489 lines
16 KiB
Python
489 lines
16 KiB
Python
import numpy as np
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import pandas as pd
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from scipy.optimize import curve_fit
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from scipy.signal import lombscargle, hilbert
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from sklearn.decomposition import PCA
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import sympy as sp
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from scipy.interpolate import interp1d
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from scipy.signal import lombscargle
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import os
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import glob
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from scipy.optimize import curve_fit
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import math
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from sklearn.decomposition import PCA
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import sympy as sp
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import matplotlib.pyplot as plt
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import seaborn as sns
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from matplotlib.patches import Patch
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from matplotlib.lines import Line2D
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from windrose import WindroseAxes
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from scipy.signal import lombscargle, find_peaks
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from itertools import permutations
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from itertools import product
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def get_top_peaks(pgram, ff, num_peaks=3):
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peaks, _ = find_peaks(pgram)
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peak_values = pgram[peaks]
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peak_frequencies = ff[peaks]
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sorted_indices = np.argsort(peak_values)[-num_peaks:][::-1] # 按照峰值从大到小排序
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top_peaks_frequencies = peak_frequencies[sorted_indices]
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top_peaks_values = peak_values[sorted_indices]
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return top_peaks_frequencies, top_peaks_values
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# 定义一个函数来计算 RSD
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def calculate_rsd(x, y, z):
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# todo: 由波数计算波长
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# lamde 垂直波长，只不过单位由10e-3 rad/m变为/km，值差不多
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λ1 = round(1 / ((x / 2.5) * 0.4), 2)
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λ2 = round(1 / ((y / 2.5) * 0.4), 2)
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λ3 = round(1 / ((z / 2.5) * 0.4), 2)
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# 计算均值
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mean = round(sum([λ1, λ2, λ3]) / 3, 2)
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# 计算相对标准差
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rsd1 = abs(round(((λ1 - mean) / λ1) * 100, 2))
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rsd2 = abs(round(((λ2 - mean) / λ2) * 100, 2))
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rsd3 = abs(round(((λ3 - mean) / λ3) * 100, 2))
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# 判断是否满足 RSD 小于 20%并返回结果和均值
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return rsd1 < 20 and rsd2 < 20 and rsd3 < 20, mean
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def calculate_n(Av, Au, Bu, Bv):
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# 计算 Fuv
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Fuv = Av * Au * np.cos(Bu - Bv)
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# 根据条件计算 n
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if Au > Av:
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n = 1
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elif Au < Av:
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if Fuv > 0:
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n = 0
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else: # Fuv <= 0
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n = 2
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else:
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raise ValueError("Au 和 Av 不应相等")
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return n
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def calculate_seta(Av, Au, Bu, Bv):
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# 计算 n
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n = calculate_n(Av, Au, Bu, Bv)
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# 计算 Fuv
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Fuv = Av * Au * np.cos(Bu - Bv)
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# 计算 arctan 部分
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arctan_value = np.atan2(2 * Fuv, Av**2 - Au**2) # 更通用，返回的角度范围是 ([-π, π])
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# arctan_value = np.atan(2 * Fuv / (Av ** 2 - Au ** 2)) # 返回的角度范围是 ([-π/2, π/2])
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# 计算 seta
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seta = round((1 / 2) * (n * np.pi + arctan_value), 2)
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return seta # 返回结果为弧度
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# 判断椭圆旋转方向
