A method for measuring marine algal bloom outbreak areas
By constructing a comprehensive slope index model of marine environmental factors and algal bloom record data, the problem of difficulty in measuring the waters where marine algal blooms occur has been solved, accurate prediction and early prevention and control of waters where algal blooms occur have been achieved, and the ability to prevent and control marine disasters and ensure food safety has been improved.
Patent Information
- Application Number
- CN202310078112.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-01-30
- Publication Date
- 2025-09-16
- Estimated Expiration
- 2043-01-30
AI Technical Summary
Existing technologies make it difficult to accurately measure the areas where marine algal blooms occur, resulting in insufficient capabilities to prevent and control marine disasters and ensure food safety.
Using the distribution data of marine environmental factors and the record data of algal bloom occurrence, the comprehensive slope index of the target distribution area is calculated through the maximum entropy model, the water area and probability of algal bloom occurrence are predicted, the relative density model of algal biomass is constructed, the dominant factors of algal bloom occurrence are determined, and the water area and probability of algal bloom occurrence are judged.
It has achieved simple and effective calculation of water areas prone to algal blooms, improved the ability to respond to marine disasters and ensure food safety, provided a basis for decision-making on disaster reduction and prevention, and reduced economic losses.
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Figure CN116070755B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of comprehensive prevention and control of marine environmental ecological disasters, and in particular to a method for measuring marine algal bloom outbreak waters. Background Art
[0002] Studying the waters where harmful algal blooms occur and their distribution patterns can not only provide new theories, technologies and methods for the prevention and control of algal bloom disasters, but also provide scientific guidance for related industries such as marine fisheries and aquaculture, reducing the economic losses and social impacts caused by disasters.
[0003] For over 30 years, numerous researchers have used species distribution models (niche models) to analyze the relationship between species distribution data and environmental factors and conduct research on the biogeography of terrestrial habitats. A number of relatively mature species distribution area models with good performance have emerged, such as Biomod2, Maxent, openModeller, and ModEco. However, these models all use species distribution models to study species invasions, habitats, and their responses to climate change, and cannot clearly define the areas and probabilities of algal blooms. Although some studies have estimated algal biomass distribution using coupled hydrodynamic-ecological dynamics models, these models have numerous parameters and are difficult to verify using survey data.
[0004] Currently, there are no reports on a simple and effective method for accurately measuring marine algal bloom outbreak areas. The present method utilizes readily available offshore distance and water depth data to calculate a comprehensive slope index within the target distribution area, thereby estimating the area of algal bloom occurrence and its probability. This method facilitates the early and comprehensive prevention and control of algal blooms, helping to enhance the ability to respond to major marine disasters and ensure food safety. Summary of the Invention
[0005] The purpose of the present invention is to provide a method for measuring the waters prone to marine algal blooms. By using the distribution data of marine environmental factors and the record data of algal blooms, the relative density of algal biomass in the study area can be obtained through model calculation and statistical analysis techniques, and the comprehensive slope index of the sea area can be determined. The waters prone to algal blooms and the probability of algal blooms can be judged. This method provides a decision-making basis for fishery and food hygiene departments to monitor algal blooms in sea areas, initiate actions such as transferring marine aquaculture products, harvesting them in advance, preventing them from being put on the market, and take disaster reduction and prevention measures.
