CN119494218B - Layered water body radiation transmission modeling method based on two-dimensional approximation - Google Patents
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Abstract
本发明涉及一种基于二流近似的分层水体辐射传输建模方法，步骤如下：通过分析水体组分浓度的垂直分层特性，设置基础假设条件实现基于二流近似的水体光场辐射量的建模，对包含直射分量的情景通过迭代法进行求解；耦合海面入射辐照度模型，综合考虑风对水面反射与透射的影响，进一步优化得到二流模型的系数；最后，结合边界条件，包括初始光照、水体属性参数以及风速影响下的波浪水面，计算水面的下降流辐照度以及直射辐照度，代入二流公式中得到水体的遥感反射率。该解析方法考虑了水体的分层效应，有效提高了真实场景水体辐射传输建模的准确性和可靠性，对于水环境遥感监测、水下目标探测与识别以及海洋工程等领域具有广泛的应用前景。
The present invention relates to a stratified water body radiation transmission modeling method based on two-stream approximation, and the steps are as follows: by analyzing the vertical stratification characteristics of the water body component concentration, setting basic assumptions to achieve the modeling of the water body light field radiation based on the two-stream approximation, and solving the scenario containing the direct component by an iterative method; coupling the sea surface incident irradiance model, comprehensively considering the influence of wind on the water surface reflection and transmission, and further optimizing the coefficients of the two-stream model; finally, combining the boundary conditions, including initial illumination, water body attribute parameters, and wavy water surface under the influence of wind speed, calculating the downwelling irradiance and direct irradiance of the water surface, and substituting them into the two-stream formula to obtain the remote sensing reflectivity of the water body. This analytical method takes into account the stratification effect of the water body, effectively improves the accuracy and reliability of the real scene water body radiation transmission modeling, and has broad application prospects in the fields of water environment remote sensing monitoring, underwater target detection and identification, and marine engineering.
Description
Technical Field
The invention relates to a layered water body radiation transmission modeling method based on two-dimensional approximation, belongs to the field of water body optics, and has important significance in the aspects of detection and identification of underwater targets and water quality monitoring application.
Background
The water body radiation transmission theory is used for quantitatively researching radiation transmission problems in water bodies, and is a core theoretical problem for researching water body optics and water color remote sensing, ocean and lake ecological dynamics and the like. In the past research of ocean optics and ocean color remote sensing, most of the research has been carried out by assuming that the inherent optical characteristics of seawater and the vertical distribution of optical components are uniform. However, this assumption is not applicable to all water conditions, and some marine observations show that vertical inhomogeneities occur substantially in the upper part of the water, and strictly speaking, vertical inhomogeneities are common. In marine biological research, it is found that chlorophyll concentration in a water body has a non-uniform characteristic on a vertical scale, and especially red tide algae grow on a subsurface layer of the water body before red tide erupts on a surface layer of the ocean. Similarly, marine sedimentology studies have shown that the inflow of fresh water from the estuary results in a re-suspension of sediment, and thus in a vertically non-uniform concentration of suspended solids. At the same time, solar radiation transmission takes the forefront in the course of atmospheric and marine cycles, and therefore an assessment of the physical process of radiation transmission is crucial for understanding the phenomena that occur in the transmission process.
The invention establishes a model capable of describing the radiation transmission process of solar electromagnetic energy, and utilizes the solution of the two-flow model to quickly and accurately evaluate the light field distribution in any layered medium, and simultaneously retains the most important physical essence in the radiation transmission model. The model is obtained by solving the improved two-stream formula through an iteration method, and the iteration method is utilized to converge the solution of the layered two-stream radiation transmission formula. The model established by the method comprises scattering below the water surface and irradiance of direct irradiation, and the boundary conditions are utilized to allow the absorption rate, the backward scattering rate, the light beam attenuation rate and the conversion rate to change along with the depth, so that the remote sensing inversion efficiency is improved, and important theoretical and practical references are provided for the research of the characteristics of the layered water body.
