wolfhece.eva.pyseries

EXTREME VALUES ANALYSIS - EVA

@author : Pierre Archambeau - ULiege - HECE @date : 2023

Module Contents

wolfhece.eva.pyseries.change_font_size(ax: matplotlib.axes.Axes, fontsize)

Adapte la taille de police d’un graphique

wolfhece.eva.pyseries.set_style(color: Literal[b, g, r, c, m, y, k], linestyle: Literal[solid, dotted, deshed, dashdot] = 'solid', linewidth=1) → dict['color':str, 'linestyle':str, 'linewidth':int]

wolfhece.eva.pyseries.get_style(style: dict['color':str, 'linestyle':str, 'linewidth':int])

wolfhece.eva.pyseries.cunnane(r, n)

Calcul de la fréquence empirique selon Cunnane(1979) MAJ de la formulation de Weibull a priori mieux adaptée aux problèmes hydrologiques

r : rang de la donnée 1<=r<=n n : nombre total de données dans l’échantillon

wolfhece.eva.pyseries.weibull(r, n)

Calcul de la fréquence empirique selon Weibull - loi “uniforme”

r : rang de la donnée 1<=r<=n n : nombre total de données dans l’échantillon

wolfhece.eva.pyseries.filliben(r, n)

Calcul de la fréquence empirique selon Filliben

r : rang de la donnée 1<=r<=n n : nombre total de données dans l’échantillon

wolfhece.eva.pyseries.aic(mle, n, k=2, corrected=True)

The Akaike information criterion (AIC) is a metric that is used to compare the fit of different regression models.

It is calculated as:

AIC = 2K – 2ln(L)

where:

K: The number of model parameters (including loc and scale) mle = ln(L): The log-likelihood of the model. This tells us how likely the model is, given the data.

https://fr.wikipedia.org/wiki/Crit%C3%A8re_d%27information_d%27Akaike https://www.statology.org/aic-in-python/

wolfhece.eva.pyseries.bic(mle, n, k=2)

the Bayesian information criterion (BIC) or Schwarz information criterion (also SIC, SBC, SBIC) is a criterion for model selection among a finite set of models Models with lower BIC are generally preferred. It is based, in part, on the likelihood function and it is closely related to the Akaike information criterion (AIC).

https://en.wikipedia.org/wiki/Bayesian_information_criterion https://fr.wikipedia.org/wiki/Crit%C3%A8re_d%27information_bay%C3%A9sien

wolfhece.eva.pyseries._get_hist_params(X, bins, mhist='numpy')

Get histogram of original data

wolfhece.eva.pyseries.rss(data, pdf, bins=100)

Residual sum of squares

based on pdf and data’s histogram

https://en.wikipedia.org/wiki/Residual_sum_of_squares

wolfhece.eva.pyseries._generate_clusters(exceedances: pandas.Series, r: pandas.Timedelta | Any) → Generator[pandas.Series, None, None]

wolfhece.eva.pyseries.MONTHS_WINTER = [10, 11, 12, 1, 2, 3]

wolfhece.eva.pyseries.MONTS_SUMMER = [4, 5, 6, 7, 8, 9]

wolfhece.eva.pyseries.SEASONS = ['annual', 'winter', 'summer']

wolfhece.eva.pyseries.SEASONS_MARKERS = ['o', '*', 'x', '2']

wolfhece.eva.pyseries.SEASONS_COLORS = ['r', 'g', 'b', 'c']

wolfhece.eva.pyseries.SEASONS_ALL

wolfhece.eva.pyseries.RETURN_PERIOD_ESTIMATE

wolfhece.eva.pyseries.INTERV_CI = [60, 75, 90, 95]

wolfhece.eva.pyseries.sanitize_seasons(seasons=None, all=False)

wolfhece.eva.pyseries.dists_4params

wolfhece.eva.pyseries.dists_3params

wolfhece.eva.pyseries.dists_2params

wolfhece.eva.pyseries.LAWS_FULL

wolfhece.eva.pyseries.LAWS_POPULAR = ['GEV', 'Log normale', 'Gumbel', 'Exponentielle', 'Pearson3', 'Gamma inverse', 'Weibull',...

class wolfhece.eva.pyseries.EVA_Serie(data, datetime_index=None, datetime_format='%Y%m%d%H%M%S', data_headers=('#DateHeure', 'Debit'), duration=1, startmonth_winter=10, startmonth_summer=4, hydrol=True, verbose=True)

One time serie

check_dupliactes()

Check if there are duplicates in the data

filter()

Set zero, negative, NaN, Nat to np.nan

get_date_max(year, seasons=None) → list

Récupère la date du maximum de l’année “year” Possibilité de traiter plusieurs saisons

get_one_maxevent(year, seasons=None) → list

Récupération de l’événement max pour une année spécifique Possibilité de traiter plusieurs saisons

get_nb_maxevents(nbevents: int, seasons=None) → dict[str, pandas.DataFrame]

