Wildfires are crucial to water and carbon cycles on earth [1
]. On one hand, they emit CO2
into the atmosphere, which may inflict damage to climate [5
], air quality [6
] and health [7
]. On the other hand, human lives, property and infrastructure are vulnerable to large, high-intensity wildfires [8
]. Thus, predicting forest wildfire risk counts for a great deal [9
Fuels consumed in wildfires are composed of dead and live plant material. Many efforts have focused on live fuels [10
], whose moisture content changes slowly throughout the day [13
]. While Dead Fuel Moisture Content (DFMC) responds rapidly to atmospheric conditions, which is of great importance in affecting fire, such as ignition probability, spread rate and intensity [1
]. Therefore, DFMC estimation is required for quantifying fire danger, and almost all fire models include DFMC as an input variable [16
DFMC is a function of fuel size and atmospheric conditions [17
]. It increases or decreases with the change of climate variables through water vapor sorption or desorption until it eventually reaches a stable moisture content, i.e., Equilibrium Moisture Content (EMC) [18
]. The time it takes to lose or gain about 63% of the difference between its initial values and EMC is defined as time-lag [19
], which is related to the diameter of fuel. With the time-lag theory, dead fuels can be divided into four categories (1-h, 10-h, 100-h and 1000-h fuels, where the number refers to the time-lag of fuel) [20
]. For instance, 10-h fuel usually is related to the fuel with a diameter ranging from 0.64 to 2.54 cm [21
]. The 10-h DFMC is a promising predictor since it can be automatically measured in real time at study sites. For dead fuel with a certain size, its water content is commonly modeled with meteorological variables such as air temperature, relative humidity, wind speed, rainfall, solar radiation, soil moisture content [22
]. Plenty of models have been proposed to explain the relationship between those variables and DFMC, and they can be summarized as two approaches: empirical and process-based models [23
]. The empirical model relies on empirical relationships between input variables and DFMC from field observations [24
]. Since empirical methods are fully data-driven, they lack explanations for physical processes such as heat, water vapor fluxes and vapor exchange [32
]. Process-based models estimate DFMC by attempting to simulate the processes that affect the water of fuel [33
]. There are three types of process-based models: bulk litter layer models, models based on Byram’s diffusion equation and complete process-based models [16
]. Bulk litter layer models such as Tamai only contain interception and evaporation processes which lead to underestimating in wetter conditions [34
]. The models based on Byram’s diffusion equation heavily rely on EMC equation such as the Nelson formula for EMC [18
]. Complete process-based models try their best to represent fluxes of energy and water in fuel with energy and water balance conservation equations [37
]. Due to the complexities of the physics processes related to dead fuel, it is challenging to include all these processes into a process-based model [16
Above all, empirical models lack explanations for physical processes and process-based models are particularly complex [16
]. Recently, the combination of process-based model and empirical model has been widely accepted in remote sensing research, such as foliage fuel load (FFL) monitoring using radiative transfer model and machine learning method [39
], estimating crop primary productivity using machine learning methods trained with radiative transfer simulations [40
], physics informed neural networks for simulating radiative transfer [41
]. The combination of the process-based model and the empirical model represents another potential approach for estimating DFMC. This approach requires a process-based model and an empirical model [42
]. The empirical models used in previous studies were traditional machine learning and deep learning algorithms [43
]. Compared to traditional machine learning algorithms, deep learning methods can more effectively mine the information in the data, especially the Long Short-Term Memory (LSTM) network [45
], which performs well in describing the temporal dynamic changes of the time-sequential data [46
]. However, to our best knowledge, there are neither deep learning methods nor their combined application with physical process models in estimating DFMC of any size dead fuel. Since approaches based on the combination of physics model and empirical model have shown competitive performance in other areas, their applicability to 10-h DFMC estimation deserves to be tested.
This study firstly used the LSTM network to estimate 10-h DFMC. Secondly, we introduced an effective process-based model to guide the LSTM network for 10-h DFMC estimating. To test the performance of the LSTM network and the hybrid model, we implemented four effective models, including multiple linear regression (MLR), random forest, artificial neural network (ANN) and the fuel stick moisture model (FSMM). All six models were tested on a continuous DFMC dataset.
provides a summary of the performance of different methods for modeling DFMC on the BC1 site. The DFMC estimated by MLR is heavily underestimated and the R2
is 0.50, which is much lower than that of other models. Compared to MLR, the black-box data science models such as random forest and ANN, can capture the non-linear relationships between variables and DFMC without using the physics process. The random forest and ANN are much better than MLR, but still cannot reach the performance level of the process-based model, FSMM. The LSTM model achieved R2
of 0.91, RMSE of 3.24% and MAE of 1.97%, which is significantly higher than that of MLR, random forest and ANN. Compared to FSMM, LSTM has a close R2
, but lower RMSE and MAE. This demonstrates that knowledge gaps of the process model may be closing as long as the information of the data is fully mined and used efficiently. If the output of the process-based model along with the variables are used as input of the FSMM-LSTM model, the results are the best, with R2
of 0.96, RMSE of 2.21% and MAE of 1.41%.