Disclosure of Invention
The invention relates to a layered water body radiation transmission modeling method based on two-dimensional approximation, which comprises the following steps of completing derivation of a two-dimensional formula by analyzing characteristics of the layered water body and setting basic assumption conditions, solving the two-dimensional formula containing direct components through an iterative method, analyzing important characteristics such as absorption rate, scattering rate, attenuation rate and the like, comprehensively considering sea surface reflectivity and transmittance under the influence of wind speed based on a sea surface incident irradiance model, further optimizing to obtain coefficients of the two-dimensional model, and finally, calculating the descending irradiance and direct irradiance of the water surface by combining an atmospheric radiation transmission model, and carrying out remote sensing reflectivity of the water body into the two-dimensional model, wherein the specific steps are as follows:
(1) Theoretical analysis is carried out on the layered medium and a two-flow formula under the condition of whether the layered medium contains direct components or not, a mathematical expression is deduced, meanwhile, important characteristics such as absorptivity, scattering rate, attenuation rate, conversion rate and the like in the expression are analyzed, a method for determining the numerical value and influence factors are found, and finally the most original input parameters of the model are found;
(2) Solving the derived two-flow formula by an iteration method, wherein the lambertian reflection cannot completely represent the characteristics of the ocean water body, so that in a gas-sea radiation transmission mode, the influence of chlorophyll, suspended matters, dissolved organic matters and wind-induced sea capillary waves in the ocean water body on each coefficient in the two-flow formula is considered, the sea surface bidirectional reflection coefficient is calculated, and the spectral change of sea surface reflection is considered;
(3) In the whole radiation transmission process, the descending irradiance is attenuated by the action of the water layer in two processes of scattering and absorption, meanwhile, the ascending irradiance becomes an increment of the descending irradiance due to the backward scattering action of the water body, and according to the principle, the irradiation of each layering is calculated through an iteration method in the whole radiation process until the successive value of the ascending flow at the sea level is converged.
A method for modeling radiation transmission of a layered water body based on two-dimensional approximation is characterized in that in the step (1), theoretical analysis is carried out on a layered medium and a two-dimensional formula under the condition of whether direct components are contained or not, a mathematical expression is deduced, meanwhile, important characteristics such as absorption rate, scattering rate, attenuation rate, conversion rate and the like in the expression are analyzed, a method for determining the numerical value and influence factors of the important characteristics are found, and finally the most original input parameters of a model are found, and the method comprises the following steps:
the first step is to set basic assumption conditions:
The assumption of some basicity was defined prior to modeling, assuming that the light distribution is time-independent and therefore the spectral properties are not allowed to change over time, assuming that in an ideal layered medium the spectral properties of each layer are uniform, assuming that the geometry of the radiation-transmitting medium boundary can be roughly estimated as a spatially infinite parallel planar plate defined between two horizontal parallel planes, which are of finite thickness and horizontally uniform but not necessarily uniform in the vertical direction, such that the medium of radiation transmission is a steady state, the refractive index is a constant and there are no other light sources, assuming that there is no internal scattering irradiance, but that this model can include parallel light sources, direct sunlight can be converted into scattered light emanating from elastic scattering, assuming that at the bottom of the medium all downflowing reflected, scattered and downflowing parallel photon streams are lambertian, and therefore upflowing photon streams can be scattered all;
and step two, deriving a flow formula by using the average cosine:
the average cosine is an apparent optical property related to the sea water surface condition, sea water surface incident light and a series of inherent optical properties including absorbance a, scattering rate b, beam decay rate c and scattering phase function, while the average cosine can relate the complete absorbance of a small volume of water to the scattering decay rates of the upward and downward flows of a large volume of water and the reflected irradiance, according to the parallel plane assumption, the original transmission equation is as follows:
integrating this in the lower hemisphere yields the down-flow scattered irradiance:
Where the shape factor r d (z) represents the dominant upward scattering rate of photons moving in the downward direction and r u (z) represents the dominant downward scattering rate of photons moving in the upward direction, therefore, the scattering in the downward direction is partly dependent on backscattered photons, further simplifying the availability of:
similarly, the original transmission equation is integrated in the upper hemisphere to obtain the up-flow scattering irradiance:
for the special case that only the direct component is included, the original transmission equation is changed to:
Since the direct irradiance is only attenuated and transmitted in the downflow direction, the direct irradiance is integrated in the lower hemisphere, and the first-order differential expression of the direct downflow irradiance is simplified:
And thirdly, equivalent substitution:
