickness of less than 1.5 km). Much better agreement and an improved correlation between the two satellite datasets are found for thicker plumes (see Fig. d). The mean difference reduces with the thickness of the plumes; the mean difference between the TROPOMI and CALIOP mid-aerosol layer is just 50 m for very thick plumes (>3 km). The geometrically thick plumes are typically optically thicker plumes, too. The reason for the reduced bias with increasing layer thickness is probably the sensitivity of the TROPOMI AER_LH algorithm to the scattering layer in the scene, which is more and more dominated by the surface if the aerosol layer is optically thinner. The correlation plot and histogram are shown in Fig.  for thin plumes (shown in blue) and thick plumes (>1.5 km; shown in red). The distribution of the differences between the TROPOMI and CALIOP plume height is a normal distribution, with a smaller spread for thick plumes. From this analysis it also appears that lower plumes, below approximately 4–4.5 km, are better captured by TROPOMI (see Fig. ). Figure e shows that the differences between CALIOP and TROPOMI increase with increasing surface albedo, consistent with the idea that the TROPOMI retrieval algorithm is more sensitive over dark surfaces and possesses smaller uncertainties .

Similar to what was done for the TROPOMI–MISR comparison, the area of the plume is defined by the expanded MISR plume outline (by 0.1∘), and all points within this enlarged polygon (an example can be seen in Fig.  – the enlarged polygon used for the model comparison is shown as a dashed blue line) are considered as part of the plume. Given that FireWork is a forecast product, this expanded polygon is used for the comparison to compensate for errors in wind forecast speeds and direction within the model and for uncertainties related to temporal interpolation between hourly output and satellite overpass. Furthermore, given the coarse model resolution compared to MISR pixel, the expanded plume footprint allows for more points to be extracted for comparison. All points with elevated PM2.5 within this extended polygon are considered part of the same plume. Again, to account for the difference in resolution when comparing the maximum plume height, MISR pixels have been binned to 0.1∘×0.1∘, to the approximate resolution of the model.

We found that the modelled plume heights are very similar but on average slightly higher than the ones observed by MISR. Overall, the modelled plume heights represent the observations very well in terms of mean and maximum plume heights, with differences of -0.06±0.68 and -0.32±1.21 km, respectively. Figure a–c summarize the results for the comparison between MISR and CFFEPSv4.0. In total 70 fire plumes were compared (all between June and August 2018) in terms of (a) maximum plume height and (b) mean plume height. A map illustrating the regional distribution of the mean plume heights is shown in Fig. d.

The FireWork modelled plume heights with forecast meteorology are on average less than 100 m higher compared to the MISR observations. The modelled plume heights correlate well with the satellite observations with R=0.73 for the mean plume heights. The maximum plume height within one plume is also well represented with a correlation coefficient of R=0.53; the model overestimates the maximum plume height on average by +0.32 km. These are very encouraging results for modelled versus satellite-observed plume heights, especially, considering the assumptions that were parameterized in the modelling fire plume height, such as amount of fuel consumed, area burned, energy released, modelled atmospheric profiles and dispersion. There were not only small mean differences small but also a good correlation between the observations and the model for both mean and maximum plume heights. The error difference for the plume plumes analysed here have a normal distribution (see Fig. c). Significant of progress has been made in recent years in terms of modelling plume rise for biomass burning. For example, found that on average the modelled plume heights agreed with the observations, but correlations between observed and simulated plume heights was poor. However, modelled plume heights in were calculated using a Briggs plume rise approach as opposed to calculating the energy balance in multiple atmospheric layers. The latter approach, used in CFFEPS, was found to result in more accurate predictions of surface daily maximum PM2.5, NO2, and O3 than the use of Briggs formula . At least part of the improved model predictive performance of the ECCC FireWork forecast may be attributable to these radiative transfer calculations within CFFEPS, with the version used here (v4.0) also including a higher vertical resolution than the v2.03 version described in . The differences between MISR- and FireWork-modelled plume heights for different biomes are summarized in Table  showing that for evergreen forest fires the modelled and MISR observations agree well on average. There were not enough fire plumes available from the FireWork–MISR comparison to compare other biomes. The number of fire plumes that have been compared to the FireWork is slightly lower than for the TROPOMI–MISR comparison; some smaller fires can be missed by the model or the modelled aerosol concentration does not reach 10 µgm-3.

For the comparison of FireWork modelled plume height to TROPOMI, the spatial extent of the plume is defined as the polygon surrounding TROPOMI's minimum and maximum latitude and longitude (shown as a dashed purple line in Fig. ) in which a predefined smoke or aerosol layer was present near a fire hotspot as identified by MODIS Aqua. Similar to the process with the MISR comparison, this polygon is then increased by 0.1∘ (dashed black line in Fig. ) to account for the errors in forecast wind direction and speed within the model. As the resolution of TROPOMI is higher than the resolution of the GEM-MACH model, for the maximum plume height comparison the TROPOMI observations are binned to 0.1∘ × 0.1∘, approximately the resolution of the model, and the TROPOMI gridded data are paired with model output sampled at the TROPOMI overpass time. Overall for North America June–August 2018, 671 coincident fire plumes were found for the model comparison. This number is significantly higher than for the comparison between FireWork and MISR, because of the better geospatial coverage of TROPOMI compared to MISR, and, thus, less fires are missed by TROPOMI. The results for the TROPOMI and model comparison are shown in Fig. , and the results summarizing the averages for different biomes are in Table .

Moderate correlation was found for the TROPOMI–model comparison (R in the 0.3 to 0.5 range; see Fig. ). The model plume height is on average higher than the TROPOMI observations. The average differences (TROPOMI-model) in the maximum and mean plume height are of -0.27±1.84 and -0.58±0.85 km, respectively.

For the plume heights for different biomes, also with the increased number of fire plumes with TROPOMI, only minor differences are observed between the different biomes. Overall, it seems that CFFEPS struggles the most with grassland fires where the average plume height is about 0.8 km higher than the TROPOMI observations. Plume heights from evergreens and woody savannas seem to agree well with the observations. Looking at the TROPOMI plume height, fire plumes from all of the here-presented biomes have on average a maximum plume height between 2.1 and 2.3 km and an average mean plume height of 0.7 km.