Dynamic Correction of Forest Fire Spread Prediction using Observation Error Covariance Matrix Estimation Technique based on FLC-GRU

Dynamic Correction of Forest Fire Spread Prediction using Observation Error Covariance Matrix Estimation Technique based on FLC-GRU | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Dynamic Correction of Forest Fire Spread Prediction using Observation Error Covariance Matrix Estimation Technique based on FLC-GRU Tianyu Wu, qixing zhang, Jiping Zhu, Jinhong Wu, Jinyang Dai, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3972535/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 14 Oct, 2024 Read the published version in Fire Ecology → Version 1 posted 4 You are reading this latest preprint version Abstract Background Data assimilation (DA) techniques have played a significant role in improving the prediction accuracy of forest fire spread. This dynamic correction technique enhances the analytical values that better reflect the fire situation by weighting the predicted values and observed values. The weighted importance of each contribution is determined by the magnitude of its associated error. However, as a crucial parameter affecting prediction accuracy, the covariance matrix of observation errors is often inaccurate and neglects its own temporal correlation. This is unfriendly to spread prediction results. To address this issue, we proposed a targeted technique for estimating the observation error covariance matrix (R matrix) based on the Fire Line Convolutional Gated Recurrent Unit (FLC-GRU). Results We integrated this method into the DA framework and validated its applicability and accuracy using Observing System Simulation Experiment (OSSE). Through comparisons with traditional methods, the results indicate that using the FLC-GRU estimated R matrix for correction calculations leads to wildfire prediction locations that are closer to the true values. Conclusion s The proposed approach learns the covariance matrix directly from time-series observed fire line data, without requiring any prior knowledge or assumptions about the error distribution, in contrast to classical posterior tuning methods. The proposed method significantly improves the rationality and accuracy of R matrix estimation, enhances the utility of observational data, and thereby improves the correction accuracy of forest fire spread predictions. Moreover, the study also demonstrates the applicability of the proposed method within the DA framework. Forest fires Spread prediction Data assimilation Observation error covariance matrix Neural networks Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1. Background Accurately predicting the development of forest fire spread is one of the most crucial aspects in emergency management of forest fires. To address the issue of low prediction accuracy in traditional computer simulation due to errors in input data or the model itself, data assimilation (DA) techniques have been applied in this field. The main idea is to assimilate observed values into the predicted values obtained through methods like physical models. This is achieved by weighting the predicted values and observed values to obtain analytical values that better reflect the system state. Mandel et al. first applied the idea of DA to the field of forest fire spread prediction (Mandel et al. 2008 ). Subsequently, scholars such as Rochoux and Trouvé conducted extensive research on ensemble Kalman filter (EnKF) algorithms (Rochoux et al. 2014 , 2015 ; Zhang et al. 2019 ), which became one of the mainstream correction methods in the field of forest fire spread prediction. In recent studies, Zhou et al. first applied the ensemble transform Kalman filter (ETKF) to forest fire spread prediction, improving the correction effect (Zhou et al. 2019 ). Building upon this, Zhou et al. explored improvements to the correction algorithm under conditions of large observation data errors or missing data (Zhou et al. 2021 ). In a recent study, the author's research team found that deterministic ensemble Kalman filter (DEnKF) has superior correction ability for forest fire spread prediction compared to EnKF. In summary, the forest fire spread prediction method based on DA has achieved widespread development and research results. In the computation of data assimilation techniques, the weighted importance of predicted values and observed values is determined by their respective error covariances, corresponding to the background error covariance matrix (Q matrix) and the observation error covariance matrix (R matrix). Moreover, the weighted results directly influence the outcome of the final analysis values. However, in practical engineering, the unavailability of true values makes it impossible to directly calculate the magnitude and distribution of errors, posing a challenge in the estimation of error covariances. In the research on dynamic correction of forest fire spread prediction, error covariance is often simplified. Specifically, regarding the estimation of Q matrix, using the Ensemble Kalman Filter (EnKF) algorithm as an example, sample covariance matrix is commonly employed to represent Q matrix. This step avoids the direct calculation of errors by implicitly advancing the ensemble forecast. However, unlike the Q matrix, the R matrix cannot be empirically estimated from the ensemble of simulated trajectories. Therefore, the treatment of the R matrix is typically more straightforward, often defined empirically as a scalar matrix, lacking theoretical rigor and potentially adversely affecting the accuracy of analytical values. Furthermore, research has indicated that observation errors are correlated and exhibit dependence on both time and state. Considering these correlated observation errors in DA can lead to more accurate analysis results (Stewart et al. 2008 ; Li et al. 2009 ; Miyoshi et al. 2013 ; Waller et al. 2014 ). In recent years, significant research on error handling methods has been conducted in various fields applying DA techniques (Desroziers and Ivanov 2001 ; Desroziers et al. 2005 ; Stewart et al. 2013 ). In a recent comprehensive review by Pierre Tandeo, existing methods are categorized into two main classes: 1) Innovation-based methods, such as the method of moments, which assumes equality between theoretical and observed moments of innovations, and 2) Likelihood-based methods, which utilize the likelihood of the observations contained in the innovations. The mentioned methods fall under traditional posterior tuning methods, and more details can be found in (Tandeo et al. 2020 ). Additionally, some covariance estimation techniques based on neural network algorithms have been proposed and achieved good results (Cheng et al. 2023 ). Chen et al. introduced an observation error covariance specification based on Long Short-Term Memory (LSTM) and demonstrated its good performance in the Lorenz twin experiment and shallow water equations, commonly used for testing DA algorithms (Cheng and Qiu 2022 ). However, for the estimation of the R matrix in predicting forest fire spread, there is still a lack of targeted research and validation. In this study, we propose a technique for estimating the R matrix based on the Fire Line Convolutional Gated Recurrent Unit (FLC-GRU). This aims to enhance the accuracy and efficiency of R matrix estimation while improving the correction accuracy of forest fire spread predictions. In contrast to traditional posterior tuning methods, this new approach does not require prior knowledge of either the background or the observation matrix. In the network design, we chose to use the more efficient GRU over LSTM to learn the error distribution. Additionally, before training, we utilized a convolutional network to not only retain the temporal information of the observed fire line data but also extract its spatial information, enhancing the network's performance. To validate the accuracy of the proposed method in correcting forest fire spread predictions, we utilize actual terrain and fuel data from the Idaho Panhandle National Forests and conduct Observing System Simulation Experiment (OSSE). 