The above three equations constitute a two-mode version of irradiance containing parallel or direct components, including the average cosine of the up-and down-flows, the shape factor, and the backscattering ratio, while representing a complex differential system with an unknowns greater than the equation, requiring a transformation to remove the unknowns, i.e., r d(z),ru (z), B btc(z),b'btc (z), B (z), c (z) assuming that the irradiance is the same for both up and down flows, i.e. r d(z)＝ru (z) =1, and assuming that a (z), B (z), c (z) are intrinsic optical properties, not apparent optical properties, then the scattering absorbance: a d(z)＝au (z) =a (z), the backscattering rate: B du(z)＝Bud (z) =b (z), the conversion rate: c f(z)＝cb (z) =c (z), the beam attenuation rate: c tc (z) sec θ=α (z), bringing the equivalent substitution above into the two-flow pattern, it is possible to:
A layered water body radiation transmission modeling method based on two-dimensional approximation is characterized in that the two-dimensional equation derived by the iterative method in the step (2) is solved, and because lambertian reflection cannot completely represent the characteristics of the ocean water body, in a gas-sea radiation transmission mode, the influence of chlorophyll, suspended matters, dissolved organic matters and wind-borne sea capillary waves in the ocean water body on each coefficient in the two-dimensional equation is considered, so that the sea surface two-way reflection coefficient is calculated,
The specific method is as follows:
the first step is to solve a two-flow formula which does not contain direct components:
for a two-stream radiation transmission model that does not contain direct light components in a homogeneous aqueous medium, that is, the absorbance and backscattering rates do not change with water depth, the boundary conditions are used, surface downflow irradiance E d (0), z=0, surface downflow slope Bottom upflow irradiance E u(h)＝RbEd (h), z=h, bottom upflow slopeCalculating the ascending flow and descending flow scattering vector irradiance:
wherein, for simplicity, a variable is defined
For stratified bodies of water that do not contain direct light components, the body of water may not be uniform, but the chemical and optical properties within the same layer are uniform, and assuming that the downflow light is completely scattered as soon as it enters the body of water, therefore, the above formula β d (0) can be rewritten to β d (0, i), where i is the i-th layer of the body of water, resulting in a downflow equation in this case:
Wherein E d(z,i)＝Ed (0, i+1) due to the energy transfer principle;
similarly, the general solution of the upflow vector irradiance at the ith layer and depth 0 can be obtained:
wherein E u(0,i)＝Eu (z, i-1) due to the energy transfer principle;
And step two, solving a two-flow formula containing direct components:
For a two-flow radiation transmission model containing direct light components in a uniform aqueous medium, the solution of a two-flow formula is divided into a general solution and a special solution, and the solutions of the two-flow formula of the direct light part of the light beam are obtained by integrating and then taking logarithms to obtain a non-uniform differential equation of the down flow and the up flow:
Es(z)＝Es(0)e-αz
the special solution of the downflow portion is a function of the scattering decay rate α of the direct irradiance, defined as E d(z)＝me-αz, where the constant m can be found by differentiating it twice: Similarly, the special solution of the up-flow portion is a function of the scattering decay rate α of the direct irradiance, defined as E u(z)＝ne-αz, solution:
Further utilizing five boundary conditions, surface downflow irradiance E d (0), z=0, surface downflow slope Bottom upflow irradiance E u(h)＝Rb(Ed(h)+Es (h)), z=h, bottom upflow slopeSurface direct irradiance E s (0), z=0, up-flow and down-flow scattering vector irradiance was found:
For a stratified water body not containing direct light components, in the same way, the formula beta d (0) can be rewritten to beta d (0, i), and m can be rewritten to m (i), wherein i is the ith layer of the water body, so that the general solution of the descending vector irradiance at the ith layer and the depth of h is obtained:
Wherein E d(z,i)＝Ed (0, i+1) due to the energy transfer principle;
Similarly, n is rewritten into n (i), wherein i is the ith layer of the water body, and finally, the general solution of the ascending flow vector irradiance on the ith layer and with the depth of 0 is obtained:
wherein E u(0,i)＝Eu (z, i-1) due to the energy transfer principle;
thirdly, calculating the sea surface bidirectional reflection coefficient:
The sea surface descending irradiance is influenced by the reflection and refraction of the air-sea interface, a rough sea surface is favorable for more light to enter a water body, the sea surface slope and the surface foam coverage rate are functions of wind speed, observation angle and zenith angle, the sea surface reflectivity can be obtained through the sea surface slope and the sea surface foam coverage rate, meanwhile, the internal scattering surface reflectivity of ascending irradiance can also be obtained, the data show that the sea surface descending irradiance increases along with the increase of the wind speed when the wind speed is less than or equal to 10m/s, then the sea surface descending irradiance remains unchanged basically after the wind speed is greater than 10m/s, the wind blowing surface is a function of the surface slope and the wind speed, the sea surface is divided into a plurality of small planes with random slopes, a possible distribution function P (theta n,ws) is obtained, and the possibility of observing sunlight incident from the direction (theta 0,φ0) can be predicted, and the method is defined as follows:
Wherein, the W s is wind speed, θ n is face pitch angle, withP (θ n,ws) is the largest when θ n =0, and P (θ n,ws) decreases with the slope;
Meanwhile, the foam reflectivity is regulated to be isotropic 55%, and increases with the increase of the white foam quantity in a solar spectrum band, and is a function of sea surface roughness, wind speed and wind pressure, and for the sea surface reflectivity, each reflectivity can be divided into two parts, namely specular reflectivity and foam reflectivity:
Rs(ω,ws)＝ρssp(ω,ws)+ρf(ws)
