PeatFire: an agent-based model to simulate fire ignition and spreading in a tropical peatland ecosystem

Keywords: agent-based model, burnt area, degraded habitat, Indonesia, peatland, tropical peat fire, watertable depth, wildlife reserve.

Tropical peatlands act as reservoirs of fresh water, which under natural condition can moderate water levels, maintain water flows and buffer against salt water (Wösten et al. 2008). They also form some of the richest concentrations of carbon reserves on the planet (Page Siegert et al. 2002; Ballhorn et al. 2009; Page et al. 2011; Hirano et al. 2012), and they are recognised as biodiversity hotspots (Morrogh-Bernard et al. 2003; Posa 2011; Posa et al. 2011). Despite their importance, tropical peatlands remain a neglected ecosystem because of high conversion rates of these ecosystems into man-made ecosystems (Cattau et al. 2016).

Peatlands in south-east Asia cover ~25 million ha, comprising ~63% of the global tropical peatland carbon (Wösten et al. 2008; Page et al. 2009a; b; Page and Hooijer 2016). Over the past two decades, more than half of Indonesian peatlands have been transformed from a pristine state of perpetual moistness and frequent surface water inundation to a degraded state, which is characterised by a relatively dry and exposed soil profile. Mostly, peatland degradation is caused by the widespread construction of drainage canals and deforestation associated with land-use change (Miettinen et al. 2011, 2013; Margono et al. 2014; Adrianto et al. 2019). This situation has increased emissions from oxidation of exposed peat (Miettinen et al. 2017), as well as the frequency of peat fires (Page and Hooijer 2016). It is now widely known that peat fires have severe impacts on emissions to the atmosphere, human health, the economy and biodiversity (Jones 2006; Taylor 2010; Posa 2011; Posa et al. 2011; Johnston et al. 2012; Marlier et al. 2013; Page et al. 2013; Hayasaka et al. 2014; Crippa et al. 2016; Uda et al. 2019).

Protecting vulnerable peatland ecosystems from fires in Indonesia is a high priority (Cochrane 2009; Page et al. 2013; Page and Hooijer 2016; Goodman and Robinson 2019). Past research demonstrates that extreme burning events in Indonesia are induced by drought conditions associated with El Niño and/or positive Indian Ocean Dipole conditions that disrupt the normal monsoonal rainfall patterns across the maritime continent (Field et al. 2015; Spessa et al. 2015; Pan et al. 2018). Furthermore, deforestation and extensive peat drainage for agriculture and plantation establishment have exacerbated the impact of climatic drivers of peatland fires through non-climatic factors such as increased ignition rates (due to more intensive land use), increased evaporation (due to reduced canopy cover) and lowering of the watertable depth leading to increased desiccation of surface and subsurface peats (Page and Hooijer 2016; Adrianto et al. 2019; Baker and Spracklen 2019; Mezbahuddin et al. 2019; Nikonovas et al. 2019).

Patterns in peat fire occurrence in Indonesia, including the climatic, ecological and socioeconomic factors causing those patterns have been extensively studied (Page et al. 2009a; Jones 2006; van der Werf et al. 2008; Wösten et al. 2008; Field et al. 2009; Miettinen and Liew 2010; Spessa et al. 2010; Marlier et al. 2013; Miettinen et al. 2013; Page et al. 2013; Toriyama et al. 2014; Hayasaka et al. 2014; Cole et al. 2015; Thorburn and Kull 2015; Cattau et al. 2016; Yong and Peh 2016; Adrianto et al. 2019; Mezbahuddin et al. 2019; Nikonovas et al. 2019). However, the mechanistic processes linking tropical peat fire and its causal elements and processes are still not well understood. Most studies to date have focused on the broad-scale patterns of fire activity (burnt area) in relation to weather conditions, peat hydrology or land-use classes. For instance, Fanin and van der Werf (2017), Field et al. (2015) and Spessa et al. (2015) reported a non-linear relationship between rainfall and fire activity. Taufik et al. (2017) demonstrated that hydrological drought was highly correlated with burning events. Miettinen et al. (2013) highlighted how peatland deforestation, drainage and conversion to agriculture correspond to higher fire frequencies in Jambi province, Indonesia. Adrianto et al. (2019) reported similar mechanisms and findings for Riau province, Indonesia. These top–down studies, which are based on statistical modelling, have provided useful insights into the relative importance of different factors driving peat fires and their interactions at regional scales, and can be used for prediction of fires at broad spatiotemporal resolutions. Nonetheless, the management and prediction of peat fires at local scales require quantitative models describing the processes controlling fires and their interactions (Page and Hooijer 2016), which is not possible using a top–down statistical-based approach.