Récupère les nbevents lus grands pics de crue

get_nb_max_hydro(nbevents: int, seasons=None) → dict[str, pandas.DataFrame]

Récupère les nbevents plus grands hydrogrammes de crue

save_max_events(filename, years_bounds: list = None, seasons=None)

Enregistrement des crues maximales dans un fichier CSV

_select_dict(method: Literal[BM, POT] = 'BM')

_get_dates(year=None, hydrol=True, season=None)

Compute date for current year and season

Parameters:

• year (integer, optional) – If None, the complete interval will be used. Defaults to None.

• hydrol (bool, optional) – Hydrological year or not. Defaults to True.

• season ('annual', 'winter' or 'summer', optional) – None == ‘annual’. Defaults to None.

_get_max(year=None, hydrol=True, season=None, method: Literal[BM, POT] = 'BM', threshold=0.0, r: pandas.Timedelta | Any = '24H')

Find maxima in specific period

get_data_for_one_season(method: Literal[BM, POT] = 'BM', season=None)

get_fit_one_season(method: Literal[BM, POT] = 'BM', season=None)

save_fit_one_season(filename: str, method: Literal[BM, POT] = 'BM', season=None, fit_method='MLE', sep=';')

find_maxima(hydrol=True, excluded_years=[], method: Literal[BM, POT] = 'BM', threshold: float = 0.0, r: pandas.Timedelta | Any = '24H', verbose=True)

Find maxima in whole data

extract_oneevent(datecenter, before=1, after=2)

Extract hydrograph around a date

Parameters:

• before – number of days before center

• after – number of days after center

extract_maxevents(before=1, after=2)

Extract hydrograph for each maximum

Parameters:

• before – number of days before maximum

• after – number of days after maximum

sort_maxima(seasons=None)

Sort maxima in increasing order to calculate empirical frequency

_fit_multistarts(data, fdist, nb=0, method='MLE')

Fit de la loi en adaptant éventuellement le point de départ Ceci n’est sans doute réellement utile que pour la loi de Weibull

_evaluate_ci(data, fdist, nboot=500, method='MLE')

Evaluate confidence interval based on bootstrap method

REMARK : CI for MLE can be analyzed by Fisher coefficients

get_fitted_params(season=None, law='GEV', method='MLE')

get_T_from_q(q: list, season: str = 'best', law: str = 'best', method: str = 'MLE', ic=False) → pandas.DataFrame

get_q_from_T(return_periods: list = [5, 10, 15, 20, 25, 50, 75, 100, 200, 500, 1000], season: str = 'best', law: str = 'best', method: str = 'MLE', ic=False) → pandas.DataFrame

save_q_from_T(filename: str = '', return_periods=[5, 10, 15, 20, 25, 50, 75, 100, 200, 500, 1000], season='best', law='best', method='MLE', ic=False)

save_T_from_q(filename: str = '', q=[5, 10, 15, 20, 25, 50, 75, 100, 200, 500, 1000], season='best', law='best', method='MLE', ic=False)

fit(seasons=None, laws=['GEV'], init_EVA=None, methods=['MLE'], ic=False, nboot=100, verbose=True)

Fitting of selected laws

select_best_func(season, law, method)

Select one function as best fit

distfit(seasons=None, laws='popular', smooth=0, bins=100)

Laws can be ‘full’, ‘popular’

* Be carefull, fit of law is based on default scipy.stats parames. In our implementation, non-default initial conditions are used for specific laws, including GEV. *

https://erdogant.github.io/distfit/pages/html/Parametric.html https://erdogant.github.io/distfit

set_mixture(laws=['GEV'], methods=['MLE'])

Set mixture model based on “50-50” “winter-summer” fitted models

set_joint(laws=['GEV'], methods=['MLE'])

Set joint model based on product probability of fitted models

set_empfreq(seasons=None)

Compute empirical frequency based on sorted maxima

compute_median_event(seasons=None, before: int = 1, after: int = 2)

Evaluation de la crue mediane Stockage dans “self.maxima[curseason][‘median_event’]”

get_median_event(seasons=None, before=1, after=2) → dict[str, pandas.DataFrame]

Get median hydrograph

plot_median_event(scale: float, seasons=None, before=1, after=2, fig: matplotlib.figure.Figure = None, ax: matplotlib.axes.Axes = None, color: str = 'red', alpha=1.0) → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes]

Plot median hydrograph scale by constant

plot_classified_flowrate_curve(fig: matplotlib.figure.Figure = None, ax: matplotlib.axes.Axes = None, label='', textvalues=True, show=False) → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes]

plot_distfit(seasons=None, n_top=20, show=False)

