KR102473061B1 - Apparatus and method for providing the forest fire risk index - Google Patents

Abstract

An apparatus and method for providing a forest fire risk index according to a preferred embodiment of the present invention generates a forest fire risk index model optimized for the Korean Peninsula and forecasts a forest fire risk index for a forecast date using the generated forest fire risk index model, It is possible to minimize damage through effective forest fire preparation (forward deployment of firefighting resources, etc.), and furthermore, reduce the frequency of forest fires by providing information necessary for forest fire prevention.

Description

Apparatus and method for providing the forest fire risk index {Apparatus and method for providing the forest fire risk index}

The present invention relates to an apparatus and method for providing a forest fire risk index, and more particularly, to a device for generating a forest fire risk index model optimized for the Korean Peninsula and predicting a forest fire risk index for a forecast date using the generated forest fire risk index model. and methods.

As the number of dry days on the Korean Peninsula increases due to climate change, the risk of forest fires is increasing, such as the lengthening of the period of forest fires throughout the year.

An object of the present invention is to provide a forest fire risk index providing device and method for generating a forest fire risk index model optimized for the Korean Peninsula and predicting a forest fire risk index for a forecast date using the generated forest fire risk index model. have.

Other non-specified objects of the present invention may be additionally considered within the scope that can be easily inferred from the following detailed description and effects thereof.

In order to achieve the above object, an apparatus for providing a forest fire risk index according to a preferred embodiment of the present invention obtains a forest fire risk index using a forest fire prone area map, a modified FFMC (Fine Fuel Moisture Code), a drought index, and a monthly weight a forest fire risk index acquisition unit; and a forecasting unit that obtains a forest fire risk index value for a forecast date based on the forest fire risk index acquired through the forest fire risk index acquisition unit, wherein the monthly weight is obtained based on all forest fires that have occurred in the past. Using the ratio of the number of forest fires per month, the higher the number of forest fires per month, the greater weight is assigned.

Here, the forest fire risk index acquisition unit obtains the forest fire risk index through the formula (the forest fire prone area map + 0.5) * (the modified FFMC) * (1.5 - the drought index) * (the monthly weight) have.

Here, the modified FFMC is the relative humidity, the amount of precipitation measured at noon, temperature, and wind speed, calculated using the equilibrium moisture content, drying rate, and minimum moisture content of the day. In the conventional FFMC that calculates FFMC, FFMC initial value , the coefficients of the formula for calculating the precipitation reference value, the FFMC reference value, and the drying rate are modified, the coefficients of the formula for calculating the moisture content of the previous day are modified, the coefficients of the expression for calculating the FFMC value using the minimum moisture content are modified, and at noon Accumulated precipitation per day is used instead of the measured precipitation, and the precipitation reference value may be larger than the conventional FFMC.

Here, a drought index acquisition unit for obtaining the drought index using a soil moisture index downscaled to a grid size of 1 km, a normalized differential water index (NDWI), and a temperature condition index (TCI); may be further included.

Here, the drought index acquisition unit may acquire the drought index through the equation 0.4 * (the downscaled soil moisture index) + 0.3 * (the NDWI) + 0.3 * (the TCI).

Here, data upscaled to a grid size of 25 km is used as training data, and TRMM (Tropical Rainfall Measuring Mission) precipitation data, ASCAT (Advanced SCATterometer) soil moisture data, and NDVI (Normalised Difference Vegetation Index) are based on the machine learning algorithm. ), LST (Land Surface Temperature) and DEM (digital Elevation Model) as input variables, and GLDAS (Global Land Data Assimilation System) soil moisture data as output variables, creating a soil moisture index downscaling model, The method may further include a soil moisture index obtaining unit configured to acquire the downscaled soil moisture index by inputting the input variable converted into a grid size into the soil moisture index downscaling model.

Here, the soil moisture index acquisition unit uses upscaled data with a grid size of 25 km as training data, and uses the TRMM precipitation data, the ASCAT soil moisture data, the NDVI, the LST, and the DEM as input variables, A first soil moisture index downscaling model having the GLDAS soil moisture data as an output variable is generated, and up-scaling data with a grid size of 25 km is used as training data to obtain the TRMM precipitation data, the NDVI, the LST and A second soil moisture index downscaling model having the DEM as an input variable and the GLDAS soil moisture data as an output variable is generated, and the input variable converted to a grid size of 1 km is used as the first soil moisture index downscaling model. to obtain a first soil moisture index downscaled to a grid size of 1 km, and input variables converted to a grid size of 1 km into the second soil moisture index downscaling model to obtain a downscaled to a grid size of 1 km A second soil moisture index may be obtained, and the downscaled soil moisture index may be obtained by replacing a part missing from the first soil moisture index with the second soil moisture index.

In order to achieve the above object, a method for providing a forest fire risk index according to a preferred embodiment of the present invention is a method for providing a forest fire risk index performed by a forest fire risk index providing device, and includes a forest fire prone area map, a modified FFMC (Fine Fuel Moisture Code), obtaining a forest fire risk index using a drought index and a monthly weight; And obtaining a forest fire risk index value for a forecast date based on the forest fire risk index, wherein the monthly weight is obtained based on all forest fires occurring in the past, Using a monthly forest fire occurrence rate, The greater the number of wildfires per month, the greater the weight.

Here, the step of obtaining the forest fire risk index is: Obtaining the forest fire risk index through the equation (the forest fire prone area map + 0.5) * (the modified FFMC) * (1.5 - the drought index) * (the monthly weight) can be made with

Here, the modified FFMC is the relative humidity, the amount of precipitation measured at noon, temperature, and wind speed, calculated using the equilibrium moisture content, drying rate, and minimum moisture content of the day. In the conventional FFMC that calculates FFMC, FFMC initial value , the coefficients of the formula for calculating the precipitation reference value, the FFMC reference value, and the drying rate are modified, the coefficients of the formula for calculating the moisture content of the previous day are modified, the coefficients of the expression for calculating the FFMC value using the minimum moisture content are modified, and at noon Accumulated precipitation per day is used instead of the measured precipitation, and the precipitation reference value may be larger than the conventional FFMC.

Here, the method may further include obtaining the drought index by using a soil moisture index downscaled to a grid size of 1 km, a normalized differential water index (NDWI), and a temperature condition index (TCI).