2. Methodology 2.1 The R matrix estimation technique based on Fire Line Convolutional Gated Recurrent Unit (FLC-GRU) Convolutional Neural Networks (CNN) are commonly employed for image processing (Krizhevsky et al. 2017 ; Lin et al. 2019 ; Huo et al. 2022 ), effectively reducing large volumes of image data to smaller datasets while retaining essential features, aligning with principles in image processing. In 2014, Cho et al. introduced the Gated Recurrent Unit (GRU), a simplified version of Long Short-Term Memory (LSTM) (Cho et al. 2014 ). GRU maintains robust memory capabilities for sequential data while enhancing computational efficiency. Leveraging the high sensitivity of convolutional Networks and GRU networks to spatial and temporal features, respectively, we aim to better provide a better solution to the estimation problem of the observation error covariance matrix in the context of forest fire spread. To achieve this, we propose the Fire Line Convolutional Gated Recurrent Unit (FLC-GRU) network, encompassing dataset generation, data preprocessing, convolutional processes, and GRU processes. The FLC-GRU network structure is illustrated in Fig. 1 . We initiate the process by employing FARSITE, a commonly used forest fire spread tool based on the Rothermel model and Huygens theory. This tool generates a set of fire line position state values X t =[X t 0 , X t 1 , ..., X t i ,..., X t T ]. X t =M(X t−1 , θ t−1 ) , (1) where M is the nonlinear forecast operator, i.e., the FARSITE fire growth model; θ denotes the related parameters, which include the topography, fuel, weather and wind parameters. Concurrently, we pre-generate a Symmetric Positive Definite (SPD) matrix R, representing the specific properties of the R matrix. Subsequently, we augment X t by introducing observation errors ϵ that follow a Gaussian distribution, resulting in the generation of observed data y t =[y t 0 , y t 1 , ..., y t i ,..., y t T ]. y t =H(X t )+ϵ , (2) where H can be simply viewed as a selection operator that pairs each marker in the simulated fire fronts with its closest neighbor along the observed fire fronts, and ϵ~N(0, R). This process is iterated N times to produce N sets of 'Observation y' and 'R matrix' with precise corresponding relationships. In this study, T is set to 20 hours, and the fireline state X t i at each time step is composed of a set of k = 100 fire points, i.e., X t i =[e i,1 , n i,1 , e i,2 , n i,2 , ..., e i,j , n i,j , ..., e i,100 , n i,100 ]T. Where (e i,j , n i,j ) represents the coordinates of the j-th observed fire point at time i. In accordance with the requirements of the DA analysis steps, it is stipulated that the generated R matrix is a SPD matrix of size 2k*2k, i.e., 200*200. The values of the diagonal elements follow a random distribution in the range of (0, 200). The aforementioned N sets of samples, consisting of 'Observation yt' and labels 'R matrix,' serve as the training set for the FLC-GRU network in this study. A total of 14,000 data sets were generated, with 11,200 sets allocated for training and 2,800 for validation. The network's input is y t =[y t 0 , y t 1 , ..., y t i ,..., y t T ], and the output is the R matrix. As mentioned earlier, GRU possesses the capability to handle time-series data and often significantly improves training efficiency compared to LSTM while maintaining similar training effectiveness. Therefore, we aim to utilize the GRU network to learn the distribution of observation errors. In the network design for dynamic correction in predicting forest fire spread, our goal is to retain the temporal information of the observed fire line data while fully leveraging the spatial information contained in the data. To achieve this, before initiating the training of the GRU network, we applied convolutional processing to the observed fire line data to extract its spatial features. Building upon this, given the suitability of convolutional networks for extracting image features, prior to the convolution operation, we remapped the observed data, represented as y t , to multiple layers of fire images by transforming the coordinate matrix at time T. In this study, Stochastic Gradient Descent (SGD) is employed as the weight update algorithm, with a learning rate of 1e-5, exponential learning rate decay strategy, the application of weight decay, beta set to 0.8, and the Mean Squared Error (MSE) as the loss function. Ultimately, given a set of observation data with an unknown error distribution, the network can output the predicted R matrix. 2.2 The core idea of the method In summary, the core of this method is to address the challenge of accurately estimating the R matrix when observing the fire line in forest fire incidents, given the inherent uncertainty in determining the true fire line positions. To tackle this issue, the method adopts a reverse-thinking approach to identify the precise correspondence between observation data and the R matrix. By pre-generating a specific R matrix and generating observation data following the distribution specified by this matrix, a training set is established. Subsequently, the FLC-GRU network can learn such error distributions, improving the efficiency and accuracy of estimating the R matrix in dynamic correction for predicting forest fire spread. This approach involves a proactive generation of observation error covariance matrices, creating a training set that facilitates the learning of error distributions through convolutional and GRU networks. 2.3 Forest fire spread prediction dynamic correction system based on FLC-GRU Building upon this, the estimation technique is integrated into the DA-based forest fire spread prediction process to enhance the precision of dynamic corrections in predicting forest fire spread. As illustrated in Fig. 2 , in response to a sudden forest fire, while conducting computer-simulated predictions of forest fire spread, real-time observations of the fire scene can be obtained through satellite remote sensing, unmanned aerial vehicles, or human observation. This provides observed fire lines for assimilation. Subsequently, the FLC-GRU network proposed in this paper is employed to estimate the observation error covariance matrix for assimilation calculations, yielding improved estimates of the fire line's position. The output of the current time's fire line position serves as the input for the next moment's prediction of forest fire spread, enhancing the results for the next time step. This process forms a rational and comprehensive dynamic correction method for predicting forest fire spread. It is noteworthy that in this study, FARSITE is utilized as the tool for predicting forest fire spread, and the DA method employs the DEnKF algorithm, serving as an example. The applicability of this method remains unaffected by the choice of other forest fire spread prediction models or tools, as well as alternative DA algorithms. 3. Experimental designs 3.1 Study area Taking into consideration the variations in terrain, we selected the Idaho Panhandle National Forests located in the state of Idaho, United States (latitude 47.5° N to 48° N, longitude 115.7° W to 116.7° W) as our research focus. This region experiences a warm climate and substantial fuel accumulation, posing a higher risk of forest fire incidents. We obtained the landscape file (.LCP) for the study area from LANDFIRE ( http://landfire.gov/ ), encompassing topographical and fuel data essential for conducting forest fire spread predictions based on FARSITE. The study area is depicted in Fig. 3 . 3.2 Experiment set up To validate the applicability of the proposed method, we designed an Observing System Simulation Experiment (OSSE), which is one of the most commonly used methods to assess the performance of DA algorithms. The OSSE for this study comprised four groups: 1) Real group: Simulating without input errors to generate a simulation result that serves as the true fire lines. 2) Simulation group: Introducing input errors to simulate real-world scenarios where, due to errors in input data and the model, only uncorrected predictions can be obtained. 3) DA group (Data Assimilation group): Applying DA algorithms to correct the results of the simulation group. However, common rough handling methods were used for the R matrix. 