Signal Processing#
The plots created in the last section show a strong annual harmonic component. Lets, identify this components, subtract them from the signal and the re-plot to see if there is any transannual trend.
import pandas as pd
import numpy as np
from funciones import*
import matplotlib.pyplot as plt
import iceclassic as ice
from importlib import reload
file3=ice.import_data_browser('https://raw.githubusercontent.com/iceclassic/mude/main/book/data_files/time_serie_data.txt')
Data=pd.read_csv(file3,skiprows=162,index_col=0,sep='\t')
Data.index = pd.to_datetime(Data.index, format="%Y-%m-%d")
Power Spectral density#
A simple way to estimate the Power Spectral Density (PSD) of signal is using the Welch method.
do we explain the theory behind the method?
Exercise 1
Read the documentation for compute_and_plot_psd() function from the ice_classic package and estimate te PSD for all columns
¿ Do all the variable experience the same seasonal behavior? Is there any multiyear harmonic?
_=ice.compute_and_plot_psd(Data,plot_period=False)
# given the frequency of our signal, using the period (T) instead of the frequency (1/F) might be better
PSD_info=ice.compute_and_plot_psd(Data,plot_period=True,find_peaks_kwargs={"distance":100,"threshold":10})
In the last figures, multiple peaks can be observed with the most prominent being the associated with a period of 350-370, which is expected as is represent the yearly variation.
One common way to identify the peak of PSD is to use find_peaks() from scipy.The function compute_and_plot_psd() uses internally this function to find the peaks of each column, and saves them in a dictionary.
::{card} Exercise 2 Extract the peak of each column and compare them.
Tips/Help
Look-up the documentation of [find_peaks](https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.find_peaks.html). Considering what you expect the peaks to look like, change the values of prominence, distance and or threshold to refine the search for peaks
for col, psd_info in PSD_info.items():
peak_periods =np.round(psd_info['peak_periods']).astype(int)
print(f"Column: {col}")
print(f"Peak Periods: {peak_periods}\n")
import pprint
pprint.pprint(PSD_info)
Column: Regional: Air temperature [C]
Peak Periods: [371 123 61 43 33 27 22 19 17 15 14 13 12 11 10 10 9 9
8 8 7 7 7 6 6 6 5 5 5 5 5 5 4 4]
Column: Days since start of year
Peak Periods: [371 123 73 52 41 33 28 24 20 18 16 15 13 12 11 10 10 9
9 8 8 7 7 7 7 6 6 6 6 5 5 5 5 5 5 4
4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2]
Column: Days until break up
Peak Periods: [371 123 73 52 41 33 28 24 20 18 16 15 13 12 11 10 10 9
9 8 8 7 7 7 7 6 6 6 6 5 5 5 5 5 5 4
4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2]
Column: Nenana: Rainfall [mm]
Peak Periods: [369 76 49 36 27 22 19 16 14 13 11 10 9 9 8 8 7 6
6 6 6 5 5 5 5 4 4 4 4 4 4 3 3 3 3 3
3 3 3 3 3 2 2 2 2 2 2 2]
Column: Nenana: Snowfall [mm]
Peak Periods: [384 66 29 20 16 14 12 10 9 8 7 7 6 5 5 5 4 4
4 4 4 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2
2 2]
Column: Nenana: Snow depth [mm]
Peak Periods: [381 65 36 22 16 11 9 8 7 7 6 5 5 4 4 4 3 3
3 3 3 3 3 2 2 2 2 2 2 2]
Column: Nenana: Mean water temperature [C]
Peak Periods: [403]
Column: Nenana: Mean Discharge [m3/s]
Peak Periods: [376 73 37 26 19 16 13 11 10 9 8 8 7 6 6 6 5 5
5 5 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 2
2 2 2 2 2 2 2]
Column: Nenana: Air temperature [C]
Peak Periods: [371 99 56 37 25 19 16 14 12 11 10 9 8 8 7 7 7 6
6 6 5 5 5 5 4 4 4 4 4 4 4 3 3 3 3 3
3 3 3 3 2 2]
Column: Fairbanks: Average wind speed [m/s]
Peak Periods: [408 25 16 10 8 7 6 5 4 3]
Column: Fairbanks: Rainfall [mm]
Peak Periods: []
Column: Fairbanks: Snowfall [mm]
Peak Periods: [370]
Column: Fairbanks: Snow depth [mm]
Peak Periods: [369 92 52 36 29 24 18 16]
Column: Fairbanks: Air Temperature [C]
Peak Periods: [370 74 49 33 27 22 19 16 14 12 11 10 9 8 7 7 7 6
6 6 5 5 5 5 5 4 4 4 4 4 4 3 3 3 3 3]
Column: IceThickness [cm]
Peak Periods: [230 2]
Column: Regional: Solar Surface Irradiance [W/m2]
Peak Periods: [11]
Column: Regional: Cloud coverage [%]
Peak Periods: [12 4 2]
Column: Global: ENSO-Southern oscillation index
Peak Periods: [31]
Column: Gulkana Temperature [C]
Peak Periods: [355 42 29 18 15 12 11 10 9 8 7 6 6 5 5 5 4 4
4]
Column: Gulkana Precipitation [mm]
Peak Periods: [371 72 38 22 17 14 12 11 9 8 7 7 6 6 5 5 5 4
4 4 4 4 3 3 3 3 3 3 3 3 2 2 2 2 2 2]
Column: Gulkana: Glacier-wide winter mass balance [m.w.e]
Peak Periods: []
Column: Gulkana: Glacier-wide summer mass balance [m.w.e]
Peak Periods: []
Column: Global: Pacific decadal oscillation index
Peak Periods: [673]
Column: Global: Artic oscillation index
Peak Periods: []
{'Days since start of year': {'frequencies': array([0.00000000e+00, 5.18645298e-05, 1.03729060e-04, ...,
4.99870339e-01, 4.99922203e-01, 4.99974068e-01]),
'peak_frequencies': array([0.00269696, 0.00814273, 0.01364037, 0.01913801, 0.02458379,
0.03008143, 0.0355272 , 0.04102484, 0.04921944, 0.05471708,
0.06291167, 0.06840931, 0.07660391, 0.08210155, 0.09029615,
0.09579379, 0.10123956, 0.1067372 , 0.1149318 , 0.12042944,
0.12862403, 0.13412167, 0.14231627, 0.14781391, 0.15325969,
0.15875733, 0.16695192, 0.17244956, 0.18064416, 0.1861418 ,
0.19433639, 0.19983403, 0.20527981, 0.21077745, 0.21897205,
0.22446969, 0.23266428, 0.23816192, 0.24635652, 0.25185416,
0.25729993, 0.26279757, 0.27099217, 0.27648981, 0.2846844 ,
0.292879 , 0.29837664, 0.30387428, 0.30932006, 0.3148177 ,
0.32301229, 0.32850993, 0.33670453, 0.34489912, 0.35039676,
0.3558944 , 0.36134018, 0.36683782, 0.37503242, 0.38053006,
0.38872465, 0.39422229, 0.39966807, 0.40516571, 0.4133603 ,
0.41885794, 0.42705254, 0.43524713, 0.44074477, 0.44624241,
0.45168819, 0.45718583, 0.46538043, 0.47087807, 0.47907266,
0.48726726, 0.4927649 , 0.49893678]),
'peak_periods': array([370.78846154, 122.8089172 , 73.31178707, 52.25203252,
40.67721519, 33.24310345, 28.14744526, 24.37547408,
20.31717597, 18.27582938, 15.89530091, 14.61789234,
13.05416385, 12.1800379 , 11.07466973, 10.43909042,
9.87756148, 9.36880466, 8.70081227, 8.30361757,
7.77459677, 7.45591647, 7.0266035 , 6.76526316,
6.5248731 , 6.29892192, 5.98974837, 5.79879699,
5.53574505, 5.37224854, 5.14571657, 5.00415261,
4.8713997 , 4.74434055, 4.56679299, 4.45494455,
4.29803834, 4.19882404, 4.05915789, 3.97055189,
3.88651482, 3.80521018, 3.69014354, 3.61676984,
3.51266169, 3.41437932, 3.3514688 , 3.29083461,
3.23289738, 3.17644152, 3.09585742, 3.04404799,
2.96996303, 2.8993985 , 2.85390764, 2.80982221,
2.76747524, 2.72600028, 2.66643618, 2.62791332,
2.57251501, 2.53663992, 2.5020763 , 2.46812596,
2.41919699, 2.38744428, 2.34163226, 2.29754528,
2.2688868 , 2.24093445, 2.21391664, 2.18729438,
2.14877967, 2.12369204, 2.08736603, 2.05226184,
2.02936533, 2.00426195]),
'peak_psd_values': array([8.19897987e+07, 8.11270451e+06, 3.46029752e+06, 1.31046219e+06,
1.05983174e+06, 6.25258238e+05, 4.74041729e+05, 3.71670839e+05,
2.55645645e+05, 2.02939274e+05, 1.60503028e+05, 1.24992396e+05,
1.10073063e+05, 8.28069354e+04, 7.98633929e+04, 5.75269502e+04,
6.11357105e+04, 5.28508845e+04, 4.85154506e+04, 3.98580316e+04,
3.92801037e+04, 3.05816065e+04, 3.22608131e+04, 2.37480784e+04,
2.69730430e+04, 2.36683942e+04, 2.31874992e+04, 1.92079402e+04,
2.00331154e+04, 1.56478610e+04, 1.73607748e+04, 1.27716996e+04,
1.52014489e+04, 1.33037347e+04, 1.35945484e+04, 1.12035761e+04,
1.21496599e+04, 9.42171778e+03, 1.08418289e+04, 7.90432840e+03,
9.78472496e+03, 8.48064281e+03, 8.95370704e+03, 7.29868436e+03,
8.16581039e+03, 6.46421309e+03, 7.41881970e+03, 5.33834414e+03,
6.84764019e+03, 5.85702048e+03, 6.35822901e+03, 5.11101200e+03,
5.87514918e+03, 4.77611919e+03, 5.40091146e+03, 3.82684755e+03,
5.07623118e+03, 4.27610027e+03, 4.75976278e+03, 3.76616594e+03,
4.43726492e+03, 3.29584049e+03, 4.13165922e+03, 3.64417573e+03,
3.92487478e+03, 3.25193755e+03, 3.70513090e+03, 2.98418011e+03,
3.47538816e+03, 2.53685225e+03, 3.28185074e+03, 2.84548415e+03,
3.13380496e+03, 2.55162284e+03, 2.97237247e+03, 2.44724614e+03,
2.80009609e+03, 2.43785078e+03]),
'psd_values': array([3.04832156e+03, 9.78712452e+01, 6.12194410e+00, ...,
1.03920091e-03, 2.70411965e-04, 1.10916369e-04])},
'Days until break up': {'frequencies': array([0.00000000e+00, 5.18645298e-05, 1.03729060e-04, ...,
4.99870339e-01, 4.99922203e-01, 4.99974068e-01]),
'peak_frequencies': array([0.00269696, 0.00814273, 0.01364037, 0.01913801, 0.02458379,
0.03008143, 0.0355272 , 0.04102484, 0.04921944, 0.05471708,
0.06291167, 0.06840931, 0.07660391, 0.08210155, 0.09029615,
0.09579379, 0.10123956, 0.1067372 , 0.1149318 , 0.12042944,
0.12862403, 0.13412167, 0.14231627, 0.14781391, 0.15325969,
0.15875733, 0.16695192, 0.17244956, 0.18064416, 0.1861418 ,
0.19433639, 0.19983403, 0.20527981, 0.21077745, 0.21897205,
0.22446969, 0.23266428, 0.23816192, 0.24635652, 0.25185416,
0.25729993, 0.26279757, 0.27099217, 0.27648981, 0.2846844 ,
0.292879 , 0.29837664, 0.30387428, 0.30932006, 0.3148177 ,
0.32301229, 0.32850993, 0.33670453, 0.34489912, 0.35039676,
0.3558944 , 0.36134018, 0.36683782, 0.37503242, 0.38053006,
0.38872465, 0.39422229, 0.39966807, 0.40516571, 0.4133603 ,
0.41885794, 0.42705254, 0.43524713, 0.44074477, 0.44624241,
0.45168819, 0.45718583, 0.46538043, 0.47087807, 0.47907266,
0.48726726, 0.4927649 , 0.49893678]),
'peak_periods': array([370.78846154, 122.8089172 , 73.31178707, 52.25203252,
40.67721519, 33.24310345, 28.14744526, 24.37547408,
20.31717597, 18.27582938, 15.89530091, 14.61789234,
13.05416385, 12.1800379 , 11.07466973, 10.43909042,
9.87756148, 9.36880466, 8.70081227, 8.30361757,
7.77459677, 7.45591647, 7.0266035 , 6.76526316,
6.5248731 , 6.29892192, 5.98974837, 5.79879699,
5.53574505, 5.37224854, 5.14571657, 5.00415261,
4.8713997 , 4.74434055, 4.56679299, 4.45494455,
4.29803834, 4.19882404, 4.05915789, 3.97055189,
3.88651482, 3.80521018, 3.69014354, 3.61676984,
3.51266169, 3.41437932, 3.3514688 , 3.29083461,
3.23289738, 3.17644152, 3.09585742, 3.04404799,
2.96996303, 2.8993985 , 2.85390764, 2.80982221,
2.76747524, 2.72600028, 2.66643618, 2.62791332,
2.57251501, 2.53663992, 2.5020763 , 2.46812596,
2.41919699, 2.38744428, 2.34163226, 2.29754528,
2.2688868 , 2.24093445, 2.21391664, 2.18729438,
2.14877967, 2.12369204, 2.08736603, 2.05226184,
2.02936533, 2.00426195]),
'peak_psd_values': array([8.19548470e+07, 8.10941344e+06, 3.45879477e+06, 1.30996092e+06,
1.05937047e+06, 6.24999631e+05, 4.73838676e+05, 3.71509061e+05,
2.55533317e+05, 2.02850835e+05, 1.60430683e+05, 1.24937904e+05,
1.10022151e+05, 8.27708818e+04, 7.98254713e+04, 5.75020079e+04,
6.11063008e+04, 5.28258374e+04, 4.84912536e+04, 3.98389063e+04,
3.92597869e+04, 3.05667853e+04, 3.22435059e+04, 2.37364957e+04,
2.69581915e+04, 2.36555986e+04, 2.31741581e+04, 1.91973223e+04,