Rd(ws)＝ρdsp(ws)+ρf(ws)
Where R s is the external specular reflectance, R d is the external diffuse reflectance, ρ ssp is the direct reflectance, ρ dsp is the specular diffuse reflectance specified as 0.057, ρ f is the foam reflectance, when the upflow irradiance reaches below the water surface, a portion of the irradiance is reflected back into the body of water, only a portion projects into the air through the sea surface, the sea surface internal reflectance is set independent of wavelength and the angle of incidence of the upflow irradiance is a function of wind speed:
the internal reflectance of the sea surface decreases with increasing wind speed, and when the incident angle is greater than the half-cone angle, the irradiance of the upflow totally reflects, here specified as 0.485;
Fourth step, calculating two-stream model coefficients:
A water body mainly comprises water molecules, phytoplankton, yellow substances, suspended sediment and the like, and the absorption and scattering processes of direct and indirect irradiance of downflow can be caused, and the absorption and scattering processes can be measured through water-leaving radiation or remote sensing radiation, and the specific calculation method is as follows:
The absorbance is a function of wavelength, related to chlorophyll a, dissolved organic carbon, inorganic suspended matter:
a(λ)=awater(λ)+achl(λ)cchl+adoc(λ)cdoc+ass(λ)css
Wherein a chl is chlorophyll a absorption rate, a doc is dissolved organic carbon absorption rate, a ss is suspended matter absorption rate, c chl is chlorophyll a concentration, c doc is dissolved organic carbon concentration, and c ss is suspended matter concentration;
Likewise, backscatter rate and conversion rate:
b(λ)=bwater(λ)+bchl(λ)cchl+bss(λ)css
c(λ)=2.85×b(λ)
And assuming that the conversion rates of the up-flow and the down-flow are the same, while the two-flow model requires a beam attenuation rate, which is defined as the combination of attenuation due to absorption and scattering, attenuation due to absorption is found from the absorbance, and attenuation due to scattering is found from the backscattering rate:
α(λ)=a(λ)+53×b(λ)
A layered water body radiation transmission modeling method based on two-stream approximation is characterized in that in the whole radiation transmission process, the descending irradiance is attenuated by the action of two processes of scattering and absorption of a water layer, meanwhile, the ascending irradiance becomes an increment of the descending irradiance due to the backward scattering action of the water body, according to the principle, the irradiation process is calculated by an iteration method to each layered irradiance until the successive value of the ascending irradiance at sea level converges, and the specific method is as follows:
The falling irradiance is partially absorbed while traversing the body of water, a portion of the backward scattering becomes rising irradiance, the last portion reaches the bottom of the body of water, and the rising irradiance under the sea surface is derived from the backward scattering of the falling irradiance and the lambertian reflection of the bottom of the sea, the rising irradiance being a function of the falling irradiance and the bottom reflectance when the bottom of the body of water, in shallow bodies of water, the rising irradiance below the water surface is composed of the backward scattering of the falling irradiance and the bottom irradiance, the rising irradiance being transferred to the surface at the bottom to become rising irradiance energy, so that the rising irradiance is related to the type of water bottom and the composition of the body of water, the rising irradiance is affected by the bottom reflectance, the strong backward scattering can be caused by the bottom particles and sediment, assuming the bottom of the body of water to be a lambertian surface, i.e., the incident light is isotropic when the direct irradiance reaches the bottom, the rising irradiance is totally reflected as the rising irradiance, the bottom reflectance is defined as the ratio of the rising irradiance to the direct irradiance and the direct irradiance when the direct irradiance reaches the bottom:
in optically shallow bodies of water, the bottom type has a great influence on the bottom reflectivity, so for ease of analysis, it is specified that the bottom type is a seaweed type, which can be measured in particular by a spectroradiometer or a fiber probe, so that shadow problems can be avoided, the surface reflectivity being defined as the ratio of the up-flow irradiance to the sum of the down-flow irradiance and the direct irradiance, the subsurface and on-sea reflectivities:
Remote sensing reflectivity:
Wherein the off-water radiation L w is related to E u and L u, the up-flow irradiance is converted into an up-flow radiation amount by the Q factor:
The remote sensing algorithm operates on the up-flow irradiance, so that the condition of solar flare is avoided, that is, the sensor measures the part of the off-water irradiance, the up-flow irradiance must be converted into up-flow radiation through a Q factor, and if the bottom of the water body is a lambertian surface, Q=pi is a function of wavelength, solar vertex angle, solar azimuth angle and illumination condition;
For a layered water medium, the two-stream formula cannot be easily obtained because the rising stream irradiance at the bottom is unknown until the falling stream scattering and direct irradiance reach the bottom, but this limitation can be solved by an iterative method, in order to calculate the falling stream irradiance at the next interface, the falling stream irradiance at the top of the layer can be added with the rising stream irradiance back-scattered into the irradiance of the layer and added with the parallel irradiance to be converted into the falling stream irradiance, the rising stream irradiance is also obtained by this method, in the first iterative process, the rising stream back-scattered irradiance entering each layer is initialized to 0, and the whole iterative process is calculated by repeatedly using the current back-scattered irradiance and the converted irradiance until the successive value of the rising stream at sea level converges.