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def analyze_direction(df1, df2, seta_degrees):
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# 初始值
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# a = 0
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# b = 0
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# 计算元素
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element1 = df1.iloc[0, 1] * df1.iloc[1, 2] - \
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df1.iloc[0, 2] * df1.iloc[1, 1]
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element2 = df2.iloc[0, 1] * df2.iloc[1, 2] - \
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df2.iloc[0, 2] * df2.iloc[1, 1]
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# 判断 element1
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if element1 < 0:
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a = 1 # 表示顺时针，重力波向上传播
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else:
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a = -1
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# 判断 element2
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if element2 < 0:
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b = seta_degrees # 表示顺时针，水平传播方向与假设方向同，seta
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else:
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b = seta_degrees + 180 # 逆时针，seta+180
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return a, b
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# 计算u_v椭圆长短轴之比（先标准化椭圆，再计算最远距离最近距离之比）
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def calculate_axial_ratio(u_fit, v_fit):
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# 将 ucmp 和 vcmp 组成一个数据矩阵
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data_matrix = np.vstack((u_fit, v_fit)).T
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# 使用 PCA 进行主成分分析
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pca = PCA(n_components=2)
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transformed_data = pca.fit_transform(data_matrix)
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# 提取主成分
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principal_components = pca.components_
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# 计算每个数据点在标准椭圆上的坐标
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scaling_factors = np.linalg.norm(principal_components, axis=1)
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standardized_data = transformed_data / scaling_factors
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# 创建 DataFrame
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standardized_df = pd.DataFrame(standardized_data, columns=["PC1", "PC2"])
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# 获取第一列和第二列的最大值和最小值
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col1_max = standardized_df.iloc[:, 0].max()
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col1_min = standardized_df.iloc[:, 0].min()
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col2_max = standardized_df.iloc[:, 1].max()
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col2_min = standardized_df.iloc[:, 1].min()
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# 计算长短轴比值
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axial_ratio = (col1_max - col1_min) / (col2_max - col2_min)
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return axial_ratio
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def calculate_wave(data: pd.DataFrame, lat: float, g: float):
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height = data["alt"].values
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temp = data["temp"].values
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ucmp = data["u"].values
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vcmp = data["v"].values
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wcmp = data["wspeed"].values
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press = (data["press"].values) * 100 # 单位Pa
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coef_temp = np.polyfit(height, temp, 2)
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poly_temp = np.poly1d(coef_temp)
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coef_ucmp = np.polyfit(height, ucmp, 2)
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poly_ucmp = np.poly1d(coef_ucmp)
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coef_vcmp = np.polyfit(height, vcmp, 2)
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poly_vcmp = np.poly1d(coef_vcmp)
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coef_wcmp = np.polyfit(height, wcmp, 2)
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poly_wcmp = np.poly1d(coef_wcmp)
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residual_temp = temp - poly_temp(height)
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residual_ucmp = ucmp - poly_ucmp(height)
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residual_vcmp = vcmp - poly_vcmp(height)
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residual_wcmp = wcmp - poly_wcmp(height)
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ff = np.linspace(0.01, 25, 1000) # 横坐标范围
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pgram_temp = lombscargle(height, residual_temp, ff)
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pgram_ucmp = lombscargle(height, residual_ucmp, ff)
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pgram_vcmp = lombscargle(height, residual_vcmp, ff)
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# BEGIN CHANGE
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# BACK
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# todo: 我的频率等于垂直波数（单位10-3rad/m）？