[0006] To achieve the above functions, the present invention designs a method for measuring marine algal bloom outbreak waters. For a target water area, the following steps S1 to S6 are performed to complete the prediction of algal bloom outbreak in the target water area:
[0007] Step S1: Gridding the target waters into distribution areas, collecting algae distribution information in each distribution area, calculating the probability density of algal blooms in each distribution area, and constructing an algae biomass relative density model for each distribution area based on the probability density of algal blooms in each distribution area;
[0008] Step S2: Calculate the average entropy of the environmental variables using the maximum entropy model based on the environmental variables in each distribution area, and construct a probability model for the relative density of algal biomass based on the probability density of algal blooms in each distribution area and the average entropy of the environmental variables;
[0009] Step S3: setting thresholds for the relative algae biomass density and the probability of occurrence of the relative algae biomass density in each distribution area, and taking the distribution area where the relative algae biomass density and the probability of occurrence of the relative algae biomass density are both greater than their respective corresponding thresholds as the target distribution area;
[0010] Step S4: For each target distribution area, based on each environmental variable, construct a cumulative environmental variable contribution model, calculate the cumulative environmental variable contribution of each environmental variable, sort the cumulative environmental variable contribution of each environmental variable in descending order from large to small, and take the top k environmental variables in the cumulative environmental variable contribution ranking as the dominant factors for algal bloom occurrence in the target distribution area;
[0011] Step S5: Based on the dominant factors of algal bloom occurrence in the target distribution area obtained in step S4, a comprehensive slope index calculation function is constructed to calculate the comprehensive slope index of each target distribution area;
[0012] Step S6: construct a series distribution based on the comprehensive slope index of each target distribution area, calculate the percentile of the confidence of the series distribution, and take each target distribution area in the series distribution with a comprehensive slope index less than the percentile as the water area where algal blooms may occur in the target water area, thereby completing the prediction of algal bloom outbreaks in the target water area.
[0013] As a preferred technical solution of the present invention: in step S1, algae distribution points in each distribution area are collected, a maximum entropy model is constructed, the probability density of algal bloom occurrence in each distribution area is calculated, and the algae biomass relative density model of each distribution area is constructed as follows:
[0014]
[0015] Where, DB i is the relative density of algal biomass in distribution area i, n is the total number of distribution areas, p i is the probability density of algal bloom occurrence in distribution area i.
[0016] As a preferred technical solution of the present invention: the probability model of the relative density of algae biomass constructed in step S2 is as follows:
[0017] P i =1-exp(-exp(H)·p i )
[0018] Where, P i is the probability of occurrence of relative density of algal biomass in distribution area i, H is the average entropy of environmental variables, p i is the probability density of algal bloom occurrence in distribution area i.
[0019] As a preferred technical solution of the present invention: the cumulative environmental variable contribution model constructed in step S4 is as follows:
[0020]
[0021] Where, EAC j is the cumulative environmental variable contribution of environmental variable j, m is the total number of environmental variables, G j is the increase in the regularization model gain of the environment variable j, Q j is the area under the receiver operating characteristic curve after rearrangement of environmental variable j, SG j is the single factor regularization model gain of environmental variable j, LG j is the factor-less regularization model gain of environmental variable j, and R0 is the regularization model gain of all environmental variables.
[0022] As a preferred technical solution of the present invention: the comprehensive slope index calculation function constructed in step S5 is as follows:
[0023]
[0024] Where S i is the comprehensive slope index of distribution area i, V ik is the dominant factor for the occurrence of the kth algal bloom in distribution area i.
[0025] Beneficial effects: Compared with the prior art, the advantages of the present invention include:
[0026] The present invention designs a method for measuring marine algal bloom outbreak waters. Based on the marine environmental factor data layer and the algal bloom occurrence record data layer, the comprehensive slope index of the target distribution area is calculated to determine the water area and probability of algal bloom occurrence. The comprehensive slope index of China's coastal waters tends to be close to the offshore distance, which is easy to promote and use. It breaks through the technical bottleneck of simply measuring algal bloom-occurring waters and solves the problem of difficult estimation of the probability of algal bloom occurrence in marine areas. It provides a decision-making basis for aquaculture and environmental protection departments to prevent toxic red tides and carry out disaster reduction and prevention actions, thereby enhancing the disaster prevention and mitigation capabilities of relevant departments. BRIEF DESCRIPTION OF THE DRAWINGS
[0027] Figure 1This is a flow chart of a method for measuring marine algal bloom outbreak waters provided in an embodiment of the present invention;
[0028] Figure 2 is a relative density map of Gymnodinium catenatum biomass in the target sea area provided by an embodiment of the present invention;
[0029] Figure 3 It is a target distribution area for monitoring algal blooms of Gymnodinium catenatum in a target sea area provided by an embodiment of the present invention;
[0030] Figure 4 3. A comparison diagram of the cumulative environmental variable contributions calculated based on the maximum entropy model of Gymnodinium catenatum provided in an embodiment of the present invention;
[0031] Figure 5 is a comprehensive slope index map of the target distribution area of Gymnodinium catenatum in China Seas according to an embodiment of the present invention;
[0032] Figure 6 This is a map of waters where Gymnodinium catenellae blooms occur, with a confidence level of 95%, provided according to an embodiment of the present invention. DETAILED DESCRIPTION
[0033] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.
