Fitting IDF curves with Scipy and Pandas

# -*- coding: utf-8 -*-
"""
Created on Tue Jul 10 11:19:37 2018

@author: rodrigo.goncalves
"""
import pandas as pd
from scipy.optimize import minimize
 
# This is the IDF function, returning the sum of squared errors (SSE)
def func2(par, res):
    p1 =  (par[0] * res.index.values  **par[1])
    p2 = ((res.columns.values.astype(float)+par[2])**par[3])
    f = pd.DataFrame([p/p2 for p in p1],index=res.index,columns=res.columns)
    erroTotQ=((f-res)**2).sum(axis=1).sum()    
    return erroTotQ
 
# copy your rainfall intensities table from excel
# with column headers with rainfall durations
# and row names with Return period value in years
dfInt=pd.read_clipboard()

#initial guess
param1 = [5000, 0.1, 10, 0.9]

res2 = minimize(func2, param1, args=(dfInt,), method='Nelder-Mead')
print(res2)
cs=['K=','a=','b=','c=']
dfResult=pd.DataFrame(res2.x,index=cs).transpose()
print(dfResult)
dfResult.to_clipboard(index=None)

IDF table from equation - Pandas

How to fill a table (pandas DataFrame) with rainfall intensity values, extracted from idf equation:


import pandas as pd

durs = [5,10,15,20,30,60,120,180,360,540,720,1440] # rainfall durations
rps=[5,10,25,50,100] # return periods

t1 = pd.DataFrame(index=rps,columns=durs) # initialize DataFrame with rp's and durations

cf = [942.76,.1242,17.0,.650] #example idf equation coefficients

table = t1.apply(lambda x: (cf[0]*x.index**cf[1])/((x.name+cf[2])**cf[3]))

Alternating Block Hyetograph Method with Python

To generate hypothetic storm events, we can use some methods as Alternating block method, Chicago method, Balanced method, SCS Storms among others.

In this post I show a way to generate a hypothetic storm event using the Alternating block method.

This python code uses the numpy library. The altblocks functions uses as input the idf parameters as list, and total duration, delta time and return period as floats.

import numpy as np

def altblocks(idf,dur,dt,RP):
    aDur = np.arange(dt,dur+dt,dt)    # in minutes
    aInt = (idf[0]*RP**idf[1])/((aDur+idf[2])**idf[3])  # idf equation - in mm/h
    aDeltaPmm = np.diff(np.append(0,np.multiply(aInt,aDur/60.0)))
    aOrd=np.append(np.arange(1,len(aDur)+1,2)[::-1],np.arange(2,len(aDur)+1,2))
    prec = np.asarray([aDeltaPmm[x-1] for x in aOrd])
    aAltBl = np.vstack((aDur,prec))
    return aAltBl

Python and Pandas - How to plot Multiple Curves with 5 Lines of Code

In this post I will show how to use pandas to do a minimalist but pretty line chart, with as many curves we want.

In this case I will use a I-D-F precipitation table, with lines corresponding to Return Periods (years) and columns corresponding to durations, in minutes. as shown below:

For the code to work properly, the table must have headers in the columns and lines, and the first cell have to be blank. Select the table you want in your SpreadSheet Editor, and copy it to clipboard.

Then, run the following code:

import pandas as pd

table = pd.read_clipboard()
tabTr = table.transpose().convert_objects(convert_numeric=True)
eixox = tabTr.index.values.astype(float)
tabTr.set_index(eixox).plot(grid=True)

And Voila!: