# -*- coding: utf-8 -*- """ Generate membership functions for hydrometeor types based on scattering models. Construct Membership Beta Functions (MBFs) parameters for each hydrometeor type and fuzzy set based on scattering simulations (Dolan and Rutledge, 2009). Smaller b values means falloff is slower. Basic form of a Membership Beta Function is:: 1 --------------------- beta(x) = | |^b 1+ | ((x-m)/a)^2 | | | Where x = input data (Zh, Zdr, etc) m = center a = width b = slope Anticipate having 6 input data fields and 10 fuzzy sets (HID types):: Input data fields: HID types: Fuzzy set: ------------------- ---------- ---------- Z_h Drizzle 1 Z_dr Rain 2 K_dp Ice Crystals 3 LDR Aggregates 4 rho_hv Wet Snow 5 Temperature Vertical Ice 6 Low Density Graupel 7 High Density Graupel 8 Hail 9 Big Drops 10 Contact ------- Kyle C. Wiens Brenda Dolan bdolan@atmos.colostate.edu 26 April 2002. """ from __future__ import division from __future__ import print_function import numpy as np import pandas as pd import matplotlib.pyplot as plt import os # Beta function parameters stored in individual CSVs in separate directory CSV_DIR = os.sep.join([os.path.dirname(__file__), 'beta_function_parameters'])+'/' ################################ # Helper Functions Below ################################ def _get_beta_example(var, mbf_sets, field, i): """Internal beta function calculator""" return 1.0/(1.0 + (((var - mbf_sets[field]['m'][i]) / mbf_sets[field]['a'][i])**2)**mbf_sets[field]['b'][i]) def plot_beta_functions(mbf_sets, band, temp_factor, pdir='./', n_types=10): """ Optional plotting routine that produces basic beta function curves for every hydrometeor species mbf_sets = Membership beta function sets band = 'X', 'C' or 'S' temp_factor = Factor to modify depth of T effects fdir = Path to plot locations n_types = Number of hydrometeor species """ label = ['Drizzle', 'Rain', 'Ice_Crystals', 'Aggregates', 'Wet_Snow', 'Vertical_Ice', 'Low-Density_Graupel', 'High-Density_Graupel', 'Hail', 'Big_Drops'] # 'Large_Hail','SmHail_Rain','LgHail_Rain'] # DUMMY ARRAYS TO PLOT OVER dz = np.arange(701)/10. zdr = -2.0 + np.arange(801)/100. kdp = -2.0 + np.arange(901)/100. ldr = -60.0 + np.arange(5900)/100. rho_hv = 0.75 + np.arange(2501)/10000. T = -50. + np.arange(1001)/10. for i in range(n_types): dz_beta = _get_beta_example(dz, mbf_sets, 'Zh_set', i) kdp_beta = _get_beta_example(kdp, mbf_sets, 'Kdp_set', i) zdr_beta = _get_beta_example(zdr, mbf_sets, 'Zdr_set', i) ldr_beta = _get_beta_example(ldr, mbf_sets, 'LDR_set', i) rho_beta = _get_beta_example(rho_hv, mbf_sets, 'rho_set', i) T_beta = _get_beta_example(T, mbf_sets, 'T_set', i) fig, ax = plt.subplots(3, 2, figsize=(8, 5)) fig.subplots_adjust(top=0.90, bottom=0.1, left=0.05, right=0.95, hspace=0.45) ax = ax.flatten() fig.suptitle('%s band %s, temp_factor: %.1f' % (band, label[i], temp_factor)) ax[0].plot(dz, dz_beta, linewidth=2) ax[0].set_title('dBZ') ax[1].plot(kdp, kdp_beta, linewidth=2) ax[1].set_title('Kdp') ax[2].plot(zdr, zdr_beta, linewidth=2) ax[2].set_title('Zdr') ax[3].plot(ldr, ldr_beta, linewidth=2) ax[3].set_title('LDR') ax[3].set_ylim(0, 1) ax[4].plot(rho_hv, rho_beta, linewidth=2) ax[4].set_title(r'$\rho$$_{hv}$') ax[5].plot(T, T_beta, linewidth=2) ax[5].set_title('T') plt.savefig(pdir+'%s_beta_%s.png' % (label[i], band)) plt.close() def get_beta_set(filename, factor=1.0): """ Function to read the CSVs that contain the beta function parameters for each variable and frequency band filename = Name of file factor = Modifier to effect of variable (normally only used for T) """ beta_parameters = pd.read_csv(filename, index_col=0) set_values = {} for label in ['m', 'a', 'b']: set_values[label] = np.array(beta_parameters.loc[:, label]) / factor return set_values ################################ def get_mbf_sets_winter(use_temp=False, plot_flag=False, n_types=2, temp_factor=1, band='S', fdir=CSV_DIR, verbose=False, pdir='./'): """ Define structures to hold the beta function parameters for each input variable and fuzzy set. Valid for summer precip. HID types: Fuzzy set: ------------------------------- other 1 ML 2 