[0034] Reference Figure 1 The present invention provides a method for predicting marine algal bloom outbreak areas. For a target water area, the following steps S1 to S6 are performed to complete the prediction of algal bloom outbreaks in the target water area:
[0035] Step S1: Grid the target water area and divide it into distribution areas. Collect algae distribution information in each distribution area, calculate the probability density of algal blooms in each distribution area, and construct an algae biomass relative density model for each distribution area based on the probability density of algal blooms in each distribution area.
[0036] In step S1, global marine algae distribution information is collected, an algae distribution point database is established, the global ocean is gridded, an algae distribution area (sea area) database is established, and a data layer of environmental variables such as seawater depth and offshore distance is produced. Combined with the data of the marine ecological simulation data layer, a maximum entropy model (Maxent model) is constructed to calculate the probability density of algal blooms in each distribution area. Through the normalization method, a relative density model of algae biomass in each distribution area is constructed as follows:
[0037]
[0038] Where, DB iis the relative density of algal biomass in distribution area i, n is the total number of distribution areas, p i is the probability density of algal bloom occurrence in distribution area i.
[0039] Step S2: According to the environmental variables in each distribution area, the average entropy of the environmental variables is calculated through the maximum entropy model (Maxent model), and based on the probability density of algal blooms in each distribution area and the average entropy of environmental variables, a probability model for the relative density of algal biomass is constructed.
[0040] The probability model of the relative density of algae biomass constructed in step S2 is as follows:
[0041] P i =1-exp(-exp(H)·p i )
[0042] Where, P i is the probability of occurrence of relative density of algal biomass in distribution area i, H is the average entropy of environmental variables, p i is the probability density of algal bloom occurrence in distribution area i.
[0043] Step S3: setting thresholds for the relative density of algae biomass and the probability of occurrence of relative algae biomass density in each distribution area, and taking the distribution area where the relative density of algae biomass and the probability of occurrence of relative algae biomass density are greater than their respective corresponding thresholds as the target distribution area.
[0044] The probability P of the relative density of algal biomass being greater than DBm and the relative density of algal biomass occurring is i The distribution area larger than Pm is used as the target distribution area for algal bloom monitoring.
[0045] Step S4: For each target distribution area, based on each environmental variable, construct a cumulative environmental variable contribution model, and calculate the cumulative environmental variable contribution of each environmental variable. Arrange the cumulative environmental variable contribution of each environmental variable in descending order from large to small, and take the top k environmental variables in the cumulative environmental variable contribution ranking as the dominant factors for the occurrence of algal blooms in the target distribution area.
[0046] Step S4 calculates the increase G of the regularization model gain of the environmental variable j based on the maximum entropy model (Maxent model) j , the area under the receiver operating characteristic curve after rearrangement of environmental variable j is reduced by Q j , single factor regularization model gain SG of environmental variable j j , the missing factor regularization model gain LG of the environmental variable j j , the constructed cumulative environmental variable contribution model is as follows:
[0047]
[0048] Where, EAC j is the cumulative environmental variable contribution of environmental variable j, m is the total number of environmental variables, and R0 is the regularized model gain of all environmental variables.
[0049] In the cumulative environmental variable contribution model, the first item on the right side of the equal sign is the relative contribution of the environmental variable to the model's predictive ability, the second item on the right side of the equal sign is the ranking importance, the third item on the right side of the equal sign is the gain percentage of the single-factor model, and the fourth item on the right side of the equal sign is the gain loss percentage of the missing factor model.
[0050] Step S5: Based on the dominant factors of algal bloom occurrence in the target distribution area obtained in step S4, a comprehensive slope index calculation function is constructed to calculate the comprehensive slope index of each target distribution area.
[0051] In step S5, a data layer of dominant factors of the target distribution area is established. Using the data layer of dominant factors, a comprehensive slope index calculation function is constructed to calculate the comprehensive slope index of each target distribution area in the study sea area. The constructed comprehensive slope index calculation function is as follows:
[0052]
[0053] Where S i is the comprehensive slope index of distribution area i, V ik is the dominant factor for the occurrence of the kth algal bloom in distribution area i.
