CN117312808B - Calculation method for sea surface aerodynamic roughness - Google Patents
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Abstract
The invention relates to the field of ocean atmospheric boundary layers, and discloses a method for calculating sea surface aerodynamic roughness, which comprises the following steps: acquiring parameter data; establishing an initial parameter combination interval and sampling, and obtaining the sensibility of various parameterization schemes in different parameter combination intervals by using a sensibility analysis method in different combination intervals; reestablishing a new parameter combination interval according to the sensitivity result; analyzing the applicability of each parameterized scheme in the new parameter combination interval to obtain the scheme with the highest applicability in the current parameter combination interval; and searching optimal coefficients of the scheme in different parameter combination intervals by using an intelligent optimization algorithm to obtain an optimal method for calculating the roughness. The method disclosed by the invention can improve the calculation precision of the sea surface aerodynamic roughness and provide technical support for the aspects of sea electromagnetic wave propagation path diagnosis, communication link channel analysis, evaporation waveguide diagnosis, radar target detection, remote sensing information acquisition and the like.
Description
Technical Field
The invention relates to the field of ocean atmospheric boundary layers, in particular to a method for calculating sea surface aerodynamic roughness.
Background
The concept of aerodynamic roughness on the sea surface is derived from the application of roughness extensions in the log-wind profile theory on the land to the sea surface, defined as the altitude at which the wind speed is equal to zero, commonly usedTo represent. The sea surface aerodynamic roughness is a quantity for describing the sea surface small-scale roughness, the size of the sea surface aerodynamic roughness represents the sea surface micro-scale fluctuation degree, and the change rule describes the main characteristics of momentum transmission between the sea and the atmosphere to a certain extent.
At present, the research of the aerodynamic roughness of the sea surface mainly establishes a roughness parameterization scheme according to the relation between relevant parameters such as the sea surface wind speed, the wave age, the spectral energy of wind waves and the like and the sea surface roughness, and then verifies the accuracy of the roughness parameterization scheme by means of relevant data obtained by measuring wind fields by means of equipment such as a microwave scatterometer, a satellite altimeter, a synthetic aperture radar and the like. The accuracy of sea surface aerodynamic roughness acquisition has important influence on researches such as offshore electromagnetic wave propagation path diagnosis, communication link channel analysis, evaporation waveguide diagnosis, radar target detection, remote sensing information acquisition and the like, and therefore, the method is particularly important for sea surface aerodynamic roughness research.
Because the sea surface aerodynamic roughness is unevenly distributed in space, so that large-scale measurement is difficult, the sea surface aerodynamic roughness cannot be measured in real time and in the field by the traditional sea investigation, the current research is based on a sea surface aerodynamic roughness parameterization scheme of dimension analysis, different parameterization schemes are empirical schemes established based on weather hydrographic parameter data of different sea areas, and the determination of the empirical schemes is highly dependent on weather hydrographic conditions of the research sea areas, so that the different sea surface aerodynamic roughness parameterization schemes are needed to be selectively used for the weather hydrographic parameter data in different ranges in practical application calculation, and the empirical schemes are needed to be further optimized and improved according to the weather hydrographic parameter data of the research sea areas, so that the sea surface aerodynamic roughness calculation method suitable for the sea areas is obtained.
Disclosure of Invention
In order to solve the technical problems, the invention provides a calculation method of sea surface aerodynamic roughness, which is established in different parameter combination intervals according to sea actual measurement data and a whirl correlation method to use a sea surface aerodynamic roughness parameterization scheme with optimal coefficients, so as to achieve the aim of improving the applicability of the parameterization scheme in the sea area.
In order to achieve the above purpose, the technical scheme of the invention is as follows:
a method for calculating aerodynamic roughness of a sea surface, comprising the steps of:
step one, data acquisition:
installing an anemograph, three-dimensional ultrasonic wind and millimeter wave radar on an offshore observation platform to obtain average wind speed at the sea level 10m heightThree-dimensional wind speed at sea level 10m、、) Wave heightSum wave periodParameter data;
step two, sensitivity analysis:
according to the average wind speed at sea level 10m altitudeWave heightSum wave periodSetting an initial interval, dividing an initial parameter interval and combining the initial parameter interval to establish an initial parameter combination interval; sampling parameters in each combination interval by adopting a Monte Carlo sampling method in the initial parameter combination interval to obtain a required parameter sample; in different combination intervals, calculating a first-order sensitivity index and a global sensitivity index of the sea surface aerodynamic roughness parameterization scheme by using a sensitivity analysis method by using a parameter sample to obtain the sensitivity of various sea surface aerodynamic roughness parameterization schemes in different parameter combination intervals for three parameters; splitting or merging the initial combination interval according to the sensitivity result, and reestablishing a new parameter combination interval;
step three, applicability analysis:
in the new parameter combination interval, according to the three-dimensional wind speed at the measured sea level 10m height、、) Friction speed calculated by whirl correlation methodFriction speed calculated by combining different sea surface aerodynamic roughness parameterization schemes with CAORE3.0 modelBased on comparison of root mean square errors of different schemesAnalyzing the applicability of each sea surface aerodynamic roughness parameterization scheme in the new parameter combination interval to obtain the sea surface aerodynamic roughness parameterization scheme with the highest applicability in the current parameter combination interval;
step four, establishing a coefficient optimization and new method:
and gradually iterating in different parameter combination intervals by using an intelligent optimization algorithm according to the fitness function value, and searching the optimal coefficient of the sea surface aerodynamic roughness parameterization scheme with the highest applicability in the current parameter combination interval to obtain a method for calculating roughness by using different sea surface aerodynamic roughness parameterization schemes with the optimal coefficient in different parameter combination intervals.
