Method and system for calculating mixing proportion of multi-end-member water mass mixed particles

Abstract

The invention discloses a method and a system for calculating the mixing proportion of multi-end-member water mass mixed particles. The method comprises the following steps: calculating the contribution proportion of each water mass end member of a mixing area by adopting an isotope mixing model; generating initialization information of a multi-end-member water mass mixed particle model by using the delta < 18 > O and salinity of each end member and derivative information; based on the contribution proportion and the initialization information, constructing a multi-end-member water mass mixed particle model; simulating a simulated delta < 18 > O-salinity linear relation of a mixing area under all iterative mixing proportion combinations based on a multi-end-member water mass mixed particle model; and calculating the mixing ratio of each end member by comparing the simulated delta 18O-salinity linear relationship with the actual delta 18O-salinity linear relationship. According to the method, the multi-end-member water mass mixed particle model is constructed, and iterative calculation and fluctuation simulation are combined, so that accurate quantification of a water mass mixing ratio and quantitative analysis of mixing sufficiency are realized.

Description

Technical Field

[0001] This invention belongs to the fields of isotope application technology, physical mixing process quantification, and particle modeling technology, specifically involving a method and system for calculating the mixing ratio of multi-terminal water mass mixing particles. Background Technology

[0002] Water masses are water bodies with similar source areas and formation mechanisms, sharing largely the same physical, chemical, and biological characteristics and trends, but exhibiting significant differences from surrounding water bodies. The boundary waters where different water masses meet and converge are often well-known fishing grounds, closely linked to the proliferation of marine phytoplankton. Therefore, studying the movement and mixing of water masses is crucial for fisheries, aquaculture, and even global marine primary productivity. In the 1940s and 50s, some scholars first applied temperature-salinity maps to study the classification of water masses. Subsequently, they focused on the quantitative contribution of different water masses to sea areas. Some studies continued to use temperature-salinity physical indicators, while others adopted biogeochemical indicators, such as the deuterium and oxygen-18 isotopes of water (later referred to as hydrogen and oxygen isotopes of water).

[0003] In reality, some water molecules in the sampling area do not participate in the mixing within that area but flow to other areas. From a stability perspective, if all water masses flowing through the area flow out without interference, their marine biogeochemical processes would not likely undergo significant changes, such as phytoplankton blooms. However, this scenario is almost nonexistent because water masses with different physical properties can form fronts, and the instability of ocean fronts is crucial for the exchange of seawater properties. Therefore, in sea areas with multiple water mass sources, there must be a mixed biogeochemical process involving multiple water masses, and the strength of this mixing is inextricably linked to changes in marine biogeochemical processes. However, traditional physics focuses more on the strength of mixing and rarely quantifies the adequacy of mixing from a macroscopic perspective, and lacks quantitative research on the mixing of water masses from different sources.

[0004] Since the 1950s, researchers have studied the oxygen isotopes of seawater and, based on their stable and conserved properties, have investigated global hydrological cycles, ocean circulation, and past climate trends. In the ocean, the oxygen isotope composition (δ¹²⁸O⁻) of seawater... 18 O3 is used as a conserved tracer to study seawater sources and physical processes, such as sea surface evaporation and precipitation, as well as continental and glacial runoff and ice melt. Evaporation typically increases seawater salinity and enriches heavy oxygen isotopes, while precipitation may lead to decreased salinity and increased δ¹⁸O isotopes. 18 The decrease of O. Different water masses tend to have different δ values. 18 O-salinity (δ) 18 The OS line corresponds to the evaporation, precipitation, and land runoff of different water masses in the sea areas they are located on.

