A method for calculating momentum flux at sea-air interface coupled with boundary layer meteorological conditions

Abstract

The application discloses a kind of sea-air interface momentum flux calculation methods of coupling boundary layer meteorological conditions, it is related to marine atmospheric boundary layer flux observation technical field, including threshold screening to the turbulent flux element required based on eddy correlation method calculation, outlier processing, and three-dimensional wind speed is rotated to coordinate;The sea surface undulation data obtained are processed to obtain sea wave spectrum and wave parameter;Based on Morning-Obukhov similarity theory, Morning-Obukhov length, atmospheric stability, sea 10m wind speed U 10 ;Based on the above data, the friction velocity is split into wind speed term and wave mixing term to fit, finally the momentum flux is obtained;The application reduces the requirement for observation instrument on the basis of ensuring the accuracy of flux calculation, realizes the accurate calculation of sea-air boundary layer momentum flux, meets the demand of momentum flux data in the field of marine meteorological research, weather forecast and marine resource development.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of marine atmospheric boundary layer flux observation, and particularly relates to a sea-air interface momentum flux calculation method coupled with boundary layer meteorological conditions. BACKGROUND

[0002] Sea-air interface flux exchange, as an initial link of sea-air interaction, has a decisive influence on prediction and simulation of climate models and optimization of marine resource management.

[0003] At present, a variety of parameterization schemes are used for calculation of sea-air boundary layer momentum flux, and some of the schemes usually calculate the momentum flux only based on the wind speed at 10 m above the sea, which ignores other important influencing factors in the marine and atmospheric environment. In fact, the sea is a complex system, and factors such as the wave condition of the sea surface and the atmospheric stability will have a significant impact on the sea-air boundary layer momentum flux.

[0004] The wave period and wave direction of the sea change the roughness of the sea surface, and then affect the transmission efficiency of momentum at the sea-air interface; the atmospheric stability determines the turbulence structure and strength in the atmospheric boundary layer, and also plays a key role in the momentum flux. Under complex and variable marine meteorological conditions, the parameterization scheme based on a single wind speed is difficult to meet the actual demand, and a series of problems may be caused by inaccurate calculation of the momentum flux in the fields of marine climate research, weather forecasting, and marine resource development. Therefore, it is of urgent practical significance to develop a sea-air boundary layer momentum flux parameterization scheme that can comprehensively consider various influencing factors and reduce the requirements for observation instruments and observation complexity on the premise of ensuring the accuracy of flux calculation.

[0005] The sea-air boundary layer momentum flux parameterization scheme in the prior art has two defects: one is that only the wind speed at 10 m above the sea is considered, and key influencing factors such as the wave period, wave direction and atmospheric stability are ignored, resulting in insufficient calculation accuracy; the other is that the eddy correlation method observation process is complex and requires high-performance instruments, which is difficult to be widely applied. SUMMARY

[0006] In order to overcome the above problems in the prior art, the present application provides a sea-air interface momentum flux calculation method coupled with boundary layer meteorological conditions.

[0007] The technical scheme adopted by the present application to solve the technical problems is as follows: a sea-air interface momentum flux calculation method coupled with boundary layer meteorological conditions, comprising the following steps:

[0008] Step 1, threshold screening and outlier processing are performed on the turbulent flux elements required for calculation based on the eddy correlation method, and coordinate rotation is performed on the three-dimensional wind speed;

[0009] Step 2: Process the acquired sea surface undulation data to obtain the wave spectrum and wave parameters;

[0010] Step 3: Calculate the Monin-Obukhov length, atmospheric stability, and 10-meter wind speed U at sea based on the Monin-Obukhov similarity theory. 10 ;

[0011] Step 4: Based on the data obtained in Steps 1-3, the friction velocity is decomposed into a wind speed term and a wave mixture term for fitting, and finally the momentum flux is obtained.

[0012] Friction speed in step 4 The specific calculation formula is as follows:

[0013] ;

[0014] ;

[0015] ;

[0016] ;

[0017] Where F is a mixed term function of wave and atmospheric stability. The friction velocity is obtained from the preliminary calculation; A, B, C, and D are the fitting parameters. The wave effect term is represented by Tp, where Tp is the peak wave period and angle_off is the wind-wave angle. for The function that is influenced by atmospheric stability zoL, with k, m, and n as parameters, is used to characterize the modulation effect of atmospheric stability on the wave term.