Among the above schemes, the sea surface aerodynamic roughness parameterization scheme comprises YT96, TY01, O02, GW06 and PS07; sensitivity analysis methods include Sobol index method and extended fourier amplitude sensitivity test method.
In the above scheme, the sensitivity parameter comprises the average wind speed at the sea level 10m altitudeWave heightSum wave periodParameter value range、、The units are m/s, m, s, and the interval is set to 1.
In the scheme, in the second step, according to the maximum global sensitivity index of a certain input parameter of each model in the same section as the judgment basis of section division, the parameter section with larger parameter sensitivity index is split, and the sections with smaller sensitivity index are combined.
In the above scheme, the whirl correlation method is calculated as follows:
；
wherein,for the amount of weft wind speed pulsation,for the amount of radial wind speed pulsation,is the fluctuation amount of the wind speed in the vertical direction,representing the product of the average of the weft and warp pulsations over 20 seconds; the fluctuation amount calculation formula is as follows:
；
；
；
wherein,for the wind speed in the weft direction,for the radial wind speed,is the wind speed in the vertical direction,、、within 30 minutesAverage value of (2).
In the above scheme, in the third step, the data are stored in different data intervalsFor the standard, the root mean square error between the friction speeds of five sea surface aerodynamic roughness parameterization schemes and the friction speeds calculated by the whirl correlation method is calculated、、、Each sea surface aerodynamic roughness parameterization scheme is calculated separately, and the root mean square error is calculated as follows:
；
where n is the total number of samples,the calculated friction speed for the mth sample using the vortex motion correlation method,the friction velocities calculated separately for each of the five sea surface aerodynamic roughness parameterization schemes were used for the mth sample.
In the above scheme, in the fourth step, the intelligent optimization algorithm includes one of a particle swarm algorithm, a genetic algorithm, an ant colony algorithm, and a simulated annealing algorithm.
In the above scheme, in the fourth step, the process of optimizing using the particle swarm algorithm is as follows:
s1: firstly, determining the number D of parameters to be optimized in the current scheme, and randomly generating N D-dimensional particles containing coefficients to be optimized in a particle swarm search space to serve as primary particle swarms;
s2: the inverse number of the root mean square error of the friction speed is selected as the fitness function, when the root mean square error is smaller, the fitness is larger, the particle group moves towards the direction of the solution with large fitness, and the fitness function is calculated as follows:
；
s3: calculating fitness function value of particles in t-th generation particle swarm，，…，；
S4: determining the flying speed and the moving direction of the particles according to the fitness function value of the t-th generation particles, and determining the position of the i-th particle in the t-th generation particle groupFlight speed of ith particle in jth dimension；
S5: the ith particle is shown as followsEvolution method of formula from generation t to generation tEvolution is carried out;
；
；
wherein t is the iteration number,as the weight of the inertia is given,learning factors for individuals,For group learning factors, the value range is [0,2 ]]，Andis [0,1]A uniform random number within;is the position corresponding to the optimal adaptive value of the ith particle in the previous t generation of evolution process,the position of the particle with the highest adaptability in the particle group from the 1 st generation to the t generation,representing the ith particle in the jth dimensionThe speed of the generation of the new product,represents the ith particleIn the j-th dimensionSubstitution position;
s6: repeating steps S3-S5 until the evolution times G=100, and obtaining the optimal position searched by the ith particle in the generation G=100 as followsThe optimal position searched by the group in the generation g=100 isWherein the particle swarm updates the optimal position after 100 generationsThe corresponding coefficients a and b are the optimal coefficients.