Here, data upscaled to a grid size of 25 km is used as training data, and TRMM (Tropical Rainfall Measuring Mission) precipitation data, ASCAT (Advanced SCATterometer) soil moisture data, and NDVI (Normalised Difference Vegetation Index) are based on the machine learning algorithm. ), LST (Land Surface Temperature) and DEM (digital Elevation Model) as input variables, and GLDAS (Global Land Data Assimilation System) soil moisture data as output variables, creating a soil moisture index downscaling model, The method may further include obtaining the downscaled soil moisture index by inputting the input variable converted into a grid size into the soil moisture index downscaling model.

A computer program according to a preferred embodiment of the present invention for achieving the above technical problem is stored in a computer-readable recording medium and executes any one of the above forest fire risk index providing methods on a computer.

According to an apparatus and method for providing a forest fire risk index according to a preferred embodiment of the present invention, a forest fire risk index model optimized for the Korean Peninsula is generated, and a forest fire risk index for a forecast date is predicted using the generated forest fire risk index model, It is possible to minimize damage through efficient on-site preparation for forest fires (forward deployment of firefighting resources, etc.), and furthermore, reduce the frequency of forest fires by providing information necessary for forest fire prevention.

The effects of the present invention are not limited to the effects mentioned above, and other effects not mentioned will be clearly understood by those skilled in the art from the description below.

1 is a block diagram illustrating an apparatus for providing a forest fire risk index according to a preferred embodiment of the present invention.
2 is a diagram for explaining a soil moisture index downscaling model according to a preferred embodiment of the present invention.
3 is a diagram for explaining the results of a soil moisture index downscaling model according to a preferred embodiment of the present invention.
4 is a diagram for explaining the results of a soil moisture index downscaling model excluding ASCAT soil moisture data according to a preferred embodiment of the present invention.
5 is a diagram for explaining a final downscaled soil moisture index according to a preferred embodiment of the present invention, the left side of FIG. 5 shows the result of a first soil moisture index downscaling model, and the right side of FIG. It shows that the missing part in the result of the soil moisture index downscaling model is replaced with the result of the second soil moisture index downscaling model.
6 is a diagram for explaining a drought factor according to a preferred embodiment of the present invention.
7 is a diagram for explaining the results of a drought index model to which weights are applied according to a preferred embodiment of the present invention.
8 is a diagram for explaining a forest fire prone area map according to a preferred embodiment of the present invention.
9 is a diagram for explaining why FFMC according to a preferred embodiment of the present invention is used as a factor of a forest fire risk index. FIG. 9 (a) compares FFMC with the number of forest fires per month in 2015, and FIG. (b) compares FFMC to the number of wildfires per 10 days in 2015.
10 is a diagram for explaining the result of comparing the spatial distribution of a modified FFMC according to a preferred embodiment of the present invention and a conventional FFMC.
11 is a diagram for explaining the result of comparing the number of forest fires per month between a modified FFMC and a conventional FFMC according to a preferred embodiment of the present invention.
12 is a diagram for explaining a drought index used to obtain a forest fire risk index according to a preferred embodiment of the present invention.
13 is a diagram for explaining first monthly weights used to obtain a forest fire risk index according to a preferred embodiment of the present invention.
14 is a diagram for explaining a second monthly weight used to obtain a forest fire risk index according to a preferred embodiment of the present invention.
15 is a flowchart illustrating a method for providing a forest fire risk index according to a preferred embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. Advantages and features of the present invention, and methods for achieving them, will become clear with reference to the embodiments described below in detail in conjunction with the accompanying drawings. However, the present invention is not limited to the embodiments disclosed below and may be implemented in various different forms, only the present embodiments make the disclosure of the present invention complete, and common knowledge in the art to which the present invention belongs. It is provided to completely inform the person who has the scope of the invention, and the present invention is only defined by the scope of the claims. Like reference numbers designate like elements throughout the specification.

Unless otherwise defined, all terms (including technical and scientific terms) used in this specification may be used in a meaning commonly understood by those of ordinary skill in the art to which the present invention belongs. In addition, terms defined in commonly used dictionaries are not interpreted ideally or excessively unless explicitly specifically defined.

In this specification, terms such as "first" and "second" are used to distinguish one component from another component, and the scope of rights should not be limited by these terms. For example, a first element may be termed a second element, and similarly, a second element may be termed a first element.

In this specification, identification codes (eg, a, b, c, etc.) for each step are used for convenience of explanation, and identification codes do not describe the order of each step, and each step is clearly Unless a specific order is specified, it may occur in a different order from the specified order. That is, each step may occur in the same order as specified, may be performed substantially simultaneously, or may be performed in the reverse order.

In this specification, expressions such as "has", "may have", "includes" or "may include" indicate the existence of a corresponding feature (eg, numerical value, function, operation, or component such as a part). indicated, and does not preclude the presence of additional features.

In addition, the term '~unit' described in this specification means software or a hardware component such as a field-programmable gate array (FPGA) or ASIC, and '~unit' performs certain roles. However, '~ part' is not limited to software or hardware. '~bu' may be configured to be in an addressable storage medium and may be configured to reproduce one or more processors. Therefore, as an example, '~unit' refers to components such as software components, object-oriented software components, class components, and task components, processes, functions, properties, and procedures. , subroutines, segments of program code, drivers, firmware, microcode, circuitry, data structures and variables. Functions provided within components and '~units' may be combined into smaller numbers of components and '~units' or further separated into additional components and '~units'.

Hereinafter, preferred embodiments of an apparatus and method for providing a forest fire risk index according to the present invention will be described in detail with reference to the accompanying drawings.

First, an apparatus for providing a forest fire risk index according to a preferred embodiment of the present invention will be described with reference to FIG. 1 .

1 is a block diagram illustrating an apparatus for providing a forest fire risk index according to a preferred embodiment of the present invention.

Referring to FIG. 1, an apparatus 100 for providing a forest fire risk index according to a preferred embodiment of the present invention generates a forest fire risk index model optimized for the Korean Peninsula, and uses the generated forest fire risk index model to forest fire risk on a forecast day. forecast indices.

To this end, the forest fire risk index providing device 100 may include a soil moisture index acquisition unit 110, a drought index acquisition unit 130, a forest fire risk index acquisition unit 150, and a forecasting unit 170.