Plots of distfit module

plot_ci(seasons=None, laws=['GEV'], methods=['MLE'], fig: matplotlib.figure.Figure = None, ax: matplotlib.axes.Axes = None, show=False, alpha=0.1) → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes]

Plotting confidence interval

plot_annual(years=None, hydrol=True, fig: matplotlib.figure.Figure = None, ax: matplotlib.axes.Axes = None, show=False, withdatemax=True) → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes]

Tracé en superposition des différentes années sur l’emprise d’une année civile ou hydrologique

plot_serie(fig: matplotlib.figure.Figure = None, ax: matplotlib.axes.Axes = None, show=False, background=True, backcolor='lemonchiffon') → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes]

Tracé de l’ensemble de la série pour toutes les années

plot_cdf(seasons=None, fig: matplotlib.figure.Figure = None, ax: matplotlib.axes.Axes = None, show=False, n_bins=100) → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes]

Plotting empirical cdf

plot_T_Qmaxima(seasons=None, empirical_func='Cunnane', fig: matplotlib.figure.Figure = None, ax: matplotlib.axes.Axes = None, show=False, alpha=1.0, color_marker_label=None) → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes]

Plotting Q vs return period

plot_maxevents(seasons=None, before=1, after=2, adim=True, fig: matplotlib.figure.Figure = None, ax: matplotlib.axes.Axes = None, show=False, alpha=0.2, nbevents=None) → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes]

Tracé des événements/hydrogrammes associés aux maxima identifiés Les ordonnées sont adimensionnaliées sur base de la valeur maximale

plot_comp_maxevents(seasons=None, before=1, after=2, fig: matplotlib.figure.Figure = None, ax: matplotlib.axes.Axes = None, show=False, alpha=0.2, nbevents=None) → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes]

Tracé des événements médians Les ordonnées sont adimensionnaliées sur base de la valeur maximale

plot_one_event(datecenter, before=1, after=2, adim=True, color='k', fig: matplotlib.figure.Figure = None, ax: matplotlib.axes.Axes = None, show=False, alpha=0.2) → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes]

Tracé d’un événement quelconque autour d’une date

plot_one_maxevents(season, year, before=1, after=2, adim=True, color='k', fig: matplotlib.figure.Figure = None, ax: matplotlib.axes.Axes = None, show=False, alpha=0.2) → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes]

Tracé d’un événement spécifique associés au maxima identifié Les ordonnées sont adimensionnaliées sur base de la valeur maximale

plot_fit(seasons=None, laws=['GEV'], methods=['MLE'], fig: matplotlib.figure.Figure = None, ax: matplotlib.axes.Axes = None, show=False, alpha=1.0, styles: dict = None) → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes]

Plotting fitted models

plot_qq(seasons=None, laws=['GEV'], methods=['MLE'], fig: matplotlib.figure.Figure = None, ax: matplotlib.axes.Axes = None) → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes]

Q-Q Plot

Comparaison de la valeur théorique avec la mesure (attention scipy.probploit n’utilise pas Cunnane mais Filliben cf https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.probplot.html)

plot_summary(seasons=None, nb_laws=None, forced_laws=[], sort: Literal[RSS, AICc, AIC, BIC] = 'RSS', fig: matplotlib.figure.Figure = None, ax: matplotlib.axes.Axes = None, show=False) → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes]

Plot summary results.

Parameters:

• n_top (int, optional) – Show the top number of results. The default is None.

• figsize (tuple, optional (default: (10,8))) – The figure size.

• ylim (Float, optional (default: None)) – Limit figure in y-axis.

• fig (Figure, optional (default: None)) – Matplotlib figure

• ax (Axes, optional (default: None)) – Matplotlib Axes object

Return type:

tuple (fig, ax)

summary_max(seasons=None)

class wolfhece.eva.pyseries.EVA_Series(data, datetime_index=None, datetime_format='%Y%m%d%H%M%S', data_headers=('#DateHeure', 'Debit'), startmonth_winter=10, startmonth_summer=4, hydrol=True)

activate_serie(key: int = 1)

plot_T_Qmaxima(seasons=None, empirical_func='Cunnane', fig: matplotlib.figure.Figure = None, ax: matplotlib.axes.Axes = None, show=False, alpha=1.0, color_marker_label=None) → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes]

plot_fit(seasons=None, laws=['GEV'], methods=['MLE'], fig: matplotlib.figure.Figure = None, ax: matplotlib.axes.Axes = None, show=False, alpha=1.0, styles: dict = None) → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes]

get_q_from_T(return_periods: list = [5, 10, 15, 20, 25, 50, 75, 100, 200, 500, 1000], season: str = 'best', law: str = 'best', method: str = 'MLE', ic=False) → pandas.DataFrame