In the above scheme, in the fourth step, the optimization process using the genetic algorithm is as follows:
step 1, setting crossover probability, mutation probability and iteration times according to experience, determining 2 coefficients a and b to be optimized according to a sea surface aerodynamic roughness parameterization scheme to be optimized, setting the dimension as D=2, setting the initial population size as N=30, setting the precision of a to 0.1 and the precision of b to 0.001, determining the individual length L, and setting the numerical value solution range a of parameters a and b to a range a[，]，b[，]；
The accuracy calculation formula is as follows:
；
；
step 2, generating a binary form of a primary population containing N individuals at random，，…，The method comprises the steps of carrying out a first treatment on the surface of the Calculating solutions corresponding to decimal solutions in solution intervals corresponding to binary codes of individuals in initial populationThe calculation formula is as follows:
；
wherein,decimal values corresponding to binary values of the individuals are bounded by A, B;
step 3, performing cross operation on binary forms corresponding to each individual in the primary population, namely exchanging 9 th to 13 th bits of binary numbers of the two individuals;
performing mutation operation on binary forms corresponding to each individual in the primary population, namely performing negation on the last bit of each individual;
calculating decimal solutions corresponding to each individual in the cross mutated population by using the formula in the step 2;
step 4, using measured 10m average wind speed data, wave height data and wave period data, and in the data combination interval of the first group, according to the sea surface aerodynamic roughnessParameterization scheme in combination with COARE3.0 model calculates the calculated friction speeds for all samples in the combined interval；
In the first group of data combination interval, the measured 10m three-dimensional wind speed fluctuation quantity is used to calculate the friction speed by combining the vortex motion correlation method；
In the first group of data combination interval, calculating the fitness value of each individual in the second generation population according to all sample data in the interval，，…，Fitness calculation function of s generationThe following is shown:
；
wherein s represents algebra，Selecting an inverse of the root mean square error of the friction speed for the fitness function for the total number of all measured data samples within the interval, the fitness being greater when the root mean square error is smaller, whereinThe calculated friction speed for the mth sample using the vortex motion correlation method,a friction speed calculated using a sea surface aerodynamic roughness parameterization scheme for the mth sample;
step 5, using roulette method to calculate the ratio of fitness value of each individual in the second generation to the total fitness valueK=1, 2, …, N; dividing a wheel disc into a plurality of sectors, randomly selecting individuals as next generation by rotating the wheel disc, wherein the probability of each individual being selected is proportional to the fitness of each individual, and the ratio of the fitness value of the s generation to the total fitness valueThe calculations are as follows:
；
the roulette method comprises the following steps: the wheel is unfolded into intervals, which are expressed as the sum of the ratio of each individual fitness to the sum of all individual fitness, at interval 0,]randomly generating N numbers in the population, and carrying out selection operation on individuals corresponding to the interval where the random numbers are located to form a new generation population;
and judging whether the iteration times G reach 100, if not, continuing iteration, and if so, outputting optimal solutions a and b as optimal coefficients.
In the scheme, the method further comprises a step five, and experimental verification is carried out: according to the measured data, the comparative analysis uses the whirl correlation method to calculate the friction speedAnd the friction speed calculated by combining the roughness calculation method obtained in the step four with the COARE3.0 modelVerifying whether the roughness calculating method obtained in the fourth step meets the practical applicationA need.
Through the technical scheme, the method for calculating the aerodynamic roughness of the sea surface has the following beneficial effects:
the invention uses a sensibility analysis method to obtain sensibility intervals of different sea surface aerodynamic roughness parameterization schemes on different meteorological hydrologic parameters, and indicates the direction for a sea surface aerodynamic roughness interval calculation method.
The method for combining the traditional sea surface aerodynamic roughness parameterization scheme with the artificial intelligence related intelligent optimization algorithm improves the coefficient of each traditional sea surface aerodynamic roughness parameterization scheme and improves the applicability of each traditional sea surface aerodynamic roughness parameterization scheme in the research sea area.
The invention builds a roughness parameterization scheme in a combined form by relying on the traditional sea surface aerodynamic roughness parameterization scheme, optimizes each sea surface aerodynamic roughness parameterization scheme in the combined form according to actual measurement sea data to obtain the optimal coefficient of the sea area, so compared with the single sea surface aerodynamic roughness parameterization scheme, the sea surface aerodynamic roughness calculation method optimized by using the invention is more reasonable in theory and higher in calculation precision.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below.
FIG. 1 is a flow chart of a method for calculating aerodynamic roughness of a sea surface disclosed in an embodiment of the invention.
FIG. 2 is an exemplary graph of an initial combination interval of 10m average wind speed, wave height and wave period parameters.
FIG. 3 is an exemplary graph of new parameter combination intervals for an average wind speed, wave height and wave period of 10 m.
FIG. 4 is a flow chart of the applicability analysis of the roughness parameterization scheme in the new parameter combination interval.
FIG. 5 is an exemplary graph of a roughness parameterization scheme distribution with highest applicability in a new parameter combination interval.
FIG. 6 is a flow chart of particle swarm optimization.
FIG. 7 is a genetic algorithm optimization flow chart.
FIG. 8 is a schematic diagram of selection of a next generation population using the roulette method.
FIG. 9 is an exemplary graph of the results of a roughness parameterization scheme optimization.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
The invention provides a method for calculating sea surface aerodynamic roughness, which is shown in figure 1 and comprises the following steps:
step one, data acquisition:
installing an anemograph, three-dimensional ultrasonic wind and millimeter wave radar on an offshore observation platform to obtain average wind speed at the sea level 10m heightThree-dimensional wind speed at sea level 10m、、) Wave heightSum wave periodParameter data.
The offshore observation platform comprises, but is not limited to, an offshore meteorological gradient tower, a carrier-based meteorological gradient observer, an offshore buoy and other platforms capable of meeting the installation of the measuring instrument.
