The MODIS dataset used in this study consists of the level-2 (L2) Fire Radiative Power retrievals MOD14 and MYD14 from the instrument onboard Terra (2000–2023) and Aqua (2002–2023) satellites respectively. Hereinafter, the common notation will be MxD14. The L2 products were downloaded from Atmosphere Archive & Distribution System (LAADS) Distributed Active Archive Center (DAAC) (https://ladsweb.nascom.nasa.gov/, last access: 12 October 2025) (Giglio and Justice, 2021a, b). The data after 2023 were not used to avoid impact of the TERRA constellation exit maneuvers.

The MODIS L2 products are organized in granules, i.e., chunks of data collected during 5 min intervals. Each MxD14 granule contains a field of flags for every pixel in a granule indicating if a detection was possible or not (cloud obscuration, failed retrieval, sun glint, water surface etc.) and a list of overheated pixels with FRP, geolocation, position in the swath, pixel size, etc. The geolocation of non-overheated pixels was picked from the MODIS cloud products MxD35 collection 6.1 (MODIS Atmosphere Science Team, 2017a, b).

The key variables used in the assessment are: (i) the pixel-wise FRP expressed in megawatts throughout the paper; (ii) quality flags of MxD14, (iii) geolocation information of individual pixels of MxD35.

The FRP retrievals were censored by removing ∼ 0.6 % of pixels with unphysically strong FRP, Pp>500 MW. Secondly, the first months of MODIS Terra operations, until November 2000, were removed entirely due to known problems with the sensor (Giglio et al., 2021). No other filtering was applied.

The VIIRS data from the instruments onboard SUOMI-NPP (2012–2024) and NOAA-20 (2018–2024) satellites were obtained from the same NASA LAADS DAAC Earth Data server as the MODIS products. We used VNP14IMG and VJ114IMG (Giglio, 2024a, b) for FRP, locations of detected overheated pixels, and the detection mask, and VNP03IMG and VJ103IMG products (VIIRS Calibration Support Team (VCST), 2021a, b) for pixel geolocation. The corresponding common notations hereinafter are Vxx14 and Vxx03. Data before February 2012 were discarded to avoid suspiciously large number of fires reported in the first days of the instrument operation. No other filtering was applied.

An approximate formula for the pixel size calculations for both MODIS and VIIRS has been suggested by Ichoku and Kaufman (2005) with a reference to Masahiro Nishihama (personal communication, 2004) and the MODIS Algorithm Technical Basis Document ATBD (Nishihama et al., 1997). A ground pixel size along the scan ΔS and the satellite track ΔT directions are functions of the scanning angle θ and orbit parameters: 1ΔS=RescosθRe/r2-sin2θ-12ΔT=rscosθ-Re/r2-sin2θ where Re= 6378.137 km is radius of Earth, r=Re+h, h is altitude of the orbit (705 km for MODIS), p is pixel nadir size (1 km for MODIS), s=p/h=0.0014184397 (MODIS), and scanning angle θ is determined by the pixel number i in the scan line consisting for MODIS of totally N=2030 pixels: 3θi=si-N+12 These formulas can also be applied to VIIRS with h=825.2 km, N=6400 non-aggregated pixels, s=0.375 km (Schroeder et al., 2014b; Wolfe et al., 2013). Accuracy of this approximation has been verified against the instrument look-up table (Wilfrid Schroeder, personal communication, 2022) and showed the error not exceeding 0.2 % for all variables of Eqs. (1–3).

Equations (1–3) are illustrated in Fig. 1 for MODIS and Fig. 2 for VIIRS. The total width of the MODIS scan over the Earth surface is ∼ 2063 km, and the pixel area varies from 1 km² in nadir view at θ=0 up to 9.66 km² at the edge of the swath at θ=55 ° (Fig. 1a). About 40 % of the swath is covered by pixels with Ap < 2 km² and only 20 % – by pixels with Ap > 6 km² (Fig. 1b, c). MODIS swath has 10 detectors in the track direction (Nishihama et al., 1997). The growing size of the pixels towards the edge of the swath means that the neighboring swaths partly overlap along the track direction (Fig. 1d, see also Fig. 3-1 of Nishihama et al. (1997) for MODIS).

The VIIRS swath geometry (Fig. 2) is generally similar but with peculiarities. To limit the pixel size growth along the scan direction, individual pixels of both I- and M-bands are aggregated as 3 × 1 (three scan-direction samples by one track-direction sample), 2 × 1, and 1 × 1 for the scan angles of 0°–30°, 30°–45° and 45°–56°, respectively (Fig. 1 in Schroeder et al., 2014b).

