find_bps: Find breakpoints in DFI curve

In modche/delayedflow: Delayed-flow separation for streamflow data

Find breakpoints in DFI curve

Description

Estimates n breakpoints in the DFI curve. DFI values are compared against n+1 piecewise linear segments and the minimization of the residuals (between linear segments and DFI curve). Several parameters can be customized. If q_obs is given in daily temporal resolution then also n can be interpreted as delay in days for different contributions (default).

Usage

find_bps(
  dfi,
  n_bp = 2,
  bp_mingap = 5,
  bp_min = 0,
  bp_max = length(dfi) - 1,
  nmax = length(dfi),
  of_weights = c(0.5, 0.5),
  desc = TRUE,
  print = FALSE,
  plotting = FALSE,
  experimental = FALSE
)

Arguments

dfi	numeric, a vector with the DFI values between 1 and 0, dummy data dfi_example can be used.
n_bp	numeric, How many breakpoints (1, 2, 3) should be estimated (default = 2)? If n_bp = 3 calculation time could be longer if also nmax is high. nmax could be estimated with find_nmax. For testing also n_bp = 4 is possible See experimental setting.
bp_mingap	numeric, smallest interval between two breakpoints (default = 5).
bp_min	numeric, bp_min+1 is minimum allowed breakpoint position (default = 0).
bp_max	numeric, bp_max-1 is maximum allowed breakpoint position.
nmax	numeric parameter to truncate the tailing of the CDC (i.e. the length of dfi vector). Note, nmax should not be confused with bp_max (i.e. maximum breakpoint position).
of_weights	vector with two elements, first is weight of the RMSE, second is weight of the MAE. Default is c(0.5, 0.5), i.e. equal weights. Sum of vector must be 1. To switch of one measure use c(1, 0) or c(0,1). With the weighting more or less focus could be given to the upper parts of the DFI curve (i.e. when block length n for separation is between 1 and 10).
desc	logical, if TRUE (recommended) DFI values are converted to be monotonically decreasing with cummin()
print	logical, if TRUE best breakpoint estimates during calculation are printed (debug mode)
plotting	logical, if TRUE the DFI curve, piecewise linear segments and the breakpoints are plotted with plot() whit DFI curve in blue and linear segments in red.
experimental	logical, if TRUE four breakpoints can be estimated.

Value

Returns a list with 3 elements.

breakpoints	estimates for the n breakpoints with names bp_n
bias	value of the objective function, default: OF = 1/2 RMSE + 1/2 MAE, where OF is to be minimized.
rel_contr	Relative streamflow contributions between bp_min, the breakpoints and bp_max, e.g. 2 breakpoints lead to 3 relative contributions, 3 breakpoints lead to 4 relative contributions. The first rel_contr-value is the fastest contribution to streamflow, the last rel_contr-value is the slowest contribution to streamflow. All contributions add up to 1.

References

Stoelzle, M., Schuetz, T., Weiler, M., Stahl, K., & Tallaksen, L. M. (2020). Beyond binary baseflow separation: a delayed-flow index for multiple streamflow contributions. Hydrology and Earth System Sciences, 24(2), 849-867.

Examples

# use dfi_example as an DFI vector with 121 values
find_bps(dfi_example, n_bp = 3, bp_max = 90, plotting = TRUE)

modche/delayedflow documentation built on March 17, 2022, 5:28 p.m.