[0018] The above-mentioned method for calculating the momentum flux at the air-sea interface under coupled boundary layer meteorological conditions, specifically includes step 1:

[0019] Step 1.1: Collect data on ultrasonic false temperature diagnostic values, infrared gas analyzer diagnostic values, water vapor concentration, CO2 concentration, CO2 signal intensity, H2O signal intensity, three-dimensional wind speed, air temperature, and air pressure parameters, and perform threshold filtering and outlier removal on the collected parameter data.

[0020] Step 1.2: Perform a first rotation of the three-dimensional wind speed in the xy-plane around the z-axis, so that the xz-plane is aligned with the average wind direction, and the average components... Satisfaction = 0;

[0021] Step 1.3: Rotate the xz plane obtained in Step 1.2 around the y-axis to make the average components... =0, so that the average wind speed u satisfies .

[0022] The above-mentioned method for calculating the momentum flux of the air-sea interface under coupled boundary layer meteorological conditions, in step 1.1, the outlier removal principle is as follows: Calculate the data for each parameter type within a 30-minute time period; calculate the difference Δx between adjacent time series data, and use Δx to obtain the overall standard deviation σΔx of the differences between adjacent points; compare all data differences with the standard deviation one by one, and if a data point satisfies the formula: Δx ≥ 6σΔx, then directly remove that point; compare all data differences with the standard deviation one by one, and if a data point satisfies the formula: Δx ≥ 3*σΔx, then mark that point as an outlier; if 5 or more consecutive points are marked as outliers, then mark them as normal data; judge all outliers, and data values ​​adjacent to an outlier that differ from the outlier by 30% are considered outliers; remove all outliers and perform linear interpolation to supplement them; if there are too many outliers within a 30-minute time period, directly remove that time period.

[0023] The above-mentioned method for calculating the momentum flux at the air-sea interface under coupled boundary layer meteorological conditions, wherein the specific calculation formula for step 3 is as follows:

[0024] ;

[0025] ;

[0026] ;

[0027] ;

[0028] ;

[0029] Where κ is the von Kármán constant. U is the friction speed. z Z represents the average wind speed at a height z above the sea surface, and z0 represents the sea surface roughness. For stability general functions, This is a dimensionless profile formula, where L is the Moning-Obukhov length. where is the average air temperature; g is the acceleration due to gravity; The horizontal line represents the Reynolds average, and the apostrophe indicates the turbulent fluctuation of the physical quantity.

[0030] The above-mentioned method for calculating the momentum flux at the air-sea interface under coupled boundary layer meteorological conditions, in step 4, the momentum flux is represented by wind stress. The specific calculation formula is as follows:

[0031] ;

[0032] ;

[0033] in, air density, This is the drag coefficient.

[0034] The above-mentioned method for calculating the momentum flux at the air-sea interface under coupled boundary layer meteorological conditions, wherein... The specific calculation formula is as follows:

[0035] ;

[0036] Where a, b, and c are fitting parameters, reflecting the 10-meter wind speed U at sea. 10 The basic relationship between friction speed and friction velocity.

[0037] The beneficial effects of this invention are: (1) From the perspective of calculation accuracy, this invention significantly improves the accuracy of momentum flux calculation results. Traditional schemes rely solely on a 10m wind speed at sea, neglecting the influence of key factors such as wave period, wave direction, and atmospheric stability on momentum flux. However, this invention, by comprehensively coupling these important data and taking into account the interactions between various factors, more accurately simulates the real situation of momentum flux in the air-sea boundary layer. Compared with existing technologies, it greatly improves calculation accuracy, providing more reliable data support for marine meteorological research, weather forecasting, and marine resource development.