A single VIIRS sensor has 32 I-band sensors in the track direction, and subsequent scans substantially overlap at high scan angles leading to up to a triple coverage at the edge of the swath. To reduce the redundancy and to limit the amount of data to transfer, data readings from two and four I-detectors from the top and bottom of the arrays (the largest scan angles) are not transmitted in the 2 × 1 and 1 × 1 aggregation zones, respectively (a “bow-tie deletion”). The current study used data of the higher-resolution I-band detectors, which provide ∼ 375 m nadir pixel size (Wolfe et al., 2013) and explicitly accounted for the pixel aggregation and the bow-tie deletion (Fig. 2).

Since all considered satellites are on sun-synchronous orbits and because the fires are heavily influenced by the local diurnal cycle, the analysis was performed in local solar time (LST). Two types of statistics were computed: for individual pixels and for gridded data.

In the above derivations, it is assumed that fire is either obscured by a cloud or not. However, the cloud can be thin, or a fire can be dimmed by its own smoke or other aerosols. The satellite would then process the pixel like a non-obscured one, but the signal strength would be lower. Denoting aerosol column optical depth (AOD) at the wavelength of the fire detection (4 µm for MODIS and VIIRS, Eq. (6) in Giglio et al., 2016) as τ4, one should replace the model-predicted FRP Pmdl with Pmdl̃ in Eqs. (7) and (11): 12Pmdl̃=Pmdlexp-τ4 All other terms remain the same. This approach should be considered as indicative because aerosol obscuration will impact the retrieval at other wavelengths too thus influencing the fire detection/rejection procedure and indirectly affecting the gridded FRP (see Table 1, Giglio et al. (2016) and Sect. 3 of Schroeder et al. (2014b)).

The OOp has been developed for projecting a model-predicted FRP onto the observational space, but it can also be used for projecting one FRP dataset onto another. A complexity, however, is that the OOp implies a space-time co-location of the datasets, which is impossible for the low-orbit satellites. For instance, the accurate spatial co-location of MODIS AQUA and VIIRS Suomi NPP retrievals is straightforward, but their retrieval times differ by 1–2 h, leading to different cloud obscuration and fire stages. The imperfect temporal co-location can be accounted for by symmetric OOp application:

For a given day, select overlapping granules of MYD14 and MYD35 of MODIS Aqua and VNP14 and VNP03 of VIIRS Suomi NPP

The cloud-related term in Eq. (10) leads to a space-dependent probability of missing a fire regardless of its intensity. A rough estimate of such probability is a mean of (1-βret) for a particular region (see Eq. (10) for definition of βret), averaged over the satellite overpasses (Fig. 8a, mean fraction of missing pixels in the MODIS granules). This fraction is computed from MxD35 and Vxx03 products for MODIS and VIIRS, respectively. Pixels with “sunglint” or “cloud” flags are considered missing. However, this fraction should be considered as the upper estimate of (1-βret) because fires tend to occur in dry periods when the cloud cover (the main reason for missing observations) is lower than the annual mean.

A way to account for the mutual anticorrelation of clouds and fire occurrences is to calculate the mean cloud cover only during a fire season in the region. A quantitative criterion can be the non-zero sum of FRP for the surrounding area of, for instance, 1°×1° (Fig. 8b for MODIS and Fig. 8c for VIIRS).

Due to anticorrelation between cloud cover and detection probability, the missing fractions in Fig. 8b, c, being more realistic than the mean cloud cover of Fig. 8a, probably underestimate the omission error, thus being the lower estimate of the omission probability.

The results in Fig. 8 depend on the arbitrarily selected size of the inspected area around the cloudy grid cell. Impact of this area has been quantified via a sensitivity study by varying it from 0.1° up to 20° (Fig. 9). Calculations showed low sensitivity, e.g., doubling the area from 1° × 1° to 2° × 2° adds less than 10 % to the omission probability of Fig. 8b, c (see also Fig. 9). Further expansion eventually leads to the same map as that of Fig. 8a (for MODIS). A wider inspected area also leads to less steep curves and smoother patterns (Fig. 9). However, a wide search is not justified: already 200 km is too large as a correlation distance for regional fires. A smaller area leads to a patchy non-representative map.

The maps of Fig. 8 suggests that, even during the fire seasons, the omission error of low-orbit satellite instruments like MODIS or VIIRS is typically within 20 %–40 % for most fire-prone regions, with VIIRS showing 10 %–20 % lower omission error than MODIS. In equatorial regions, omissions can be much higher: the fraction of missed fires can exceed 60 % for MODIS and 40 % for VIIRS.

The lower omission error of VIIRS may be due to (i) higher resolution, (ii) higher sensitivity, as shown in the discussion below, (iii) overpass time in the middle of day when cloudiness may be at its daily lowest level. Another peculiarity of VIIRS is a very high omission in Arctic, where MODIS shows the “usual” 40 %. This is caused by the high sensitivity of VIIRS: it detects more fire pixels in partly cloudy conditions and outside the main fire season. Clouds during these periods then contribute to the VIIRS omission error, whereas MODIS misses them altogether and thus does not consider these times as fire-prone at all.