2.00210699e+04, 1.56390428e+04, 1.73498669e+04, 1.27643921e+04,
1.51915612e+04, 1.32952379e+04, 1.35852591e+04, 1.11962044e+04,
1.21409386e+04, 9.41535193e+03, 1.08336558e+04, 7.89886754e+03,
9.77705099e+03, 8.47409333e+03, 8.94630460e+03, 7.29284455e+03,
8.15869429e+03, 6.45840422e+03, 7.41200755e+03, 5.33380851e+03,
6.84108380e+03, 5.85147091e+03, 6.35179700e+03, 5.10597315e+03,
5.86887012e+03, 4.77084679e+03, 5.39481536e+03, 3.82280390e+03,
5.07025354e+03, 4.27108492e+03, 4.75383088e+03, 3.76155341e+03,
4.43141226e+03, 3.29163739e+03, 4.12598400e+03, 3.63910589e+03,
3.91916295e+03, 3.24718817e+03, 3.69941557e+03, 2.97941661e+03,
3.46970496e+03, 2.53279548e+03, 3.27626584e+03, 2.84054505e+03,
3.12814582e+03, 2.54695960e+03, 2.96667321e+03, 2.44241328e+03,
2.79439366e+03, 2.43277024e+03]),
'psd_values': array([2.81778383e+04, 2.89646220e+04, 3.30659955e+04, ...,
1.13875085e-01, 1.19601237e-01, 5.15108279e-02])},
'Fairbanks: Air Temperature [C]': {'frequencies': array([0.00000000e+00, 6.75995403e-05, 1.35199081e-04, ...,
4.99831001e-01, 4.99898601e-01, 4.99966200e-01]),
'peak_frequencies': array([0.00270398, 0.01351991, 0.02034746, 0.0300142 , 0.03697695,
0.04583249, 0.05299804, 0.06273237, 0.07057392, 0.08125465,
0.09227337, 0.10423849, 0.11633881, 0.12965592, 0.13918745,
0.1468262 , 0.15372135, 0.1612249 , 0.16805246, 0.1758264 ,
0.18610153, 0.19407828, 0.20110863, 0.20867978, 0.21557493,
0.22794565, 0.24220915, 0.2500507 , 0.25937944, 0.27357534,
0.28398567, 0.29182722, 0.30440073, 0.32177381, 0.33407693,
0.34097208]),
'peak_periods': array([369.825 , 73.965 , 49.1461794 , 33.31756757,
27.04387569, 21.81858407, 18.86862245, 15.94073276,
14.16954023, 12.30698835, 10.83736264, 9.59338521,
8.59558396, 7.71272158, 7.18455561, 6.81077348,
6.50527704, 6.20251572, 5.95052293, 5.68742791,
5.37341082, 5.15256008, 4.97243697, 4.7920311 ,
4.63875823, 4.38701068, 4.12866313, 3.99918897,
3.85535575, 3.65530022, 3.52130445, 3.4266852 ,
3.28514324, 3.10777311, 2.99332254, 2.93279144]),
'peak_psd_values': array([1.54759411e+06, 1.55731321e+03, 1.87380905e+03, 1.49864062e+03,
1.09998249e+03, 8.43507609e+02, 5.01694388e+02, 4.21682204e+02,
5.10321240e+02, 4.14990953e+02, 3.02729286e+02, 2.77002370e+02,
1.79432310e+02, 2.10047395e+02, 1.90919708e+02, 7.11006722e+01,
1.14505466e+02, 9.89270864e+01, 1.49242847e+02, 8.70250850e+01,
1.05560079e+02, 4.33633562e+01, 8.39126044e+01, 3.90586709e+01,
8.83993291e+01, 7.70409655e+01, 3.22544111e+01, 5.37658163e+01,
3.40555677e+01, 3.43606910e+01, 2.19681123e+01, 3.27782215e+01,
3.10007478e+01, 2.16896124e+01, 2.18318385e+01, 1.89933039e+01]),
'psd_values': array([1.59509454e+03, 1.12260432e+03, 3.33107992e+02, ...,
2.03836094e+00, 1.49675490e+00, 6.66736082e-01])},
'Fairbanks: Average wind speed [m/s]': {'frequencies': array([0.00000000e+00, 2.04164965e-04, 4.08329931e-04, ...,
4.99591670e-01, 4.99795835e-01, 5.00000000e-01]),
'peak_frequencies': array([0.00244998, 0.04042466, 0.06267864, 0.100245 , 0.12249898,
0.14842793, 0.16986525, 0.20253165, 0.24785627, 0.30175582]),
'peak_periods': array([408.16666667, 24.73737374, 15.95439739, 9.97556008,
8.16333333, 6.73727648, 5.88701923, 4.9375 ,
4.03459638, 3.31393775]),
'peak_psd_values': array([4574.40914007, 91.53916086, 50.78926333, 56.23085071,
33.70260298, 38.17024144, 29.96177735, 38.5950413 ,
31.45484844, 21.15199451]),
'psd_values': array([143.08974239, 226.23286296, 166.56763074, ..., 2.69973105,
7.74603568, 3.87713771])},
'Fairbanks: Rainfall [mm]': {'frequencies': array([0.00000000e+00, 6.75995403e-05, 1.35199081e-04, ...,
4.99831001e-01, 4.99898601e-01, 4.99966200e-01]),
'peak_frequencies': array([], dtype=float64),
'peak_periods': array([], dtype=float64),
'peak_psd_values': array([], dtype=float64),
'psd_values': array([0.02167195, 0.04889796, 0.02571655, ..., 0.01249868, 0.00171392,
0.00682316])},
'Fairbanks: Snow depth [mm]': {'frequencies': array([0.00000000e+00, 6.76727347e-05, 1.35345469e-04, ...,
4.99830818e-01, 4.99898491e-01, 4.99966164e-01]),
'peak_frequencies': array([0.00270691, 0.01089531, 0.01915138, 0.02808418, 0.03491913,
0.0424308 , 0.05488259, 0.06422143]),
'peak_periods': array([369.425 , 91.7826087 , 52.2155477 , 35.60722892,
28.6375969 , 23.56778309, 18.22071517, 15.5711275 ]),
'peak_psd_values': array([4.43946218e+05, 4.02794494e+03, 8.49682862e+02, 2.29426035e+02,
1.56415383e+02, 9.92790315e+01, 4.19565662e+01, 3.99242244e+01]),
'psd_values': array([1.09578335e+04, 1.75923072e+04, 1.07929393e+04, ...,
3.20734389e-01, 2.22963342e-01, 1.70144579e-01])},
'Fairbanks: Snowfall [mm]': {'frequencies': array([0.00000000e+00, 6.75995403e-05, 1.35199081e-04, ...,
4.99831001e-01, 4.99898601e-01, 4.99966200e-01]),
'peak_frequencies': array([0.00270398]),
'peak_periods': array([369.825]),
'peak_psd_values': array([194.14278563]),
'psd_values': array([6.43177103, 4.54009248, 3.27430651, ..., 0.99568015, 0.55045556,
0.41973773])},
'Global: Artic oscillation index': {'frequencies': array([0. , 0.00225225, 0.0045045 , 0.00675676, 0.00900901,
0.01126126, 0.01351351, 0.01576577, 0.01801802, 0.02027027,
0.02252252, 0.02477477, 0.02702703, 0.02927928, 0.03153153,
0.03378378, 0.03603604, 0.03828829, 0.04054054, 0.04279279,
0.04504505, 0.0472973 , 0.04954955, 0.0518018 , 0.05405405,
0.05630631, 0.05855856, 0.06081081, 0.06306306, 0.06531532,
0.06756757, 0.06981982, 0.07207207, 0.07432432, 0.07657658,
0.07882883, 0.08108108, 0.08333333, 0.08558559, 0.08783784,
0.09009009, 0.09234234, 0.09459459, 0.09684685, 0.0990991 ,
0.10135135, 0.1036036 , 0.10585586, 0.10810811, 0.11036036,
0.11261261, 0.11486486, 0.11711712, 0.11936937, 0.12162162,
0.12387387, 0.12612613, 0.12837838, 0.13063063, 0.13288288,
0.13513514, 0.13738739, 0.13963964, 0.14189189, 0.14414414,
0.1463964 , 0.14864865, 0.1509009 , 0.15315315, 0.15540541,
0.15765766, 0.15990991, 0.16216216, 0.16441441, 0.16666667,
0.16891892, 0.17117117, 0.17342342, 0.17567568, 0.17792793,
0.18018018, 0.18243243, 0.18468468, 0.18693694, 0.18918919,
0.19144144, 0.19369369, 0.19594595, 0.1981982 , 0.20045045,
0.2027027 , 0.20495495, 0.20720721, 0.20945946, 0.21171171,
0.21396396, 0.21621622, 0.21846847, 0.22072072, 0.22297297,
0.22522523, 0.22747748, 0.22972973, 0.23198198, 0.23423423,
0.23648649, 0.23873874, 0.24099099, 0.24324324, 0.2454955 ,
0.24774775, 0.25 , 0.25225225, 0.2545045 , 0.25675676,
0.25900901, 0.26126126, 0.26351351, 0.26576577, 0.26801802,
0.27027027, 0.27252252, 0.27477477, 0.27702703, 0.27927928,
0.28153153, 0.28378378, 0.28603604, 0.28828829, 0.29054054,
0.29279279, 0.29504505, 0.2972973 , 0.29954955, 0.3018018 ,
0.30405405, 0.30630631, 0.30855856, 0.31081081, 0.31306306,
0.31531532, 0.31756757, 0.31981982, 0.32207207, 0.32432432,
0.32657658, 0.32882883, 0.33108108, 0.33333333, 0.33558559,
0.33783784, 0.34009009, 0.34234234, 0.34459459, 0.34684685,
0.3490991 , 0.35135135, 0.3536036 , 0.35585586, 0.35810811,
0.36036036, 0.36261261, 0.36486486, 0.36711712, 0.36936937,
0.37162162, 0.37387387, 0.37612613, 0.37837838, 0.38063063,
0.38288288, 0.38513514, 0.38738739, 0.38963964, 0.39189189,
0.39414414, 0.3963964 , 0.39864865, 0.4009009 , 0.40315315,
0.40540541, 0.40765766, 0.40990991, 0.41216216, 0.41441441,
0.41666667, 0.41891892, 0.42117117, 0.42342342, 0.42567568,
0.42792793, 0.43018018, 0.43243243, 0.43468468, 0.43693694,
0.43918919, 0.44144144, 0.44369369, 0.44594595, 0.4481982 ,
0.45045045, 0.4527027 , 0.45495495, 0.45720721, 0.45945946,
0.46171171, 0.46396396, 0.46621622, 0.46846847, 0.47072072,
0.47297297, 0.47522523, 0.47747748, 0.47972973, 0.48198198,
0.48423423, 0.48648649, 0.48873874, 0.49099099, 0.49324324,
0.4954955 , 0.49774775, 0.5 ]),
'peak_frequencies': array([], dtype=float64),
'peak_periods': array([], dtype=float64),
'peak_psd_values': array([], dtype=float64),
'psd_values': array([4.66528071, 6.89800996, 5.01212047, 5.7655564 , 5.3977988 ,
4.54951547, 3.75957705, 4.35504025, 4.92104594, 4.85617003,
3.8072384 , 4.12391591, 9.06088155, 5.85592612, 4.79851881,
4.53142095, 1.6555986 , 2.80118164, 0.74551431, 1.24399779,
2.15020339, 3.2604406 , 0.88937289, 2.64267654, 2.57601434,
1.1842196 , 1.37050668, 4.14840645, 4.32185857, 1.05707105,
2.92144893, 6.81201801, 4.35922547, 2.64849277, 4.12332629,
4.78045356, 5.26638492, 3.3330609 , 3.56880886, 2.88407315,
2.31023993, 1.30178099, 0.45777708, 2.37974995, 3.98911661,
6.19324133, 6.22391128, 2.85145976, 1.00007864, 1.07179101,
2.13705974, 2.97045641, 2.93491972, 3.17171133, 4.83860358,
2.43268369, 1.30969028, 0.96841796, 1.60947309, 1.89382641,
2.31714178, 0.579934 , 1.05384409, 3.66978867, 6.65271802,
5.35306987, 1.35484124, 4.08957722, 6.48076139, 3.14326989,
2.93469584, 1.20185073, 4.61108192, 5.87326031, 3.66541458,
1.95539178, 1.27380943, 2.34340517, 2.94519468, 0.85209185,
0.66316679, 2.17281734, 0.84839942, 0.41393169, 1.26491582,
1.14562496, 0.53844537, 0.75805338, 0.98472392, 2.06128856,
2.25151567, 1.62834135, 0.80185692, 0.67884642, 1.86771174,
3.00418178, 2.18262149, 3.07912885, 0.91313102, 0.86825032,
1.62194507, 1.61911383, 1.43117946, 1.19235498, 2.22571303,
2.27095185, 1.59919722, 1.07938634, 1.28792845, 0.70384586,
0.29706954, 1.71749223, 1.97902908, 0.79493081, 3.1843992 ,
1.92196674, 0.55013053, 0.70079563, 0.47082797, 0.81095472,
0.73359614, 1.99083915, 2.84464146, 2.26559767, 1.28541269,
0.85564859, 2.4647963 , 2.69842467, 1.80150583, 1.01054542,
0.01495798, 1.62850998, 2.94328729, 2.45821383, 2.00394076,
1.60699969, 1.26748109, 0.7367154 , 1.88714368, 1.25298589,
0.93941634, 2.55011761, 1.04694367, 0.95175848, 1.58494093,
1.0991961 , 0.64500114, 0.68135622, 0.94803904, 1.37558395,
1.12853816, 1.4568748 , 0.81796647, 0.20557387, 0.87398816,
1.34181561, 1.14274498, 0.65800009, 1.01280973, 1.88208519,
1.49880682, 2.99935409, 3.6243321 , 0.95323879, 0.65806514,
0.15443585, 0.49892518, 0.92071085, 1.66334047, 2.12994052,
1.44788438, 0.35131871, 0.37806123, 0.89466507, 1.15812282,
1.38122765, 1.10192309, 1.39371893, 0.88797553, 2.45149062,
1.71378718, 0.16298991, 1.11261395, 0.95315428, 0.58971972,
0.73996779, 0.412283 , 0.67796221, 0.80071951, 1.36872534,
1.10848035, 1.54269309, 1.34188149, 1.23836469, 0.94481958,
1.08783506, 1.51053066, 2.00078987, 3.29636692, 2.29178867,
0.56036327, 0.42419744, 0.20930151, 0.46170102, 0.30707966,
1.39238172, 2.05121211, 1.54155473, 1.14092079, 1.28175279,
2.33319264, 3.05363443, 0.63807504, 0.85949065, 0.83712731,
0.44551134, 0.67049914, 0.82827278, 1.08778679, 1.43063447,
1.0022211 , 0.3668177 ])},
'Global: ENSO-Southern oscillation index': {'frequencies': array([0. , 0.00228311, 0.00456621, 0.00684932, 0.00913242,
0.01141553, 0.01369863, 0.01598174, 0.01826484, 0.02054795,
0.02283105, 0.02511416, 0.02739726, 0.02968037, 0.03196347,
0.03424658, 0.03652968, 0.03881279, 0.04109589, 0.043379 ,