4) FLC-GRU group (Data Assimilation with Fire Line Convolutional Gated Recurrent Unit group): Employing DA for correction while utilizing the R matrix estimation method proposed in this paper. See Table 1 for details. Table 1 Experimental designs. Input fire source DA method R matrix Real group No error No No Simulation group With error No No DA group With error DEnKF Defining a scalar matrix FLC-GRU group With error DEnKF Estimating based on FLC-GRU In this study, we adopted the Deterministic Ensemble Kalman Filter (DEnKF) as the DA method, with a set ensemble size of 20. The duration of the forest fire spread simulation experiment based on FARSITE was set at 20 hours, with assimilation performed every 1 hour. We assumed a spatially uniform distribution of wind, with a globally set southeastern wind speed of 3.5 m/s. It is important to note that the primary focus of this paper is to validate the applicability and accuracy of the proposed new method in dynamic correction of forest fire spread predictions by comparing it with traditional methods. Therefore, some simplifications were made in the experimental settings for certain parameters, which is a reasonable approach. In this experiment, observational data is derived from the Real group, where we added errors following an unknown R matrix to generate observational data based on the real fire line. In the DA group, we assume observation errors to be random noise with a standard deviation of 200 meters. The R matrix is empirically defined as a scalar matrix, which is a common practice in DA for correcting forest fire spread predictions. This setup is also designed to address the fact that in previous approaches, people typically assigned values to the R matrix based on empirical considerations, lacking a certain degree of theoretical basis. In the DA with FLC-GRU group, we employed the FLC-GRU network proposed in this study to compute the R matrix. 3.3 Evaluation criteria In this study, we will utilize the Otsuka-Ochiai Similarity Index (OOSI) to assess the improvement in forest fire spread prediction accuracy achieved by the proposed method. OOSI is primarily employed for comparing similarity between two sets, commonly used in the field of image analysis. Zhou et al. (Zhou et al. 2020 , 2021 )applied this metric to the domain of forest fire research. Assuming Sf and St represent the burned surfaces enclosed by the simulated fire perimeter and true fire perimeter, respectively. OOSI is defined as the intersection area of Sf and St divided by the geometric mean of the two, with values ranging between 0 and 1. A value closer to 1 indicates a higher degree of similarity between the two sets. The calculation formula is as follows. $$OOSI=\frac{\left|{S}^{f}\cap {S}^{t}\right|}{\sqrt{\left|{S}^{f}\right|\times \left|{S}^{t}\right|}}$$ 3 , 4. Result and discussion 4.1 Results To assess the performance of the proposed method, in this section, we compare the fire spread prediction results of the four control groups from both qualitative and quantitative perspectives The results of the four control groups at T = 1, 7, 13, and 20 hours are illustrated in Fig. 4 . A comparison between the real group and the simulation group reveals significant deviations in the predicted results, with simulation errors gradually increasing over simulation time. This discrepancy is attributed to errors in the input ignition source. Furthermore, as time progresses, the errors accumulate, making predictions challenging for guiding on-site emergency management of forest fires. This underscores the inherent limitations of traditional methods or tools for predicting forest fire spread. In comparison to the simulation group, both the DA group and the FLC-GRU group exhibit predictions that are closer to the real fire line position. This suggests that DA techniques, through the incorporation of observational data, correct the simulated predictions and yield positive feedback. Building upon this, the FLC-GRU group demonstrates superior correction effects compared to the DA group. This is particularly evident in regions of the fire line where significant discrepancies exist between the simulation and real groups (highlighted by black dashed rectangles in Fig. 4 ). Analysis attributes this difference to the nature of DA technology, which fundamentally involves the fusion of prior and posterior knowledge. In this study, the DA group achieves ideal predictions by weighting simulated and observed values. However, due to the inability of the R matrix involved in the calculations to accurately reflect the weighted importance of observational contributions, the DA group struggles to effectively merge prior and posterior knowledge when computing analysis values. In contrast, the FLC-GRU group, utilizing the FLC-GRU network proposed in this study, successfully predicts the R matrix corresponding to observational data, enhancing the value of the observational data and directly improving the correction results. Subsequently, using the Real group as a baseline, we calculate the OOSI between the predicted results of the remaining three groups and the true fire perimeter, quantitatively comparing the prediction results. As shown in Fig. 5 , with the increase in simulation time, the similarity between the uncorrected simulation results and the spread results of the Real group shows a decreasing trend. It is foreseeable that as time progresses, the similarity will decrease, rendering it less valuable as a reference. The first correction of the DA group and FLC-GRU group yielded good results and consistently maintained high similarity. Specifically, the OOSI of the DA group remained around 90%, while the OOSI of the FLC-GRU group remained above 95%. This further illustrates that based on the proposed method in this paper, the advantages of DA in dynamic correction of forest fire spread predictions can be better utilized, enhancing prediction accuracy and assisting in the organizational scheduling of forest fire extinguishment. 4.2 Discussion In summary, utilizing the FLC-GRU network for R matrix estimation has enhanced both the theoretical foundation and the accuracy of the estimates. In the testing conducted through OSSE, the involvement of the estimated R matrix in DA calculations demonstrated an improvement in the corrective impact of DA compared to defining the R matrix empirically as a scalar matrix. This enhancement is advantageous for the dynamic correction of forest fire spread predictions, providing valuable guidance for emergency management in the context of forest fires. This study indicates that the proposed method is beneficial for the estimation of the R matrix and improves the predictions of forest fire spread. However, a limitation in this work is that, during network training, the dimensionality of the R matrix was predefined to ensure that the observational data y and the R matrix shared the same horizontal dimensions, a requirement for the format in DA calculations. This resulted in the transformation of each observation fire line into a finite number of point coordinates for computation, potentially overlooking crucial observational information. Particularly for forest fires, as the fire line perimeter increases over time, more observational information is needed to guide forest fire spread predictions. Therefore, the current approach is limited for larger-scale forest fire spread predictions, highlighting the need for an improved data preprocessing method that allows more observational information to be incorporated into the correction calculations. For instance, exploring ways to represent observational data in the form of "lines" to contribute to the network's learning process could be beneficial. On the other hand, the current network outputs a single R matrix for a set of observational data to preserve the spatiotemporal information of the data. However, in real-world scenarios, it might be more advantageous to perform R matrix estimation for each moment of observational data. This could require the design of a more sophisticated network capable of increasing the frequency of R matrix estimation without losing the temporal information of observation errors. The current research suggests that the novel method proposed in this paper has the potential to enhance the accuracy of forest fire spread prediction corrections. Despite areas mentioned above that could benefit from improvement, the method effectively advances existing approaches. By leveraging the characteristics of forest fire spread and incorporating neural network principles, it enhances the rationale and accuracy of R matrix estimation. Furthermore, this study integrates the method into the DA framework, exploring its applicability within the DA context, which is beneficial. 