Ran Zhang · Haiqing Hu · Zhilin Qu · Tongxin Hu

Abstract Studying diurnal variation in the moisture content of f ine forest fuel (FFMC) is key to understanding forest f ire prevention. This study established models for predicting the diurnal mean, maximum, and minimum FFMC in a boreal forest in China using the relationship between FFMC and meteorological variables. A spline interpolation function is proposed for describing diurnal variations in FFMC. After 1 day with a 1 h f ield measurement data testing, the results indicate that the accuracy of the sunny slope model was 100% and 84% when the absolute error was < 3% and < 10%, respectively, whereas the accuracy of the shady slope model was 72% and 76% when the absolute error was < 3% and < 10%, respectively. The results show that sunny slope and shady slope models can predict and describe diurnal variations in f ine fuel moisture content, and provide a basis for forest f ire danger prediction in boreal forest ecosystems in China.

Keywords Forest fuel · Forest f ire · Moisture content ·Prediction model · Diurnal variation

Introduction

Forest f ires have signif icant impact on forest ecosystems,often resulting in the release of large amounts of energy in short periods of time, causing massive deaths of wildlife (Gisborne 1 925; Wotton et al. 2010; Nolan et al. 2016).Simultaneously, forest f ires aff ect air temperatures, humidity,light availability and other factors within forests and change the composition, structure, and function of understory communities (Meyn et al. 2007; Jonathan et al. 2016; Santín et al. 2016; Hu et al. 2019), thereby causing ecosystem imbalances (Viegas et al. 1992; Shan et al. 2005; Fulé and Laughlin 2007). The majority of forest f ires are surface f ires and the moisture content of dead surface fuel is a major factor in forest f ire occurrences (Bradstock 2010; Jin and Chen 2012). The moisture content of f ine forest fuel (FFMC),def ined as litter and woody debris with diameters < 2.54 cm(Schiks and Wotton 2015; Slijepcevic et al. 2018), is particularly important in f ire danger rating systems (McArthur 1966; Bradshaw et al. 1984; Rothermel et al. 1986; Van Wagner 1987), which are subsequently used to make shortterm decisions about staffi ng and the movement of resources from low to high risk areas (Beck and Armitage 2001; De Dios et al. 2015). Therefore, establishing methods to accurately predict the moisture content of f ine forest fuel (FFMC)is key to understanding forest f ire danger prediction (Simard 1968; Van Wagner 1969), and understanding variation in FFMC can help predict the occurrence and the control of forest f ires (Matthews 2014; Slijepcevic et al. 2013).

Several studies have reported that variation in FFMC is inf luenced by a variety of factors, with meteorological ones having a dominant role. Therefore, studying the relationship between meteorological factors and variations in FFMC is key to establishing reliable forest f ire prediction models(McCammon 1976; Van Wagner and Pickett 1985; Saglam et al. 2006; Aguado et al. 2007; Pellizzaro et al. 2007). The methods currently used to predict FFMC are based on equilibrium moisture content, meteorological factors, remote sensing, and process models (Toomey and Vierling 2005;Yebra et al. 2006; Liu and Jin 2007; Yu et al. 2013). The equilibrium moisture content method has been widely used in the United States, Canada, and other countries that use a forest f ire danger rating system (Ralph and Nelson 1984;Anderson 1990; Viney and Catchpole 1991; Catchpole et al.2001), where the equilibrium moisture content response to environmental factors is used to calculate the equilibrium moisture content at diff erent temperature and humidity levels. In addition, diff erential equations have been established to describe the continuous variation in FFMC (Matthews 2006), using an initial FFMC and associated meteorological factors (Van Wagner 1972; Viegas et al. 2001). As such,models based on the equilibrium moisture content can accurately estimate FFMC over a short time. However, prediction error increases with increasing time interval (Matthews 2010). Variability in the diurnal variation of moisture content of f ine fuels is complex, which reduces the accuracy of the method based on the equilibrium moisture content(Page et al. 2013). Therefore, establishing a suitable model for the diurnal variation of FFMC is key to improving the precision of FFMC prediction. Few studies have investigated the prediction of short-term diurnal variation in FFMC (Slijepcevic and Anderson 2006; Sun et al. 2015). A previous study selected a particular time (e.g., 14:00) for FFMC as today’s FFMC to study diurnal variation, whereas other studies have used various indicators (e.g. maximum, minimum, or average FFMC) to describe diurnal variations (Slijepcevic et al. 2015). However, it is diffi cult to accurately describe the diurnal variation of FFMC using such methods(Viney 1991; Castro et al. 2003; Li et al. 2012). Forest f ires are a major disturbance factor to forest ecosystems of the Daxing’an Mountain region. However, an in-depth study of diurnal variations in fuel moisture is lacking. The aims of this study are to investigate diurnal variations in moisture content of f ine forest fuels using f ield data to establish a predictive model that would use current forest fuel moisture content estimations and related meteorological factors to predict future FFMC. This study will provide a theoretical basis for predicting FFMC in the Daxing’an Mountains of China, thereby improving the accuracy of diurnal f ire risk.