[0005] Traditionally, we stop after calculating the contribution ratio of end-source sources, assuming that the incoming seawater from these sources is sufficiently mixed in the region, and discuss marine biogeochemical cycles based on this assumption. However, this is only an ideal scenario. Now, let's consider a situation where two regions have completely identical end-source characteristics and contributions: one in the open ocean and the other in a semi-enclosed bay. Clearly, their biogeochemical cycles are likely to have significant differences. These differences are related to the residence time of seawater in the region, the degree of mixing in each sub-region, and the interactions between the sub-regions. These more microscopic aspects cannot be explained by traditional end-source contributions and require new models and indicators. Summary of the Invention

[0006] This invention aims to address the shortcomings of existing technologies and provides the following solutions:

[0007] A method for calculating the mixing ratio of multi-terminal water mass mixing particles includes the following steps:

[0008] The contribution ratio of each water mass endmember in the mixing region was calculated using an isotopic mixing model.

[0009] Utilizing the δ of each endmember 18 O and salinity, along with derived information, generate initialization information for a multi-terminal water mass mixing particle model;

[0010] Based on the contribution ratio and the initialization information, a multi-terminal water mass hybrid particle model is constructed.

[0011] Based on the multi-terminal water mass mixing particle model, the simulation δ of the mixing zone under all iterative mixing ratio combinations was performed. 18 O-Salinity linear relationship;

[0012] By comparing the simulated δ 18 O-salinity linear relationship and actual δ 18 The O-salinity linear relationship was used to calculate the mixing ratio of each endmember.

[0013] Preferably, the process of generating the initialization information includes:

[0014] Establish δ of three endmembers 18 O-Salinity linear characteristic, the linear characteristic includes: average salinity S i Slope k i and intercept b i ;

[0015] Set the fluctuation range for each variable, and set the default value for salinity to S. dev =0.7, the default slope is k dev =0.0001, the default value of the intercept is bdev =0.1, thus obtaining the initialization information.

[0016] Preferably, the method for constructing the multi-terminal water mass hybrid particle model includes:

[0017] Set the total number of simulated water particles N, and proportional to n i =N×f i Allocate the number of particles to each endmember, where f i Contribution ratio to end-users;

[0018] Mix the proportions of each endmember m i Iterate from 0 to 1, with an iteration step size of a preset increment Δm;

[0019] According to the mixing ratio m of each endmember i Calculate the number m of each end-member particle involved in the mixing. i ×n i The number of mixed particles for each endmember is obtained;

[0020] The mixing region δ is calculated based on the number of mixed particles in each endmember and the linear characteristics of each endmember in the initialization information. 18 O-salinity linearity features were used to complete the construction of the multi-terminal water mass mixed particle model.

[0021] Preferably, the mixing region δ is calculated. 18 Methods for linear characterization of O-salinity include:

[0022]

[0023]

[0024] Where, k mix Indicates the mixing region δ 18 The slope of the O-salinity line, b mix Indicates the mixing region δ 18 The intercept of the O-salinity line.

[0025] Preferably, the simulated δ is obtained. 18 Methods for establishing a linear relationship between O-salinity include:

[0026] Based on the linear characteristics k of the mixing region mix and b mix The mixture of particles in the mixing region is generated by taking the standard deviations of the variables in the initialization information and the initialization information.

[0027] The simulated δ of the mixing region is obtained based on the fitting of the mixed particles and the unmixed particles. 18 O-Salinity linear relationship.

[0028] Preferably, the method for generating the mixed particles includes:

[0029]

[0030]

[0031]

[0032]

[0033] Among them, S j δ represents the salinity of the mixed particle j. 18 O j S represents the oxygen isotope of the mixed particle j. mean R represents the average salinity of the original mixed particles, K represents the slope of the simulated mixed particles, B represents the intercept of the simulated mixed particles, and R1, R2, and R3 represent random numbers in the range [-1, 1].

[0034] Preferably, the method for calculating the mixing ratio of each endmember includes:

[0035] Based on the simulated δ 18 O-salinity linear relationship, establishing mixing linear characteristics and endmember mixing ratio m i The mapping relationship;

[0036] Based on the aforementioned mapping relationship, through actual δ 18 O-salinity linear characteristics are used to invert the target mixing ratio, and the average value is calculated.

