inversion: Estimate net rainfall by inversion
In transfR: Transfer of Hydrograph from Gauged to Ungauged Catchments

inversion

R Documentation

Estimate net rainfall by inversion

Description

Estimate net rainfall by inverse modelling, where the model is a convolution between net rainfall and a unit hydrograph in order to simulate discharge.

Usage

inversion(Qobs, ...)

## Default S3 method:
inversion(Qobs, uh, RnAp, deltat, ...)

## S3 method for class 'units'
inversion(
  Qobs,
  uh,
  RnAp,
  deltat,
  Bd = 0.01,
  Dd = 1,
  Bp = 0.001,
  Tp = 20,
  Ad = 0.01,
  Ap = 0.9,
  warmup = 10,
  cooldown = 8,
  dosplit = TRUE,
  split = 30,
  fixedpar = TRUE,
  parallel = FALSE,
  cores = NULL,
  cluster = NULL,
  ...
)

## S3 method for class 'transfR'
inversion(
  Qobs,
  verbose = TRUE,
  parallel = FALSE,
  cores = NULL,
  cluster = NULL,
  ...
)

Arguments

`Qobs`	discharge vector or object of class `transfR`. If no unit is provided, `Qobs` is assumed to be in [mm/h]
`...`	further arguments passed to or from other methods
`uh`	unit hydrograph vector
`RnAp`	a priori estimate of net rainfall. If no unit is provided, `RnAp` is assumed to be in [mm/h]
`deltat`	time step of the time series. If no unit is provided, `deltat` is assumed to be in [min]
`Bd`	parameter used to maintain a minimum value of standard deviation for low discharge values. If no unit is provided, `Bd` is assumed to be in [mm/h]
`Dd`	decorrelation time of discharge errors. If no unit is provided, `Dd` is assumed to be in [h]
`Bp`	parameter used to maintain a minimum value of standard deviation for low net rainfall values. If no unit is provided, `Bp` is assumed to be in [mm/h]
`Tp`	decorrelation time of net rainfall errors. If no unit is provided, `Tp` is assumed to be in [h]
`Ad`	parameter equivalent to the coefficient of variation of the discharge measurement error. If no unit is provided, `Ad` is assumed to be dimensionless
`Ap`	parameter equivalent to the coefficient of variation of the net rainfall error. If no unit is provided, `Ap` is assumed to be dimensionless
`warmup`	length of the warmup period. If no unit is provided, `warmup` is assumed to be in [days]
`cooldown`	length of the period removed at the end of the simulation. If no unit is provided, `cooldown` is assumed to be in [days]
`dosplit`	logical, if true the inversion is performed by subperiods of length defined by `split`
`split`	length of the subperiods if dosplit is true. If no unit is provided, `split` is assumed to be in [days]
`fixedpar`	logical; if FALSE, Ap and Ad are calibrated dynamically according to the coefficient of variation of RnAp and Qobs respectively (see details)
`parallel`	logical indicating whether the computation should be parallelised. Subperiods are parallelised for a single time series, whereas catchments are parallelised for a `transfR` object
`cores`	the number of cores to use for parallel execution if `parallel` is TRUE. If not specified, the number of cores is set to the value of `parallel::detectCores()`
`cluster`	an optional parallel cluster to reuse
`verbose`	logical indicating if information messages should be written to the console

Details

Given a convolution between the unit hydrograph (uh) and net rainfall that simulates streamflow at the outlet (Qobs), where net rainfall is the only unknown variable, this function estimates net rainfall by inversion \insertCiteTarantola1982,Menke1989,Boudhraa2018transfR. It requires an a priori estimate of net rainfall (which can be obtained with rapriori) and a description of errors in discharge (Ad, Bd, Dd) and net rainfall (Ap, Bp, Tp); these errors are assumed to be Gaussian and unbiased. Default values of these parameters are taken from \insertCitedeLavenne2016;textualtransfR. If fixedpar is deactivated, Ap is estimated at 20 of variation of Qobs.

It is recommended to use warmup and cooldown periods to reduce oscillations caused by inversion.

If Qobs is a transfR object, results are stored in a new space-time attribute called "RnInv".

Value

An object of the same class as Qobs. If Qobs is a transfR object, it is returned with the computed results added as new attributes.

References

\insertRef

Boudhraa2018transfR

\insertRef

deLavenne2016transfR

\insertRef

Menke1989transfR

\insertRef

Tarantola1982transfR

Examples

data(Oudon)
icatch <- 1 # Catchment index
itime <- 1:1000 # Using the first values for a quicker example
Qobs <- Oudon$obs[["Qobs"]][itime,icatch]
Qspec <- units::set_units(Qobs/st_area(st_geometry(Oudon$obs)[icatch]), "mm/h")
deltat <- units::set_units(1, "h")
uc <- velocity(hl = Oudon$hl[[icatch]])
uh <- uh(hl = Oudon$hl[[icatch]], uc = uc, deltat = units::set_units(1,"h"))$prob
RnAp <- rapriori(Qobs = Qspec, lagtime = lagtime(hl = Oudon$hl[[icatch]], uc = uc),
deltat = deltat)
RnInv <- inversion(Qobs = Qspec, RnAp = RnAp, uh = uh, deltat = deltat, parallel = TRUE, cores=2)

transfR documentation built on July 24, 2026, 5:06 p.m.