Compared with the prior art, the invention has the advantages that:
(1) The prior art is generally based on the assumption of a single water layer, ignoring the multilayer structures present in the water, such as differences in optical properties of the surface and bottom layers. This simplifying assumption may be applicable in a homogeneous water environment, but in a complex layered water environment, the propagation and reflection of light is more complex to influence. The two-flow approximate simulation layered water body method can more accurately simulate the optical behavior of the water body by considering different layers and optical characteristics of the water body, thereby improving the simulation precision of the reflectivity of various components (such as plankton, sediment and the like) in the water body;
(2) When the level change in the water body is treated, the water body is affected by background noise and measurement saturation effect, so that the measurement of the characteristic parameters of the water body is not accurate enough. By introducing a layering optical model, the two-flow approximate simulation layering water body method effectively reduces the interference of background noise and saturation effect on simulation results, thereby improving the sensitivity to the optical characteristics of the water body and remarkably enhancing the expressive ability of the model in complex water body environments.
Drawings
FIG. 1 is a technical flow of the invention, FIG. 2 is a comparison of MC-two-stream model results, wherein (a) is a two-stream approximation model simulation result, (b) is a Monte Carlo Model (MC) simulation result, FIG. 3 is an accuracy verification of MC-two-stream model, (a) is a pure water body, and (b) is a turbid water body.
Detailed Description
In order to better illustrate the two-flow approximation-based layered water body radiation transmission modeling method, the model and the Monte Carlo model are utilized to perform testing and analysis, good effects are obtained, and the specific implementation method is as follows:
(1) Theoretical analysis is carried out on the layered medium and a two-flow formula under the condition of whether the layered medium contains direct components or not, a mathematical expression is deduced, meanwhile, important characteristics such as absorptivity, scattering rate, attenuation rate, conversion rate and the like in the expression are analyzed, a method for determining the numerical value and influence factors are found, and finally the most original input parameters of the model are found;
(2) Solving the derived two-flow formula by an iteration method, wherein the lambertian reflection cannot completely represent the characteristics of the ocean water body, so that in a gas-sea radiation transmission mode, the influence of chlorophyll, suspended matters, dissolved organic matters and wind-induced sea capillary waves in the ocean water body on each coefficient in the two-flow formula is considered, the sea surface bidirectional reflection coefficient is calculated, and the spectral change of sea surface reflection is considered;
(3) In the whole radiation transmission process, the descending irradiance is attenuated by the action of the water layer in two processes of scattering and absorption, meanwhile, the ascending irradiance becomes an increment of the descending irradiance due to the backward scattering action of the water body, and according to the principle, the irradiation of each layering is calculated through an iteration method in the whole radiation process until the successive value of the ascending flow at the sea level is converged.
And comparing the two-stream model result of the water body layering iterative calculation with the result of the MC model simulation. A two-stream model of water stratification is applied and validated by calculating surface reflectivity and irradiance distribution in a natural water body at different wavelengths. Also, the varying absorption and scattering rates due to the changing biochemical factors in the body of water can change the irradiance distribution of the surface light field. FIG. 2 shows the variation of the surface irradiance reflectivity with wavelength for a certain two seawater optically active substances as quantitative and another optically active substance as a function of wavelength, the layer thickness of the two-stream model being the optical thickness. When the chlorophyll a concentration is 1 μg/L or less, the two-flow model performs better than the MC model in the wavelength band of 400nm to 685nm, but does not perform as well as the MC model in the wavelength band of more than 685 nm. At a chlorophyll a concentration of 5. Mu.g/L, the two-stream model performed better than the MC model in the 475nm to 600nm band, but did not perform as well as the MC model in the 400nm to 475nm and 600nm to 700nm bands. When the chlorophyll a concentration is 10. Mu.g/L or more, the two-flow model does not perform as well as the MC model in the 400nm to 700nm band.
When the suspension concentration was 0 to 1mg/L, the water layer thickness was 1m. The thickness of the aqueous layer was 0.5m at a suspension concentration of 5mg/L and 0.1m at a suspension concentration of 10 to 20 mg/L. The two-flow model performs better than the MC model in the 400nm to 700nm band at a suspension concentration of 0 to 1mg/L, does not perform as well as the MC model in the 400nm to 510nm band at a concentration of 5mg/L, but performs better than the MC model in the 510nm to 700nm band, and performs better than the MC model in the 400nm to 700nm band at a suspension concentration of 10 to 20 mg/L. The two-stream model performs less well than the MC model in the 400nm to 500nm band for all ranges of dissolved organic carbon concentrations, but better than the MC model in the 500nm to 700nm band.
