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MISDc_WEB_2L_snow_IE.m
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MISDc_WEB_2L_snow_IE.m
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%-----------------------------------------------------------------------------------------------
% MISDc rainfall-runoff model (lumped version, daily)
%------------------------------------------------------------------------------------------------
function [NS,ANSE,KGE,NS_radQ,Qsim,WW,WW2]=MISDc_WEB_2L_snow_IE(DPEQ,PAR,Ab,FIG,dir,name,name_suff)
% Loading input data
[M,~]=size(DPEQ);
D=DPEQ(:,1); PIO_=DPEQ(:,2); TEMPER=DPEQ(:,3); Qobs=DPEQ(:,4);
delta_T=round(nanmean(diff(D))*24*10000)/10000;
MESE=month(D);
% Model parameter
W_p = PAR(1); % initial conditions, fraction of W_max (0-1)
W_max2 = PAR(2); % total water capacity of 2nd layer
m2 = PAR(3); % exponent of drainage for 1st layer
Ks = PAR(4); % hydraulic conductivity for 1st layer
gamma1 = PAR(5); % coefficient lag-time relationship
Kc = PAR(6); % parameter of potential evapotranspiration
alpha = PAR(7); % exponent runoff
Cm = PAR(8); % Snow module parameter degree-day
m22 = PAR(9); % exponent of drainage for 2nd layer
Ks2 = PAR(10); % hydraulic conductivity for 2nd layer
W_max = 150; % FIXED WATER CAPACITY 1st LAYER
% Other data
dt = 0.2; % computation time step in hour
Ks = Ks.*delta_T; % mm/h --> mm/delta_T
Ks2 = Ks2.*delta_T; % mm/h --> mm/delta_T
% Snow Module
[PIO,SWE]=snow_model(PIO_, TEMPER, -0.5, 0.5, Cm);
% Potential Evapotranspiration parameter
% L=[0.2100;0.2200;0.2300;0.2800;0.3000;0.3100;
% 0.3000;0.2900;0.2700;0.2500;0.2200;0.2000];
L=[0.2500;0.2500;0.2500;0.2500;0.2500;0.2500;
0.2500;0.2500;0.2500;0.2500;0.2500;0.2500];
Ka=1.26;
EPOT=(TEMPER>0).*(Kc*(Ka*L(MESE).*(0.46*TEMPER+8)-2))/(24/delta_T);
% EPOT=Kc.*EPOT;
clear DPEQ TEMPER
% Initialization
BF=zeros(M,1);
QS=zeros(M,1);
WW=zeros(M,1);
WW2=zeros(M,1);
% Main ROUTINE
W=W_p*W_max;
W2=W_p*W_max2;
S=NaN;
Pcum=0;
IE=0;
for t=1:M
IE=PIO(t)*((W/W_max).^alpha);
E=EPOT(t)*W/W_max;
if W2<W_max2
PERC=Ks*(W/W_max).^(m2);
else
PERC=0;
end
PERC2=Ks2*(W2/W_max2).^(m22);
PERC(PERC>0.6.*W_max)=0.6.*W_max;
% PERC2(PERC2>0.6.*W_max2)=0.6.*W_max2;
W=max(0,W+(PIO(t)-IE-PERC-E)+SWE(t));
W2=max(0,W2+PERC-PERC2);
if W>=W_max
SE=W-W_max;
W=W_max;
else
SE=0;
end
if W2>=W_max2
SE2=W2-W_max2;
W2=W_max2;
else
SE2=0;
end
if W<0, W=0; end
if W2<0, W2=0; end
WW(t)=W./W_max;
WW2(t)=W2./W_max2;
% Runoff contribution
BF(t)=Ks2*((W+W2)/(W_max+W_max2)).^(m22);
QS(t)=IE+SE+SE2; % surface flow
end
% Convolution (GIUH)
IUH1=IUH_comp(gamma1,Ab,dt,delta_T)*dt;IUH1=IUH1./sum(IUH1);
IUH2=IUH_NASH(1,0.5*gamma1,Ab,dt,delta_T)*dt;IUH2=IUH2./sum(IUH2);
QSint=interp1(1:M,QS,1:dt:M)';
BFint=interp1(1:M,BF,1:dt:M)';
temp1=conv(IUH1,QSint);
temp2=conv(IUH2,BFint);
Qsim1=temp2(1:round(1/dt):M*round(1/dt)).*(Ab.*1000./delta_T./3600);
Qsim=(temp1(1:round(1/dt):M*round(1/dt))+temp2(1:round(1/dt):M*round(1/dt)))...
