!------------------------------------------------------------------------------
! Subroutines relative to the annual GR6J model
!------------------------------------------------------------------------------
! TITLE : airGR
! PROJECT : airGR
! FILE : frun_GR6J.f
!------------------------------------------------------------------------------
! AUTHORS
! Original code: R. Pushpalatha
! Cleaning and formatting for airGR: L. Coron
! Further cleaning: G. Thirel
!------------------------------------------------------------------------------
! Creation date: 2010
! Last modified: 25/11/2019
!------------------------------------------------------------------------------
! REFERENCES
! Pushpalatha, R., C. Perrin, N. Le Moine, T. Mathevet and V. Andréassian!
! (2011). A downward structural sensitivity analysis of hydrological models to
! improve low-flow simulation. Journal of Hydrology, 411(1-2), 66-76.
! doi:10.1016/j.jhydrol.2011.09.034.
!------------------------------------------------------------------------------
! Quick description of public procedures:
! 1. frun_gr6j
! 2. MOD_GR6J
!------------------------------------------------------------------------------
SUBROUTINE frun_gr6j(LInputs,InputsPrecip,InputsPE,NParam,Param,
& NStates,StateStart,NOutputs,IndOutputs,
& Outputs,StateEnd)
! Subroutine that initializes GR6J, get its parameters, performs the call
! to the MOD_GR6J subroutine at each time step, and stores the final states
! Inputs
! LInputs ! Integer, length of input and output series
! InputsPrecip ! Vector of real, input series of total precipitation [mm/day]
! InputsPE ! Vector of real, input series of potential evapotranspiration (PE) [mm/day]
! NParam ! Integer, number of model parameters
! Param ! Vector of real, parameter set
! NStates ! Integer, number of state variables
! StateStart ! Vector of real, state variables used when the model run starts (store levels [mm] and Unit Hydrograph (UH) storages [mm])
! NOutputs ! Integer, number of output series
! IndOutputs ! Vector of integer, indices of output series
! Outputs
! Outputs ! Vector of real, output series
! StateEnd ! Vector of real, state variables at the end of the model run (store levels [mm] and Unit Hydrograph (UH) storages [mm])
!DEC$ ATTRIBUTES DLLEXPORT :: frun_gr6j
Implicit None
!! dummies
! in
integer, intent(in) :: LInputs,NParam,NStates,NOutputs
doubleprecision, dimension(LInputs), intent(in) :: InputsPrecip
doubleprecision, dimension(LInputs), intent(in) :: InputsPE
doubleprecision, dimension(NParam), intent(in) :: Param
doubleprecision, dimension(NStates), intent(in) :: StateStart
integer, dimension(NOutputs), intent(in) :: IndOutputs
! out
doubleprecision, dimension(NStates), intent(out) :: StateEnd
doubleprecision, dimension(LInputs,NOutputs),
& intent(out) :: Outputs
!! locals
integer :: I,K
integer, parameter :: NH=20,NMISC=30
doubleprecision, dimension(3) :: St
doubleprecision, dimension(NH) :: StUH1, OrdUH1
doubleprecision, dimension(2*NH) :: StUH2, OrdUH2
doubleprecision, dimension(NMISC) :: MISC
doubleprecision :: D,P1,E,Q
!--------------------------------------------------------------
! Initializations
!--------------------------------------------------------------
! initialization of model states to zero
St=0.
StUH1=0.
StUH2=0.
! initialization of model states using StateStart
St(1) = StateStart(1)
St(2) = StateStart(2)
St(3) = StateStart(3)
DO I=1,NH
StUH1(I)=StateStart(7+I)
ENDDO
DO I=1,2*NH
StUH2(I)=StateStart(7+I+NH)
ENDDO
! parameter values
! Param(1) : production store capacity (X1 - PROD) [mm]
! Param(2) : intercatchment exchange coefficient (X2 - CES1) [mm/day]
! Param(3) : routing store capacity (X3 - ROUT) [mm]
! Param(4) : time constant of unit hydrograph (X4 - TB) [day]
! Param(5) : intercatchment exchange threshold (X5 - CES2) [-]
! Param(6) : time constant of exponential store (X6 - EXP) [day]
! computation of HU ordinates
OrdUH1 = 0.
OrdUH2 = 0.