Agent-based models (ABMs) belong to a category of ‘bottom–up’ simulation models that simulate the actions and interactions of autonomous agents (individual or collective groups) within a defined system (Grimm 1999; Grimm and Railsback 2005). This approach can derive insights and assess emergent system-level behaviours (Abar et al. 2017). ABMs have been widely used in different scientific disciplines such as conservation ecology (Imron et al. 2011; Heinonen et al. 2014), agriculture (Valbuena et al. 2010) and climate change mitigation (Purnomo et al. 2013; Dislich et al. 2018), where the research questions involve the interaction of biophysical condition and human activities.

The problem of peat fires in Indonesia lends itself to an ABM approach because ignitions and fire spread are controlled by both biophysical factors (e.g. peat hydrology and precipitation) and anthropological factors (e.g. human-caused ignitions, land-use and land-cover change). Previous applications of ABMs in Indonesia exist, notably to examine the impact of land-use choices on deforestation (Purnomo et al. 2013) and carbon sequestration (Dislich et al. 2018); however, an ABM approach focusing on the peat fire problem itself has not yet been developed.

Using a case study of rural peatland area in South Sumatra, this paper describes the PeatFire model, an ABM that captures phenomenologically key biophysical processes and human activities triggering fire occurrences. The paper also presents the results of a series of simulations we performed to assess model behaviour, sensitivity and accuracy through benchmarking against observed fire data in 2015, which was the most severe fire season recorded in the last two decades (Field et al. 2016). Finally, we present the results of simulation experiments carried out to assess different scenarios on fire mitigation, which enable us to derive evidence-based recommendations for improved tropical peatland fire management at local scales.

The Padang Sugihan landscape, situated between 2°41′59′′S–3°7′20′′S and 104°58′39′′E–105°18′18′′E in the South Sumatra province of Indonesia (Fig. 1), mainly consists of a protected area, the Padang Sugihan Wildlife Reserve (PSWR), dedicated to Sumatran elephants (Elephas maximus sumatrae). The surrounding land uses consist in forest plantations and agricultural areas. Fires occur every year because fire is the cheapest and most effective land-clearing method available to farmers in the region (Cattau et al. 2016; Imron et al. 2018).

Fig. 1.  Map of the study area of Padang Sugihan landscape located in South Sumatra Province, Indonesia. Unburnt patches are shaded green, and burnt patches are shaded red. The map image was taken on 11 November 2015. The colour scheme dark green, green and brown in the inset represents high to low vegetation density.

The following model description conforms with the ODD (Overview, Design concepts, Details) protocol for describing individual- and agent-based models (Grimm et al. 2006, 2010).

The purpose of the PeatFire model is to understand the role of human-induced fire ignition (considering both the capability of ignition and the number of dry days after a rainy day before the next ignition trial), the spread and interaction of above- and belowground fires, and the watertable dynamics for the fire dynamics in a peat forest. Fire data observed in the PSWR in 2015 serve as benchmark for the suitability of the model to reproduce observed patterns of aboveground fires.

Fire ignitions in Indonesian peatlands, like most other tropical ecosystems, are predominately human-caused, with lightning having a negligible role (Field et al. 2009). Hence, for our modelling case study, human activities are assumed to be the only source of peat-fire ignitions. Fires occur above and below ground so long as sufficient biomass is available to burn. Above- and belowground fires can spread horizontally separately, but can also ignite mutually (Huang and Rein 2014; Hu et al. 2018).

We decided to include three entities in the PeatFire model: humans (seen rather as household locations from which human activities can be initiated than individual persons), fire, and grid patches of peatland area. Humans have three state variables, namely their location (loc), the maximum radius within which patches can be reached and thus potentially be ignited (dst), and the actual capability to ignite a patch, described as number of opportunities (frp). Fire has two state variables, namely the location and the fire type, which specifies whether the fire occurs above ground, below ground, or both above and below ground. The patches are characterised by three state variables: (1) the watertable depth (wtd), (2) the aboveground biomass (bia), and (3) the belowground biomass (bib). Both bia and bib are considered as relative values bounded between 0 and 100% (see Table 1 for further details).

Table 1.  List of entities and state variables used in the PeatFire model
μ, mean; σ, standard deviation; λ, number of events

In addition to the state variables, we defined several global variables (Table 2) that are either assumed to be the same for all agents of an entity (for example, the evapotranspiration rate (evp) of patches) or that are basic for some processes (e.g. the wind speed, which defines the speed of the aboveground fire spread).