[0038] (2) It has significant advantages in terms of observation cost and ease of operation. Compared with the eddy covariance method, the number of observations involved in this invention is significantly reduced, and the requirements for observation instruments are relatively low. The eddy covariance method requires high-precision, complex, and expensive observation instruments, and has extremely demanding requirements for observation conditions. It is difficult and costly to implement in complex marine environments. In contrast, this invention only requires the acquisition of relatively conventional data such as 10m wind speed, wind direction, stability, wave period Tp, and wave direction over 30 minutes. The observation equipment used, such as anemometers and wave buoys, is more common and easier to operate, which greatly reduces the observation cost and operational difficulty. This enables more accurate air-sea boundary layer momentum flux measurement and research to be carried out in more marine areas, especially in areas with relatively limited resources. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the air-sea interface momentum flux of the present invention;

[0040] Figure 2 This is a schematic diagram of the process of this invention;

[0041] Figure 3 This is the polynomial fitting result of the relationship between wind speed at 10m and friction speed in an embodiment of the present invention;

[0042] Figure 4 This is the power function fitting result of the relationship between the wind speed at 10m sea and the friction speed in the embodiment of the present invention;

[0043] Figure 5 This is the result of fitting an exponential function to the relationship between wind speed at 10m and friction speed in an embodiment of the present invention;

[0044] Figure 6 This is a graph showing the relationship between the vertical velocity spectrum (blue line zoL>0, red line zoL<0) and the wave spectrum (black line) during August 9, 2024, in an embodiment of the present invention.

[0045] Figure 7 This is a graph showing the relationship between the vertical velocity spectrum (blue line zoL > 0, red line zoL < 0) and the wave spectrum (black line) during August 21, 2024, in an embodiment of the present invention.

[0046] Figure 8 This is a graph showing the relationship between the vertical velocity spectrum (blue line zoL>0, red line zoL<0) and the wave spectrum (black line) during August 24, 2024, in an embodiment of the present invention.

[0047] Figure 9 This is the polynomial fitting result of the wave and stability hybrid function in the embodiment of the present invention;

[0048] Figure 10 This is the power function fitting result of the wave and stability hybrid function in the embodiment of the present invention;

[0049] Figure 11 This is the fitting result of the wave and stability hybrid function exponential function in the embodiment of the present invention. Detailed Implementation

[0050] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] This embodiment discloses a method for calculating the momentum flux at the air-sea interface coupled with boundary layer meteorological conditions. The air-sea interface momentum flux is as follows: Figure 1 As shown, the Air-Sea Interface is the interface between the atmosphere and the ocean, and is the core region for momentum exchange; Wind Stress is the force exerted by the atmosphere on the sea surface through wind, which is the direct driving force for momentum transfer from the atmosphere to the ocean; Ocean is the area below the diagram, representing the marine environment below the air-sea interface. Ocean Currents are spiral arrows within the ocean region, representing water currents driven by momentum transfer in the ocean; Momentum Transfer is a dashed arrow connecting the air-sea interface and ocean currents, representing the process by which wind stress transfers momentum to the ocean through the air-sea interface, thereby driving ocean currents. The calculation method is as follows: Figure 2As shown, the specific steps include: Step 1, threshold screening and outlier removal are performed on the turbulent flux elements required for calculation based on the eddy covariance method, and the coordinates of the three-dimensional wind speed are rotated.

[0052] This embodiment utilizes data acquired by the observation system aboard the Yangjiang platform in the South China Sea, leveraging the eddy covariance observation system (including one CSAT3A three-dimensional ultrasonic anemometer, an EC150 carbon dioxide and water vapor analyzer, one PTB110 atmospheric pressure sensor, and an HMP155 thermometer) and the underwater wave observation system (AD2CP) on the Yangjiang platform. The three-dimensional ultrasonic anemometer provides the 10Hz wind speed components (u, v, w) and ultrasonic virtual temperature Ts required for flux calculation; the carbon dioxide and water vapor analyzer observes the water vapor and carbon dioxide densities in the measured area; the atmospheric pressure sensor provides the atmospheric pressure value P in the measured area; and the thermometer monitors the atmospheric temperature T in the area. Both observation systems maintained their attitude during the experiment, acquiring meteorological and wave data for a total of 31 days.

[0053] For parameters such as ultrasonic false temperature diagnostic values, infrared gas analyzer diagnostic values, water vapor concentration, CO2 concentration, CO2 signal intensity, and H2O signal intensity, their values ​​are screened and evaluated to check for data anomalies and remove values ​​exceeding physically reasonable thresholds; the outlier removal principles adopted are as follows:

[0054] 1. Perform calculations for each type of parameter data within a 30-minute time period;

[0055] 2. Calculate the difference Δx between adjacent time series data, and use Δx to obtain the overall standard deviation (σΔx) of the difference between adjacent points.

