Characterizing and predicting smoldering temperature variations based on non-linear mixed eff ects models

Sainan Yin · Yanlong Shan · Bo Gao ·Shuyuan Tang · Xiyue Han · Guojiang Zhang ·Bo Yu · Shan Guan

Abstract Underground f ires are slow spreading, long-lasting and low temperature smoldering combustion without f lames, mainly occurring in peatlands and wetlands with rich organic matter. The spread of the smoldering is maintained by heat released during combustion and monitoring this is an important approach to detect underground f ires.The Daxing’an Mountains region is a hotspot for underground f ires in northeast China. This study examined a Larix gmelinii plantation in the Tatou wetlands of the Daxing’an Mountains and determined the maximum temperature variation of humus of varying particle sizes, and the temperature rising process based on non-linear mixed eff ects models by an indoor combustion experiment. Maximum combustion temperatures up to 897.5 °C, increased with humus depth;among the three models tested, Richard’s equations were best for characterizing temperature variations; a non-linear equation with three parameters had the highest accuracy in f itting the combustion temperature variations with varying humus particle sizes. These results are informative for predicting temperature variations and provide technical support for underground f ire monitoring.

Keywords Underground f ire · NLME modeling ·Smoldering temperature · Daxing’an mountains

Introduction

Forest f ires are classif ied into surface, canopy, and underground f ires. Underground f ires occur less frequently than the other types, but the damage can be signif icant (Watts and Kobziar 2013). Underground forest f ire is slow spreading,long-lasting and having low temperature smoldering combustion without f lame (Ohlemiller 1985; Rein 2013). These f ires cause fatal damage to plant roots (Page et al. 2002;Davies et al. 2013), destruction of soil structure and ground collapse (Hadden et al. 2013), and higher greenhouse gas emissions than other categories of forest f ires (Turetsky et al.2004). Forested peatlands and wetlands with rich organic matter, such as those in boreal and tropical forests, are prone to underground f ire (Huang et al. 2016). Soil carbon in these forests accounts for 25% of carbon reserves on land and plays essential roles in ecosystem stability, biodiversity maintenance, and hydrological cycling (Page et al. 2011).Therefore, large underground f ires will substantially impact global climate, ecology, and human health (Davies et al.2013; Hu et al. 2018). Wetlands were previously assumed to be f ire-resistant due to their high humidity (Kuhry 1994).However, recent studies reported that smoldering has been widely observed in wetlands (Turetsky et al. 2004; Shetler et al. 2008). Quantitative studies in the f ield on smouldering events are seldom conducted as they are challenging due to their randomness and unpredictability (Davies et al. 2013).Therefore, combustion studies simulating underground f ires are often carried out in the laboratory (Huang et al. 2015).

Large-scale underground f ires have been recorded in Indonesia, Russia, Spain, and in other countries in recent years (Page et al. 2002; Cancellieri et al. 2012; Turetsky et al. 2015; Pastor et al. 2018). Underground f ires are caused by surface f ires or lightning (Davies 2016; Restuccia et al.2017) with strong concealment and always accompanied by surface f ires. There are considerable diffi culties in monitoring and extinguishing them (Rein et al. 2008a, b). Their behavior is signif icantly diff erent from other types of f ires(Rein 2013), and could occur with a fuel moisture content of 100% or higher (Reardon et al. 2007; Lin et al. 2019), and persist through heavy rains, weather changes, extinguishing of surface f ires, and may last for months or even years(Zaccone et al. 2014). The spread of an underground f ire is maintained by heat released during combustion (Pastor et al. 2018), which is key to monitoring (Hartford and Frandsen 1992 ). Studies of smoldering have mainly focused on combustion characteristics (Pastor et al. 2018), contributing factors (Achtemeier 2006; Wang et al. 2017), combustion spread (Huang and Rein 2017), carbon release (Davies et al.2013; Hu et al. 2018) and other aspects.

Non-linear mixed eff ects (NLME) modeling was f irst proposed by Sheiner and Beal ( 1980), which included both f ixed and random eff ects parameters, and could identifying average prediction and individual prediction by calculating the estimated value of random eff ect parameters (Leites and Robinson 2004; Dorado et al. 2006; Yang et al. 2009). A mixed-eff ects model is a statistical method used in forestry,agriculture, ecology, biomedicine, sociology, economics, and in other f ields (Calegario et al. 2005). In forestry,NLME modeling has been used in the studies of tree heights and diameters, growth processes, average growth, and basal area (Budhathoki et al. 2008; Mehtatalo et al. 2014; Ciceu et al. 2020) but has been seldom applied to forest f ires. The mechanism of underground f ire smoldering is complicated,so its occurrence and development are diffi cult to predict.The gradually rising temperature of a smoldering f ire is like the growth process of a tree, so NLME modeling is applicable to smoldering. NLME modeling can achieve prediction accuracy with fewer independent variables and is suitable for studies on underground f ire.