[0054] Step S6: construct a series distribution based on the comprehensive slope index of each target distribution area, calculate the percentile of the confidence of the series distribution, and take each target distribution area in the series distribution with a comprehensive slope index less than the percentile as the water area where algal blooms may occur in the target water area, thereby completing the prediction of algal bloom outbreaks in the target water area.
[0055] The following is an example of the present invention. Based on a marine environmental factor data layer and algal bloom records, a maximum entropy model is constructed using the maximum entropy principle. This model calculates the relative density of algal biomass and its probability of occurrence within a distribution area, identifying target distribution areas for algal bloom monitoring. By constructing cumulative environmental variable contributions, the dominant factors for algal bloom occurrence in the marine area are determined. This dominant factor is then used to calculate the comprehensive slope index for the target distribution area. The distribution of the comprehensive slope index for the target distribution area is then calculated, and the percentiles of the distribution are calculated to determine the area of algal bloom occurrence and its probability. The scientific validity of this method can be assessed by comparing the calculated results with actual bloom records.
[0056] (1) Calculation of relative density of algae biomass
[0057] We collected information on the distribution of Gymnodinium catenellae by searching the Ocean Biogeographic Information System (OBIS) database, consulting literature databases such as Elsevier, Springer-Verlag, China National Journal Database, and the (VIP) Chinese Science and Technology Journal Database, and established a global database of Gymnodinium catenellae distribution points in the ocean. We gridded the global ocean, (in principle) using 0.5 degrees of longitude and latitude as one block, with the latitude ranging from -75 to 100 degrees. ° S to 85 ° N is divided into 348 grids, and the longitude is from the center point 0 ° to 360 ° It is divided into 720 grids, from -7.5 ° Gradually transition to 7.5 at 0.4, 0.3, 0.25, 0.25, 0.3, 0.4 latitudes ° Excluding land, the global ocean is divided into 176,340 distribution blocks. The number of distribution areas of chain-shaped dinoflagellates in the global ocean is 111, and the number of distribution areas in Chinese seas is 17.
[0058] Download the Marine Data Layers forecological Modeling data from the Bio-ORACLE website, using a uniform spatial resolution of 5 arcmin. Just as land elevation is an important environmental variable influencing species distribution, environmental variables such as seawater depth and distance from shore are dominant environmental variables affecting the distribution of harmful dinoflagellates. Create data layers for these environmental variables, saving them in a format consistent with Bio-ORACLE. Bio-ORACLE was used to collect 48 environmental variable data layers of 8 environmental factors, including seawater temperature, salinity, current rate, sea ice thickness, dissolved oxygen, nitrate concentration, phosphate concentration, and primary productivity, plus 2 environmental variable data layers of 2 environmental factors, including seawater depth and offshore distance, for a total of 50 environmental variable data layers. The maximum entropy principle was used to construct a maximum entropy model for the distribution of Gymnodinium catenatum. The probability density of Gymnodinium catenatum blooms in various distribution areas of the global ocean was calculated. The probability density of Gymnodinium catenatum blooms in the distribution area was converted into the relative biomass density of Gymnodinium catenatum through normalization. The relative biomass density map of Gymnodinium catenatum in the target sea area was used for reference. Figure 2 .
[0059] (2) Probability distribution of relative density of algal biomass
[0060] The average entropy of environmental variables calculated by the maximum entropy model of Gymnodinium catenatum distribution is 8.19, and the function for calculating the probability of occurrence of relative density of algal biomass is constructed as follows:
[0061] P i =1-exp(-3605p i )
[0062] P i is the occurrence probability of the relative biomass density of Gymnodinium catenatum in distribution area i, p i is the probability density of algal bloom occurrence in distribution area i.
[0063] The relative biomass density and occurrence probability of Gymnodinium catenatum in the target sea area are used as the i The distribution area with a value greater than 0.66 is taken as the target distribution area for monitoring the bloom of Gymnodinium catenatum. The target distribution area for monitoring the bloom of Gymnodinium catenatum in the target sea area is referred to as Figure 3 The white part in the middle sea area;
[0064] (3) Determination of the dominant factors for algal blooms in China's waters
[0065] The increase in the gain of the regularized model of each environmental variable (G j ), the area under the receiver operating characteristic curve (AUC) reduction value (Q j ), single factor regularization model gain (SG j ), missing factor regularization model gain (LG j ), and then calculate the cumulative environmental variable contribution (EAC) of each environmental variable j ), the result is as follows Figure 4 shown.