D=2.5
CALL UH1(OrdUH1,Param(4),D)
CALL UH2(OrdUH2,Param(4),D)
! initialization of model outputs
Q = -999.999
MISC = -999.999
! StateEnd = -999.999 !initialization made in R
! Outputs = -999.999 !initialization made in R
!--------------------------------------------------------------
! Time loop
!--------------------------------------------------------------
DO k=1,LInputs
P1=InputsPrecip(k)
E =InputsPE(k)
! Q = -999.999
! MISC = -999.999
! model run on one time step
CALL MOD_GR6J(St,StUH1,StUH2,OrdUH1,OrdUH2,Param,P1,E,Q,MISC)
! storage of outputs
DO I=1,NOutputs
Outputs(k,I)=MISC(IndOutputs(I))
ENDDO
ENDDO
! model states at the end of the run
StateEnd(1) = St(1)
StateEnd(2) = St(2)
StateEnd(3) = St(3)
DO K=1,NH
StateEnd(7+K)=StUH1(K)
ENDDO
DO K=1,2*NH
StateEnd(7+NH+K)=StUH2(K)
ENDDO
RETURN
ENDSUBROUTINE
!################################################################################################################################
!**********************************************************************
SUBROUTINE MOD_GR6J(St,StUH1,StUH2,OrdUH1,OrdUH2,Param,P1,E,Q,
&MISC)
! Calculation of streamflow on a single time step (day) with the GR6J model
! Inputs:
! St Vector of real, model states in stores at the beginning of the time step [mm]
! StUH1 Vector of real, model states in Unit Hydrograph 1 at the beginning of the time step [mm]
! StUH2 Vector of real, model states in Unit Hydrograph 2 at the beginning of the time step [mm]
! OrdUH1 Vector of real, ordinates in UH1 [-]
! OrdUH2 Vector of real, ordinates in UH2 [-]
! Param Vector of real, model parameters [various units]
! P1 Real, value of rainfall during the time step [mm]
! E Real, value of potential evapotranspiration during the time step [mm]
! Outputs:
! St Vector of real, model states in stores at the end of the time step [mm]
! StUH1 Vector of real, model states in Unit Hydrograph 1 at the end of the time step [mm]
! StUH2 Vector of real, model states in Unit Hydrograph 2 at the end of the time step [mm]
! Q Real, value of simulated flow at the catchment outlet for the time step [mm/day]
! MISC Vector of real, model outputs for the time step [mm or mm/day]
!**********************************************************************
Implicit None
!! locals
integer, parameter :: NParam=6,NMISC=30,NH=20
doubleprecision :: A,EN,ER,PN,PR,PS,WS,tanHyp,AR
doubleprecision :: PERC,PRUH1,PRUH2,EXCH,QR,QD,QRExp
doubleprecision :: AE,AEXCH1,AEXCH2
integer :: K
doubleprecision, parameter :: B=0.9, C=0.4
doubleprecision, parameter :: stored_val=25.62890625
doubleprecision :: TWS, Sr, Rr ! speed-up
!! dummies
! in
doubleprecision, dimension(NParam), intent(in) :: Param
doubleprecision, intent(in) :: P1,E
doubleprecision, dimension(NH), intent(inout) :: OrdUH1
doubleprecision, dimension(2*NH), intent(inout) :: OrdUH2
! inout
doubleprecision, dimension(3), intent(inout) :: St
doubleprecision, dimension(NH), intent(inout) :: StUH1
doubleprecision, dimension(2*NH), intent(inout) :: StUH2
! out
doubleprecision, intent(out) :: Q
doubleprecision, dimension(NMISC), intent(out) :: MISC
A=Param(1)
! Production store
IF(P1.LE.E) THEN
EN=E-P1
PN=0.
WS=EN/A
IF(WS.GT.13) WS=13.
! speed-up
TWS = tanHyp(WS)
Sr = St(1)/A
ER=St(1)*(2.-Sr)*TWS/(1.+(1.-Sr)*TWS)
! ER=X(2)*(2.-X(2)/A)*tanHyp(WS)/(1.+(1.-X(2)/A)*tanHyp(WS))
! end speed-up
AE=ER+P1
St(1)=St(1)-ER
PS=0.
PR=0.
ELSE
EN=0.
AE=E
PN=P1-E
WS=PN/A
IF(WS.GT.13) WS=13.
! speed-up
TWS = tanHyp(WS)
Sr = St(1)/A
PS=A*(1.-Sr*Sr)*TWS/(1.+Sr*TWS)
! PS=A*(1.-(X(2)/A)**2.)*tanHyp(WS)/(1.+X(2)/A*tanHyp(WS))
! end speed-up
PR=PN-PS
St(1)=St(1)+PS
ENDIF
! Percolation from production store
IF(St(1).LT.0.) St(1)=0.