Table 2.  Global parameters used in PeatFire model

The PeatFire model comprises 100 × 100 grid cells (patches), each representing 210 × 210 m (= 4.41 ha, which corresponds to the areal extent of the study site). The timestep is 1 day, and a typical simulation run lasts 1 year (365 days).

At every timestep, the following submodels are executed: search-and-ignite, fire-burning, fire-spreading and update-watertable (Fig. 2).

Fig. 2.  A summary of processes in the PeatFire model for each time-step. At the beginning of model run, the submodel ‘search-and-ignite’ is called and may start the ignition of fire. The ‘fire-burning’ submodel is called after, and represents the biomass burning on each patch. If the neighbouring patch (on the same or the other layer) is vulnerable to fire, the submodel ‘fire-spreading’ will spread fire to the adjacent patches. Finally, the submodel ‘update-watertable’ will update the watertable value of each patch according to the current precipitation rate and the evapotranspiration rate.

If the sufficient number of dry days after the last rainy day is achieved, a grid cell is randomly selected within the maximum radius around the location of each human. Depending on the fire capability of the household, the dryness index of the patch and the available aboveground biomass, the patch may ignite or not.

In all ignited patches, the available biomass burns according to the burning rate.

At each timestep, all eight neighbouring patches of a burning patch are checked for their vulnerability to fire (defined by the dryness index and the available biomass). Belowground fires spread with the probability psb to the eight neighbouring cells and can trigger aboveground fire. Aboveground fires spread not only isometrically according to the wind speed (see Fig. 3a for details), but can also jump below ground (NB: this is only described by the states of the fire variable type but not as separate fire layers; see also Fig. 3b for details).

Fig. 3.  (a) The mechanism of aboveground spreading is based on the wind speed, which is assumed to go in one direction during simulation. (b) The process of fire ignition and spreading is based on a patch’s susceptibility to fire. Fire starts burning the biomass from the patch surface (aboveground). Aboveground fire can spread to the adjacent patches in the same layer only if aboveground biomass is available and not inundated with water (dark grey, grey or light-blue grid cell). When the belowground layer of the patch is dry and has available biomass (dark grey grid cell), aboveground fire can spread below the surface and start a belowground fire. Belowground fire can spread to the adjacent patches in the belowground layer only if biomass is available and dry (dark grey grid cell) or jump above ground if the cell is vulnerable (dryness and biomass).

At the end of every timestep, the watertable depth value for each patch is updated, taking into account the daily amount of precipitation and the evapotranspiration rate.

The vulnerability of peat soil to fire is determined by the variables watertable depth (wtd) and biomass (bia and bib). These variables represent soil moisture and organic matter content respectively, as existing studies have emphasised (Huang and Rein 2014; Hu et al. 2019; Christensen et al. 2020). The simulation of watertable dynamics and fire ignition follows the principles introduced by Taufik et al. (2017). Thus, the watertable depth is influenced by the weather (increasing during dry days and decreasing during rainy days).

We further adapted the detailed physical model of belowground fire smouldering of He et al. (2009) and simplified the set of rules governing fire spread both downwards and vertically. Aboveground fire spread simplifies the more detailed description of global fire models like the SPITFIRE model (Thonicke et al. 2010; Spessa et al. 2013; Lehsten et al. 2016; Hantson et al. 2017), which in turn is based on Rothermel’s physical model of fire spread (Rothermel 1972; Rothermel and Rinehart 1983).

The spatial pattern of burnt patches is an important emergent property, which arises from the interaction between patch ignition, the dynamics of the peat watertable, and the behaviour of above- and belowground fires.

There are no interactions among humans, only between neighbouring cells due to the spread of fire.

The initial location of human activities, watertable depth, amount of belowground biomass, ignition of a patch and fire spread have stochastic components.

At model start-up time, values are assigned to state variables and global variables. Owing to the limited available empirical data, we mainly used mathematical distributions (uniform, Poisson, Gaussian) for them. That way, we were able to consider estimated variabilities of these variables. Uniform distributed variables are the number of humans (better seen as human activity points – nof), which were placed randomly across the simulated landscape and the maximum distance within which a human household can reach patches to ignite (dst) as well as the global variables including the minimum dry-days-before ignition (ddb), biomass burning rate (bbr), the probability of belowground fire spreading (psb), evapotranspiration rate (evp) and wind speed. The human capability to ignite a patch (= the number of opportunities they have for ignition – frp) was described as a Poisson distribution.

Two state variables of patches are described as Gaussian distributed variables, namely watertable depth (wtd) and the availability of belowground biomass (bib – restricted to the limits between 0 and 1 to use them as relative values). The global variable peat-dry-index (pdi) is also assumed to be normally distributed. Tables 1 and 2 provide further details of the parameters used in PeatFire.

