Calibration and Assessment of Burned Area Simulation Capability of the LPJ-WHyMe Model in Northeast China

: Fire isone of the major forest disturbances in northeast China.In this study, simulations of the burned area in northeast Chinafrom 1997 to 2015 were conducted with the Lund–Potsdam–Jena wetland hydrology and methane (LPJ-WHyMe) model. The ﬁre modeling ability in northeast China was assessed by calibrating parameters in the model. The parameters in the model were calibrated against the satellite-based global ﬁre product (Global Fire Emission Database, version 4.1 (GFEDv4)) for the simulated burned area over the calibration period (1997–2010). Compared to the results with the uncalibrated parameters, the results obtained with the calibrated parameters in the LPJ-WHyMe model better described the spatial and interannual variability of the burned area. The spatial correlation coe ﬃ cient between the GFEDv4 and the simulations increased from − 0.14 for the uncalibrated version to 0.46 for the calibrated version over the calibration period. The burned area simulation ability was also improvedover the validation period (2011–2015), and the spatial correlation coe ﬃ cient between the GFEDv4 and the simulations increased from 0.20 for the uncalibrated version to 0.60 for the calibrated version. The mean absolute error (MAE) between the GFEDv4 and the simulations decreased from 0.018 for the uncalibrated version to 0.011 for the calibrated version (a decrease of 39%) over the calibration period and decreased from 0.020 to 0.016 (a decrease of 20%) over the validation period. Further numerical results showed that the improved simulation abilitiesof soil moisture and total aboveground litterhad an important contribution to improving the burned area simulation ability.Sensitivity analysis suggested that determining the uncertainty ranges for parameters in northeast China was important to further improving the burned area simulation ability in northeast China.


Introduction
Forestsare an important part of terrestrial ecosystems [1] and have a significant impact on carbon storage and dynamics in terrestrial ecosystems [2]. Fire is one of the main disturbances in forest ecosystems [3][4][5][6]. Previous studies indicated that the effects of fire on forest composition and forest productivity may equal or exceed the direct effects of climatic change [7,8]. For example, Schumacher and Bugmann [8] showed that fire was likely to become almost as important in shaping the forest landscape in the Swiss Alps as the direct effects of climate warming. Carbon cycling refers to the cyclic state of carbon elements in nature. Carbon cycling in forests mainly occurs when green plants store Simulations that have been improved by optimizing model parameters are even more accurate when fire models are applied at landscape and regional scales, as global parameterization might lead to misleading results. In northeast China, studies onfire simulation have often focused on the landscape scale [7,[47][48][49], whereas few studies have focused on the regional scale. Wang [50] used the BEPS (boreal ecosystem productivity simulator) model to simulate the temporal and spatial distributions of forest fires at a regional scale in northeast China from 2001 to 2010;however, the corresponding uncertainty of the simulations was not analyzed, and Wang noted that uncertainty should be considered in follow-up works. In a literature review, studies that focused on improving the fire simulation ability of DGVMs at the regional scale in northeast China were not found. Therefore, to improve the ability of fire simulation in northeast China, optimizing the parameters of the Lund-Potsdam-Jena wetland hydrology and methane (LPJ-WHyMe) model at a regional scale is necessary.
The objective of this study is to improve the ability of fire simulation in northeast China by using the parameter optimization method to calibrate the parameters (see Table 1) in the model. We used the LPJ-WHyMe model as a model platform, and the simulated burned area was calibrated against a satellite-based global fire product (Global Fire Emission Database version 4.1 (GFEDv4)) [51].

