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MOVE.py
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#-------------------------------------------------------------------------------
# Name MOVE method USGS
# Description: Tool to conduct gauge extension on a short record
# using data from a long record gage. Conducted based
# on guidance in Guidelines for Determining Flood Flow Frequency
# Bulletin 17C, version 1.1 USGS May 2019
# Author: Chandler Engel
# US Army Corps of Engineers
# Cold Regions Research and Engineering Laboratory (CRREL)
# Chandler.S.Engel@usace.army.mil
# Created: 14 February 2020
# Updated: -
#
#-------------------------------------------------------------------------------
import numpy as np
def comp_variance(record):
n1 = len(record)
ybar = np.mean(record)
s_sq_y = sum([(yi-ybar)**2 for yi in record]) / (n1-1)
return s_sq_y
def comp_extended_record(short_years, short_record, long_years, long_record):
"""MOVE method to extend short flow gage record using appropriate long record
"""
long_record = np.log10(long_record)
short_record = np.log10(short_record)
suppress_params = False
concurrent_years = list(set(short_years) & set(long_years))
ind1 = [long_years.index(year) for year in concurrent_years if year in long_years]
con_long_record = np.array(long_record)[ind1]
ind2 = [short_years.index(year) for year in concurrent_years if year in short_years]
con_short_record = np.array(short_record)[ind2]
additional_years = list(set(long_years)-set(short_years))
ind3 = [long_years.index(year) for year in additional_years if year in long_years]
additional_record = np.array(long_record)[ind3]
n1 = len(con_short_record)
n2 = len(additional_record)
ybar1 = np.mean(con_short_record)
xbar1 = np.mean(con_long_record)
xbar2 = np.mean(additional_record)
s_sq_y1 = comp_variance(con_short_record)
s_sq_x1 = comp_variance(con_long_record)
s_sq_x2 = comp_variance(additional_record)
alpha_sq = (n2*(n1-4)*(n1-1))/((n2-1)*(n1-3)*(n1-2))
bhat_top = 0
bhat_bottom = 0
for i, xi in enumerate(con_long_record):
bhat_top += (xi - xbar1)*(con_short_record[i]-ybar1)
bhat_bottom += (xi-xbar1)**2
beta_hat = bhat_top/bhat_bottom
p_hat = beta_hat * (np.sqrt(s_sq_x1)/np.sqrt(s_sq_y1))
mu_hat_y = ybar1 + n2/(n1+n2)*beta_hat*(xbar2-xbar1)
sigma_hat_y_sq = (1/(n1+n2-1))*((n1-1)*s_sq_y1 + (n2-1)*beta_hat**2*s_sq_x2 + (n2-1)*alpha_sq*(1-p_hat**2)*s_sq_y1+(n1*n2)/(n1+n2)*beta_hat**2*(xbar2-xbar1)**2)
print('p_hat = '+str(p_hat))
print('mu_hat_y = '+str(mu_hat_y))
print('sigma_hat_y_sq = '+str(sigma_hat_y_sq))
A1 = (n2+2)*(n1-6)*(n1-8)/(n1-5)
A2 = n1-4
A3 = (n1*n2*(n1-4)/((n1-3)*(n1-2)))
A4 = 2*n2*(n1-4)/(n1-3)
A = A1 + A2*(A3-A4-4)
B1 = 6*(n2+2)*(n1-6)/(n1-5)
B2 = 2*(n1**2-n1-14)
B3 = n1-4
B4 = 2*n2*(n1-5)/(n1-3)
B5 = 2*(n1+3)
B6 = (2*n1*n2*(n1-4))/((n1-3)*(n1-2))
B = B1 + B2 + B3*(B4-B5-B6)
C1 = 2*(n1+1)
C2 = 3*(n2+2)/(n1-5)
C3 = (n1+1)*(2*n1+n2-2)*(n1-3)/(n1-1)
C4 = n1-4
C5 = 2*n2/(n1-3)
C6 = 2*(n1+1)
C7 = n1*n2*(n1-4)/((n1-3)*(n1-2))
C = C1 + C2 - C3 + C4*(C5+C6+C7)
ne = 2/ ( (2/(n1-1)) + (n2/(((n1+n2-1)**2) * (n1-3))) * (A*p_hat**4 +B*p_hat**2 + C )) + 1 - n1
ne_int = int(round(ne))
extension_record = additional_record[-ne_int:]
extension_years = additional_years[-ne_int:]
xe_bar = np.mean(extension_record)
s_sq_xe = comp_variance(extension_record)
a = ((n1+ne_int)*mu_hat_y-n1*ybar1)/ne_int
b_sq1 = (n1 + ne_int-1)*sigma_hat_y_sq
b_sq2 = (n1-1)*s_sq_y1
b_sq3 = n1*(ybar1-mu_hat_y)**2
b_sq4 = ne_int*(a-mu_hat_y)**2
b_sq5 = (ne_int-1)*s_sq_xe
b_sq = (b_sq1 - b_sq2 - b_sq3 - b_sq4)/b_sq5
b = np.sqrt(b_sq)
extension_short_record = [int(round(10**(a+b*(xi-xe_bar)))) for xi in extension_record]
if suppress_params == False:
print('a = '+str(a))
print('b**2 = '+ str(b_sq))
print('b = '+str(np.sqrt(b_sq)))
print('xe_bar = '+str(xe_bar))
print('s_sq_xe = '+str(s_sq_xe))
print('A = '+str(A))
print('B = ' +str(B))
print('C = '+str(C))
print('ne = '+str(ne))
print('ne_int = '+str(ne_int))
print('n1 = '+str(n1))
print('n2 = '+str(n2))
print('ybar1 = '+str(ybar1))
print('xbar1 = '+str(xbar1))
print('xbar2 = '+str(xbar2))
print('sy1 = '+str(np.sqrt(s_sq_y1)))
print('sx1 = '+str(np.sqrt(s_sq_x1)))
print('sx2 = '+str(np.sqrt(s_sq_x2)))
short_record_flows = [int(round(10**x)) for x in short_record]
extended_short_record = extension_short_record + short_record_flows
extended_short_years = extension_years + short_years
return extended_short_record, extended_short_years
def main():
import csv
with open('Suwanee.csv', 'r') as f:
reader = csv.reader(f)
y = list(reader)
short_years = [int(y1[0]) for y1 in y]
short_record = [int(y1[1]) for y1 in y]
with open('Etowah.csv', 'r') as f:
reader = csv.reader(f)
x = list(reader)
long_years = [int(x1[0]) for x1 in x]
long_record = [int(x1[1]) for x1 in x]
out = comp_extended_record(short_years, short_record, long_years, long_record)
print(out)
if __name__ == "__main__":
main()