Materials and methods

Study area

The research area was located in the Daxing’an Mountains,Nanwenghe Forest Ecological Station, northeast China (51°05′ 07″ N-51° 39′ 24″ N, 125° 07′ 55″ E-125° 50′ 05″ E).Elevations range in 500-800 m a.s.l.; the climate is a cold temperate continental monsoon zone aff ected by the Siberian cold air mass. The frost-free period is approximately 98 days and mean annual precipitation and temperature are 500 mm and − 3 °C, respectively. The area receives about 2500-h sunshine annually, the growing season generally starts in May and ends in September, whereas the dormant is from October and to April. All soils in the area are podzols, infertile acidic soils formed over granite bedrock, and typical of boreal forests from which minerals have been leached into a lower stratum. The dominant tree species includeLarix gmeliniiRupr.,Betula platyphyllaSuk., andPopulus davidianaDode; the dominant herb species areLespedeza bicolourTurcz.,Rosa davuricaPall.,Vaccinium vitis-idaeaL.,Rhododendron simsiiPlanch.,Calamagrostis angustifoliaKom.,andMaianthemum bifolium.

The Daxing’an Mountains have the largest boreal forest area in China. The predominant forest type isL. gmelinii,which covers 80% of the area and accounts for about 30%of timber production (Xu 1998; Hu et al. 2019). Over 1600 f ires occurred in the area from 1965 to 2010, burning nearly 3.5 × 10 6 ha with an average annual burn of 7.7 × 10 4 ha (Hu et al. 2012, 2017).

Measurement of the moisture content of f ine forest fuel

Data were collected from experimental plots at the Nanweng River Forest Ecological Stationin the Da Xing’an Mountains, from May 26 to June 24, 2015, and from May 18 to June 8, 2016. The plots were located downhill of areas with sunny slopes or shady slopes, both wereB. platyphyllaandL. gmeliniimixed forest. A total of six 40 m × 80 m plots were established, with three each in both the sunny slope and shady slope areas (Table 1).

Three instruments were installed in each plot to automatically measure and record FFMC on an hourly basis (Fig. 1).The moisture contents of small dead sticks (20 cm × 0.6 cm)were used as a proxy for FFMC in each of the corresponding plots. Metal probes were inserted into both ends of each stick, and the density calibrated according to the fuel air-dry density and the temperature recorded as the ambient temperature. The instrument was capable of measuring moisture content values of 0.0-99.9%, densities of 0.10-1.25 g cm −3 ,and temperatures from − 20 to 70 °C; it had an output signal of 4-20 mA, measurement accuracy of ± 3%, and calibration range of from − 5.0 to + 5.0. The metal probes were 2-mmdiameter 10-mm long stainless steel attached to the instrument by 2-m wires. A battery powered the instrument in order to achieve 24-h measurements. The ecological station provided hourly meteorological data (i.e. air temperature,relative humidity, wind speed, and rainfall) for the periods May 26-June 24, 2015, and May 18-June 8, 2016 (Table 2).The ecological station was located at about 200 m from the study plots.