[0056] 3. Compare all data differences with the standard deviation one by one. If a data point satisfies the formula: Δx≥6*σΔx, then remove the point directly.

[0057] 4. Compare all the data differences with the standard deviation one by one again. If a data point satisfies the formula: Δx≥3*σΔx, then mark the point as an outlier.

[0058] 5. If five or more consecutive points are marked as outliers, then mark them as normal data.

[0059] 6. Identify all outliers. Data points adjacent to an outlier that differ from the outlier's value by 30% are considered outliers.

[0060] 7. Remove all outliers and perform linear interpolation to fill in the gaps;

[0061] 8. If there are too many wild points within a 30-minute time period, remove that time period directly.

[0062] Outlier removal is performed on three-dimensional wind speed (u, v, w), ultrasonic virtual temperature, water vapor concentration, CO2 concentration, air temperature, and air pressure. When the eddy covariance system is working, environmental factors such as rain, snow, and dust particles, or unstable power supply voltage and power outages can interfere with the sensors, resulting in large instantaneous noise, which are outliers. Outliers may significantly affect the results of data calculation of variance and covariance, thus affecting the flux calculation results.

[0063] The three-dimensional wind speeds (u, v, w) are rotated according to coordinates. Since the original turbulence data's wind speed components are measured by an ultrasonic instrument (such as CSAT3), the data corresponding to the three components are not in the natural coordinate system, but rather in the so-called 'ultrasonic coordinate system.' If the instrument is tilted, it will severely affect the measurement accuracy of the three components. This error is eliminated by a double rotation:

[0064] 1. Achieve the first rotation of the xy-plane around the z-axis using a rotation matrix, aligning the xz-plane with the mean wind direction, and the average components... Satisfaction = 0:

[0065] 2. The second rotation is a new rotation of the xz plane around the y-axis, which in turn affects the average components. =0:

[0066] Ultimately, the average wind speed u is satisfied. .

[0067] Step 2: After acquiring sea surface undulation data for 1024 seconds per hour, the data is processed using Nortek's SignatureWaves post-processing software to obtain the wave spectrum and wave parameters (wave period, wave direction).

[0068] Step 3: Calculate the Monin-Obukhov length, atmospheric stability, and 10-meter wind speed U at sea based on the Monin-Obukhov similarity theory. 10 .

[0069] Based on the Monin–Obukhov (MO) similarity theory (MOST), the wind speed at the observation height is converted into a 10-meter wind speed U by applying a logarithmic wind profile. 10 This process requires atmospheric stability correction, and the conversion formula is as follows:

[0070] ;

[0071] ;

[0072] In the formula, κ=0.4 is the von Kármán constant, and U z Let z be the average wind speed at a height z above the sea surface. Let z be the air friction velocity, and z0 be the sea surface roughness. This is a general stability function, which has a value of 0 under near-neutral conditions. Its specific expression is as follows:

[0073] ;

[0074] ;

[0075] Where L is the Moning-Obukhov length (MO length), its expression is:

[0076] ;

[0077] In the formula: ρ is the average air temperature; g is the acceleration due to gravity, taken as 9.8 m / s². 2 ; The horizontal line represents the Reynolds average, and the apostrophe indicates the turbulent fluctuation of the physical quantity.

[0078] Quality control of the above data includes:

[0079] 1. Removal of wind shadow area data

[0080] Because the airflow from behind the ultrasonic anemometer (wind shadow area) is affected by the tower structure during observation, the uncertainty of the data increases. Based on the anemometer's installation orientation, observation data within the 225°–315° range are discarded.

[0081] 2. Stability parameter selection

[0082] Based on the Moning-Obukhov similarity theory, an excessively large stability parameter z / L (the ratio of observation height to Moning-Obukhov length) can lead to unreasonable wind speed conversion results (such as negative wind speeds at low wind speeds). Referring to existing research standards, data with z / L > 2 and z / L < -2 were excluded.

