A method for calculating sub-mesoscale vertical heat flux based on satellite remote sensing data

Abstract

The present invention discloses a method for calculating submesoscale vertical heat flux based on satellite remote sensing data, belonging to the technical field of marine satellite remote sensing applications, and comprising the following steps: Step 1, based on the parameterization scheme of submesoscale vertical buoyancy flux, derive the calculation formula for submesoscale vertical heat flux; Step 2, based on in-situ observation and numerical simulation data, determine the empirical coefficient in the submesoscale vertical heat flux formula based on the parameterization scheme; Step 3, use current eddy-resolution satellite remote sensing data to calculate submesoscale vertical heat flux. The present invention can utilize the current popular eddy-resolution satellite remote sensing data to achieve the calculation of global or regional ocean submesoscale vertical heat transport, overcoming the problem that it is difficult to achieve the calculation of submesoscale dynamics due to the high requirement for data spatial resolution.

Description

Technical Field

[0001] The present invention belongs to the technical field of marine satellite remote sensing applications, and particularly relates to a method for calculating submesoscale vertical heat flux based on satellite remote sensing data. Background Art

[0002] Marine satellite remote sensing is an advanced means of earth observation. By installing different types of remote sensors, it can directly detect or indirectly retrieve marine elements and marine phenomena. It is also the only current observation platform that can long-term and rapidly detect global marine environmental information, providing a data source that cannot be replaced by other observation methods for humans to deeply understand and recognize the ocean. Since its rise in the late twentieth century, with the rapid development of marine satellite remote sensing technology, the observation data resolution of most current marine dynamic environment satellites has reached the order of 10 - 25 kilometers (abbreviated as eddy resolution). At this resolution, only part of the mesoscale process can be resolved, and the submesoscale process cannot be resolved. However, the submesoscale process can break the constraint of geostrophic balance, thus generating strong vertical motion, which can lead to large-scale vertical transport of heat, nutrients, and other tracers in the upper ocean. Through this transport, the submesoscale process significantly regulates the dynamics and biogeochemical processes in the upper ocean. Therefore, to obtain the vertical transport information of the submesoscale process on a global scale, it is necessary to diagnose through a parameterization formula based on satellite remote sensing data.

[0003] Currently, there are few techniques for calculating the vertical heat flux of the submesoscale process based on satellite remote sensing data. There is only one method for diagnosing the vertical heat flux using a submesoscale vertical buoyancy flux parameterization scheme (abbreviated as the F08 scheme) based on the theory of baroclinic instability in the mixed layer. However, this method has the following two limitations. First, the parameterization scheme used in this method assumes that the vertical buoyancy flux below the mixed layer is zero, so it can only diagnose the heat flux above the mixed layer. This is contrary to the in-situ observation results. In fact, the vertical heat flux caused by the submesoscale process can penetrate the mixed layer to a depth of several hundred meters below. Second, this method only considers the baroclinic instability mechanism in the mixed layer, while the main generation mechanism of the submesoscale process should also include the stretching-induced frontogenesis process. The incomplete consideration of the generation mechanism also leads to a large error between the calculated submesoscale vertical heat flux based on this method and the observation. Summary of the Invention

[0004] To solve the above problems, the present invention proposes a new method for calculating the submesoscale vertical heat flux based on satellite remote sensing data. According to the parameterization scheme of the submesoscale vertical buoyancy flux under the "mixing-transition layer instability under frontogenesis control" mechanism established by the research team through long-term observational studies of ocean submesoscale processes, the parameterization calculation formula for the submesoscale vertical heat flux is theoretically derived. At the same time, by performing a least-squares fit on the true value calculated from the definition formula of the submesoscale vertical heat flux and the parameterized diagnostic value calculated by the parameterization scheme, the empirical coefficient in the parameterization calculation formula for the submesoscale vertical heat flux is determined, thereby realizing the calculation of the submesoscale vertical heat flux using vortex-resolution satellite remote sensing data.

[0005] The technical solution of the present invention is as follows:

[0006] A method for calculating the submesoscale vertical heat flux based on satellite remote sensing data, comprising the following steps:

[0007] Step 1: Based on the parameterization scheme of the submesoscale vertical buoyancy flux, derive the calculation formula for the submesoscale vertical heat flux;

[0008] Step 2: Based on in-situ observational and numerical simulation data, determine the empirical coefficient in the submesoscale vertical heat flux formula based on the parameterization scheme;

[0009] Step 3: Use current vortex-resolution satellite remote sensing data to calculate the submesoscale vertical heat flux.