get_T_from_q(q: list, season: str = 'best', law: str = 'best', method: str = 'MLE', ic=False) → pandas.DataFrame

save_q_from_T(filename: str = '', return_periods=[5, 10, 15, 20, 25, 50, 75, 100, 200, 500, 1000], season='best', law='best', method='MLE', ic=False)

save_T_from_q(filename: str = '', q=[5, 10, 15, 20, 25, 50, 75, 100, 200, 500, 1000], season='best', law='best', method='MLE', ic=False)

get_serie(key=1) → EVA_Serie

find_maxima(excluded_years=[], hydrol=True, method: Literal[BM, POT] = 'BM', threshold: float = 0.0, r: pandas.Timedelta | Any = '24H', verbose=True)

Recherche des maxima pour toutes les saisons et toutes les durées

create_all_durations(durations=[1], verbose=True)

Création des chroniques pour toutes les durées souhaitées [heures]

bake_data(durations=[1], excluded_years=[], hydrol=True, method: Literal[BM, POT] = 'BM', threshold: float = 0.0, r: pandas.Timedelta | Any = '24H', verbose=True)

plot_series(durations=None, oneyear=True, show=False, background=True, backcolor='lemonchiffon')

Viauslaisation des chroniques

plots_spw(stationcode: str, fontsize: int = 12, width=20, height=10, durations=[1], backcolor='lemonchiffon')

eva(durations=[1], laws='popular', hydrol=True, excluded_years=[], plot=True, method: Literal[BM, POT] = 'BM', threshold: float = 0.0, r: pandas.Timedelta | Any = '24H', verbose=True, show=False) → dict[str, tuple]

Extreme Value Analysis

durations : (list) durations in hours - default [1] laws : (str) laws to fit - default ‘GEV’ hydrol : (bool) use hydrological year - default True excluded_years : (list) years to exclude plot : (bool) creation of different plots method : (str) selection of maxima - default ‘BM’ == Block Maxima

return : dict of tuples (fig,axes) of the plots

evaluate_ci(seasons=None, durations=[1], laws=['GEV'], nboot=100, show=False) → dict

Intervalles de confiance

Retourne une liste contenant des tuples (fig,ax) pour chaque durée et chaque saison

La boucle principale est sur les durées La boucle interne est sur les saisons

evaluate_ic(seasons=None, durations=[1], laws=['GEV'], nboot=100, show=False) → dict

alias evaluate_ci

test_distfit(durations=[1], plot=True)

Ajustement de lois avec la toolbox distfit

plot_qdf(seasons=None, durations=None, law='GEV', show=False)

Graphique de toutes les relations fittées pour chaque durée sur une même figure

select_best_func(season='mixture', law='GEV', method='MLE')

Sélection de la fonction à retenir comme meilleur ajustement

get_one_MFSH(rising_time: float = 6.0, return_period: float = 50.0, deltat: float = 1.0) → wolfhece.eva.hydrogramme_mono.Hydro_HSMF

opti_mfsh(label, rising_time=6, return_period=[2, 5, 10, 25, 50, 100, 200, 500, 1000], deltat=1)

## CALCUL DES HYDROGRAMMES ##

plot_msfh(label, return_period=[2, 5, 10, 25, 50, 100, 200, 500, 1000], ref_season='annual', ylim=None, before=1, after=3, show=False) → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes, matplotlib.axes.Axes]

## GRAPHIQUES ##

plot_msfh_mainplot(label, return_period=[2, 5, 10, 25, 50, 100, 200, 500, 1000], ref_season='annual', ylim=None, before=1, after=2, show=False) → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes]

## GRAPHIQUES ##

save_max_event(filename: str, years_bounds: list, seasons=None)

save_msfh(label, filename, return_period=[2, 5, 10, 25, 50, 100, 200, 500, 1000])

## SAUVEGARDE ##

plot_one_fit(seasons=None, durations=None, laws='popular', split_duration=True, split_season=True, xbounds=None, ybounds=None, show=False) → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes]

print_summary(seasons=None, durations=None, show=False)

plot_selected_max(seasons=None, durations=None, split_seasons=False, scaling=False, show=False) → tuple[matplotlib.figure.Figure, matplotlib.axes.Axes]

Graphique des dates des événements sélectionnés pour chaque durée (par défaut, toutes les durées)

wolfhece.eva.pyseries.example1()

wolfhece.eva.pyseries.example1bis()

wolfhece.eva.pyseries.example2()

wolfhece.eva.pyseries.example3()

wolfhece.eva.pyseries.example4()

wolfhece.eva.pyseries.example5()

wolfhece.eva.pyseries.example6_POT()

wolfhece.eva.pyseries.strPath