0.0456621 , 0.04794521, 0.05022831, 0.05251142, 0.05479452,
0.05707763, 0.05936073, 0.06164384, 0.06392694, 0.06621005,
0.06849315, 0.07077626, 0.07305936, 0.07534247, 0.07762557,
0.07990868, 0.08219178, 0.08447489, 0.08675799, 0.0890411 ,
0.0913242 , 0.09360731, 0.09589041, 0.09817352, 0.10045662,
0.10273973, 0.10502283, 0.10730594, 0.10958904, 0.11187215,
0.11415525, 0.11643836, 0.11872146, 0.12100457, 0.12328767,
0.12557078, 0.12785388, 0.13013699, 0.13242009, 0.1347032 ,
0.1369863 , 0.13926941, 0.14155251, 0.14383562, 0.14611872,
0.14840183, 0.15068493, 0.15296804, 0.15525114, 0.15753425,
0.15981735, 0.16210046, 0.16438356, 0.16666667, 0.16894977,
0.17123288, 0.17351598, 0.17579909, 0.17808219, 0.1803653 ,
0.1826484 , 0.18493151, 0.18721461, 0.18949772, 0.19178082,
0.19406393, 0.19634703, 0.19863014, 0.20091324, 0.20319635,
0.20547945, 0.20776256, 0.21004566, 0.21232877, 0.21461187,
0.21689498, 0.21917808, 0.22146119, 0.22374429, 0.2260274 ,
0.2283105 , 0.23059361, 0.23287671, 0.23515982, 0.23744292,
0.23972603, 0.24200913, 0.24429224, 0.24657534, 0.24885845,
0.25114155, 0.25342466, 0.25570776, 0.25799087, 0.26027397,
0.26255708, 0.26484018, 0.26712329, 0.26940639, 0.2716895 ,
0.2739726 , 0.27625571, 0.27853881, 0.28082192, 0.28310502,
0.28538813, 0.28767123, 0.28995434, 0.29223744, 0.29452055,
0.29680365, 0.29908676, 0.30136986, 0.30365297, 0.30593607,
0.30821918, 0.31050228, 0.31278539, 0.31506849, 0.3173516 ,
0.3196347 , 0.32191781, 0.32420091, 0.32648402, 0.32876712,
0.33105023, 0.33333333, 0.33561644, 0.33789954, 0.34018265,
0.34246575, 0.34474886, 0.34703196, 0.34931507, 0.35159817,
0.35388128, 0.35616438, 0.35844749, 0.36073059, 0.3630137 ,
0.3652968 , 0.36757991, 0.36986301, 0.37214612, 0.37442922,
0.37671233, 0.37899543, 0.38127854, 0.38356164, 0.38584475,
0.38812785, 0.39041096, 0.39269406, 0.39497717, 0.39726027,
0.39954338, 0.40182648, 0.40410959, 0.40639269, 0.4086758 ,
0.4109589 , 0.41324201, 0.41552511, 0.41780822, 0.42009132,
0.42237443, 0.42465753, 0.42694064, 0.42922374, 0.43150685,
0.43378995, 0.43607306, 0.43835616, 0.44063927, 0.44292237,
0.44520548, 0.44748858, 0.44977169, 0.45205479, 0.4543379 ,
0.456621 , 0.45890411, 0.46118721, 0.46347032, 0.46575342,
0.46803653, 0.47031963, 0.47260274, 0.47488584, 0.47716895,
0.47945205, 0.48173516, 0.48401826, 0.48630137, 0.48858447,
0.49086758, 0.49315068, 0.49543379, 0.49771689, 0.5 ]),
'peak_frequencies': array([0.03196347]),
'peak_periods': array([31.28571429]),
'peak_psd_values': array([24.40985097]),
'psd_values': array([ 7.62376449, 6.82841474, 23.61168443, 11.4208944 , 3.63630996,
7.00258983, 14.88722668, 13.9947084 , 15.90415956, 21.03411609,
8.05164611, 11.85124361, 9.64202096, 11.37451863, 24.40985097,
13.5654722 , 9.61701935, 1.61882988, 3.04870919, 5.37852081,
6.26217191, 4.72355087, 1.95633483, 6.9758111 , 3.17228601,
1.37853435, 1.47502318, 2.16283543, 3.03489842, 2.70467715,
2.21359087, 0.29278103, 1.27348023, 0.76558326, 1.16801989,
2.63659742, 2.3023074 , 1.06074712, 0.60483436, 1.06904134,
0.82188393, 0.98215552, 1.13685884, 0.92660387, 0.45219695,
1.89901743, 2.0132173 , 0.46727549, 2.85937614, 0.67549916,
0.70513431, 1.09194097, 0.7248551 , 0.4769849 , 0.19972806,
1.56254087, 1.6620916 , 1.58170328, 0.68208595, 0.5104859 ,
1.09639056, 1.09684792, 1.32871421, 1.57630369, 0.69039327,
0.41800297, 0.99298219, 0.30047415, 0.43477865, 0.8049694 ,
0.74075326, 0.68471603, 0.51937145, 0.46418841, 0.47452612,
0.855789 , 1.26200141, 1.54150005, 1.84063488, 1.34070604,
0.49966397, 1.35390445, 0.8531496 , 0.24119377, 0.18017819,
0.43017512, 0.42050237, 0.4548048 , 0.70484153, 0.57726433,
0.67353223, 0.47165974, 0.46968253, 0.97125269, 0.91418618,
0.48568498, 0.53831183, 0.6791256 , 1.0404763 , 0.87291787,
0.45665716, 0.49333823, 0.64141511, 0.25962838, 0.07908622,
0.39724843, 0.79435326, 0.73285298, 0.59002703, 0.3004798 ,
0.61881878, 0.44556536, 0.3649907 , 0.31022109, 0.71529408,
1.08627346, 0.46498013, 0.26533861, 0.54317375, 0.30697482,
0.66955018, 0.54348001, 0.0409494 , 0.49382418, 0.65773115,
0.18261718, 0.20865169, 0.29562346, 0.52059829, 0.60754708,
0.28074523, 0.21630562, 0.62736827, 1.15244308, 1.04759424,
1.34044467, 1.23496836, 0.73628188, 0.56206022, 0.7284683 ,
0.71369419, 0.75099131, 0.90554416, 0.8336855 , 0.94732467,
0.8825736 , 0.75642145, 0.44770126, 0.16167874, 0.37583072,
0.49170166, 0.62661955, 1.17759442, 1.13456412, 0.81572232,
0.41234312, 0.65581183, 0.97742496, 0.60654986, 0.93989235,
0.3209337 , 0.40003933, 0.22460937, 0.22376612, 0.35738675,
0.25082471, 0.36082391, 0.87557048, 0.56917109, 0.62395665,
0.93293627, 1.35902588, 0.92405105, 1.1858419 , 0.75914695,
1.2864399 , 2.18757562, 1.10487411, 0.62778377, 0.3521758 ,
0.18305856, 0.48937403, 0.36927745, 0.13971112, 0.37641196,
0.61303729, 0.52464364, 0.23130329, 0.23908297, 0.87270856,
0.85981729, 0.48510761, 0.34068953, 0.31490984, 0.61073675,
1.15894439, 0.66759108, 0.4199722 , 0.6677563 , 0.56886879,
0.44900438, 0.48603735, 0.44350253, 0.35566352, 0.3870675 ,
0.62394692, 0.21026368, 0.31721833, 1.14678446, 0.48930036,
0.46354566, 1.227985 , 0.76603183, 0.46495124, 0.52992553,
0.59606329, 0.23303733, 0.39130388, 0.21495893])},
'Global: Pacific decadal oscillation index': {'frequencies': array([0. , 0.00148588, 0.00297177, 0.00445765, 0.00594354,
0.00742942, 0.0089153 , 0.01040119, 0.01188707, 0.01337296,
0.01485884, 0.01634473, 0.01783061, 0.01931649, 0.02080238,
0.02228826, 0.02377415, 0.02526003, 0.02674591, 0.0282318 ,
0.02971768, 0.03120357, 0.03268945, 0.03417533, 0.03566122,
0.0371471 , 0.03863299, 0.04011887, 0.04160475, 0.04309064,
0.04457652, 0.04606241, 0.04754829, 0.04903418, 0.05052006,
0.05200594, 0.05349183, 0.05497771, 0.0564636 , 0.05794948,
0.05943536, 0.06092125, 0.06240713, 0.06389302, 0.0653789 ,
0.06686478, 0.06835067, 0.06983655, 0.07132244, 0.07280832,
0.07429421, 0.07578009, 0.07726597, 0.07875186, 0.08023774,
0.08172363, 0.08320951, 0.08469539, 0.08618128, 0.08766716,
0.08915305, 0.09063893, 0.09212481, 0.0936107 , 0.09509658,
0.09658247, 0.09806835, 0.09955423, 0.10104012, 0.102526 ,
0.10401189, 0.10549777, 0.10698366, 0.10846954, 0.10995542,
0.11144131, 0.11292719, 0.11441308, 0.11589896, 0.11738484,
0.11887073, 0.12035661, 0.1218425 , 0.12332838, 0.12481426,
0.12630015, 0.12778603, 0.12927192, 0.1307578 , 0.13224368,
0.13372957, 0.13521545, 0.13670134, 0.13818722, 0.13967311,
0.14115899, 0.14264487, 0.14413076, 0.14561664, 0.14710253,
0.14858841, 0.15007429, 0.15156018, 0.15304606, 0.15453195,
0.15601783, 0.15750371, 0.1589896 , 0.16047548, 0.16196137,
0.16344725, 0.16493314, 0.16641902, 0.1679049 , 0.16939079,
0.17087667, 0.17236256, 0.17384844, 0.17533432, 0.17682021,
0.17830609, 0.17979198, 0.18127786, 0.18276374, 0.18424963,
0.18573551, 0.1872214 , 0.18870728, 0.19019316, 0.19167905,
0.19316493, 0.19465082, 0.1961367 , 0.19762259, 0.19910847,
0.20059435, 0.20208024, 0.20356612, 0.20505201, 0.20653789,
0.20802377, 0.20950966, 0.21099554, 0.21248143, 0.21396731,
0.21545319, 0.21693908, 0.21842496, 0.21991085, 0.22139673,
0.22288262, 0.2243685 , 0.22585438, 0.22734027, 0.22882615,
0.23031204, 0.23179792, 0.2332838 , 0.23476969, 0.23625557,
0.23774146, 0.23922734, 0.24071322, 0.24219911, 0.24368499,
0.24517088, 0.24665676, 0.24814264, 0.24962853, 0.25111441,
0.2526003 , 0.25408618, 0.25557207, 0.25705795, 0.25854383,
0.26002972, 0.2615156 , 0.26300149, 0.26448737, 0.26597325,
0.26745914, 0.26894502, 0.27043091, 0.27191679, 0.27340267,
0.27488856, 0.27637444, 0.27786033, 0.27934621, 0.2808321 ,
0.28231798, 0.28380386, 0.28528975, 0.28677563, 0.28826152,
0.2897474 , 0.29123328, 0.29271917, 0.29420505, 0.29569094,
0.29717682, 0.2986627 , 0.30014859, 0.30163447, 0.30312036,
0.30460624, 0.30609212, 0.30757801, 0.30906389, 0.31054978,
0.31203566, 0.31352155, 0.31500743, 0.31649331, 0.3179792 ,
0.31946508, 0.32095097, 0.32243685, 0.32392273, 0.32540862,
0.3268945 , 0.32838039, 0.32986627, 0.33135215, 0.33283804,
0.33432392, 0.33580981, 0.33729569, 0.33878158, 0.34026746,
0.34175334, 0.34323923, 0.34472511, 0.346211 , 0.34769688,
0.34918276, 0.35066865, 0.35215453, 0.35364042, 0.3551263 ,
0.35661218, 0.35809807, 0.35958395, 0.36106984, 0.36255572,
0.3640416 , 0.36552749, 0.36701337, 0.36849926, 0.36998514,
0.37147103, 0.37295691, 0.37444279, 0.37592868, 0.37741456,
0.37890045, 0.38038633, 0.38187221, 0.3833581 , 0.38484398,
0.38632987, 0.38781575, 0.38930163, 0.39078752, 0.3922734 ,
0.39375929, 0.39524517, 0.39673105, 0.39821694, 0.39970282,
0.40118871, 0.40267459, 0.40416048, 0.40564636, 0.40713224,
0.40861813, 0.41010401, 0.4115899 , 0.41307578, 0.41456166,
0.41604755, 0.41753343, 0.41901932, 0.4205052 , 0.42199108,
0.42347697, 0.42496285, 0.42644874, 0.42793462, 0.42942051,
0.43090639, 0.43239227, 0.43387816, 0.43536404, 0.43684993,
0.43833581, 0.43982169, 0.44130758, 0.44279346, 0.44427935,
0.44576523, 0.44725111, 0.448737 , 0.45022288, 0.45170877,
0.45319465, 0.45468053, 0.45616642, 0.4576523 , 0.45913819,
0.46062407, 0.46210996, 0.46359584, 0.46508172, 0.46656761,
0.46805349, 0.46953938, 0.47102526, 0.47251114, 0.47399703,
0.47548291, 0.4769688 , 0.47845468, 0.47994056, 0.48142645,
0.48291233, 0.48439822, 0.4858841 , 0.48736999, 0.48885587,
0.49034175, 0.49182764, 0.49331352, 0.49479941, 0.49628529,
0.49777117, 0.49925706]),
'peak_frequencies': array([0.00148588]),
'peak_periods': array([673.]),
'peak_psd_values': array([87.55363836]),
'psd_values': array([7.30263298e+01, 8.75536384e+01, 5.44772840e+01, 2.48461890e+01,
1.64116971e+01, 1.50413521e+01, 8.42070290e+00, 1.01883801e+01,
4.04610701e+01, 8.06755441e+01, 4.04335869e+01, 2.01714594e+01,
9.12215694e+00, 5.42897503e+00, 1.01121209e+01, 7.95831065e+00,
1.47274594e+01, 8.97558427e+00, 9.15294458e+00, 8.75577782e+00,
2.43398177e+00, 2.74130453e+00, 4.03562177e+00, 8.05983933e+00,
1.35742456e+01, 9.90228239e+00, 3.36072780e+00, 3.84461079e-01,
4.81149418e+00, 9.50309918e+00, 9.97846565e+00, 1.43719023e+00,
1.05244074e+01, 1.13306617e+01, 3.58600131e+00, 1.26699546e+01,
5.42575540e+00, 3.53503353e+00, 2.17215300e+00, 3.49626931e+00,
2.20465701e+00, 7.86071293e-01, 3.67728445e+00, 4.26931329e+00,
8.84545043e+00, 8.60813260e+00, 4.47208064e+00, 1.66151262e+00,
3.16080815e+00, 9.72885529e-01, 2.36008829e+00, 5.21611367e+00,
5.17220622e+00, 1.70269461e+00, 4.79210925e+00, 8.35959493e+00,
4.71403620e+00, 2.12560183e+00, 2.67324442e+00, 1.20326352e+00,
1.58646782e+00, 2.24234394e+00, 2.68616346e+00, 1.05896165e+00,
4.32806772e-01, 1.38816408e+00, 1.38222854e+00, 4.27882937e-01,
1.36663559e+00, 1.84128933e+00, 5.10867477e+00, 5.15163046e+00,
3.44680411e+00, 2.96354650e+00, 2.26814744e+00, 3.35177944e+00,
1.94640403e+00, 8.84978857e-01, 2.43236881e-01, 3.45705602e-01,