[0037] Perform a preset number of independent mixing ratio calculations, regenerate end-member particle parameters in each iteration to introduce volatility, aggregate all iteration results and take the average to output the mixing ratio.

[0038] The present invention also provides a calculation system for the mixing ratio of multi-terminal water mass mixing particles. The system applies the above-mentioned method and includes: a contribution ratio calculation module, an initialization information generation module, a model building module, a simulation module, and a calculation module.

[0039] The contribution ratio calculation module uses an isotope mixing model to calculate the contribution ratio of each water mass endmember in the mixing region.

[0040] The initialization information generation module utilizes the δ of each terminal. 18 O and salinity, along with derived information, generate initialization information for a multi-terminal water mass mixing particle model;

[0041] The model building module constructs a multi-terminal water mass hybrid particle model based on the contribution ratio and the initialization information;

[0042] The simulation module simulates the mixing zone under all iterative mixing ratio combinations based on the multi-terminal water mass mixing particle model. 18 O-Salinity linear relationship;

[0043] The calculation module compares the simulated δ 18 O-salinity linear relationship and actual δ 18 The O-salinity linear relationship was used to calculate the mixing ratio of each endmember.

[0044] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0045] This invention proposes an isotope mixing model and system for indicating the degree of water mass mixing. By constructing a multi-terminal water mass mixing particle model and combining iterative calculation and wave simulation, it achieves accurate quantification of the water mass mixing ratio and quantitative analysis of the sufficiency of mixing.

[0046] This invention is based on δ 18 A particle model is constructed using the O-salinity linear relationship. By introducing the fluctuation range of each endmember parameter (such as salinity, slope, and standard deviation of the intercept), the natural fluctuations in the water mass mixing process are dynamically simulated. This avoids the deviation between the "complete mixing" assumption in traditional models and the actual marine environment, making the model more closely resemble the real water mass mixing scenario and improving the reliability of the mixing process simulation. It breaks through the limitation of traditional endmember contribution calculations, which only focus on proportional allocation, and achieves a quantitative analysis of the sufficiency of water mass mixing in the mixing zone.

[0047] The particle model-based mixing simulation process does not rely on complex fluid dynamics equations. It can achieve efficient calculation of multi-end-member mixing processes through linear feature iteration fitting, reducing the computational complexity of the model, improving the processing efficiency of large-scale ocean observation data, and providing a generalizable quantitative tool for monitoring water mass mixing dynamics and studying regional ecological processes. Attached Figure Description

[0048] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention;

[0050] Figure 2 This is a particle distribution diagram of the particle model after particle mixing in an embodiment of the present invention;

[0051] Figure 3 This is a particle initialization diagram of the particle model in an embodiment of the present invention;

[0052] Figure 4 The mixing region δ generated by traversing all mixing ratios in this embodiment of the invention 18 Distribution of the slope k of the O-salinity line;

[0053] Figure 5 The mixing region δ generated by traversing all mixing ratios in this embodiment of the invention 18 Distribution of the intercept b of the O-salinity line;

[0054] Figure 6 Measured δ in the matching mixing region of this invention embodiment 18 Mixing ratio distribution diagram of the slope of the O-salinity line;

[0055] Figure 7 Measured δ in the matching mixing region of this invention embodiment 18 Mixing ratio distribution of the O-salinity linear intercept. Detailed Implementation

[0056] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0057] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0058] Example 1

[0059] In this embodiment, as Figure 1 As shown, a method for calculating the mixing ratio of multi-terminal water clusters includes the following steps:

[0060] S1. The contribution ratio of each water mass endmember in the mixing region is calculated using an isotopic mixing model.

