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tangchao
310
sif_methods.py
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310
sif_methods.py
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import numpy as np
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from scipy.special import eval_legendre
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from scipy import optimize
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# 所有提取方法均基于xarray数据，xarray数据的变量与波长、时间、光谱仪绑定
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def cal_inside_bands_ave(data):
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'''
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根据多个光谱找出窗口内数据最低点对应波长
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'''
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sky_spec = data.sky
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veg_spec = data.veg
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wvl_inside_band_l = np.mean(veg_spec.idxmin(dim='Wavelength')).values
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wvl_inside_band_e = np.mean(sky_spec.idxmin(dim='Wavelength')).values
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return[wvl_inside_band_l,wvl_inside_band_e]
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def cal_outside_values_mean(data,outer):
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'''
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计算肩部窗口的均值
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'''
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_data = data.where((data.Wavelength>outer[0])&(data.Wavelength<outer[1]),drop=True)
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wvl_outer_mean = _data['Wavelength'].mean().values
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_mean = _data.mean(dim = 'Wavelength')
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E_out = _mean.sky.values
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L_out = _mean.veg.values
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return L_out,E_out,wvl_outer_mean
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def sfld(data,wl_range,outer):
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"""
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Standard FLD (Huaize Feng)
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input:
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data,xarray dataset
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wl_range, a window around Fraunhofer lines position, [start,end]
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outer, a window outside the Fraunhofer lines, [start,end]
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"""
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sif = []
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refl = []
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nmeas_ = data.Measures.size
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data = data.where((data.Wavelength>wl_range[0])&(data.Wavelength<wl_range[1]),drop=True)
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[wvl_inside_band_l,wvl_inside_band_e]=cal_inside_bands_ave(data)
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for i in range(0,nmeas_):
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_data = data.isel(Measures=i)
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veg_out,sky_out,_ = cal_outside_values_mean(_data,outer)
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veg_in = _data.veg.sel(Wavelength = wvl_inside_band_l,method='nearest').values
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sky_in = _data.sky.sel(Wavelength = wvl_inside_band_e,method='nearest').values
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_sif = (sky_out*veg_in - sky_in*veg_out)/(sky_out - sky_in)
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_refl = (veg_in - _sif)/ sky_in
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sif.append(_sif)
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refl.append(_refl)
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return[sif,refl]
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def fld3(data,wl_range,outer_left,outer_right):
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"""
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3FLD (Huaize Feng)
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input:
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data,xarray dataset
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wl_range, a window around Fraunhofer lines position, [start,end]
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outer_*, a window outside the Fraunhofer lines, [start,end]
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outer_left, left window outside the Fraunhofer lines
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outer_right, left window outside the Fraunhofer lines
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return:
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list[sif,reflectance]
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"""
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sif = []
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refl = []
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nmeas_ = data.Measures.size
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data = data.where((data.Wavelength>wl_range[0])&(data.Wavelength<wl_range[1]),drop=True)
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[wvl_inside_band_l,wvl_inside_band_e]=cal_inside_bands_ave(data)
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for i in range(0,nmeas_):
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_data = data.isel(Measures=i)
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veg_out_left,sky_out_left,wvl_outer_left = cal_outside_values_mean(_data,outer_left)
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veg_out_right,sky_out_right,wvl_outer_right = cal_outside_values_mean(_data,outer_right)
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veg_in = _data.veg.sel(Wavelength = wvl_inside_band_l,method='nearest').values
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sky_in = _data.sky.sel(Wavelength = wvl_inside_band_e,method='nearest').values
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# 根据离吸收峰的距离的反比进行赋权
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wight_left = (wvl_outer_right - wvl_inside_band_e)/(wvl_outer_right - wvl_outer_left)
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wight_right = (wvl_inside_band_e - wvl_outer_left)/(wvl_outer_right - wvl_outer_left)
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_sif = (veg_in - (sky_in/((wight_left*sky_out_left) + (wight_right*sky_out_right))) * ((wight_left*veg_out_left) + (wight_right*veg_out_right))) / (1-(sky_in / ((wight_left*sky_out_left) + (wight_right*sky_out_right))))
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_refl = (veg_in - _sif)/ sky_in
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sif.append(_sif)
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refl.append(_refl)
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return[sif,refl]
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def sfm(data,wl_range,band):
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"""
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Spectral Fitting Method (Huaize Feng)
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input:
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data,
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xarray dataset
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wl_range,[start,end]
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a window around Fraunhofer lines position, ,about 10 nm
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for fitting a ployniam or gussian function.
