Modeling the drying process of Masson pine needle fuel beds under different packing ratios based on two-phase models in the laboratory

Investigation of fuel bed characteristics and sample collection in the field

A representative Masson pine forest was selected to set a sample plot of 25.82 m × 25.82 m. The basic information of the sample plot is shown in Table 1. The fire prevention period in the study area is from October to May, with February through April considered the period of highest fire risk. Because the drying process of fallen pine needles and weathered pine needles are different (Anderson, 1990), and to make the research more applicable to forest fire prediction, weathered Masson pine needles were collected at peak fire risk in March.

Indoor fuel bed construction with different packing ratios

The packing ratio of the fuel bed is a measure of how tightly compacted the Masson pine needles are in the fuel bed. The higher the packing ratio, the tighter the needles are. Packing ratio is calculated using the following formula: $\beta =\frac{{\rho }_b}{{\rho }_p}$, where β is the packing ratio; ρ_b is the bulk density of the needle bed, which is calculated by the quality and volume of the bed (kg m⁻³); and ρ_p is the particle density of Masson pine needles, which is a fixed value, obtained from the literature, of 543.6 kg m⁻³ (Hu, 2005). To ensure our indoor research samples represented the field, the fuel bed thickness in this study was uniformly set to 6.9 cm, which was the average thickness of the field needle bed, and the packing ratio was set to 5 gradients identified in the field: 0.016, 0.021, 0.027, 0.040 and 0.061.

A topless iron frame with a length of 29 cm and a width of 21 cm was chosen to hold the Masson pine needles, and a cloth was placed on the sidewalls to prevent vapor exchange. The bed volume of the Masson pine needles was 4.2 × 10⁻³ m⁻³ (volume of the fuel bed = length * width * thickness = (29 cm * 21 cm * six cm)/10°⁶). Using the packing ratio gradients set in this study and the particle density (ρ_p) of Masson pine needles, we calculated the quality of needles corresponding to each packing ratio, using the equation: w = ρ_bv = ρ_pβv, where w is the quality of needles corresponding to each packing ratio and v is the volume of the fuel bed.

Simulating the fuel bed drying process

To more accurately determine the effect of the fuel bed packing ratio on the drying process, we conducted all drying process experiments under one consistent temperature and humidity ratio, excluding the effects of temperature, humidity, solar radiation, wind, and duff moisture code. The temperature and humidity were set at 25 °C and 0.60 g g⁻¹, respectively, which represent the average conditions of the high fire risk period in the study area.

The drying process used in this study is outlined as follows: (1) The collected needles were dried in an oven until the weight did not change, and then needles corresponding with the quality of each gradient of packing ratio were soaked in water for 24 h to reach the saturated moisture content Pan, Yang & Qu, 2002). (2) The saturated needles were then removed and drained, the free surface water was wiped off, and the weight was recorded, similar to the methods of Jin & Chen (2012). (3) The needles prepared in step (2) were placed in the tray to construct fuel beds with different packing ratios. The needle beds were then placed in a constant temperature and humidity box, with an automatic weighing balance (AS. US) in the box to automatically record the data every 10 min until the weight of the needle bed remained constant. This drying process experiment was repeated three times for each packing ratio, and the arithmetic mean moisture content value of the three experiments was recorded for each packing ratio. The basic outline of the experiment is shown in Table 2.

Model description

Research shows that when the temperature and humidity are constant, for dead fuels with a small Biot number (the ratio of internal moisture diffusion and external convection resistance to water vapor movement), the moisture content of the fuel bed can be calculated, as shown in Formula Eq. (1), (Byram & Nelson, 1963; Viney, 1991). This formula is especially effective for simulating the drying process of dead fuel in forests (Jin, Li & Li, 2000). The EMC and time lag in the drying process under different packing ratios can also be calculated using Formula Eq. (1), hereafter referred to as the one-time lag model: (1)${\displaystyle M=E+A\ast exp\left(-\frac{t}{\tau }\right)}$ where M is the moisture content of the fuel bed (g g⁻¹); E is the equilibrium moisture content of the fuel bed (g g⁻¹); τ is the time lag of the fuel bed (h); and t is the time (h).

A moisture cut-off point distinguishes the transition between the evaporation phase of the drying process and the diffusion phase. Since the two phases of the drying process are controlled by different mechanisms, different models need to be applied to represent the two drying phases. In this study, the moisture content cut-off point was set at 0.35 g g⁻¹ (saturated moisture content, Luke & McArthur, 1978) for the two drying phases. Based on this, a two-time lag model was developed to describe the drying process in two phases, from the initial moisture content to 0.35 g g⁻¹ and from 0.35 g g⁻¹ to the EMC, with each phase having an independent set of parameters, including EMC and time lag (Jin & Chen, 2012).

For the first phase of the drying process, when the moisture content of the fuel bed is greater than or equal to 0.35 g g⁻¹, the formula was written as: (2)${\displaystyle M_1=E_1+A_1\ast exp\left(-\frac{t}{{\tau }_1}\right).}$

For the second phase of the drying process, when the moisture content of the fuel bed is less than 0.35 g g⁻¹, the formula was written as: (3)${\displaystyle M_2=E_2+A_2\ast exp\left(-\frac{t}{{\tau }_2}\right)}$ with the symbols representing the same variables as in Formula Eq. (1), and the subscripts 1 and 2 denoting the first and second phases of the drying process.

Data analysis

The EMC and time lag of each fuel bed was calculated using the nonlinear least squares regression model based on the moisture content value at 10-minute intervals and formulas Eqs. (1)–(3). A t test was selected to analyze and compare whether there was a significant difference between the results of the two-time lag model and the results of the one-time lag model. K-fold cross-validation was used to calculate the mean absolute error (MAE) and mean relative error (MRE) of the two models (Formulas Eqs. (4)–(5)). The error of the two-time lag model was defined as the sum of the errors of the two phases. The MAE and MRE were then compared between the two methods to determine whether there was a significant difference. (4)${\displaystyle MAE=\frac{1}{n}{\sum }_{i=1}^n\left|m_i-\widehat{m_i}\right|}$ (5)${\displaystyle MRE=\frac{1}{n}{\sum }_{i=1}^n\frac{\left|m_i-\widehat{m_i}\right|}{m_i}}$ where m_i is the observed value of the fuel bed moisture content (g g⁻¹); $\widehat{m_i}$ is the predicted value of the fuel bed moisture content (g g⁻¹); and n is the number of samples in the drying process.

One-way ANOVA and multiple comparisons were used to analyze the effect of the fuel bed packing ratio on the EMC and time lag calculated by the two models, and the best-fitting equation was chosen to represent the effect of the packing ratio. The MAE and MRE of the model were calculated, and the accuracy of the prediction model was compared. Taking the observed values of key parameters as the abscissa and the predicted values as the ordinate, we drew a 1:1 graph, comparing the deviation of the fitted line and the 1:1 line to analyze the prediction effect of the model.

All data analyses were performed in Statistica 10.0 (http://www.statsoft.com; StatSoft, Inc., Tulsa, OK, USA) and in R Studio (RStudio Team, 2022).

Parameter estimations

The EMC and time lag of each fuel bed were calculated using formulas Eqs. (1)–(3), and the results are shown in Tables 3 and 4. The range of the EMC using the one-time lag model of the fuel beds with different packing ratios was 0.145 to 0.174 g g⁻¹, with a mean value of 0.162 g g⁻¹; the time lag range was 7.102–25.783 h, with a mean value of 12.500 h. For the two-time lag model, the EMC and time lag in the first phase ranged from 0.268 to 0.289 g g⁻¹ and 4.768 to 16.783 h, respectively, and the mean values were 0.280 g g⁻¹ and 8.200 h, respectively; the range of the EMC and time lag in the second phase were 0.134 to 0.160 g g⁻¹ and 8.325 to 27.657 h, respectively, and the mean values were 0.152 g g⁻¹ and 13.836 h, respectively.

Regardless of how the packing ratio of the fuel bed changed, E₂ was significantly higher than E. When the packing ratio was 0.040, E was significantly higher than E₁, but there was no significant difference found in other packing ratios. No significant difference was found between τ₂, τ₁ and τ, regardless of fuel bed packing ratio (Fig. 1).

Model comparison under different fuel bed packing ratios

Figure 2 shows the prediction errors of the one-time lag model and the two-time lag model at different fuel bed packing ratios. Without considering the packing ratio, the MAEs of the one-time lag model and the two-time lag model were 0.0087 g g⁻¹ and 0.0071 g g⁻¹, respectively, and the MRE values were 2.38% and 1.77%, respectively. The MAE and MRE values from the two models did not significantly differ between packing ratios, but the two-time lag model results were consistently lower than the MAE and MRE values calculated using the one-time lag model, while the coefficient of variation was higher using the two-time lag model than the one-time lag model.

Effects of fuel bed packing ratio on EMC and time lag

Table 5 shows the effect of fuel bed packing ratio on the EMC and time lag. The packing ratio of the fuel bed had no significant effect on the EMC in either model, but the time lag in the one-time lag model and the two-time lag model were both significantly affected by the fuel bed packing ratio.

Since the packing ratio of the fuel bed had no effect on the EMC, only the time lag was analyzed below. All time lag calculations increased as the packing ratio of the fuel bed increased, but only when the packing ratio of the fuel bed was 0.061 was this increase significant (Fig. 3).

Model of time lag with fuel bed packing ratio

According to Fig. 3, when the temperature was 25 °C and the humidity was 0.6 g g⁻¹, the time lag increased exponentially with the increase of the fuel bed packing ratio. Therefore, the time lag prediction model based on the packing ratio was: τ = a∗e^b∗β (where τ is time lag; β is the packing ratio; and a and b are parameters to be estimated in the model). The MAE of the prediction model of τ was 2.174 h, and the MRE was 17.0%; the sums of the MAE and MRE of the prediction model of τ₁ and τ₂ were 0.732 h and 9.69%, respectively (Table 6).