Measuring average wind speed at 10m altitude using anemometerMeasuring three-dimensional wind speed using three-dimensional ultrasonic wind、、) Measuring wave height using millimeter wave radarSum wave period。
Step two, sensitivity analysis:
according to the average wind speed at sea level 10m altitudeWave heightSum wave periodSetting an initial interval, dividing an initial parameter interval and combining the initial parameter interval to establish an initial parameter combination interval; sampling parameters in each combination interval by adopting a Monte Carlo sampling method in the initial parameter combination interval to obtain a required parameter sample; in different combination intervals, calculating a first-order sensitivity index and a global sensitivity index of the sea surface aerodynamic roughness parameterization scheme by using a sensitivity analysis method by using a parameter sample to obtain the sensitivity of various sea surface aerodynamic roughness parameterization schemes in different parameter combination intervals for three parameters; and splitting or merging the initial combination interval according to the sensitivity result, and reestablishing a new parameter combination interval.
Sea surface aerodynamic roughness parameterization schemes include YT96, TY01, O02, GW06, PS07; sensitivity analysis methods include Sobol index method and extended fourier amplitude sensitivity test method.
The sensitivity parameter comprises the average wind speed at sea level 10m altitudeWave heightSum wave periodParameter value range、、The units are m/s, m, s, and the interval is set to 1.
Dividing and combining parameter intervals according to the parameter value range and the interval, and establishing an initial parameter combination interval.
And splitting the parameter interval with larger parameter sensitivity index according to the maximum global sensitivity index of a certain input parameter of each model in the same interval as the judgment basis of interval division, and merging the intervals with smaller sensitivity index.
As shown in table 1, the present invention is illustrated with five roughness parameterization schemes YT96, TY01, O02, PS07, GW 06.
Table 1 five sea surface aerodynamic roughness parameterization schemes:
10m average wind speedWave heightSum wave periodThe range of values and initial interval settings for the parameters are shown in table 2.
Table 2 average wind speed, wave height and wave period parameter ranges and initial intervals of 10 m:
as shown in fig. 2, the intervals are divided and combined according to the parameter value ranges and intervals in table 2, and 3750 groups of initial combination intervals are obtained. The monte carlo sampling method is used in 3750 groups of initial combination intervals, and in each initial combination interval, required input parameter samples are respectively acquired. With 1 st initial combination interval、、For example, n groups of input parameter samples (10M average wind speed, wave height and wave period) are obtained in the combination interval, and if the number of sample parameters is e=3, a sample matrix M of n×2e is generated as follows:
；
wherein the first columnAnd the fourth columnRepresenting 10m wind speed data, second columnAnd the fifth columnRepresenting wave height data, third columnAnd the sixth columnRepresenting wave period data, the first E columns of the matrix are set to matrix a and the last E columns are set to matrix B, and the matrix A, B is as follows:
；
for matrix A, the ith column of matrix B is replaced by the ith column of matrix B to obtain(i=1, 2, …, E) and thus creating n×5 sets of input sample data、Andthe following are provided:
；
taking the TY01 scheme as an example, substituting n.5 groups of input parameter sample data into a TY01 roughness parameterization scheme formula to combine with a COARE3.0 model to calculate roughness to obtain n.5 groups of TY01 scheme roughness data, and combining the n.5 groups of input parameter sample data and n.5 groups of input parameter sample dataData combining constructs n 5 sets of sample data.
Taking a Sobol index method as an example for sensitivity analysis, calculating a first-order response index of the parameters in each initial interval according to n.5 groups of sample data、、And global response index、、The calculation method is as shown in formulas (1) and (2):
（1）
（2）
where i=1, 2, …, E.
The first order response index and the global response index of each roughness parameterization scheme in other initial combination intervals are calculated in the same way, and the global sensitivity index distribution of different roughness schemes in different parameter combination intervals is shown in table 3.
Table 3 global sensitivity index distribution table for different roughness schemes over different parameter combination intervals:
taking the maximum global sensitivity index of a certain input parameter of each model in the same section as a judgment basis of section division, densely splitting a part of the combined section to obtain more combined sections when the sensitivity index of the parameter in the part of the combined section is larger than 0.5, combining the combined sections to obtain a combined section when the sensitivity index of the parameter in the part of the combined section is smaller than 0.3, and otherwise, establishing a new parameter combined section by the method.
For example: if the ST index is large in the sections of 10-11 m/s, 11-12 m/s and 12-13 m/s …, splitting the sections of 10-11 m/s and 11-12 m/s …, for example, splitting the sections of 10-11 m/s into two sections of 10-10.5 m/s and 10.5-11 m/s, and splitting the sections of 11-12 m/s into two sections of 11-11.5 m/s and 11.5-12 m/s; if the wind speed is smaller in the interval of 0-1 m/s and the ST index of 0-2 m/s, combining the two intervals into one interval of 0-2 m/s, wherein the specific splitting and combining mode is based on the sensitivity index.
And re-combining the split and combined intervals to obtain a new parameter combination interval. The combination is similar to the initial combination interval. Such as: the wind speed is in the 1 st section, the wave height is in the 1 st section, and the 1 st section of the wave period is a first group of combined sections; the wind speed is in the 1 st section, the wave height is in the 1 st section, and the 2 nd section of the wave period is a second group of combined sections; and the like, the wind speed is in the P-th interval, the wave height is in the M-th interval, and the N-th interval of the wave period is the P-th and M-th combined interval. An example of a new combination interval is shown in fig. 3.
