A Time Series Model-Based Method for Predicting the Abundance of Squid Resources in the Northwest Pacific

Abstract

This invention relates to a method for predicting the abundance of squid resources in the Northwest Pacific based on a time series model, belonging to the field of marine fisheries analysis and processing technology. The method includes the following steps: dividing historical catch data of Northwest Pacific squid into training and test sets; using catch per unit catch effort to characterize resource abundance; calculating the average catch per unit catch effort for each fishing location and the monthly average catch per unit catch effort; performing a unit root test on the training set data to meet stationarity requirements; establishing a seasonal single autoregressive moving average model using the training set data; establishing a seasonal multivariate autoregressive moving average model by combining data from squid spawning grounds and feeding grounds; using the test set to perform white noise testing on the residuals, goodness of fit, and prediction accuracy evaluation to obtain the optimal model; and using the optimal model to predict the abundance of Northwest Pacific squid resources. This invention establishes a more accurate resource abundance prediction model, enabling more precise prediction of Northwest Pacific squid resource abundance.

Description

Technical Field

[0001] This invention belongs to the field of marine fisheries analysis and processing technology, specifically relating to a method for predicting the abundance of squid resources in the Northwest Pacific based on a time series model. Background Technology

[0002] Squid (Ommastrephes bartramii) is an important economically important cephalopod, widely distributed in the North Pacific Ocean. The convergence of the Kuroshio Current and the Oyashio Current in the Northwest Pacific creates a complex marine environment. Driven by factors such as temperature and nutrients, squid migrate between spawning grounds in subtropical waters and feeding grounds in subarctic waters. my country began commercial squid fishing in the Northwest Pacific in 1994. Based on their distribution areas and peak spawning season, the area east of 170°E is designated as the winter-spring spawning population, while the area west is designated as the autumn spawning population. Currently, the winter-spring spawning population is the primary target. Due to the short fishing season, there is a high demand for predicting the abundance of squid resources in the Northwest Pacific.

[0003] Currently, scholars both domestically and internationally have explored the impact of marine environmental factors such as sea surface temperature (SST) and seawater chlorophyll concentration (Chl_a) on squid resource abundance. The results reflect, to some extent, the mechanisms underlying squid resource fluctuations. However, the selection of these environmental factors is mostly based on the spatiotemporal distribution of fishing locations, i.e., feeding grounds, without considering the marine environment of the spawning grounds during the early life cycle stages of squid (e.g., spawning stages) or the lagged response of squid resource abundance to marine environmental factors. As a short-life-cycle species, squid is highly sensitive to environmental changes. The marine environment of its spawning grounds during its early life cycle is a key factor determining the amount of squid replenishment. Current prediction methods do not consider relevant covariates of biological characteristics, resulting in short effective prediction times, large confidence intervals, and limited guidance for actual squid fisheries production. Therefore, when predicting squid resource abundance in the Northwest Pacific, it is necessary to simultaneously consider the mechanisms by which marine environmental factors of both feeding and spawning grounds affect resource abundance. Summary of the Invention

[0004] The purpose of this invention is to address the problems existing in the prior art by providing a time series model-based method for predicting the abundance of squid resources in the Northwest Pacific. This method combines the existing single time series model with a multi-covariate time series model based on squid habitat and climate, taking into account the marine environmental factors experienced by squid during their life history. The method uses catch per unit effort (CPUE), which reflects the fishing situation, as a benchmark indicator to increase the effective prediction time of squid resource abundance and reduce the range of uncertainty.

[0005] The technical solution is as follows:

[0006] A method for predicting the abundance of squid resources in the Northwest Pacific based on time series models includes the following steps:

[0007] Step 1: Divide the historical catch data of squid in the Northwest Pacific into training set and test set, use catch per unit catch effort (CPUE) to characterize the abundance of squid resources in the Northwest Pacific, and calculate the catch per unit catch effort and the monthly average catch per unit catch effort for each fishing point.