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# main_frequency_temp = round(ff[np.argmax(pgram_temp)], 2)
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# main_frequency_ucmp = round(ff[np.argmax(pgram_ucmp)], 2)
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# main_frequency_vcmp = round(ff[np.argmax(pgram_vcmp)], 2)
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# # 由波数计算波长
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# λ1 = round(1 / ((main_frequency_temp / 2.5) * 0.4), 2)
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# λ2 = round(1 / ((main_frequency_ucmp / 2.5) * 0.4), 2)
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# λ3 = round(1 / ((main_frequency_vcmp / 2.5) * 0.4), 2)
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# mean = round(sum([λ1, λ2, λ3]) / 3, 2)
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# rsd_temp = abs(round(((λ1 - mean) / λ1) * 100, 2))
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# rsd_ucmp = abs(round(((λ2 - mean) / λ2) * 100, 2))
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# rsd_vcmp = abs(round(((λ3 - mean) / λ3) * 100, 2))
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# BACK
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# if not (rsd_temp < 20 and rsd_ucmp < 20 and rsd_vcmp < 20):
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# return []
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# begin new
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peaks_ucmp_frequencies, _ = get_top_peaks(pgram_ucmp, ff)
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peaks_vcmp_frequencies, _ = get_top_peaks(pgram_vcmp, ff)
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peaks_temp_frequencies, _ = get_top_peaks(pgram_temp, ff)
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# 获取所有可能的频率组合（9 种组合）
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combinations = list(product(peaks_ucmp_frequencies,
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peaks_vcmp_frequencies,
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peaks_temp_frequencies))
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result = "0" # 初始结果为 "0"
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for combo in combinations:
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x, y, z = combo # 获取每个组合的三个频率
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valid_rsd, mean = calculate_rsd(x, y, z) # 计算 RSD，并获取均值
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if valid_rsd: # 如果有任何组合满足 RSD 小于 20%，设置 result 为 "1"
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result = "1"
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break # 找到一个符合条件的组合后，退出循环，避免继续检查其他组合
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if result != "1":
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return []
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# end new
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# END CHANGE
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# 定义正弦波模型函数
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def sine_wave(height, A, B, omega):
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omega = 2 * np.pi / mean
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return A * np.sin(omega * height + B)
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def fit_sine_wave(height, data, mean):
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# 提供初始猜测值，例如 A=1, B=0, omega=2 * np.pi / mean
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initial_guess = [1, 0, 2 * np.pi / mean]
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# 设置参数的边界：A的下限为0（确保A为正值），B和omega没有边界限制
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bounds = ([0, -np.inf, -np.inf], [np.inf, np.inf, np.inf])
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# curve_fit 函数通过调整 sine_wave 函数的参数（A、B 和 omega）来最小化模型预测值与实际数据 data 之间的残差平方和。
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params, covariance = curve_fit(
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sine_wave, height, data, p0=initial_guess, bounds=bounds)
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return params
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# 对 u 风、v 风、温度扰动量进行拟合
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params_u = fit_sine_wave(height, residual_ucmp, mean) # 输出3个参数分别是振幅，相位，角频率
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u_fit = sine_wave(height, *params_u)
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params_v = fit_sine_wave(height, residual_vcmp, mean)
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v_fit = sine_wave(height, *params_v)
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params_T = fit_sine_wave(height, residual_temp, mean)
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T_fit = sine_wave(height, *params_T)
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params_w = fit_sine_wave(height, residual_wcmp, mean)
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w_fit = sine_wave(height, *params_w)
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# 将高度、u_fit、v_fit创建一个数据框df1
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df1 = pd.DataFrame({"Height": height, "u_fit": u_fit, "v_fit": v_fit})
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# 计算假设的水平传播方向
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rad_seta = calculate_seta(
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params_v[0], params_u[0], params_u[1], params_v[1]) # 输入、输出都为弧度
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# 转换为角度并保留2位小数
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seta_degrees = round(np.degrees(rad_seta), 2) # 38.41°
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# 计算水平风
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uh = u_fit * np.sin(seta_degrees * np.pi / 180) + \