The aboveground biomass (bia) of the patches is estimated based on the vegetation index using NDVI (Normalized Difference Vegetation Index). NDVI serves as a proxy for biomass availability, as has been used in another fire study (Segah et al. 2010). The data were imported as a raster map derived from Landsat 8 (https://earthexplorer.usgs.gov/, accessed 23 March 2018) taken from the study site on 26 June 2015. The values were divided into 15 classes and translated into the model input with a range from 0 to 1 as follows:

Rainfall data to describe daily precipitation were directly taken from 2015 records obtained at the Sultan Baharudin II Airport Palembang of South Sumatra province (https://dataonline.bmkg.go.id, accessed 20 March 2018).

Fire ignition of a patch mimics the first step for peat-land conversion to other land-use forms, such as agriculture. We assume that this can occur in every timestep, but only up to a maximum number (human-capability frp) per year and household. If the number of required dry days after a rain event is achieved, grid cells are randomly selected within the maximum distance around each human location with frp > 0. The human-capability to ignite a fire (frp) is decreased after each trial by one.

In ignited patches, aboveground biomass (bia) will burn according to the biomass burning rate bbr until the biomass runs out or the patch becomes inundated with water (wtd < 0). The same applies for belowground fires, with the difference being that fires stop if the patch becomes wet (watertable depth wtd < peat-dry-index pdi). A patch that is depleted of aboveground biomass from fire is considered a burnt patch and cannot be ignited again, as the model does not account for biomass regrowth or peat accumulation.

When a patch is ignited, a check is made whether the adjacent neighbouring patches are vulnerable to fire. This is the case if dry biomass is available (aboveground, wtd < 0; belowground, wtd > pdi). Aboveground fire can spread to the neighbouring patches with non-isometric probabilities defined by the wind speed (Fig. 3a). Belowground fires spread isometrically to neighbouring cells with probability psb. On top, fire can jump over from aboveground to belowground and vice versa with the same probability psb.

At the end of each time-step, the watertable-depth value (wtd) is actualised based on the daily precipitation and evapotranspiration rate:

The daily precipitation_t is read into the model as an input file containing the amount of rainfall per day during the simulated year. The evapotranspiration rate is a constant global variable applied to all patches containing biomass and does not change during the simulation.

To assess PeatFire’s behaviour, we analysed the sensitivity of individual parameters and parameter interactions. We then optimised the most important parameters of the model through a process of benchmarking model outputs of burnt area against observed fire patterns using standard techniques from previous ABM studies (Saltelli et al. 2006; Imron et al. 2012; Jakoby et al. 2014).

We performed a global sensitivity analysis using Morris screening to consider the entire parameter space (Saltelli et al. 2006; Imron et al. 2012; Kautz et al. 2014) in order to rank the importance of the input parameters on the number of burnt patches. The process generated 120 input sets of parameters and each set of parameters was simulated as part of a 30-member replication ensemble. The three most important parameters were selected.

We performed a local sensitivity analysis with the OAT (one-at-a-time) technique (Saltelli et al. 2006) to examine the effects of the three selected parameters on the model’s behaviour in more detail. In this study, we not only analysed the total number of fires simulated by the model, but also further differentiated these into the number of above- and belowground fires. While varying one parameter in its plausible range, all other parameter values were kept at their median value. Simulation runs were repeated 30 times.

The effects of interactions among the three most influential parameters on the output were examined by a full factorial simulation design using 30 replicates per parameter setting.

We conducted another full factorial experiment in order to identify the best combinations of the input parameter values that reproduce the spatial patterns in observed fire for our case-study region using a pattern-oriented analysis (Wiegand et al. 2003; Railsback and Grimm 2011; Grimm and Railsback 2012). The experiment simulated 1815 different parameter combinations, which were each replicated 30 times (54 450 simulation runs). Comparisons between observed and simulated burnt area maps were performed using Cohen’s kappa statistic (Cohen 1960), following the procedure described in Lehsten et al. (2016), who used the kappa statistic to compare simulated v. observed vegetation maps. The simulated results were sorted based on the highest kappa score.

