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etregimes.py
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etregimes.py
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# Based on Qin Kong's modified ET regime script
# use Hsu's method: scipy.optimize.curve_fit
# doing segmented linear regression on slhf against swvl1 with the aim to classify the data to dry, wet and transitional regime
# fit different segmented model to the data and find which one has lowest AIC/BIC
# extract the critical thresholds that separate transitional regime
# which is then used for calculating sensitivity index within this transitional regime
# try to deal with x0<x1 issue
import os
import sys
import numpy as np
import xarray as xr
from scipy import optimize
from scipy import stats
from tqdm import tqdm
def piecewise3sg_linear(x, x0, x1, y0, k1,k2,k3):
condlist = [x < x0, (x >= x0) & (x < x1), x >= x1]
funclist = [lambda x: k1*(x-x0)+y0, lambda x:k2*(x-x0) + y0, lambda x:k3*(x-x1) + k2*(x1-x0) + y0]
return np.piecewise(x, condlist, funclist)
def fit1110(data):
SM=data[0]
LH=data[1]
n=len(SM)
param_num=6
p0=[SM.min()+(SM.max()-SM.min())/3,
SM.max()-(SM.max()-SM.min())/3,
LH.min()+(LH.max()-LH.min())/3,
0,
50,
0]
bounds=([np.min(np.array(SM)),np.min(np.array(SM)),np.min(np.array(LH)),-0.0010,0,-0.0010],
[np.max(np.array(SM)),np.max(np.array(SM)),np.max(np.array(LH)),0.0010,np.inf,0.0010])
res= optimize.curve_fit(piecewise3sg_linear, np.array(SM), np.array(LH),p0=p0,bounds=bounds,full_output=True,maxfev=1e10)
X=np.r_[SM.min(),res[0][0],res[0][1],SM.max()]
Y=np.r_[res[0][3]*(SM.min()-res[0][0])+res[0][2],
res[0][2],
res[0][4]*(res[0][1]-res[0][0])+res[0][2],
res[0][5]*(SM.max()-res[0][1])+res[0][4]*(res[0][1]-res[0][0])+res[0][2]]
Xnew = np.take_along_axis(X, X.argsort(axis=0),axis=0)
Ynew = np.take_along_axis(Y, X.argsort(axis=0),axis=0)
Y2=np.interp(SM, Xnew, Ynew)
MRSS=np.mean((LH - Y2)**2)
AIC = n * np.log(MRSS) + 2*param_num
BIC = n * np.log(MRSS) + param_num * np.log(n)
if "is satisfied" in res[3] or "are satisfied" in res[3]:
flag=1
else:
flag=0
xc=res[0][1] # critical soil moisture
mt=res[0][4] # transition regime slope
return {'type':'1110','flag1':res[4],'flag2':flag,'p':res[0],'AIC':AIC,'BIC':BIC,'line':[Xnew,Ynew],'xc':xc,'yp':Y2,'mt':mt}
def piecewise2sg_linear_LHSflat(x, x0, y0, k1,k2):
condlist = [x < x0, x >= x0]
funclist = [lambda x: k1*(x-x0)+y0, lambda x:k2*(x-x0) + y0]
return np.piecewise(x, condlist, funclist)
def fit1100(data):
SM=data[0]
LH=data[1]
n=len(SM)
param_num=4
p0=[SM.min()+(SM.max()-SM.min())/3,
LH.min()+(LH.max()-LH.min())/3,
0,
50]
bounds=([np.min(np.array(SM)),np.min(np.array(LH)),-0.0010,0],
[np.max(np.array(SM)),np.max(np.array(LH)),0.0010,np.inf])
res= optimize.curve_fit(piecewise2sg_linear_LHSflat, np.array(SM), np.array(LH),p0=p0,bounds=bounds,full_output=True,maxfev=1e10)
X=np.r_[SM.min(),res[0][0],SM.max()]
