fix(RunModel_LLR): wrong parameter transformation

Previous one was from Munier but the model is not the same as Munier one.

This formulation is from https://doi.org/10.5194/nhess-14-2899-2014

Refs HYCAR-Hydro/airgr#152, HYCAR-Hydro/airgr#153

R/RunModel_LLR.R

@@ -68,19 +68,19 @@ RunModel_LLR <- function(InputsModel, RunOptions, Param, QcontribDown) {
   TParam <- Param[1L]
   KParam <- Param[2L]
 
-  ## propagation time from upstream meshes to outlet
-  PT <- ifelse(InputsModel$LengthHydro == 0, 0, InputsModel$LengthHydro/max(InputsModel$LengthHydro)) *
-    (TParam + KParam) - ifelse(InputsModel$LengthHydro == 0, 0,
-                               sqrt(InputsModel$LengthHydro/max(InputsModel$LengthHydro))) * KParam
-  PT[PT < 0] <- 0
-  PK <- ifelse(InputsModel$LengthHydro == 0,
-               0,
-               sqrt(InputsModel$LengthHydro/max(InputsModel$LengthHydro)) * KParam)
+  PT <-  InputsModel$LengthHydro * 1e3 / Param[1L] / RunOptions$FeatFUN_MOD$TimeStep
+  PK <- KParam * PT
 
   C0 <- ifelse(PK ==0, 0, exp(-1/PK))
   C1 <- ((PK/1) * (1-C0))-C0
   C2 <- 1 - (PK/1) * (1-C0)
 
+  ## Lag set up
+
+  Lag <-  function(t, Qroute, Qupstream){
+    Q <-  c(Qupstream[1 : floor(t)], Qroute[1 : (length(Qroute) - floor(t))])
+    return(Q)
+  }
   ## set up initial states
   IniSD <- RunOptions$IniStates[grep("SD", names(RunOptions$IniStates))]
   if (length(IniSD) > 0) {
@@ -135,10 +135,9 @@ RunModel_LLR <- function(InputsModel, RunOptions, Param, QcontribDown) {
         Qroute_t1 <- Qroute[q_upstream - 1]
       }
       Qroute[q_upstream] <- C0[upstream_basin] * Qroute_t1 + C1[upstream_basin] * Qupstream_m3[q_upstream - 1] + C2[upstream_basin] * Qupstream_m3[q_upstream]
-      Qllr[q_upstream + PT[upstream_basin]] <- Qroute[q_upstream]
     }
-    Qsim_m3[, upstream_basin] <- Qllr[(1 +length(Qllr) - length(IndPeriod1)) :
-                                        (length(IndPeriod1) + (length(Qllr) - length(IndPeriod1)))]
+    Qllr <- Lag(PT[upstream_basin], Qroute, Qupstream_m3)[IndPeriod1]
+    Qsim_m3[, upstream_basin] <- Qllr
 
   }
   Qsim_m3 <- cbind(QsimDown_input, Qsim_m3)