Owing to the unavailability of observations of belowground fires, we could only use the spatial distribution of remotely sensed aboveground fires for model benchmarking. A raster map of burnt and unburnt cells taken at the study site on 11 November 2015 (https://earthexplorer.usgs.gov/, accessed 23 March 2018) served as the benchmark. The image was taken as this date is closest to the reported time of fire events in the study site in this particular year (Martín et al. 2006). We used the Normalised Burnt Ratio – Thermal /NBRT1 to identify burnt areas because it is known to have a good ability to separate burnt and unburnt land (Holden et al. 2005). We used a quick atmospheric correction (QUAC) to process the Landsat image with ENVI 5.2. The accuracy of the burnt–unburnt map used for model benchmarking was assessed following Veraverbeke et al. (2010). For this, two high-resolution Sentinel-2 images taken on 25 November 2015 and 5 December 2015 were selected. The assessment showed 83.89% accuracy with 4.05 and 22.83% error of omission and commission respectively. We resized the burnt–unburnt raster map into a 100 × 100-grid cells matrix in order to compare the observed spatial fire pattern with the simulated ones. For this, we examined the probability distribution of each grid cell to have 0–4 burnt adjacent neighbours (Fig. 4). This analysis was done using a four-neighbourhood window mask provided by the function focal in the R raster package (Fig. S1).

Fig. 4.  Raster map of burnt and unburnt patches from (a) the study area, and (b) the selected model simulation output. The histograms below each map shows probability distribution of a cell in the raster to have 0 to 4 adjacent burnt neighbouring cell.

The parameter set that produced the closest match between simulated and observed spatial fire patterns was used for model application on the effect of management scenarios influencing watertable depth (wtd) on fire dynamics above and below ground. The results are discussed in terms of the potential to improve peat watertable depth management and fire risk mitigation in Indonesia.

All simulation experiments were performed using the open source R package nlrx (Salecker et al. 2019). It provides a comfortable link between the PeatFire model implemented in NetLogo (version 6.1.1) and the statistical software environment R (version 3.4.4). This allowed us to benefit from the high-performance computing facility available at Technische Universität Dresden (Germany).

The results revealed that the number of burnt patches is most sensitive to the parameters watertable depth (wtd), peat-dry-index (pdi) and dry-days-before (ddb) (Fig. 5 and Table 3). The larger the value of μ* for a specific output parameter, the stronger the effect of changes in the particular input. The larger the value of σ for a specific parameter, the stronger the interaction effect of the input parameters on model output.

Fig. 5.  The projection of μ* and σ from the sensitivity analysis of the PeatFire model using Morris screening methods for the burnt patches variable. μ* represents the effect of a parameter on the model output, whereas the value of σ shows the interaction of a parameter on the model output.

Table 3.  Values of µ* and σ from Morris parameter screening
μ* corresponds to the effect of the particular parameter and σ corresponds to the strength of the parameter to the output

All three tested parameters have a pronounced effect on the numbers of fire occurrences (Fig. 6). The model exhibits increasing threshold behaviour with respect to variation in parameter wtd. This is characterised by a fairly constant low number of fire occurrences for wtd <0.2 m; then an upward shift for wtd ≤0.7 m; which then remains steadily stable for wtd >0.7 m. Gradual change of parameter pdi resulted in a sudden increase of belowground fires, but less impact on aboveground fires. Interestingly, fire occurrence showed a slight sudden decrease at different points during gradual increase of the parameter ddb.

Fig. 6.  One-at-a-time (OAT) sensitivity analysis of parameter behaviour in PeatFire model. The total fire occurrences comprise the aboveground + belowground fires during one simulation run. (a) Sudden jump of above- and belowground fire occurrences is shown with gradual increase in watertable depth. (b) Number of above- and belowground fire drops at certain points when given a gradual increase of the cumulative dry days before ignition. (c) The change of peat-dry-index has a more pronounced effect on the belowground fires, with little effect on the aboveground fires.

To investigate the behaviour of the sudden shift mechanism in the ddb values, we plotted the occurrence of fire and precipitation during simulations for ddb values of 5, 10 and 14 days, as shown in Fig. 7. Fewer dry days before ignition led the system to burn all the aboveground biomass early in the year, lowering fire occurrences during the late dry season. Conversely, having more dry days before ignition lowers the chance of fire occurrence early in the year (wet season), thus causing fire to emerge in the dry season (mid to end of year).

Fig. 7.  Different output of simulated daily fire occurrences (red bars) depending on the parameter dry-days-before-ignition (ddb) using the same input data for daily precipitation (millimetres; light blue bars). It is shown that with higher waiting time before fire igniting, the fire event shifts further towards the end of year (wet season). The total fire occurrences (averaged from 30 simulations) decreases with the dry days before ignition (plot (a) 133 834; plot (b) 124 293; plot (c) 108 426). NB: the total number does exceed the number of grid cells because fire may repeatedly occur in the same grid cell as long as biomass is still available.