2.24601846e-01, 1.94302938e+00, 1.95824282e+00, 1.56804141e+00,
4.66103124e+00, 4.42894047e+00, 1.66804453e+00, 3.77796500e-01,
4.25200682e-01, 2.61988104e-01, 8.69347079e-01, 1.18989967e+00,
1.67823329e+00, 9.79435380e-01, 8.21815998e-01, 4.94585406e-01,
1.13801178e+00, 1.07291306e+00, 7.77569877e-01, 1.86329883e+00,
2.90808148e+00, 1.56279828e+00, 1.77662744e-01, 1.52002881e+00,
1.64227263e+00, 2.65140740e-01, 5.31356146e-01, 2.52986078e+00,
3.69192914e+00, 2.19740186e+00, 2.35117205e+00, 3.93220069e+00,
9.68730882e-01, 3.31999438e-01, 8.52252746e-02, 1.40691123e-01,
7.11311690e-01, 1.59929331e+00, 5.36404280e-01, 5.78362608e-01,
1.54418416e+00, 1.97905723e+00, 1.47183643e+00, 1.30164599e+00,
8.29856684e-01, 1.10057768e+00, 1.16570879e+00, 3.63890748e-01,
3.39839511e-01, 5.69684691e-01, 9.41211557e-01, 1.28655277e+00,
1.15616494e+00, 2.55581851e-01, 5.87480507e-01, 5.36361951e-01,
3.47011310e-01, 6.90239003e-01, 5.22687157e-01, 4.89337327e-01,
3.19074130e-01, 5.71329347e-01, 2.97403004e-01, 4.33843525e-01,
9.06788576e-01, 5.53994238e-01, 6.10582587e-01, 5.89480158e-01,
8.82516509e-01, 1.56710858e+00, 6.10336127e-01, 3.37682061e-01,
2.76618994e-01, 1.93255418e-01, 2.42485123e-01, 2.06907659e-01,
7.99936271e-01, 2.29539422e+00, 5.31995064e-01, 3.80201344e-01,
4.62699710e-01, 3.38620070e-01, 4.06214729e-01, 1.21450955e-01,
4.53119446e-01, 3.08129081e-01, 3.54558541e-01, 4.89383640e-01,
3.74259754e-01, 4.47938820e-01, 5.57006778e-01, 4.86549716e-01,
7.33793416e-01, 1.40293821e+00, 1.41342223e+00, 4.62229353e-01,
1.00563240e-01, 3.18203819e-02, 8.35110466e-02, 4.69416656e-01,
6.79673395e-01, 4.63487546e-01, 2.22563068e-01, 2.98971550e-01,
4.07293303e-01, 2.51623148e-01, 6.31055737e-01, 5.04051136e-01,
3.21435879e-01, 9.64814460e-01, 4.55645588e-01, 4.43662173e-02,
1.58633048e-01, 2.92549992e-01, 5.17201936e-01, 4.19910876e-01,
4.27515053e-01, 4.29267038e-01, 1.32939935e-01, 2.29607645e-01,
2.86810485e-01, 5.42810150e-01, 5.32120147e-01, 3.21304976e-01,
2.43594954e-01, 6.90996022e-01, 6.84777975e-01, 1.07480674e-01,
4.06342421e-01, 7.03159624e-02, 9.86383746e-02, 3.23060120e-01,
4.54121780e-01, 2.48637390e-01, 2.49848855e-01, 5.57646275e-01,
3.07731033e-01, 4.87344177e-01, 2.28552004e-01, 1.06300914e-01,
1.03018898e-01, 2.33773169e-01, 7.60978497e-01, 9.22338509e-01,
5.18287074e-01, 2.71593742e-01, 1.87561008e-01, 2.89256211e-01,
1.18777153e-01, 1.97771868e-01, 3.97308248e-01, 1.74660580e-01,
2.09779882e-01, 2.41289229e-01, 2.03776568e-01, 1.51815198e-01,
2.50878865e-01, 3.90686984e-01, 8.63720378e-02, 2.15189763e-01,
3.50710750e-01, 2.52521029e-01, 1.51719770e-01, 1.63283792e-02,
1.96393064e-01, 5.39367770e-02, 5.82984244e-02, 2.90489636e-02,
1.08520052e-01, 2.52161165e-01, 7.77690035e-02, 1.70958262e-01,
5.52453452e-02, 1.64342524e-01, 3.82480123e-01, 7.21494677e-02,
3.72159598e-01, 3.52608380e-01, 6.14311106e-01, 2.01501658e-01,
1.07267595e-01, 6.14219840e-02, 5.96106705e-02, 3.03011680e-02,
6.43902574e-02, 3.66833882e-01, 3.19109514e-01, 6.75562755e-02,
2.41911573e-02, 7.44132446e-02, 2.03056769e-01, 1.32534105e-01,
1.80146841e-01, 2.82097176e-01, 5.41816604e-01, 3.02333192e-01,
1.73366498e-01, 1.52334781e-01, 2.76238048e-01, 3.49839975e-01,
4.45557502e-01, 2.70338204e-01, 1.63662168e-01, 1.35246118e-01,
9.87512443e-02, 2.38566863e-01, 1.62330118e-01, 1.05063514e-01,
5.45032292e-02, 8.67442719e-02, 3.56183304e-01, 2.00297637e-01,
9.50413691e-02, 1.52570103e-01, 3.84265602e-02, 9.10092949e-02,
1.39631004e-01, 1.72024870e-01, 1.12622077e-01, 1.42159867e-01,
1.45688652e-01, 1.01445197e-01, 6.34095698e-02, 1.21695152e-01,
1.05274253e-01, 6.16446902e-02, 1.72310179e-01, 3.86636415e-01,
6.13958468e-02, 3.21095699e-01, 3.96037016e-01, 9.30953018e-02,
1.79779458e-01, 1.69852881e-01, 1.04810298e-01, 1.26552651e-01,
2.16745324e-01, 2.79697253e-01, 1.51173213e-01, 6.84311277e-02,
7.52348572e-02, 5.61113689e-02, 2.62734968e-02, 8.23441467e-02,
1.22786896e-01, 2.55240877e-01, 4.34498899e-01, 3.07628546e-01,
8.02615243e-02, 1.11791682e-01, 9.55789376e-02, 2.33528522e-02,
1.00838277e-02, 3.16547452e-01, 5.67975003e-01, 4.51457787e-01])},
'Gulkana Precipitation [mm]': {'frequencies': array([0.00000000e+00, 1.07839965e-04, 2.15679931e-04, ...,
4.99730400e-01, 4.99838240e-01, 4.99946080e-01]),
'peak_frequencies': array([0.002696 , 0.01380352, 0.02598943, 0.04496927, 0.06028254,
0.07160574, 0.08325245, 0.09489917, 0.11053596, 0.12498652,
0.1402998 , 0.15129947, 0.16359323, 0.17631834, 0.1902297 ,
0.20112154, 0.21255257, 0.22538553, 0.23681656, 0.24943384,
0.26302168, 0.27660951, 0.29494231, 0.30960854, 0.33063733,
0.34519573, 0.35641109, 0.36956756, 0.3804594 , 0.39900787,
0.41227219, 0.4336245 , 0.45411409, 0.46824113, 0.48172113,
0.49800496]),
'peak_periods': array([370.92 , 72.4453125 , 38.47717842, 22.23741007,
16.58855098, 13.96536145, 12.01165803, 10.5375 ,
9.04682927, 8.00086281, 7.12759416, 6.60940841,
6.11272248, 5.67155963, 5.25680272, 4.97211796,
4.70471842, 4.43684211, 4.2226776 , 4.00907912,
3.80196802, 3.61520468, 3.3904936 , 3.22988506,
3.02446184, 2.89690722, 2.80574887, 2.70586519,
2.62840136, 2.50621622, 2.425582 , 2.30614275,
2.20208976, 2.13565177, 2.07588986, 2.00801213]),
'peak_psd_values': array([8293.3889375 , 737.67791188, 1572.50039717, 778.31800513,
1155.50285013, 330.60126179, 784.42481218, 616.18074158,
797.30760273, 747.66046808, 479.23472733, 424.18319152,
516.24793142, 347.91055435, 575.69124633, 276.59917161,
717.64383458, 377.86112108, 220.47230389, 473.23859201,
215.06912252, 372.68289231, 500.6701488 , 318.78781673,
516.93876574, 349.71316677, 342.97524775, 400.58885036,
243.04753007, 389.87612096, 162.4818307 , 231.51450854,
406.82355238, 301.22531192, 328.74159042, 139.94629912]),
'psd_values': array([1899.18113862, 1904.0688527 , 1341.45523253, ..., 95.65396457,
23.833302 , 72.8203625 ])},
'Gulkana Temperature [C]': {'frequencies': array([0.00000000e+00, 1.04460462e-04, 2.08920923e-04, ...,
4.99738849e-01, 4.99843309e-01, 4.99947770e-01]),
'peak_frequencies': array([0.00282043, 0.02392145, 0.03436749, 0.05411052, 0.06675024,
0.08106132, 0.09338765, 0.10498276, 0.11657788, 0.12796407,
0.1447822 , 0.16483861, 0.1762248 , 0.18865559, 0.19941502,
0.21508409, 0.23106654, 0.25968871, 0.28172987]),
'peak_periods': array([354.55555556, 41.80349345, 29.09726444, 18.48069498,
14.98122066, 12.33634021, 10.70805369, 9.52537313,
8.57795699, 7.81469388, 6.90692641, 6.06653992,
5.67457024, 5.30066445, 5.01466737, 4.64934434,
4.32775769, 3.85076428, 3.54949944]),
'peak_psd_values': array([1.11760359e+05, 9.23754842e+02, 4.30953799e+02, 5.00534106e+02,
2.29575073e+02, 2.57625752e+02, 1.29920325e+02, 2.19999423e+02,
1.89625638e+02, 7.43277714e+01, 8.74375419e+01, 1.12966403e+02,
6.36422948e+01, 6.98871397e+01, 3.85459405e+01, 5.38120097e+01,
2.91849522e+01, 3.25633603e+01, 3.85414191e+01]),
'psd_values': array([1.30522518e+03, 1.17982857e+03, 7.58749746e+02, ...,
9.74803032e-01, 3.15761961e+00, 2.36110452e+00])},
'Gulkana: Glacier-wide summer mass balance [m.w.e]': {'frequencies': array([0. , 0.03448276, 0.06896552, 0.10344828, 0.13793103,
0.17241379, 0.20689655, 0.24137931, 0.27586207, 0.31034483,
0.34482759, 0.37931034, 0.4137931 , 0.44827586, 0.48275862]),
'peak_frequencies': array([], dtype=float64),
'peak_periods': array([], dtype=float64),
'peak_psd_values': array([], dtype=float64),
'psd_values': array([0.80730905, 0.47516993, 0.19731403, 0.22750331, 0.13724289,
0.26656137, 0.44239662, 0.73287754, 0.33620088, 0.16657124,
1.19729943, 1.53717933, 0.7832844 , 0.98041009])},
'Gulkana: Glacier-wide winter mass balance [m.w.e]': {'frequencies': array([0. , 0.03448276, 0.06896552, 0.10344828, 0.13793103,
0.17241379, 0.20689655, 0.24137931, 0.27586207, 0.31034483,
0.34482759, 0.37931034, 0.4137931 , 0.44827586, 0.48275862]),
'peak_frequencies': array([], dtype=float64),
'peak_periods': array([], dtype=float64),
'peak_psd_values': array([], dtype=float64),
'psd_values': array([0.37409391, 0.26779092, 0.17050665, 0.18600453, 0.57240264,
0.25159897, 0.01326362, 0.01773063, 0.19835878, 0.34267589,
0.24984783, 0.39845999, 0.54194315, 0.17329202])},
'IceThickness [cm]': {'frequencies': array([0. , 0.00434783, 0.00869565, 0.01304348, 0.0173913 ,
0.02173913, 0.02608696, 0.03043478, 0.03478261, 0.03913043,
0.04347826, 0.04782609, 0.05217391, 0.05652174, 0.06086957,
0.06521739, 0.06956522, 0.07391304, 0.07826087, 0.0826087 ,
0.08695652, 0.09130435, 0.09565217, 0.1 , 0.10434783,
0.10869565, 0.11304348, 0.1173913 , 0.12173913, 0.12608696,
0.13043478, 0.13478261, 0.13913043, 0.14347826, 0.14782609,
0.15217391, 0.15652174, 0.16086957, 0.16521739, 0.16956522,
0.17391304, 0.17826087, 0.1826087 , 0.18695652, 0.19130435,
0.19565217, 0.2 , 0.20434783, 0.20869565, 0.21304348,
0.2173913 , 0.22173913, 0.22608696, 0.23043478, 0.23478261,
0.23913043, 0.24347826, 0.24782609, 0.25217391, 0.25652174,
0.26086957, 0.26521739, 0.26956522, 0.27391304, 0.27826087,
0.2826087 , 0.28695652, 0.29130435, 0.29565217, 0.3 ,
0.30434783, 0.30869565, 0.31304348, 0.3173913 , 0.32173913,
0.32608696, 0.33043478, 0.33478261, 0.33913043, 0.34347826,
0.34782609, 0.35217391, 0.35652174, 0.36086957, 0.36521739,
0.36956522, 0.37391304, 0.37826087, 0.3826087 , 0.38695652,
0.39130435, 0.39565217, 0.4 , 0.40434783, 0.40869565,
0.41304348, 0.4173913 , 0.42173913, 0.42608696, 0.43043478,
0.43478261, 0.43913043, 0.44347826, 0.44782609, 0.45217391,
0.45652174, 0.46086957, 0.46521739, 0.46956522, 0.47391304,
0.47826087, 0.4826087 , 0.48695652, 0.49130435, 0.49565217,
0.5 ]),
'peak_frequencies': array([0.00434783, 0.48695652]),
'peak_periods': array([230. , 2.05357143]),
'peak_psd_values': array([6442.40258027, 170.71553402]),
'psd_values': array([2038.90454268, 6442.40258027, 6060.09966608, 2696.60610746,
5602.57919492, 3617.42416932, 3593.06497521, 1475.88287254,
894.46548039, 1817.83349286, 3726.56574999, 1343.72703125,
663.76479143, 244.76164471, 384.53002539, 595.42231833,
955.16732804, 1344.28125765, 512.33779965, 879.67864866,
999.68264299, 500.46721802, 175.47556778, 224.42698547,
692.72814303, 683.85026416, 292.71267229, 177.51436936,
246.00606211, 177.5920678 , 170.65921956, 121.47256609,
254.94771823, 691.61706005, 569.59036187, 280.83169328,
239.61945746, 290.47087085, 226.58874868, 130.42932994,
168.93546175, 213.49586937, 322.92354807, 82.08078751,
172.25938294, 240.68668137, 177.54836061, 126.25588944,
120.21801258, 121.09168287, 126.51064576, 190.71180511,
372.19076479, 301.47650916, 251.06322965, 110.9286811 ,
208.49129526, 197.63371103, 74.11051896, 112.89355998,
113.14251113, 114.01335792, 68.09365588, 34.48172839,
34.1587445 , 28.59409015, 43.87355968, 35.17736843,
58.59269569, 84.78452505, 126.79132205, 91.99260528,
85.07669003, 17.25982591, 56.7066658 , 80.04197289,