Y=np.r_[res[0][1]+(SM.min()-res[0][0])*res[0][2],res[0][1],res[0][1]+res[0][3]*(SM.max()-res[0][0])]
Y2=np.interp(SM, X, Y)
MRSS=np.mean((LH - Y2)**2)
AIC = n * np.log(MRSS) + 2*param_num
BIC = n * np.log(MRSS) + param_num * np.log(n)
if "is satisfied" in res[3] or "are satisfied" in res[3]:
flag=1
else:
flag=0
xc=np.inf
mt=res[0][3]
return {'type':'1100','flag1':res[4],'flag2':flag,'p':res[0],'AIC':AIC,'BIC':BIC,'line':[X,Y],'xc':xc,'yp':Y2,'mt':mt}
def piecewise2sg_linear_RHSflat(x, x0, y0, k1,k2):
condlist = [x < x0, x >= x0]
funclist = [lambda x: y0+k1*(x-x0), lambda x:k2*(x-x0)+y0]
return np.piecewise(x, condlist, funclist)
def fit0110(data):
SM=data[0]
LH=data[1]
n=len(SM)
param_num=4
p0=[SM.max()-(SM.max()-SM.min())/3,
LH.max()-(LH.max()-LH.min())/3,
50,
0]
bounds=([np.min(np.array(SM)),np.min(np.array(LH)),0,-0.0010],
[np.max(np.array(SM)),np.max(np.array(LH)),np.inf,0.0010])
res= optimize.curve_fit(piecewise2sg_linear_RHSflat, np.array(SM), np.array(LH),p0=p0,bounds=bounds,full_output=True,maxfev=1e10)
X=np.r_[SM.min(),res[0][0],SM.max()]
Y=np.r_[res[0][1]-res[0][2]*(res[0][0]-SM.min()),res[0][1],res[0][3]*(SM.max()-res[0][0])+res[0][1]]
Y2=np.interp(SM, X, Y)
MRSS=np.mean((LH - Y2)**2)
AIC = n * np.log(MRSS) + 2*param_num
BIC = n * np.log(MRSS) + param_num * np.log(n)
if "is satisfied" in res[3] or "are satisfied" in res[3]:
flag=1
else:
flag=0
xc=res[0][0]
mt=res[0][2]
return {'type':'1100','flag1':res[4],'flag2':flag,'p':res[0],'AIC':AIC,'BIC':BIC,'line':[X,Y],'xc':xc,'yp':Y2,'mt':mt}
def noflat(x,y0,k):
return k*x+y0
def fit0100(data):
SM=data[0]
LH=data[1]
n=len(SM)
param_num=2
p0=[np.median(LH),
50]
bounds=([np.min(np.array(LH)),0],
[np.max(np.array(LH)),np.inf])
res= optimize.curve_fit(noflat, np.array(SM), np.array(LH),p0=p0,bounds=bounds,full_output=True,maxfev=1e10)
X=np.r_[SM.min(),SM.max()]
Y=np.r_[res[0][1]*SM.min()+res[0][0],res[0][1]*SM.max()+res[0][0]]
Y2=np.interp(SM, X, Y)
MRSS=np.mean((LH - Y2)**2)
AIC = n * np.log(MRSS) + 2*param_num
BIC = n * np.log(MRSS) + param_num * np.log(n)
if "is satisfied" in res[3] or "are satisfied" in res[3]:
flag=1
else:
flag=0
xc=np.inf
mt=res[0][1]
return {'type':'0100','flag1':res[4],'flag2':flag,'p':res[0],'AIC':AIC,'BIC':BIC,'line':[X,Y],'xc':xc,'yp':Y2,'mt':mt}
def allflat(x,y0):
return y0
def fit0010(data):
SM=data[0]
LH=data[1]
n=len(SM)
param_num=1
p0=np.median(LH)
bounds=(LH.min(),LH.max())
res= optimize.curve_fit(allflat, np.array(SM), np.array(LH),p0=p0,bounds=bounds,full_output=True,maxfev=1e10)
X=np.r_[SM.min(),SM.max()]
Y=np.r_[res[0][0],res[0][0]]
Y2=np.interp(SM, X, Y)
MRSS=np.mean((LH - Y2)**2)
AIC = n * np.log(MRSS) + 2*param_num
BIC = n * np.log(MRSS) + param_num * np.log(n)
if "is satisfied" in res[3] or "are satisfied" in res[3]:
flag=1
else:
flag=0
xc=np.nan
mt=np.nan
return {'type':'0010','flag1':res[4],'flag2':flag,'p':res[0],'AIC':AIC,'BIC':BIC,'line':[X,Y],'xc':xc,'yp':Y2,'mt':mt}
def piecewise2sg_linear_LHSflat_negative_slope(x, x0, y0, k1,k2):
condlist = [x < x0, x >= x0]
funclist = [lambda x: k1*(x-x0)+y0, lambda x:k2*(x-x0) + y0]
return np.piecewise(x, condlist, funclist)
def fit0011(data):
SM=data[0]
LH=data[1]
n=len(SM)
param_num=4
p0=[SM.min()+(SM.max()-SM.min())/3,
LH.min()+(LH.max()-LH.min())/3,
0,
-50]
bounds=([np.min(np.array(SM)),np.min(np.array(LH)),-0.0010,-np.inf],
[np.max(np.array(SM)),np.max(np.array(LH)),0.0010,0])
res= optimize.curve_fit(piecewise2sg_linear_LHSflat_negative_slope, np.array(SM), np.array(LH),p0=p0,bounds=bounds,full_output=True,maxfev=1e10)
X=np.r_[SM.min(),res[0][0],SM.max()]
Y=np.r_[res[0][1]+(SM.min()-res[0][0])*res[0][2],res[0][1],res[0][1]+res[0][3]*(SM.max()-res[0][0])]
Y2=np.interp(SM, X, Y)
MRSS=np.mean((LH - Y2)**2)
AIC = n * np.log(MRSS) + 2*param_num
BIC = n * np.log(MRSS) + param_num * np.log(n)
if "is satisfied" in res[3] or "are satisfied" in res[3]:
flag=1
else:
flag=0
xc=-np.inf
mt=np.nan
return {'type':'0011','flag1':res[4],'flag2':flag,'p':res[0],'AIC':AIC,'BIC':BIC,'line':[X,Y],'xc':xc,'yp':Y2,'mt':mt}
def noflat_negative_slope(x,y0,k):
return k*x+y0
def fit0001(data):
SM=data[0]
LH=data[1]
n=len(SM)
param_num=2
p0=[np.median(LH),
-50]
bounds=([np.min(np.array(LH)),-np.inf],
[np.max(np.array(LH)),0])
res= optimize.curve_fit(noflat_negative_slope, np.array(SM), np.array(LH),p0=p0,bounds=bounds,full_output=True,maxfev=1e10)
X=np.r_[SM.min(),SM.max()]
Y=np.r_[res[0][1]*SM.min()+res[0][0],res[0][1]*SM.max()+res[0][0]]
Y2=np.interp(SM, X, Y)
MRSS=np.mean((LH - Y2)**2)
AIC = n * np.log(MRSS) + 2*param_num
BIC = n * np.log(MRSS) + param_num * np.log(n)
if "is satisfied" in res[3] or "are satisfied" in res[3]:
flag=1
else:
flag=0
xc=-np.inf
mt=np.nan
return {'type':'0001','flag1':res[4],'flag2':flag,'p':res[0],'AIC':AIC,'BIC':BIC,'line':[X,Y],'xc':xc,'yp':Y2,'mt':mt}
###
# new fits
def fit0101(data):
SM=data[0]
LH=data[1]
n=len(SM)
param_num=4
p0=[SM.min()+(SM.max()-SM.min())/3,
LH.min()+(LH.max()-LH.min())/3,
50,
-50]
bounds=([np.min(np.array(SM)),np.min(np.array(LH)),0,-np.inf],
[np.max(np.array(SM)),np.max(np.array(LH)),np.inf,0])
res= optimize.curve_fit(piecewise2sg_linear_LHSflat_negative_slope, np.array(SM), np.array(LH),p0=p0,bounds=bounds,full_output=True,maxfev=1e10)
X=np.r_[SM.min(),res[0][0],SM.max()]
Y=np.r_[res[0][1]+(SM.min()-res[0][0])*res[0][2],res[0][1],res[0][1]+res[0][3]*(SM.max()-res[0][0])]
Y2=np.interp(SM, X, Y)
MRSS=np.mean((LH - Y2)**2)
AIC = n * np.log(MRSS) + 2*param_num
BIC = n * np.log(MRSS) + param_num * np.log(n)
if "is satisfied" in res[3] or "are satisfied" in res[3]:
flag=1
else:
flag=0
xc=res[0][0]
mt=res[0][2]
return {'type':'0101','flag1':res[4],'flag2':flag,'p':res[0],'AIC':AIC,'BIC':BIC,'line':[X,Y],'xc':xc,'yp':Y2,'mt':mt}
def fit0111(data):
SM=data[0]
LH=data[1]
n=len(SM)
param_num=6
p0=[SM.min()+(SM.max()-SM.min())/3,
