Implements the Lyne and Hollick filter for baseflow seperation. This function utilizes the approach in Ladson et al. (2013).

## Arguments

- discharge
numeric vector of daily discharge values

- a
alpha, numeric values between

`[0-1]`

.- n
number of passes for the filter. Must be a numeric value, defaults to 3.

- reflect
the number of values to reflect at the start and end of

`discharge`

to reduce "warm-up" and "cool-down" issues with the recursive filter. Must be less than or equal to the length of`discharge`

. For long discharge records this value does not matter much, for short records the reflection should approach the length of`discharge`

. The default is 30 as implemented in Ladson et al. (2013).

## Details

This function implements the Lyne-Hollick filter (Lyne and Hollick, 1979) using the approach detailed in Ladson et al. (2013). The filter is:

$$Y_{k} = \alpha \times Y_{k-1} + \frac{1+\alpha}{2} \times (Q_k - Q_{k-1}),$$

where \(Y_k\) is the filtered quick response at the \(k^{th}\) sample.
\(Q_k\) if the original streamflow and \(\alpha\) is the filter
parameter between `[0-1]`

.

Ladson et al. (2013) suggest a standardized approach for applying the filter by: (1) reflecting streamflow at the start and end of the series to address warm-up and cool-down; (2) specify the initial value of each pass as the measured flow; and (3) using three passes for the filter (forward, backward, forward); Ladson et al. (2013) also provide additional suggestions for handling missing values and appropriate alpha parameter values that are not covered here.

## Note

This function an updated and modified version of the `baseflows()`

function in the hydrostats package by Nick Bond. The hydrostats version
returns additional summary measures and utilizes different starting values.
Outputs between the two packages will slightly vary.

## References

Lyne, V., & Hollick, M. (1979, September). Stochastic time-variable rainfall-runoff modelling. In Institute of Engineers Australia National Conference (Vol. 79, No. 10, pp. 89-93). Barton, Australia: Institute of Engineers Australia.

Ladson, A. R., Brown, R., Neal, B., & Nathan, R. (2013). A standard approach to baseflow separation using the Lyne and Hollick filter. Australian Journal of Water Resources, 17(1), 25-34, doi:10.7158/W12-028.2013.17.1 .

## Author

Nick Bond n.bond@latrobe.edu.au modified by Michael Schramm

## Examples

```
bf <- bf_sep_lh(lavaca$Flow, a = 0.975)
head(bf)
```