Step three, applicability analysis:
in the new parameter combination interval, according to the three-dimensional wind speed at the measured sea level 10m height、、) Friction speed calculated by whirl correlation methodAnd five different sea surface aerodynamic roughness parameterization schemes in combination with a CAORE3.0 model、、、、Based on comparison of root mean square errors of different schemesAnd analyzing the applicability of each sea surface aerodynamic roughness parameterization scheme in the new parameter combination interval to obtain the sea surface aerodynamic roughness parameterization scheme with the highest applicability in the current parameter combination interval. The applicability analysis method is shown in fig. 4.
According to the new combination interval rule in fig. 3, three parameter data of measured 10m average wind speed, wave height and wave period and measured 10m three-dimensional wind speed data are divided into corresponding intervals.
In each data combination interval, according to three parameter data, five roughness parameterization schemes are combined with a COARE3.0 model to calculate friction speeds corresponding to the five roughness parameterization schemes、、、、。
Using measured 10m three-dimensional wind speed data (whereinIs in the weft directionThe wind speed is set to be the same as the wind speed,for the radial wind speed,vertical wind speed) and vortex motion correlation method to calculate friction speed。
The whirl correlation method is calculated as shown in formula (3):
（3）；
wherein,for the amount of weft wind speed pulsation,for the amount of radial wind speed pulsation,is the fluctuation amount of the wind speed in the vertical direction,representing the product of the average of the weft and warp pulsations over 20 seconds;
the fluctuation amount calculation formulas are shown in formulas (4), (5) and (6):
（4）；
（5）；
（6）；
wherein,for the wind speed in the weft direction,for the radial wind speed,is the wind speed in the vertical direction,、、within 30 minutesAverage value of (2).
Within different data intervalsFor the standard, the root mean square error between the friction speeds of five sea surface aerodynamic roughness parameterization schemes and the friction speeds calculated by the whirl correlation method is calculated、、、Each sea surface aerodynamic roughness parameterization scheme is calculated independently, and the calculation method of the root mean square error is shown as a formula (7):
（7）；
where n is the total number of samples,the calculated friction speed for the mth sample using the vortex motion correlation method,the friction velocities calculated separately for each of the five sea surface aerodynamic roughness parameterization schemes were used for the mth sample.
The scheme with the smallest root mean square error is selected as the sea surface aerodynamic roughness parameterization scheme with the highest applicability in the current parameter combination interval, as shown in fig. 5.
Step four, establishing a coefficient optimization and new method:
and gradually iterating in different parameter combination intervals by using an intelligent optimization algorithm according to the fitness function value, and searching the optimal coefficient of the sea surface aerodynamic roughness parameterization scheme with the highest applicability in the current parameter combination interval to obtain a method for calculating roughness by using different sea surface aerodynamic roughness parameterization schemes with the optimal coefficient in different parameter combination intervals.
The intelligent optimization algorithm comprises one of particle swarm algorithm, genetic algorithm, ant colony algorithm and simulated annealing algorithm.
Taking a particle swarm algorithm and a genetic algorithm optimization roughness parameterization scheme TY01 as examples, the coefficients a and b are 2 coefficients to be optimized. The roughness parameterization to be optimized TY01 is shown in Table 4.
Table 4 roughness parameterization scheme to be optimized TY01:
as shown in fig. 6, the process of optimizing using the particle swarm algorithm is as follows:
s1: firstly, determining the maximum iteration number G=100 to be optimized of the current scheme, the number D=2 of coefficients to be optimized, and setting a position limit aE [0,2000 ]]、b∈[0,10]Setting a speed limit. Randomly generating n=30 d=2-dimensional particles containing parameters a, b within a particle swarm search spaceAs a first generation population, the ith particleIs a two-dimensional vector form such as，i=1，2，…，N。
S2: the inverse number of the root mean square error of the friction speed is selected as a fitness function, when the root mean square error is smaller, the fitness is larger, the particle group moves towards the direction of the solution with large fitness, and the fitness function is calculated as shown in a formula (8):
（8）；
s3: calculating fitness function value of particles in t-th generation particle swarm，，…，；
S4: determining the flying speed and the moving direction of the particles according to the fitness function value of the t-th generation particles, and determining the position of the i-th particle in the t-th generation particle groupFlight speed of ith particle in jth dimension；
S5: the ith particle is evolved from the t generation to the th generation by the evolution method of formulas (9) and (10)Evolution is carried out;
（9）；
（10）
wherein t is the iteration number,as the weight of the inertia is given,learning factors for individuals,For group learning factors, the value range is [0,2 ]]，Andis [0,1]A uniform random number within;is the position corresponding to the optimal adaptive value of the ith particle in the previous t generation of evolution process,the position of the particle with the highest adaptability in the particle group from the 1 st generation to the t generation,representing the ith particle in the jth dimensionThe speed of the generation of the new product,represents the ith particle in the jth dimensionSubstitution position;
s6: repeating steps S3-S5 until the evolution times G=100, and obtaining the optimal position searched by the ith particle in the generation G=100 as followsThe optimal position searched by the group in the generation g=100 isWherein the particle swarm updates the optimal position after 100 generationsThe corresponding coefficients a and b are the optimal coefficients.