The soil moisture index acquisition unit 110 is based on a machine learning algorithm, TRMM (Tropical Rainfall Measuring Mission) precipitation data, ASCAT (Advanced SCATterometer) soil moisture data, NDVI (Normalized Difference Vegetation Index), LST (Land Surface Temperature) and A soil moisture index downscaling model is created with DEM (digital elevation model) as an input variable and GLDAS (Global Land Data Assimilation System) soil moisture data as an output variable.

Here, the machine learning algorithm may use one of random forest (RF), support vector regression (SVR), and artificial neural network (ANN). In particular, the present invention can generate a soil moisture index downscaling model using a random forest (RF).

At this time, the soil moisture index acquisition unit 110 uses up-scaling data with the same grid size of 25 km as the grid size of the GLDAS soil moisture data as training data for uniformity of spatial resolution between data, and uses the soil moisture index downscaling model. generate

Then, the soil moisture index obtaining unit 110 acquires the soil moisture index downscaled to the grid size of 1 km by inputting the input variable converted to the grid size of 1 km into the soil moisture index downscaling model.

More specifically, the soil moisture index acquisition unit 110 uses the upscaled data with a grid size of 25 km as training data, and uses TRMM precipitation data, ASCAT soil moisture data, NDVI, LST and DEM as input variables, A first soil moisture index downscaling model having GLDAS soil moisture data as an output variable may be generated.

In addition, the soil moisture index acquisition unit 110 uses the data upscaled to a grid size of 25 km as training data, and uses TRMM precipitation data, NDVI, LST, and DEM as input variables, and GLDAS soil moisture data as output variables. A second soil moisture index downscaling model may be generated. That is, the soil moisture index obtaining unit 110 may generate a second soil moisture index downscaling model by using remaining input variables except for ASCAT soil moisture data among input variables of the first soil moisture index downscaling model.

Then, the soil moisture index acquisition unit 110 inputs the input variable converted to the grid size of 1 km into the first soil moisture index downscaling model to obtain a first soil moisture index downscaled to the grid size of 1 km, The input variable converted to the grid size of 1 km is input into the second soil moisture index downscaling model to obtain the second soil moisture index downscaled to the grid size of 1 km, and the missing part from the first soil moisture index is the second soil moisture index downscaling model. Substitute the soil moisture index to obtain the final soil moisture index downscaled to a grid size of 1 km.

The drought index acquisition unit 130 uses the soil moisture index downscaled to a grid size of 1 km obtained through the soil moisture index acquisition unit 110, a normalized differential water index (NDWI), and a temperature condition index (TCI). get the index

That is, the drought index obtaining unit 130 may acquire the drought index through the following equation.

Drought index = 0.4 * (downscaled soil moisture index) + 0.3 * (NDWI) + 0.3 * (TCI)

In more detail, the drought index acquisition unit 130 may obtain the drought index using the downscaled soil moisture index, NDWI, and TCI, which are factors showing high correlation with drought among the following drought-related factors.

- Soil moisture index downscaled to a grid size of 1 km

-Normalized Different Drought Index (NDDI)

- NDWI (Normalized Differential Water Index)

- NMDI (Normalized Multi-band Drought Index)

- TCI (Temperature Condition Index)

- Vegetation Condition Index (VCI)

- TRMM (Tropical Rainfall Measuring Mission) 1 (1 week cumulative precipitation) / TRMM 2 (2 weeks cumulative precipitation)

Meanwhile, the drought index acquisition unit 130 may generate a drought index model using One-Class SVM and acquire a drought index using the generated drought index model, but the drought index acquisition unit 130 according to the present invention ) obtains the drought index through the above equation.

The forest fire risk index acquisition unit 150 obtains a forest fire risk index using a forest fire prone area map, a modified Fine Fuel Moisture Code (FFMC), a drought index acquired through the drought index acquisition unit 130, and a monthly weight.

Here, as the monthly weight, a greater weight may be assigned as the number of monthly forest fires increases, using a ratio of monthly forest fires obtained based on all forest fires that have occurred in the past. For example, the monthly weight is a first monthly weight that assigns a greater weight as the number of wildfires per month increases according to the ratio of the number of forest fires per month based on all forest fires that have occurred in the past, or a monthly forest fire that has occurred based on all forest fires that have occurred in the past. It may be a second monthly weight that gives weight only to a specific month (March to May) having the largest number of cases. In particular, the present invention may obtain a forest fire risk index using the first monthly weight.

In addition, the modified FFMC is based on the equilibrium moisture content, drying rate and minimum moisture content of the day calculated using the relative humidity, precipitation measured at noon, temperature, and wind speed. Says FFMC. That is, in the modified FFMC, in the conventional FFMC, the coefficients of the formula for calculating the FFMC initial value, the precipitation reference value, the FFMC reference value, and the drying rate are modified, the coefficient of the formula for calculating the moisture content of the previous day is modified, and the minimum moisture content is used. The coefficient of the formula for calculating the FFMC value is modified, the accumulated precipitation for the day is used instead of the precipitation measured at noon, and the reference value for the precipitation is larger than the conventional FFMC.

That is, the forest fire risk index acquisition unit 150 may obtain the forest fire risk index through the following equation.

Wildfire Hazard Index = (Fire Area Map + 0.5) * (Adjusted FFMC) * (1.5 - Drought Index) * (Weighted by Month)

The forecasting unit 170 obtains a forest fire risk index value for a forecast date based on the forest fire risk index obtained through the forest fire risk index acquisition unit 150 .

Then, a soil moisture index downscaling model according to a preferred embodiment of the present invention will be described in more detail with reference to FIGS. 2 to 5 .

In the present invention, in order to perform soil moisture downscaling in the Korean Peninsula, GLDAS (Global Land Data Assimilation System) soil moisture data, ASCAT (Advanced SCATterometer) soil moisture data, NDVI (Normalized Difference Vegetation Index), Soil moisture in situ observation data after constructing a soil moisture index downscaling model using 5-day and 7-day cumulative precipitation data using LST (Land Surface Temperature), DEM (Digital Elevation Model), and daily TRMM (Tropical Rainfall Measuring Mission) precipitation data The model was verified with

First, GLDAS used as soil moisture data is a data assimilation data system based on three land models: Mosaic, Noah, and Community Land Model. In the present invention, the Noah model was used among the three land models. In the Noah model, moisture data of 1 cm to 10 cm soil layer with 25 km spatial resolution were provided four times a day (03, 09, 15, and 12:00), and the daily average of the soil moisture data (m ³ /m ³ ) was used. As the soil moisture data calculated by ASCAT, the daily average of ascending and descending pass data for one day was used. As auxiliary variables, MOD13A2, 16-day synthetic NDVI data with 1 km spatial resolution calculated from MODIS (Moderate resolution Imaging Spectroradiometer) of the Terra satellite, and MOD11A2, 8-day synthetic LST data with 1 km spatial resolution, were used. In addition, the DEM used the global DEM data of the Shuttle Radar Topography Mission (SRTM) with a spatial resolution of 90 m. In the case of precipitation data, TRMM 3B42 daily data with a spatial resolution of 25 km were accumulated and used over a period of 5 days and 7 days, respectively. The soil moisture field observation data (%) provided by the Agricultural Promotion Administration was used for model validation after unit conversion to m ³ /m ³ . Except for field observation data, all data were used after masking to the study area. However, in the case of LST and NDVI outputs, they were used after masking after mosaic.