.*(Ab.*1000./delta_T./3600);
Qsim=real(Qsim);
% Calculation of model performance
RMSE=nanmean((Qsim-Qobs).^2).^0.5;
NS=1-nansum((Qsim-Qobs).^2)./nansum((Qobs-nanmean(Qobs)).^2);
ANSE=1-nansum((Qobs+nanmean(Qobs)).*(Qsim-Qobs).^2)./...
nansum((Qobs+nanmean(Qobs)).*(Qobs-nanmean(Qobs)).^2);
NS_radQ=1-nansum((sqrt(Qsim)-sqrt(Qobs)).^2)./nansum((sqrt(Qobs)-nanmean(sqrt(Qobs))).^2);
NS_lnQ=1-nansum((log(Qsim+0.00001)-log(Qobs+0.00001)).^2)...
./nansum((log(Qobs+0.00001)-nanmean(log(Qobs+0.00001))).^2);
X=[Qsim,Qobs]; X(any(isnan(X)'),:) = [];
RRQ=corrcoef(X).^2; RQ=RRQ(2);
KGE=klinggupta(Qsim,Qobs);
% Figure
if FIG==1
clf
% saturation degree
set(gcf,'paperpositionmode','manual','paperposition',[1 1 24 13])
set(gcf,'position',[50 50 900 500])
h(1) = axes('Position',[0.1 0.77 0.8 0.10]);
hold on
plot(D,WW,'r');
plot(D,WW2,'k');
legend('SSM','RZSM','location','best');
set(gca,'XAxisLocation','top')
datetick('x',12,'keeplimits')
ylabel({'saturation','[-]'});
grid on, box on,
s=(['NSE= ',num2str(NS,'%3.3f'),...
' ANSE= ',num2str(ANSE,'%3.3f'),...
' NSE(radQ)= ',num2str(NS_radQ,'%3.3f'),...
' R^2= ',num2str(RQ,'%3.3f'),...
' KGE= ',num2str(KGE,'%3.3f')]);
nname=[name,name_suff];nname(nname=='_')='-';
title(['\bf',nname,': ',s]); hold on
axis([D(1) D(end)+1 -0.05 1.05])
% observed rainfall
h(2) = axes('Position',[0.1 0.65 0.8 0.10]);
plot(D,PIO),hold on,
datetick('x',12,'keeplimits')
set(gca,'ydir','reverse')
set(gca,'Xticklabel','')
ylabel({'rainfall','[mm]'});
grid on, box on
axis([D(1) D(end)+1 0 nanmax(PIO).*1.05])
% observed and simulated discharge
h(3) = axes('Position',[0.1 0.1 0.8 0.54]);
plot(D,Qobs,'-g','Linewidth',3);hold on
plot(D,Qsim,'--r','Linewidth',1.0);
legend('Q_o_b_s','Q_s_i_m','location','best');
ylabel({'discharge',' [m^3/s]'})
grid on, box on, axis tight
axis([D(1) D(end)+1 0 nanmax(Qobs).*1.2]);
datetick('x',11,'keeplimits')
print(gcf,[dir,'\',name,name_suff],'-dpng','-r250')
end
% -------------------------------------------------------------------------------
% Calculation of Geomorphological Instantaneous Unit Hydrograph
% -------------------------------------------------------------------------------
function IUH=IUH_comp(gamma,Ab,dt,deltaT)
Lag=(gamma*1.19*Ab^0.33)/deltaT;
hp=0.8/Lag;
data=load('IUH.txt');
t=data(:,1)*Lag;IUH_0=data(:,2)*hp;
ti=0:dt:max(t);
IUH=interp1(t,IUH_0,ti)';
% -------------------------------------------------------------------------------
% Calculation of Nash Instantaneous Unit Hydrograph
% -------------------------------------------------------------------------------
function IUH=IUH_NASH(n,gamma,Ab,dt,deltaT)
K=(gamma*1.19*Ab.^.33)./deltaT;
time=0:dt:100;
IUH=((time/K).^(n-1).*exp(-time/K)/factorial(n-1)/K)';
%--------------------------------------------------------------------------
% Snow accumulation-melting MODEL
%--------------------------------------------------------------------------
function [rainfall,SWE_melting,SWE_snowpack]=snow_model(precipitation, temperature, temp_min, temp_max, Cm)
rainfall = zeros(length(precipitation),1);
snowfall = zeros(length(precipitation),1);
SWE_snowpack = zeros(length(precipitation),1);
SWE_melting = zeros(length(precipitation),1);
% The precipitation is divided into rainfall and snowfall
% REFERENCES:
% U.S. Army Corps of Engineers (1956)
% Boscarello, L., Ravazzani, G., Pellegrini, M., Dedieu, J. P., & Mancini, M. (2014). Calibration of hydrological model FEST from MODIS images in Alpine Catchments. Politecnico di Milano, Dipartimento di Ingegneria Idraulica, Ambientale, Infrastrutture viarie, Rilevamento.