Table 1 Characteristics of study plots

Fig. 1 Instrument used to measure the moisture content of f ine forest fuel

Table 2 Variation in meteorological data

Model construction

Thirty variables were identif ied, including today’s mean,maximum and minimum temperatures (TTmean ,TTmax ,TTmin ,respectively), today’s mean, maximum and minimum relative humidity (TRHmean,TRHmax,TRHmin, respectively), today’s rainfall (TR), today’s mean and maximum wind speed(TWmean,TWmax, respectively), today’s mean, maximum and minimum sunny slope FFMC (TMCmean,TMCmax, andTMC-max, respectively), today’s mean, maximum and minimum shady slope FFMCrespectively) tomorrow’s mean, maximum and minimum temperature (NTmean, NTmax,NTmin, respectively), tomorrow’s mean,maximum and minimum relative humidity (NRHmean,NRH-max,NRHmin), tomorrow’s rainfall (NR), tomorrow’s mean and maximum wind speed (NWmean ,NWmax , respectively),tomorrow’s mean, maximum and minimum sunny slope FFMC (NMCmean,NMCmax,NMCmin, respectively), tomorrow’s mean, maximum and minimum shady slope FFMCrespectively).

Correlation analysis was used to calculate coeffi cients between the variables and were used to analyse linear correlations between FFMC and meteorological variables. A shady slope mean FFMC prediction model was established and used to predict maximum and minimum moisture contents. In addition, tomorrow’s mean, maximum, and minimum sunny slope FFMC were predicted using the relationship between mean sunny slope FFMC and mean shady slope FFMC. Interpolation theory was then used to establish diurnal variation curves for tomorrow’s sunny slope and shady slope FFMC and the data used to test the accuracy of the models (Habermann and Kindermann 2007). The data were processed and analysed using STATISTICA 6.0 (Statsoft Inc., Tulsa, OK, USA). Pearson’s correlation analysis was used for all correlation analyses, and all statistical analyses were performed using a signif icance level of 0.05. Variance inf lation factor (VIF) tested for multicollinearity among variables. When VIF < 10, there was no multicollinearity between variables, and when VIF > 10, multicollinearity existed (Craney and Surles 2002).

Results

Diurnal variation in f ine fuel moisture content

Mean, maximum, and minimum FFMC values were calculated for each day in the 51-day dataset (Figs. 2 and 3).

The average sunny slope FFMC was greater than the mean shady slope FFMC and accounted for 43.1% over the 51 days. The maximum sunny slope FFMC was greater than the maximum shady slope FFMC, accounting for 41.2% over the period. The minimum sunny slope FFMC was greater than the minimum shady slope FFMC and accounted for 51.0% over the 51 days. In addition, compared with the shady slope values, the average f ine fuel moisture content was 12.5% lower than that of the sunny slope values. These results indicate that there were considerable diff erences between the FFMC values of sunny and shady slopes under the same meteorological conditions, and that slope strongly aff ected the moisture content of f ine fuels.

Correlation analysis of FFMC and meteorological variables

The correlation of FFMC and meteorological factors are shown in Tables S1-3. Because some of the FFMC factors could not be obtained directly, they were estimated using the correlation results in Tables S1-3.NMC mean−TMC meanwas strongly correlated withNR,NTmax−TTmax,NRHmean−TRHmean, andNTmax−NTmin, andTMCmeanwithTMCmaxandTMCminin both the sunny and shady areas (Table S1).Accordingly,NR,NTmax−TTmax,NRHmean−TRHmean, andNTmax−NTmincould be used to predictTMCmean,TMCmax, andTMCmin. Meanwhile, none of the wind factors (TWmean,TWmax,NWmean, andNWmax) were signif icantly correlated with the FFMCs of either the sunny or shady areas (Tables S2-3). Therefore, wind factors were not considered when constructing the prediction model for diurnal variation in f ine fuel moisture content.