[0010] Further, the specific process of step 1 is as follows:

[0011] The definition formula of the submesoscale vertical buoyancy flux is:

[0012] (1);

[0013] where is the vertical velocity of the submesoscale process; is the submesoscale buoyancy perturbation; is the submesoscale available potential energy release rate;

[0014] Based on the "mixing-transition layer instability under frontogenesis control" mechanism, a parameterization scheme for the submesoscale vertical buoyancy flux is established, and its mathematical expression is:

[0015] (2);

[0016] (3);

[0017] where is the empirical coefficient; is the background stretching rate; is the zonal background flow velocity; is the meridional background flow velocity; is the zonal coordinate; is the meridional coordinate; is the mixed layer depth; is the Coriolis parameter; is the background buoyancy, , is the potential density, is the reference density, is the gravitational acceleration; is the horizontal gradient; is the vertical structure function; is the depth; is the exponential function with base e;

[0018] The potential density is determined by the temperature and salinity , and the state equation of the potential density satisfies:

[0019] (4);

[0020] where, is the thermal expansion coefficient; is the salinity contraction coefficient; is the reference temperature; is the reference salinity;

[0021] Given the upper ocean where the submesoscale processes are active, the potential density is determined by the temperature, and the state equation is further simplified to:

[0022] (5);

[0023] where, is the approximation symbol;

[0024] Substituting the simplified state equation into the definition formula (1) of the submesoscale vertical buoyancy flux, we get:

[0025] (6);

[0026] where, is the submesoscale temperature perturbation; is the submesoscale vertical temperature flux;

[0027] The submesoscale vertical heat flux is defined as:

[0028] (7);

[0029] where, is the heat capacity of seawater;

[0030] Combining Equation (6) and Equation (7), the relationship between the submesoscale vertical buoyancy flux and the heat flux is expressed as:

[0031] (8);

[0032] Substituting the simplified equation of state into the parameterization formula (2) of the submesoscale vertical buoyancy flux, and after rearrangement, the calculation formula of the submesoscale vertical heat flux based on the parameterization scheme is obtained:

[0033] (9);

[0034] where, is the background temperature.

[0035] Furthermore, the specific process of Step 2 is as follows:

[0036] Based on the in-situ observations or numerical simulation data at submesoscale resolution, the true value and the parameterized diagnostic value of the submesoscale vertical heat flux are calculated according to Equation (7) and Equation (9) respectively. The true value and the parameterized diagnostic value are fitted by the least squares method to obtain the empirical coefficient :

[0037] (10);

[0038] where, and are the true value and the parameterized diagnostic value of the submesoscale vertical heat flux respectively; and are respectively and the average values; is the number of sample points for calculation.

[0039] Furthermore, the specific process of Step 3 is as follows: Based on the satellite remote sensing observation data of the global sea surface temperature and horizontal flow velocity at the current eddy resolution, combined with the mixed layer depth data observed by global ocean drifting buoys or other instruments, substitute them into Equation (9) to calculate the submesoscale vertical heat flux.

[0040] Beneficial technical effects brought by the present invention: Based on the parameterization scheme of submesoscale vertical buoyancy flux under the "mixing-transition layer instability under frontogenesis regulation" mechanism established by the research team through long-term observational research on oceanic submesoscale processes, the present invention can calculate the submesoscale vertical heat flux at different depths, and the calculation results can naturally extend below the mixed layer, overcoming the defect that the existing technical methods can only diagnose the heat flux above the mixed layer; in addition, the vertical heat flux calculation formula of the present invention simultaneously considers the two main generation mechanisms of submesoscale processes, namely baroclinic instability and frontogenesis process induced by stretching. The calculation results are closer to the real situation of the ocean than the existing technologies. The present invention can calculate the global submesoscale vertical heat flux using vortex-resolution satellite data, form fixed data products of satellite inversion, and be used for the research on the vertical transport of submesoscale processes, which is conducive to improving the understanding and prediction ability of key processes in Earth system science. Brief Description of the Drawings

[0041] Figure 1 It is a flowchart of the method for calculating submesoscale vertical heat flux based on satellite remote sensing data in the present invention.

[0042] Figure 2 It is a fitting result diagram of the true value and parameterized diagnostic value of submesoscale vertical heat flux in the embodiment of the present invention.

[0043] Figure 3 It is a result diagram of the submesoscale vertical heat flux averaged at 100 meters in different sea areas calculated based on vortex-resolution satellite remote sensing data in the embodiment of the present invention. Detailed Embodiment

[0044] The present invention will be further described in detail below in conjunction with the drawings and specific embodiments:

[0045] As Figure 1 shown, a method for calculating submesoscale vertical heat flux based on satellite remote sensing data includes the following steps:

[0046] Step 1: Based on the parameterization scheme of submesoscale vertical buoyancy flux, deduce the calculation formula of submesoscale vertical heat flux. The specific process is as follows:

[0047] The definition formula of submesoscale vertical buoyancy flux is:

[0048] (1);

[0049] Among them, is the vertical velocity of the submesoscale process; is the submesoscale buoyancy perturbation; is the release rate of submesoscale available potential energy.

