New fire diurnal cycle characterizations to improve fire radiative 1 energy assessments made from MODIS observations

Accurate near real time fire emissions estimates are required for air quality forecasts. To date, most 18 approaches are based on satellite-derived estimates of fire radiative power (FRP), which can be 19 converted to fire radiative energy (FRE) which is directly related to fire emissions. Uncertainties in 20 these FRE estimations are often substantial. This is for a large part because the most often used low- 21 Earth orbit satellite-based instruments such as the MODerate-resolution Imaging Spectroradiometer 22 (MODIS) have a relatively poor sampling of the usually pronounced fire diurnal cycle. In this paper we 23 explore the spatial variation of this fire diurnal cycle and its drivers using data from the geostationary 24 Meteosat Spinning Enhanced Visible and Infrared Imager (SEVIRI). In addition, we sampled data from 25 the SEVIRI instrument at MODIS detection opportunities to develop two approaches to estimate 26 hourly FRE based on MODIS active fire detections. The first approach ignored the fire diurnal cycle, 27 assuming persistent fire activity between two MODIS observations, while the second approach 28 combined knowledge on the climatology of the fire diurnal cycle with active fire detections to 29 estimate hourly FRE. The full SEVIRI time-series, providing full coverage of the fire diurnal cycle, were 30 used to evaluate the results. Our study period comprised of three years (2010–2012), and we 31 focussed on Africa and the Mediterranean basin to avoid the use of potentially lower quality SEVIRI 32 data obtained at very far off-nadir view angles. We found that the fire diurnal cycle varies 33 substantially over the study region, and depends on both fuel and weather conditions. For example, 34 more “intense” fires characterized by a fire diurnal cycle with high peak fire activity, long duration 35 over the day, and with nighttime fire activity are most common in areas of large fire size (i.e., large 36 burned area per fire event). These areas are most prevalent in relatively arid regions. Ignoring the 37 fire diurnal cycle generally resulted in an overestimation of FRE, while including information on the 38 climatology of the fire diurnal cycle improved FRE estimates. The approach based on knowledge of 39 the climatology

Landscape fires are a global phenomena, and the annually burned area is roughly equivalent to the 49 area of India (Giglio et al., 2013). Most burned area occurs in the savannas of Africa, Australia, and 50 South America, where they shape ecosystem dynamics and due to their scale are an important 51 source of global emissions of (greenhouse) gases and aerosols (Seiler and Crutzen, 1980;Bowman et 52 al., 2009). Fires affect air quality both locally and regionally (Langmann et al., 2009), with recent 53 studies putting mortality rates over 300000 annually due to exposure to smoke (Johnston et al.,54 2012). 55 56 Traditionally, the amount of dry matter burned and quantity of trace gases and aerosols emitted 57 have been calculated using biome-specific fire return intervals and estimates of the total amount of 58 biomass as well as the fraction of biomass burned, the combustion completeness (Seiler and Crutzen, 59 1980). Thanks to new satellite input streams that better capture the spatial and temporal diffuse 60 nature of fires, the estimated fire return intervals have been replaced by direct estimates of monthly, 61 weekly or even daily area burned (Roy et  Atmospheric Composition and Climate III (MACC-III). GFAS is currently using fire observations from 83 the polar orbiting MODerate-resolution Imaging Spectroradiometer (MODIS) instruments aboard the 84 Terra and Aqua satellites (Giglio et al., 2006). Due to their relative proximity to the Earth, the Terra 85 and Aqua MODIS instruments have a high sensitivity to even quite low FRP (smaller and/or lower 86 intensity) fires. However, they only provide four daily observations under ideal conditions but less 87 when optically thick clouds are present, which may not be enough to fully characterize how fire 88 activity varies over the course of the day. Observations with a much higher temporal resolution are 89 available from geostationary satellites. However, as a consequence of their geostationary position, 90 these satellites individually do not provide global data and are located at greater distance from the 91 Earth resulting in typically coarser pixel sizes than polar orbiting instruments. Since the threshold of 92 detectability of a fire is not only dependent on the instrument but also a function of the pixel area, 93 geostationary sensors have a higher minimum FRP detection limit ( Previous studies found that fire activity shows a strong diurnal cycle, and one that is both temporally 98 and spatially variable (Prins and Menzel, 1992;Giglio, 2007;Roberts