[0008] Step 2: Perform a unit root test on the training set data to meet the stationarity requirement;

[0009] Step 3: Build a seasonal single autoregressive moving average model (SARIMA) using the training set data;

[0010] Step 4: Based on a seasonal single autoregressive moving average model, combined with the sea surface temperature (SST) of the squid spawning grounds (S), S Sea surface salinity SSS S Chlorophyll concentration at sea surface (Chl_a) S Sea surface height (SSH) S Mixed layer depth MLD S Oxygen content (O2) at sea surface S and the SST of the baiting area (F) F SSS F Chl_a F SSH F MLD F O2 F Values ​​were used to establish a seasonal multivariate autoregressive moving average model (SARIMAX);

[0011] Step 5: Use the test set to perform white noise test on the residuals, and screen and evaluate the goodness of fit and prediction accuracy of the seasonal multivariate autoregressive moving average model to obtain the optimal model.

[0012] Step 6: Use the optimal model to predict the abundance of squid resources in the Northwest Pacific.

[0013] Furthermore, in step 1, the test set consists of the catch and number of fishing vessels in the area between 144.5°E and 170°E, and between 35°N and 49.5°N, from June to November within two years of the time when the method was used; the training set consists of the catch and number of fishing vessels in the area between 144.5°E and 170°E, and between 35°N and 49.5°N, from June to November two years before the time when the method was used.

[0014] Furthermore, the method for calculating the catch per unit fishing effort in step 1 is as follows: first, calculate the CPUE for each fishing point using the following formula.ymij value: CPUE ymij C ymij E ymij Let y be the year, m be the month, i be the longitude, and j be the unit fishing effort (tons / vessel, t / v), the catch, and the number of fishing vessels in operation; then calculate the monthly average catch per unit fishing effort using the following formula: CPUE ym CPUE represents the average monthly catch per unit of fishing effort for year y and month m. k(ymij) For CPUE ymij The formula calculates the average catch per unit fishing effort at the k-th fishing location, where M is the total data volume within m months.

[0015] Furthermore, in step 2, the unit root test is based on the relationship between stationary sequences and unit roots to construct the unit root for testing time series data. If all the characteristic roots of the sequence are inside the unit circle, the sequence is a stationary sequence. If the sequence has characteristic roots on or outside the unit circle, then the sequence is a non-stationary sequence.

[0016] Furthermore, the unit root test is performed using the `adf.test` function in the `tseries` package of R language for time series analysis. If the p-value is less than 0.05, the series is stationary; if the p-value is greater than 0.05, the series is non-stationary. In this case, d-th order differencing and D-th order seasonal differencing are performed sequentially to stabilize the series, where d / D ≤ 2. The order of d-th order differencing and D-th order seasonal differencing does not affect the results. When the series has strong seasonality, seasonal differencing is preferred.

[0017] Furthermore, in step 3, the seasonal single autoregressive moving average model

[0018] The expression for SARIMA(p, d, q)(P, D, Q)[S] is:

[0019] Where p, d, and q correspond to the three processes of autoregression, differencing, and moving average, respectively; P, D, Q, and S represent the seasonal autoregressive term, differencing term, moving average term, and frequency; and Y represents the frequency. t Let δ be the observation value of the time series at time t, where δ is a constant term and B is the delay operator; (1-B) d This indicates performing a d-th order difference; (1-B s ) D This represents performing a seasonal difference of D times with a seasonal cycle of S; polynomial Φ (P) (B s )=1-Φ1B s -…-Φ p B sPolynomial action on Y t The left side of the equation is... The AR(p / P) component of the model is represented by the equation on the right side. This represents the MA(q / Q) component of the model.

[0020] Furthermore, the expression for the seasonal multi-covariate autoregressive moving average model SARIMAX in step 4 is: Y t ′=Y t +βX i , where Y t Y' represents the fitted value of the seasonal multivariate autoregressive moving average model at time t; t X represents the fitted value of the seasonal single autoregressive moving average model at time t; i β represents the environmental covariates of the spawning grounds or feeding grounds; β is the coefficient vector of the covariates, describing the degree of influence of the covariates on the dependent variable.