2 is a diagram for explaining a soil moisture index downscaling model according to a preferred embodiment of the present invention.

Referring to FIG. 2 , in the present invention, a downscaling model for detailing soil moisture was developed using various machine learning and artificial intelligence techniques. As machine learning and artificial intelligence methods used, three techniques were used: random forest (RF), support vector regression (SVR), and artificial neural network (ANN), respectively. A downscaling model was developed for each technique by setting the GLDAS soil moisture data as a dependent variable and setting a total of five data excluding the field observation data of soil moisture as independent variables. For uniformity of spatial resolution between data, all input data were up-scaled to a spatial resolution of 25 km, the same grid size as GLDAS, and then applied to model construction. Then, five input data converted to a 1km grid size are applied to the developed model to finally obtain the result of downscaling soil moisture in a 1km grid. In the present invention, a model was built by dividing the data from 2013 to 2014 into training data and verification data at a ratio of 8:2, and additionally, 10-fold cross-validation was performed with data from the same period. In addition, the soil moisture downscaling results produced by each model were verified by comparison with the field observation soil moisture data of the Agricultural Promotion Administration.

3 is a diagram for explaining the results of a soil moisture index downscaling model according to a preferred embodiment of the present invention.

In order to find the optimal method for the soil moisture index downscaling model in the Korean Peninsula, downscaling models were developed and compared using three methods (RF, SVR, and ANN). Figure 3 shows the soil moisture downscaling results of each model as a scatter plot. The correlation coefficient value between the actual variable value and the predicted value of the model was large in the order of RF, ANN, and SVR, and RMSE (Root Mean Square Error) also showed a small value. In particular, the distribution of RF results was the narrowest in the scatter plot regarding cross-validation. Overall, all three models tended to underpredict for high soil moisture values and to overpredict for low soil moisture values. Accordingly, the soil moisture index downscaling model according to the present invention was created using RF.

4 is a diagram for explaining the results of a soil moisture index downscaling model excluding ASCAT soil moisture data according to a preferred embodiment of the present invention, and FIG. 5 is a final downscaled soil moisture index according to a preferred embodiment of the present invention. As a diagram for explaining, the left side of FIG. 5 shows the result of the first soil moisture index downscaling model, and the right side of FIG. Indicates the replacement with the result of the downscaling model.

It can be seen that the results of the soil moisture index downscaling model are missing for the Jeju Island area and near some coastlines. This is dependent on the value of ASCAT soil moisture data with 25 km spatial resolution used as an input variable. In order to solve the omission problem, a soil moisture index downscaling model was additionally built with a total of four input variables excluding ASCAT from the soil moisture downscaling method mentioned above, and the missing part due to ASCAT data in the original model was replaced with the result of the additional model. 4 and 5 show examples of soil moisture maps and the resulting performance of the additional model, respectively.

In order to verify the results of each soil moisture index downscaling model, comparative verification was performed with field observation-based soil moisture data provided by the Agricultural Promotion Administration. The soil moisture data of the observation station used for verification were subjected to time-series analysis to verify the results of the soil moisture index downscaling model. As a result of the time series analysis, it was confirmed that the increase and decrease patterns of soil moisture were similar at all stations.

Then, the drought index according to a preferred embodiment of the present invention will be described in more detail with reference to FIGS. 6 and 7 .

The main causes of forest fires in Korea are accidental fires by residents and cigarette butts, and forest fires caused by drought are extremely rare. However, if a forest fire occurs during a drought, the damage (area) can be aggravated. Therefore, in the present invention, the correlation between drought and forest fire was analyzed using actual forest fire occurrence data of 1 ha or more from 2013 to 2018. Later, satellite data available in real time were used for use in developing a forest fire risk index. The drought-related factors used are the soil moisture downscaling data mentioned above, NDDI (Normalized Different Drought Index), and NDWI (Normalized Different Water Index) 5, 6, 7 (divided into 5, 6, and 7 depending on the use of SWIR band) , NMDI (Normalized Multi-band Drought Index), TCI (Temperature Condition Index), VCI (Vegetation Condition Index), TRMM 1, 2 (1st and 2nd week cumulative precipitation) data. The formula below is based on MODIS (based on MODIS band).

NDDI = (NDVI - NDWI) / (NDVI + NDWI)

NDWI = (band2 - SWIR) / (band2 + SWIR)

NMDI = (band2 - (band6 - band7)) / (band2 + (band6 - band7))

6 is a diagram for explaining a drought factor according to a preferred embodiment of the present invention.

As a result of analyzing the value distribution of each factor and index based on the forest fire area of 1 ha or more (left side of FIG. 6) and 10 ha or more (right side of FIG. 6), the results shown in FIG. 6 were shown. A value closer to 1 means no drought, and a value closer to 0 means more severe drought. Over 1 ha, the ranges of 1-week cumulative precipitation (TRMM 1) and 2-week cumulative precipitation (TRMM 2) values showed the most drought phenomena, and in order, soil moisture (SM) and NDWI showed a correlated distribution. NDDI, NMDI, and VCI showed values close to non-drought, showing poor correlation with forest fire occurrence (left side of FIG. 6). Even over 10 ha, the same correlation as 1 ha was observed, and there were relatively few cases of non-drought (right side of FIG. 6). When the forest fire area was over 50 ha (13 cases), the average values for each factor were soil moisture 0.37, NDDI 0.49, NDWI 5 0.32, NDWI 6 0.28, NDWI 7 0.38, NMDI 0.41, TCI 0.45, VCI 0.56, TRMM 1 0.01, TRMM 2 showed a higher correlation with drought, such as 0.02.