5. Conclusion In this study, to enhance the dynamic correction accuracy in predicting forest fire spread, we purposefully designed a novel FLC-GRU network based on neural network principles. Initially, we preprocessed and extracted spatial features from the observed fire line data with temporal information. Subsequently, we utilized GRU to learn the distribution of observation errors for estimating R matrix. We conducted OSSE tests to assess the impact of this method on the correction of forest fire spread predictions. The results of the tests indicate that the R matrix predicted through the FLC-GRU network contributes beneficially to the improvement of forest fire spread prediction accuracy compared to commonly used simplified approaches. The experimental tests also highlight the applicability of the proposed method within the DA framework. Declarations Authors’ contributions First author’s contributions: Designed research, Performed research, Wrote the paper. Second author’s contribution: Designed research, Reviewed and wrote the paper. Third author’s contribution: Reviewed and wrote the paper. Fourth author’s contribution: Designed the neural network. Fifth author’s contribution: Constructed the neural network. Sixth author’s contribution: Reviewed the paper. Funding This work was financially supported by the National Key Research and Development Plan under Grant No. 2021YFC3000300, the Anhui Provincial Science and Technology Major Project under Grant No. 202203a07020017, and Fundamental Research Funds for the Central Universities under Grant No. WK2320000052. The authors gratefully acknowledge all of these supports. Availability of data and materials The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request. Ethics approval and consent to participate Not applicable. Consent for publication Not applicable. Competing interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References Cheng, S. B., and M. M. Qiu. 2022. Observation error covariance specification in dynamical systems for data assimilation using recurrent neural networks. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3972535","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":275697411,"identity":"5ee49e5f-6881-48c7-85b7-33e26c091a89","order_by":0,"name":"Tianyu Wu","email":"","orcid":"","institution":"University of Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Tianyu","middleName":"","lastName":"Wu","suffix":""},{"id":275697412,"identity":"aefa8355-85aa-4d63-abac-b955d5611358","order_by":1,"name":"qixing zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzklEQVRIiWNgGAWjYDACZgaGAwwMNlAeG/Fa0qCqidICAYdJ0MJ3nMfwcMGv84nz5zc/YPhQdpiBf3YDfi2Sh9kSDs/su5244RibAeOMc4cZJO4cwK/F4DDzgcO8PUAtbDwMzLxthxkMJBIIaWFsAGo5lzi/DajlL3FagLbw/DiQ2HAMqIWRGC1gv/A2JBtvOJZmcLDnXDqPxA0CWvjOnzH+zPPHTnZ+8+GHD36UWcvxzyCgBRSPDIxtCDYPAfVQZQx/CKsbBaNgFIyCEQwA/5BF/Z6n4mwAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-8784-8674","institution":"University of Science and Technology of China","correspondingAuthor":true,"prefix":"","firstName":"qixing","middleName":"","lastName":"zhang","suffix":""},{"id":275697413,"identity":"3857b64f-4cdc-4f60-bee2-0df1f9a97a2b","order_by":2,"name":"Jiping Zhu","email":"","orcid":"","institution":"University of Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Jiping","middleName":"","lastName":"Zhu","suffix":""},{"id":275697414,"identity":"529bfbda-2c3f-46d9-8816-052b8b2b7d94","order_by":3,"name":"Jinhong Wu","email":"","orcid":"","institution":"University of Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Jinhong","middleName":"","lastName":"Wu","suffix":""},{"id":275697415,"identity":"aa5cc14d-7d9e-4ef3-9247-a0f0de0b65c2","order_by":4,"name":"Jinyang Dai","email":"","orcid":"","institution":"University of Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Jinyang","middleName":"","lastName":"Dai","suffix":""},{"id":275697416,"identity":"2b3b645c-e5f1-4f7b-8aad-719995f004c6","order_by":5,"name":"Yongming Zhang","email":"","orcid":"","institution":"University of Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Yongming","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2024-02-20 10:41:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3972535/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3972535/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s42408-024-00329-0","type":"published","date":"2024-10-14T15:57:37+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":52045767,"identity":"0850a4a6-7c59-46d1-a151-1d902d3bc3b6","added_by":"auto","created_at":"2024-03-05 19:54:39","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":5320252,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic Diagram of the FLC-GRU Network.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-3972535/v1/64cec6a68743c786cc5d57e5.png"},{"id":52045765,"identity":"9b2b0ef1-f83b-4650-b7f3-f9ecaca8611c","added_by":"auto","created_at":"2024-03-05 19:54:39","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":418902,"visible":true,"origin":"","legend":"\u003cp\u003eFlowchart of the Forest Fire Spread Prediction Dynamic Correction System Based on FLC-GRU.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-3972535/v1/ed3b8b85e6d56cef242ae216.png"},{"id":52045768,"identity":"da31d3e1-6cef-4792-8a0f-467be90f0d71","added_by":"auto","created_at":"2024-03-05 19:54:39","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1391325,"visible":true,"origin":"","legend":"\u003cp\u003eStudy Area\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-3972535/v1/a2db47a1586b3d1387489794.png"},{"id":52045769,"identity":"0c45e7e1-d4c2-487b-a9e1-d6dedc4b2465","added_by":"auto","created_at":"2024-03-05 19:54:40","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":2739254,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the fire perimeter predictions at 1, 7, 13, and 20 hours of the Real group, Simulation group, DA group and FLC-GRU group.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-3972535/v1/cb1b27b7ae1cc20f3b3e85e6.png"},{"id":52045766,"identity":"3eca32a3-247e-4aae-93af-a0108996f336","added_by":"auto","created_at":"2024-03-05 19:54:39","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":148239,"visible":true,"origin":"","legend":"\u003cp\u003eThe Otsuka-Ochiai Similarity Index (OOSI) between the predicted results of the Simulation group, DA group, and FLC-GRU group, and the predictions of the Real group, respectively.\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3972535/v1/f385eb94f7b7fe44674883d6.jpeg"},{"id":67148983,"identity":"468e0a99-3f68-4449-a10a-94928ec165ac","added_by":"auto","created_at":"2024-10-21 16:10:37","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":9061499,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3972535/v1/e5427e35-aa1f-49e3-a432-71f98ec54e7f.pdf"}],"financialInterests":"","formattedTitle":"Dynamic Correction of Forest Fire Spread Prediction using Observation Error Covariance Matrix Estimation Technique based on FLC-GRU","fulltext":[{"header":"1. Background","content":"\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eAccurately predicting the development of forest fire spread is one of the most crucial aspects in emergency management of forest fires. To address the issue of low prediction accuracy in traditional computer simulation due to errors in input data or the model itself, data assimilation (DA) techniques have been applied in this field. The main idea is to assimilate observed values into the predicted values obtained through methods like physical models. This is achieved by weighting the predicted values and observed values to obtain analytical values that better reflect the system state. Mandel et al. first applied the idea of DA to the field of forest fire spread prediction (Mandel et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). Subsequently, scholars such as Rochoux and Trouv\u0026eacute; conducted extensive research on ensemble Kalman filter (EnKF) algorithms (Rochoux et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2014\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Zhang et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), which became one of the mainstream correction methods in the field of forest fire spread prediction. In recent studies, Zhou et al. first applied the ensemble transform Kalman filter (ETKF) to forest fire spread prediction, improving the correction effect (Zhou et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Building upon this, Zhou et al. explored improvements to the correction algorithm under conditions of large observation data errors or missing data (Zhou et al. \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). In a recent study, the author's research team found that deterministic ensemble Kalman filter (DEnKF) has superior correction ability for forest fire spread prediction compared to EnKF. In summary, the forest fire spread prediction method based on DA has achieved widespread development and research results.