[0021] Furthermore, in step 5, the checkresiduals function from the Forecast package in R, a toolkit for time series forecasting, is used to perform a white noise test on the residuals of the seasonal multivariate autoregressive moving average model. If the p-value is greater than 0.05, the model passes the white noise test; if the p-value is less than 0.05, the model fails the test and needs to be remodeled.

[0022] Furthermore, in step 5, the Akaike Information Content Criterion (AICc) is used to evaluate the goodness of fit of the seasonal multivariate autoregressive moving average model. The calculation formula is as follows: Where L represents the likelihood function value of the model, indicating the goodness of fit of the model; k is the number of parameters in the model, and n is the number of samples. The smaller the AICc value, the better the model fit. The root mean square error (RMSE) index is used for prediction accuracy screening and evaluation, and its calculation formula is: Where Y i Indicates the actual value. denoted by , n represents the number of test set samples, and RMSE measures the average error between the model's predicted value and the true value. The smaller the value, the better the model's predictive performance.

[0023] Beneficial effects:

[0024] 1) This invention constructs a time series model based on multiple covariates of squid habitat and climate by combining marine environmental covariates with the original single time series model. This model can effectively capture changes in squid resources and establish a more accurate resource abundance prediction model, enabling more accurate prediction of squid resource abundance in the Northwest Pacific. Attached Figure Description

[0025] Figure 1 This is a flowchart illustrating the method of the present invention.

[0026] Figure 2 Table 1 shows the optimal SARIMA models for different difference types.

[0027] Figure 3 Table 2: SARIMAX model constructed based on the basic model and traversing marine environmental factors.

[0028] Figure 4 Table 3: Squid CPUE prediction from June to November 2021 based on the selected optimal SARIMAX model.

[0029] Figure 5 This is a line graph showing the abundance prediction of Northwest Pacific squid resources using the optimal model in the example. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. Terms such as "upper," "lower," "front," "rear," "left," "right," "bottom," "inner," and "outer" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention.

[0031] like Figure 1 The method for predicting the abundance of squid resources in the Northwest Pacific based on a time series model, as shown, includes the following steps:

[0032] Step 1: Divide the historical catch data of Northwest Pacific squid into training and test sets. Use catch per unit effort (CPUE) to characterize the abundance of Northwest Pacific squid resources. Calculate the catch per CPUE and the monthly average catch per CPUE for each fishing location. The test set includes catches and fishing vessel numbers from June to November within two years of the method's application, at locations of 144.5°E-170°E and 35°N-49.5°N. The training set includes catches and fishing vessel numbers from June to November within the same location (144.5°E-170°E and 35°N-49.5°N) from the beginning of records to two years prior to the application of the method. The catch per CPUE is calculated using the following formula: First, calculate the CPUE for each fishing location. ymij value: CPUE ymij C ymij E ymijLet y be the year, m be the month, i be the longitude, and j be the unit fishing effort, the catch, and the number of fishing vessels in operation; then calculate the monthly average catch per unit fishing effort using the following formula: CPUE ym CPUE represents the average monthly catch per unit of fishing effort for year y and month m. k(ymij) (for CPUE) ymij The formula calculates the average catch per unit fishing effort at the kth fishing location, where M is the total data volume within m months.

[0033] Step 2: Perform a unit root test on the training set data. The unit root test is based on the relationship between stationary sequences and unit roots to construct a unit root for testing time series data. If all the eigenvalues ​​of the sequence are inside the unit circle, the sequence is stationary. If any eigenvalues ​​of the sequence are on or outside the unit circle, the sequence is non-stationary. The unit root test is performed using the `adf.test` function in the `tseries` package of R language for time series analysis. If the p-value is less than 0.05, the sequence is stationary. If the p-value is greater than 0.05, the sequence is non-stationary. To stabilize the sequence, d-order differencing and D-order seasonal differencing are performed sequentially, where d / D≤2. The order of d-order differencing and D-order seasonal differencing does not affect the result. When the sequence has strong seasonality, seasonal differencing is preferred.