et al., 2009). The ideal set-up to 99 detect fires would be a high temporal resolution imaging system, sensitive to even the lowest FRP 100 fires, and providing global coverage, but due to the limitations of the orbital characteristics outlined 101 above there is no single platform available to provide this. Therefore the estimation of FRE at a global 102 scale is difficult, with polar orbiting satellites lacking observations to accurately represent the fire 103 diurnal cycle and geostationary satellites being limited to certain regions of the globe and omitting 104 the (rather common) low FRP fires. The SEVIRI instrument aboard the geostationary Meteosat Second Generation (MSG) series of 171 satellites provides coverage of the full Earth disk every 15 min in 12 spectral bands (Schmetz et al., 172 2002). The Meteosat SEVIRI FRP-PIXEL product contains per-pixel fire radiative power data along with 173 FRP uncertainty metrics produced from the full spatial and temporal resolution SEVIRI observations 174 (Wooster et al., 2015). The FRP-PIXEL product is produced using an operational version of the 175 geostationary Fire Thermal Anomaly (FTA) algorithm described in Roberts and Wooster (2008), and 176 the product and its performance characteristics are described in Wooster et al. (2015).  193 194 The two MODIS sensors on board of the Terra and Aqua satellites provide 4 daily overpasses in most 195

MODIS detection opportunity
Earth locations, albeit sometimes at view angles in excess of 45° where the product performance is 196 somewhat degraded . At nadir the MODIS thermal channel spatial resolution is 197 1 km, but decreases away from the swath centre . We used the MODIS MOD03 198 (Terra) and MYD03 (Aqua) geolocation products to determine where and when MODIS data were 199 collected within the SEVIRI Earth disk. As cloud cover may further limit the fire detection opportunity, 200 we used the data quality and cloud cover information of the MOD14 and MYD14 active fire products 201 to filter out grid cells with cloud cover (Giglio et al., 2006). Here we define the detection opportunity 202 as the ability to make unobstructed observations, and the MODIS detection opportunity was derived 203 by combining the MOD03, MYD03, MOD14 and MYD14 products, combining overpass times and 204 cloud cover. We used MODIS data from Collection 5. Like the SEVIRI data, these data were rescaled 205 to hourly 0.1° resolution with the GFAS gridding algorithm and archived in MARS (Kaiser et al., 2012). 206 The data were archived for the Terra and Aqua satellites separately. The original MODIS swath data 207 can be downloaded from NASA at http://reverb.echo.nasa.gov. 208 209

MODIS Land cover
The dominant land cover type was derived from the MODIS MCD12C1 land cover product, which 212 provides 0.05° spatial resolution annual information on land cover (Friedl et al., 2002). We calculated 213 the dominant land cover type for each grid cell as the land cover type that on average covered the 214 largest fraction during the study period (2010-2012). The University of Maryland (UMD) classification 215 scheme was used, and data was rescaled to 0.1° resolution. Because we only considered Africa and 216 the Mediterranean basin in this study, and because in some land cover classes very few fires 217 occurred, we could merge some land cover classes that were of relatively little importance for our 218 study. Specifically, all forest classes within the tropics were binned into the tropical forest class, while 219 extratropical forests were all labelled temperate forest. Open and closed shrublands were merged 220 into one shrubland class, and urban and built-up, barren or sparsely vegetated into grasslands. 221 222 223 224

Fire size
Here we define the fire size for a certain grid cell as the mean burned area per fire event, weighted 225 by their total area burnt (when calculating the mean, a fire event burning 100 km 2 is assigned one 226 hundred times the weight of an event burning 1 km 2 ). The MODIS MCD64A1 burned area product 227 provides daily mapped estimates of global burned area ). We applied the methods 228 described by Archibald and Roy (2009) to derive a global mean fire "size" (area) map using data over 229 our study period (2010-2012). We made one modification to the approach described by Archibald 230 and Roy (2009): we assumed that two neighbouring burned area grid cells only belonged to the same 231 fire if the burn date was no longer than two days apart (instead of 8 days). We believe that overall 232 this provides a better estimation of the fire size in our study region, as the vast majority of fires here 233 are grass fires, occurring outside tropical forest zones and thus spreading relatively fast while being 234 relatively less often obstructed by cloud cover. Consequently, the uncertainty in burn date is 235 generally low in our study region (Giglio et al., 2013) and so the two day thresholds was deemed 236 more appropriate. 237 238