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band,float/int
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exact position of the Fraunhofer line
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return:
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list[sif,reflectance,rmse,B]
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sif, numpy array, sif at the Fraunhofer line for each measurement
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reflectance, numpy array
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rmse, RMSE
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B, numpy array, the parameters of the fitting equation
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[a,b,c,d,e,f]: a, b, c for polynimal refelectance
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d, float, MAX sif value [0,10] mw/m2/nm/sr
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e, position of MAX sif value - wl_range, [0,wavelength.size], nm
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f, full width at half maximum, [0,wavelength.size*5]
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"""
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sif,refl,rmse,B = [],[],[],[]
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data = data.where((data.Wavelength>wl_range[0])&(data.Wavelength<wl_range[1]),drop=True)
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abosorb_line_position = np.where(data.Wavelength == data.Wavelength.sel(Wavelength=760,method='nearest').values)
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_nmeas = data.Measures.size
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_nwvl = data.Wavelength.size
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_x = (data.Wavelength -np.min(data.Wavelength)).values
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poly_refl = [_x**2,_x,np.ones(_nwvl)]
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poly_sif = [_x**2,_x,np.ones(_nwvl)]
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for i in range(0,_nmeas):
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sky_spec = data.sky[i].values
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veg_spec = data.veg[i].values
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_X = np.concatenate([poly_refl*sky_spec,poly_refl]).T
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_B = np.linalg.lstsq(_X,veg_spec,rcond=-1)
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_sif = np.array(poly_sif).T.dot(_B[0][-3:])
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_refl = (veg_spec - _sif) / (sky_spec+0.000001)
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sif.append(_sif[abosorb_line_position][0])
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refl.append(_refl[abosorb_line_position][0])
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rmse.append(np.sqrt(np.sum(_B[1]**2)/_nwvl))
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B.append(_B[0])
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return [sif,refl,rmse,B]
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def f(x, a, b, c, d, e, f):
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sky_spec = x['sky_spec']
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_x = x['_x']
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refl = a * _x**2*sky_spec + b* _x*sky_spec + c*sky_spec
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sif = d*np.exp(-(_x-e)**2/f)
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y_hat = refl + sif
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return y_hat
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def f_cal(X, a,b,c,d,e,f):
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sky_spec = X['sky_spec']
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_x = X['_x']
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refl = a * _x**2*sky_spec + b* _x*sky_spec + c*sky_spec
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sif = d*np.exp(-(_x-e)**2/f)
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y_hat = refl + sif
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return sif,refl
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def sfm_gaussian(data,wl_range,band=760):
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'''
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Spectral Fitting Method (Gaussian Ver. (Huaize Feng))
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input:
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data,
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xarray dataset
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wl_range,[start,end]
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a window around Fraunhofer lines position, ,about 10 nm
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for fitting a polynomial or gaussian function.
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band,float/int
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exact position of the Fraunhofer line
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return:
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list[sif,reflectance,rmse,B]
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sif, numpy array, sif at the Fraunhofer line for each measurement
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reflectance, numpy array
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rmse, RMSE
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B, numpy array, the parameters of the fitting equation
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[a,b,c,d,e,f]: a, b, c for polynimal refelectance
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d, float, MAX sif value [0,10] mw/m2/nm/sr
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e, position of MAX sif value - wl_range, [0,wavelength.size], nm
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f, full width at half maximum
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'''
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sif,refl,rmse,B = [],[],[],[]
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data = data.where((data.Wavelength>wl_range[0])&(data.Wavelength<wl_range[1]),drop=True)
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abosorb_line_position = np.where(data.Wavelength == data.Wavelength.sel(Wavelength=band,method='nearest').values)
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_nmeas = data.Measures.size
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_nwvl = data.Wavelength.size
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_x = (data.Wavelength -np.min(data.Wavelength)).values
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poly_refl = [_x**2,_x,np.ones(_nwvl)]
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poly_sif = [_x**2,_x,np.ones(_nwvl)]
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bounds=((-np.inf, -np.inf,-np.inf, 0, 0, 0), (np.inf, np.inf,np.inf, 10, _nwvl, _nwvl*5))
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for i in range(0,_nmeas):
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sky_spec = data.sky[i].values
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veg_spec = data.veg[i].values
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_X = {'sky_spec':sky_spec,'_x':_x}
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_B = optimize.curve_fit(f, _X, veg_spec,bounds=bounds)[0]
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# print(_B)
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_sif,_ = f_cal(_X,*_B)
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# print(_sif)
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_rmse = np.sqrt(np.sum((f(_X,*_B)-veg_spec)**2)/_nwvl)
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_refl = (veg_spec - _sif) / sky_spec
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sif.append(_sif[abosorb_line_position][0])
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refl.append(_refl[abosorb_line_position][0])
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rmse.append( _rmse)
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B.append(_B[0])
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return [sif,refl,rmse,B]
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def doas(data,wl_range,band=760):
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"""
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Spectral Fitting Method (Huaize Feng)
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input:
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data,
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xarray dataset
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wl_range,[start,end]
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a window around Fraunhofer lines position, ,about 10 nm
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for fitting a ployniam or gussian function.