[0083] 3. Low wind speed data removal

[0084] When the wind speed is below 1 m / s, the uncertainty of wind direction observation increases significantly, and the relevant data cannot accurately reflect the wind stress characteristics, so U is directly discarded. 10 Low wind speed data <1m / s;

[0085] 4. Rainfall data removal

[0086] During rainfall, raindrops passing through the probe's measurement path may affect the ultrasonic propagation time, thus causing errors. Therefore, the rainfall rate P is directly discarded. rain Low wind speed data ≥0.5m / s;

[0087] 5.95 confidence interval screening

[0088] With friction speed u ∗ With a wind speed of 10 meters U 10 Using the second-order polynomial fitting curve as a benchmark, a 95% confidence interval was defined, and outlier data points outside the interval were removed.

[0089] Step 4: Based on the data obtained in Steps 1-3, the friction velocity is decomposed into a wind speed term and a wave mixture term for fitting, and finally the momentum flux is obtained.

[0090] The momentum flux at the air-sea interface is often represented by wind stress, and the formula for calculating wind stress is:

[0091] ;

[0092] ;

[0093] in, air density, This is the drag coefficient.

[0094] The calculation method in this embodiment uses friction speed. The momentum flux is calculated by separating the momentum flux into wind speed and wave mixture terms and fitting them separately.

[0095] 1. Wind speed calculation

[0096] Numerous studies have found that the drag coefficient is primarily controlled by sea wind speed and is typically expressed as a linear function of wind speed. This embodiment first uses the least squares method to fit the relationship between the 10m sea wind speed and the friction velocity. The data used are ultrasonic wind speed data from an ultrasonic anemometer mounted on the Yangjiang platform in the South China Sea and friction velocity calculated based on the eddy covariance method. Furthermore, based on MOST, the ultrasonic wind speed data is converted into a 10m wind speed U by applying a logarithmic wind profile. 10。 In the fitting stage, the Levenberg-Marquardt algorithm is used to iteratively optimize the parameters. Fitting forms include polynomials, power functions, and exponential functions. The obtained parameter estimates satisfy the unbiasedness, efficiency, and consistency requirements of the Gauss-Markov theorem. Finally, the results are calculated based on the coefficient of determination (R²). 2 The optimal results are selected by using quantitative evaluation indicators such as root mean square error (RMSE), residual distribution law, and 95% confidence interval of parameters. Finally, the optimal result is obtained by polynomial fitting and optimal parameter solution.

[0097] Results of different fitting methods are as follows Figures 3-5 As shown in Table 1, to determine the optimal fitting relationship between variables, this embodiment constructs three fitting models: polynomial, power function, and exponential function, respectively, and uses the coefficient of determination (R²). 2 Ri and root mean square error (RMSE) are used as evaluation metrics for model fit. Among them, Ri... 2The R-squared value represents the model's ability to explain data variation; a value closer to 1 indicates a better fit. RMSE reflects the average deviation between the fitted values ​​and the measured values; a smaller value indicates higher model fitting accuracy. The fitting evaluation indices for the three models are shown in Table 1. As can be seen from the table, the R-squared value of the polynomial fitting model... 2 The goodness-of-fit (RMSE) of the polynomial fitting model is 0.7232, higher than both the power function and exponential function models, indicating that this model has the strongest explanatory power for the data variation patterns. Meanwhile, the RMSE of the polynomial fitting model is 0.05903, lower than both the power function and exponential function models, indicating that its fitted values ​​have the smallest deviation from the measured values ​​and the highest fitting accuracy. Considering both the goodness-of-fit and fitting accuracy, the polynomial fitting model performs best among the three models. Therefore, this study selects the polynomial fitting model as the representation model for the relationship between variables.

[0098] ;

[0099] Where a = 0.001365, b = 0.02258, c = 0.07564, the preliminary friction speed is calculated based on the above formula. .

[0100] Table 1

[0101]

[0102] 2. Calculation of the combined wave and stability term

[0103] South China Sea Yangjiang in-situ observation experimental data ( Figures 6-8 Comparative analysis shows that the influence of ocean waves on near-surface turbulence elements is not universal, but is subject to the dual regulation of ocean wave spectrum peak frequency and atmospheric stability.