240
Our overall goal within GFAS is to provide hourly estimates of FRE at 0.1° spatial resolution, based on 241 the limited number of MODIS overpasses available each day at each grid cell location. This limited 242 number of daily MODIS observations, in combination with the often pronounced fire diurnal cycle, 243 are the major obstacles in providing the required output. We first studied the spatiotemporal 244 variation of the fire diurnal cycle, in an attempt to understand its variability (Sect. 3.1). Then, we 245 explored the way the fire diurnal cycle affects active fire detections made at the MODIS sampling 246 times (Sect. 3.2). Using this knowledge we explored a new method to parameterize the fire diurnal 247 cycle, and compared results to a modelling approach in which the fire diurnal cycle is ignored. 248 Building on the work of Freeborn et al. (2009Freeborn et al. ( , 2011, to drive the modelling approaches we used 249 SEVIRI data sampled at the MODIS detection opportunities (according to the hourly data 250 representation introduced above), rather than actual MODIS observations (Sect. 3.2). This allowed us 251 to focus on the issue of diurnal cycle sampling rather than simultaneously dealing with the issue of 252 MODIS and SEVIRI's differential sensitivity to active fires (Freeborn et al., 2009 derived the "virtual MODIS" fire product that has the temporal sampling of SEVIRI and the sensitivity 290 to fire of MODIS. They found that the full-width at half maximum height (i.e., the width of the diurnal 291 cycle at half of the daily FRP maximum value) of the diurnal cycles derived from the SEVIRI and the 292 "virtual MODIS" datasets are very similar, it is the amplitude and the full-width at base height of the 293 two cycles, which are more different. In terms of total FRE emitted, the latter is of less importance, 294 here we followed Freeborn et al. (2011) in assuming that the diurnal cycles from SEVIRI and MODIS 295 are sufficiently similar. 296 297 In order to visualize the spatial distribution of the fire diurnal cycle, the climatological diurnal cycle 298 was calculated for each grid cell depending on the mean parameter values of the Gaussian function 299 weighted for daily FRE, including all days of fire activity during the study period without cloud 300 obscurance. To get a better understanding of the drivers of the fire diurnal cycle these results were 301 compared to land cover and aspects of the fire regime (fire size, total annual FRE, and the annual 302 number of days with fire activity), see Sect. 2. 303 304

Sampling SEVIRI data at MODIS detection opportunities
During the data assimilation, SEVIRI observations at MODIS detection opportunities were used to 307 drive the models. Here, SEVIRI observations for a given hour t are given by and SEVIRI fraction 308 of observed area by ; in the same way, observations of the MODIS instruments are given by 309 and . Therefore input for the models, i.e., the SEVIRI observations at MODIS 310 detection opportunity times ( and ) for a given hour t are given by: 311 312 (2) insights in the ability to get overall budgets right. In a similar way the two spatial resolutions provide 403 information on the ability of the model to resolve high resolution distribution of fire activity and 404 more regional model performance. When calculating Pearson's r between the hourly model results 405 and SEVIRI data we included cloud free days only, while the daily model results were compared to 406 the full cloud cover corrected SEVIRI times series, using a simple cloud cover correction method 407 explained below. 408 409 Finally, we compared daily regional aggregated FRE time-series for several study regions of the two 410 modelling approaches and SEVIRI. In order to compare daily regional time-series to the model, a 411 cloud cover correction needed to be carried out. Since persistent cloud cover is relatively rare during 412 the burning season in most parts of Africa, we chose a simple gap filling approach where the value of 413 the last cloud-free observation is assumed to be valid until the next cloud-free observation, which is 414 consistent with the observation gap filling in the daily GFAS. First, we present the results related to the spatial distribution of the fire diurnal cycle, and assess the 421 impact of the fire diurnal cycle on active fire observations made at the times of the MODIS overpass. 