140.14234433, 199.71727561, 122.48739111, 30.66331789,
40.35277329, 74.37047178, 65.76215765, 99.93299497,
186.69992178, 215.42117546, 107.3325055 , 46.66264006,
59.38550859, 88.86145232, 62.91992579, 81.44716541,
73.84183006, 96.60356129, 90.96559311, 77.04710039,
118.16212626, 116.30340765, 90.21691336, 172.48160492,
206.83479107, 185.02333059, 138.95445905, 100.56077912,
66.36013848, 102.31948873, 138.33209003, 134.89583688,
120.7012705 , 29.19970266, 43.56733458, 108.88233889,
170.71553402, 73.01409915, 9.16183195])},
'Nenana: Air temperature [C]': {'frequencies': array([0.00000000e+00, 6.41642605e-05, 1.28328521e-04, ...,
4.99839589e-01, 4.99903754e-01, 4.99967918e-01]),
'peak_frequencies': array([0.0026949 , 0.01007379, 0.01790183, 0.02714148, 0.03978184,
0.05158807, 0.06108438, 0.07372474, 0.08379852, 0.09496311,
0.10445942, 0.11254411, 0.1217196 , 0.12986846, 0.13711902,
0.14424126, 0.15360924, 0.16034649, 0.16695541, 0.17439846,
0.18415143, 0.19088868, 0.20410651, 0.2105871 , 0.22329163,
0.23593199, 0.24497915, 0.25158807, 0.2605069 , 0.27475136,
0.28405518, 0.29541226, 0.30317613, 0.30991338, 0.3181264 ,
0.33128008, 0.35065768, 0.35777992, 0.36843118, 0.3883221 ,
0.4 , 0.47276227]),
'peak_periods': array([371.07142857, 99.26751592, 55.86021505, 36.84397163,
25.13709677, 19.38432836, 16.37079832, 13.56396867,
11.93338438, 10.53040541, 9.57309582, 8.88540479,
8.21560358, 7.70009881, 7.29293402, 6.93282918,
6.51002506, 6.2364946 , 5.98962337, 5.73399558,
5.43031359, 5.23865546, 4.8994027 , 4.74862888,
4.47844828, 4.23850965, 4.08198009, 3.97475134,
3.83866995, 3.63965437, 3.52044274, 3.38509991,
3.2984127 , 3.22670807, 3.1434046 , 3.01859384,
2.85178408, 2.79501435, 2.71421108, 2.57518176,
2.5 , 2.11522801]),
'peak_psd_values': array([5.67533127e+05, 2.11163225e+03, 2.31505820e+03, 1.53413785e+03,
1.20001575e+03, 9.79552106e+02, 7.05762628e+02, 6.84195822e+02,
4.18372197e+02, 3.08106728e+02, 3.64078679e+02, 2.77862809e+02,
2.61147557e+02, 1.96780148e+02, 2.38172600e+02, 1.60568846e+02,
2.07970931e+02, 9.46077813e+01, 1.28056895e+02, 8.95140493e+01,
1.26907511e+02, 9.28820775e+01, 1.16705788e+02, 8.10763796e+01,
7.25824933e+01, 4.52498570e+01, 7.04614172e+01, 3.92970031e+01,
6.46356327e+01, 5.23690491e+01, 3.94513506e+01, 3.92750166e+01,
4.57110886e+01, 2.75389291e+01, 3.14667635e+01, 3.56657323e+01,
2.13117031e+01, 3.47196696e+01, 2.76368349e+01, 3.38162112e+01,
2.55219166e+01, 1.78796596e+01]),
'psd_values': array([2.49240513e+03, 2.63040195e+03, 2.57191672e+03, ...,
1.19073826e+00, 6.97820475e+00, 3.73503547e+00])},
'Nenana: Mean Discharge [m3/s]': {'frequencies': array([0.00000000e+00, 8.86446237e-05, 1.77289247e-04, ...,
4.99778388e-01, 4.99867033e-01, 4.99955678e-01]),
'peak_frequencies': array([0.00265934, 0.01365127, 0.02730254, 0.03829448, 0.05150253,
0.06160801, 0.07455013, 0.09227905, 0.10185267, 0.11222409,
0.1211772 , 0.13252371, 0.14777059, 0.16062406, 0.17126141,
0.18021452, 0.18907898, 0.19918447, 0.20866944, 0.2177112 ,
0.22684159, 0.2365925 , 0.25157344, 0.26052655, 0.26939101,
0.28676536, 0.29749136, 0.30688769, 0.32018438, 0.33161954,
0.34137045, 0.35023491, 0.36335431, 0.37478947, 0.38764294,
0.40218066, 0.41920043, 0.42992642, 0.43985462, 0.45084656,
0.46715717, 0.48107437, 0.49135715]),
'peak_periods': array([376.03333333, 73.25324675, 36.62662338, 26.11342593,
19.41652324, 16.23165468, 13.4137931 , 10.83669549,
9.8181027 , 8.9107425 , 8.25237747, 7.5458194 ,
6.76724655, 6.22571744, 5.83902692, 5.54894245,
5.28879512, 5.02047174, 4.79226848, 4.59324104,
4.40836264, 4.22667666, 3.97498238, 3.8383804 ,
3.71207634, 3.48717156, 3.36144219, 3.25852109,
3.12320044, 3.01550388, 2.929369 , 2.85522652,
2.75213467, 2.66816462, 2.57969357, 2.48644479,
2.38549376, 2.32597938, 2.27347844, 2.21804955,
2.14060721, 2.07868067, 2.03517951]),
'peak_psd_values': array([1.97347465e+09, 7.13200486e+06, 1.48687985e+06, 1.00862360e+06,
6.40562754e+05, 2.67229637e+05, 1.97652700e+05, 1.17822021e+05,
7.86753285e+04, 3.07328020e+04, 5.57642460e+04, 4.71390322e+04,
3.78985936e+04, 2.40824919e+04, 3.71329082e+04, 1.44500769e+04,
1.75820387e+04, 1.19263395e+04, 9.79225924e+03, 6.96176567e+03,
1.27232816e+04, 4.45365028e+03, 6.68365608e+03, 2.58500776e+03,
3.89493031e+03, 2.97364870e+03, 1.61231939e+03, 1.41310117e+03,
1.41572988e+03, 2.04611883e+03, 1.37318573e+03, 1.11339858e+03,
1.09381737e+03, 1.05420895e+03, 7.37732880e+02, 5.54595796e+02,
7.37047162e+02, 3.96594668e+02, 6.43667946e+02, 4.50435745e+02,
4.88648504e+02, 3.57807460e+02, 6.35960852e+02]),
'psd_values': array([1.40812012e+07, 9.80146018e+06, 5.14824865e+06, ...,
6.70054304e+01, 4.97560088e+01, 2.83304428e+01])},
'Nenana: Mean water temperature [C]': {'frequencies': array([0. , 0.00082713, 0.00165426, 0.00248139, 0.00330852,
0.00413565, 0.00496278, 0.00578991, 0.00661704, 0.00744417,
0.0082713 , 0.00909843, 0.00992556, 0.01075269, 0.01157982,
0.01240695, 0.01323408, 0.01406121, 0.01488834, 0.01571547,
0.0165426 , 0.01736973, 0.01819686, 0.01902399, 0.01985112,
0.02067825, 0.02150538, 0.02233251, 0.02315964, 0.02398677,
0.0248139 , 0.02564103, 0.02646816, 0.02729529, 0.02812242,
0.02894955, 0.02977667, 0.0306038 , 0.03143093, 0.03225806,
0.03308519, 0.03391232, 0.03473945, 0.03556658, 0.03639371,
0.03722084, 0.03804797, 0.0388751 , 0.03970223, 0.04052936,
0.04135649, 0.04218362, 0.04301075, 0.04383788, 0.04466501,
0.04549214, 0.04631927, 0.0471464 , 0.04797353, 0.04880066,
0.04962779, 0.05045492, 0.05128205, 0.05210918, 0.05293631,
0.05376344, 0.05459057, 0.0554177 , 0.05624483, 0.05707196,
0.05789909, 0.05872622, 0.05955335, 0.06038048, 0.06120761,
0.06203474, 0.06286187, 0.063689 , 0.06451613, 0.06534326,
0.06617039, 0.06699752, 0.06782465, 0.06865178, 0.06947891,
0.07030604, 0.07113317, 0.0719603 , 0.07278743, 0.07361456,
0.07444169, 0.07526882, 0.07609595, 0.07692308, 0.07775021,
0.07857734, 0.07940447, 0.0802316 , 0.08105873, 0.08188586,
0.08271299, 0.08354012, 0.08436725, 0.08519438, 0.08602151,
0.08684864, 0.08767577, 0.08850289, 0.08933002, 0.09015715,
0.09098428, 0.09181141, 0.09263854, 0.09346567, 0.0942928 ,
0.09511993, 0.09594706, 0.09677419, 0.09760132, 0.09842845,
0.09925558, 0.10008271, 0.10090984, 0.10173697, 0.1025641 ,
0.10339123, 0.10421836, 0.10504549, 0.10587262, 0.10669975,
0.10752688, 0.10835401, 0.10918114, 0.11000827, 0.1108354 ,
0.11166253, 0.11248966, 0.11331679, 0.11414392, 0.11497105,
0.11579818, 0.11662531, 0.11745244, 0.11827957, 0.1191067 ,
0.11993383, 0.12076096, 0.12158809, 0.12241522, 0.12324235,
0.12406948, 0.12489661, 0.12572374, 0.12655087, 0.127378 ,
0.12820513, 0.12903226, 0.12985939, 0.13068652, 0.13151365,
0.13234078, 0.13316791, 0.13399504, 0.13482217, 0.1356493 ,
0.13647643, 0.13730356, 0.13813069, 0.13895782, 0.13978495,
0.14061208, 0.14143921, 0.14226634, 0.14309347, 0.1439206 ,
0.14474773, 0.14557486, 0.14640199, 0.14722911, 0.14805624,
0.14888337, 0.1497105 , 0.15053763, 0.15136476, 0.15219189,
0.15301902, 0.15384615, 0.15467328, 0.15550041, 0.15632754,
0.15715467, 0.1579818 , 0.15880893, 0.15963606, 0.16046319,
0.16129032, 0.16211745, 0.16294458, 0.16377171, 0.16459884,
0.16542597, 0.1662531 , 0.16708023, 0.16790736, 0.16873449,
0.16956162, 0.17038875, 0.17121588, 0.17204301, 0.17287014,
0.17369727, 0.1745244 , 0.17535153, 0.17617866, 0.17700579,
0.17783292, 0.17866005, 0.17948718, 0.18031431, 0.18114144,
0.18196857, 0.1827957 , 0.18362283, 0.18444996, 0.18527709,
0.18610422, 0.18693135, 0.18775848, 0.18858561, 0.18941274,
0.19023987, 0.191067 , 0.19189413, 0.19272126, 0.19354839,
0.19437552, 0.19520265, 0.19602978, 0.19685691, 0.19768404,
0.19851117, 0.1993383 , 0.20016543, 0.20099256, 0.20181969,
0.20264682, 0.20347395, 0.20430108, 0.20512821, 0.20595533,
0.20678246, 0.20760959, 0.20843672, 0.20926385, 0.21009098,
0.21091811, 0.21174524, 0.21257237, 0.2133995 , 0.21422663,
0.21505376, 0.21588089, 0.21670802, 0.21753515, 0.21836228,
0.21918941, 0.22001654, 0.22084367, 0.2216708 , 0.22249793,
0.22332506, 0.22415219, 0.22497932, 0.22580645, 0.22663358,
0.22746071, 0.22828784, 0.22911497, 0.2299421 , 0.23076923,
0.23159636, 0.23242349, 0.23325062, 0.23407775, 0.23490488,
0.23573201, 0.23655914, 0.23738627, 0.2382134 , 0.23904053,
0.23986766, 0.24069479, 0.24152192, 0.24234905, 0.24317618,
0.24400331, 0.24483044, 0.24565757, 0.2464847 , 0.24731183,
0.24813896, 0.24896609, 0.24979322, 0.25062035, 0.25144748,
0.25227461, 0.25310174, 0.25392887, 0.254756 , 0.25558313,
0.25641026, 0.25723739, 0.25806452, 0.25889165, 0.25971878,
0.26054591, 0.26137304, 0.26220017, 0.2630273 , 0.26385443,
0.26468156, 0.26550868, 0.26633581, 0.26716294, 0.26799007,
0.2688172 , 0.26964433, 0.27047146, 0.27129859, 0.27212572,
0.27295285, 0.27377998, 0.27460711, 0.27543424, 0.27626137,
0.2770885 , 0.27791563, 0.27874276, 0.27956989, 0.28039702,
0.28122415, 0.28205128, 0.28287841, 0.28370554, 0.28453267,
0.2853598 , 0.28618693, 0.28701406, 0.28784119, 0.28866832,
0.28949545, 0.29032258, 0.29114971, 0.29197684, 0.29280397,
0.2936311 , 0.29445823, 0.29528536, 0.29611249, 0.29693962,
0.29776675, 0.29859388, 0.29942101, 0.30024814, 0.30107527,
0.3019024 , 0.30272953, 0.30355666, 0.30438379, 0.30521092,
0.30603805, 0.30686518, 0.30769231, 0.30851944, 0.30934657,
0.3101737 , 0.31100083, 0.31182796, 0.31265509, 0.31348222,
0.31430935, 0.31513648, 0.31596361, 0.31679074, 0.31761787,
0.318445 , 0.31927213, 0.32009926, 0.32092639, 0.32175352,
0.32258065, 0.32340778, 0.3242349 , 0.32506203, 0.32588916,
0.32671629, 0.32754342, 0.32837055, 0.32919768, 0.33002481,
0.33085194, 0.33167907, 0.3325062 , 0.33333333, 0.33416046,
0.33498759, 0.33581472, 0.33664185, 0.33746898, 0.33829611,
0.33912324, 0.33995037, 0.3407775 , 0.34160463, 0.34243176,
0.34325889, 0.34408602, 0.34491315, 0.34574028, 0.34656741,
0.34739454, 0.34822167, 0.3490488 , 0.34987593, 0.35070306,
0.35153019, 0.35235732, 0.35318445, 0.35401158, 0.35483871,
0.35566584, 0.35649297, 0.3573201 , 0.35814723, 0.35897436,
0.35980149, 0.36062862, 0.36145575, 0.36228288, 0.36311001,
0.36393714, 0.36476427, 0.3655914 , 0.36641853, 0.36724566,
0.36807279, 0.36889992, 0.36972705, 0.37055418, 0.37138131,
0.37220844, 0.37303557, 0.3738627 , 0.37468983, 0.37551696,
0.37634409, 0.37717122, 0.37799835, 0.37882548, 0.37965261,
0.38047974, 0.38130687, 0.382134 , 0.38296112, 0.38378825,
0.38461538, 0.38544251, 0.38626964, 0.38709677, 0.3879239 ,
0.38875103, 0.38957816, 0.39040529, 0.39123242, 0.39205955,
0.39288668, 0.39371381, 0.39454094, 0.39536807, 0.3961952 ,
0.39702233, 0.39784946, 0.39867659, 0.39950372, 0.40033085,
0.40115798, 0.40198511, 0.40281224, 0.40363937, 0.4044665 ,
0.40529363, 0.40612076, 0.40694789, 0.40777502, 0.40860215,
0.40942928, 0.41025641, 0.41108354, 0.41191067, 0.4127378 ,
0.41356493, 0.41439206, 0.41521919, 0.41604632, 0.41687345,