[0104] First, the spectral peak frequency determines the vertical attenuation scale of wave disturbances, which is a geometric prerequisite for whether the wave signal can reach the observation height. (Comparison) Figure 7 and Figure 8 The data shows that although both have high wave energy, Figure 8 The vertical velocity spectrum follows the classic Kolmogorov-5 / 3 decay law and has no obvious spectral peaks, indicating that the wave activity on that day was dominated by high-frequency short waves, and the wave boundary layer (WBL) thickness was insufficient to cover the sensor height; while Figure 7 The low-frequency surge (approximately 0.15 Hz) attenuated slowly, successfully transmitting the wave signal to the observation layer.

[0105] Secondly, atmospheric stability determines the signal-to-noise ratio of ocean wave signals by adjusting the intensity of background turbulence. Figure 7The data shows that under the unstable stratification indicated by the blue spectral line, the velocity spectrum exhibits a significant peak change at the position of the wave spectrum peak frequency; however, this is not the case under the stable stratification indicated by the red spectral line.

[0106] Therefore, wave spectrum peak period and stability are taken as the core of this parameterization, and the wave and stability mixed term is derived from the function... Characterization:

[0107] ;

[0108] First, define For wave influence,

[0109] ;

[0110] Where T p The peak wave period is represented by angle_off, which is the wind-wave angle, ranging from 0 to... 180. If the wind direction is clockwise, it is positive; otherwise, it is negative. When the angle is small, the value of cos(angle_off) is close to 1, making the influence of the wave term relatively large.

[0111] ;

[0112] Then, for A function that is influenced by atmospheric stability zoL, where k = 2, m = 0.6, n = 0.9, Used to characterize the modulating effect of atmospheric stability on the wave term, the influence of zoL on the wave term is not linear; when zoL is greater than zero, it affects the wave term. The numerical effect is not significant; when it is less than zero, the larger the absolute value of zoL, the more pronounced the effect. The stronger the modulation effect.

[0113] Similar to the fitted wind speed section, the fitting results using different methods are as follows: Figures 9-11 As shown, a polynomial fitting model was ultimately chosen to represent the relationship between variables, with the model including a mixture of wave and stability terms. : A=-0.002525, B=0.05815, C=-0.45, D=1.999.

[0114] 3. Calculation of final friction velocity

[0115] ;

[0116] The friction velocity obtained from the preliminary calculation Multiplying this by the mixture term F yields the final frictional velocity. This result comprehensively considers the influence of various factors such as wind speed, wave period, wave direction, and atmospheric stability on the momentum transport of the air-sea boundary layer, thus more accurately reflecting the actual air-sea boundary layer momentum flux.

[0117] In summary, by obtaining specific wind speed, wind direction, wave direction, wave period, and stability measurement data, the flux in the same area can be converted using the method of this embodiment.

[0118] To verify the effectiveness of the method in this embodiment, flux data calculated based on the eddy covariance method and flux data calculated based on COARE36 are also provided.

[0119] 1. Flux data calculated based on the eddy covariance method

[0120] The eddy covariance method divides the measured quantity into average quantity and fluctuating quantity through Reynolds averaging. Then, it calculates the covariance between the concentration fluctuating quantity of different observed elements and the vertical wind speed component w fluctuating quantity to calculate the turbulent flux. Therefore, it is necessary to first calculate the covariance matrix by combining each component to obtain the covariance between each parameter and the vertical wind speed component w, as well as the mean of each component.

[0121] (1) Momentum flux Tau (N / m 2 The calculation formula is:

[0122] ;

[0123] in, Friction speed (m / s) can be expressed as:

[0124] ;

[0125] in, Let be the covariance of the u-component and w-component of the three-dimensional ultrasonic wind. Let V be the covariance between the V and W components of the three-dimensional ultrasonic wind.

[0126] ρ is the air density (kg / m³) 3 The following formula can be used to calculate the result:

[0127] ;

[0128] Where P is air pressure (Pa), T is air temperature (°C), and R is air pressure (Pa). d =287 J / mol / K is the gas constant, e is the saturated vapor pressure, and is calculated by the following formula:

[0129] ;

[0130] Where H2O is the water vapor density and Ts is the ultrasonic virtual temperature (°C).