As shown in fig. 7, the process of optimizing using the genetic algorithm is as follows:
step 1, setting crossover probability, mutation probability and iteration times according to experience, determining 2 coefficients a and b to be optimized according to a sea surface aerodynamic roughness parameterization scheme to be optimized, setting the initial population size N=30, setting the precision of a to 0.1 and the precision of b to 0.001, determining the individual length L=20 (the number of binary digits), and setting the numerical solution range a of the parameters a and b to the numerical solution range a of the parameters a and b[0,2000]，b[0,10]；
The precision calculation formulas are shown as (11) and (12):
（11）；
（12）；
step 2, randomly generating a binary form of a primary population comprising n=30 individuals，，…，Examples of binary coded versions are as follows:
（10111010101011110111，11101010111011110101）；
（11101101010101110110，10101101011001111101）；
……
（10001101110001110101，10101101110001110100）；
calculating solutions corresponding to decimal solutions in solution intervals corresponding to binary codes of individuals in initial populationThe calculation formula is shown as (13):
（13）；
wherein,decimal values corresponding to binary values of the individuals are bounded by A, B; the solution of the initial population is:，，…，。
step 3, performing cross operation on binary forms corresponding to each individual in the primary population, namely exchanging 9 th to 13 th bits of binary numbers of the two individuals, such asAndcross to obtainAnd；、、、the following is shown:
（10111010101011110111，11101010111011110101）；
（11101101010101110110，10101101011001111101）；
（10111010010101110111，11101010011001110101）；
（11101101101011110110，10101101111011111101）；
performing mutation operation on binary forms corresponding to each individual in the primary population, namely performing negation on the last bit of each individual; such asAndvariation is obtainedAnd，、、、the following is shown:
（10111010101011110110，11101010111011110100）；
（11101101010101110111，10101101011001111100）；
（10111010010101110110，11101010011001110100）；
（11101101101011110111，10101101111011111100）；
using equation (13) to calculate the decimal solution for each individual in the cross mutated population，，…，。
Step 4, using the measured 10m average wind speed data, wave height data and wave period data, in the first group of data combination interval, calculating the friction speeds calculated by all samples in the combination interval according to the sea surface aerodynamic roughness parameterization scheme TY01 and the COARE3.0 model；
In the first group of data combination interval, the measured 10m three-dimensional wind speed fluctuation quantity is used to calculate the friction speed by combining the vortex motion correlation methodThe method comprises the steps of carrying out a first treatment on the surface of the The specific formula is shown as formula (3).
In the first group of data combination interval, calculating the fitness value of each individual in the second generation population according to all sample data in the interval，，…，Fitness calculation function of s generationSuch as a maleFormula (14):
（14）；
wherein s represents algebra，Selecting an inverse of the root mean square error of the friction speed for the fitness function for the total number of all measured data samples within the interval, the fitness being greater when the root mean square error is smaller, whereinThe calculated friction speed for the mth sample using the vortex motion correlation method,friction velocity calculated for the mth sample using the TY01 sea surface aerodynamic roughness parameterization scheme;
step 5, using roulette method to calculate the ratio of fitness value of each individual in the second generation to the total fitness valueK=1, 2, …, N; dividing a wheel disc into a plurality of sectors, randomly selecting individuals as next generation by rotating the wheel disc, wherein the probability of each individual being selected is proportional to the fitness of each individual, and the ratio of the fitness value of the s generation to the total fitness valueThe calculation is as shown in formula (15):
（15）；
the roulette method is specifically implemented as shown in fig. 8: the wheel is unfolded into intervals, which are expressed as the sum of the ratio of each individual fitness to the sum of all individual fitness, at interval 0,]n numbers are randomly generated in the population, and the selection operation is carried out on individuals corresponding to the interval where the random numbers are located, so that a new generation population is formed. According to the method, not only can individuals with higher fitness be reserved, but also individuals with lower fitness can be given a certain survival chance.
And judging whether the iteration times G reach 100, if not, continuing iteration, and if so, outputting optimal solutions a and b as optimal coefficients.
Similarly, in the second to the P-M-N group of data intervals, the optimal coefficient in each interval can be obtained according to the above method.
And for the roughness parameterization schemes with highest applicability in different combination intervals, using different intelligent optimization algorithms, and obtaining the optimal coefficient of each scheme after optimizing the schemes, thereby obtaining the optimal roughness parameterization scheme in each interval, and using different sea surface aerodynamic roughness parameterization schemes with the optimal coefficient in different parameter combination intervals, namely the novel method established by the invention. The optimization results of the different algorithms are shown in FIG. 9, wherein a, b, c, d … represents the optimal coefficients of the different roughness parameterization schemes, TY01 best ，PS07 best ，GW06 best ，…，O02 best And representing sea surface aerodynamic roughness parameterization schemes with optimal coefficients in different combination intervals.
Step five, experimental verification:
according to the three-dimensional wind speed of the sea level 10m of the actual sea area、、) Calculation of friction speed using vortex motion correlationCalculating friction speed according to average wind speed data, wave height and wave period data at sea level 10m height by using optimal sea surface aerodynamic roughness parameterization scheme of each parameter combination interval and COARE3.0 modelThe method comprises the steps of carrying out a first treatment on the surface of the According toAndcalculation using equation (7)According toAnd verifying whether the optimized sea surface aerodynamic roughness parameterization scheme meets the actual application requirements.