SM.max()-(SM.max()-SM.min())/3,
LH.min()+(LH.max()-LH.min())/3,
50,
0,
-50]
bounds=([np.min(np.array(SM)),np.min(np.array(SM)),np.min(np.array(LH)),0,-0.0010,-np.inf],
[np.max(np.array(SM)),np.max(np.array(SM)),np.max(np.array(LH)),np.inf,0.0010,0])
res= optimize.curve_fit(piecewise3sg_linear, np.array(SM), np.array(LH),p0=p0,bounds=bounds,full_output=True,maxfev=1e10)
X=np.r_[SM.min(),res[0][0],res[0][1],SM.max()]
Y=np.r_[res[0][3]*(SM.min()-res[0][0])+res[0][2],
res[0][2],
res[0][4]*(res[0][1]-res[0][0])+res[0][2],
res[0][5]*(SM.max()-res[0][1])+res[0][4]*(res[0][1]-res[0][0])+res[0][2]]
Xnew = np.take_along_axis(X, X.argsort(axis=0),axis=0)
Ynew = np.take_along_axis(Y, X.argsort(axis=0),axis=0)
Y2=np.interp(SM, Xnew, Ynew)
MRSS=np.mean((LH - Y2)**2)
AIC = n * np.log(MRSS) + 2*param_num
BIC = n * np.log(MRSS) + param_num * np.log(n)
if "is satisfied" in res[3] or "are satisfied" in res[3]:
flag=1
else:
flag=0
xc=res[0][0]
mt=res[0][3]
return {'type':'0111','flag1':res[4],'flag2':flag,'p':res[0],'AIC':AIC,'BIC':BIC,'line':[Xnew,Ynew],'xc':xc,'yp':Y2,'mt':mt}
def fit1101(data):
SM=data[0]
LH=data[1]
n=len(SM)
param_num=6
p0=[SM.min()+(SM.max()-SM.min())/3,
SM.max()-(SM.max()-SM.min())/3,
LH.min()+(LH.max()-LH.min())/3,
0,
50,
-50]
bounds=([np.min(np.array(SM)),np.min(np.array(SM)),np.min(np.array(LH)),-0.0010,0,-np.inf],
[np.max(np.array(SM)),np.max(np.array(SM)),np.max(np.array(LH)),0.0010,np.inf,0])
res= optimize.curve_fit(piecewise3sg_linear, np.array(SM), np.array(LH),p0=p0,bounds=bounds,full_output=True,maxfev=1e10)
X=np.r_[SM.min(),res[0][0],res[0][1],SM.max()]
Y=np.r_[res[0][3]*(SM.min()-res[0][0])+res[0][2],
res[0][2],
res[0][4]*(res[0][1]-res[0][0])+res[0][2],
res[0][5]*(SM.max()-res[0][1])+res[0][4]*(res[0][1]-res[0][0])+res[0][2]]
Xnew = np.take_along_axis(X, X.argsort(axis=0),axis=0)
Ynew = np.take_along_axis(Y, X.argsort(axis=0),axis=0)
Y2=np.interp(SM, Xnew, Ynew)
MRSS=np.mean((LH - Y2)**2)
AIC = n * np.log(MRSS) + 2*param_num
BIC = n * np.log(MRSS) + param_num * np.log(n)
if "is satisfied" in res[3] or "are satisfied" in res[3]:
flag=1
else:
flag=0
xc=res[0][1]
mt=res[0][4]
return {'type':'1101','flag1':res[4],'flag2':flag,'p':res[0],'AIC':AIC,'BIC':BIC,'line':[Xnew,Ynew],'xc':xc,'yp':Y2,'mt':mt}
def piecewise4sg_linear(x,x0,x1,x2,y0,k1,k2,k3,k4):
condlist = [x < x0, (x >= x0) & (x < x1), (x>=x1)&(x<x2), x >= x2]
funclist = [lambda x: k1*(x-x0)+y0, lambda x:k2*(x-x0) + y0, lambda x:k3*(x-x1) + k2*(x1-x0) + y0, lambda x:k4*(x-x2)+k3*(x2-x1)+k2*(x1-x0)+y0]
return np.piecewise(x, condlist, funclist)
def fit1111(data):
SM=data[0]
LH=data[1]
n=len(SM)
param_num=8
p0=[SM.min()+(SM.max()-SM.min())/4,
SM.min()+(SM.max()-SM.min())/2,
SM.max()-(SM.max()-SM.min())/4,
LH.min()+(LH.max()-LH.min())/3,
0,
50,
0,
-50]
bounds=([np.min(np.array(SM)),np.min(np.array(SM)),np.min(np.array(SM)),np.min(np.array(LH)),-0.0010,0,-0.0010,-np.inf],