Study Area
Northeast China (38 • 43'N-53 • 34'N, 115 • 37'E-135 • 05'E), including mainly Heilongjiang, Jilin, Liaoning, and northeastern Inner Mongolia, was the focus of this study. The geomorphological types are variable, ranging from coastal plains to mountainous areas, with elevations ranging from 0 to 2500 m. The region is located in the middle temperate zone and cold temperate zone [52]. The climate is a continental monsoon climate with a strong monsoonal windy spring, a warm and humid summer, and a dry and cold winter. Annual precipitation ranges from 427 to 680 mm, of which more than half falls in July and August. The mean annual air temperature ranges from 2.49 to 6.02 • C. The frost-free period is between 130 and 170 days, with an early frost in September and a late frost in May [53].
The main forest types in northeast China are deciduous coniferous forestdominated byLarixgmelini forest, deciduous broadleaved forest dominated by Betula ermanii forest, deciduous broadleaved and coniferous mixed forestdominated by Pinus koraiensis forest, and evergreen coniferous forest dominated by Picea and Abies mixed forest. The forests in this area are mainly distributed in the Great Xing'an Mountains, the Xiaoxing'an Mountains, and the Changbai Mountains [54]. Most of the forests in the region are located in seasonally frozen or permafrost zones [55]. Northeast China is seriously affected by forest fires [1,56]. Both the number of forest fires and the burned area are large in northeast China. For example, in the Great Xing'an Mountains, during the 43 years from 1966 to 2008, 1561 forest fires occurred in this area, with an average area of 7.85 × 10 4 ha, accounting for 27.32% of the average area of forest fires in China [1,56,57]. Many severe forest fires in China occur innortheast China. For example, the famous forest fire that occurred in the Great Xing'an Mountains in 1987 burned over 1 million hectares [1,58].

LPJ-WHyMeModel
The LPJ-WHyMe model [59][60][61][62] is a development of the LPJ DGVM that was originally described by Gerten et al. [63] and Sitch et al. [64]. The LPJ model explicitly considers photosynthesis, mortality, fire disturbance, and soil heterotrophic respiration. A detailed description and evaluation of the model can be found in Sitch et al. [64]. The LPJ model has been widely used to discuss variation in terrestrial ecosystems and the carbon cycling [65], and its simulation of plant functional types (PFTs) has been shown to be in agreement with the observations in China [37]. LPJ-WHyMe was originally described in Wania et al. [62]. LPJ-WHyMe introduces permafrost and peat into the LPJ model, which takes into account the changing characteristics of frozen soil (soil temperature, active layer depth, and water level), the carbon cycling and the vegetation nitrogen content under climate change, and fire disturbance. A detailed soil freeze-thaw process can be obtained by numerically solving the thermal diffusion. This model is used to study the photosynthesis of vegetationand the competition between 12 PFTs.

Fire Module Glob-FIRM in the LPJ-WHyMeModel
To link fire regimes and their effects on vegetation dynamics, Thonicke et al. [4] developed a general fire model, Glob-FIRM (global fire model), that has been incorporated into the LPJ-WHyMe model. The approach is a compromise between the fire history concept (a statistical relationship between the length of the fire season and the burned area) and a process-oriented model methodology (estimation of fire conditions based on soil moisture). In Glob-FIRM, the annual burned area is a nonlinear empirical function of the daily fire probability, which depends on litter moisture and a specific litter moisture threshold for each PFT. The probability of fire occurrence for a grid cell is calculated daily as a function of litter moisture with temperature and the available litter acting as limiting factors [4]. Human-changed fire regimes and other land use impacts are not considered in the LPJ-WHyMe model at present.
In the Glob-FIR model, the exponential power function (Equation (1)) is used to approximate the probability of the occurrence of at least one fire per day in a grid cell: where mis the daily moisture status in the upper soil layerand m e is the moisture of extinction. Statistically, fire is considered to be absent when mexceeds m e , with probabilities lying within the 95% confidence interval. The annual length of the fire season is estimated by adding the probability of at least one fire per day over the whole year: where A is the burned area fraction and s = N/365 (N is shown in Equation (2)).