[0034] Step 3: Use the training set to build a seasonal single autoregressive moving average model

[0035] The expression for SARIMA(p, d, q)(P, D, Q)[S] is:

[0036] Where p, d, and q correspond to the three processes of autoregression, differencing, and moving average, respectively; P, D, Q, and S represent the seasonal autoregressive term, differencing term, moving average term, and frequency; and Y represents the frequency. t Let δ be the observation value of the time series at time t, where δ is a constant term and B is the delay operator; (1-B) d This indicates performing a d-th order difference; (1-B s ) D This represents performing a seasonal difference of D times with a seasonal cycle of S; polynomial Φ (P) (B s )=1-Φ1B s -…-Φ p B s Polynomial action on Y t The left side of the equation is... The AR(p / P) component of the model is represented by the equation on the right side. This represents the MA(q / Q) component of the model;

[0037] Step 4: Based on a seasonal single autoregressive moving average model, combined with the sea surface temperature (SST) of the squid spawning grounds. S Sea surface salinity SSS S Chlorophyll concentration at sea surface (Chl_a) S Sea surface height (SSH) S Mixed layer depth MLD S Oxygen content (O2) at sea surface S And the SST of the baiting area F SSS F Chl_a F SSH F MLD F O2 F The expression for establishing a seasonal multivariate autoregressive moving average model SARIMAX is: Y t ′=Y t +βX i , where Y t ′ represents the fitted value of the seasonal multivariate autoregressive moving average model at time t; Yt is the fitted value of the seasonal single autoregressive moving average model at time t; X i β represents the environmental covariates of the spawning grounds or feeding grounds; β is the coefficient vector of the covariates, describing the degree of influence of the covariates on the dependent variable.

[0038] Step 5: Use the test set to perform white noise testing on the residuals of the seasonal multivariate autoregressive moving average model, and evaluate its goodness of fit and prediction accuracy to obtain the optimal model; use the `checkresiduals` function from the `Forecast` package in R (a toolkit for time series forecasting) to perform white noise testing on the residuals of the seasonal multivariate autoregressive moving average model. If the p-value is greater than 0.05, the model passes the white noise test; if the p-value is less than 0.05, the model fails the test and needs to be rebuilt; the goodness of fit is evaluated using the Akaike information content criterion, calculated as follows: Where L represents the likelihood function value of the model, indicating the goodness of fit of the model; k is the number of parameters in the model, and n is the number of samples. The smaller the AICc value, the better the model fit. The root mean square error (RMSE) index is used for prediction accuracy screening and evaluation, and its calculation formula is: Where Y i Indicates the actual value. denoted as the predicted value, n represents the number of samples in the test set, and RMSE measures the average error between the model's predicted value and the true value. The smaller the value, the better the model's prediction performance.

[0039] Step 6: Use the optimal model to predict the abundance of squid resources in the Northwest Pacific.

[0040] Example 1: When predicting the abundance of squid resources in the Northwest Pacific in 2021, the original dataset from June to November 1995-2020 was first divided into a training set from 1995-2018 and a test set from 2019-2020. The abundance of squid resources was represented by CPUE (tons / vessel), and the abundance was calculated for each fishing location. Then calculate the monthly average within its fishing area.

[0041] Fisheries data for fishing locations with a spatial resolution of 0.5°×0.5° were matched with corresponding environmental data. Simultaneously, marine environmental factors for the spawning grounds (130°–170°E, 20°–33°N) from December y-1 to January–May y were extracted at a resolution of 0.5°×0.5°. The `adf.test` function from the `forecast` package in R was used to perform a unit root test on the training set. The result showed a p-value of 0.299, indicating that the CPUE sequence accepts the null hypothesis and is non-stationary. Three differencing operations were attempted: d=1, D=0; d=0, D=1; and d=1, D=1, resulting in three types of differencing models. The optimal model, based on the minimum AICc fit on the training set and the minimum RMSE predicted on the test set, is as follows: Figure 2 Table 1: The optimal SARIMA model under different difference types is shown: The minimum RMSE model failed the residual white noise test, indicating that the model failed to extract all the effective information in the sequence. Therefore, this model was excluded, and SARIMA(0,1,2)(0,0,2)[6] was selected as the basic model. Substituting into the formula Get Y t =-0.548∈ t-1 -0.405∈ t-2 +0.254∈ t-6 +0.179∈ t-1 2+ε t , ε t ~N(0, 0.819).