[0050] Based on the long-term research accumulation of meso-scale processes, the research team established a meso-scale generation mechanism of "mixing-transition layer instability under frontogenesis regulation", and derived a parameterization scheme for meso-scale vertical buoyancy flux based on this mechanism. The diagnostic verification based on the meso-scale resolution ocean numerical model MITgcm llc4320 shows that, compared with the F08 scheme that only considers the baroclinic instability of the mixed layer, the parameterization scheme used in the present invention depicts the three-dimensional structure of meso-scale vertical buoyancy flux more realistically than the F08 scheme. At present, the research team has proposed a new technology to incorporate this parameterization scheme into ocean numerical simulations and demonstrated that it can effectively improve the problem of over-deep simulation of the mixed layer, thereby enhancing the model's simulation ability of the upper ocean density distribution. The mathematical expression of meso-scale vertical buoyancy flux in the parameterization scheme is:

[0051] (2);

[0052] (3);

[0053] where, is the empirical coefficient; is the background stretching rate; is the zonal background flow velocity; is the meridional background flow velocity; is the zonal coordinate; is the meridional coordinate; is the mixed layer depth; is the Coriolis parameter; is the background buoyancy, , is the potential density, is the reference density, is the acceleration due to gravity; is the horizontal gradient; is the vertical structure function; is the depth; is the exponential function with base e;

[0054] Furthermore, the potential density is determined by the temperature and the salinity , and the state equation of the potential density satisfies:

[0055] (4);

[0056] where, is the thermal expansion coefficient; is the salinity contraction coefficient; is the reference temperature; is the reference salinity;

[0057] Given the upper ocean where submesoscale processes are active, the potential density is mainly determined by temperature, and the equation of state can be further simplified as:

[0058] (5);

[0059] where, is the approximation symbol;

[0060] Substituting the simplified equation of state into the definition formula (1) of the submesoscale vertical buoyancy flux, we can get:

[0061] (6);

[0062] where, is the submesoscale temperature perturbation; is the submesoscale vertical temperature flux;

[0063] Submesoscale vertical heat flux The definition formula of is:

[0064] (7);

[0065] where, is the heat capacity of seawater;

[0066] Combining formula (6) and formula (7), the relationship between the submesoscale vertical buoyancy flux and heat flux can be expressed as:

[0067] (8);

[0068] Further substituting the simplified equation of state into the parameterization formula (2) of the submesoscale vertical buoyancy flux, and after arrangement, the calculation formula of the submesoscale vertical heat flux based on the parameterization scheme is obtained:

[0069] (9);

[0070] where, is the background temperature.

[0071] Step 2: Based on the in-situ observations and numerical simulation data, determine the empirical coefficient in the submesoscale vertical heat flux formula. The specific process is as follows:

[0072] Before calculating the submesoscale vertical heat flux according to formula (9), it is necessary to determine the empirical coefficient .

[0073] Based on the in-situ observations or numerical simulation data at submesoscale resolution, the true value and the parameterized diagnostic value of the submesoscale vertical heat flux can be calculated according to formula (7) and formula (9) respectively. Fitting the true value and the parameterized diagnostic value using the least squares method, the empirical coefficient can be obtained , namely:

[0074] (10);

[0075] Among them, and are the true value and the parameterized diagnostic value of the submesoscale vertical heat flux respectively, calculated based on formula (7), calculated based on formula (9); and are respectively and the average value of; is the number of sample points calculated.

[0076] The fitting results of the true value and the parameterized diagnostic value of the submesoscale vertical heat flux obtained through formula (7) and formula (9) are as Figure 2 shown. The abscissa and ordinate corresponding to the scatter point positions in the figure represent the calculation results of the true value and the parameterized diagnostic value of the submesoscale vertical heat flux respectively, and the straight line represents that the true value and the diagnostic value are exactly equal. Through the fitting of the two, the empirical coefficient is first determined. In addition, Figure 2 shows that the method of the present invention can better depict the distribution characteristics of the submesoscale vertical heat flux in the ocean, and the Pearson correlation coefficient between the diagnostic value and the true value reaches 0.76.

[0077] Step 3: Calculate the submesoscale vertical heat flux using the current eddy-resolution satellite remote sensing data. The specific process is as follows:

[0078] Based on the satellite remote sensing observation data of the global sea surface temperature and horizontal flow velocity with the current eddy resolution, combined with the mixed layer depth data observed by global ocean drifting buoys or other instruments, substituting into formula (9), the calculation of the submesoscale vertical heat flux can be realized.