The frequency of underground f ires in the boreal forests has increased in recent years (Sinclair et al. 2020), due to global climate change and the impact of human activities (Turetsky et al. 2015). The coniferous forests in the Daxing’an Mountains region, the southernmost margin of the Far Eastern Siberia boreal forests into China, is characterized by the largest number of underground f ires in the country. The growth ofLarix gmelinii (Rupr.) Rupr. planted in the Tatou wetlands of the Daxing’an Mountains has been poor because of the geographical and climatic conditions,and the decomposition of fallen branches and leaves slow so that the content of organic matter in humus increased, providing abundant fuel for underground f ires. Rising temperature is one of the stages during the smoldering (Pastor et al.2018); one of these is the buildup of temperatures causing signif icant damages. However, this process is easily monitored. This study focused on the process of rising temperatures in aLarix gmeliniiplantation in the Tatou wetlands,analyzed smoldering temperature variations of humus of different particle sizes, and developed a method to predict temperatures of underground f ires by non-linear mixed eff ects(NLME) modeling to provide support for underground f ire monitoring and control.

Materials and methods

Study area

Forest f ires in the Daxing’an Mountains region occur frequently; the area burned is largest in China. The study area is in the Jiagedaqi Forest Management Technology Promotion Station (123°57′-124°0′ E, 50°20′-50°23′ N), located in the northwest of Heilongjiang province, on the southeast slopes of the Daxing’an Mountains (Fig. 1 a). The region has a continental monsoon climate with four distinctive seasons, a changeable climate and large diurnal and seasonal temperature diff erences. Annual average temperatures are - 1 to 2 °C, the annual eff ective accumulative temperature 1800-2000 °C, the frost-free period 90-120 days,and annual rainfall 450-500 mm. The technology promotion station was founded in 1973, 15 km to the south of the Jiagedaqi region, the north and west portions of the station is connected with the Dongfeng Forest Station of the Jiagedaqi Forestry Bureau. The total area of the station is 7326 ha 2 . The main species in the study area areLarix gmelinii,Quercus mongolicaFisch,Betula platyphyllaSuk.,Populus davidianaDode, andBetula dahuricaPallas (Tang et al. 2022).

Sample collection and processing

Three 30 m × 20 m sample f ields were established and three 0.5 cm × 0.5 cm quadrats selected (sampling depth was the 46-cm thickness of the humus layer) in the diagonals according to Pastor ( 2018) (Fig. 1 b, c). All the humus in the quadrats was collected, and after removal of surface litter and in the humus layer, taken to the laboratory,stored in kraft paper sacks and dried for 48 h at 105 °C to remove as much moisture as possible. As an uneven distribution of humus particles will aff ect the temperature measurements accuracy (Huang and Rein 2017), the dried humus was ground and sieved into particle sizesof ≤ 20 mesh (moisture content 0.28%), ≤ 40 mesh (moisture content 0.49%), ≤ 60 mesh (moisture content 0.43%),and ≤ 80 mesh (moisture content 0.49%) for the combustion experiments(Fig. 1 d).

Fig. 1 a The study area; b,c study location and sample collection; d sample after pretreatment for the combustion experiment

Combustion experiments

Fig. 2 Schematic diagram of the smoldering combustion process

The combustion furnace was designed for studying a onedimensional downward combustion process (Fig. 2) (Huang and Rein 2017). The unit was cylindrical (20- cm high with 10- cm walls) of aluminum silicate ceramic f iber with excellent heat insulation. A K-type thermocouple (30 cm long × 2 mm diameter) recorded temperature variations of the humus during combustion. The data were transmitted to a laptop by data acquisition module composed of a 16-channel NI9213 voltage acquisition board card and DAQ-9174 case (4 card slots),with temperature measurement accuracy ＜ 0.25 °C. The data acquisition software (Labview2018) recorded temperature variations collected by the thermocouples. A far-infrared heating plate (30 cm long × 20 cm wide × 5 cm thick) was used as an ignition device. A temperature control meter between the far-infrared heating plate and the power supply kept the temperature of the heating plate constant.Humus of diff erent particle sizes were placed in the combustion furnace at ambient temperatures and the shape of the particles maintained as much as possible. Holes were arranged every 3 cm on the side of combustion furnace and K-type thermocouples inserted into the humus through the holes.The K-type thermocouples and data acquisition module were connected temperature variation data transmitted to the laptop every 10 s. To ensure combustion continued after removing the heating plate (ignition device), heating time and temperature were set to 1.5 h and 500 °C. A 2-cm gap between the heating plate and combustion furnace allowed for air f low.