In the embodiment, according to the measured data, the roughness parameterization scheme optimizing method provided by the invention uses different sea surface aerodynamic roughness parameterization schemes and optimal coefficients thereof in different parameter combination intervals, and is more reasonable theoretically compared with a single sea surface aerodynamic roughness parameterization scheme.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (8)
1. A method for calculating aerodynamic roughness of a sea surface, comprising the steps of:
step one, data acquisition:
installing an anemograph, three-dimensional ultrasonic wind and millimeter wave radar on an offshore observation platform to obtain average wind speed at the sea level 10m heightThree-dimensional wind speed at sea level 10m altitude (+)>、/>、/>) Bow height->Sum wave period->Parameter data, wherein u is weft wind speed, v is warp wind speed, and w is vertical wind speed;
step two, sensitivity analysis:
according to the average wind speed at sea level 10m altitudeBow height->Sum wave period->Setting an initial interval, dividing an initial parameter interval and combining the initial parameter interval to establish an initial parameter combination interval; sampling parameters in each combination interval by adopting a Monte Carlo sampling method in the initial parameter combination interval to obtain a required parameter sample; in different combination intervals, using a sensitivity analysis method to calculate first-order sensitivity of a sea surface aerodynamic roughness parameterization scheme by using a parameter sampleThe sensitivity index and the global sensitivity index are used for obtaining the sensitivity of various sea surface aerodynamic roughness parameterization schemes to three parameters in different parameter combination intervals; splitting or merging the initial combination interval according to the sensitivity result, and reestablishing a new parameter combination interval; sea surface aerodynamic roughness parameterization schemes include YT96, TY01, O02, GW06, PS07;
step three, applicability analysis:
in the new parameter combination interval, according to the three-dimensional wind speed at the measured sea level 10m height、/>、/>) Friction speed calculated by vortex motion correlation method>And friction speeds calculated by different sea surface aerodynamic roughness parameterization schemes in combination with the CAORE3.0 model +.>For the basis, the root mean square error of different schemes is compared>Analyzing the applicability of each sea surface aerodynamic roughness parameterization scheme in the new parameter combination interval to obtain the sea surface aerodynamic roughness parameterization scheme with the highest applicability in the current parameter combination interval;
the whirl correlation method is calculated as follows:
；
wherein,is the weft wind speed fluctuation +.>For the radial wind speed fluctuation>Is the fluctuation of wind speed in the vertical direction>Representing the product of the average of the weft and warp pulsations over 20 seconds; the fluctuation amount calculation formula is as follows:
；
；
；
wherein,for weft wind speed->For wind speed in warp direction>Wind speed in vertical direction>、/>、/>Is +.30 min->Average value of (2);
within different data intervalsFor the standard, the root mean square error between the friction speeds of five sea surface aerodynamic roughness parameterization schemes and the friction speeds calculated by the whirl correlation method is calculated>、/>、/>、/>Each sea surface aerodynamic roughness parameterization scheme is calculated separately, and the root mean square error is calculated as follows:
；
where n is the total number of samples,friction speed calculated for sample m using vortex motion correlation, +.>The friction velocities calculated individually for each of the five sea surface aerodynamic roughness parameterization schemes were used for the mth sample;
the scheme with the minimum root mean square error is selected as a sea surface aerodynamic roughness parameterization scheme with the highest applicability in the current parameter combination interval;
step four, establishing a coefficient optimization and new method:
and gradually iterating in different parameter combination intervals by using an intelligent optimization algorithm according to the fitness function value, and searching the optimal coefficient of the sea surface aerodynamic roughness parameterization scheme with the highest applicability in the current parameter combination interval to obtain a method for calculating roughness by using different sea surface aerodynamic roughness parameterization schemes with the optimal coefficient in different parameter combination intervals.
2. A method of calculating aerodynamic roughness of sea surface according to claim 1, characterized in that the sensitivity analysis method comprises Sobol index method and extended fourier amplitude sensitivity test method.
3. A method of calculating aerodynamic roughness of a sea surface according to claim 1, wherein the sensitivity parameter comprises an average wind speed at sea level 10m altitudeBow height->Sum wave period->Parameter value range、/>、/>，/>、/>、/>The units of (a) are m/s, m and s respectively; />、/>、/>The interval of (2) is set to 1.
4. The method for calculating aerodynamic roughness of sea surface according to claim 1, wherein in the second step, according to the maximum global sensitivity index of some input parameter of each model in the same section as the judgment basis of section division, splitting the parameter section with larger parameter sensitivity index, and merging the sections with smaller sensitivity index.
5. The method according to claim 1, wherein in the fourth step, the intelligent optimization algorithm comprises one of a particle swarm algorithm, a genetic algorithm, an ant colony algorithm, and a simulated annealing algorithm.