The analysis of parameter interactions revealed that the watertable depth (wtd) has a much smaller interaction effect compared with dry-days-before (ddb) and peat-dry-index (pdi). The interaction of parameters ddb and pdi has a pronounced effect both on the total number of fires and the numbers of belowground fires (Fig. 8).

Fig. 8.  Heatmaps show the interactions between the three most important parameters of the PeatFire model, namely the watertable-depth (wtd), the peat-dry-index (pdi) and the dry-days-before (ddb). The total number of fires is defined as accumulation of above and belowground fires. Parallel lines indicate interacting effects of the varied parameters on the particular outcome. (a) Interaction between parameters wtd and pdi has a more pronounced effect on belowground rather than aboveground fire. (b) Similar behaviour is shown from the interaction of parameters wtd and ddb to above- and belowground fire occurrences. (c) Pronounced effect on belowground fire is shown from the interaction of parameters pdi and ddb.

The optimal set of the most influential parameters is wtd = 0.6, pdi = 0.15 and ddb = 11. Fig. 9 shows the spatial pattern of burnt patches from selected simulation results that comprise four different possible states (burnt at the surface only; burnt below ground only; burnt above and below ground; and did not burn). Comparison between burnt area pattern and burnt neighbour probability of observed pattern and selected simulation results are shown in Fig. S2. The three highest-ranked parameter settings produced similar result compared with the observed pattern. Meanwhile, the three middle- and lowest-ranked parameter settings produced different patterns of burnt patches compared with the observed data.

Fig. 9.  Spatial pattern from selected model simulation result with the different combinations of parameters watertable-depth, dry-days-before-ignition and peat-dry-index. The spatial pattern is illustrated with a colour scheme showing four possible states of a grid patch in the model (unburnt, burnt aboveground, burnt belowground, and burnt above- + belowground). Simulation results were ranked based on the similarity in the number of burnt patches with the observation and the highest kappa score. The first row (a) shows the three highest-ranked patterns obtained from the simulation. The second row (b) shows the three middle-ranked patterns, and the third row (c) shows the three lowest-ranked spatial patterns.

Table 4 shows the kappa scores used to evaluate the accuracy of the model under different parameter settings. The closest match to observed data (highest kappa score 0.338) was obtained with the parameter setting of wtd = 0.6, ddb = 11 and pdi = 0.15 (Table 4).

Table 4.  Evaluation score of ranked simulation results (ranked) with regards to the kappa score

We used the optimised PeatFire version to examine the effect of the watertable depth (wtd) on the numbers of total fires, aboveground fires and belowground fires (Fig. 10). A clear threshold is seen at wtd = 0.5 with a sudden increase in all fire types.

Fig. 10.  Box plots showing the effect of varying parameter watertable-depth (wtd) on model output (total fire, aboveground fire, belowground fire). The influential parameters pdi and ddb were set to 0.15 and 11 respectively according to the result of pattern-oriented analysis. Both above- and belowground fire showed a sudden increase when given a gradual change of watertable-depth. This behaviour caused a pronounced sudden shift of the total fire occurrences, from no ignition to a completely severe burning.

We developed an ABM PeatFire that accounts for simplified processes governing fire ignition and fire spreading as known from Indonesian tropical peatland landscapes. To the best of our knowledge, PeatFire is the first ABM developed for tropical peatlands. It thus extends previous regional-scale studies in Indonesia reporting close correlations between burnt area and rainfall (Spessa et al. 2015); fire weather (Field et al. 2015) and hydrological drought (Taufik et al. 2017); and between burnt area and land-use or land-cover change (Stolle and Lambin 2003; Stolle et al. 2003; Cattau et al. 2016). By explicitly modelling landscape processes (human-induced fire ignition, watertable dynamics and fire spread, both above and below ground), we have shown that PeatFire is suitable to describe fire activity patterns observed in 2015 in our study area. Besides its simplicity, PeatFire supports the assessments of key mechanisms driving fire activities, and this is important for future management of tropical peatlands.

Despite their importance to the terrestrial carbon cycle, belowground fires have received comparatively less research attention than aboveground fires, as the former occur in difficult-to-access locations. Also, they are nearly impossible to observe using optical satellite remote sensing, the prime vehicle by which burnt area is diagnosed globally (Justice et al. 2002; Page et al. 2002, 2013; Reid et al. 2013; Giglio et al. 2016). Although most of direct field observations of peat fires have occurred in boreal peatlands and in associated laboratory experiments (Frandsen 1987, 1997; Huang and Rein 2014; Prat-Guitart et al. 2015), relatively few studies have directly measured vertical smouldering of peat fires in either boreal or tropical peatlands (Ballhorn et al. 2009; Chen et al. 2015). Although there is comparatively little data available quantifying the smouldering of organic material both downwards and laterally in peatlands (Frandsen 1987, 1997; Ballhorn et al. 2009; He et al. 2009), we were able to use the limited information available to construct a belowground fire spreading module within the PeatFire model (Fig. 3b). PeatFire can be used to test alternative hypotheses of fire ignition and spread in tropical peatland ecosystems, and importantly, model predictions are amenable to further assessments and improvements through future field and laboratory work.