[0061] In this embodiment, the isotope mixing model framework is as follows:

[0062]

[0063]

[0064]

[0065]

[0066] Among them, Xij Let s represent the j-th observed isotope at the i-th mixing point. jk The j-th observed isotope from the k-th source is usually represented as the mean μ. jk and variance The normal distribution; c jk It is the fractionation factor of the j-th observed isotope from the k-th source, usually expressed as the mean λ. jk and variance The normal distribution of p is set to 0 in this embodiment; k q represents the contribution ratio of source k, which needs to be estimated using the SIAR model; jk Let ε represent the concentration value of the j-th observed isotope from the k-th source; ε is the residual, i.e., the additional inter-observation variance not described by the model, expressed as mean 0 and variance. The normal distribution, where It is estimated by the model. Ultimately, a p-value consistent with the data is generated using the Markov chain-Monte Carlo method. k The simulation yielded the water volume contribution ratio f of the three endmembers. i .

[0067] S2. Utilize the δ of each terminal member 18 O, salinity, and derived information are used to generate initialization information for a multi-terminal water mass mixed particle model.

[0068] The process of generating initialization information includes: establishing the delta of three endpoints. 18 O-Salinity linear characteristic, linear characteristics include: average salinity S i Slope k i and intercept b i Set the fluctuation range for each variable, and set the default value for salinity to S. dev =0.7, the default slope is k dev =0.0001, the default value of the intercept is b dev =0.1, and the initialization information is obtained.

[0069] S3. Based on the contribution ratio and initialization information, construct a multi-terminal water mass hybrid particle model.

[0070] The method for constructing a multi-terminal water mass hybrid particle model includes: setting the total number of simulated water mass particles N, and proportionally n... i =N×f i Allocate the number of particles to each endmember, where f i The contribution ratio of each endmember; the mixing ratio of each endmember m i Iterate from 0 to 1, with an iteration step size of a preset increment Δm; based on the mixing ratio m of each endmember. i Calculate the number m of each end-member particle involved in the mixing. i ×ni The number of mixed particles for each endmember is obtained; the mixing region δ is calculated based on the number of mixed particles for each endmember and the linear characteristics of each endmember in the initialization information. 18 O-salinity linear characteristics were used to complete the construction of a multi-terminal water mass mixing particle model.

[0071] Calculate the mixing region δ 18 Methods for linear characterization of O-salinity include:

[0072]

[0073]

[0074] Where, k mix Indicates the mixing region δ 18 The slope of the O-salinity line, b mix Indicates the mixing region δ 18 The intercept of the O-salinity line. Figure 2 The results show the mixture when all three endmembers are mixed at a ratio of 90%.

[0075] S4. Simulation of the mixing region under all iterative mixing ratio combinations based on a multi-terminal water mass mixing particle model. 18 O-Salinity linear relationship.

[0076] Obtain simulated δ 18 Methods for establishing a linear relationship between O-salinity include: based on the linear characteristics k of the mixing zone. mix and b mix The standard deviations of each variable in the initialization information are used to generate the mixed particles in the mixing region; the simulated δ of the mixing region is obtained by fitting the mixed particles and the unmixed particles. 18 O-Salinity linear relationship.

[0077] Methods for generating mixed particles include:

[0078]

[0079]

[0080]

[0081]

[0082] Among them, S j δ represents the salinity of the mixed particle j. 18 O j S represents the oxygen isotope of the mixed particle j. meanR represents the average salinity of the original mixed particles, K represents the slope of the simulated mixed particles, B represents the intercept of the simulated mixed particles, and R1, R2, and R3 represent random numbers in the range [-1, 1]. The results are as follows: Figure 3 As shown.

[0083] In this embodiment, the mixing region δ is simulated for all mixing ratios. 18 The O-salinity linear characteristic process includes: mixing each endmember in proportion m i Iterate from 0 to 1, with an iteration step size of a preset increment Δm = 2%; based on the mixing ratio m i Calculate the number m of each end-member particle involved in the mixing. i ×n i Proceed to step S3 to execute the results; Based on the mixed water particles and the remaining unmixed particles, fit the mixing region δ 18 O-salinity linearity yields the slope k of the simulated mixing zone straight line. mix 'and intercept b mix '. Figure 4 and Figure 5 The results of the above process are shown, namely the mixing zone δ for all mixing ratios. 18 O-Salinity linear characteristic slope k mix 'and intercept b mix 'distributed.