% Degree Day Method (Mockus, 1964)
% INITIALIZATION
if precipitation(1,1) == NaN || temperature(1,1) == NaN
rainfall(1,1) = NaN;
snowfall(1,1) = NaN;
elseif temperature(1,1) <= temp_min
snowfall(1,1) = precipitation(1,1);
rainfall(1,1) = 0;
SWE_snowpack(1,1) = snowfall(1,1); % [mm]
SWE_melting(1,1) = 0; % [mm]
elseif temperature(1,1) >= temp_max
snowfall(1,1) = 0;
rainfall(1,1) = precipitation(1,1);
SWE_snowpack(1,1) = 0; % [mm]
SWE_melting(1,1) = 0; % [mm]
else
rainfall(1,1) = precipitation(1,1) * ((temperature(1,1)-temp_min)/(temp_max-temp_min));
snowfall(1,1) = precipitation(1,1) - rainfall(1,1);
SWE_snowpack(1,1) = snowfall(1,1);
SWE_melting(1,1) = 0;
end
% rho_fresh_snow(1,1) = 10^3 * (0.05 + ((temperature(1,1) * 1.8 + 32) / 100)^2); % Fresh snow density [kg/m3]
for i=2:length(precipitation)
if precipitation(i,1) == NaN || temperature(i,1) == NaN
% se manca il dato, metto i NaN
rainfall(i,1) = NaN;
snowfall(i,1) = NaN;
elseif temperature(i,1) <= temp_min
% if the temperature is less than the low threshold,
% the precipitation is entirely snowfall
rainfall(i,1) = 0;
snowfall(i,1) = precipitation(i,1);
SWE_snowpack(i,1) = SWE_snowpack(i-1,1) + snowfall(i,1);
SWE_melting(i,1) = 0;
elseif temperature(i,1) > temp_max
% if the temperature is more than the high threshold,
% the precipitation is entirely rainfall
rainfall(i,1) = precipitation(i,1);
snowfall(i,1) = 0;
SWE_melting(i,1) = Cm * (temperature(i,1) - temp_max);
% h_melting(i,1) = rho_water * SWE_melting(i,1) / rho_snow;
% Check the snowpack SWE
if SWE_snowpack(i-1,1) >= SWE_melting(i,1)
SWE_snowpack(i,1) = SWE_snowpack(i-1,1) - SWE_melting(i,1);
% h_snowpack(i,1) = h_snowpack(i-1,1) - h_melting(i,1);
else
SWE_melting(i,1) = SWE_snowpack(i-1,1);
% h_melting(i,1) = h_snowpack(i-1,1);
% h_snowpack(i,1) = 0;
SWE_snowpack(i,1) = 0;
end
else
rainfall(i,1) = precipitation(i,1) * ((temperature(i,1)-temp_min)/(temp_max-temp_min));
snowfall(i,1) = precipitation(i,1) - rainfall(i,1);
SWE_snowpack(i,1) = SWE_snowpack(i-1,1) + snowfall(i,1);
SWE_melting(i,1) = 0;
end
end
function [ kge , r, relvar, bias ] = klinggupta(modelled,observed)
%Nash Sutcliffe Efficiency measure
modelled(isnan(observed))=NaN;
cflow=[modelled,observed];
cflow=rem_nan(cflow);
sdmodelled=nanstd(modelled);
sdobserved=nanstd(observed);
mmodelled=nanmean(modelled);
mobserved=nanmean(observed);
r=corrcoef(cflow,'rows','pairwise');
r=r(1,2);
relvar=sdmodelled/sdobserved;
bias=mmodelled/mobserved;
%KGE timeseries
kge=1- sqrt( ((r-1)^2) + ((relvar-1)^2) + ((bias-1)^2) );
function [X,ID_NaN] = rem_nan(X)
ID_NaN=any(isnan(X)');
X(ID_NaN,:) = [];
% X(any(isnan(X),2),:) = [];