Arguments: use_temp = Flag to create T beta function sets plot_flag = Flag to turn on optional beta function plots band = 'C' or 'S' temp_factor = Factor to modify depth of T effects; > 1 will broaden the slopes of T MBFs fdir = Path to CSV locations n_types = Number of hydrometeor species verbose = Set to True to get text updates pdir = Directory to stash beta function plots (if made) Returns: mbf_sets = Membership beta function sets """ me = '-->get_mbf_sets_winter ' if verbose: print(me + ' 2 Category ML %s-band HID' % band) # Horizontal Reflectivity (Zh) fname = band + '-band_Reflectivity_winter.csv' Zh_set = get_beta_set(fdir+fname) # Differential Reflectivity (Zdr) fname = band + '-band_Differential_Reflectivity_winter.csv' Zdr_set = get_beta_set(fdir+fname) # Specific Differential Phase (Kdp) fname = band + '-band_Specific_Differential_Phase_winter.csv' Kdp_set = get_beta_set(fdir+fname) # Linear depolarization ratio (LDR) fname = band + '-band_Linear_Depolarization_Ratio_winter.csv' LDR_set = get_beta_set(fdir+fname) # Correlation coefficient at zero lag (rho) fname = band + '-band_Correlation_Coefficient_winter.csv' rho_set = get_beta_set(fdir+fname) # Temperature (T) if use_temp: fname = band + '-band_Temperature_winter.csv' T_set = get_beta_set(fdir+fname, factor=temp_factor) if verbose: print(me+'Using Temperature in HID') else: T_set = None if verbose: print(me+'No Temperature used in HID') # Now populate the full mbf_sets dictionary mbf_sets = {'Zh_set': Zh_set, 'Zdr_set': Zdr_set, 'Kdp_set': Kdp_set, 'LDR_set': LDR_set, 'rho_set': rho_set, 'T_set': T_set} if plot_flag: plot_beta_functions(mbf_sets, band, temp_factor, pdir=pdir, n_types=n_types) return mbf_sets def get_mbf_sets_winterML(use_temp=False, plot_flag=False, n_types=2, temp_factor=1, band='S', fdir=CSV_DIR, verbose=False, pdir='./'): """ Define structures to hold the beta function parameters for each input variable and fuzzy set. Valid for summer precip. HID types: Fuzzy set: ------------------------------- other 1 ML 2 Arguments: use_temp = Flag to create T beta function sets plot_flag = Flag to turn on optional beta function plots band = 'C' or 'S' temp_factor = Factor to modify depth of T effects; > 1 will broaden the slopes of T MBFs fdir = Path to CSV locations n_types = Number of hydrometeor species verbose = Set to True to get text updates pdir = Directory to stash beta function plots (if made) Returns: mbf_sets = Membership beta function sets """ me = '-->get_mbf_sets_summer ' if verbose: print(me + ' 2 Category ML %s-band HID' % band) # Horizontal Reflectivity (Zh) fname = band + '-band_Reflectivity_ML.csv' Zh_set = get_beta_set(fdir+fname) # Differential Reflectivity (Zdr) fname = band + '-band_Differential_Reflectivity_ML.csv' Zdr_set = get_beta_set(fdir+fname) # Specific Differential Phase (Kdp) fname = band + '-band_Specific_Differential_Phase_ML.csv' Kdp_set = get_beta_set(fdir+fname) # Linear depolarization ratio (LDR) fname = band + '-band_Linear_Depolarization_Ratio_ML.csv' LDR_set = get_beta_set(fdir+fname) # Correlation coefficient at zero lag (rho) fname = band + '-band_Correlation_Coefficient_ML.csv' rho_set = get_beta_set(fdir+fname) # Temperature (T) if use_temp: fname = band + '-band_Temperature_ML.csv' T_set = get_beta_set(fdir+fname, factor=temp_factor) if verbose: print(me+'Using Temperature in HID') else: T_set = None if verbose: print(me+'No Temperature used in HID') # Now populate the full mbf_sets dictionary mbf_sets = {'Zh_set': Zh_set, 'Zdr_set': Zdr_set, 'Kdp_set': Kdp_set, 'LDR_set': LDR_set, 'rho_set': rho_set, 'T_set': T_set} if plot_flag: plot_beta_functions(mbf_sets, band, temp_factor, pdir=pdir, n_types=n_types) return mbf_sets def get_mbf_sets_summerML(use_temp=False, plot_flag=False, n_types=2, temp_factor=1, band='S', fdir=CSV_DIR, verbose=False, pdir='./'): """ Define structures to hold the beta function parameters for each input variable and fuzzy set. Valid for summer precip. def get_mbf_sets_winter(use_temp=False, plot_flag=False, n_types=2, temp_factor=1, band='S', fdir=CSV_DIR, verbose=False, pdir='./'): Define structures