\u003c/p\u003e \u003cp\u003eIn the computation of data assimilation techniques, the weighted importance of predicted values and observed values is determined by their respective error covariances, corresponding to the background error covariance matrix (Q matrix) and the observation error covariance matrix (R matrix). Moreover, the weighted results directly influence the outcome of the final analysis values. However, in practical engineering, the unavailability of true values makes it impossible to directly calculate the magnitude and distribution of errors, posing a challenge in the estimation of error covariances. In the research on dynamic correction of forest fire spread prediction, error covariance is often simplified. Specifically, regarding the estimation of Q matrix, using the Ensemble Kalman Filter (EnKF) algorithm as an example, sample covariance matrix is commonly employed to represent Q matrix. This step avoids the direct calculation of errors by implicitly advancing the ensemble forecast. However, unlike the Q matrix, the R matrix cannot be empirically estimated from the ensemble of simulated trajectories. Therefore, the treatment of the R matrix is typically more straightforward, often defined empirically as a scalar matrix, lacking theoretical rigor and potentially adversely affecting the accuracy of analytical values. Furthermore, research has indicated that observation errors are correlated and exhibit dependence on both time and state. Considering these correlated observation errors in DA can lead to more accurate analysis results (Stewart et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Li et al. \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Miyoshi et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Waller et al. \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn recent years, significant research on error handling methods has been conducted in various fields applying DA techniques (Desroziers and Ivanov \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Desroziers et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Stewart et al. \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). In a recent comprehensive review by Pierre Tandeo, existing methods are categorized into two main classes: 1) Innovation-based methods, such as the method of moments, which assumes equality between theoretical and observed moments of innovations, and 2) Likelihood-based methods, which utilize the likelihood of the observations contained in the innovations. The mentioned methods fall under traditional posterior tuning methods, and more details can be found in (Tandeo et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Additionally, some covariance estimation techniques based on neural network algorithms have been proposed and achieved good results (Cheng et al. \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Chen et al. introduced an observation error covariance specification based on Long Short-Term Memory (LSTM) and demonstrated its good performance in the Lorenz twin experiment and shallow water equations, commonly used for testing DA algorithms (Cheng and Qiu \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). However, for the estimation of the R matrix in predicting forest fire spread, there is still a lack of targeted research and validation.\u003c/p\u003e \u003cp\u003eIn this study, we propose a technique for estimating the R matrix based on the Fire Line Convolutional Gated Recurrent Unit (FLC-GRU). This aims to enhance the accuracy and efficiency of R matrix estimation while improving the correction accuracy of forest fire spread predictions. In contrast to traditional posterior tuning methods, this new approach does not require prior knowledge of either the background or the observation matrix. In the network design, we chose to use the more efficient GRU over LSTM to learn the error distribution. Additionally, before training, we utilized a convolutional network to not only retain the temporal information of the observed fire line data but also extract its spatial information, enhancing the network's performance. To validate the accuracy of the proposed method in correcting forest fire spread predictions, we utilize actual terrain and fuel data from the Idaho Panhandle National Forests and conduct Observing System Simulation Experiment (OSSE).\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e"},{"header":"2. Methodology","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 The R matrix estimation technique based on Fire Line Convolutional Gated Recurrent Unit (FLC-GRU)\u003c/h2\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eConvolutional Neural Networks (CNN) are commonly employed for image processing (Krizhevsky et al. \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Lin et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Huo et al. \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), effectively reducing large volumes of image data to smaller datasets while retaining essential features, aligning with principles in image processing. In 2014, Cho et al. introduced the Gated Recurrent Unit (GRU), a simplified version of Long Short-Term Memory (LSTM) (Cho et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). GRU maintains robust memory capabilities for sequential data while enhancing computational efficiency. Leveraging the high sensitivity of convolutional Networks and GRU networks to spatial and temporal features, respectively, we aim to better provide a better solution to the estimation problem of the observation error covariance matrix in the context of forest fire spread. To achieve this, we propose the Fire Line Convolutional Gated Recurrent Unit (FLC-GRU) network, encompassing dataset generation, data preprocessing, convolutional processes, and GRU processes. The FLC-GRU network structure is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eWe initiate the process by employing FARSITE, a commonly used forest fire spread tool based on the Rothermel model and Huygens theory. This tool generates a set of fire line position state values X\u003csub\u003et\u003c/sub\u003e=[X\u003csub\u003et\u003c/sub\u003e\u003csup\u003e0\u003c/sup\u003e, X\u003csub\u003et\u003c/sub\u003e\u003csup\u003e1\u003c/sup\u003e, ..., X\u003csub\u003et\u003c/sub\u003e\u003csup\u003ei\u003c/sup\u003e,..., X\u003csub\u003et\u003c/sub\u003e\u003csup\u003eT\u003c/sup\u003e].\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eX\u003c/em\u003e \u003csub\u003e \u003cem\u003et\u003c/em\u003e \u003c/sub\u003e \u003cem\u003e=M(X\u003c/em\u003e \u003csub\u003e \u003cem\u003et\u0026minus;1\u003c/em\u003e,\u003c/sub\u003e \u003cem\u003eθ\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u0026minus;1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e)\u003c/em\u003e, (1)\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003ewhere M is the nonlinear forecast operator, i.e., the FARSITE fire growth model; θ denotes the related parameters, which include the topography, fuel, weather and wind parameters.\u003c/p\u003e\u003cp\u003eConcurrently, we pre-generate a Symmetric Positive Definite (SPD) matrix R, representing the specific properties of the R matrix. Subsequently, we augment X\u003csub\u003et\u003c/sub\u003e by introducing observation errors ϵ that follow a Gaussian distribution, resulting in the generation of observed data y\u003csub\u003et\u003c/sub\u003e=[y\u003csub\u003et\u003c/sub\u003e\u003csup\u003e0\u003c/sup\u003e, y\u003csub\u003et\u003c/sub\u003e\u003csup\u003e1\u003c/sup\u003e, ..., y\u003csub\u003et\u003c/sub\u003e\u003csup\u003ei\u003c/sup\u003e,..., y\u003csub\u003et\u003c/sub\u003e\u003csup\u003eT\u003c/sup\u003e].