[0042] Combined with the sea surface temperature (SST) of the squid spawning grounds (S) S Sea surface salinity SSS S Chlorophyll concentration at sea surface (Chl_a) S Sea surface height (SSH) S Mixed layer depth MLD S Oxygen content (O2) at sea surface S and the SST of the baiting area (F) F SSS F Chl_a F SSH F MLD F O2 FThe values, with all covariate data lengths consistent with the original CPUE data length, were used to construct multivariate SARIMAX models. By traversing marine environmental variables, the model's predictive performance on the test set was compared. The results are as follows: Figure 3 Table 2: SARIMAX model constructed based on the basic model and traversing marine environmental factors. Considering the model's fitting and prediction performance, the optimal model selected is the SARIMAX model incorporating two covariates: spawning ground sea surface salinity and spawning ground sea surface temperature. Its expression is:

[0043] Y t =-0.528∈ t-1 -0.325∈ t-2 +0.139∈ t-6 +0.175∈ t-12 +7.006SSS S -0.031SST S +ε t , ε t ~N(0, 0.746).

[0044] Based on the optimal model, the monthly average values ​​of sea surface salinity and temperature in the spawning grounds from 1995 to 2020 were used as the monthly average values ​​of environmental covariates for 2021. Based on these average values, the abundance of squid resources in 2021 was predicted. The specific CPUE data and their confidence intervals for June to November 2021 are as follows: Figure 4 Table 3 shows the predicted CPUE and confidence intervals for squid from June to November 2021 based on the selected optimal SARIMAX model. The prediction results are as follows: Figure 5 As shown in Table 2, the predicted abundance of squid resources in the Northwest Pacific is based on the optimal model. Table 2 shows that compared to the basic model, most SARIMAX models incorporating covariates show reduced AICc and RMSE values, indicating improved fitting and prediction performance. However, the addition of marine environmental factor covariates from feeding grounds only improves model fitting, while decreasing prediction accuracy on the test set. The addition of marine environmental factors from spawning grounds, especially sea surface salinity, effectively improves model fitting and prediction accuracy. Overall, the addition of spawning ground environmental covariates improves prediction performance more than that from feeding grounds. The optimal model selected after considering all marine environmental factors is the combination of sea surface salinity and sea surface temperature covariates from spawning grounds, indicating that spawning ground environmental factors better reflect squid resource fluctuations. This also confirms that environmental factors in the early life history of squid are key factors determining their resource abundance. Accurately identifying these marine environmental factors can effectively improve the prediction of squid resource abundance and better serve fisheries forecasting.

[0045] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the principles and spirit of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the abundance of squid resources in the Northwest Pacific based on time series models, characterized by: Includes the following steps: Step 1: Divide the historical catch data of Northwest Pacific squid into training and testing sets. Use catch per unit catch effort to characterize the abundance of Northwest Pacific squid resources. Calculate the catch per catch effort and the monthly average catch per unit catch effort for each fishing location. The catch per unit catch effort is calculated as follows: First, calculate the catch per unit catch effort for each fishing location using the following formula. value: ,in , , Let y be the year, m be the month, i be the longitude, and j be the unit fishing effort, the catch, and the number of fishing vessels in operation; then calculate the monthly average catch per unit fishing effort using the following formula: ,in The average monthly catch per unit of fishing effort for year y and month m. for The formula calculates the average catch per unit fishing effort at the kth fishing location, where M is the total data volume within m months. Step 2: Perform a unit root test on the training set data to meet the stationarity requirement; Step 3: Build a seasonal single autoregressive moving average model using the training set data. The expression for the seasonal single autoregressive moving average model SARIMA(p,d,q)(P,D,Q)[S] is: Where p, d, and q correspond to the three processes of autoregression, differencing, and moving average, respectively, and P, D, Q, and S represent the seasonal autoregressive term, differencing term, moving average term, and frequency. These are the observations of a time series at time t. For constant terms, For delay operators; This indicates performing a d-th order difference; This represents performing a seasonal difference of D times with a seasonal cycle of S; polynomial = B; = Polynomial action in The left side of the equation is... The AR(p / P) component of the model is represented by the equation on the right side. + This represents the MA(q / Q) component of the model; Step 4: Based on a seasonal single autoregressive moving average model, combined with sea surface temperature at squid spawning grounds. sea ​​surface salinity , sea surface chlorophyll concentration Sea surface height Hybrid layer depth Oxygen content at sea surface and the baiting area , Values ​​were used to establish a seasonal multivariate autoregressive moving average model; Step 5: Use the test set to perform white noise test on the residuals, and screen and evaluate the goodness of fit and prediction accuracy of the seasonal multivariate autoregressive moving average model to obtain the optimal model. Step 6: Use the optimal model to predict the abundance of squid resources in the Northwest Pacific.