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v_fit * np.cos(seta_degrees * np.pi / 180) # 水平风
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# temp = T_fit
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# 将高度、水平风、温度创建一个数据框df2
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df2 = pd.DataFrame({"Height": height, "uh": uh, "temp": T_fit})
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a, b = analyze_direction(df1, df2, seta_degrees) # 计算垂直、水平传播方向
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Axial_ratio = round(calculate_axial_ratio(u_fit, v_fit),
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2) # 计算长短轴之比并保留2位小数，后续计算本征频率会用到
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# 计算剩余几个参数
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# 常量
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# f = 1.32e-4 # rad/s
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# N = 2.13e-2 # 浮力频数，单位 rad/s
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# 根据站点纬度，计算惯性频率f
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ou = 7.27e-5 # 单位rad/s，地球自转频率
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# lat = 64.5
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f = 2 * ou * np.sin(lat * np.pi / 180)
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# print(f"f = {f:.3e} rad/s")
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# 求浮力频率N
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df3 = pd.DataFrame({"height": height, "temp": temp,
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"temp_bar": poly_temp(height)})
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Cp = 1005 # 单位：J/kgK
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df3["temp_bar_derivative"] = np.gradient(
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df3["temp_bar"], (df3["height"]) * 1000) # 求背景温度对高度的偏导
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gen = (g / temp) * (df3["temp_bar_derivative"] + (g / Cp))
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sqrt_gen = np.sqrt(np.abs(gen)) # np.sqrt()对列表求根号，np.sqrt()对数字求根号
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N = sqrt_gen.mean() # 计算平均值，得到浮力频率的均值
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# 1. 本征频率omega_upper
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omega_upper = sp.symbols("omega_upper")
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eq1 = sp.Eq(Axial_ratio, omega_upper / f)
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omega_upper = (sp.solve(eq1, omega_upper))[0]
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omega_upper = sp.N(omega_upper)
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# 求本征频率与惯性频率的比值
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w_f = omega_upper / f # todo:总是大于1
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# 本征周期
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zhou_qi = 2 * np.pi / omega_upper / 3600
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# 2. 垂直波长λ_z、水平波长λ_h
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# 垂直波数
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λ_z = mean # 保留两位小数
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# 在北半球，重力波向上传播，垂直波数k_z＜0
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if a == 1:
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k_z = -(2 * np.pi / λ_z / 1000)
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else:
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k_z = 2 * np.pi / λ_z / 1000
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# 水平波数
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k_h = sp.symbols("k_h")
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eq2 = sp.Eq(k_h**2, (omega_upper**2 - f**2) * (k_z**2) / N**2)
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k_h = sp.solve(eq2, k_h)
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k_h = [sol.evalf() for sol in k_h if sol.evalf() > 0][0]
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k_h = sp.N(k_h) # 正值
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# 在北半球，重力波向上传播，垂直波数k_h＜0
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if b > 180: # 说明水平传播方向与假定方向相反
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k_h = -k_h
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else:
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k_h = k_h
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λ_h = abs(round((2 * np.pi / k_h / 1000), 2)) # 水平波长，取绝对值，因为波数可能为负数
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# 纬向、经向水平波长λ_x, λ_y
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# λ_x = abs(λ_h * np.sin(b * np.pi / 180))
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# λ_y = abs(λ_h * np.cos(b * np.pi / 180))
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# 本征相速度
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c_x = omega_upper / (abs(k_h) * np.sin(b * np.pi / 180))
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c_y = omega_upper / (abs(k_h) * np.cos(b * np.pi / 180))
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c_z = omega_upper / k_z
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"""
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# 群速度
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C_gz = -((omega_upper ** 2 - f ** 2)) / (omega_upper * k_z)
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C_gh = sp.symbols('C_gh')
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eq3 = sp.Eq(C_gz / C_gh, sp.sqrt(omega_upper ** 2 - f ** 2) / N)
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C_gh = (sp.solve(eq3, C_gh))[0]
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C_gh = sp.N(C_gh) # 转成数值
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"""