\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003ey\u003c/em\u003e \u003csub\u003e \u003cem\u003et\u003c/em\u003e \u003c/sub\u003e \u003cem\u003e=H(X\u003c/em\u003e \u003csub\u003e \u003cem\u003et\u003c/em\u003e \u003c/sub\u003e \u003cem\u003e)+ϵ\u003c/em\u003e, (2)\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003ewhere H can be simply viewed as a selection operator that pairs each marker in the simulated fire fronts with its closest neighbor along the observed fire fronts, and ϵ~N(0, R).\u003c/p\u003e\u003cp\u003eThis process is iterated N times to produce N sets of 'Observation y' and 'R matrix' with precise corresponding relationships.\u003c/p\u003e\u003cp\u003eIn this study, T is set to 20 hours, and the fireline state X\u003csub\u003et\u003c/sub\u003e\u003csup\u003ei\u003c/sup\u003e at each time step is composed of a set of k\u0026thinsp;=\u0026thinsp;100 fire points, i.e., X\u003csub\u003et\u003c/sub\u003e\u003csup\u003ei\u003c/sup\u003e=[e\u003csub\u003ei,1\u003c/sub\u003e, n\u003csub\u003ei,1\u003c/sub\u003e, e\u003csub\u003ei,2\u003c/sub\u003e, n\u003csub\u003ei,2\u003c/sub\u003e, ..., e\u003csub\u003ei,j\u003c/sub\u003e, n\u003csub\u003ei,j\u003c/sub\u003e, ..., e\u003csub\u003ei,100\u003c/sub\u003e, n\u003csub\u003ei,100\u003c/sub\u003e]T. Where (e\u003csub\u003ei,j\u003c/sub\u003e, n\u003csub\u003ei,j\u003c/sub\u003e) represents the coordinates of the j-th observed fire point at time i. In accordance with the requirements of the DA analysis steps, it is stipulated that the generated R matrix is a SPD matrix of size 2k*2k, i.e., 200*200. The values of the diagonal elements follow a random distribution in the range of (0, 200).\u003c/p\u003e\u003cp\u003eThe aforementioned N sets of samples, consisting of 'Observation yt' and labels 'R matrix,' serve as the training set for the FLC-GRU network in this study. A total of 14,000 data sets were generated, with 11,200 sets allocated for training and 2,800 for validation. The network's input is y\u003csub\u003et\u003c/sub\u003e=[y\u003csub\u003et\u003c/sub\u003e\u003csup\u003e0\u003c/sup\u003e, y\u003csub\u003et\u003c/sub\u003e\u003csup\u003e1\u003c/sup\u003e, ..., y\u003csub\u003et\u003c/sub\u003e\u003csup\u003ei\u003c/sup\u003e,..., y\u003csub\u003et\u003c/sub\u003e\u003csup\u003eT\u003c/sup\u003e], and the output is the R matrix. As mentioned earlier, GRU possesses the capability to handle time-series data and often significantly improves training efficiency compared to LSTM while maintaining similar training effectiveness. Therefore, we aim to utilize the GRU network to learn the distribution of observation errors. In the network design for dynamic correction in predicting forest fire spread, our goal is to retain the temporal information of the observed fire line data while fully leveraging the spatial information contained in the data. To achieve this, before initiating the training of the GRU network, we applied convolutional processing to the observed fire line data to extract its spatial features. Building upon this, given the suitability of convolutional networks for extracting image features, prior to the convolution operation, we remapped the observed data, represented as y\u003csub\u003et\u003c/sub\u003e, to multiple layers of fire images by transforming the coordinate matrix at time T. In this study, Stochastic Gradient Descent (SGD) is employed as the weight update algorithm, with a learning rate of 1e-5, exponential learning rate decay strategy, the application of weight decay, beta set to 0.8, and the Mean Squared Error (MSE) as the loss function. Ultimately, given a set of observation data with an unknown error distribution, the network can output the predicted R matrix.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 The core idea of the method\u003c/h2\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eIn summary, the core of this method is to address the challenge of accurately estimating the R matrix when observing the fire line in forest fire incidents, given the inherent uncertainty in determining the true fire line positions. To tackle this issue, the method adopts a reverse-thinking approach to identify the precise correspondence between observation data and the R matrix. By pre-generating a specific R matrix and generating observation data following the distribution specified by this matrix, a training set is established. Subsequently, the FLC-GRU network can learn such error distributions, improving the efficiency and accuracy of estimating the R matrix in dynamic correction for predicting forest fire spread. This approach involves a proactive generation of observation error covariance matrices, creating a training set that facilitates the learning of error distributions through convolutional and GRU networks.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Forest fire spread prediction dynamic correction system based on FLC-GRU\u003c/h2\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eBuilding upon this, the estimation technique is integrated into the DA-based forest fire spread prediction process to enhance the precision of dynamic corrections in predicting forest fire spread. As illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, in response to a sudden forest fire, while conducting computer-simulated predictions of forest fire spread, real-time observations of the fire scene can be obtained through satellite remote sensing, unmanned aerial vehicles, or human observation. This provides observed fire lines for assimilation. Subsequently, the FLC-GRU network proposed in this paper is employed to estimate the observation error covariance matrix for assimilation calculations, yielding improved estimates of the fire line's position. The output of the current time's fire line position serves as the input for the next moment's prediction of forest fire spread, enhancing the results for the next time step. This process forms a rational and comprehensive dynamic correction method for predicting forest fire spread. It is noteworthy that in this study, FARSITE is utilized as the tool for predicting forest fire spread, and the DA method employs the DEnKF algorithm, serving as an example. The applicability of this method remains unaffected by the choice of other forest fire spread prediction models or tools, as well as alternative DA algorithms.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3. Experimental designs","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Study area\u003c/h2\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eTaking into consideration the variations in terrain, we selected the Idaho Panhandle National Forests located in the state of Idaho, United States (latitude 47.5\u0026deg; N to 48\u0026deg; N, longitude 115.7\u0026deg; W to 116.7\u0026deg; W) as our research focus. This region experiences a warm climate and substantial fuel accumulation, posing a higher risk of forest fire incidents. We obtained the landscape file (.LCP) for the study area from LANDFIRE (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://landfire.gov/\u003c/span\u003e\u003cspan address=\"http://landfire.gov/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e), encompassing topographical and fuel data essential for conducting forest fire spread predictions based on FARSITE. The study area is depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Experiment set up\u003c/h2\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eTo validate the applicability of the proposed method, we designed an Observing System Simulation Experiment (OSSE), which is one of the most commonly used methods to assess the performance of DA algorithms. The OSSE for this study comprised four groups: 1) Real group: Simulating without input errors to generate a simulation result that serves as the true fire lines. 2) Simulation group: Introducing input errors to simulate real-world scenarios where, due to errors in input data and the model, only uncorrected predictions can be obtained. 3) DA group (Data Assimilation group): Applying DA algorithms to correct the results of the simulation group. However, common rough handling methods were used for the R matrix. 4) FLC-GRU group (Data Assimilation with Fire Line Convolutional Gated Recurrent Unit group): Employing DA for correction while utilizing the R matrix estimation method proposed in this paper. See Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e for details.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExperimental designs.