[0084] S5. By comparing the simulated δ 18 O-salinity linear relationship and actual δ 18 The O-salinity linear relationship was used to calculate the mixing ratio of each endmember.

[0085] Methods for calculating the mixing ratio of each endmember include: based on simulation δ 18 O-salinity linear relationship, establishing mixed linear feature k mix 'and b mix 'Mixing ratio with endmembers m i The mapping relationship (often many-to-one); based on the mapping relationship, through actual δ 18 The target mixing ratio is obtained by inverting the linear feature of O-salinity and calculating the average value; the independent mixing ratio calculation is performed a preset number of times, and the end-member particle parameters are regenerated in each iteration to introduce volatility. All iteration results are aggregated and the average value is taken to output the mixing ratio.

[0086] Figure 6 and Figure 7 The mixed linear features k are shown respectively. mix 'and b mix 'Mixing ratio with endmembers m i The mapping relationship is shown in Table 1. Table 1 illustrates the mapping relationship based on the slope k. mix 'and intercept b mix'The inverted mixing ratio, and the final average.'

[0087] Table 1

[0088]

[0089] As shown in Table 1, the mixing ratios derived from the two linear features based on measured data exhibit a very high degree of consistency, demonstrating the robustness of the linear simulation mixing ratio method. In fact, endmembers 1, 2, and 3 represent the Kuroshio Current, South China Sea water, and nearshore water endmembers of a certain strait, respectively. The Kuroshio Current has a very high flow velocity, exhibiting a strong dynamic process in the strait, which is consistent with the high mixing ratio of 82.77% calculated in this embodiment. This also verifies the reliability of the invention from the perspective of actual physical context.

[0090] Example 2

[0091] In this embodiment, a calculation system for the mixing ratio of multi-terminal water clumps includes: a contribution ratio calculation module, an initialization information generation module, a model building module, a simulation module, and a calculation module.

[0092] The contribution ratio calculation module uses an isotope mixing model to calculate the contribution ratio of each water mass endmember in the mixing zone; the initialization information generation module utilizes the δ of each endmember. 18 O, salinity, and derived information are used to generate initialization information for the multi-terminal water mass mixing particle model; the model building module constructs the multi-terminal water mass mixing particle model based on the contribution ratio and initialization information; the simulation module simulates the δ-axis of the mixing region under all iterative mixing ratio combinations based on the multi-terminal water mass mixing particle model. 18 O-salinity linear relationship; the calculation module compares the simulated δ 18 O-salinity linear relationship and actual δ 18 The O-salinity linear relationship was used to calculate the mixing ratio of each endmember.

[0093] The above embodiments are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for calculating the mixing ratio of multi-terminal water clusters, characterized in that, Includes the following steps: The contribution ratio of each water mass endmember in the mixing region was calculated using an isotopic mixing model. Utilizing the δ of each endmember 18 O and salinity, along with derived information, generate initialization information for a multi-terminal water mass mixing particle model; Based on the contribution ratio and the initialization information, a multi-terminal water mass hybrid particle model is constructed. Based on the multi-terminal water mass mixing particle model, the simulation δ of the mixing zone under all iterative mixing ratio combinations was performed. 18 O-Salinity linear relationship; By comparing the simulated δ 18 O-salinity linear relationship and actual δ 18 The O-salinity linear relationship was used to calculate the mixing ratio of each endmember.