The pixel-wise OOp was applied to the MODIS AQUA and VIIRS Suomi-NPP FRP retrievals for a full year of 2020, taken as an example. The procedure followed the symmetric approach (Eq. 13). The outcome (example in Fig. 10) expectedly showed that VIIRS registered ∼ 30 % more FRP than MODIS (Fig. 10a, b) due to its lower detection limit. Application of MODIS-based OOp zeroed pixels with small FRP resulting in a 1.5 times lower granule total (Fig. 10d). Accounting for the differences in cloudiness via application of VIIRS OOp to the MODIS fire pixels led to ∼ 30 % reduction of the total FRP, thus leaving only those locations that were visible for both satellites (Fig. 10c).

Analysis of the whole year 2020 brought over 40 000 MODIS AQUA granules with fire pixels registered by at least one instrument. Total FRP retrieved by MODIS and VIIRS within these granules was 128 and 177 TW, respectively. Symmetric application of ΞpixVIIRSPMODIS and ΞpixMODISPVIIRS lead to 88 and 106 TW, respectively. This is illustrated in Fig. 11, which compares VIIRS retrievals before and after the MODIS OOp application (PVIIRS, blue dots and ΞpixMODISPVIIRS, orange dots) with the MODIS FRP processed by the VIIRS OOp (ΞpixVIIRSPMODIS, x-axis in Fig. 11).

The OOp-processed datasets match closely: the initial 38 % difference, VIIRS registering more FRP, turns to 20 % more OOp-processed FRP of MODIS. This 20 % difference originates from different overpass times of the satellites (see the Discussion section below), so accounting for it results in a close match of the OOp-processed datasets (Fig. 11).

The first percentiles of the distribution densities πfAp,Pf and πnAp,Pf (Figs. 3 and 4) (the red-dots and orange regression lines) are linear functions of the pixel area for both MODIS and VIIRS, with correlation coefficient > 0.99. For both satellites, the 1^st percentile of the nighttime FRP is lower than that of daytime, for all pixel sizes, with the difference being larger for VIIRS than for MODIS.

Panels e and f of the figures show that the smallest pixels register most of the FRP and the total number of fires. For MODIS, 50 % of fires are from 1–1.2 km² area pixels while the fraction of the swath covered by such pixels is about 20 % (see the swath geometry in Fig. 1b, c). For VIIRS, pixels < 0.3 km² occupy 60 % of the swath area but provide ∼ 90 % of fire detections (Fig. 2b, c).

The results reported above can be compared with case studies presented in literature. For instance, the cloud obscuration of fires in Brazilian Amazon (Schroeder et al., 2007) led to the omission error of 11 % for GOES geostationary fire products. This estimate expectedly differs from the MODIS/VIIRS statistics (Fig. 8): e.g., the mean cloud cover of MODIS overpasses over that area is 0.4–0.7. For fire seasons, Fig. 7b suggests the omission error from 0.2–0.6 for MODIS and 0.1–0.3 for VIIRS. The difference from the value of (Schroeder et al., 2007) refers to the ability of geostationary satellites to follow the fire over time thus avoiding some clouds. As follows from the comparison, it can about-half the omission error, at a price of 16 times lower resolution (GOES sub-satellite pixel was 4 km × 4 km), with the corresponding loss of small- and mid-sized fires.

The only study reporting the dependence of the fire detection probability on the pixel size was made for MxD14 Collection 5 data by (Maier et al., 2013) for Australia. The study suggested that fires with FRP < 3.6 MW are never detected (practically no fires were recorded up to 5 MW) whereas the frequency distribution of FRP is significantly disturbed already at 15 MW. According to the FREEVAL study (Schultz et al., 2008), the minimum-FRP detection threshold for MODIS Collection 4 was about 7–10 W m⁻² (7-10 MW for 1 km² pixel). This is in agreement with the predicted sensitivity limit of 10–20 W m⁻² of (Kaufman et al., 1998). Finally, our earlier estimates made for Collection 5 (Soares et al., 2015) pointed out that noticeable distortions of the FRP distribution start at 15 W m⁻². Except for (Maier et al., 2013), none of these works referred to the pixel size and the overpass time, and should therefore be attributed to the smallest nadir pixel of MODIS, 1 km². These numbers are about-twice higher than the limit obtained above for Collection 6, which confirms the better detection of small fires in Collection 6 in comparison with the earlier Collections.