Non-linear mixed eff ects model

The general form of a non-linear mixed eff ects model is:

whereTiis the dependent variable of subjectiand refers to the predicted combustion temperature;fis the actual value,specif ic parameter vectorφiand variable value vectortiof the diff erentiable function in the subject, and refers to actual combustion temperature of the underground f ire;βis thep-dimensional f ixed eff ect parameter vector;biis theq-dimensional random eff ect parameter vector;Dis the covariance matrix between random eff ects;AiandBiare correlation matrices with appropriate dimensions ( 0 or 1);tiis the independent matrix;εiis the random error vector associated withTi; and,σ2is the covariance matrix of the random error.

Base model

Logistic, Richards, and Korf nonlinear models, widely used in forestry to predict the tree growth, height, and DBH(Calama and Montero 2004; Rijal 2012; Sharma et al. 2016;Pan et al. 2020) (Table 1), were selected as the base models to study temperature variations in the combustion process.

Model selection and validation

The base model was selected according to the values of Akaike’s Information Criterion-(AIC) and Schwarz’s Bayesian Information Criterion-(BIC). Model accuracy was evaluated with diff erent parameters according to the values of Root Mean Square Error (RMSE). Smaller values of AIC and BIC indicate the better f itting degree of the equation;smaller values of RMSE indicates the higher accuracy of the model (Akaike 1974).

Statistical analysis

Excel and Origin were used to analyze the combustion temperature variation data with diff erent humus particle sizes and from diff erent depths, and the relationship between the maximum temperature and the combustion depth;NLMIXED and NLINE modules of Statistical AnalysisSystem-(SAS) were used to select, f it, and verify the nonlinear mixed eff ect models.

Table 1 Base models

Results

Maximum combustion temperature variations of humus of diff erent particle sizes

There was no f lame or spark during humus smoldering,and the surface was carbon black and the deep layer brick red after combustion. The maximum combustion temperature of diff erent particle sizes increased with depth. There was a positive linear relationship between depth and temperature (P＜ 0.05) in both particle ≤ 40 mesh size and ≤ 80 mesh size. The equations werey= 435.68 + 27.87xandy= 453.82 + 21.82xrespectively. The highest combustion temperature of all particle sizes was at the 15-cm depth with particles ≤ 40 mesh size (897.5 °C), the highest combustion temperature with particle ≤ 80 mesh size was 844.9 °C.

There was a positive linear relationship between depth and temperature (P＜ 0.01) in both particle ≤ 20 mesh size and ≤ 60 mesh size; the equations werey= 474.76 + 17.42xandy= 468.84 + 20.21x,respectively.Combustion temperature variations with particle size ≤ 20 mesh at diff erent depths f luctuated the lowest, the highest combustion temperature was 741.6 °C and the lowest was 543.3 °C. The highest combustion temperature with particle size ≤ 60 mesh was 780.4 °C and the lowest was 553.3 °C(Fig. 3).

Selection and validation of NLME models

The NLME models were selected based on 60% of the humus combustion data with diff erent particle sizes. AIC,BIC evaluated the approximation based on the three models.The AIC (135,343) and BIC (135,373) values of the Richards equation with diff erent particle sizes were the smallest.It may be concluded that Richards equation provided the best approximation and was therefore chosen as the basic equation for the relationship between humus combustion temperature and time (Table 2).

Richards equations of combustion temperature variation were set with no parameter mixing, and one, two, and three parameters mixing for diff erent particle sizes. All equations with diff erent parameters were convergent, and the RMSE values of models with mixed parameters were smaller than the traditional models. The precision of models with mixed parameters was higher than the conventional models. The RMSE value of the three parameters was the least, therefore,the accuracy of Richards equation with three parameters mixing was the highest (Table 3).

Fig. 3 Maximum combustion temperature of humus for diff erent depths and particle sizes; lower panel are photos of humus after combustion

Table 2 Fit statistics

Mixed-eff ects model approximation of Richards equation

The relationship between combustion temperature and time at diff erent depths with diff erent particle sizes was f itted by Richards equation with three parameters mixing. According to the temperature variation,β1,β2andβ3were the estimated values of equations at 15- cm depth for each particle size,andbijwas the parameter mixing eff ect at diff erent depths(Table 4). The approximation of Richards equations with diff erent particle sizes is shown in Fig. 4

Discussion and conclusions

Variation characteristics of humus combustion temperature

Peatland and humus are the main combustibles of underground f ires, and peatland f ires is of wide concern for the frequent occurrence of large-scale f ires (Davies et al. 2013).Commercial peat moss with its homogenous texture and consistent components has been widely used in characterizing smoldering and contributing factors, instead of using peatlands in the f ield (Huang and Rein 2017). More researchers have started using underground combustibles to approximate reality (Pastor et al. 2018). In this study, actual humus from the Tatou wetlands of the Daxing’an Mountains was used to study temperature variations of vertical smoldering, and the results are reliable and highly applicable.