FIG. 3 shows a comparative scatter plot of the MC model and the two-stream model with pure water and a more turbid water. R 2 in both cases was 0.9579 and 0.9806, respectively, and in the case of pure water, only pure water absorption and pure water backscattering have an effect on the total reflectance when all variables, chlorophyll a, dissolved organic carbon and suspended matter concentrations were 0. The errors in pure water are higher than those in muddy water, regardless of the depth and the type of water bottom, and meanwhile, the errors of the two layered two-flow models and the MC model are related to the selection of the thickness of the layers, and the reflectivity values can be better approximated by smaller layers. However, since all variables in the previous hierarchy are used to calculate the input values for the lower hierarchy, a greater number of hierarchies will affect the error distribution across the body of water. These errors will be particularly pronounced in clear bodies of water in the blue band (400 nm to 480 nm) because of the high backscattering and absorption.
The two-flow approximate simulation layered water body method established by the invention is beneficial to deeper and scientific exploration of the relationship between the layered structure and the optical characteristics of the water body, and simultaneously, the space-time continuous simulation capability of the optical characteristics of the water body is remarkably improved. The method can accurately simulate the optical behaviors of different layers in the water body, and obviously improves the simulation accuracy of the reflectivity of the water body. By effectively reducing background noise and measuring the interference of saturation effect, the sensitivity to the optical characteristics and the level change of the water body is enhanced, and the universality and the reliability of the model under the complex water body environment are ensured.
Claims (4)
1. A layered water body radiation transmission modeling method based on two-dimensional approximation is characterized by comprising the following steps:
(1) The method comprises the following steps of carrying out theoretical deduction on a vertically layered water body medium and a radiation transmission equation under the condition of whether the vertically layered water body medium contains direct components or not, deducing a mathematical expression of the light field radiation quantity of the vertically layered water body, namely a two-flow approximation model, and carrying out integration on the radiation transmission equation in a lower hemisphere according to a parallel plane hypothesis to obtain the down-flow scattering irradiance:
Wherein E represents irradiance, z represents vertical position coordinates, a represents absorption coefficient, B represents conversion coefficient caused by scattering process, c represents total attenuation coefficient, subscript d and u represent downward direction and upward direction respectively, subscript s represents solar incidence direction, subscript f represents forward scattering, and similarly, radiation transmission equation is integrated in an upper hemisphere to obtain upward flow scattering irradiance:
For special cases where only direct component is included, the original transmission equation is integrated in the lower hemisphere to obtain a first-order differential expression of the irradiance of direct downflow:
wherein c tc represents the attenuation coefficient of the downlink radiation, and θ represents the zenith angle of observation;
Meanwhile, analyzing the important optical characteristics of absorption rate, scattering rate, attenuation rate and conversion rate in the model, finding out a method for determining the numerical value and influence factors, and finally finding out the most original input parameters of the model;
(2) Carrying out numerical solution on the derived two-flow approximation model by an iteration method, wherein the lambertian reflection cannot completely represent the characteristics of the ocean water body, so that in an atmosphere-ocean coupling system radiation transmission mode, the influence of chlorophyll, suspended matters, dissolved organic matters and wind-borne sea surface capillary waves in the ocean water body on each coefficient in the two-flow approximation model is considered, and therefore the sea surface bidirectional reflection coefficient is calculated, and the spectral change of sea surface reflection is considered;
(3) In the radiation transmission process of the whole water body medium layer, the conversion mechanism of backward scattering of the irradiance of the downward flow and the upward flow in the scattering process is considered, and the downward irradiance and the upward irradiance of each layer are calculated through an iteration method until the successive value of the upward flow of the sea level is converged.