2. The method for calculating the mixing ratio of multi-terminal water clusters according to claim 1, characterized in that, The process of generating the initialization information includes: Establish δ of three endmembers 18 O-Salinity linear characteristic, the linear characteristic includes: average salinity S i Slope k i and intercept b i ; Set the fluctuation range for each variable, and set the default value for salinity to S. dev =0.7, the default slope is k dev =0.0001, the default value of the intercept is b dev =0.1, thus obtaining the initialization information.

3. The method for calculating the mixing ratio of multi-terminal water clusters according to claim 2, characterized in that, The method for constructing the multi-terminal water mass hybrid particle model includes: Set the total number of simulated water particles N, and proportional to n i =N×f i Allocate the number of particles to each endmember, where f i Contribution ratio to end-users; Mix the proportions of each endmember m i Iterate from 0 to 1, with an iteration step size of a preset increment Δm; According to the mixing ratio m of each endmember i Calculate the number m of each end-member particle involved in the mixing. i ×n i The number of mixed particles for each endmember is obtained; The mixing region δ is calculated based on the number of mixed particles in each endmember and the linear characteristics of each endmember in the initialization information. 18 O-salinity linearity features were used to complete the construction of the multi-terminal water mass mixed particle model.

4. The method for calculating the mixing ratio of multi-terminal water clusters according to claim 3, characterized in that, Calculate the mixing region δ 18 Methods for linear characterization of O-salinity include: Where, k mix Indicates the mixing region δ 18 The slope of the O-salinity line, b mix Indicates the mixing region δ 18 The intercept of the O-salinity line.

5. The method for calculating the mixing ratio of multi-terminal water clusters according to claim 4, characterized in that, The simulated δ was obtained 18 Methods for establishing a linear relationship between O-salinity include: Based on the linear characteristics k of the mixing region mix and b mix The mixture of particles in the mixing region is generated by taking the standard deviations of the variables in the initialization information and the initialization information. The simulated δ of the mixing region is obtained based on the fitting of the mixed particles and the unmixed particles. 18 O-Salinity linear relationship.

6. The method for calculating the mixing ratio of multi-terminal water clusters according to claim 5, characterized in that, The method for generating the mixed particles includes: Among them, S j δ represents the salinity of the mixed particle j. 18 O j S represents the oxygen isotope of the mixed particle j. mean R represents the average salinity of the original mixed particles, K represents the slope of the simulated mixed particles, B represents the intercept of the simulated mixed particles, and R1, R2, and R3 represent random numbers in the range [-1, 1].

7. The method for calculating the mixing ratio of multi-terminal water clusters according to claim 6, characterized in that, The method for calculating the mixing ratio of each endmember includes: Based on the simulated δ 18 O-salinity linear relationship, establishing mixing linear characteristics and endmember mixing ratio m i The mapping relationship; Based on the aforementioned mapping relationship, through actual δ 18 O-salinity linear characteristics are used to invert the target mixing ratio, and the average value is calculated. Perform a preset number of independent mixing ratio calculations, regenerate end-member particle parameters in each iteration to introduce volatility, aggregate all iteration results and take the average to output the mixing ratio.

8. A system for calculating the mixing ratio of multi-terminal water clusters, said system employing the method described in any one of claims 1-7, characterized in that, include: The module includes a contribution ratio calculation module, an initialization information generation module, a model building module, a simulation module, and a calculation module. The contribution ratio calculation module uses an isotope mixing model to calculate the contribution ratio of each water mass endmember in the mixing region. The initialization information generation module utilizes the δ of each terminal. 18 O and salinity, along with derived information, generate initialization information for a multi-terminal water mass mixing particle model; The model building module constructs a multi-terminal water mass hybrid particle model based on the contribution ratio and the initialization information; The simulation module simulates the mixing zone under all iterative mixing ratio combinations based on the multi-terminal water mass mixing particle model. 18 O-Salinity linear relationship; The calculation module compares the simulated δ 18 O-salinity linear relationship and actual δ 18 The O-salinity linear relationship was used to calculate the mixing ratio of each endmember.

Images