! speed-up
! (9/4)**4 = 25.62890625 = stored_val
Sr = St(1)/Param(1)
Sr = Sr * Sr
Sr = Sr * Sr
PERC=St(1)*(1.-1./SQRT(SQRT(1.+Sr/stored_val)))
! PERC=X(2)*(1.-(1.+(X(2)/(9./4.*Param(1)))**4.)**(-0.25))
! end speed-up
St(1)=St(1)-PERC
PR=PR+PERC
! Split of effective rainfall into the two routing components
PRUH1=PR*B
PRUH2=PR*(1.-B)
! Convolution of unit hydrograph UH1
DO K=1,MAX(1,MIN(NH-1,INT(Param(4)+1.)))
StUH1(K)=StUH1(K+1)+OrdUH1(K)*PRUH1
ENDDO
StUH1(NH)=OrdUH1(NH)*PRUH1
! Convolution of unit hydrograph UH2
DO K=1,MAX(1,MIN(2*NH-1,2*INT(Param(4)+1.)))
StUH2(K)=StUH2(K+1)+OrdUH2(K)*PRUH2
ENDDO
StUH2(2*NH)=OrdUH2(2*NH)*PRUH2
! Potential intercatchment semi-exchange
EXCH=Param(2)*(St(2)/Param(3)-Param(5))
! Routing store
AEXCH1=EXCH
IF((St(2)+(1-C)*StUH1(1)+EXCH).LT.0) AEXCH1=-St(2)-(1-C)*StUH1(1)
St(2)=St(2)+(1-C)*StUH1(1)+EXCH
IF(St(2).LT.0.) St(2)=0.
! speed-up
Rr = St(2)/Param(3)
Rr = Rr * Rr
Rr = Rr * Rr
QR=St(2)*(1.-1./SQRT(SQRT(1.+Rr)))
! QR=X(1)*(1.-(1.+(X(1)/Param(3))**4.)**(-1./4.))
! end speed-up
St(2)=St(2)-QR
! Update of exponential store
St(3)=St(3)+C*StUH1(1)+EXCH
AR=St(3)/Param(6)
IF(AR.GT.33.) AR=33.
IF(AR.LT.-33.) AR=-33.
IF(AR.GT.7.)THEN
QRExp=St(3)+Param(6)/EXP(AR)
GOTO 3
ENDIF
IF(AR.LT.-7.)THEN
QRExp=Param(6)*EXP(AR)
GOTO 3
ENDIF
QRExp=Param(6)*LOG(EXP(AR)+1.)
3 CONTINUE
St(3)=St(3)-QRExp
! Runoff from direct branch QD
AEXCH2=EXCH
IF((StUH2(1)+EXCH).LT.0) AEXCH2=-StUH2(1)
QD=MAX(0.d0,StUH2(1)+EXCH)
! Total runoff
Q=QR+QD+QRExp
IF(Q.LT.0.) Q=0.
! Variables storage
MISC( 1)=E ! PE ! observed potential evapotranspiration [mm/day]
MISC( 2)=P1 ! Precip ! observed total precipitation [mm/day]
MISC( 3)=St(1) ! Prod ! production store level (St(1)) [mm]
MISC( 4)=PN ! Pn ! net rainfall [mm/day]
MISC( 5)=PS ! Ps ! part of Ps filling the production store [mm/day]
MISC( 6)=AE ! AE ! actual evapotranspiration [mm/day]
MISC( 7)=PERC ! Perc ! percolation (PERC) [mm/day]
MISC( 8)=PR ! PR ! PR=PN-PS+PERC [mm/day]
MISC( 9)=StUH1(1) ! Q9 ! outflow from UH1 (Q9) [mm/day]
MISC(10)=StUH2(1) ! Q1 ! outflow from UH2 (Q1) [mm/day]
MISC(11)=St(2) ! Rout ! routing store level (St(2)) [mm]
MISC(12)=EXCH ! Exch ! potential third-exchange between catchments (EXCH) [mm/day]
MISC(13)=AEXCH1 ! AExch1 ! actual exchange between catchments from routing store (AEXCH1) [mm/day]
MISC(14)=AEXCH2 ! AExch2 ! actual exchange between catchments from direct branch (after UH2) (AEXCH2) [mm/day]
MISC(15)=AEXCH1+AEXCH2+EXCH ! AExch ! actual total exchange between catchments (AEXCH1+AEXCH2+EXCH) [mm/day]
MISC(16)=QR ! QR ! outflow from routing store (QR) [mm/day]
MISC(17)=QRExp ! QRExp ! outflow from exponential store (QRExp) [mm/day]
MISC(18)=St(3) ! Exp ! exponential store level (St(3)) (negative) [mm]
MISC(19)=QD ! QD ! outflow from UH2 branch after exchange (QD) [mm/day]
MISC(20)=Q ! Qsim ! simulated outflow at catchment outlet [mm/day]
ENDSUBROUTINE