In the present invention, a method of applying weights to drought factors selected through correlation analysis and one-class SVM, one of machine learning types, were applied to develop a drought index model. An index was developed using soil moisture, NDWI, TCI, NMDI, and TRMM, which showed high correlation.

(1) Weighting

Correlation analysis showed that the precipitation factor had the greatest effect. However, in the case of precipitation, the drought index shows an extreme value depending on whether or not precipitation occurs, and it shows drought or non-drought in all regions spatially, so it was judged that it is not appropriate to use it as essential for developing a drought index. Therefore, as shown in [Table 1] below, soil moisture and NDWI, which had the highest correlation after precipitation, were combined with other factors.

Scheme Equation One 0.7 * Soil Moisture Index + 0.3 * NDWI 2 0.4 * Soil Moisture Index + 0.3 * NDWI + 0.3 * TCI 3 0.4 * Soil Moisture Index + 0.3 * NDWI + 0.3 * NMDI 4 0.4 * Soil Moisture Index + 0.2 * NDWI + 0.4 * TRMM 5 0.3 * Soil Moisture Index + 0.2 * NDWI + 0.3 * TRMM + 0.1 * TCI

7 is a diagram for explaining the results of a drought index model to which weights are applied according to a preferred embodiment of the present invention.

7 shows the results of each scheme for actual forest fire occurrence. Schemes 4 and 5, which include precipitation factors, exhibited severe drought conditions compared to other schemes, and showed drought conditions regardless of the forest fire damage area. However, it also showed drought conditions in areas where forest fires did not occur. In addition, since TCI has a relatively greater correlation than NMDI, Scheme 2, which does not include precipitation factors, and Scheme 4 and 5, which include precipitation factors, were used to develop forest fire risk indices.

(2) Application of One-Class SVM

One-class SVM distinguishes one class from outliers using a hyperplane, the same as existing binary classification and multi-class SVMs. Based on Margin Support vectors, internal vectors are assigned classes, and external vectors are classified as outliers.

When developing a machine learning model using the existing binary classification, the developer's subjective opinion on extracting a non-fire sample is included, so the present invention attempted to develop a drought index related to forest fires through One-Class SVM. The kernel function used Gaussian, and the result was derived by normalizing the score calculated through the model. The results were compared by dividing a narrow range of normalization (One-Class SVM 1, minimum: 0, maximum: 0.5) and a wide range of normalization (One-Class SVM 2, minimum: 0, maximum: 0.1). As a result of comparison, the smaller the forest fire damage area, the one-class SVM model showed a non-drought state, and the non-drought area was higher than when weights were applied. However, as mentioned above, forest fires in Korea are generally caused by human ignition, so forest fires can occur in non-drought conditions. Therefore, the results of the One-Class SVM were also tested in developing a wildfire risk index.

Next, the forest fire risk index according to a preferred embodiment of the present invention will be described in more detail with reference to FIGS. 8 to 14 .

8 is a diagram for explaining a forest fire prone area map according to a preferred embodiment of the present invention.

In order to add information on areas vulnerable to wildfires, the forest fire-prone area map provided by the National Institute of Forest Science was used. The forest fire-prone area map is a data that numerically maps the location information of all forest fires (10,560 cases) that occurred from 1991 to 2015. Based on this location information, density analysis is conducted to identify areas of concern where forest fires may occur frequently. This is the selected map. In order to select areas with frequent forest fires, the average distance between forest fires was estimated by performing the average distance method and nearest proximity analysis. The causes of forest fires were largely classified into 6 categories: misfires by mountain residents, incineration of rice paddies/fields, incineration of garbage, misfires by visitors to graves, misfires by lit cigarettes, and others. From 1991 to 2015, an average of 422 forest fires occurred annually, burning 2,102 ha of forest annually. The region with the highest number of forest fires was Busan (477 cases), followed by Seoul (412 cases), Incheon (391 cases), Ulsan (350 cases), Daegu (285 cases), Daejeon (263 cases), and Gwangju (203 cases). case), the frequency of forest fires was high in metropolitan areas (see Fig. 8). The most frequent forest fires by month was April, with 3,250 forest fires, accounting for 30.8% of the total. Looking at the statistics on forest fires by cause, 4,392 cases of forest fires were caused by misfires by mountain residents, accounting for 41.6% of the total number of forest fires, followed by incineration of rice paddies/fields with 18.5% (1,952 cases), incineration of garbage (830 cases (7.9%)), and misfires by cigarettes. followed by 813 cases (7.7%).

9 is a diagram for explaining why FFMC according to a preferred embodiment of the present invention is used as a factor of a forest fire risk index. FIG. 9 (a) compares FFMC with the number of forest fires per month in 2015, and FIG. (b) compares FFMC to the number of wildfires per 10 days in 2015.

The Canada Fire Weather Index (CFWI) is a combination of FFMC (Fine Fuel Moisture Code), DMC (Duff Moisture Code), DC (Drought Code) calculated using weather information such as temperature, relative humidity, wind speed, and precipitation , ISI (Initial Spread Index), and BUI (Build Up Index) information. FFMC predicts the moisture content of fine fuel in the forest by indexing, and DMC predicts the humidity of the fuel layer in the forest surface. DC predicts the possibility of seasonal drought and subterraneanization by predicting the moisture of the deep organic matter layer and coarse fuel in the ground, and ISI is calculated by combining FFMC and wind speed factors. Among them, FFMC predicts the moisture content of micro fuel using temperature, relative humidity, wind speed, and precipitation information, and the range is 0 to 99. The higher the number, the higher the probability of ignition. Among the existing studies, when CFWI was applied to Korea, FFMC had a higher correlation than CFWI, the final calculation index, and a regression analysis model using FFMC predicted the probability of wildfire occurrence, resulting in a statistical significance of 5% ( Park Heung-seok et al., 2009). When CFWI and FFMC were compared with Korea's existing forest fire index, DWI (Daily Weather Index) and forest fire standards in 2015 (see Fig. 9), it was found that FFMC was more suitable for Korea than CFWI, and FFMC was used in the present invention decided to do it.

10 is a diagram for explaining the result of comparing the spatial distribution of the modified FFMC and the conventional FFMC according to a preferred embodiment of the present invention, and FIG. It is a diagram for explaining the result of comparing with the number of forest fires per month.