[0079] In order to prove the feasibility and superiority of the parameterization method of the present invention, the submesoscale vertical heat flux of the global ocean is calculated based on the ocean mixed layer depth data fused by the sea surface temperature observed by infrared remote sensing, the sea surface flow velocity observed by altimeter, and ocean drifting buoys and other observations.

[0080] Figure 3It shows the submesoscale vertical heat fluxes in the western boundary current regions of the global ocean based on the diagnosis of the present invention (including the Kuroshio Extension region, the Gulf Stream region, the recirculation region, the Leeuwin Current region, the East Australian Current region, the Brazil Current region), the North Pacific Subtropical Countercurrent region, and the Antarctic Circumpolar Current region (all hotspots where submesoscale processes are active). It can be seen that the present invention can utilize the current mainstream eddy-resolution satellite remote sensing data to achieve the diagnosis of the global ocean submesoscale vertical heat fluxes, overcoming the problem that the calculation of submesoscale dynamics is difficult to achieve due to the high requirement for data spatial resolution. Through this technology, researchers can establish data products of submesoscale vertical heat fluxes for related research on ocean submesoscale processes, which is crucial for improving the understanding and prediction of ocean material and energy cycles and sea-air interaction processes.

[0081] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions, or substitutions made by those skilled in the art within the essence of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for calculating submesoscale vertical heat flux based on satellite remote sensing data, characterized in that: The steps include: Step 1: Based on the parameterization scheme of sub-mesoscale vertical buoyancy flux, derive the calculation formula of sub-mesoscale vertical heat flux; Step 2: Based on field observations and numerical simulation data, determine the empirical coefficients in the submesoscale vertical heat flux formula based on the parameterization scheme; Step 3, using current eddy resolution satellite remote sensing data to calculate sub-mesoscale vertical heat flux; The specific process of step 1 is as follows: The definition of submesoscale vertical buoyancy flux VBF is: Where w′ is the vertical velocity of the submesoscale process; b′ is the submesoscale buoyancy disturbance; is the submesoscale effective potential energy release rate; Based on the mechanism of "mixing-transition layer instability under frontogenesis regulation", a submesoscale vertical buoyancy flux parameterization scheme is established, and its mathematical expression is: Where, C is the empirical coefficient; is the background stretching rate; is the zonal background velocity; is the meridional background velocity; x is the latitudinal coordinate; y is the meridional coordinate; H is the depth of the mixed layer; f is the Coriolis parameter; is the background buoyancy, ρ is the potential density, ρ0 is the reference density, and g is the gravitational acceleration; is the horizontal gradient; ξ(·) is the vertical structure function; z is the depth; exp(·) is the exponential function with e as the base; The potential density is determined by temperature T and salinity S. The state equation of the potential density satisfies: ρ=ρ0[1-k·(T-T0)+c·(S-S0)] (4); Wherein, k is the thermal expansion coefficient; c is the salinity contraction coefficient; T0 is the reference temperature; S0 is the reference salinity; Considering the upper ocean where submesoscale processes are active, the potential density is determined by the temperature, and the equation of state is further simplified to: ρ~ρ0[1-k·(T-T0)] (5); Among them, ~ is an approximate symbol; Substituting the simplified state equation into the definition of submesoscale vertical buoyancy flux in formula (1), we obtain: Where T′ is the submesoscale temperature disturbance; is the submesoscale vertical temperature flux; The definition of submesoscale vertical heat flux VHF is: Among them, C p is the heat capacity of seawater; Combining formula (6) and formula (7), the relationship between submesoscale vertical buoyancy flux and heat flux is expressed as: Substituting the simplified state equation into the parameterization formula (2) of the submesoscale vertical buoyancy flux, the calculation formula of the submesoscale vertical heat flux based on the parameterization scheme is obtained: in, is the background temperature; The specific process of step 2 is as follows: Based on the field observation or numerical simulation data with sub-mesoscale resolution, the true value and parameterized diagnostic value of the sub-mesoscale vertical heat flux are calculated according to formula (7) and formula (9) respectively. The true value and parameterized diagnostic value are fitted by the least squares method to obtain the empirical coefficient C: Among them, VHF true and VHF para are the true value and parameterized diagnostic value of submesoscale vertical heat flux, respectively; and VHF true and VHF para The average value of ; n is the number of sample points for calculation.

2. The method for calculating submesoscale vertical heat flux using satellite remote sensing data according to claim 1, characterized in that: The specific process of step 3 is: based on the satellite remote sensing observation data of global sea surface temperature and horizontal flow velocity at the current eddy resolution, combined with the mixed layer depth data observed by global ocean drifting buoys or other instruments, it is substituted into formula (9) to realize the calculation of sub-mesoscale vertical heat flux.

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