Data
As input data, the LPJ-WHyMe model requires monthly climate data (air temperature, total precipitation, cloud cover, and wet days), soil texture information, and annual values of global atmospheric CO 2 concentrations. For the simulation, we used CRU05 (1901-2016) 0.5 • ×0.5 • longitude/latitude monthly climate data provided by the Climate Research Unit, University of East Anglia, UK. [66]. The CO 2 concentrations were derived from ice core and atmospheric measurements [67]. The soil texture information was obtained from the Food and Agriculture Organization (FAO) soil dataset [68].
The 1997-2015 monthly burned area data had a spatial resolution of 0.25 degrees (latitude) by 0.25 degrees (longitude) and were provided by GFEDv4 (https://daac.ornl.gov/VEGETATION/guides/ fire_emissions_v4.html) [51]. The GFEDv4 burned area data were a mixture of observations and satellite-based estimates. These data were derived by combining 500-mmoderate resolution imaging spectroradiometer (MODIS) burned area maps with active fire data from the Tropical Rainfall Measuring Mission (TRMM),visible and infrared scanner (VIRS), and the along-track scanning radiometer (ATSR) family of sensors. For additional information, refer to Giglio et al. [69]. The GFEDv4 fire product represents the most comprehensive attempt to derive the burned area and fire emissions from remote sensing data, and this dataset is suitable for calibrating functions and parameters and for evaluating present-day simulations of global fire models [70].

Model Optimization
The standard approach to solve an optimization problem begins by designing an objective function. In most cases, the objective function defines the optimization problem as a minimization task. The objective function is used to quantitatively describe deviations between a simulated value and an observed value in a model and is used as an optimization criterion in parameter optimization. Different objective functions are used to evaluate different features of a model, and therefore, the choice of the objective function is very important. Gupta et al. [71] listed 9 objective functions for parameter optimization. To make the mode analog value close to the observed value in a time series, the root mean squared error (RMSE), correlation coefficient (r), absolute mean difference (bias), and the transformation form of the bias are often used as objective functions. Previous studies have not been able to clearly demonstrate the superiority of any particular objective function for model calibration. Among them, the RMSE is the most widely used in recent studies [72][73][74][75]. Therefore, we used the RMSE as the objective function. The specific expression was as follows: where n denotes the number of years for which we have observed values, m is the modeled value, and o is the observed value. In our study, the differential evolution (DE) algorithm was employed to obtain the minimum value of Equation (4). The DE algorithm was first developed by Storn and Price [76] and was determined to be the best type of evolution algorithm for solving the real-valued test function [77]. The DE algorithm has been developed extensively and has been applied widely [78][79][80][81][82][83][84][85][86][87][88][89]. Due to its simplicity in principle and convenience in computer programming, the DE algorithm has been successfully applied in diverse fields [79][80][81], such as power electronics [82,83], chemical engineering [84], hydrology [85], and numerical optimization [86]. The DE algorithm has been applied to explore terrestrial ecosystem responses to climate change, and details regarding the algorithm have been provided [87][88][89]. In addition, the validity of the DE algorithm was checked before it was applied to search for the optimal value with the LPJ-WHyMe model [90]. Table 1 shows the physical meanings, standard values, and minimum and maximum values of the 28 parameters that are directly or indirectly related to the fire module in the LPJ-WHyMe model. In addition to the parameters of the fire module, the parameters of other physical processes, such as photosynthesis and plant evapotranspiration, are also included. These physical processes affect soil moisture and litter, and therefore, they are also important factors contributing to the uncertainty in burned area simulations.

Experimental Design
The study period was 1997-2015 (n =19), which was the common period between the GFEDv4 and the model forcing data. The period was separated into a calibration period from 1997 to 2010 (n =14) and a validation period from2011 to 2015 (n =5). During the calibration period, the parameters in the model were calibrated with the observed data, and the parameter set was optimal when the objective function satisfied the minimum value. During the validation period, the optimal parameter set of the calibration period was used to simulate the burned area, and the simulation results were evaluated with the observed data.
To explore whether changing the parameter range could further improve the simulation ability and find a more reasonable range in parameters for northeast China, we performed parameter sensitivity tests. The parameter uncertainty range was set to 25%, 50%, and 100% of the intrinsic parameter uncertainty range in the model. The specific expressionsare described in Table 2. Table 2. Parameter sensitivity analysis.