9 above, it was determined that FFMC is more suitable for Korea than CFWI, and that FFMC is used in the present invention. FFMC was developed in the 1970s and has been continuously updated and used since then. In order to create a more accurate forest fire risk index model, the process of optimizing the existing FFMC for the Korean environment was carried out. FFMC calculates the equilibrium moisture content, drying rate, and minimum moisture content of the day using relative humidity, precipitation, temperature, and wind speed data, and finally calculates FFMC. Accordingly, in the present invention, FFMC was optimized by modifying some coefficients according to the Korean environment. That is, the coefficients of the formula for calculating the initial FFMC value, the reference value for precipitation, the reference value for FFMC, and the drying rate were modified, and the coefficients for the formula for calculating the moisture content of the previous day and the formula for calculating FFMC using the minimum amount were modified. After determining the range of coefficients by comparing the first equation developed in the 1970s with the equation currently used, the optimal coefficients were found by comparing the number and area of forest fires in Korea while modifying the coefficients within each coefficient range. Existing FFMC used precipitation measured at noon, but in the present invention, daily accumulated precipitation was used to create daily FFMC. The precipitation reference value was increased by changing the precipitation data from instantaneous precipitation to cumulative precipitation. 10 is a result of comparing the spatial distribution of the existing FFMC and the optimized FFMC (i.e., the modified FFMC according to the present invention). Since precipitation determines the degree of dryness and is an important variable in calculating FFMC, FFMC is the most predictive pattern of precipitation. I could see a lot of following. While modifying the FFMC to suit the Korean environment, the existing FFMC, which was heavily biased towards precipitation, was modified to have a more gentle effect.

11 is a result of comparing the existing FFMC and the optimized FFMC with the number of forest fires in Korea, and it can be seen that the optimized FFMC shows the time series better than the existing FFMC (see purple arrow).

As shown in [Table 2] below, after calculating the FFMC index of all forest fire pixels and pixels where forest fires did not occur for each forest fire day with the existing FFMC and the optimized FFMC, the CDF (Cumulative Distribution Function) values of the forest fire pixels were calculated. After averaging, they were compared. The CDF is the probability that a random variable is less than or equal to a certain value for a certain probability distribution. For example, if the CDF is 0.95, it is a high index corresponding to the top 5%. Since the existing FFMC and optimized FFMC value distributions are different, in order to compare them, each index value was converted into a CDF and the accuracy was analyzed.

wildfire area >= 50 ha < 50 ha < 10 ha < 1ha existing
FFMC FFMC Average 87.0244 86.0494 83.8506 80.9751 CDF mean 0.769 0.791 0.575 0.429 optimized
FFMC FFMC Average 60.9135 58.9741 51.8598 49.2367 CDF mean 0.972 0.978 0.960 0.924

Compared to the existing FFMC, the average CDF value of the optimized FFMC was higher than 0.9, and the larger the damage area, the higher the average CDF value. Through this, it can be seen that the optimized FFMC is more suitable for Korea than the existing FFMC.

A forest fire risk index (FRI) was developed by integrating the modified FFMC to suit the Korean environment with a forest fire-prone area map and a drought index. The existing Canadian Wildfire Risk Index (CFWI) calculation method is generated by multiplying a function for wind and FFMC, a function for DMC and DC, and a coefficient as follows.

CFWI = coefficient * f(wind,FFMC) * f(DMC,DC)

Therefore, the forest fire risk index (FRI) according to the present invention was developed using the modified FFMC (revised FFMC), drought index (drought idx), and forest fire frequent area map (frequency) as coefficients as follows, considering seasonal characteristics A process for giving different temporal weights for each month was added.

FRI = (frequency + 0.5) * (revised FFMC) * (1.5 - drought idx) * (temporal weight)

Here, the constants added to the forest fire-prone area map (frequency) and the drought index (drought idx) are to prevent the situation in which FRI becomes 0 when multiplied when each index has a minimum value of 0, and various constants are CDF Through the analysis of the top percentage of all pixels on the same day, the constant that was judged to best simulate the occurrence of a forest fire was finally used.

12 is a diagram for explaining a drought index used to obtain a forest fire risk index according to a preferred embodiment of the present invention.

12 compares the distribution of previously developed drought indices related to forest fire occurrence with respect to fire and nonfire pixels, and various previously developed drought indices were tested to develop forest fire risk indices, The distribution of drought indices that showed the most significant results among them is shown. After deriving the forest fire risk index using these drought indices, as a result of analyzing the CDF and top %, Scheme 2 was judged to be the most suitable for developing the forest fire risk index among the drought indices. Thus, the drought index used to obtain the forest fire risk index according to the present invention used the drought index according to Scheme 2 among weighted drought indices.

The method of giving the temporal weight is the weighting method (FRI_M1) so that the greater the number of monthly occurrences, the larger the FRI value according to the ratio of monthly occurrences for all forest fires that occurred from 2014 to 2017 (FRI_M1) and the monthly forest fires Two methods were tested (FRI_M2) in which only the months of March to May, which have the highest number of occurrences, were weighted.

In order to determine the suitability of FRI_M1 and FRI_M2, which were multiplied by monthly weights to consider seasonal characteristics, CDF analysis was conducted as in the case of comparing the existing FFMC and the modified FFMC. The probability of being less than or equal to a certain value. For comparison, after calculating the FFMC and FRI of all forest fire pixels and non-forest fire pixels for days when forest fires occurred from 2014 to 2017, the CDF values of forest fire pixels were averaged as shown in [Table 3].

wildfire area >= 50 ha < 50 ha < 10 ha < 1ha existing
FFMC CDF mean 0.769 0.791 0.575 0.429 Modified
FFMC CDF mean 0.972 0.978 0.960 0.924 FRI_M1 CDF mean 0.945 0.994 0.953 0.895 FRI_M2 CDF mean 0.959 0.979 0.974 0.928

As a result, it was confirmed that the numbers were noticeably improved compared to the existing FFMC, and even when compared to the modified FFMC, the FRI was similar to or higher than the modified FFMC, so the FRI values of wildfire pixels were higher than those of non-fire pixels. Interpretation is possible. In order to determine the accuracy of the spatial simulation only on the day of the wildfire occurrence, not for all study periods, we analyzed the top percentage of the FFMC and FRI of each forest fire among the national forest fire risk indexes. As a result, as shown in [Table 4] below, the proportion of forest fires within the top 5% of the FRI increased by about two times compared to the existing FFMC, and the forest fires within the top 40% increased from 58.55% to 67.91% on average. did

difference% <= 5% <= 10% <= 20% <= 30% <= 40% <= 50% > 50% sum existing
FFMC 12.134 10.434 14.448 12.181 9.348 8.593 32.861 100 FRI_M1 20.608 10.161 16.144 11.728 9.497 7.028 24.834 100 FRI_M2 20.560 10.446 15.907 11.728 9.544 7.028 24.786 100

13 is a diagram for explaining a first monthly weight used to obtain a forest fire risk index according to a preferred embodiment of the present invention, and FIG. 2 It is a diagram to explain the weight of each month.