0.41770058, 0.41852771, 0.41935484, 0.42018197, 0.4210091 ,
0.42183623, 0.42266336, 0.42349049, 0.42431762, 0.42514475,
0.42597188, 0.42679901, 0.42762614, 0.42845327, 0.4292804 ,
0.43010753, 0.43093466, 0.43176179, 0.43258892, 0.43341605,
0.43424318, 0.43507031, 0.43589744, 0.43672457, 0.4375517 ,
0.43837883, 0.43920596, 0.44003309, 0.44086022, 0.44168734,
0.44251447, 0.4433416 , 0.44416873, 0.44499586, 0.44582299,
0.44665012, 0.44747725, 0.44830438, 0.44913151, 0.44995864,
0.45078577, 0.4516129 , 0.45244003, 0.45326716, 0.45409429,
0.45492142, 0.45574855, 0.45657568, 0.45740281, 0.45822994,
0.45905707, 0.4598842 , 0.46071133, 0.46153846, 0.46236559,
0.46319272, 0.46401985, 0.46484698, 0.46567411, 0.46650124,
0.46732837, 0.4681555 , 0.46898263, 0.46980976, 0.47063689,
0.47146402, 0.47229115, 0.47311828, 0.47394541, 0.47477254,
0.47559967, 0.4764268 , 0.47725393, 0.47808106, 0.47890819,
0.47973532, 0.48056245, 0.48138958, 0.48221671, 0.48304384,
0.48387097, 0.4846981 , 0.48552523, 0.48635236, 0.48717949,
0.48800662, 0.48883375, 0.48966088, 0.49048801, 0.49131514,
0.49214227, 0.4929694 , 0.49379653, 0.49462366, 0.49545079,
0.49627792, 0.49710505, 0.49793218, 0.49875931, 0.49958644]),
'peak_frequencies': array([0.00248139]),
'peak_periods': array([403.]),
'peak_psd_values': array([12188.54860403]),
'psd_values': array([1.02603885e+03, 8.56058921e+02, 8.56255899e+03, 1.21885486e+04,
1.06633723e+04, 8.56274663e+03, 3.79239891e+03, 4.22078323e+02,
3.81221960e+02, 1.50720867e+02, 1.51392089e+02, 5.94296710e+02,
2.57403908e+02, 1.41528892e+02, 9.19831794e+01, 9.71413757e+01,
1.26931795e+01, 2.70749541e+01, 6.44215324e+01, 4.54604817e+01,
8.46806619e+01, 4.25869435e+01, 5.63140675e+01, 7.81833803e+01,
6.62594955e+01, 5.00394103e+01, 5.85903509e+01, 4.79881345e+01,
1.01950435e+01, 1.97448668e+01, 9.02821890e+00, 5.39979811e+01,
6.21016677e+01, 2.65796874e+01, 6.33528901e+00, 1.04696601e+01,
4.17255064e+00, 2.40725451e+01, 4.20335400e+01, 2.80534005e+01,
2.02505858e+01, 3.41844905e+01, 3.08770323e+01, 3.28474693e+01,
1.64385848e+01, 1.30132187e+01, 2.09592556e+01, 8.65378049e+00,
1.76779647e+01, 6.29786974e+00, 4.93396475e+00, 1.05150169e+01,
1.95213923e+01, 8.32307161e+00, 2.89541776e+00, 7.95164168e+00,
1.03882428e+01, 5.50743293e+00, 1.56132420e+00, 7.43886207e+00,
2.45102533e+01, 1.82760861e+01, 5.52774234e+00, 9.53116749e+00,
3.14262574e+00, 7.62587857e+00, 1.12237344e+01, 5.85203249e+00,
9.01912627e+00, 6.69445986e+00, 5.61127134e+00, 4.85410059e+00,
2.76306247e+00, 6.78696754e+00, 8.85227740e+00, 5.33137296e+00,
3.24361345e+00, 6.07265558e+00, 1.08448120e+01, 1.06485321e+01,
5.67688232e+00, 2.24705059e+00, 3.32841797e+00, 4.35566561e+00,
6.33784510e+00, 3.75793061e+00, 1.87338226e+00, 3.61856481e+00,
3.01959161e+00, 2.38573944e+00, 8.85012131e+00, 4.56825717e+00,
3.72094509e+00, 4.36170848e+00, 2.96982636e+00, 2.19623324e+00,
4.74794465e+00, 8.51260934e-01, 5.47201285e-01, 3.31098908e+00,
5.88828744e+00, 4.73017973e+00, 3.01249791e+00, 5.42065847e-01,
4.71430868e-01, 5.06263626e+00, 5.98075528e+00, 8.31242974e-01,
8.90950093e-01, 3.41585535e+00, 3.15019675e+00, 1.30147439e+00,
3.09337700e+00, 5.77785606e+00, 5.59633725e+00, 2.98852480e+00,
1.12228696e+00, 2.93346242e-01, 4.05334382e+00, 2.69450113e+00,
3.59686059e-01, 1.46182078e+00, 1.95933759e+00, 8.57514213e-01,
1.56679558e+00, 2.80191942e+00, 2.02089400e+00, 2.12782663e+00,
4.52811851e+00, 6.31065659e+00, 6.90176525e+00, 6.33143504e+00,
2.68828962e+00, 4.13200539e+00, 6.58055261e+00, 4.29948207e+00,
2.37180412e+00, 3.28029440e+00, 3.51551609e+00, 2.77115208e+00,
3.83811222e+00, 4.61032099e+00, 5.84949916e+00, 2.92071184e+00,
3.16614921e+00, 4.35327561e+00, 1.92254307e+00, 1.10009479e+00,
2.36284538e+00, 2.07433653e+00, 2.59653265e+00, 2.76909293e+00,
2.06788859e+00, 1.23436162e+00, 1.64903379e+00, 3.24584200e+00,
1.51732773e+00, 7.54534661e-01, 2.43971830e+00, 1.68260876e+00,
4.12207835e+00, 4.43556143e+00, 2.77426006e+00, 2.66243718e+00,
2.09276311e+00, 6.82576145e-01, 6.84074238e-01, 3.14398221e-01,
6.23285188e-01, 1.71319203e+00, 1.63177677e+00, 9.29950352e-01,
2.74029961e+00, 2.01501195e+00, 4.87187569e-01, 4.39944788e+00,
3.64543765e+00, 1.14556950e+00, 2.81609721e+00, 3.77901633e+00,
2.34382517e+00, 1.52331936e+00, 3.91915597e+00, 3.47681497e+00,
8.26035995e-01, 1.80281864e+00, 1.43964426e+00, 1.05030976e+00,
2.70578808e+00, 1.95971524e+00, 2.68781431e-01, 7.80898872e-02,
5.28705881e-01, 7.89819890e-01, 6.95427049e-01, 2.57883158e-01,
6.00753080e-02, 7.46425383e-01, 2.10621568e+00, 1.70287859e+00,
9.23724141e-01, 1.67061103e+00, 2.25626866e+00, 2.39382979e+00,
1.87281381e+00, 1.29737186e+00, 1.07967833e+00, 1.21785599e+00,
1.32127459e+00, 1.25268354e+00, 8.35092711e-01, 7.02368508e-01,
7.10298144e-01, 3.15023535e-01, 2.73638612e-02, 2.84668803e-01,
3.97177134e-01, 4.09767615e-01, 6.64749224e-01, 7.49162240e-01,
5.16749935e-01, 3.95687774e-01, 4.07486579e-01, 6.05135060e-01,
6.38424782e-01, 1.58864464e+00, 1.24405132e+00, 1.38242876e-01,
3.08962877e-01, 1.32090898e-01, 8.82894808e-01, 7.58955686e-01,
4.20501029e-01, 8.32972894e-02, 7.83535251e-01, 3.31309265e-01,
4.95292196e-01, 1.15571800e+00, 4.46440393e-01, 5.30556741e-01,
9.94077472e-01, 5.16738352e-01, 5.69734618e-01, 7.70564509e-01,
4.65175917e-01, 2.64647416e-01, 4.70489349e-01, 2.04554632e-01,
1.30876626e-01, 9.22625847e-02, 7.52747298e-01, 3.64810167e-01,
3.76787497e-01, 7.32026308e-01, 2.43273847e-01, 2.94595206e-01,
1.67517054e-01, 4.59232520e-01, 1.38691341e+00, 1.02322149e+00,
7.87895183e-01, 4.46615431e-01, 1.33065141e-01, 7.15684474e-02,
3.05190072e-01, 1.50436106e-01, 2.09517722e-01, 3.08386691e-01,
3.75132065e-01, 1.68848083e-01, 9.57440161e-02, 2.18990185e-01,
1.93342375e-01, 4.70187865e-01, 9.65950677e-01, 9.28076820e-01,
5.82988714e-01, 3.64753034e-01, 1.58159933e-01, 2.72911291e-01,
6.52282630e-01, 8.06450626e-01, 8.45571166e-01, 6.31989616e-01,
1.76273494e-01, 2.59366815e-01, 4.61435413e-01, 4.04139278e-01,
4.16103564e-01, 1.94464942e-01, 2.86862955e-01, 5.22301380e-01,
6.21660020e-01, 2.45793564e-01, 1.01720446e-01, 2.29199207e-01,
4.28902515e-01, 3.28007436e-01, 4.51459751e-01, 1.52698965e-01,
7.88521120e-02, 2.52109878e-01, 1.89743089e-01, 1.18235138e-01,
4.27952530e-01, 3.77112031e-01, 1.88242994e-01, 2.52714895e-01,
1.94917465e-01, 2.67218540e-01, 4.53213495e-01, 5.29932617e-01,
6.21076503e-01, 2.41088817e-01, 7.82283240e-02, 1.25368463e-01,
2.16787101e-01, 7.96015052e-02, 2.69002643e-02, 1.96455346e-01,
2.40760939e-01, 3.91226283e-01, 6.30617548e-01, 4.83935919e-01,
9.22386911e-02, 3.01430286e-01, 1.12342436e-01, 1.83402812e-01,
2.77945180e-01, 1.76450408e-01, 1.96645954e-01, 2.01795684e-01,
1.60761390e-01, 1.36451965e-01, 2.67641486e-01, 2.33490284e-01,
1.27947909e-01, 2.86546986e-01, 2.78452901e-01, 1.23957247e-01,
7.18110756e-02, 6.54655196e-02, 6.14194404e-02, 3.48521294e-02,
2.63894888e-01, 2.67564843e-01, 2.81084352e-01, 2.09808835e-01,
1.08348614e-01, 3.54627267e-01, 6.93382336e-01, 3.42237755e-01,
1.30102504e-01, 2.25073004e-01, 2.06707583e-01, 1.64304585e-01,
3.65633892e-01, 3.87601764e-01, 1.07161578e-01, 2.20441882e-01,
3.73306887e-01, 9.09824558e-02, 1.70925000e-01, 2.11144667e-01,
2.66640409e-01, 2.76621830e-01, 1.48806688e-01, 1.69082074e-01,
7.28710803e-02, 6.99607334e-02, 1.06174074e-01, 1.62933459e-01,
1.76800326e-01, 9.15427297e-02, 1.27442651e-02, 4.75318402e-03,
3.91707008e-02, 2.24437611e-01, 3.28008188e-01, 8.48998057e-02,
5.04208089e-02, 2.24809213e-02, 3.47180820e-01, 5.29769644e-01,
2.83444944e-01, 2.96927789e-01, 2.90859970e-01, 1.03430019e-01,
7.24689339e-02, 3.82134017e-01, 3.24803660e-01, 1.19021455e-01,
1.62395678e-01, 1.31914903e-01, 3.54677030e-02, 1.71525044e-01,
2.41254503e-01, 1.01081618e-01, 1.74630226e-01, 1.24023894e-01,
2.25390992e-03, 4.50570667e-02, 1.65977805e-01, 5.37443574e-02,
1.10983325e-01, 3.18741653e-01, 1.46944835e-01, 7.81110838e-02,
1.26289550e-01, 1.31770960e-01, 1.31742245e-01, 3.48706707e-01,
3.14276436e-01, 3.12357354e-02, 3.15304187e-02, 5.81135150e-02,
1.24695517e-01, 2.27894394e-01, 1.16689358e-01, 9.06596360e-02,
1.00104494e-01, 2.12020106e-01, 6.75505484e-02, 1.51772192e-01,
2.91146899e-01, 1.50224024e-01, 4.30662246e-02, 1.34650895e-01,
7.36381888e-02, 6.15758312e-02, 8.25665860e-02, 4.48942631e-02,
1.31761519e-01, 1.40110850e-01, 1.42803207e-01, 2.35113001e-01,
1.49799265e-01, 1.13459311e-01, 1.52743571e-01, 1.26733886e-01,
4.68175883e-02, 7.12078406e-02, 2.48569118e-02, 1.07798557e-01,
2.17302346e-01, 1.31338378e-01, 7.91022065e-02, 1.05887099e-01,
1.01669721e-01, 2.86130392e-02, 1.59341658e-01, 2.92199211e-01,
5.97927893e-02, 6.70415885e-02, 8.08309762e-02, 2.50544904e-02,
1.25677546e-01, 2.35701743e-01, 1.45510084e-01, 8.50473271e-02,
5.66459538e-02, 1.46208373e-02, 5.29674504e-02, 1.31422145e-01,
5.54715606e-02, 2.60657074e-02, 7.43438266e-02, 3.84888056e-02,
3.57729230e-02, 1.30419616e-01, 1.09490897e-01, 5.51299760e-02,
1.35849712e-01, 1.92397785e-01, 4.86093362e-02, 7.06809267e-02,
1.60471603e-01, 4.40804906e-02, 1.09774761e-01, 2.02831083e-01,
1.23552134e-01, 7.52118251e-02, 5.45313358e-02, 9.41817205e-02,
1.99640407e-01, 1.17679938e-01, 5.49429228e-02, 2.36575598e-02,
1.57120375e-02, 9.16453487e-02, 1.35847490e-01, 1.71884810e-01,
8.56399439e-02, 3.96926783e-02, 7.04520651e-02, 1.31100098e-01,
2.96502818e-01, 1.77149792e-01, 9.03213610e-02, 1.42424708e-01,
1.09795366e-01, 3.95899738e-02, 1.17626066e-01, 1.53391601e-01,
1.13731755e-01, 2.33600368e-01, 1.49579797e-01, 9.77589922e-02,
9.88778999e-02, 1.31109816e-01, 7.64476921e-02, 6.86255849e-02,
1.48917352e-01, 6.03576423e-02, 7.17731422e-02, 1.44928678e-01,
4.69626897e-02, 9.86396997e-02, 2.30252375e-01, 6.16923696e-02,
2.72200075e-02, 1.19138446e-01, 2.58550646e-02, 8.93866319e-02,
2.34558526e-01, 1.24734534e-01, 5.61778322e-03, 4.97112554e-02,
5.11852088e-02, 5.85843046e-02, 2.09383824e-01, 2.75398725e-01,
8.92476174e-02, 5.48205008e-02, 1.13403952e-01, 8.71811917e-02,
1.83586867e-01, 1.93600771e-01, 8.38636091e-02, 6.33708280e-02,
7.04389253e-02, 7.99341675e-02, 1.03105342e-01, 6.05313330e-02,
4.40981231e-02, 5.88190891e-02, 7.12207200e-02, 8.48736172e-02,
1.21452601e-01, 1.28364451e-01, 1.60780335e-01, 1.75392824e-01,
1.16382245e-01, 7.48731626e-02, 9.80759925e-02, 1.09759380e-01,
9.27914766e-02, 9.25002451e-02, 1.54307187e-01, 9.37133322e-02,
1.21835525e-01, 5.64561559e-02, 3.85518685e-02, 1.83770263e-01,
1.59625099e-01, 4.31957463e-02, 7.74825029e-02, 5.31271239e-02,
2.22552725e-02, 1.56467019e-01, 2.42440470e-01, 8.91339726e-02,
2.65345901e-02, 5.42666103e-02, 4.29512185e-02, 7.62506510e-02,
2.32184048e-01, 1.15666073e-01, 3.60927744e-02, 1.46464203e-01,
8.94927190e-02, 4.70840779e-02, 1.74284939e-01, 1.06792770e-01,
2.49297513e-02, 1.13347452e-01, 6.43531203e-02, 3.43156977e-02,