Results
The LPJ-WHyMe model simulations with the parameter optimization method introduced in Section 2 (calibrated LPJ-WHyMe) were evaluated against the GFEDv4 fire product and the original fire parameterization in the LPJ-WHyMe model (the uncalibrated LPJ-WHyMe model).

Calibration Period
The spatial correlation coefficient of the burned area between the GFEDv4 and the uncalibrated LPJ-WHyMe model was −0.14 (p value (p) < 0.01; Figure 1b). The uncalibrated LPJ-WHyMe model tended to underestimate the burned area in northeast China, and the simulation results were quite different from the observations (Figure 1a,b). The spatial correlation coefficient of the burned area between the GFEDv4 and the calibrated LPJ-WHyMe model was 0.46 (p < 0.01; Figure 1c). The calibrated LPJ-WHyMe model could reproduce the main features of the spatial distribution of the burned area (Figure 1a,c). The model correctly captured the lightly burned area in the southern part of the study area and the moderately burned area in the central part of the study area.The mean absolute error (MAE) between the GFEDv4 and the simulations decreased from 0.018 for the uncalibrated LPJ-WHyMe model to 0.011 for the calibrated LPJ-WHyMe model, a decrease of 39% (Figure 1b,c).

Validation Period
The calibration period and the validation period had similar conclusions.The simulation results ofthe uncalibrated LPJ-WHyMe model were quite different from the observations (Figure 2a,b). The calibrated LPJ-WHyMe model could reproduce the main features of the spatial distribution of the burned area (Figure 2a,c). The spatial correlation coefficient between the GFEDv4 and the simulations increased from 0.20(p < 0.01) for the uncalibrated LPJ-WHyMe model to 0.60 (p < 0.01)for the calibrated LPJ-WHyMe model (Figure 2b,c). The MAE between the GFEDv4 and the simulation decreased from 0.020 for the uncalibrated LPJ-WHyMe model to 0.016 for the calibrated LPJ-WHyMe model, a decrease of 20% (Figure 2b,c). The simulation of the calibrated LPJ-WHyMe model was closer to the GFEDv4 than the uncalibrated LPJ-WHyMe model.

Case Analysis
To further explore the results, we randomly selected two cases (point A and B) with good simulation results in areas with high correlation coefficients ( Figure 3b) and two cases (point C and D) with poor simulation results in areas with low correlation coefficients separately.
For both points A and B (Figures 4 and 5a,b),the time series correlation coefficientbetween the GFEDv4 and the calibrated LPJ-WHyMe model was higher than that between the GFEDv4 and the uncalibrated LPJ-WHyMe model, andthe values of the calibrated LPJ-WHyMe model in most individual years were closeto those in the GFEDv4 and were therefore more accurate than those of the uncalibrated LPJ-WHyMe model.  As for both point Cand D (Figures 4 and 5c,d), the time series correlation between the GFEDv4 and both model simulations waspoor, and the calibrated LPJ-WHyMe model still failed to capture interannual variation in the GFEDv4, although, for point D, the values of the calibrated LPJ-WHyMe model in most individual years were closer to those in the GFEDv4 than those of the uncalibrated LPJ-WHyMe model.
After parameter optimization, the simulation ability of the fire module improved for most areas in northeast China, but there were still some areas where improving the simulation capability was difficult.

Parameter Sensitivity Analysis
After parameter optimization, the simulation ability of the fire module improved, but there were still some areas where the simulation effects were poor. We suspect that this result may be because the parameter uncertainty range of the orginal model was not suitable for northeast China. Therefore, we conducted sensitivity tests to explore whether changing the uncertainty range of parameters could further improve the simulation ability.

Calibration Period
The results of the sensitivity tests are shown in Figure 6. When the parameter uncertainty range was 25%, 50%, and 100% of the original parameter uncertainty range, the spatial correlation coefficients between the GFEDv4 and the simulation were 0.21, 0.31, and 0.46, respectively, and the MAE between the GFEDv4 and the simulation were 0.017, 0.016, and 0.011, respectively. That is, as the range of parameter uncertainty increased, the spatial correlation coefficient increased, and the MAE decreased.

Validation Period
There was also a regularity in the validation period that was consistent with the calibration period. As shown in Figure 7, when the parameter uncertainty range was 25%, 50%, and 100% of the original parameter uncertainty range, the spatial correlation coefficients between the GFEDv4 and the simulation were 0.53, 0.58, and 0.60, respectively, and the MAE between the GFEDv4 and the simulation were 0.020, 0.019, and 0.016, respectively. That is, as the range of parameter uncertainty increased, the spatial correlation coefficient increased, and the MAE decreased.

Soil Moistureand Total Aboveground Litter
By adjusting the parameters in the model, the calibrated LPJ-WHyMe model improved the burned area simulation capability. Then, we want to figure out which aspects of the simulation ability of the burned area improved.
To model fire on a global scale, some simplified hypotheses were made in the fire module of the LPJ-WHyMe model. First, fire occurrence depends only on the fuel load and soil moisture (i.e., the amount of dry material available), which combines both the influences of climate and vegetation [4]. Second, ignition is assumed to eventually occur without specific considerations. That is, the burned area in the LPJ-WHyMe model was mainly determined by soil moisture and the total aboveground litter. The simulation results of soil moisture and total aboveground litter are as follows.
Compared with the results of the uncalibrated LPJ-WHyMe model, the soil moisture results simulated by the calibrated LPJ-WHyMe model were reduced during the calibration period and the validation period (Figure 8). The regional average from 1997 to 2015 was reduced from 0.33 m 3 ·m −3 (the uncalibrated LPJ-WHyMe model) to 0.30 m 3 ·m −3 (the calibrated LPJ-WHyMe model). The range of regional average observations of soil moisture from 1981 to 2007 is from 0.10to 0.30 m 3 ·m −3 in northeast China [91], and the simulation results for CLM3.5 from 1979 to 2008 range from 0.20 to 0.35 m 3 ·m −3 [92].Compared with the value obtained with the uncalibrated LPJ-WHyMe model, the regional average value simulated by the calibrated LPJ-WHyMe model was closer to the observed value [91] and the result of other simulation model [92]. Compared with the results of the uncalibrated LPJ-WHyMe model, the results of total aboveground litter simulated by the calibrated LPJ-WHyMe model were higher during the calibration period and during the validation period ( Figure 9). The regional average from 1997 to 2015 increased from 3.24 g C·m −2 (the uncalibrated LPJ-WHyMe model) to 5.64 g C·m −2 (the calibrated LPJ-WHyMe model).

Analysis of the Mechanism to Improve Fire Simulation Ability
According to the model principle, the burned area is negatively correlated with soil moisture and positively correlated with total aboveground litter. Our results showed an underestimate of the burned area in northeast China. Therefore, improving the simulation results of burned area can be achieved by reducing the soil moisture and increasing the amount of total aboveground litter to make the burned area resultscloser to the observed value. Therefore, we analyzed the results of soil moisture and total aboveground litter that were simulated during the calibration and validation periods.
The calibrated LPJ-WHyMe model improved the accuracy of the simulated burned area by reducing the soil moisture and made the burned area value closer to the observed value; in other words, there was a negative feedback between the burned area and soil moisture, as we expected. Arora and Boer [93] developed a fire module that was incorporated into the Canadian terrestrial ecosystem model (CTEM). The CTEM fire module also contained a negative feedback between the burned area and soil moisture.Bistinaset al. [94] showed that the burned area decreased as the fuel moisture increased, and they suggest that this relation is because soil moisture controls the moisture content of live fuels.
The calibrated LPJ-WHyMe model improved the burned area estimation by increasing the total aboveground litter; in other words, there was a positive feedback between the burned area and the total aboveground litter, as we expected. Li and Levis [38] developed a fire module in the CLM-DGVM that featured a positive feedback between the burned area and aboveground litter pools. The fire module in the integrated biosphere simulator (IBIS) [95] also had a positive feedback between the burned area and litter amount (modelcode version 2.5, released November 2000, http://www.sage.wisc.edu/download/IBIS/ibis.html). Therefore, we can use fire to reduce aboveground litter either intentionally (prescribed burning) or opportunistically (letting a naturally ignited fire burn as a "managed wildfire") under moderate weather conditions [96]. That is an efficient, cost-effective, and ecologically beneficial way to reduce theburned area.

Limitations of the Research
We have concludedthat the calibrated LPJ-WHyMe model improved the accuracy of the simulated burned area by reducing the soil moisture and increasing the total aboveground litter after mechanism analysis. However, due to the lack of sufficient observation data, we cannot conclude that the improved simulation abilities of soil moisture and total aboveground litter improve the burned area simulation ability of the model. Therefore, more observational datasets are required for soil moisture and total aboveground litter to further support model validation.
After parameter optimization, the simulation ability of the fire module improved, but there were still some areas where the simulation effects were poor. Therefore, there are limitations in the use of the parameter optimization method to improve the fire simulation ability within the parameter uncertainty ranges of the original model.According to the parameter sensitivity test, the parameter uncertainty range impacted the simulation capabilityboth in the calibration period and the verification period. Therefore, we propose determining the parameter uncertainty ranges in northeast China to further improve the simulation capability of the numerical model.
Many parameters are included in the model, and it would be costly and impractical to determine the uncertainty rangesof all the parameters. Therefore, we suggest usinga more effective approach, such as CNOP-P [97], to choose certain key parameters that are inferred to be sensitive and important to improving the simulation ability of the model.Then, the uncertainty rangesofthese sensitive and important parameters in northeast China can be obtained by observation and other methods to further improve the simulation ability.This approach is both economical and viable.

Conclusions
Comparisons between satellite-based burned area data from the GFEDv4 and the burned area data simulated by the fire module in the LPJ-WHyMe model indicated that the LPJ-WHyMe model failed to represent the observed spatial and temporal properties of fire and that there were large discrepancies between the model and observations with regard to the average annual burned area. We found that when applied at the regional scale, the use of the parameterization developed for global-scale application is limited. Therefore, to improve the ability of fire simulation in northeast China, we proposed a region-specific parameterization for use in northeast China by using a parameter optimization method to calibrate the parameters in the LPJ-WHyMe model against the GFEDv4.
After parameter optimization, the calibrated LPJ-WHyMe model reasonably simulated the spatial distribution of the annual burned area and was shown to have a higher spatial correlation with the GFEDv4 than the uncalibrated LPJ-WHyMe model.
Further numerical results showed that the improved simulation abilities of soil moisture and total aboveground litter had an important contribution to improving the burned area simulation ability. However, due to the lack of sufficient observation data, more observational datasets are required for soil moisture and total aboveground litter to further support model validation.
Nevertheless, there were still some areas where improving the simulation capability was difficult. Therefore, we conducted sensitivity analysis and found that as the parameter uncertainty range increased, the spatial correlation coefficient increased, and the MAE decreased. Sensitivity analysis suggested that determining the uncertainty ranges for parameters in northeast China was important for further improving the burned area simulation ability in northeast China. We suggest using an effective and economical approach, such as CNOP-P, to choose certain key parameters that are determined to be sensitive and important to improving the simulation ability of the model. This work improved the ability to simulate forest fire in northeast China and provided technical support for accurately quantifying the impact of fire disturbance on the carbon cycle of forest ecosystems in northeast China.

Conflicts of Interest:
The authors declare no conflict of interest.