422 The spatial distribution of the fire diurnal cycle was explored by optimally fitting a Gaussian function 423 to the hourly, 0.1° SEVIRI FRP time-series. Reasonable overall correlations between SEVIRI and the 424 optimally fitted Gaussian functions were found (Pearson's r = 0.55; weighted mean for all grid cells), 425 while a Gaussian was better able to describe hourly fire activity in regions where fires could spread 426 over large areas and were characterized by high (e.g., for fire size < 10 km 2 r = 0.51, for 10-50 427 km 2 r = 0.56, and > 50 km 2 r = 0.63). This is likely to be in part related to the fact that characterisation 428 of the diurnal cycle of "smaller" fires will be more affected by instances of SEVIRI failing to detect one 429 or more of their fire pixels than would larger fires, hence introducing more variability into the 430 apparent diurnal cycle. Whilst the SEVIRI FRP-PIXEL product shows apparently the best performance 431 metrics of any current geostationary fire product derived from SEVIRI data ( appears to drop to zero, or near zero, every night. This is a consequence both of the actual FRP from 440 the fire significantly diminishing at this time due to, for example, fuel moisture, wind and other 441 ambient atmospheric conditions being far less conducive to intense fire activity by night than by day 442 (Hély et al., 2003;Gambiza et al., 2005), but also because some fire pixels will have FRPs below the 443 SEVIRI active fire pixel detection limit of around 40 MW (Roberts and Wooster, 2008). At the start of 444 the following day, fuel moisture and ambient atmospheric conditions generally become more 445 conducive to fire, and fire intensities and rates of spread typically increase once more such that more 446 of the fire-affected pixels breach the SEVIRI FRP detection limit ). 447 448 The results shown in Fig. 1 indicate that high FRP, relatively long-lived fire activity is rather well 449 described by a Gaussian function, even at this 0.1°, hourly resolution which is significantly higher 450 than that used in previous studies fitting Gaussian descriptors to remotely sensed measures of active 451 fire activity. At the same time, it also became apparent that observations from a MODIS-type 452 sampling interval are not always representative of the daily fire activity. The inability of the MODIS 453 sampling times to provide representative observations is well illustrated in Fig. 1a, where on the first 454 day of the fire the morning and afternoon time of MODIS sampling slot almost completely missed the 455 fire activity. 456 457 The shape of the Gaussian function, and consequently the parameters: SD (σ) peak fire activity (ρ peak ) 458 and corresponding hour (h peak ), varied considerably over the individual days (Fig. 1). For example, in 459 the African savanna grid cell (Fig. 1c), fire activity on day 3 continued longer in the afternoon 460 compared to day 4, when conditions some-how became less favourable for maintaining the fire 461 earlier in the afternoon. Therefore, the shape of the fire diurnal cycle is dependent on 462 spatiotemporal scale. When diurnal fire activity was aggregated over several days, which can be 463 compared to using a coarser temporal or spatial resolution, increased as compared to fire activity for 464 individual days (compare Fig. 1a with b, and Fig. 1c with d). The relatively narrow diurnal cycle of the 465 individual days have varying peak hours of fire activity, so that the sum of it is wider than any of the 466 individual cycles and the peak fire activity less pronounced. 467 468 In addition to an observed variability in the fire diurnal cycle seen on different days, we found 469 distinct spatial patterns in the optimal fitted Gaussian parameters (Fig. 2). Some of these patterns 470 were similar for the different parameters. In particular, there were zones of generally more intense 471 fires (e.g., South Sudan, northern Central African Republic, Botswana, Namibia and parts of Angola 472 and the Democratic Republic of Congo (DRC)), showing relatively high values of ρ peak , ρ base and σ 473 compared to other zones where values for all three parameters were relatively low (e.g., Zambia, 474 Mozambique, Tanzania, Nigeria and Cameroon). On top of this general pattern, a clear gradient is 475 visible as you move from drier to more humid regions, seen most clearly when moving from Namibia 476 via Angola to DRC. In more humid savannas, when fuel conditions were optimal, high ρ peak values 477 could be reached but fire duration over the day was generally short and night time FRP values were 478 more likely to fall below the SEVIRI FRP detection threshold (Fig. 2). h peak varied considerably over the 479 study region, with areas showing most fire activity late in the afternoon generally in more humid or 480 forested regions but also in some more arid regions (Fig. 2d). 