Fig. 2 Diurnal variation in the moisture content of f ine forest fuel in sunny slope and shady slope (2015)

Fig. 3 Diurnal variation in the moisture content of f ine forest fuel in sunny slope and shady slope (2016)

FFMC prediction model

The mean variance expansion factor ofTRHmaxandTRHminindicated that there was no collinearity.However, because theTRHmeanwas signif icantly correlated withTRHmin, a prediction model was established:

Similarly, the mean variance expansion factor ofTRHmean,NR,NTmax−NTmin, andNTmax−TTmaxindicated that there was no collinearity, and because the factors were signif icantly correlated withNRHmean, a prediction model could be established:

In addition, the mean variance expansion factor ofNR,NTmax−TTmax,NRHmean−TRHmean,NTmax−NTminindicated that there was no collinearity, and because the factors were signif icantly correlated withNMCmean −TMCmean , a prediction model was established:

f inally the relationships betweenNMCmeanand bothNMCmaxandNMCminwere used to establish prediction models for bothNMCmaxandNMCmin:

wherea i,b i,i= 1, 2…, 5,c2,c3,d2,d3,e2are the model parameters.

Prediction of maximum and minimum FFMC occurrence

Because the minimum and maximum f ine fuel moisture content values occurred at diff erent times each day, it was necessary to accurately estimate these to predict diurnal variation in FFMC. The timing of the minimum and maximum FFMC values on the sunny and shady slopes are summarized in Table 3.

The maximum sunny slope FFMC values occurred from 6:00 to 8:00 am on 92% of the 51 days (Table 3), whereas the minimum occurred from 16:00 to 19:00 am on 74% of the 51 days. The maximum shady slope FFMC values occurred from 5:00 to 8:00 am on 90.9% of the 51 days (Table 3),whereas the minimum occurred from 17:00 to 20:00 am on 83.6% of the 51 days. The maximum sunny slope moisture content values occurred earlier than the maximum shady slope values in 10.2% of the 51 days, at the same time in 28.6% of the 51 days, and later in 61.2% of the 51 days.The minimum sunny slope values occurred earlier than the minimum shady slope ones in 40.8% of the 51 days, at the same time in 20.4% of the 51 days, and later in 38.8% of the 51 days. The intervals between the minimum and maximum FFMC of the shady area were greater than that of the sunny area in 61.2% of the 51 days and less than that of the sunny area in 38.8% of the 51 days.

Table 3 Temporal distribution of maximum and minimum f ine fuel moisture content

Table 4 Correlations among factors aff ecting temporal distribution of minimum and maximum sunny slope f ine fuel moisture content values

The diff erences between tomorrow’s maximum FFMC and today’s minimum FFMC (MC1) and between tomorrow’s maximum FFMC and tomorrow’s minimum FFMC(MC2) were calculated as follows:

wheret1is the time of today’s minimum FFMC occurrence,t2the time of tomorrow’s maximum, andt3the time of tomorrow’s minimum.

Correlations amongMC1,MC2,NMCmax−TMCmin, andNMCmax−NMCminare summarized in Tables 4 and 5.

BecauseMC1 was signif icantly correlated withNMCmax−TMCminandMC2 was signif icantly correlated withNMCmax−NMCmin(Tables 4 and 5), prediction models were established for bothMC1 andMC2:

wherea i,b i,i= 7, 8 are the model parameters.

Table 5 Correlations among factors aff ecting temporal distribution of minimum and maximum shady slope f ine fuel moisture content values

Models for tomorrow’s maximum and minimum occurrence times were also established:

wheret1is the time of today’s minimum FFMC occurrence,t2is the time of tomorrow’s maximum FFMC occurrence, andt3is the time of tomorrow’s minimum FFMC occurrence.

Diurnal FFMC variation models

Based on the prediction models presented above [Eqs. 3- 11],tomorrow’s maximum FFMC (NMCmax) and its time of occurrence (t2), tomorrow’s minimum FFMC (NMCmin)and its occurrence time (t3 ), the day-after-tomorrow’s maximum FFMC (NNMCmax ) and its time of occurrence (t4 ), can be predicted and combined with today’s minimum FFMC occurrence time (t1). Finally, models for diurnal variation in FFMC were established using the spline interpolation method:

Equation 12 can be used to predict diurnal variation patterns in FFMC over the following day.

FFMC model prediction and validation

The parameter estimates of each model were determined by the least square method.

