Smooth Discounted Flow

Applies exponential smoothing to discharge data.

Usage

sdf(discharge, delta = 0.95)

Arguments

discharge

vector of discharge data (numeric).

delta

the discount factor which can be any value between (0,1), defaults to 0.95. As delta approaches one, the average discounted flow approaches mean flow. Small values of delta return values closer to the current daily flow.

Value

vector of values the same length as discharge.

Details

The smooth discounted flow (SDF) was proposed by Kuhnert et al. (2012). The premise of SDF is to incorporate the influence of historical flows on flux:

$$SDF(\delta) = d\kappa_{i-1} + (1-\delta)\hat{q}_{i-1},$$

and

$$\kappa_{i} = \sum_{m=1}^{i}\hat{q}_m,$$ for discount factor \(\delta\), where \(\kappa_{i}\) represents cumulative flow up to the \(i\)th day.

References

Kuhnert, Petra M., Brent L. Henderson, Stephen E. Lewis, Zoe T. Bainbridge, Scott N. Wilkinson, and Jon E. Brodie. 2012. “Quantifying Total Suspended Sediment Export from the Burdekin River Catchment Using the Loads Regression Estimator Tool” Water Resources Research 48 (4). doi:10.1029/2011WR011080 .

Examples

# Standard use case
ma <- sdf(lavaca$Flow, delta=0.95)
head(ma)