Our sensitivity analyses and pattern-oriented approach for finding key parameters affecting PeatFire behaviour follow a common procedure for examining the influence of poorly constrained parameters in an ABM (Wang and Grimm 2007; Imron et al. 2012; Kautz et al. 2014; Carter et al. 2015).We found that wtd (watertable-depth), pdi (peat-dry-index) and ddb (dry-days-before) play roles on the emergent dynamics of peat fire patterns (Fig. 5, Fig. 6). The wtd and pdi parameters are physical factors of peatlands related to watertable condition, which is critical in peatlands (Wösten et al. 2008; Kettridge et al. 2015; Mezbahuddin et al. 2015). The dry-days-before-ignition (ddb) parameter captures what has been reported as an important ‘rule of thumb’ helping local landholders whether decide to ignite fires or not in Indonesian peatlands (Cattau et al. 2016).

Further improvements to PeatFire could be achieved by considering more local climate data. For instance, parameters such as wind speed (wsp) were shown to be influential in determining fire spread in PeatFire. Yet in the absence of local wind speed data, the values for these parameters were taken as estimates using an index from 0 to 1, representing low to high wind speed, whereas we used 0–1 m to represent watertable (wtd), which determines the critical region for peat fire (Wösten et al. 2008; Kettridge et al. 2015; Mezbahuddin et al. 2015). In addition, biophysical parameters such biomass burning rate (bbr) also affected the number of burnt patches, albeit only slightly (Table 3). Future work should try to unpack the effect of these parameters and incorporate the results of field studies into the effect of vegetation, soil moisture and bulk density on fire spread and organic matter combustion, including smouldering combustion (Frandsen 1997; Leach et al. 2000; Cochrane 2009; He et al. 2009; He and Behrendt 2011). Finally, the incorporation of data on local solar radiation, as previous work has demonstrated in a more sophisticated peatland hydrological process modelling (Mezbahuddin et al. 2015; Valipour 2015), and other physical properties (i.e. water retention, unsaturated conductivity) on humification (Taufik et al. 2019) should lead to marked improvements in the simulation of evapotranspiration and watertable depth dynamics in PeatFire.

To improve the representation of both below- and aboveground fires in PeatFire, future work is needed to improve the representation of key hydrological parameters under different vegetation cover categories ranging from pristine to disturbed. Evapotranspiration is a key driver of soil moisture in tropical ecosystems, but comparatively little work has examined hydrological thresholds in tropical peatlands, particularly in relation to changes in vegetation cover (Segah et al. 2010; Hirano et al. 2012, 2015; Mezbahuddin et al. 2014, 2015, 2019). Although PeatFire does not represent disturbed peat swamp forests, our results confirm the importance of watertable, which is also influential in determining soil moisture, and hence aboveground fire occurrence.

Decisions governing fire ignitions in rural settings, such as Indonesian peatlands, involve various considerations by farmers ranging from socioeconomic factors (Cattau et al. 2016) and traditional reasons (Ryan et al. 2012) to political strategy (Barber and Schweithelm 2000; Yong and Peh 2016). Our modelling results clearly demonstrate the importance of the watertable (wtd), and the peat dryness index (pdi) contribution to burnt area patterns in the study area along with number of dry days before ignition (ddb) (Fig. 5, Fig. 6). This in general reflects current observations and knowledge in Indonesian peatlands (Cochrane 2003; Hooijer et al. 2010; Page et al. 2011), and thereby improves on past assessments of fire activity drivers based around biophysical factors alone (Wösten et al. 2008; Mezbahuddin et al. 2014, 2015; Brown et al. 2015; Prat-Guitart et al. 2015; Hayasaka et al. 2016; Taufik et al. 2017).