2.44003545e-02, 9.12126887e-02, 9.82367464e-02, 7.41718323e-02,
9.91564967e-02, 5.47604182e-02, 6.43084705e-02, 1.01041104e-01,
5.15225248e-02, 1.32066826e-01, 1.94259025e-01, 7.35538037e-02,
3.26383455e-02, 4.30259137e-02, 6.03619613e-02, 1.75221408e-01])},
'Nenana: Rainfall [mm]': {'frequencies': array([0.00000000e+00, 6.76910580e-05, 1.35382116e-04, ...,
4.99830772e-01, 4.99898463e-01, 4.99966154e-01]),
'peak_frequencies': array([0.00270764, 0.01313207, 0.02037501, 0.02755026, 0.03750085,
0.04582685, 0.05306979, 0.0613281 , 0.07107561, 0.07953699,
0.08847221, 0.09632438, 0.10553036, 0.11419481, 0.12231774,
0.13091451, 0.14093278, 0.15690787, 0.16543695, 0.17328911,
0.18107358, 0.18838421, 0.19711636, 0.20720233, 0.21464834,
0.22602044, 0.233128 , 0.24098017, 0.25505991, 0.26561971,
0.27428417, 0.28795776, 0.30095444, 0.30988966, 0.31814797,
0.34617207, 0.35388885, 0.36986394, 0.38116835, 0.38929127,
0.39694036, 0.41460773, 0.42476139, 0.44012726, 0.45210858,
0.46760983, 0.47661274, 0.48615718]),
'peak_periods': array([369.325 , 76.14948454, 49.07973422, 36.2972973 ,
26.66606498, 21.82127031, 18.84311224, 16.30573951,
14.06952381, 12.57276596, 11.30298393, 10.38158819,
9.47594612, 8.75696503, 8.17542889, 7.63857291,
7.09558117, 6.37316652, 6.04459902, 5.77070313,
5.52261682, 5.3083004 , 5.0731456 , 4.82620059,
4.65878272, 4.42437856, 4.28948897, 4.1497191 ,
3.92064756, 3.76478084, 3.6458539 , 3.47273155,
3.32276203, 3.226955 , 3.14319149, 2.8887368 ,
2.82574598, 2.70369693, 2.6235127 , 2.56877065,
2.51927012, 2.41191837, 2.35426295, 2.27207013,
2.21185806, 2.13853503, 2.09813947, 2.05694793]),
'peak_psd_values': array([1113.98589858, 64.12663935, 76.8496656 , 68.31602308,
71.12236981, 73.61608763, 77.62166056, 44.10635139,
48.00238994, 52.13832507, 25.21445839, 64.30458483,
57.91811892, 51.38306536, 54.48154507, 35.59044945,
39.47695669, 41.98256203, 52.82329786, 56.75891339,
27.43135811, 61.72498764, 36.80043823, 28.82474738,
31.67806585, 44.4432828 , 24.97228115, 39.48180371,
42.04329997, 51.04065917, 41.7759226 , 27.37185093,
50.85100477, 47.8990802 , 34.64183816, 22.98738245,
48.84415165, 34.00570521, 30.97451406, 24.52651833,
47.11418099, 43.0117962 , 33.86989951, 28.29727943,
35.58349193, 18.80463052, 33.12364605, 27.81834763]),
'psd_values': array([36.23502551, 59.26600343, 27.25616306, ..., 37.90268703,
35.10213406, 17.22773561])},
'Nenana: Snow depth [mm]': {'frequencies': array([0.00000000e+00, 1.25125125e-04, 2.50250250e-04, ...,
4.99749750e-01, 4.99874875e-01, 5.00000000e-01]),
'peak_frequencies': array([0.00262763, 0.01539039, 0.0279029 , 0.04542042, 0.06293794,
0.08721221, 0.10860861, 0.12174675, 0.13726226, 0.15377878,
0.17154655, 0.18706206, 0.20182683, 0.2256006 , 0.246997 ,
0.27127127, 0.28841341, 0.30455455, 0.3292042 , 0.34784785,
0.36236236, 0.37587588, 0.38913914, 0.41003504, 0.42317317,
0.43906406, 0.45895896, 0.47234735, 0.48523524, 0.49912412]),
'peak_periods': array([380.57142857, 64.97560976, 35.83856502, 22.01652893,
15.88866799, 11.46628407, 9.20737327, 8.21377184,
7.28532361, 6.50284784, 5.82932166, 5.3458194 ,
4.95474272, 4.43261231, 4.04863222, 3.68634686,
3.46724512, 3.28348398, 3.03762828, 2.87482014,
2.75966851, 2.66045273, 2.56977492, 2.43881599,
2.36309876, 2.27757196, 2.17884406, 2.11708609,
2.06085611, 2.00350965]),
'peak_psd_values': array([9.56587200e+07, 3.96305727e+05, 1.48189479e+05, 6.57966348e+04,
2.97239185e+04, 2.03728183e+04, 1.64148427e+04, 4.23587510e+03,
7.00028841e+03, 5.23645990e+03, 4.96934468e+03, 3.63198260e+03,
3.46183079e+03, 4.51305229e+03, 3.39568523e+03, 1.97814754e+03,
1.89981477e+03, 2.58678924e+03, 1.40454325e+03, 1.88000447e+03,
1.01540600e+03, 1.45506407e+03, 1.11747845e+03, 1.55061966e+03,
6.62967740e+02, 1.89012475e+03, 1.01171105e+03, 7.78809210e+02,
1.71529783e+03, 8.29317224e+02]),
'psd_values': array([9.74136689e+06, 2.11533541e+07, 1.29933528e+07, ...,
4.31513470e+01, 1.73914523e+02, 1.38753590e+02])},
'Nenana: Snowfall [mm]': {'frequencies': array([0.00000000e+00, 1.00280786e-04, 2.00561572e-04, ...,
4.99799438e-01, 4.99899719e-01, 5.00000000e-01]),
'peak_frequencies': array([0.0026073 , 0.01504212, 0.03449659, 0.04913759, 0.06066988,
0.07119936, 0.08584035, 0.09647012, 0.11522262, 0.12695548,
0.1403931 , 0.15172483, 0.16837144, 0.18301243, 0.19825511,
0.21570397, 0.22673486, 0.23686322, 0.24779382, 0.25902527,
0.27787806, 0.28820698, 0.29873646, 0.3131769 , 0.3241075 ,
0.34426394, 0.3548937 , 0.36492178, 0.37855997, 0.38969114,
0.39971921, 0.4112515 , 0.4284998 , 0.44023265, 0.45266747,
0.47212194, 0.4827517 , 0.49749298]),
'peak_periods': array([383.53846154, 66.48 , 28.98837209, 20.35102041,
16.48264463, 14.04507042, 11.64953271, 10.36590437,
8.67885117, 7.87677725, 7.12285714, 6.59087905,
5.93924955, 5.46410959, 5.04400607, 4.63598326,
4.41043786, 4.22184589, 4.03561311, 3.86062718,
3.59870083, 3.4697286 , 3.34743202, 3.19308357,
3.08539604, 2.90474803, 2.81774513, 2.74031327,
2.6415894 , 2.56613484, 2.50175615, 2.43160205,
2.33372338, 2.2715262 , 2.20912716, 2.11809686,
2.07145825, 2.01007861]),
'peak_psd_values': array([24349.18542556, 3143.67508619, 2283.62863265, 1997.2964818 ,
1480.12563308, 2246.40538387, 1650.47939038, 1681.05261666,
1369.97309225, 1538.99886728, 1269.68131788, 2166.62796729,
1489.41179579, 1446.07195632, 1491.50725667, 1173.95505098,
1346.16057714, 1140.44150764, 1141.27214186, 1170.25749803,
1555.66356962, 834.18652673, 1122.53528072, 799.11670471,
1252.34007282, 1025.82735463, 1281.03010328, 1286.12816208,
1636.99726083, 1120.54912124, 1259.67904076, 965.63182882,
1320.1250837 , 824.1394084 , 1076.15375269, 1276.30793435,
1342.17167773, 950.9413792 ]),
'psd_values': array([1639.35021187, 2263.00691167, 3088.23424851, ..., 37.8383367 ,
62.46582058, 56.09444299])},
'Regional: Air temperature [C]': {'frequencies': array([0.00000000e+00, 5.18645298e-05, 1.03729060e-04, ...,
4.99870339e-01, 4.99922203e-01, 4.99974068e-01]),
'peak_frequencies': array([0.00269696, 0.00814273, 0.01628546, 0.02307972, 0.03008143,
0.03697941, 0.04584824, 0.05160521, 0.05788082, 0.06685338,
0.07302526, 0.07821171, 0.08355376, 0.09231886, 0.09880193,
0.1042477 , 0.11078264, 0.1174213 , 0.12499352, 0.13075048,
0.13858202, 0.14537628, 0.15165189, 0.16124682, 0.16809294,
0.17582076, 0.18214823, 0.19210622, 0.19760386, 0.20424252,
0.21020694, 0.21560085, 0.22462528, 0.24708262]),
'peak_periods': array([370.78846154, 122.8089172 , 61.4044586 , 43.32808989,
33.24310345, 27.04207574, 21.81108597, 19.37788945,
17.27688172, 14.95810706, 13.69389205, 12.78580902,
11.96834264, 10.83202247, 10.12125984, 9.59253731,
9.02668539, 8.51634276, 8.00041494, 7.64815549,
7.21594311, 6.87870139, 6.59404925, 6.20167256,
5.94908979, 5.68761062, 5.49003417, 5.20545356,
5.06062992, 4.89614017, 4.75721688, 4.63820063,
4.45185869, 4.04722922]),
'peak_psd_values': array([2.06759676e+06, 3.05682509e+03, 1.94041594e+03, 1.75372650e+03,
1.11522154e+03, 1.19100482e+03, 6.88458631e+02, 6.31177761e+02,
4.11639510e+02, 3.99387423e+02, 3.59568470e+02, 1.55916802e+02,
3.37379997e+02, 2.16413827e+02, 1.16586371e+02, 2.40224602e+02,
1.27597088e+02, 1.15933634e+02, 1.70709014e+02, 9.74476970e+01,
1.26322934e+02, 6.37369046e+01, 7.26269082e+01, 7.83764099e+01,
8.88371753e+01, 4.58924171e+01, 4.76550683e+01, 4.85393485e+01,
3.56192681e+01, 1.97069949e+01, 3.81996196e+01, 4.48756160e+01,
3.31429514e+01, 2.40919000e+01]),
'psd_values': array([1.35267863e+03, 1.52088472e+03, 1.95195474e+03, ...,
7.12925332e-02, 1.15579132e-01, 2.91106473e-01])},
'Regional: Cloud coverage [%]': {'frequencies': array([0. , 0.00136799, 0.00273598, 0.00410397, 0.00547196,
0.00683995, 0.00820793, 0.00957592, 0.01094391, 0.0123119 ,
0.01367989, 0.01504788, 0.01641587, 0.01778386, 0.01915185,
0.02051984, 0.02188782, 0.02325581, 0.0246238 , 0.02599179,
0.02735978, 0.02872777, 0.03009576, 0.03146375, 0.03283174,
0.03419973, 0.03556772, 0.0369357 , 0.03830369, 0.03967168,
0.04103967, 0.04240766, 0.04377565, 0.04514364, 0.04651163,
0.04787962, 0.04924761, 0.0506156 , 0.05198358, 0.05335157,
0.05471956, 0.05608755, 0.05745554, 0.05882353, 0.06019152,
0.06155951, 0.0629275 , 0.06429549, 0.06566347, 0.06703146,
0.06839945, 0.06976744, 0.07113543, 0.07250342, 0.07387141,
0.0752394 , 0.07660739, 0.07797538, 0.07934337, 0.08071135,
0.08207934, 0.08344733, 0.08481532, 0.08618331, 0.0875513 ,
0.08891929, 0.09028728, 0.09165527, 0.09302326, 0.09439124,
0.09575923, 0.09712722, 0.09849521, 0.0998632 , 0.10123119,
0.10259918, 0.10396717, 0.10533516, 0.10670315, 0.10807114,
0.10943912, 0.11080711, 0.1121751 , 0.11354309, 0.11491108,
0.11627907, 0.11764706, 0.11901505, 0.12038304, 0.12175103,
0.12311902, 0.124487 , 0.12585499, 0.12722298, 0.12859097,
0.12995896, 0.13132695, 0.13269494, 0.13406293, 0.13543092,
0.13679891, 0.13816689, 0.13953488, 0.14090287, 0.14227086,
0.14363885, 0.14500684, 0.14637483, 0.14774282, 0.14911081,
0.1504788 , 0.15184679, 0.15321477, 0.15458276, 0.15595075,
0.15731874, 0.15868673, 0.16005472, 0.16142271, 0.1627907 ,
0.16415869, 0.16552668, 0.16689466, 0.16826265, 0.16963064,
0.17099863, 0.17236662, 0.17373461, 0.1751026 , 0.17647059,
0.17783858, 0.17920657, 0.18057456, 0.18194254, 0.18331053,
0.18467852, 0.18604651, 0.1874145 , 0.18878249, 0.19015048,
0.19151847, 0.19288646, 0.19425445, 0.19562244, 0.19699042,
0.19835841, 0.1997264 , 0.20109439, 0.20246238, 0.20383037,
0.20519836, 0.20656635, 0.20793434, 0.20930233, 0.21067031,
0.2120383 , 0.21340629, 0.21477428, 0.21614227, 0.21751026,
0.21887825, 0.22024624, 0.22161423, 0.22298222, 0.22435021,
0.22571819, 0.22708618, 0.22845417, 0.22982216, 0.23119015,
0.23255814, 0.23392613, 0.23529412, 0.23666211, 0.2380301 ,
0.23939808, 0.24076607, 0.24213406, 0.24350205, 0.24487004,
0.24623803, 0.24760602, 0.24897401, 0.250342 , 0.25170999,
0.25307798, 0.25444596, 0.25581395, 0.25718194, 0.25854993,
0.25991792, 0.26128591, 0.2626539 , 0.26402189, 0.26538988,
0.26675787, 0.26812585, 0.26949384, 0.27086183, 0.27222982,
0.27359781, 0.2749658 , 0.27633379, 0.27770178, 0.27906977,
0.28043776, 0.28180575, 0.28317373, 0.28454172, 0.28590971,
0.2872777 , 0.28864569, 0.29001368, 0.29138167, 0.29274966,
0.29411765, 0.29548564, 0.29685363, 0.29822161, 0.2995896 ,
0.30095759, 0.30232558, 0.30369357, 0.30506156, 0.30642955,
0.30779754, 0.30916553, 0.31053352, 0.3119015 , 0.31326949,
0.31463748, 0.31600547, 0.31737346, 0.31874145, 0.32010944,
0.32147743, 0.32284542, 0.32421341, 0.3255814 , 0.32694938,
0.32831737, 0.32968536, 0.33105335, 0.33242134, 0.33378933,
0.33515732, 0.33652531, 0.3378933 , 0.33926129, 0.34062927,
0.34199726, 0.34336525, 0.34473324, 0.34610123, 0.34746922,
0.34883721, 0.3502052 , 0.35157319, 0.35294118, 0.35430917,