13 and 14 show the forest fire risk index (DWI) provided by the existing forest fire risk forecasting system of the Forest Service, Institute of Forest Science, the present invention, so that the FRI can have a higher value as the number of forest fires per month increases. As a result of comparing the weighted model (FRI_M1) and the weighted model (FRI_M2) for March to May, which had the highest number of forest fires, with the number of forest fires in Korea from 2014 to 2017, both FRI_M1 and FRI_M2 were DWI Compared to the number of forest fires per month, it showed a good match with the rising and falling time series pattern. It can be seen that is in better agreement with the time series shown by (see purple box). Therefore, as the monthly weight used to obtain the forest fire risk index according to the present invention, the first monthly weight was used so that the FRI can have a higher value as the number of forest fires per month increases.

Next, a method for providing a forest fire risk index according to a preferred embodiment of the present invention will be described with reference to FIG. 15 .

15 is a flowchart illustrating a method for providing a forest fire risk index according to a preferred embodiment of the present invention.

Referring to FIG. 15 , the apparatus 100 for providing a forest fire risk index may obtain a downscaled soil moisture index with a grid size of 1 km based on a machine learning algorithm (S110).

That is, the apparatus 100 for providing a forest fire risk index is based on a machine learning algorithm, soil moisture with TRMM precipitation data, ASCAT soil moisture data, NDVI, LST and DEM as input variables and GLDAS soil moisture data as an output variable. Create an exponential downscaling model. Here, the machine learning algorithm may use one of random forest (RF), support vector regression (SVR), and artificial neural network (ANN). In particular, the present invention can generate a soil moisture index downscaling model using a random forest (RF).

At this time, the forest fire risk index providing device 100 uses up-scaling data with a grid size of 25 km identical to the grid size of the GLDAS soil moisture data as training data for uniformity of spatial resolution between data, and uses a soil moisture index downscaling model. generate Further, the apparatus 100 for providing a forest fire risk index acquires a soil moisture index downscaled with a grid size of 1 km by inputting an input variable converted to a grid size of 1 km into a soil moisture index downscaling model.

In more detail, the forest fire risk index providing device 100 uses upscaled data with a grid size of 25 km as training data, and uses TRMM precipitation data, ASCAT soil moisture data, NDVI, LST and DEM as input variables, A first soil moisture index downscaling model having GLDAS soil moisture data as an output variable may be generated. In addition, the forest fire risk index providing device 100 uses the upscaled data with a grid size of 25 km as training data, and uses TRMM precipitation data, NDVI, LST, and DEM as input variables, and GLDAS soil moisture data as output variables. A second soil moisture index downscaling model may be generated. Then, the apparatus 100 for providing a forest fire risk index obtains a first soil moisture index downscaled to a grid size of 1 km by inputting an input variable converted to a grid size of 1 km into a first soil moisture index downscaling model, The input variable converted to the grid size of 1 km is input into the second soil moisture index downscaling model to obtain the second soil moisture index downscaled to the grid size of 1 km, and the missing part from the first soil moisture index is the second soil moisture index downscaling model. Substitute the soil moisture index to obtain the final soil moisture index downscaled to a grid size of 1 km.

Then, the apparatus 100 for providing a forest fire risk index may obtain a drought index by using the downscaled soil moisture index, NDWI, and TCI with a grid size of 1 km (S130).

That is, the forest fire risk index providing device 100 may obtain the drought index through the equation 0.4 * (downscaled soil moisture index) + 0.3 * (NDWI) + 0.3 * (TCI).

Then, the forest fire risk index providing apparatus 100 may obtain a forest fire risk index using the forest fire prone area map, the modified FFMC, the drought index, and the monthly weight (S150).

That is, the forest fire risk index providing device 100 may obtain the forest fire risk index through the formula (forest fire prone area map + 0.5) * (modified FFMC) * (1.5 - drought index) * (monthly weight).

Here, as the monthly weight, a greater weight may be assigned as the number of monthly forest fires increases, using a ratio of monthly forest fires obtained based on all forest fires that have occurred in the past.

In addition, the modified FFMC is based on the equilibrium moisture content, drying rate and minimum moisture content of the day calculated using the relative humidity, precipitation measured at noon, temperature, and wind speed. Says FFMC. That is, in the modified FFMC, in the conventional FFMC, the coefficients of the formula for calculating the FFMC initial value, the precipitation reference value, the FFMC reference value, and the drying rate are modified, the coefficient of the formula for calculating the moisture content of the previous day is modified, and the minimum moisture content is used. The coefficient of the formula for calculating the FFMC value is modified, the accumulated precipitation for the day is used instead of the precipitation measured at noon, and the reference value for the precipitation is larger than the conventional FFMC.

Thereafter, the forest fire risk index providing device 100 obtains a forest fire risk index value for the forecast date based on the acquired forest fire risk index (S170).

Even though all components constituting the embodiments of the present invention described above are described as being combined or operated as one, the present invention is not necessarily limited to these embodiments. That is, within the scope of the object of the present invention, all of the components may be selectively combined with one or more to operate. In addition, although all of the components may be implemented as a single independent piece of hardware, some or all of the components are selectively combined to perform some or all of the combined functions in one or a plurality of pieces of hardware. It may be implemented as a computer program having. In addition, such a computer program can implement an embodiment of the present invention by being stored in a computer readable recording medium such as a USB memory, a CD disk, a flash memory, etc., and read and executed by a computer. A recording medium of a computer program may include a magnetic recording medium, an optical recording medium, and the like.