481 482 Table 1 shows the land cover-averaged values and SD of the results presented in Fig. 2. In addition 483 we calculated the ratio of the mean SEVIRI FRP at MODIS daytime detection opportunities to the 484 maximum daytime FRP ρ peak . These results were used in the climatological modelling approach that 485 combined the fire diurnal cycle climatology with observations made at the MODIS sampling times to 486 derive the daily fire diurnal cycle predictions (Sect. 3.5). More intense fires with long duration and 487 high peak values were associated with fires in shrublands, savannas and grasslands, while a more 488 pronounced fire diurnal cycle was present in more humid woody savannas or tropical forests. For σ, 489 ρ peak and ρ base SD was typically about half of the average value, while SD of h peak was largest for 490 temperate forests, shrublands and grasslands. The ratio of mean daytime FRP made at the MODIS 491 sampling times and ρ peak was relatively constant for various land cover types with ρ peak generally 492 about three times as large as the mean FRP at the daytime MODIS detection opportunities (Table 1). 493 494 In order to better understand the spatial distribution of the fire diurnal cycle features, we studied 495 characteristics of the fire regime that were expected to be related to fuel properties and the diurnal 496 cycle (Fig. 3a, c and d). To guide the interpretation we have included a land cover map, partly 497 governing fuel loads, in Fig. 3b. Annual emitted FRE varied widely over the study region, and highest 498 values were found in the savannas and woody savannas (compare Fig. 3a with b) and coincided with 499 regions of large fire size and/or a high number of annual fire days (compare Fig. 3a with c and d). 500 Similarities with characteristics of the fire diurnal cycle were also found, the earlier mentioned zones 501 of generally more intense fires (high values of ρ peak, ρ base and σ) often coincided with regions of large 502 fire size (Figs. 2a-c and 3c). In the more humid tropical areas, high ρ peak values occurred in areas of 503 relatively large fire size and/or a high number of annual fire days (Figs. 2a and 3c, d). 504 505 The relative fraction of FRE emitted on days that SEVIRI data sampled at MODIS observation times 506 did not observe active fires is an important factor affecting model performance, and showed similar 507 spatial patterns as σ, indicating that duration of fires over the day plays an important role (Figs. 2c 508 and 4a). In addition, the geographical location and cloud cover during the burning season played a 509 role by affecting the effective number of daily MODIS observations (Fig. 4b). The peak hour of fire 510 activity also played a role, and especially in more humid areas with frequent cloud cover and late 511 afternoon fire activity sometimes over 50% of FRE was emitted on days without any SEVIRI active fire 512 detections at MODIS detection opportunities (compare Figs. 2d and 4a). The most important biomass 513 burning regions were typically characterized by relatively long fire duration over the day (Fig. 2c) and 514 the effect of omission of active fires on continental scale FRE estimates was therefore relatively low 515 (cf. Fig. 3a, 4a and 5). However, frequent omission of relatively small fires of short duration may 516 strongly affect FRE estimates for some regions (Fig. 5). These results clearly demonstrate the value of 517 the data provided by the very high temporal resolution geostationary systems, even though they are 518 unable to resolve and detect fire pixels as low in FRP as those from polar orbiters (Roberts and 519 Wooster, 2008). 520 521

523
To evaluate the two modelling approaches that estimated FRE from SEVIRI data only at the MODIS 524 sampling times we started with comparing the spatial distribution of mean estimated FRE for each 525 method with the cloud corrected SEVIRI FRE calculated using the entire hourly, 0.1° SEVIRI FRP 526 dataset (Fig. 5). The persistent approach resulted in a general overestimation of FRE, while the 527 climatological approach showed overall good performance in terms of total estimated FRE when 528 compared to the full SEVIRI dataset. Moreover, the more narrow distribution of modelled FRE as a 529 fraction of SEVIRI FRE by the climatological approach as opposed to the persistent approach suggests 530 that results are not only more accurate but also more precise (Fig. 5). While this reflects the general 531 pattern, the performance bias was not homogeneous over the region. The persistent approach 532 showed best results for regions with long daytime fire durations (i.e., large σ) and with a late peak in 533 fire activity; and although performing generally better, the climatological approach showed a general 534 underestimation for areas of relatively late peak fire activity (compare Figs. 2 and 5). To a certain 535 extent these regional differences correspond to the distribution of the different land cover types 536 (Table 2). For example, for temperate forests and shrublands the persistent modelling approach 537 showed notably better comparison to the FRE derived via the entire SEVIRI dataset, while the 538 climatological modelling approach overestimated FRE. 539 540 Equally important as the absolute FRE estimates shown in Fig. 5 and Table 2 are their temporal  541 dynamics. Figure 6 shows regional daily budgets for several study regions with different geographical 542 positions and land cover. Similar to the results in Fig. 5, we found a general overestimation by the 543 persistent approach, and better overall estimation by the climatological approach. Overestimation of 544 the persistent approach was occurring mostly in the tropics (e.g., Nigeria and DRC), where also 545 stronger day to day variability was observed as compared to that derived with the complete SEVIRI 546 data or the other modelling approaches (Fig. 5). The climatological approach showed a small delay in 547 FRE estimations compared to the complete SEVIRI dataset. 