0.35567715, 0.35704514, 0.35841313, 0.35978112, 0.36114911,
0.3625171 , 0.36388509, 0.36525308, 0.36662107, 0.36798906,
0.36935705, 0.37072503, 0.37209302, 0.37346101, 0.374829 ,
0.37619699, 0.37756498, 0.37893297, 0.38030096, 0.38166895,
0.38303694, 0.38440492, 0.38577291, 0.3871409 , 0.38850889,
0.38987688, 0.39124487, 0.39261286, 0.39398085, 0.39534884,
0.39671683, 0.39808482, 0.3994528 , 0.40082079, 0.40218878,
0.40355677, 0.40492476, 0.40629275, 0.40766074, 0.40902873,
0.41039672, 0.41176471, 0.41313269, 0.41450068, 0.41586867,
0.41723666, 0.41860465, 0.41997264, 0.42134063, 0.42270862,
0.42407661, 0.4254446 , 0.42681259, 0.42818057, 0.42954856,
0.43091655, 0.43228454, 0.43365253, 0.43502052, 0.43638851,
0.4377565 , 0.43912449, 0.44049248, 0.44186047, 0.44322845,
0.44459644, 0.44596443, 0.44733242, 0.44870041, 0.4500684 ,
0.45143639, 0.45280438, 0.45417237, 0.45554036, 0.45690834,
0.45827633, 0.45964432, 0.46101231, 0.4623803 , 0.46374829,
0.46511628, 0.46648427, 0.46785226, 0.46922025, 0.47058824,
0.47195622, 0.47332421, 0.4746922 , 0.47606019, 0.47742818,
0.47879617, 0.48016416, 0.48153215, 0.48290014, 0.48426813,
0.48563611, 0.4870041 , 0.48837209, 0.48974008, 0.49110807,
0.49247606, 0.49384405, 0.49521204, 0.49658003, 0.49794802,
0.49931601]),
'peak_frequencies': array([0.08207934, 0.24897401, 0.41586867]),
'peak_periods': array([12.18333333, 4.01648352, 2.40460526]),
'peak_psd_values': array([17216.57201745, 595.2315853 , 275.13588555]),
'psd_values': array([1.62143429e+02, 1.72012074e+02, 3.20004462e+02, 1.36730990e+02,
1.22902898e+01, 9.72897664e+01, 1.97478820e+02, 7.57691459e+01,
5.53422152e+01, 6.17433535e+01, 8.34925868e+01, 9.06702430e+01,
7.10207819e+01, 3.51038807e+01, 4.60558841e+01, 4.05095297e+01,
5.37487210e+01, 8.19021176e+01, 7.36707528e+01, 8.12166261e+01,
7.27038351e+01, 8.68661255e+01, 9.75315223e+01, 1.26509825e+02,
6.00765181e+01, 2.54176199e+01, 1.02180979e+01, 6.88701770e+01,
1.00175647e+02, 1.27131938e+02, 4.01962948e+01, 2.30334877e+01,
6.91948562e+01, 2.78898896e+01, 4.08106838e+01, 7.24434921e+01,
8.51192744e+01, 2.88292948e+01, 1.95171128e+01, 8.59488526e+01,
1.39549249e+02, 1.29247740e+02, 1.51353886e+02, 1.47379670e+02,
6.95331751e+01, 2.56090776e+01, 3.40846829e+01, 3.08064677e+01,
2.82958270e+01, 2.65825326e+01, 2.22177253e+01, 3.89124314e+01,
8.83452353e+01, 6.69979365e+01, 2.51717024e+01, 5.34735230e+01,
1.34552268e+02, 1.40156661e+02, 7.35553615e+01, 5.50079241e+03,
1.72165720e+04, 3.66405280e+03, 1.11137078e+02, 5.48417429e+01,
1.12382249e+02, 1.21003575e+02, 1.19072295e+02, 1.53757611e+02,
5.08765205e+01, 2.61425569e+01, 4.11664691e+01, 3.75742262e+01,
4.04326483e+01, 1.10751940e+01, 3.15463219e+00, 2.99303076e+01,
2.41417188e+01, 4.17309250e+00, 2.25527482e+01, 3.80570736e+01,
2.33175198e+01, 4.66427988e+01, 8.43199617e+01, 6.18168080e+01,
4.52886398e+01, 4.17800296e+01, 3.03412525e+01, 1.42269417e+01,
7.46536525e+00, 2.87039012e+01, 6.31851579e+01, 2.74557992e+01,
4.13940932e+01, 3.37194532e+01, 1.90617475e+01, 1.63262237e+01,
5.11859771e+01, 4.53726865e+01, 4.26211178e+01, 3.49239474e+01,
4.20530951e+01, 8.45744134e+01, 2.22125223e+01, 1.56974076e+01,
4.74342890e+00, 2.00808674e+01, 2.04213702e+01, 3.27307702e+01,
5.61871717e+01, 8.18360654e+01, 6.21670734e+01, 3.00075725e+01,
3.06775359e+01, 2.88923458e+01, 4.18816977e+01, 2.09053726e+01,
3.96193628e+01, 1.05608631e+02, 5.31000467e+01, 4.92860814e+01,
2.07474249e+02, 3.19250230e+02, 2.32024939e+02, 4.55093864e+01,
4.92855164e+01, 2.16814525e+02, 1.78250069e+02, 1.83159125e+01,
2.23353850e+01, 3.41628226e+01, 3.57048249e+01, 3.48638935e+01,
1.07305277e+02, 7.28019080e+01, 3.18908570e+01, 5.93332124e+01,
1.65198243e+01, 2.51829459e+01, 4.36656187e+01, 9.78660322e+00,
2.36932318e+01, 2.79894081e+01, 3.16822156e+01, 3.62474548e+01,
5.25350931e+01, 9.96412754e+01, 8.91771348e+01, 6.53661097e+01,
8.89495091e+01, 1.32735428e+02, 9.39503951e+01, 9.29647714e+01,
7.35727297e+01, 1.14848388e+02, 1.00648853e+02, 6.47605369e+01,
4.23448952e+01, 2.43173971e+01, 7.39023786e+00, 1.66780131e+01,
2.78708367e+01, 9.66050564e+01, 1.13192764e+02, 7.03998661e+01,
4.96884592e+01, 3.96667254e+01, 4.87084740e+01, 6.19037719e+01,
7.80705173e+01, 8.08233904e+01, 7.04777529e+01, 1.46376183e+01,
3.07949458e+01, 2.63672908e+01, 7.19327864e+01, 2.60948438e+01,
2.65336923e+01, 1.36108170e+02, 1.07191124e+02, 4.81102083e+01,
6.11194499e+01, 4.01193108e+02, 5.95231585e+02, 2.85611327e+02,
1.31465551e+02, 2.22073273e+01, 2.88430482e+01, 2.14212527e+01,
2.31016574e+01, 4.27479355e+01, 2.92304006e+01, 1.99499063e+01,
1.53733678e+01, 5.25995546e+01, 8.66512662e+01, 5.58698244e+01,
2.97397730e+01, 1.99613479e+01, 3.11673421e+01, 4.87258963e+01,
4.32993587e+01, 3.30644784e+01, 3.97698146e+01, 8.12140446e+01,
1.60941774e+02, 5.36459451e+01, 4.81105043e+01, 4.06287823e+01,
2.01162463e+01, 4.51898341e+01, 5.94632796e+01, 4.24048427e+01,
3.20911469e+01, 2.27526139e+01, 4.27007681e+01, 5.70706727e+01,
3.69457110e+01, 3.64185018e+01, 8.12398086e+01, 8.03299821e+01,
3.22162296e+01, 7.90121981e+00, 2.15595594e+01, 5.72599004e+01,
3.52659920e+01, 1.27266895e+01, 2.76757027e+01, 4.73909601e+01,
2.44358573e+01, 1.82242832e+01, 2.26705788e+01, 2.52616897e+01,
2.86256096e+01, 4.21440744e+01, 5.80002691e+01, 6.26925249e+01,
3.32800736e+01, 5.73626383e+01, 6.53859227e+01, 6.70088308e+01,
5.78296873e+01, 8.49386906e+01, 1.29758368e+02, 1.45476524e+02,
1.36844755e+02, 7.45100357e+01, 8.01452617e+01, 1.35000832e+02,
5.05743519e+01, 1.67315514e+01, 1.86290859e+01, 1.36014156e+01,
2.03193307e+01, 1.13298862e+01, 1.63143665e+01, 3.46278604e+01,
2.34812816e+01, 2.72980824e+01, 2.20578655e+01, 1.74121682e+01,
3.67554460e+01, 3.75166108e+01, 2.93003952e+01, 8.63793778e+01,
8.23625035e+01, 6.18883158e+01, 7.62946729e+01, 9.43783503e+01,
5.13793735e+01, 4.02642564e+01, 1.53658697e+01, 6.21070926e+01,
5.52674631e+01, 5.00888957e+01, 2.91789934e+01, 3.55873892e+01,
4.66340738e+01, 6.35970294e+01, 8.61783928e+01, 9.09471011e+01,
4.58377220e+01, 1.70336881e+01, 3.94304078e+01, 5.42877944e+01,
2.62661722e+01, 5.80827859e+01, 1.97445401e+01, 9.28463197e+00,
7.14681331e+01, 5.63350915e+01, 6.50011783e+00, 2.35953043e+01,
1.96100510e+01, 2.19174926e+01, 1.05851853e+01, 2.97456187e+01,
5.68848963e+01, 8.41001907e+01, 6.55276315e+01, 3.78211587e+01,
5.03392190e+01, 3.82544934e+01, 2.40121968e+01, 2.58632973e+02,
2.75135886e+02, 4.07659941e+01, 2.61266291e+01, 2.95857275e+01,
3.53938453e+01, 4.68179920e+01, 9.96606352e+01, 8.75426454e+01,
6.44937419e+01, 3.82130596e+01, 9.87385827e+00, 1.23749774e+01,
6.25859904e+01, 4.53591655e+01, 5.72168536e+00, 5.66517202e+01,
4.55580565e+01, 2.72979041e+01, 2.42207550e+01, 3.26299850e+01,
4.11843156e+01, 2.15845914e+01, 6.43654473e+01, 7.30267240e+00,
1.21692602e+01, 3.03847551e+01, 1.46479924e+01, 3.35388914e+01,
3.51886349e+01, 8.47494904e+00, 1.51522090e+01, 3.16115820e+01,
2.71719668e+01, 2.44289371e+01, 3.52842226e+01, 4.42350927e+01,
4.39007314e+01, 6.83111492e+01, 7.43946620e+01, 2.15592913e+01,
3.92794949e+01, 5.00499933e+01, 4.64351035e+01, 2.71617725e+01,
5.53406837e+01, 1.07270641e+02, 6.15159230e+01, 4.09936939e+01,
2.11603850e+01, 2.91342320e+01, 3.46454170e+01, 5.25341812e+01,
5.33318179e+01, 4.33041538e+01, 3.78541994e+01, 5.59494516e+01,
4.79183306e+01, 5.97184459e+01, 2.79309287e+01, 4.39322016e+01,
7.17219173e+02])},
'Regional: Solar Surface Irradiance [W/m2]': {'frequencies': array([0. , 0.02325581, 0.04651163, 0.06976744, 0.09302326,
0.11627907, 0.13953488, 0.1627907 , 0.18604651, 0.20930233,
0.23255814, 0.25581395, 0.27906977, 0.30232558, 0.3255814 ,
0.34883721, 0.37209302, 0.39534884, 0.41860465, 0.44186047,
0.46511628, 0.48837209]),
'peak_frequencies': array([0.09302326]),
'peak_periods': array([10.75]),
'peak_psd_values': array([985427.50965176]),
'psd_values': array([ 4129.35375538, 4717.92395498, 9001.52075181, 490025.88477686,
985427.50965176, 140983.98644645, 2181.39244656, 2484.50896213,
70076.64703765, 77129.50006355, 7148.93808181, 3488.64153108,
8615.44208796, 40075.92286143, 25763.63970605, 6017.00425144,
5933.88837442, 10724.95461909, 34286.28873382, 12871.97147513,
5319.0997938 ])}}
Another issue wiht the plot above is that we can observe a lot of high-frequency component, which are most likely associate with noise. Lets apply a low-pass filter, that block higher frequencies and lets low frequencies pass and re-plot.
show that similarities between rolling mean and low pass filter (mention? math, external resources)?
Exercise 4
Use the same function as before, but consider the argument chagninf the default of apply_filter, max_allowed_freqand filter_order
_=ice.compute_and_plot_psd(Data,plot_period=False,find_peaks_kwargs={"distance":100,"threshold":10,"height":1e-2},apply_filter=True,max_allowed_freq=1/14,filter_order=4)
PSD_info=ice.compute_and_plot_psd(Data,plot_period=True,find_peaks_kwargs={"distance":100,"threshold":10,"height":1e-2},apply_filter=True,max_allowed_freq=1/30,filter_order=4)
for col, psd_info in PSD_info.items():
peak_periods =np.round(psd_info['peak_periods']).astype(int)
print(f"Column: {col}")
print(f"Peak Periods: {peak_periods}\n")
Column: Regional: Air temperature [C]
Peak Periods: [371 123 61 43 34 28]
Column: Days since start of year
Peak Periods: [371 123 73 52 41 33 28 24 22 19]
Column: Days until break up
Peak Periods: [371 123 73 52 41 33 28 24 22 19]
Column: Nenana: Rainfall [mm]
Peak Periods: [369 76 49 35]
Column: Nenana: Snowfall [mm]
Peak Periods: [384 66 38 27]
Column: Nenana: Snow depth [mm]
Peak Periods: [381 65 36 25]
Column: Nenana: Mean water temperature [C]
Peak Periods: [403]
Column: Nenana: Mean Discharge [m3/s]
Peak Periods: [376 73 37 26 21 17]
Column: Nenana: Air temperature [C]
Peak Periods: [371 99 56 41 32 26]
Column: Fairbanks: Average wind speed [m/s]
Peak Periods: [408 41]
Column: Fairbanks: Rainfall [mm]
Peak Periods: []
Column: Fairbanks: Snowfall [mm]
Peak Periods: [370]
Column: Fairbanks: Snow depth [mm]
Peak Periods: [369 92 52 36]
Column: Fairbanks: Air Temperature [C]
Peak Periods: [370 74 49 37 29]
Column: IceThickness [cm]
Peak Periods: [230]
Column: Regional: Solar Surface Irradiance [W/m2]
Peak Periods: []
Column: Regional: Cloud coverage [%]
Peak Periods: [366]
Column: Global: ENSO-Southern oscillation index
Peak Periods: [219]
Column: Gulkana Temperature [C]
Peak Periods: [355 42 29]
Column: Gulkana Precipitation [mm]
Peak Periods: [371 56 33]
Column: Gulkana: Glacier-wide winter mass balance [m.w.e]
Peak Periods: []
Column: Gulkana: Glacier-wide summer mass balance [m.w.e]
Peak Periods: []
Column: Global: Pacific decadal oscillation index
Peak Periods: [673]
Column: Global: Artic oscillation index
Peak Periods: []
theory behind filters, welch psd, windowing,etc??? A lot of content could be added