to hold the beta function parameters for each input variable and fuzzy set. Valid for summer precip. HID types: Fuzzy set: ------------------------------- other 1 ML 2 Arguments: use_temp = Flag to create T beta function sets plot_flag = Flag to turn on optional beta function plots band = 'C' or 'S' temp_factor = Factor to modify depth of T effects; > 1 will broaden the slopes of T MBFs fdir = Path to CSV locations n_types = Number of hydrometeor species verbose = Set to True to get text updates pdir = Directory to stash beta function plots (if made) Returns: mbf_sets = Membership beta function sets """ me = '-->get_mbf_sets_summerML ' if verbose: print(me + ' 2 Category ML %s-band HID' % band) # Horizontal Reflectivity (Zh) fname = band + '-band_Reflectivity_winter.csv' Zh_set = get_beta_set(fdir+fname) # Differential Reflectivity (Zdr) fname = band + '-band_Differential_Reflectivity_winter.csv' Zdr_set = get_beta_set(fdir+fname) # Specific Differential Phase (Kdp) fname = band + '-band_Specific_Differential_Phase_winter.csv' Kdp_set = get_beta_set(fdir+fname) # Linear depolarization ratio (LDR) fname = band + '-band_Linear_Depolarization_Ratio_winter.csv' LDR_set = get_beta_set(fdir+fname) # Correlation coefficient at zero lag (rho) fname = band + '-band_Correlation_Coefficient_winter.csv' rho_set = get_beta_set(fdir+fname) # Temperature (T) if use_temp: fname = band + '-band_Temperature_winter.csv' T_set = get_beta_set(fdir+fname, factor=temp_factor) if verbose: print(me+'Using Temperature in HID') else: T_set = None if verbose: print(me+'No Temperature used in HID') # Now populate the full mbf_sets dictionary mbf_sets = {'Zh_set': Zh_set, 'Zdr_set': Zdr_set, 'Kdp_set': Kdp_set, 'LDR_set': LDR_set, 'rho_set': rho_set, 'T_set': T_set} if plot_flag: plot_beta_functions(mbf_sets, band, temp_factor, pdir=pdir, n_types=n_types) return mbf_sets def get_mbf_sets_summer(use_temp=True, plot_flag=False, n_types=10, temp_factor=1, band='S', fdir=CSV_DIR, verbose=False, pdir='./'): """ Define structures to hold the beta function parameters for each input variable and fuzzy set. Valid for summer precip. HID types: Fuzzy set: ------------------------------- Drizzle 1 Rain 2 Ice Crystals 3 Aggregates 4 Wet Snow 5 Vertical Ice 6 Low-Density Graupel 7 High-Density Graupel 8 Hail 9 Big Drops 10 Arguments: use_temp = Flag to create T beta function sets plot_flag = Flag to turn on optional beta function plots band = 'C' or 'S' temp_factor = Factor to modify depth of T effects; > 1 will broaden the slopes of T MBFs fdir = Path to CSV locations n_types = Number of hydrometeor species verbose = Set to True to get text updates pdir = Directory to stash beta function plots (if made) Returns: mbf_sets = Membership beta function sets """ me = '-->get_mbf_sets_summer ' if verbose: print(me + ' 10 Category Summer %s-band HID' % band) # Horizontal Reflectivity (Zh) fname = band + '-band_Reflectivity.csv' Zh_set = get_beta_set(fdir+fname) # Differential Reflectivity (Zdr) fname = band + '-band_Differential_Reflectivity.csv' Zdr_set = get_beta_set(fdir+fname) # Specific Differential Phase (Kdp) fname = band + '-band_Specific_Differential_Phase.csv' Kdp_set = get_beta_set(fdir+fname) # Linear depolarization ratio (LDR) fname = band + '-band_Linear_Depolarization_Ratio.csv' LDR_set = get_beta_set(fdir+fname) # Correlation coefficient at zero lag (rho) fname = band + '-band_Correlation_Coefficient.csv' rho_set = get_beta_set(fdir+fname) # Temperature (T) if use_temp: fname = band + '-band_Temperature.csv' T_set = get_beta_set(fdir+fname, factor=temp_factor) if verbose: print(me+'Using Temperature in HID') else: T_set = None if verbose: print(me+'No Temperature used in HID') # Now populate the full mbf_sets dictionary mbf_sets = {'Zh_set': Zh_set, 'Zdr_set': Zdr_set, 'Kdp_set': Kdp_set, 'LDR_set': LDR_set, 'rho_set': rho_set, 'T_set': T_set} if plot_flag: plot_beta_functions(mbf_sets, band, temp_factor, pdir=pdir, n_types=n_types) return mbf_sets ################################ if __name__ == '__main__': a = cdf_betas_sum(plot_flag=True, use_temp=True, temp_factor=2, band='C')