[0066] Figure 4The horizontal axis represents the accumulated variable contributions, and the vertical axis represents the various environmental variables, namely: Distance.Mean: average distance from the shore; Depth.Mean: average water depth; Temperature.Lt.min: multi-year average minimum temperature; Current.Velocity.Lt.max: multi-year average maximum velocity; Temperature.Range: temperature variation range; Ice.thickness.Lt.max: multi-year average maximum sea ice thickness; Salinity.Range: salinity range; Primary.productivity.Min: minimum primary productivity; Dissolved.oxygen.Range: dissolved oxygen range; Salinity.Min: minimum salinity; Nitrate.Mean: average nitrate concentration; Primary.productivity.Range: primary productivity variation range; Current.Velocity.Min: minimum velocity; Nitrate.Range: nitrate variation range; Ice.thickness.Min: minimum sea ice thickness;
[0067] Figure 4 The shades of color in the middle bar graph represent: Percent contribution: the relative contribution of environmental variables to the model's predictive ability; Permutation importance: ranking importance; Percent gain loss without variable: the percentage of gain loss of the missing factor model; Percent gain with only variable: the percentage of gain of the single factor model.
[0068] The cumulative contributions of environmental variables are arranged in descending order. Since the cumulative contributions of the top two environmental variables are much greater than the sum of the cumulative contributions of other environmental variables, the top two environmental variables in terms of cumulative contribution values - offshore distance and water depth - are taken as the dominant factors affecting the occurrence of Gymnodinium catenatum blooms in Chinese waters.
[0069] (4) Comprehensive slope index construction
[0070] Extract the target distribution area dominant factor data layer from the above offshore distance and seawater depth data layer (environmental variable data layer), and use the target distribution area dominant factor data layer to construct the target distribution area comprehensive slope index:
[0071]
[0072] Si is the comprehensive slope index of distribution area i, V i1 V is the first dominant factor in calculating the comprehensive slope index of distribution area i—the distance from the shore. i2 It is the second dominant factor of the comprehensive slope index of distribution area i - sea water depth.
[0073] Statistical analysis shows that the seawater depth in the target distribution area is less than 100 meters, and the square of the offshore distance is much greater than the square of the seawater depth. That is S i ≈V i1 Therefore, the comprehensive slope index of the continental shelf area is approximately equal to the offshore distance.
[0074] Calculate the comprehensive slope index of each target distribution area in the target sea area, and the results are as follows Figure 5 shown.
[0075] The cumulative contributions of environmental variables are arranged in descending order. Since the cumulative contributions of the top two environmental variables are much greater than the sum of the cumulative contributions of other environmental variables, the top two environmental variables in terms of cumulative contribution values - offshore distance and water depth - are taken as the dominant factors affecting the occurrence of Gymnodinium catenatum blooms in Chinese waters.
[0076] (5) Algal bloom occurrence waters and probability assessment
[0077] The comprehensive slope index of each target distribution area is used to construct a series distribution. The 50% quantile of the series distribution is calculated to be 6.3 km. The comprehensive slope index S i The target distribution area less than 6.3 km is the water area where the algal bloom of Gymnodinium catenatum occurs, and the probability (confidence) of occurrence is 0.5. The 95% quantile of the calculated series distribution is 63 km, and the comprehensive slope index S i The target distribution area less than 63 km is the water area where the algal bloom of Gymnodinium catenatum occurs. Figure 6 The black part in the target sea area has an occurrence probability (confidence level) of 0.95.
[0078] (6) Calculation and verification of waters where Gymnodinium catenella blooms occur:
[0079] Based on the Ocean Biogeographic Information System (OBIS) database and literature databases such as Elsevier, Springer-Verlag, China National Journal Full-text Database, and (VIP) Chinese Science and Technology Journal Database, a global marine chain-shaped dinoflagellate distribution point database was established, and then the waters where chain-shaped dinoflagellate blooms occurred in the target sea area were obtained through model calculation and comprehensive slope index calculation.