In many tropical countries, including Indonesia, land use-cover change and associated changes to human-caused ignitions intensify the impact of interannual variability in climate on fire activity (Langner et al. 2007; Aldersley et al. 2011; Miettinen et al. 2012; Spessa et al. 2015; Cattau et al. 2016). Existing ABMs of forest fire (Karsai et al. 2016; Spies et al. 2017) have not implemented the presence of human agents as ignition sources, thereby limiting their usefulness in situations where human ignitions and biophysical factors interact to cause fire, as is the case in Indonesian peatlands. The PeatFire model goes beyond this approach, although it addresses ignitions through farmer activities only as local probabilities. A future direction of model development would be to directly address human activities, for example, by considering human settlements and hotspots of activities by means of GIS (geographic information systems) layers. Further improvements in the way PeatFire simulates farmer agent impacts on ignitions should account for local data on the number of households actively using fires and their knowledge and behaviours to manage fire when deciding to convert peatland into agricultural land use.

The PeatFire model does not currently represent interactions between individual or groups of farmers. This omission potentially prevents the model from simulating real-world situations in which farmers may be influenced by other farmers through active communication or simply copying the behaviour of neighbouring farmers or communities when deciding to convert peatland (Hettig et al. 2016). The inclusion of a range of possible interactions between farmers on land-use change (Valbuena et al. 2010) would improve the simulation of ignitions in the model, and would lead to a richer array of emergent outcomes compared with the case where interactions between actors in an ABM are ignored (Grimm et al. 2006).

Under a gradual change in watertable depth, our model showed a sudden shift of fire occurrence, from moderate to severe burning (Fig. 10). Hydrological changes including peat drainage are known to be a trigger for severe burning events (Wösten et al. 2008; Miettinen et al. 2012). In peat swamp forests, drought and fire lead to peat soil degradation and increase the risk of repeated burning (Page et al. 2009b). Degraded peatland entails poor quality of soil, which needs a long time to be restored (Könönen et al. 2018). Efforts to restore degraded tropical peatland, such as rewetting and canal blocking (Jaenicke et al. 2010; Ritzema et al. 2014) and revegetation (Blackham et al. 2014; Lampela et al. 2017) have been carried out. However, the process requires expensive resources (Budiharta et al. 2014) with various limitation and barriers (Dohong et al. 2018).

Our model represented burn severity by explicitly introducing the effects of above- and belowground fire. Furthermore, by simulating possible sudden shift of fire events, PeatFire has also been able to demonstrate that most burnt patches are damaged both in their above- and belowground layers of peat (Fig. 9). Smouldering fire that spreads vertically underneath peat is a serious threat on tropical peatlands, as it limits the ability of the peat to fully recover after fire (Hu et al. 2018). Studies in boreal peatlands have shown that fire could cause peatland to experience a regime shift to mineral soil environment, where a reversal would be hardly possible (Kettridge et al. 2015). By showing a potential sudden increase of burning severity, our model reveals the risk of a catastrophic shift (Scheffer et al. 2001) if the main drivers of fire cannot be controlled properly. Further development of the model by including modules related to peat restoration would enable the model to simulate different strategies for post-fire recovery.

Despite certain limitations of PeatFire, described above, simulated burnt area patterns generally reflected observed burnt area patterns, supporting the robustness of our findings with respect to peat management. A peat fire study by Ballhorn et al. (2009) in Kalimantan reported a burning depth of 30 cm that decreased with repeated burns – key information that we could use for future model improvement. This type of model improvement would increase the utility of PeatFire because the model could then be used to examine peatland management options for peat forest restoration, including canal blocking and rewetting of drained peatlands (Page et al. 2009b; Jaenicke et al. 2010).

Our work demonstrating a strong relationship between the watertable depth (wtd) and fire incidence in the model confirms current peatland management practice that applies canal blocking and rewetting to effect peat restoration and protection (Page et al. 2009b; Ritzema et al. 2014; Sekretariat Negara Republik Indonesia 2016). Although precipitation and evapotranspiration have significant effects on fire occurrence, our analyses also demonstrate that initial fire ignition by farmers is the most important driver of fire ignition. Although the importance of both climate and land-use factors in driving fire ignitions and spread in Indonesian peatlands is well known and accepted (Field et al. 2009; Miettinen et al. 2012, 2013; Page et al. 2013; Brown et al. 2015; Spessa et al. 2015; Page and Hooijer 2016), we have shown here that an ABM, which captures the underlying processes associated with fire ignition and spread at a local scale even approximately can, through emergent model behaviour, reproduce broad-scale patterns in burnt area. The explicit consideration of fire-causing mechanisms in PeatFire underlines its potential usefulness in assessing and developing effective policies for peatland management focused on maintaining natural peat watertable depths and setting limits to land conversion.

Supplementary material PeatFire model is available to download at https://peatfire-abm.github.io/. Two supplementary figures are available online with this paper.

The authors declare that there is no conflict of interest.