The above description is merely an example of the technical idea of the present invention, and those skilled in the art can make various modifications, changes, and substitutions without departing from the essential characteristics of the present invention. will be. Therefore, the embodiments disclosed in the present invention and the accompanying drawings are not intended to limit the technical idea of the present invention, but to explain, and the scope of the technical idea of the present invention is not limited by these embodiments and the accompanying drawings. . The protection scope of the present invention should be construed according to the claims below, and all technical ideas within the equivalent range should be construed as being included in the scope of the present invention.

100: forest fire risk index providing device,
110: soil moisture index acquisition unit,
130: drought index acquisition unit,
150: forest fire risk index acquisition unit,
170: forecast department

Claims (13)

A forest fire risk index acquisition unit for acquiring a forest fire risk index using a forest fire prone area map, a modified FFMC (Fine Fuel Moisture Code), a drought index, and a monthly weight; and
a forecasting unit acquiring a forest fire risk index value for a forecast date based on the forest fire risk index obtained through the forest fire risk index acquisition unit;
Including,
The monthly weight is given a greater weight as the number of monthly forest fires increases, using the ratio of monthly forest fires obtained based on all forest fires that have occurred in the past.
The forest fire risk index acquisition unit,
Obtaining the forest fire risk index through the equation (the forest fire prone area map + 0.5) * (the modified FFMC) * (1.5 - the drought index) * (the monthly weight),
A wildfire risk index providing device. delete In paragraph 1,
The modified FFMC,
In the conventional FFMC that calculates FFMC based on the equilibrium moisture content, drying rate, and minimum moisture content of the day calculated using relative humidity, precipitation measured at noon, temperature, and wind speed, FFMC initial value, precipitation reference value, FFMC reference value and dry The coefficients of the formula for calculating the coordination are corrected, the coefficients of the formula for calculating the moisture content of the previous day are corrected, the coefficients of the formula for calculating the FFMC value using the minimum moisture content are corrected, and the accumulated precipitation for the day is not the precipitation measured at noon. This is used, and the precipitation reference value is larger than the conventional FFMC,
A wildfire risk index providing device. In paragraph 1,
a drought index obtaining unit acquiring the drought index by using a soil moisture index downscaled to a grid size of 1 km, a normalized differential water index (NDWI), and a temperature condition index (TCI);
Wildfire risk index providing device further comprising a. In paragraph 4,
The drought index acquisition unit,
Obtaining the drought index through the equation 0.4 * (the downscaled soil moisture index) + 0.3 * (the NDWI) + 0.3 * (the TCI),
A wildfire risk index providing device. In paragraph 4,
Using data upscaled to a grid size of 25 km as training data, TRMM (Tropical Rainfall Measuring Mission) precipitation data, ASCAT (Advanced SCATterometer) soil moisture data, NDVI (Normalized Difference Vegetation Index), A soil moisture index downscaling model is created with Land Surface Temperature (LST) and digital Elevation Model (DEM) as input variables and Global Land Data Assimilation System (GLDAS) soil moisture data as output variables, and a grid size of 1 km a soil moisture index acquisition unit configured to obtain the downscaled soil moisture index by inputting the input variable converted to ? into the soil moisture index downscaling model;
Wildfire risk index providing device further comprising a. In paragraph 6,
The soil moisture index acquisition unit,
Using upscaled data with a grid size of 25 km as training data, the TRMM precipitation data, the ASCAT soil moisture data, the NDVI, the LST, and the DEM are used as input variables, and the GLDAS soil moisture data are used as output variables To create a first soil moisture index downscaling model,
2nd soil moisture, using upscaled data with a grid size of 25 km as training data, using the TRMM precipitation data, the NDVI, the LST, and the DEM as input variables, and the GLDAS soil moisture data as output variables generate an exponential downscaling model;
An input variable converted to a grid size of 1 km is input to the first soil moisture index downscaling model to obtain a first soil moisture index downscaled to a grid size of 1 km, and an input variable converted to a grid size of 1 km is input to the first soil moisture index downscaling model. The second soil moisture index is input to the downscaling model to obtain a second soil moisture index downscaled to a grid size of 1 km, and the missing part in the first soil moisture index is replaced with the second soil moisture index to perform the downscaling. to obtain the soil moisture index,
A wildfire risk index providing device. A method for providing a forest fire risk index performed by a forest fire risk index providing device,
Obtaining a forest fire risk index using a forest fire prone area map, a modified Fine Fuel Moisture Code (FFMC), a drought index, and a monthly weight; and
obtaining a forest fire risk index value for a forecast date based on the forest fire risk index;
Including,
The monthly weight is given a greater weight as the number of monthly forest fires increases, using the ratio of monthly forest fires obtained based on all forest fires that have occurred in the past.
The forest fire risk index acquisition step,
Acquiring the forest fire risk index through the formula (the forest fire prone area map + 0.5) * (the modified FFMC) * (1.5 - the drought index) * (the monthly weight),
Wildfire risk index providing method comprising a. delete In paragraph 8,
The modified FFMC,
In the conventional FFMC that calculates FFMC based on the equilibrium moisture content, drying rate, and minimum moisture content of the day calculated using relative humidity, precipitation measured at noon, temperature, and wind speed, FFMC initial value, precipitation reference value, FFMC reference value and dry The coefficients of the formula for calculating the coordination are corrected, the coefficients of the formula for calculating the moisture content of the previous day are corrected, the coefficients of the formula for calculating the FFMC value using the minimum moisture content are corrected, and the accumulated precipitation for the day is not the precipitation measured at noon. This is used, and the precipitation reference value is larger than the conventional FFMC,
How to provide a wildfire risk index. In paragraph 8,
Acquiring the drought index using a soil moisture index downscaled to a grid size of 1 km, a normalized differential water index (NDWI), and a temperature condition index (TCI);
A method for providing a forest fire risk index further comprising a. In paragraph 11,
Using data upscaled to a grid size of 25 km as training data, TRMM (Tropical Rainfall Measuring Mission) precipitation data, ASCAT (Advanced SCATterometer) soil moisture data, NDVI (Normalized Difference Vegetation Index), A soil moisture index downscaling model is created with Land Surface Temperature (LST) and digital Elevation Model (DEM) as input variables and Global Land Data Assimilation System (GLDAS) soil moisture data as output variables, and a grid size of 1 km acquiring the downscaled soil moisture index by inputting the input variable converted to ? into the soil moisture index downscaling model;
A method for providing a forest fire risk index further comprising a. A computer program stored in a computer-readable recording medium in order to execute the forest fire risk index providing method according to any one of claims 8 and 10 to 12 on a computer.

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