To compare the performance of the six models in time-series more accurately, we provide their time series pattern in Figure 7
. The MLR model is still the worst, which will overestimate or underestimate the DFMC. The results, estimated by random forest and ANN algorithms, can basically agree with measurements in the time series, but there are still plenty of significant overestimations and underestimations. Furthermore, the process-based FSMM model, generates a satisfying result, except for the underestimates from May 20 to May 28 and August 14 to 16. The LSTM model generally shares a similar underestimation as FSMM, but it is more minor. The FSMM-LSTM algorithm still achieved the best results, that the estimated results are in perfect agreement with the measured values, with no overestimations and underestimations over the entire time series.
In the practical application of the model, a non-negligible aspect is computation efficiency. Thus, we listed the calibration time and the test time for all models on our dataset in Table 3
. When the process-based model FSMM was used, the computing time is enormous on both calibration (53.75 h) and test (7.53 h). However, all the data-driven models including the LSTM network did not take much time to train and test. Of all data-driven models, the LSTM network showed a comparative result with FSMM with higher efficiency. When the FSMM model and the LSTM network were combined, the total time cost is the same as FSMM, but the test time cost is very tiny.
The classical deep learning network-LSTM and its combination with a physics model FSMM were introduced to estimate DFMC. Furthermore, the effective process-based model FSMM and excellent empirical methods (MLR, random forest and ANN) were implemented for comparison.
Our results suggest that the MLR model has the worst performance, this may be because the linear model is insufficient to characterize the non-linear relationship between the input variables and the DFMC. Except for this, when black-box data science models such as random forest and ANN were used, the result did not become much better. The reason is that although random forest and ANN try to learn the non-linear relationships between drivers and DFMC, they cannot capture the information on a time series, that is what the LSTM network performs better in. The results of the LSTM network showed that the information in the data if it is fully mined, may help in closing knowledge gaps of the process model. Even though the process-based model FSMM performed well as the LSTM network, it is at the expense of enormous time (total about 61.28 h), which may be due to the continuous iteration hour by hour and the 3600 times incessant iteration in each hour. When we combined LSTM and FSMM (FSMM-LSTM), we can achieve even better results. This is because the output of FSMM contains important physical information about the dynamics of DFMC which when coupled with powerful data science frameworks such as the LSTM network, can result in great improvements in R2
and RMSE (Table 3
The LSTM network is a classic deep learning algorithm that performs well in capturing the temporal relationship in data. Furthermore, there are plenty of variants of the LSTM network. For example, SLSTM [53
], in which the quality variable vector is additionally regarded as the input of the intermediate cell and the three gates. In addition, when the residual connection was applied to the LSTM network, a more efficient deep learning algorithm was developed [65
]. It was beyond the scope of our study to investigate whether variants of the LSTM network performed best. We introduced the classic LSTM network only to show the superior performance of the deep learning network in estimating DFMC.
This study focuses on 10-h DFMC while there are four sizes of fuel in total: 1-h, 10-h, 100-h, 1000-h. The results showed that both the LSTM network and FSMM-LSTM model worked excellently in 10-h DFMC estimating. Since LSTM is a data-driven algorithm, it is not difficult to figure out its excellent performance on 1-h DFMC, 100-h DFMC and 1000-h DFMC. The FSMM-LSTM model performed better than the LSTM network, based on the hybrid of the LSTM network and a complex process-based model. Since the FSMM model has shown outstanding performances for all-size fuel [49
], it seems that the FSMM-LSTM model also applies to all types of fuel.
In addition, some other methods are effective at estimating DFMC, such as Aguado et al. (2007) [66
], Matthews et al. (2010) [23
]. Aguado et al. (2007) focused on the lack of calibration of moisture codes to different ecosystem or climate characteristics. They built the relationship between moisture and DFMC based on regression analysis. On the contrary, Matthews et al. (2010) is a complete process-based model which simulated the processes that occur in the fuel with energy and water balance conservation equations. These two methods are the typical example of the empirical method and the process-based model. However, empirical models lack explanations for physical processes, and process-based models may provide an incomplete representation of DFMC. Our study provides a kind of idea to combine them. Going forward, there are some directions that can be exploited future as a continuation of this work. Firstly, the LSTM network used in this study is not a state-of-the-art recurrent neural network and can be replaced. Second, for the specific problem of DFMC estimating, given its temporal and spatial nature, a promising extension would be to explore the temporal and spatial dependencies in DFMC. Third, we present a simple way for constructing a hybrid physics process and data information model by using the output of the process-based model as an input of the data science model, more complex ways of constructing models need to be explored to make the process-based and data science parts are tightly coupled.