[0131] (2) Sensitive heat flux H (W / m 2 This can be represented as:

[0132] ;

[0133] In the formula C represents the covariance of the ultrasonic virtual temperature Ts and the three-dimensional ultrasonic wind w component. p The specific heat at constant pressure can be calculated using the following formula:

[0134] ;

[0135] In the formula C pd =1004.67 (J / kg / K) is the specific heat at constant pressure of dry air, and q is the specific humidity, calculated by the following formula:

[0136] .

[0137] (3) Ultrasonic virtual temperature correction:

[0138] The initial sensible heat flux was calculated by subtracting the covariance between the ultrasonic imaginary temperature fluctuation and the vertical wind component. The ultrasound virtual temperature is obtained, but there is a certain deviation between the actual temperature and the virtual temperature, which needs to be verified. The final sensible heat flux H can be derived by reverse calculation:

[0139] ;

[0140] .

[0141] 2. Flux data calculated based on COARE36

[0142] COARE (Coupled Ocean-Atmosphere Response Experiment) 36 is a flux algorithm widely used in air-sea interaction research. Based on a series of physical parameterization schemes, it comprehensively considers various meteorological factors such as sea surface temperature, wind speed, and humidity, and uses complex formulas and algorithms to calculate momentum flux, heat flux, and water vapor flux at the air-sea interface. To calculate flux data using COARE 36, the following input data is required: sea surface temperature, wind speed, wind direction, atmospheric temperature and humidity, and atmospheric pressure (P).

[0143] The flux calculated based on the eddy covariance method was used as the true value, and compared with COARE36 and the proposed parameterization scheme. The results from August 29th to September 4th, 2024 (7 days in total) were analyzed. The evaluation index for the calculation results included the coefficient of determination (R²). 2 ), mean absolute error (MAE) and root mean square error (RMSE).

[0144] Coefficient of determination (R) 2 The value is used to measure the goodness of fit of the model to the observed data. The closer the value is to 1, the stronger the model's ability to interpret the data, that is, the higher the correlation between the calculated results and the true values.

[0145] ;

[0146] Where n is the total number of data points. The observed value (here referring to the true flux value calculated based on the eddy covariance method). This is the predicted value (the flux value recalculated by this parameterization scheme or COARE36). That is, the average of the observed values. Table 2 shows the coefficient of determination (R²) of friction velocity calculated by COARE36 and the method of this embodiment with respect to the observed values. 2 As can be seen from Table 2, the coefficient of determination (R²) of the method in this embodiment is higher than that in the 7-day data. 2 The results are all much greater than those of the COARE36 method, indicating that the calculation results of the method in this embodiment are more correlated with the true value.

[0147] Table 2

[0148]

[0149] The mean absolute error (MAE) reflects the magnitude of the average error between the predicted and actual values. The smaller the value, the closer the model's prediction is to the actual value.

[0150] ;

[0151] Where n is the total number of data points. The observed value (here referring to the true flux value calculated based on the eddy covariance method). The values ​​are predicted (flux values ​​recalculated by this parameterization scheme or COARE36). Table 3 shows a comparison of the mean absolute error (MAE) between the friction velocity calculated by COARE36 and the method of this embodiment and the observed values. As can be seen from Table 3, the mean absolute error (MAE) of the method of this embodiment is much smaller than that of the COARE36 method in the 7 days of data, indicating that the calculation results of the method of this embodiment are closer to the true values.

[0152] Table 3

[0153]

[0154] The root mean square error (RMSE) not only considers the average size of the error, but also measures the degree of fluctuation of the error. The smaller the value, the higher the stability and accuracy of the model prediction.

[0155] ;

[0156] Where n is the total number of data points. The observed value (here referring to the true flux value calculated based on the eddy covariance method). The values ​​are predicted (flux values ​​recalculated by this parameterization scheme or COARE36). Table 4 shows a comparison of the root mean square error (RMSE) of the friction velocity calculated by COARE36 and this scheme with the observed values. As can be seen from Table 4, the root mean square error (RMSE) of the method in this embodiment is much smaller than that of the COARE36 method in the 7-day data, indicating that the calculation results of the method in this embodiment are more stable and accurate.

[0157] Table 4

[0158]

[0159] The above embodiments are merely exemplary embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art can make various modifications or equivalent substitutions to the present invention within its scope and spirit, and such modifications or equivalent substitutions should also be considered to fall within the scope of protection of the present invention.