[np.max(np.array(SM)),np.max(np.array(SM)),np.max(np.array(SM)),np.max(np.array(LH)),0.0010,np.inf,0.0010,0])
res= optimize.curve_fit(piecewise4sg_linear, np.array(SM), np.array(LH),p0=p0,bounds=bounds,full_output=True,maxfev=1e10)
X=np.r_[SM.min(),res[0][0],res[0][1],res[0][2],SM.max()]
Y=np.r_[res[0][4]*(SM.min()-res[0][0])+res[0][3],
res[0][3],
res[0][5]*(res[0][1]-res[0][0])+res[0][3],
res[0][6]*(SM.max()-res[0][1])+res[0][5]*(res[0][1]-res[0][0])+res[0][3],
res[0][7]*(SM.max()-res[0][2])+res[0][6]*(res[0][2]-res[0][1])+res[0][5]*(res[0][1]-res[0][0])+res[0][3] ]
Xnew = np.take_along_axis(X, X.argsort(axis=0),axis=0)
Ynew = np.take_along_axis(Y, X.argsort(axis=0),axis=0)
Y2=np.interp(SM, Xnew, Ynew)
MRSS=np.mean((LH - Y2)**2)
AIC = n * np.log(MRSS) + 2*param_num
BIC = n * np.log(MRSS) + param_num * np.log(n)
if "is satisfied" in res[3] or "are satisfied" in res[3]:
flag=1
else:
flag=0
xc=res[0][1]
mt=res[0][5]
return {'type':'1111','flag1':res[4],'flag2':flag,'p':res[0],'AIC':AIC,'BIC':BIC,'line':[Xnew,Ynew],'xc':xc,'yp':Y2,'mt':mt}
#
###
def remove_outlier(SM,LH):
LH_copy=np.sort(LH)
thre=0
for k in range(50):
tmp0=LH_copy[-1-k]
tmp1=LH_copy[-1-(k+1)]
if tmp0-tmp1<50:
continue
else:
thre=tmp0
if thre>0:
SMnew=SM[np.where(LH<thre)]
LHnew=LH[np.where(LH<thre)]
else:
SMnew=SM
LHnew=LH
SMnew2=SMnew[np.where(~np.isnan(SMnew))]
LHnew2=LHnew[np.where(~np.isnan(SMnew))]
return [SMnew2,LHnew2]
def runfit(sm,lf,fitfunc):
# remove outliers
# sm,lf=remove_outlier(sm,lf)
return fitfunc([sm,lf])
def bestfit(sm,lf):
#################################
# fit various segment models
#################################
fmodels=[fit1111,fit0111,fit1110,fit1100,fit0110,fit0100,fit0010,fit0011,fit0001]
# fmodels=[fit1111,fit0111,fit0101,fit1101,fit1110,fit1100,fit0110,fit0100,fit0010,fit0011,fit0001]
lfits=[runfit(sm,lf,fitfunc) for fitfunc in fmodels]
lcrit1=[fit['AIC'] for fit in lfits]
lcrit2=[fit['BIC'] for fit in lfits]
# best fit determined by min[AIC,BIC]
bfits=[ lfits[lcrit1.index(min(lcrit1))],
lfits[lcrit2.index(min(lcrit2))]]
return bfits
def bestfit_ef(sm,lf):
#################################
# fit various segment models
#################################
fmodels=[fit1110,fit0110,fit1100,fit0010]
lfits=[runfit(sm,lf,fitfunc) for fitfunc in fmodels]
lcrit1=[fit['AIC'] for fit in lfits]
lcrit2=[fit['BIC'] for fit in lfits]
# best fit determined by min[AIC,BIC]
bfits=[ lfits[lcrit1.index(min(lcrit1))],
lfits[lcrit2.index(min(lcrit2))]]
return bfits
def bestfit_hd22(sm,lf):
#################################
# fit various segment models
#################################
fmodels=[fit1110,fit1100,fit0110,fit0100,fit0010]
lfits=[runfit(sm,lf,fitfunc) for fitfunc in fmodels]
lcrit1=[fit['AIC'] for fit in lfits]
lcrit2=[fit['BIC'] for fit in lfits]
# best fit determined by min[AIC,BIC]
bfits=[ lfits[lcrit1.index(min(lcrit1))],
lfits[lcrit2.index(min(lcrit2))]]
return bfits