548 549 To further test the ability of the two modelling approaches to allocate FRE to the individual grid cells 550 at the right moment in time, correlation coefficients were calculated. Table 3 shows Pearson's r  551 between SEVIRI and the two modelling approaches at four spatiotemporal resolutions (0.1° and 1° 552 spatial and hourly and daily temporal resolution). A striking increase in correlation was observed 553 when aggregating model results both temporally or spatially. Freeborn et al. (2009Freeborn et al. ( , 2011 previously 554 demonstrated the value of such spatial aggregation when deriving relationships between SEVIRI and 555 MODIS datasets, and this technique is currently used within the near real-time SEVIRI FRP-GRID 556 products produced by the LSA SAF from the SEVIRI FRP-PIXEL data (Wooster et al., 2015). At 0.1° 557 resolution the best correlations were found for shrublands and savannas while for aggregated data 558 best performance was found for woody savannas and savannas. At hourly resolution, the 559 climatological approach generally performed better than the persistent approach. However, at 0.1° 560 daily the persistent approach performed best while at 1° spatial resolution the persistent and 561 climatological approaches did equally well. 562 563 Here we start discussing the spatial distribution of the fire diurnal cycle, and its drivers (Sect. 5.1). 585

Discussion
Building on previous work, we explored two new methods to estimate hourly FRE in near real time 586 from observations made by SEVIRI at MODIS detection opportunities. The results illustrate how 587 MODIS observations might be used to calculate hourly FRE, and where errors can be expected due to 588 the diurnal cycle and the limited temporal sampling provided by MODIS (Sect. 5.2). 589 590

Exploring the fire diurnal cycle using a Gaussian function
The fire diurnal cycle characteristics were explored by fitting of a Gaussian function to the hourly 593 SEVIRI time-series. Vermote et al. (2009) and Ellicott et al. (2009) found that at a 0.5° monthly 594 resolution the fire diurnal cycle can be described by a Gaussian function, using MODIS observations 595 to resolve the unknown parameters. They choose the spatiotemporal size of the study regions such 596 that a statistical representative number of fires and MODIS FRP detections were included, and the 597 observations covered the full range of MODIS view angles -since the sensitivity of MODIS to fire 598 depends upon this . Although later work showed that in fact fire activity may 599 be somewhat skewed in the afternoon, here we found that even at a high spatiotemporal resolution 600 (0.1°; hourly) a Gaussian function provides a fairly robust description of the fire diurnal cycle. 601 However, at 0.1° hourly resolution, SEVIRI data sampled at the MODIS detection opportunities does 602 not always provide enough information to adequately depict fire activity for an individual grid cell 603 and day (Fig. 1). Moreover, the spatiotemporal scale at which we observe the fire diurnal cycle has a 604 significant impact on its shape. When moving to a coarser spatiotemporal resolution, the shape of 605 the diurnal cycle likely becomes wider, with less pronounced peaks. This is mostly a consequence of 606 the spatiotemporal variation in hour of peak fire activity of the individual fires or fire days (Fig. 1). 607 Therefore, typical values of the parameters of the Gaussian found in this study (Fig. 2)  Although the shape of the "average" fire diurnal cycle is scale dependent, regional patterns in the 613 diurnal cycle characteristics (Fig. 2) remain similar over different scales, and therefore we found 614 similar land cover dependent characteristics as previous studies. For example, shrublands and 615 grasslands generally faced drier conditions when burning than did woody savannas or tropical forest, 616 and therefore fire activity typically continued longer over the day and the hour of peak fire activity 617 was generally located later in the afternoon ( Fig. 2; Table 1 The three parameters determining the shape of the Gaussian can be used to visualize the spatial 624 distribution of the fire diurnal cycle. The daily FRP-maximum is given by ρ peak , fire duration over the 625 