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# 波动能E_k
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u2_mean = np.mean(np.square(u_fit))
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v2_mean = np.mean(np.square(v_fit))
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Ek = (1 / 2) * (u2_mean + v2_mean) # 3.11 J/kg
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# 势能E_p
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T_normalized = T_fit / poly_temp(height) # 归一化处理
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T2_mean = np.mean(np.square(T_normalized))
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E_p = ((g**2) * T2_mean) / (2 * (N**2)) # 1.02J/kg
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# 动量通量
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# 经、纬向风动量通量
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P = press # 单位Pa
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R = 287 # 单位：J/(kgK)，气体常量
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T = temp # 温度已经是开尔文
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densi = P / (R * T) # 向量
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c = (omega_upper * g) / (N**2)
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S = 1 - (f**2) / (omega_upper**2) # 常数
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# 归一化温度90°相位变换
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hilb = hilbert(T_normalized)
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hilb1 = np.imag(hilb) # 获取虚部作为90°相位变换的结果
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uT = u_fit * hilb1 # 向量
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uT1 = np.mean(uT) # 均值
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MFu = (np.mean(-densi * c * uT1 * S)) * 1000 # 单位mPa
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vT = v_fit * hilb1
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vT1 = np.mean(vT)
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MFv = (np.mean(-densi * c * vT1 * S)) * 1000
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# 调整动量通量符号与本征相速度符号一致
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# 调整b的符号与a一致
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MFu1 = abs(MFu) if c_x >= 0 else -abs(MFu)
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MFv1 = abs(MFv) if c_y >= 0 else -abs(MFv)
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omega_upper = float(omega_upper)
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# make wf, c_x, c_y, c_z, MFu, MFv, zhouqi float
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w_f = float(w_f)
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c_x = float(c_x)
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c_y = float(c_y)
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c_z = float(c_z)
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MFu1 = float(MFu1)
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MFv1 = float(MFv1)
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zhou_qi = float(zhou_qi)
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return [
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a,
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b,
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omega_upper,
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w_f,
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λ_z,
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λ_h,
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c_x,
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c_y,
|
||
c_z,
|
||
Ek,
|
||
E_p,
|
||
MFu1,
|
||
MFv1,
|
||
params_u[0],
|
||
params_v[0],
|
||
params_T[0],
|
||
ucmp,
|
||
vcmp,
|
||
temp,
|
||
height,
|
||
poly_ucmp,
|
||
poly_vcmp,
|
||
poly_wcmp,
|
||
poly_temp,
|
||
residual_ucmp,
|
||
residual_vcmp,
|
||
residual_temp,
|
||
u_fit,
|
||
v_fit,
|
||
T_fit,
|
||
uh,
|
||
zhou_qi,
|
||
]
|
||
|
||
|
||
def extract_wave(data: pd.DataFrame, lat: float, g: float):
|
||
wave = calculate_wave(
|
||
data[(data["alt"] >= 15) & (data["alt"] <= 25)], lat, g)
|
||
if len(wave) == 0:
|
||
return []
|
||
return [
|
||
wave[0],
|
||
wave[1],
|
||
round(wave[2], 6),
|
||
round(wave[3], 2),
|
||
round(wave[4], 2),
|
||
round(wave[5], 2),
|
||
round(wave[6], 2),
|
||
round(wave[7], 2),
|
||
round(wave[8], 3),
|
||
round(wave[9], 4),
|
||
round(wave[10], 4),
|
||
round(wave[11], 4),
|
||
round(wave[12], 4),
|
||
round(wave[13], 2),
|
||
round(wave[14], 2),
|
||
round(wave[15], 2),
|
||
round(wave[31], 2),
|
||
]
|
||
|
||
|
||
def is_terrain_wave(data: pd.DataFrame, lat: float, g: float):
|
||
wave = calculate_wave(
|
||
data[(data["alt"] >= 2) & (data["alt"] <= 10)], lat, g)
|
||
if len(wave) == 0:
|
||
return False
|
||
|
||
# 计算观测u风v风的均值，为后边合成背景速度
|
||
mean_ucmp = np.mean(wave[16]) # 11.34
|
||
mean_vcmp = np.mean(wave[17]) # 0.38
|
||
|
||
x1, y1 = mean_ucmp, mean_vcmp # 背景风的分量
|
||
x2, y2 = float(wave[6]), float(wave[7]) # 相速度的分量
|
||
# wave[18](wave[19])
|
||
|
||
"""
|
||
# 二阶拟合的u风v风
|
||
mean_ucmp = np.mean(poly_ucmp(height))
|
||
mean_vcmp = np.mean(poly_vcmp(height))
|
||
|
||
x1, y1 = mean_ucmp, mean_vcmp # 背景风的分量
|
||
x2, y2 = float(c_x), float(c_y) # 相速度的分量
|
||
"""
|
||
# 计算两个风的方向
|
||
direction1 = np.arctan2(y1, x1)
|
||
direction2 = np.arctan2(y2, x2)
|
||
# 转化为角度（该角度是以x轴逆时针旋转），取特殊值用于验证。
|
||
# direction1_degrees = np.degrees(direction1)
|
||
# direction2_degrees = np.degrees(direction2)
|
||
|
||
# 计算夹角（弧度）
|
||
angle_radians = np.abs(direction1 - direction2)
|
||
# 确保夹角在0到π之间
|
||
if angle_radians > np.pi:
|
||
angle_radians = 2 * np.pi - angle_radians
|
||
# 将夹角转换为度
|
||
angle_degrees = np.degrees(angle_radians)
|
||
|
||
# 判断是否超过150，或者165
|
||
if round(angle_degrees, 2) > 150:
|
||
return True
|
||
return False
|