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band,float/int
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exact position of the Fraunhofer line
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return:
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list[sif,reflectance,rmse,B]
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sif, numpy array, sif at the Fraunhofer line for each measurement
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reflectance, numpy array
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rmse, RMSE
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B, numpy array, the parameters of the fitting equation
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[a,b,c,d,e,f]: a, b, c for polynimal refelectance
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d, float, MAX sif value [0,10] mw/m2/nm/sr
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e, position of MAX sif value - wl_range, [0,wavelength.size], nm
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f, full width at half maximum, [0,wavelength.size*5]
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"""
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sif,refl,rmse,B = [],[],[],[]
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data = data.where((data.Wavelength>wl_range[0])&(data.Wavelength<wl_range[1]),drop=True)
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absorb_line_position = np.where(data.Wavelength == data.Wavelength.sel(Wavelength=band,method='nearest').values)
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_nmeas = data.Measures.size
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_wvl = data.Wavelength.values
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_nwvl = _wvl.size
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_x = np.interp(_wvl, (_wvl.min(),_wvl.max()),(-1,1))
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# normalize standard SIF template by the mean value
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_hf = data.hf.values/(np.mean(data.hf.values))
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# create base function by legendre polynomial equations
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_ref_base = np.array([eval_legendre(n, _x) for n in np.arange(6)])
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for i in range(0,_nmeas):
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print(data.Measures[i].values)
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sky_spec = data.sky[i].values
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veg_spec = data.veg[i].values
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_X = np.concatenate([_ref_base,(_hf/(veg_spec+0.000001111)).reshape(1,-1)]).T
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_y = np.log(veg_spec+0.000001111) - np.log(sky_spec+0.00000111111)
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_B = np.linalg.lstsq(_X,_y,rcond=-1)
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_sif = _hf * _B[0][-1]
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_refl = (veg_spec - _sif) / (sky_spec+0.0000011111)
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sif.append(_sif[absorb_line_position][0])
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refl.append(_refl[absorb_line_position][0])
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rmse.append(np.sqrt(np.sum(_B[1]**2)/_nwvl))
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B.append(_B[0])
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return [sif,refl,rmse,B]
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def svd(data,wl_range,band=760,num_vector=20,pow_of_refl = 5):
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"""
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Singular Vector Decomposition (Huaize Feng)
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input:
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data,
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xarray dataset
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wl_range,[start,end]
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a window around Fraunhofer lines position, ,about 10 nm
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for fitting a polynomial or gaussian function.
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band,float/int
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exact position of the Fraunhofer line
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num_vector,int
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pca保留的观测维度（个数），相当于去除大气的噪音
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pow_of_refl,int
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反射率所用多项式的最高次数
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Highest power of the polynomial equation denoting reflectance
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return:
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list[sif,reflectance,rmse,B]
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sif, numpy array, sif at the Fraunhofer line for each measurement
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reflectance, numpy array
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rmse, RMSE
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B, numpy array, the parameters of the fitting equation
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[a,b,c,d,e,f]: a, b, c for polynimal refelectance
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d, float, MAX sif value [0,10] mw/m2/nm/sr
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e, position of MAX sif value - wl_range, [0,wavelength.size], nm
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f, full width at half maximum, [0,wavelength.size*5]
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"""
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sif,refl,rmse,B = [],[],[],[]
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data = data.where((data.Wavelength>wl_range[0])&(data.Wavelength<wl_range[1]),drop=True)
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abosorb_line_position = np.where(data.Wavelength == data.Wavelength.sel(Wavelength=band,method='nearest').values)
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_nmeas = data.Measures.size
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_wvl = data.Wavelength.values
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_nwvl = _wvl.size
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_hf = data.hf.values # 重采样后的标准sif
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u, s, vh = np.linalg.svd(data.sky) # Svd分解----------------------------------------------------------------------------------------------------
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v = -vh
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tmp1=(_wvl-np.mean(_wvl)).reshape(-1,1)
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tmp2=np.arange(pow_of_refl+1)
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p1 = np.power(tmp1, tmp2)*v[0].reshape(-1,1)
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p2 = np.power((_wvl-np.mean(_wvl)).reshape(-1,1), np.arange(pow_of_refl+1))*v[1].reshape(-1,1)
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p3 = v[:,2:num_vector]
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_X = np.concatenate([p1,p2,p3,_hf.reshape(-1,1)],axis=1)
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for i in range(0,_nmeas):
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sky_spec = data.sky[i].values
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veg_spec = data.veg[i].values
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_y = veg_spec
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_B = np.linalg.lstsq(_X,_y,rcond=-1) # https://www.zhihu.com/question/40540185?sort=created
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_sif = _hf * _B[0][-1]
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_refl = (veg_spec - _sif) / (sky_spec + 0.0000001)
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sif.append(_sif[abosorb_line_position][0])
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refl.append(_refl[abosorb_line_position][0])
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rmse.append(np.sqrt(np.sum(_B[1]**2)/_nwvl))
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B.append(_B[0])
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return [sif,refl,rmse,B]
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