Today’s maximum % relative humidity (TRHmax ) was determined by:

Tomorrow’s mean % relative humidity (NRHmean ) was predicted by:

Tomorrow’s mean sunny slope FFMC % (NMCmean) was predicted using:

Tomorrow’s maximum sunny slope FFMC % (NMCmax)was predicted (Fig. 4) by Eq. 16 :

Fig. 5 Relationship between the mean and minimum sunny slope f ine fuel moisture content

Tomorrow’s minimum sunny slope FFMC % (NMCmin)was predicted as follows (Fig. 5):

Tomorrow’s mean shady slope FFMC %was predicted by:

Tomorrow’s maximum shady-slope FFMCwas predicted (Fig. 6) as follows:

Tomorrow’s minimum shady-slope FFMCwas predicted (Fig. 7) using Eq. 20:

The time of maximum sunny slope FFMC occurrence was determined by:

Fig. 4 Relationship between the mean and maximum sunny slope f ine fuel moisture content

Fig. 6 Relationship between the mean and maximum shady slope f ine fuel moisture content

The time of minimum sunny slope FFMC occurrence was determined by:

The time of maximum shady slope FFMC occurrence was predicted by:

The time of minimum shady slope FFMC occurrence was determined by:

The parameters estimated using these models all signif icantly passed the hypothesis test.

Moisture content values for f ine fuel on sunny and shady slopes and meteorological data from June 12-14, 2015 were used to validate the FFMC prediction models. Equations 15 and 17 estimated the mean, maximum (29.3%), and minimum (20.9%) FFMC on sunny slopes for June 13 and to estimate the mean and maximum (26.2%) for June 14.Equations 21 and 22 estimated times of maximum (6.1 h)and minimum (17.2 h) sunny slope FFMC values for June 13, and maximum time (8.0 h) for June 14. In addition, the pattern of diurnal variation in sunny slope moisture content values on June 13, 2015 was estimated as follows (Fig. 8):

Fig. 7 Relationship between the mean and minimum shady-slope f ine fuel moisture content

Fig. 8 Model validation for predicting f ine fuel moisture content on sunny slopes

Equations 18 and 20 estimated the mean, maximum(34.8%), and minimum (24.0%) moisture contents of f ine fuels on shady slopes for June 13 and the mean and maximum (28.9%) for June 14. Equations 23 and 24 estimated times of maximum (7.4 h) and minimum (20 h) shady slope f ine fuel moisture content for June 13 and the time maximum(7.2 h) for June 14. In addition, the pattern of diurnal variation in moisture content on shady slopes on June 13, 2015 was estimated as follows (Fig. 9):

The predicted mean, maximum, and minimum values for the sunny slope areas predicted for June 13, 2015, were 25.0%, 29.3%, and 20.9%, respectively, whereas the actual measurements were 23.6%, 27.0%, and 22.4%. The accuracies of the sunny slope model over 24 h were 100% and 84%when the absolute errors were < 3% and < 10%, respectively.Meanwhile, the predicted mean, maximum, and minimum FFMC values for the shady slope areas for June 13, 2015,were 29.8%, 34.8%, and 24.0%, respectively, whereas the actual values were 26.7%, 32.5%, and 23.6%. The accuracies of the shady slope model over 24 h were 72% and 76% when the absolute errors was < 3% and < 10%, respectively. The lower accuracy was mainly due to the relatively low FFMC.Overall, the model predicted diurnal variation of sunny slope FFMC better than shady slope FFMC, and validation conf irmed that the developed models are suitable for describing and predicting diurnal variation in f ine fuel moisture content.

Discussion and conclusion

In this study, models were developed for predicting the diurnal mean, the maximum, and minimum moisture content of f ine fuels of boreal forests in China by investigating the relationships between fuel moisture contents and meteorological variables. The results provide a basis for forest f ire danger prediction which is of considerable importance for scientif ic forest f ire management in the context of global climate change.