day by σ, and the baseline FRP by ρ base . Similar spatial patterns were found for all three parameters 626 mentioned above (Fig. 2a, b and c). This indicates that there are zones of generally more "intense" 627 fires with high ρ peak , large σ and higher ρ base , while other zones are characterised by lower intensity 628 fires. In land cover classes where most of the fires were grass fuelled (grasslands, savannas and 629 woody savannas), a considerable part of the spatial variation in fire diurnal cycle could be explained 630 by fire size (see Sect. 2.4; Figs. 2 and 3). Large fires were often found in frequently burnt and/or more 631 arid areas (Fig. 3a) where high fuel connectivity, low fuel density and low fuel moisture allow 632 relatively fast moving fires with large fire fronts to form (Hély et al., 2003;Sow et al., 2013). Besides 633 fire size and land cover, part of the variability in the fire diurnal cycle could be explained by a 634 gradient in diurnal weather conditions. Grass fuelled large fires were also common in the more 635 humid savannas of southern Africa, but here nighttime weather conditions appear to become rather 636 unfavourable for fire ( Figs. 2b and 3c). In humid savannas ρ peak values were not solely associated with 637 large fire size, but also with areas showing a high number of annual days with fire activity and may be 638 explained by several relatively small fires burning at the time. The high number of fire days may 639 indicate a larger number of fire ignitions and/or that fires are spreading at a slower rate due to the 640 more pronounced fire diurnal cycle, higher humidity, or higher fuel density (Hély et al., 2003;Sow et 641 al., 2013). Finally, in the Mediterranean basin the relatively low fire return period, and consequently 642 higher fuel density, may also cause relative intense fires with long duration over the day (Fig. 2;  643 Archibald et al., 2013). 644 645 The peak hour of fire activity found here corresponds to the moment of day at which 50% of the total 646 FRE has been emitted (assuming ), and it did not always correspond to the peak hour 647 of fire activity found by previous studies (Fig. 2d;  to a part of the actual fire resulting in large variation in h peak between neighbouring grid cells ( Fig. 2d  653 and Table 1). 654 655 656   657 Data assimilation and two modelling approaches, were used to estimate hourly FRE from SEVIRI FRP 658 data sampled at the times of MODIS detection opportunities. Here we start discussing the 659 performance of the different methods with respect to their total FRE estimates and daily regional 660 FRE estimations. Then we discuss the more uncertain model performance at higher spatiotemporal 661

Model performance and the MODIS sampling design
resolutions. 662 663 The persistent approach is comparable to a direct hourly extension of the current GFAS methods 664 (Kaiser et al., 2012) observations due to orbital convergence will typically be somewhat earlier or later in the afternoon 672 and may therefore lower the FRE estimation. In the persistent approach, missing nighttime 673 observations may cause an overestimation and missing daytime observation an underestimation of 674 daily FRE, resulting in erroneous regional day-to-day variations in FRE estimates in the tropics (Fig. 6). 675 Following previous research, we found that due to the spatiotemporal variation of the fire diurnal 676 cycle FRE was overestimated more for some land cover types than for others (Table 2; Freeborn et  677 al., 2011). Land cover classes that typically showed longer fire durations (Fig. 2c) with peak fire 678 activity later in the afternoon (Fig. 2d) were not as much overestimated as land cover classes with 679 more pronounced fire diurnal cycles (Figs. 5 and 6; The climatological approach showed better performance in terms of absolute FRE estimations, while 686 also better able to reproduce its spatial variability (Fig. 5). In contrast to the persistent approach, the 687 hourly predictions were based on the last 24h of fire activity, enabling more realistic gap filling during 688 periods without observations. This resulted in an advantage during periods of cloud cover or missing 689 observations due to the satellite orbits, but because of the low number of actual daily observations 690 the climatological approach had the tendency to continue predicting fire activity after fires had 691 ceased, seen as a small delay in the signals in Fig. 6. 