The dependence of the detection limit on the pixel size is dictated by the geometry of the instrument and the basic principle of the temperature-contrast based fire detection, leading to qualitatively similar dependencies obtained by (Maier et al., 2013) and in the current work. Among the differences, one can notice an almost-perfect linear relation of the detection limit in the current study in contrast to a “saturation” noticed for large viewing angles by Maier et al, who attributed it to the randomly selected 1 % threshold. However, in the current study, there is no saturation for 1 % threshold either (Figs. 3 and 4). A more probable reason is an insufficient number of fire detections in the large-pixel size range: only 57.2 thousand events were counted in the Maier et al analysis vs ∼90 million cases for MODIS in this study. Should this saturation be ignored, the detection limit for the largest pixels at the edge of the swath would exceed 55 MW for Collection 5, compared to 42 and 39 MW for day and night overpasses for Collection 6 in this study.

The sensitivity of SEVIRI has been evaluated within the FREEVAL project (Schultz et al., 2008). That study concluded that “SEVIRI should be able to confidently detect actively burning fires whose FRP reaches a minimum of around 100 MW, and in certain cases may be able to detect fires whose FRP is even lower than this, down to around 50 MW.” That generic conclusion was refined by the fire histogram of the sub-satellite pixels (Fig. 4.2 in the FREEVAL report), whose size (3 km × 3 km) closely matches pixels at the edge of the MODIS swath. In the FREEVAL histogram, strong disturbances start from FRP of 43 MW, with detection limit being between 35–40 MW. This result corroborates very well with the current assessment because the 9 km² area corresponds to 40.5–40.9 MW detection limit (day–night) according to Eq. (5) and Table 1. Therefore, the lowest detection limit of SEVIRI (sub-satellite fires) is 10 % lower than the corresponding detection limit of MODIS near the edge of its swath. The difference can originate from the differences in the instruments, the FRP retrieval algorithms, and the accumulated statistics (the FREEVAL SEVIRI histogram is based on 3 months in 2004).

Comparison with VIIRS is not unequivocal. Schroeder et al. (2014b) related the fire size and temperature to the probability of VIIRS to detect it and concluded that a small (1.5 m radius) but hot (1000 K) fire can be noticed at night. In a qualitative agreement with that prediction, a histogram of VIIRS FRP data (Fig. 4) suggests ∼ 0.7 MW detection limit at night in the center of the swath.

A direct comparison of the detection limit formulas and coefficients for MODIS and VIIRS (Tables 1 and 2, Fig. 12) reveals both the effect of the pixel size on the detection limit and the difference between the instruments and processing algorithms: VIIRS is about 3× more sensitive than MODIS for comparable pixel size of ∼ 1 km² at night, but about 25 % less sensitive during day (within 5 % for the first percentile).

Application of the OOp-s matches the datasets (Figs. 8 and 9): the remaining difference of 23 % between the ΞpixMODISPVIIRS and ΞpixVIIRSPMODIS is a result of the later overpasses of AQUA, which registers most fires around 13:00–14:00 local time, compared to 12:00–13:30 of Suomi-NPP. The absolute peak of fire intensity, however, was estimated at 14:00–15:00 local time from the geostationary SEVIRI retrievals (Soares et al., 2015), practically independently from the land use type. According to those calculations (see Fig. 5 there), the difference between Suomi-NPP and AQUA observations corresponds to ∼ 20 % higher total FRP for MODIS AQUA (depending on actual retrieval times, the difference is within 0 %–50 % range), which closely matches the 23 % difference between OOp-processed FRPs (this correction is applied to the scatterplots in Fig. 11).

A substantial fraction of fires missed by MODIS and VIIRS, either due to cloud obscuration or finite detection limit, can lead to inconsistencies in the fire retrievals. The first problem is that the satellites register more fires in centres of the swaths than at their edges. Moreover, the orbits shift every day with revisit time of 16 d. As a result, application of an atmospheric composition model with such fires as input would lead to appearing / disappearing fire detections, missing smoke plumes, and incorrectly reproduced episodes.

The second issue is more general. The atmospheric models are calibrated and evaluated against a variety of independent observations, and mean bias of predicted concentrations is one of critical parameters. Many assessments of non-anthropogenic emissions rely on inverse problem solutions (a.k.a. top-down emission inventories). Having a fraction of fires missing, the emission inversion algorithm may tend to offset the bias due to missing fires by exaggerating the emission factors for the observed ones. Such artificial increase might partly explain the factor of 3.4 between the top-down and bottom-up approaches to PM emission from fires, as noted in earlier studies (Kaiser et al., 2012; Soares et al., 2015). Conversely, missing fires lead to distorted pollution patterns and lower correlation with observations. In the inverse problems context, lower model-measurement correlation leads to under-estimation of optimized emission fluxes (Sofiev et al., 2024).

One of possible ways to address the problem of the omission error is to construct a fire prediction model capable of assimilating the active-fire products into the model state that exists regardless of specific observations. Such a model would allow for fires in areas not observed due to clouds or below-detection-limit. The vital part of such exercise would be the FRP observation operator constructed in this paper.