N-Year Thresholds

The N-Year thresholds, which are defined by Bulletin 70, describe how much precipitation must fall in a given time frame to be classified as an n-year storm. In this notebook, I take a look at the thresholds themselves



In [1]:

    
from __future__ import absolute_import, division, print_function, unicode_literals

import pandas as pd
from datetime import datetime, timedelta
import operator
import matplotlib.pyplot as plt
from collections import namedtuple
%matplotlib inline



In [2]:

    
# N-Year Storm variables
# These define the thresholds laid out by bulletin 70, and transfer mins and days to hours
n_year_threshes = pd.read_csv('../../n-year/notebooks/data/n_year_definitions.csv')
n_year_threshes = n_year_threshes.set_index('Duration')
dur_str_to_hours = {
    '5-min':0.0833,
    '10-min':0.1667,
    '15-min':15/60.0,
    '30-min':0.5,
    '1-hr':1.0,
    '2-hr':2.0,
    '3-hr':3.0,
    '6-hr':6.0,
    '12-hr':12.0,
    '18-hr':18.0,
    '24-hr':24.0,
    '48-hr':48.0,
    '72-hr':72.0,
    '5-day':5*24.0,
    '10-day':10*24.0
}
n_s = [int(x.replace('-year','')) for x in reversed(list(n_year_threshes.columns.values))]
duration_strs = sorted(dur_str_to_hours.items(), key=operator.itemgetter(1), reverse=False)
n_year_threshes = n_year_threshes.iloc[::-1]
n_year_threshes



In [3]:

    
n_year_threshes.transpose().loc[['1-year', '10-year', '100-year']].plot(kind='bar', title='Rainfall durations for n-year storms')









    Out[3]:





<matplotlib.axes._subplots.AxesSubplot at 0x7e88b38>



In [4]:

    
n_year_threshes[['1-year', '10-year', '100-year']].plot(kind='bar', title='How much rainfaill it takes for n-years given duration')









    Out[4]:





<matplotlib.axes._subplots.AxesSubplot at 0x867ee10>



In [5]:

    
# Convert durations to hours, so that they make more sense on an axis
n_year_threshes['duration'] = n_year_threshes.index.values
def find_duration_hours(duration_str):
    return dur_str_to_hours[duration_str]
n_year_threshes['hours_duration'] = n_year_threshes['duration'].apply(find_duration_hours)
n_year_threshes = n_year_threshes.drop('duration', 1)
n_year_threshes = n_year_threshes.set_index('hours_duration')
n_year_threshes.head()









    Out[5]:






  
    
      
      1-year
      2-year
      5-year
      10-year
      25-year
      50-year
      100-year
    
    
      hours_duration
      
      
      
      
      
      
      
    
  
  
    
      0.0833
      0.30
      0.36
      0.46
      0.54
      0.66
      0.78
      0.91
    
    
      0.1667
      0.55
      0.67
      0.84
      0.98
      1.21
      1.42
      1.67
    
    
      0.2500
      0.68
      0.82
      1.03
      1.21
      1.49
      1.75
      2.05
    
    
      0.5000
      0.93
      1.12
      1.41
      1.65
      2.04
      2.39
      2.80
    
    
      1.0000
      1.18
      1.43
      1.79
      2.10
      2.59
      3.04
      3.56



In [6]:

    
n_year_threshes.plot(kind='line', title='Duration vs Inches for the N-Year Storm')









    Out[6]:





<matplotlib.axes._subplots.AxesSubplot at 0x8cca128>

We know that 2 inches of rainfall in 10 days ain't bad, but in 1 hour is. Let's take a look at that relationship, so that we can ask the question -- if we get n inches of rainfall, let's see how fast it must fall to be considered an n-year storm



In [7]:

    
# This method takes in a number of inches, and plots various durations and how they're classified as n-year storms
# as a bar chart
def inches_to_storm(inches):
    ret_val = []
    thresholds = n_year_threshes.transpose()
    for storm in list(thresholds.index.values):
        the_storm = thresholds.loc[storm]
        storms_higher = the_storm.loc[the_storm > inches]
        if len(storms_higher) == 0:
            continue
        upper_hours = the_storm.loc[the_storm >= inches].index[0]
        upper_inches = the_storm.loc[the_storm >= inches].iloc[0]
        try:
            lower_hours = the_storm.loc[the_storm < inches].iloc[::-1].index[0]
            lower_inches = the_storm.loc[the_storm < inches].iloc[::-1].iloc[0]
        except:
            lower_hours = 0
            lower_inches = 0
        percent_across = (inches-lower_inches) / (upper_inches - lower_inches)
        duration = lower_hours + ((upper_hours - lower_hours) * percent_across)
        ret_val.append({'storm': storm, 'hours': duration})
    ret_val = pd.DataFrame(ret_val)
    ret_val = ret_val.set_index('storm')
    ret_val.plot(kind='bar', title='%s Inches over Duration to Classify the N-Year Storms' % str(inches))



In [8]:

    
inches_to_storm(3.2)



In [ ]:

	1-year	2-year	5-year	10-year	25-year	50-year	100-year
Duration
5-min	0.30	0.36	0.46	0.54	0.66	0.78	0.91
10-min	0.55	0.67	0.84	0.98	1.21	1.42	1.67
15-min	0.68	0.82	1.03	1.21	1.49	1.75	2.05
30-min	0.93	1.12	1.41	1.65	2.04	2.39	2.80
1-hr	1.18	1.43	1.79	2.10	2.59	3.04	3.56
2-hr	1.48	1.79	2.24	2.64	3.25	3.82	4.47
3-hr	1.60	1.94	2.43	2.86	3.53	4.14	4.85
6-hr	1.88	2.28	2.85	3.35	4.13	4.85	5.68
12-hr	2.18	2.64	3.31	3.89	4.79	5.62	6.59
18-hr	2.30	2.79	3.50	4.11	5.06	5.95	6.97
24-hr	2.51	3.04	3.80	4.47	5.51	6.46	7.58
48-hr	2.70	3.30	4.09	4.81	5.88	6.84	8.16
72-hr	2.93	3.55	4.44	5.18	6.32	7.41	8.78
5-day	3.25	3.93	4.91	5.70	6.93	8.04	9.96
10-day	4.12	4.95	6.04	6.89	8.18	9.38	11.14

	1-year	2-year	5-year	10-year	25-year	50-year	100-year
hours_duration
0.0833	0.30	0.36	0.46	0.54	0.66	0.78	0.91
0.1667	0.55	0.67	0.84	0.98	1.21	1.42	1.67
0.2500	0.68	0.82	1.03	1.21	1.49	1.75	2.05
0.5000	0.93	1.12	1.41	1.65	2.04	2.39	2.80
1.0000	1.18	1.43	1.79	2.10	2.59	3.04	3.56