6. The method for calculating aerodynamic roughness of sea surface according to claim 5, wherein in the fourth step, the optimization process using the particle swarm algorithm is as follows:
s1: firstly, determining the number D of parameters to be optimized in the current scheme, and randomly generating N D-dimensional particles containing coefficients to be optimized in a particle swarm search space to serve as primary particle swarms;
s2: the inverse number of the root mean square error of the friction speed is selected as the fitness function, when the root mean square error is smaller, the fitness is larger, the particle group moves towards the direction of the solution with large fitness, and the fitness function is calculated as follows:
；
s3: calculating fitness function value of particles in t-th generation particle swarm，/>，…，/>；
S4: determining the flying speed and the moving direction of the particles according to the fitness function value of the t-th generation particles, and determining the position of the i-th particle in the t-th generation particle groupFlight speed of ith particle in jth dimension；
S5: the ith particle is evolved from the t th generation to the th generation by the following formulaEvolution is carried out;
；
；
wherein t is the iteration number,is inertial weight, ++>Learning factors for individuals>For group learning factors, the value range is [0,2 ]]，/>And->Is [0,1]A uniform random number within; />For the position corresponding to the optimal adaptation value of the ith particle during the previous t generations of evolution,/->The position of the most adaptable particle in the 1 st generation to the t th generation particle group is +.>Represents the ith particle in the jth dimension +.>Speed of substitution,/->Represents the ith particle in the jth dimension +.>Substitution position;
s6: repeating steps S3-S5 until the evolution times G=100, and obtaining the optimal position searched by the ith particle in the generation G=100 as followsGroup is atThe optimal position searched in the generation g=100 isWherein the particle swarm is updated by the optimal position +.>The corresponding coefficients a and b are the optimal coefficients.
7. The method for calculating aerodynamic roughness of sea surface according to claim 1, wherein in the fourth step, the optimization process using genetic algorithm is as follows:
step 1, setting crossover probability, mutation probability and iteration times according to experience, determining 2 coefficients a and b to be optimized according to a sea surface aerodynamic roughness parameterization scheme to be optimized, setting the dimension as D=2, setting the initial population size as N=30, setting the precision of a to 0.1 and the precision of b to 0.001, determining the individual length L, and setting the numerical value solution range a of parameters a and b to a range a[/>，/>]，b/>[/>，/>]；
The accuracy calculation formula is as follows:
；
；
step 2, generating a binary form of a primary population containing N individuals at random，/>，…，/>The method comprises the steps of carrying out a first treatment on the surface of the Calculating solution ++of decimal corresponding to binary code of individual in initial population in solution interval>The calculation formula is as follows:
；
wherein,decimal values corresponding to binary values of the individual, A, B is the boundary of the parameters a, b for which a=a 1 ，B=B 1 For parameter b, a=a 2 ，B=B 2 ；
Step 3, performing cross operation on binary forms corresponding to each individual in the primary population, namely exchanging 9 th to 13 th bits of binary numbers of the two individuals;
performing mutation operation on binary forms corresponding to each individual in the primary population, namely performing negation on the last bit of each individual;
calculating decimal solutions corresponding to each individual in the cross mutated population by using the formula in the step 2;
step 4, using the measured 10m average wind speed data, wave height data andwave cycle data, in a first group of data combination intervals, calculating friction speeds calculated by all samples in the combination intervals according to a sea surface aerodynamic roughness parameterization scheme and a COARE3.0 model；
In the first group of data combination interval, the measured 10m three-dimensional wind speed fluctuation quantity is used to calculate the friction speed by combining the vortex motion correlation method；
In the first group of data combination interval, calculating the fitness value of each individual in the second generation population according to all sample data in the interval，/>，…，/>Fitness calculation function of s generation +.>The following is shown:
；
wherein s represents algebra，/>The fitness function selects the inverse of the root mean square error of the friction speed for the total number of all measured data samples in the interval, the fitness is greater when the root mean square error is smaller, wherein + ->Friction speed calculated for sample m using vortex motion correlation, +.>A friction speed calculated using a sea surface aerodynamic roughness parameterization scheme for the mth sample;
step 5, using roulette method to calculate the ratio of fitness value of each individual in the second generation to the total fitness valueK=1, 2, …, N; dividing a wheel disc into a plurality of sectors, randomly selecting individuals as next generation by rotating the wheel disc, wherein the probability of each individual being selected is proportional to the fitness of each individual, and the ratio of the fitness value of the s generation to the total fitness value is->The calculations are as follows:
；
the roulette method comprises the following steps: the wheel is unfolded into intervals, which are expressed as the sum of the ratio of each individual fitness to the sum of all individual fitness, at interval 0,]randomly generating N numbers in the population, and carrying out selection operation on individuals corresponding to the interval where the random numbers are located to form a new generation population;
and judging whether the iteration times G reach 100, if not, continuing iteration, and if so, outputting optimal solutions a and b as optimal coefficients.
8. The method for calculating aerodynamic roughness of sea surface according to claim 1, further comprising the step of fifth, experimentalAnd (3) verification: according to the measured data, the comparative analysis uses the whirl correlation method to calculate the friction speedAnd the method for calculating roughness obtained in the fourth step is combined with the friction speed calculated by the COARE3.0 model>Verifying whether the roughness calculating method obtained in the fourth step meets the actual application requirement.
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