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInput fire source\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDA method\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eR matrix\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eReal group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNo error\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSimulation group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWith error\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDA group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWith error\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDEnKF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDefining a scalar matrix\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFLC-GRU group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWith error\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDEnKF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEstimating based on FLC-GRU\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eIn this study, we adopted the Deterministic Ensemble Kalman Filter (DEnKF) as the DA method, with a set ensemble size of 20. The duration of the forest fire spread simulation experiment based on FARSITE was set at 20 hours, with assimilation performed every 1 hour. We assumed a spatially uniform distribution of wind, with a globally set southeastern wind speed of 3.5 m/s. It is important to note that the primary focus of this paper is to validate the applicability and accuracy of the proposed new method in dynamic correction of forest fire spread predictions by comparing it with traditional methods. Therefore, some simplifications were made in the experimental settings for certain parameters, which is a reasonable approach.\u003c/p\u003e \u003cp\u003eIn this experiment, observational data is derived from the Real group, where we added errors following an unknown R matrix to generate observational data based on the real fire line. In the DA group, we assume observation errors to be random noise with a standard deviation of 200 meters. The R matrix is empirically defined as a scalar matrix, which is a common practice in DA for correcting forest fire spread predictions. This setup is also designed to address the fact that in previous approaches, people typically assigned values to the R matrix based on empirical considerations, lacking a certain degree of theoretical basis. In the DA with FLC-GRU group, we employed the FLC-GRU network proposed in this study to compute the R matrix.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Evaluation criteria\u003c/h2\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eIn this study, we will utilize the Otsuka-Ochiai Similarity Index (OOSI) to assess the improvement in forest fire spread prediction accuracy achieved by the proposed method. OOSI is primarily employed for comparing similarity between two sets, commonly used in the field of image analysis. Zhou et al. (Zhou et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2020\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2021\u003c/span\u003e)applied this metric to the domain of forest fire research. Assuming Sf and St represent the burned surfaces enclosed by the simulated fire perimeter and true fire perimeter, respectively. OOSI is defined as the intersection area of Sf and St divided by the geometric mean of the two, with values ranging between 0 and 1. A value closer to 1 indicates a higher degree of similarity between the two sets. The calculation formula is as follows.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Equ1\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$OOSI=\\frac{\\left|{S}^{f}\\cap {S}^{t}\\right|}{\\sqrt{\\left|{S}^{f}\\right|\\times \\left|{S}^{t}\\right|}}$$\u003c/div\u003e \u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Result and discussion","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Results\u003c/h2\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eTo assess the performance of the proposed method, in this section, we compare the fire spread prediction results of the four control groups from both qualitative and quantitative perspectives\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eThe results of the four control groups at T\u0026thinsp;=\u0026thinsp;1, 7, 13, and 20 hours are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. A comparison between the real group and the simulation group reveals significant deviations in the predicted results, with simulation errors gradually increasing over simulation time. This discrepancy is attributed to errors in the input ignition source. Furthermore, as time progresses, the errors accumulate, making predictions challenging for guiding on-site emergency management of forest fires. This underscores the inherent limitations of traditional methods or tools for predicting forest fire spread. In comparison to the simulation group, both the DA group and the FLC-GRU group exhibit predictions that are closer to the real fire line position. This suggests that DA techniques, through the incorporation of observational data, correct the simulated predictions and yield positive feedback.\u003c/p\u003e \u003cp\u003eBuilding upon this, the FLC-GRU group demonstrates superior correction effects compared to the DA group. This is particularly evident in regions of the fire line where significant discrepancies exist between the simulation and real groups (highlighted by black dashed rectangles in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Analysis attributes this difference to the nature of DA technology, which fundamentally involves the fusion of prior and posterior knowledge. In this study, the DA group achieves ideal predictions by weighting simulated and observed values. However, due to the inability of the R matrix involved in the calculations to accurately reflect the weighted importance of observational contributions, the DA group struggles to effectively merge prior and posterior knowledge when computing analysis values. In contrast, the FLC-GRU group, utilizing the FLC-GRU network proposed in this study, successfully predicts the R matrix corresponding to observational data, enhancing the value of the observational data and directly improving the correction results.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSubsequently, using the Real group as a baseline, we calculate the OOSI between the predicted results of the remaining three groups and the true fire perimeter, quantitatively comparing the prediction results. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, with the increase in simulation time, the similarity between the uncorrected simulation results and the spread results of the Real group shows a decreasing trend. It is foreseeable that as time progresses, the similarity will decrease, rendering it less valuable as a reference. The first correction of the DA group and FLC-GRU group yielded good results and consistently maintained high similarity. Specifically, the OOSI of the DA group remained around 90%, while the OOSI of the FLC-GRU group remained above 95%. This further illustrates that based on the proposed method in this paper, the advantages of DA in dynamic correction of forest fire spread predictions can be better utilized, enhancing prediction accuracy and assisting in the organizational scheduling of forest fire extinguishment.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Discussion\u003c/h2\u003e \u003cp\u003eIn summary, utilizing the FLC-GRU network for R matrix estimation has enhanced both the theoretical foundation and the accuracy of the estimates. In the testing conducted through OSSE, the involvement of the estimated R matrix in DA calculations demonstrated an improvement in the corrective impact of DA compared to defining the R matrix empirically as a scalar matrix. This enhancement is advantageous for the dynamic correction of forest fire spread predictions, providing valuable guidance for emergency management in the context of forest fires.