Smoldering combustion of humus is sustained by the heat released by itself. The maximum temperature was 897.5 °C in this study, close to 900 °C of a similar study using peat(Huang et al 2015). Most studies have reported that the maximum temperature of peat smoldering was around 600 °C(Bar-Ilan et al. 2004; Huang and Rein 2017), lower thanour result. Using diff erent experiment devices and materials might account for the diff erence. It could also ref lect the diff erent temperatures of humus and peat smoldering.The mass loss of combustibles was small, and the humus afterwards was brick red due to suffi cient burning and high temperatures (Fig. 3) and in addition, there was no ash after combustion, only a thin layer of carbonized humus. The heat release was impeded by the humus of the upper layers when the f ire was spreading downwards, so the temperatureof humus smoldering was higher and increased with depth.But the mass loss of combustibles in peat smoldering was larger according to Huang and Rein ( 2014). Without being impeded by upper layers, the heat released quickly so the temperature was lower than the humus.Combustion depth could go to more than 50 cm (Ballhom et al. 2009). However, the combustion depth was found to be deeper due to the increased aridity of peatlands and wetlands due to global warming (Turetsky et al. 2015). The combustion process is also affected by oxygen levels, so when oxygen decreases as depth increases, combustion might be extinguished. This observation requires further study.

Table 3 Approximation results of mixed-eff ect models with diff erent parameters

Table 4 Fitting results of Richards equation

Table 4 (continued)

Applicability of NLME in smoldering temperature variation

Unlike surface and canopy f ires, the heat released in underground f ires is the manifestation of the smoldering process,which is also the important basis for f ire monitoring and f ighting. Fire intensity and spread rate are both predicted by the heat released (Rein et al. 2008a, b; Kirschke et al. 2013);the heat released, and temperature change of the ground surface are useful for judging the occurrence of underground f ires and the direction for digging f ire breaks. Therefore,thermos physical models are essential tools for studying the mechanism of underground f ire occurrence and development (Huang and Rein 2014), and an important basis for f ire monitoring and f ighting.

This study was based on NLME modeling to predict temperatures of underground f ires and focused on the prediction of temperature during smoldering. Simple statistical models are better for prediction research, and NLME is better than ordinary regression models. Many statistical models have been applied to forest f ire prediction(Bem et al. 2018; Nadeem et al. 2020) and have increased prediction accuracy. The variation of temperatures during underground f ire combustion showed a slow rise at the beginning, then a rapid rise, and f inally, a stable temperature after reaching the maximum temperature. The change curves of the three basic models in this paper are“S” type, which are consistent with the change curves of underground f ires, so the models could be applied to the prediction of temperatures during these f ires.

In this study, well-replicated underground f ire temperatures with varying depths and particle sizes were studied(Hall and Bailey 2001). NLME modeling was shown to be signif icantly superior in handling longitudinal, multilevel and replicated data (Calegario et al. 2005). Richards equations exhibited the best applicability in f itting humus combustion temperatures after evaluating three models and have been widely used owing to their biological signif icance, strong adaptability, and high accuracy (Li and Zhang 2010). Hang et al. ( 1997) and Hall and Bailey( 2001) also found high accuracy of Richards equations,consistent with the results of our study.

Fig. 4 Approximation of Richards equations of temperature and time at diff erent depths with diff erent humus particle sizes

Conventionally, the least square method was used to estimate model parameters of multilevel data, but this method tended to use data lacking independence, time correlation and space heterogeneity, and would lead to large prediction errors (Mensah et al. 2018). NLME modeling has higher accuracy (Sharma et al. 2016) through set up, f ixed eff ect,and random eff ect parameters (Kalle 2009). Based on the results of RMSE in this study, the accuracy of models with mixing parameters were much higher than traditional nonlinear models, and the accuracy increased as the number of parameters increased. Ciceu et al. ( 2020) also reported the high precision of NLME models, although the parameters were diff erent due to the research contents and basic models. Meng et al. ( 2009) found that a NLME model with two parameters was highly accurate. Pan et al. ( 2020) reported that one with three parameters had high precision.

Prospect of using NLME modeling in forest f ire research

Studies with mixed eff ects models are emerging research areas in forestry (Calegario et al. 2005), but their applications in forest f ire research are rarely reported. Studies of forest f ires, based on multi-level aspects, such as combustible characteristics, f ire forecasting and f ire behavior, should ref lect both overall change trend and individual diff erences,so NLME has more advantages (Guillermo et al. 2006).NLME also has the advantages of high reliability, f lexibility and accuracy (Sharma et al. 2016), and have great application potential in the study of forest f ire.

Declarations

Conf licts of interest The authors declare no conf licts of interest.