692 693 An additional criterion to evaluate the model performance was the correlation between the 694 modelling approaches and the SEVIRI data at different spatiotemporal scales. Correlation between 695 the modelled and SEVIRI time-series improved considerably when moving from hourly to daily 696 resolution, showing that the models were better able to estimate daily budgets than the distribution 697 of fire activity over the day. These differences may be explained by the inability of the models to 698 correctly estimate the hour of peak fire activity, a fire diurnal cycle that is not well represented by a 699 Gaussian function, or in the case of small fires the fire diurnal cycle may not be fully detected by the 700 SEVIRI instrument. Because of the large day-to-day variation in the fire diurnal cycle and the FRP 701 measurements limited to the time of the MODIS overpasses, the individual FRP observations have a 702 low precision (i.e., large random error) and omission (i.e., non detection) of fires is frequent (Figs. 1  703 and 4), resulting in low correlation at high spatiotemporal scales (Table 3). Because fires rarely occur 704 on their own and generally form part of a regional pattern (Bella et al., 2006), the correlation 705 increased considerably when accumulating results to a 1° spatial scale. For the same reason model 706 performance was found to be best in savannas and woody savannas, where the highest number of 707 fires occur and the sample size is thus largest, or in areas of large fire size where omission was 708 relatively low. Model performance was therefore best when optimal burning conditions were 709 reached, often coinciding with the peak of the burning season. Because often only a reasonably large 710 sample of observations made at the MODIS detection opportunities is actually representative of fire 711 activity in a certain region, the added value of the 0.1° spatial resolution (e.g., GFASv1.1/1.2) is 712 somewhat limited compared to a coarser 0.5° spatial resolution (e.g., GFASv1.0). 713 714 Overall, using the climatological approach resulted in the best model performance, although in 715 specific cases using the persistent approach showed better results. 1. We considered various drivers of the spatial distribution of fire diurnal cycle: dominant land 775 cover, fire size, annual number of fire days, and diurnal climate conditions and found that all 776 played a role. The strong relation between fire size and fire diurnal cycle for grass fuelled 777 fires, and the climatic gradient in diurnal cycle, indicate that using fuel characteristics rather 778 than land cover alone to characterize the fire diurnal cycle provides a potential pathway to 779 improve these estimates. Here we showed that this information can partly be obtained by 780 studying the fire characteristics, such as fire size, which are contained within the remote 781 sensing data themselves. 782 2. Ignoring the fire diurnal cycle may cause structural errors in FRE estimates, and likely results 783 in a general overestimation of FRE due to the timing of the MODIS overpasses. The errors 784 vary regionally, mostly due to variations in the fire diurnal cycle, while results get more 785 accurate at higher latitudes due to the increasing number of daily MODIS detection 786 opportunities caused by orbital convergence. 787 3. Due to the large day-to-day variations in the fire diurnal cycle at the grid cell level, and the 788 scarce number of MODIS observations of any one location per day, daily FRP fields calculated 789 from observations made at MODIS detection opportunities are characterized by low 790 precision (i.e., observations are not representative for daily fire activity) and high omission 791 (i.e., non observation of fires). Therefore a sufficiently large sample size of MODIS 792 observations is required to accurately estimate FRE, as shown earlier by Freeborn et al. 793 (2011). In zones of frequent fires, where fires are generally part of a regional biomass 794 burning pattern, model performance greatly improved when moving to a coarser scale, 795 increasing the sample size. Model performance was also considerably better for zones of 796 relatively large fires that were characterized by low omission. Production of emission 797 inventories at very high spatiotemporal resolution using data from a limited number of low-798 Earth orbit satellite observations may therefore provide somewhat restricted added value 799 compared to those derived at coarser spatiotemporal scales. 800 4. Relative overrepresentation of day-or nighttime FRP observations may cause large day to 801 day variations in estimated FRE when the diurnal cycle is ignored. 802 5. The way we observe the fire diurnal cycle is scale dependent, mostly because of the large 803 variation in fire diurnal cycle, even within the same grid cell between different days. 804 805 We recommend implementing the climatological model within GFAS in Copernicus Atmosphere 806 Services in order to improve global and regional FRE estimates and further reconcile emission 807 estimates from the various different inventories currently available. 808 809 Acknowledgements. 810 We like to thank Samuel Remy at ECMWF for processing MODIS and SEVIRI data, and the data 811 providing agencies: NASA and the EUMETSAT LSA SAF for making their data publicly available. This 812