[0080] By applying the method of the present invention, based on the marine environmental factor data layer and algal bloom occurrence record data, and by calculating the comprehensive slope index of the target distribution area, it is possible to determine the water area and probability of algal bloom occurrence. A comparative example found that the water area where Gymnodinium catenellae occurs is consistent with the water area measured at the mesoscopic level in the actual sea area. This result further verifies the reliability of the method of the present invention. The method of the present invention can be used to demarcate key sea areas for routine inspections of aquaculture enterprises, reducing manpower and vessel costs, and can play an important role in the reduction and prevention of harmful algal blooms by fishery and environmental protection departments, which also shows that the method of the present invention has high practical value.
[0081] The embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by ordinary technicians in this field without departing from the spirit of the present invention.
Claims
1. A method for measuring marine algal bloom outbreak waters, characterized in that: For the target water area, perform the following steps S1 to S6 to complete the prediction of algal bloom in the target water area: Step S1: Gridding the target waters into distribution areas, collecting algae distribution information in each distribution area, calculating the probability density of algal blooms in each distribution area, and constructing an algae biomass relative density model for each distribution area based on the probability density of algal blooms in each distribution area; Step S2: Calculate the average entropy of the environmental variables using the maximum entropy model based on the environmental variables in each distribution area, and construct a probability model for the relative density of algal biomass based on the probability density of algal blooms in each distribution area and the average entropy of the environmental variables; Step S3: setting thresholds for the relative algae biomass density and the probability of occurrence of the relative algae biomass density in each distribution area, and taking the distribution area where the relative algae biomass density and the probability of occurrence of the relative algae biomass density are both greater than their respective corresponding thresholds as the target distribution area; Step S4: For each target distribution area, based on each environmental variable, construct a cumulative environmental variable contribution model, calculate the cumulative environmental variable contribution of each environmental variable, sort the cumulative environmental variable contribution of each environmental variable in descending order from large to small, and take the top k environmental variables in the cumulative environmental variable contribution ranking as the dominant factors for algal bloom occurrence in the target distribution area; The cumulative environmental variable contribution model is as follows: Where, EAC j is the cumulative environmental variable contribution of environmental variable j, m is the total number of environmental variables, G j is the increase in the regularization model gain of the environment variable j, Q j is the area under the receiver operating characteristic curve after rearrangement of environmental variable j, SG j is the single factor regularization model gain of environmental variable j, LG j is the factor-less regularization model gain of environmental variable j, and R0 is the regularization model gain of all environmental variables; Step S5: Based on the dominant factors of algal bloom occurrence in the target distribution area obtained in step S4, a comprehensive slope index calculation function is constructed to calculate the comprehensive slope index of each target distribution area; Step S6: construct a series distribution based on the comprehensive slope index of each target distribution area, calculate the percentile of the confidence of the series distribution, and take each target distribution area in the series distribution with a comprehensive slope index less than the percentile as the water area where algal blooms may occur in the target water area, thereby completing the prediction of algal bloom outbreaks in the target water area.
2. The method for measuring marine algal bloom outbreak areas according to claim 1, characterized in that: In step S1, algae distribution points in each distribution area are collected, a maximum entropy model is constructed, the probability density of algal blooms in each distribution area is calculated, and the relative density model of algae biomass in each distribution area is constructed as follows: Where, DB i is the relative density of algal biomass in distribution area i, n is the total number of distribution areas, p i is the probability density of algal bloom occurrence in distribution area i.
3. The method for measuring marine algal bloom outbreak areas according to claim 1, characterized in that: The probability model of the relative density of algae biomass constructed in step S2 is as follows: P i =1-exp(-exp(H)·p i ) Where, P i is the probability of occurrence of relative density of algal biomass in distribution area i, H is the average entropy of environmental variables, p i is the probability density of algal bloom occurrence in distribution area i.
4. The method for measuring marine algal bloom outbreak areas according to claim 1, characterized in that: The comprehensive slope index calculation function constructed in step S5 is as follows: Where S i is the comprehensive slope index of distribution area i, V ik is the dominant factor for the occurrence of the kth algal bloom in distribution area i.
Citation Information
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