Fig. 9 Validation of model for predicting f ine fuel moisture content on shady slopes

Even though the relationship between weather and fuel moisture content has been studied for nearly a century, reliable methods for predicting diurnal variations in fuel moisture have yet to be developed (Ralph and Nelson 1984).This study established f ine fuel moisture content prediction models for aB. platyphyllaandL. gmeliniimixed forest. The models considered mean, minimum, and maximum FFMC,as well as today’s air temperature, relative humidity, and rainfall, and meteorological variables (maximum and minimum air temperature, and rainfall) for the following 2 days.The models could predict tomorrow’s mean, minimum,and maximum moisture content, important parameters for describing the diurnal variation. Nelson and Ralph ( 2000)built a model to simulate diurnal changes in moisture content and temperature of 10-h time lag sticks, but the model did not consider rainfall, which leads to great discrepancies after rainfall. Viney and Catchpole ( 1991) proposed that the diurnal variation of fuel moisture content could be predicted using the sine function. If the maximum FFMCs of two consecutive days were signif icantly diff erent, the prediction error of the model would be relatively high. In contrast, the model constructed during this study used a piecewise cubic function to describe the diurnal variation of FFMC, thereby reducing prediction error and improving prediction accuracy.

Soil moisture aff ects fuel moisture content via evapotranspiration. At sunrise or after rain, the soil releases some of its water by evaporation, part of which is sequestered by litter (Hatton et al. 1988). Subsequently, throughout the day, solar radiation and temperature gradually reduce the fuel moisture content, typically until minimum values are attained during the early afternoon, and the moisture content then increases after sunset. Solar radiation can aff ect fuel moisture content both directly and indirectly. With regards to direct Effects, solar radiation increases air temperature,relative humidity, and fuel surface temperature. In short, the Effect of solar radiation on the moisture content dynamics of fuels on the forest f loor is not easily determined (Byram and Jemison 1943; Catchpole et al. 2001). Kreye et al. ( 2018)reported that exposure to solar radiation caused the dynamic drying of pine and oak litter, in spite of high relative humidity that generally exceeded 65%, and that the Effect of heat radiation was more signif icant for fuel sources with high moisture contents. Therefore, future studies should improve the FFMC diurnal variation model by considering soil moisture and solar radiation.

Previous studies have reported that rainfall is the most important factor inf luencing fuel moisture content (Tolhurst and Cheney 1999; Slijepcevic and Anderson 2006).However, even though mean, minimum, and maximum rainfall were considered during the construction of the diurnal variation model, little attention was given to throughfall.This is the amount of rainfall to reach the duff layer after passing through various potential interceptors in the vertical forest prof ile, relative to the volume of rainfall that would have reached the stratum without interception (Ma et al. 2014). Potential interceptors include the canopy, subcanopy, exposed boles, branches, and herbaceous f lora of the aerial component and the fallen dead wood and litter material of the forest f loor component (Wotton et al. 2005).Throughfall describes how much rain reaches the ground surface, as well as how much is absorbed by the upper part of the organic layer, and greatly aff ects the diurnal variation of fuel moisture content and f ire risk, especially after heavy rainfall (Wotton and Beverly 2007). Accordingly, the prediction models developed here should be applied cautiously in heavy rainfall conditions (Matthews et al. 2010). Future studies should also investigate several aspects of throughfall,for example, whether rainfall interception (water retention,def lection, dripping, and channelling) results in heterogeneous spatial distributions of throughfall. Future studies should also investigate the time over which throughfall absorption(into the upper 7 cm of the organic layer) aff ects f ine fuel moisture content diurnal variations (Flannigan et al. 2016).

This study focused on the f ine fuel moisture content of downhill slopes ofB. platyphyllaandL. gmeliniimixed forest. Diurnal variations of mid- and up-slope will diff er,and diurnal patterns in fuel moisture content of diff erent forest types will also vary (Holden and Jolly 2011; Rossa 2018 ). Future studies might adopt our models to investigate diurnal variations in fuel moisture content of diff erent slope positions and forest types. Although our studies were underway to identify limitations and need to improve predictions, this study still provides a simple and useful tool for predicting diurnal variations of f ine fuel moisture contents.The results provide an important theoretical basis for further improving diurnal variation models, thereby helping to improve the accuracy of forest f ire prediction in the context of global warming, which is associated with increasing f ire occurrence.

Acknowledgements We are also grateful to the staff of the Nanwenghe Forest Ecological Research Station for their assistance with f ieldwork, and to both the Northern Forest Fire Management Key Laboratory (State Forestry and Grassland Bureau) and the National Innovation Alliance (Wildland Fire Prevention and Control Technology of China) for supporting this research.

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