2. The method for modeling the radiation transmission of the layered water body based on the two-dimensional approximation, which is disclosed in claim 1, is characterized in that the specific method in the step (1) is as follows:
the first step is to set basic assumption conditions:
Modeling assumes that the distribution of light is time independent, i.e., the spectral characteristics do not change over time, that the spectral characteristics of each layer are uniform in an ideal layered medium, that the geometry of the boundaries of the radiation-transmitting medium can be roughly estimated as a spatially infinite parallel plate defined between two parallel planes, which are finite in thickness and horizontally uniform, but not necessarily uniform in the vertical direction, such that the medium of radiation transmission is a steady state, the refractive index is a constant and there are no other light sources, that there is no internal scattered irradiance, but that this model can include parallel light sources, that direct sunlight can be converted into scattered light from elastic scattering, that at the bottom of the medium, all downflowing reflected, scattered and downflowing parallel photon streams are lambertian, and that the upflowing photon streams can be scattered all together;
the second step, deducing a two-flow approximation model expression by using average cosine;
The third step, equivalent substitution, wherein the three formulas form a two-flow approximation model expression containing irradiance of parallel or direct components, the two-flow approximation model expression comprises average cosine, shape factor and backscattering rate of ascending flow and descending flow, and simultaneously represents a complex differential system containing an unknown number larger than the formula number, the unknown number needs to be removed through transformation, and the equivalent substitution is assumed to be the same for the ascending flow and the descending flow, namely ad(z)＝au(z)＝a(z),Bdu(z)＝Bud(z)＝b(z),cf(z)＝cb(z)＝c(z),ctc(z)secθ＝α(z), is obtained by substituting the equivalent substitution into the two-flow approximation model expression:
3. the method for modeling the radiation transmission of the layered water body based on the two-stream approximation, which is disclosed in claim 1, is characterized in that the specific method in the step (2) is as follows:
The first step is that a two-flow approximation model solution without direct component is carried out:
For a two-stream approximate radiation transport model that does not contain direct light components in a homogeneous aqueous medium, i.e., the absorbance and backscattering rates do not change with water depth, the boundary conditions are used, surface downflow irradiance E d (0), z=0, surface downflow slope Bottom upflow irradiance E u(h)＝RbEd (h), z=h, bottom upflow slopeCalculating the ascending flow and descending flow scattering irradiance:
Wherein, for simplicity, a variable is defined
For stratified bodies of water that do not contain direct light components, the body of water may not be uniform, but the chemical and optical properties within the same layer are uniform, and assuming that the downflow light is completely scattered once it enters the body of water, the above formula β d (0) can be rewritten to β d (0, i), where i is the i-th layer of the body of water, resulting in a downflow flow approximation model expression in this case:
Wherein E d(z,i)＝Ed (0, i+1) due to the energy transfer principle;
similarly, the general solution of the upflow irradiance at the ith layer and depth 0 can be obtained:
wherein E u(0,i)＝Eu (z, i-1) due to the energy transfer principle;
And step two, solving a two-flow approximation formula containing direct components:
For a two-flow approximate radiation transmission model containing direct light components in a uniform aqueous medium, the solution of a two-flow approximate formula is divided into a general solution and a special solution, and the two-flow approximate formula is integrated first to obtain a solution of a beam direct part two-flow approximate formula and a non-uniform differential equation of a descending flow and an ascending flow:
Es(z)＝Es(0)e-αz
the special solution of the downflow portion is a function of the scattering decay rate α of the direct irradiance, defined as E d(z)＝me-αz, where the constant m can be found by differentiating it twice: Similarly, the special solution of the up-flow portion is a function of the scattering decay rate α of the direct irradiance, defined as E u(z)＝ne-αz, solution:
Further utilizing five boundary conditions, surface downflow irradiance E d (0), z=0, surface downflow slope Bottom upflow irradiance E u(h)＝Rb(Ed(h)+Es (h)), z=h, bottom upflow slopeSurface direct irradiance E s (0), z=0, up-flow and down-flow scattering vector irradiance was found:
For a stratified water body not containing direct light components, in the same way, the formula beta d (0) can be rewritten to beta d (0, i), and m can be rewritten to m (i), wherein i is the ith layer of the water body, so that the general solution of the descending vector irradiance at the ith layer and the depth of h is obtained:
Wherein E d(z,i)＝Ed (0, i+1) due to the energy transfer principle;
Similarly, n is rewritten into n (i), wherein i is the ith layer of the water body, and finally, the general solution of the ascending flow vector irradiance on the ith layer and with the depth of 0 is obtained:
wherein E u(0,i)＝Eu (z, i-1) due to the energy transfer principle;
thirdly, calculating the sea surface bidirectional reflection coefficient:
the irradiance of the sea surface downflow is affected by the reflection and refraction of the air-sea interface, the wind blowing surface is a function of the surface slope and the wind speed, the sea surface is divided into a plurality of facets with random slopes, a probability distribution function P (theta n,ws) is obtained, and the probability that sunlight incident from the (theta 0,φ0) direction is observed in the (theta, phi) direction can be predicted by the following definition:
Wherein, the W s is wind speed, θ n is face pitch angle;
meanwhile, assuming that the sea surface foam reflectivity is isotropic, 55%, and increases with increasing foam quantity in the solar spectrum band, as a function of sea surface roughness, wind speed and wind pressure, each reflectivity can be divided into two parts, specular reflectivity and foam reflectivity for sea surface reflectivity:
Rs(ω,ws)＝ρssp(ω,ws)+ρf(ws)
Rd(ws)＝ρdsp(ws)+ρf(ws)
Where R s is specular, R d is external diffuse, ρ ssp is direct, ρ dsp is specular, given as 0.057, ρ f is foam, when the upflow irradiance reaches below the water surface, a portion of the irradiance is reflected back into the body of water, only a portion projects into the air through the sea surface, the sea surface internal reflectance is set independent of wavelength and the angle of incidence of the upflow irradiance is a function of wind speed:
The internal reflectance of the sea surface decreases with increasing wind speed, and when the angle of incidence is greater than the half-cone angle, the up-flow irradiance is totally reflected, here given as 0.485;
Fourth step, calculating the coefficients of the two-stream approximation model:
the optically active substances in the water body comprise water molecules, phytoplankton, yellow substances and suspended substances, which can cause absorption and scattering processes of direct and indirect irradiance of downflow, and can be measured by water-leaving radiation or remote sensing radiation, and the specific calculation method is as follows:
The absorbance is a function of wavelength, related to chlorophyll a, dissolved organic carbon, inorganic suspended matter:
a(λ)=awater(λ)+achl(λ)cchl+adoc(λ)cdoc+ass(λ)css
Wherein a chl is chlorophyll a absorption coefficient, a doc is dissolved organic carbon absorption coefficient, a ss is suspended matter absorption coefficient, c chl is chlorophyll a concentration, c doc is dissolved organic carbon concentration, c ss is suspended matter concentration;
Also, the backscattering coefficient and the conversion coefficient:
b(λ)=bwater(λ)+bchl(λ)cchl+bss(λ)css
c(λ)=2.85×b(λ)
And assuming that the conversion rates of the up-flow and the down-flow are the same, while the two-flow approximation model requires a beam attenuation rate, which is defined as the combination of attenuation due to absorption and scattering, attenuation due to absorption is found from the absorbance, and attenuation due to scattering is found from the backscattering rate:
α(λ)=a(λ)+53×b(λ)。
4. the method for modeling the radiation transmission of the layered water body based on the two-stream approximation, which is disclosed in claim 1, is characterized in that the specific method in the step (3) is as follows:
The falling irradiance is partially absorbed while traversing the body of water, a portion of the backscattering becomes rising irradiance, the last portion reaches the bottom of the body of water, and the rising irradiance below the sea surface is due to backscattering of the falling irradiance and lambertian reflection at the bottom of the sea, the rising irradiance being a function of the falling irradiance and the bottom reflectance at the bottom of the body of water, in shallow bodies of water, the rising irradiance below the surface being a function of backscattering of the falling irradiance and of the bottom irradiance, the rising irradiance being transferred at the bottom to the surface as rising radiant energy, whereby the rising irradiance is related to the type of water bottom and the composition of the body of water, the rising irradiance being affected by the bottom reflectance, the strong backscattering being caused by bottom particles and sediment, assuming the bottom of the body of water to be a lambertian surface, i.e. the incident light is isotropic at the time of scattering and conversion, the direct irradiance reaching the bottom, being totally reflected as rising irradiance, the bottom reflectance being defined as the ratio of the rising irradiance to the direct irradiance and the direct down irradiance at the bottom:
The surface reflectivity is defined as the ratio of the up-flow irradiance to the sum of the down-flow irradiance and the direct irradiance, the subsurface reflectance of seawater R w and the surface reflectance of seawater R a:
Remote sensing reflectivity:
Wherein the off-water radiation L w is related to E u and L u, wherein the angle mark a represents air, the angle mark w represents water, and 0 represents a position just on the water surface, and the up-flow irradiance is converted into the up-flow radiation amount by the Q factor:
the remote sensing algorithm operates on the upflow irradiance, so that the condition of solar shining is avoided, namely, the sensor measures the portion of the detached irradiance, the upflow irradiance is converted into upflow radiation through a Q factor, Q is a function of wavelength, solar vertex angle, solar azimuth angle and illumination condition, and if the water bottom is a lambertian surface, Q=pi;
For a layered water medium, the two-stream approximation model cannot be easily solved because the rising stream irradiance at the bottom is unknown until the falling stream scattering and direct irradiance reach the bottom, but the limitation can be solved by an iterative method, in order to calculate the falling stream irradiance of the next interface, the falling stream irradiance of the top layer is added with the irradiance of the rising stream irradiance back-scattered into the layer and then added with the falling stream irradiance converted by parallel irradiance, the rising stream irradiance is also calculated by the method, the rising stream back-scattered irradiance entering each layer is initialized to 0 in the process of the first iteration, and the whole iterative process is calculated by repeatedly using the current back-scattered irradiance and the converted irradiance until the successive value of the rising stream at the sea level converges.
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