Claims

1. A method for calculating the momentum flux at the air-sea interface coupled with boundary layer meteorological conditions, characterized in that, Includes the following steps: Step 1: Threshold screening and outlier removal are performed on the turbulent flux elements required for calculation based on the eddy covariance method, and the coordinates of the three-dimensional wind speed are rotated. Step 2: Process the acquired sea surface undulation data to obtain the wave spectrum and wave parameters; Step 3: Calculate the Monin-Obukhov length, atmospheric stability, and 10-meter wind speed U at sea based on the Monin-Obukhov similarity theory. 10 ; Step 4: Based on the data obtained in Steps 1-3, the friction velocity is decomposed into a wind speed term and a wave mixture term for fitting, and finally the momentum flux is obtained. Friction speed in step 4 The specific calculation formula is as follows: ； ； ； ； Where F is a mixed term function of wave and atmospheric stability. The friction velocity is obtained from the preliminary calculation; A, B, C, and D are the fitting parameters. The wave effect term is represented by Tp, where Tp is the peak wave period and angle_off is the wind-wave angle. for The function that is influenced by atmospheric stability zoL, with k, m, and n as parameters, is used to characterize the modulation effect of atmospheric stability on the wave term.

2. The method for calculating air-sea interface momentum flux under coupled boundary layer meteorological conditions according to claim 1, characterized in that, Step 1 specifically includes: Step 1.1: Collect data on ultrasonic false temperature diagnostic values, infrared gas analyzer diagnostic values, water vapor concentration, CO2 concentration, CO2 signal intensity, H2O signal intensity, three-dimensional wind speed, air temperature, and air pressure parameters, and perform threshold filtering and outlier removal on the collected parameter data. Step 1.2: Perform a first rotation of the three-dimensional wind speed in the xy-plane around the z-axis, so that the xz-plane is aligned with the average wind direction, and the average components... Satisfaction = 0; Step 1.3: Rotate the xz plane obtained in Step 1.2 around the y-axis to make the average components... =0, so that the average wind speed u satisfies .

3. The method for calculating air-sea interface momentum flux under coupled boundary layer meteorological conditions according to claim 2, characterized in that, The outlier removal principle in step 1.1 is as follows: Calculate the difference between adjacent time series data for each parameter type within the 30-minute time period; calculate the difference Δx between adjacent time series data, and use Δx to obtain the overall standard deviation σΔx of the differences between adjacent points; compare all data differences with the standard deviation one by one; if a data point satisfies the formula: Δx ≥ 6 * σΔx, then directly remove that point; compare all data differences with the standard deviation one by one; if a data point satisfies the formula: Δx ≥ 3 * σΔx, then mark that point as an outlier; if 5 or more consecutive points are marked as outliers, then mark them as normal data; judge all outliers; data values ​​adjacent to an outlier that differ from the outlier by 30% are considered outliers; remove all outliers and perform linear interpolation to supplement them; if there are too many outliers within the 30-minute time period, directly remove that time period.

4. The method for calculating air-sea interface momentum flux under coupled boundary layer meteorological conditions according to claim 2, characterized in that, The specific calculation formula for step 3 is as follows: ； ； ； ； ； Where κ is the von Kármán constant. U is the friction speed. z Let z be the average wind speed at a height z above the sea surface, and z0 be the sea surface roughness. For stability general functions, This is a dimensionless profile formula, where L is the Moning-Obukhov length. where is the average air temperature; g is the acceleration due to gravity; The horizontal line represents the Reynolds average, and the apostrophe indicates the turbulent fluctuation of the physical quantity.

5. The method for calculating air-sea interface momentum flux under coupled boundary layer meteorological conditions according to claim 4, characterized in that, In step 4, momentum flux is represented by wind stress. The specific calculation formula is as follows: ； ； in, air density, This is the drag coefficient.

6. The method for calculating air-sea interface momentum flux under coupled boundary layer meteorological conditions according to claim 1, characterized in that, The The specific calculation formula is as follows: ； Where a, b, and c are fitting parameters, reflecting the 10-meter wind speed U at sea. 10 The basic relationship between friction speed and friction velocity.

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