2. The method for predicting the abundance of squid resources in the Northwest Pacific based on a time series model as described in claim 1, characterized in that: In step 1, the test set consists of the catch and number of fishing vessels in the area between 144.5°E and 170°E, and between 35°N and 49.5°N, from June to November within two years of the time when the method was used; the training set consists of the catch and number of fishing vessels in the area between 144.5°E and 170°E, and between 35°N and 49.5°N, from the time records began until two years before the time the method was used.

3. The method for predicting the abundance of squid resources in the Northwest Pacific based on a time series model as described in claim 1, characterized in that: In step 2, the unit root test is based on the relationship between stationary sequences and unit roots to construct a unit root for testing time series data. If all the characteristic roots of the sequence are inside the unit circle, the sequence is a stationary sequence. If the sequence has characteristic roots on or outside the unit circle, then the sequence is a non-stationary sequence.

4. The method for predicting the abundance of Northwest Pacific squid resources based on a time series model as described in claim 3, characterized in that: The unit root test is performed using the `adf.test` function in the `tseries` package of R language for time series analysis. If the p-value is less than 0.05, the series is stationary; if the p-value is greater than 0.05, the series is non-stationary. In this case, d-order differencing and D-order seasonal differencing are performed sequentially to stabilize the series, where d / D ≤ 2. The order of d-order differencing and D-order seasonal differencing does not affect the result. When the series has strong seasonality, seasonal differencing is preferred.

5. The method for predicting the abundance of squid resources in the Northwest Pacific based on a time series model as described in claim 1, characterized in that: The expression for the seasonal multivariate autoregressive moving average model SARIMAX in step 4 is as follows: ,in This represents the fitted value of the seasonal multivariate autoregressive moving average model at time t; This represents the fitted value of the seasonal single autoregressive moving average model at time t. Indicates the environmental covariates of spawning grounds or feeding grounds; This is the coefficient vector of the covariates, describing the degree of influence of the covariates on the dependent variable.

6. The method for predicting the abundance of squid resources in the Northwest Pacific based on a time series model as described in claim 1, characterized in that: In step 5, the checkresiduals function from the Forecast package in R, a toolkit for time series forecasting, is used to perform a white noise test on the residuals of the seasonal multivariate autoregressive moving average model. If the p-value is greater than 0.05, the model passes the white noise test; if the p-value is less than 0.05, the model fails the test and needs to be remodeled.

7. The method for predicting the abundance of squid resources in the Northwest Pacific based on a time series model as described in claim 1, characterized in that: In step 5, the Akaike information content criterion is used to evaluate the goodness of fit of the seasonal multivariate autoregressive moving average model. The calculation formula is as follows: Where L represents the likelihood function value of the model, indicating the goodness of fit of the model; k is the number of parameters in the model, and n is the number of samples. The smaller the AICc value, the better the model fit. The root mean square error (RMSE) index is used to screen and evaluate prediction accuracy, and its calculation formula is: ,in Indicates the actual value. denoted by , where n represents the number of test set samples. A smaller RMSE value indicates better model prediction performance.

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