\u003c/p\u003e \u003cp\u003eThis study indicates that the proposed method is beneficial for the estimation of the R matrix and improves the predictions of forest fire spread. However, a limitation in this work is that, during network training, the dimensionality of the R matrix was predefined to ensure that the observational data y and the R matrix shared the same horizontal dimensions, a requirement for the format in DA calculations. This resulted in the transformation of each observation fire line into a finite number of point coordinates for computation, potentially overlooking crucial observational information. Particularly for forest fires, as the fire line perimeter increases over time, more observational information is needed to guide forest fire spread predictions. Therefore, the current approach is limited for larger-scale forest fire spread predictions, highlighting the need for an improved data preprocessing method that allows more observational information to be incorporated into the correction calculations. For instance, exploring ways to represent observational data in the form of \"lines\" to contribute to the network's learning process could be beneficial.\u003c/p\u003e \u003cp\u003eOn the other hand, the current network outputs a single R matrix for a set of observational data to preserve the spatiotemporal information of the data. However, in real-world scenarios, it might be more advantageous to perform R matrix estimation for each moment of observational data. This could require the design of a more sophisticated network capable of increasing the frequency of R matrix estimation without losing the temporal information of observation errors.\u003c/p\u003e \u003cp\u003eThe current research suggests that the novel method proposed in this paper has the potential to enhance the accuracy of forest fire spread prediction corrections. Despite areas mentioned above that could benefit from improvement, the method effectively advances existing approaches. By leveraging the characteristics of forest fire spread and incorporating neural network principles, it enhances the rationale and accuracy of R matrix estimation. Furthermore, this study integrates the method into the DA framework, exploring its applicability within the DA context, which is beneficial.\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eIn this study, to enhance the dynamic correction accuracy in predicting forest fire spread, we purposefully designed a novel FLC-GRU network based on neural network principles. Initially, we preprocessed and extracted spatial features from the observed fire line data with temporal information. Subsequently, we utilized GRU to learn the distribution of observation errors for estimating R matrix. We conducted OSSE tests to assess the impact of this method on the correction of forest fire spread predictions. The results of the tests indicate that the R matrix predicted through the FLC-GRU network contributes beneficially to the improvement of forest fire spread prediction accuracy compared to commonly used simplified approaches. The experimental tests also highlight the applicability of the proposed method within the DA framework.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthors\u0026rsquo; contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFirst author\u0026rsquo;s contributions: Designed research, Performed research, Wrote the paper. Second author\u0026rsquo;s contribution: Designed research, Reviewed and wrote the paper. Third author\u0026rsquo;s contribution: Reviewed and wrote the paper. Fourth author\u0026rsquo;s contribution: Designed the neural network. Fifth author\u0026rsquo;s contribution: Constructed the neural network. Sixth author\u0026rsquo;s contribution: Reviewed the paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was financially supported by the National Key Research and Development Plan under Grant No. 2021YFC3000300, the Anhui Provincial Science and Technology Major Project under Grant No. 202203a07020017, and Fundamental Research Funds for the Central Universities under Grant No. WK2320000052. The authors gratefully acknowledge all of these supports.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eCheng, S. B., and M. M. 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Proceedings of the Combustion Institute 38:5091\u0026ndash;5099. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.proci.2020.05.028\u003c/span\u003e\u003cspan address=\"10.1016/j.proci.2020.05.028\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"fire-ecology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"feco","sideBox":"Learn more about [Fire Ecology](https://www.springer.com/journal/42408)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/feco/default.aspx","title":"Fire Ecology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Forest fires, Spread prediction, Data assimilation, Observation error covariance matrix, Neural networks","lastPublishedDoi":"10.21203/rs.3.rs-3972535/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3972535/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eBackground \u003c/strong\u003eData assimilation (DA) techniques have played a significant role in improving the prediction accuracy of forest fire spread. This dynamic correction technique enhances the analytical values that better reflect the fire situation by weighting the predicted values and observed values. The weighted importance of each contribution is determined by the magnitude of its associated error. However, as a crucial parameter affecting prediction accuracy, the covariance matrix of observation errors is often inaccurate and neglects its own temporal correlation. This is unfriendly to spread prediction results. To address this issue, we proposed a targeted technique for estimating the observation error covariance matrix (R matrix) based on the Fire Line Convolutional Gated Recurrent Unit (FLC-GRU).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults \u003c/strong\u003eWe integrated this method into the DA framework and validated its applicability and accuracy using Observing System Simulation Experiment (OSSE). Through comparisons with traditional methods, the results indicate that using the FLC-GRU estimated R matrix for correction calculations leads to wildfire prediction locations that are closer to the true values.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConclusion\u003c/strong\u003es The proposed approach learns the covariance matrix directly from time-series observed fire line data, without requiring any prior knowledge or assumptions about the error distribution, in contrast to classical posterior tuning methods. The proposed method significantly improves the rationality and accuracy of R matrix estimation, enhances the utility of observational data, and thereby improves the correction accuracy of forest fire spread predictions. Moreover, the study also demonstrates the applicability of the proposed method within the DA framework.\u003c/p\u003e","manuscriptTitle":"Dynamic Correction of Forest Fire Spread Prediction using Observation Error Covariance Matrix Estimation Technique based on FLC-GRU","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-05 19:54:35","doi":"10.21203/rs.3.rs-3972535/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewersInvited","content":"","date":"2024-04-09T16:43:32+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2024-02-28T22:34:45+00:00","index":0,"fulltext":""},{"type":"editorAssigned","content":"","date":"2024-02-28T03:00:16+00:00","index":"","fulltext":""},{"type":"submitted","content":"Fire Ecology","date":"2024-02-19T22:42:38+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"fire-ecology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"feco","sideBox":"Learn more about [Fire Ecology](https://www.springer.com/journal/42408)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/feco/default.aspx","title":"Fire Ecology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"31a4cd3e-faa2-4c68-83fc-b54f6182a9e2","owner":[],"postedDate":"March 5th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-10-21T16:02:22+00:00","versionOfRecord":{"articleIdentity":"rs-3972535","link":"https://doi.org/10.1186/s42408-024-00329-0","journal":{"identity":"fire-ecology","isVorOnly":false,"title":"Fire Ecology"},"publishedOn":"2024-10-14 15:57:37","publishedOnDateReadable":"October 14th, 2024"},"versionCreatedAt":"2024-03-05 19:54:35","video":"","vorDoi":"10.1186/s42408-024-00329-0","vorDoiUrl":"https://doi.org/10.1186/s42408-024-00329-0","workflowStages":[]},"version":"v1","identity":"rs-3972535","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3972535","identity":"rs-3972535","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}