Using the observed value as the abscissa and the predicted value as the ordinate, we drew a 1:1 graph. This showed that the error of prediction model τ was high, while the error of τ₁ and τ₂ were both low. The τ₁ prediction model was the closest to the 1:1 line, followed by τ₂, with τ being the farthest from the line (Fig. 4).

Equilibrium moisture content

The key parameters obtained in the temperature and humidity range of this study were similar to those in previous studies. The range of the EMC using the one-time lag model was 0.145 to 0.174 g g⁻¹. Zhang, Sun & Liu (2020) obtained EMC fuel bed values of Korean pine with different packing ratios ranging from 0.131 to 0.139 g g⁻¹. Bakšić, Bakšić & Jazbec (2017) obtained an EMC of approximately 15% in Mediterranean pine when the humidity was 0.600 g g⁻¹. In our study, when using the two-time lag model, the variation range of the EMC in the first phase was 0.268−0.289 g g⁻¹ and 0.134−0.160 g g⁻¹ in the second phase. E₂ was significantly higher than E, but there was no significant difference between E₁ and E, which was mainly because the EMC was not affected by the initial moisture content but was significantly impacted by the final moisture content (Jin & Li, 2010). This study divided the drying process into two phases based on the cut-off point of the fiber saturated moisture content, and the moisture content at the end of the first phase was significantly higher than the moisture content used in the one-time lag model, so E₂ was significantly higher than E; the moisture content at the end of the second phase was the same as the moisture content value used in the one-time lag model, so there was no significant difference between E₁ and E.

Time lag

The time lag results in this study from both the one-time lag model and the two-time lag model were higher than those found by Jin & Chen (2012), which is mainly due to differences in air temperature and humidity. Studies have shown that the lower the humidity, the faster the fuel bed dries, and the lower the time lag. The humidity in this study was 0.600 g g⁻¹, while the humidity range in the Jin and Chen experiment was 0.105−0.342 g g⁻¹; the humidity interval in this study was significantly lower than that in Jin’s study, so the time lag was higher. The time lag of this study was also higher than that of Catchpole et al. (2001), mainly because their experiments were carried out in the field, and meteorological factors, such as wind speed and solar radiation, accelerated the moisture change in the fuel bed, leading to a reduction in time lag. There was no significant difference between τ₁, τ₂ and τ, but τ₁ < τ < τ₂ for different fuel bed packing ratios, which was similar to the research results of previous studies (Catchpole et al., 2001; Jin & Chen, 2012; Matthews, 2006). This is mainly due to the different mechanisms of the drying process. Pippen (2008) concluded that the evaporation process was easier than the diffusion process, explaining why τ₁ is the smallest and τ₂ is the largest.

Analysis of fitting effect under different methods

The MAE values calculated using the one-time lag model and the two-time lag model were 0.0087 g g⁻¹ and 0.0071 g g⁻¹, respectively, and the MRE values were 2.38% and 1.77%, respectively. Although the errors between the two models were not significantly different, the MAE and MRE of the two-time lag model decreased by 18.4% and 25.6%, respectively, compared to the one-time lag model. In summary, the key parameters obtained by the two models differ, and the calculation results of the two-time lag model were more accurate, meaning the results obtained from the two-time lag model are better than those from the one-time lag model, especially when the moisture content of the fuel bed was low (below 0.25 g g⁻¹). Using the two-time lag model will significantly improve the prediction accuracy of fuel bed drying calculations.

Correlation analysis

Regardless of whether the two phases of the drying process were distinguished, the packing ratio of the fuel bed had no significant effect on the EMC, similar to the findings of Anderson (1990). Packing ratio had a significant effect on τ, τ₁, and τ₂ with the highest effects seen in τ and τ₂. The drying process of the fuel bed includes both the evaporation of free water and the diffusion of bound water. As the fuel bed packing ratio increases, the paths of both the free water and bound water out of the fuel bed become more complex, making both evaporation and diffusion more difficult. Therefore, an increase in the fuel bed packing ratio causes a significant increase in time lag (Jin & Chen, 2012); Jin & Li, 2011; Matthews, Gould & McCaw, 2010). Because higher packing ratios make diffusion more difficult than evaporation, the effect of the fuel bed packing ratio on the diffusion process was greater. The effect of the packing ratio on time lag was the same whether the drying process was calculated using the one-time lag model or the two-time lag model, which may be because the fuel bed packing ratios used in this study were too low and the temperature and humidity ranges were too narrow. This experiment was conducted under high humidity conditions, and a previous study found that the effect of the fuel bed packing ratio on time lag was lower when the humidity was higher (Zhang, Sun & Jin, 2016). Therefore, the relationship between key parameters and the fuel bed packing ratio may differ when the packing ratio or humidity are higher than the values in this study.

Time lag prediction model

The time lag prediction model was established using the fuel bed packing ratio as the independent variable, and the errors were all within the allowable range. This model also revealed the influence of the fuel bed packing ratio on time lag. The prediction effect of τ₁ and τ₂ was better than τ. The sum of the errors of τ₁ and τ₂ were also lower than the error of τ.