The method developed by Greimel et al. (2016) detects and
characterizes sub-daily flow fluctuations and is implemented in the R
package **hydropeak** (available on CRAN). Based on
the events detected by the method implemented in package
**hydropeak**, **hydroroute** identifies
associated events in hydrographs from neighboring gauging stations and
models the translation and retention processes between them (Greimel et
al., 2022).

This vignette presents the main function `peaktrace()`

which given the events and relation information between gauging stations
determines the associated events and based on these, estimates
predictive models to trace initial values specified for the relevant
metrics across the neighboring gauging stations. First, an overview on
the input data required is given and the additional function
`get_lag()`

and variants thereof are presented which estimate
the mean translation time of the hydrographs between adjacent gauging
stations, if not already available. Then the individual function
`estimate_AE()`

is presented which is used by
`peaktrace()`

to identify the associated events (AEs).
Finally the application of `peaktrace()`

is illustrated and
it is shown how the return value can be inspected.

Several data files are required to perform the analysis.

`Q`

If the mean translation time between hydrographs at neighboring
gauging stations is not given or known, the raw dataset `Q`

,
containing (equispaced) date-time values and the corresponding flow
fluctuations, is needed. Based on these data the mean translation time
between hydrographs at neighboring gauging stations may be estimated
using `get_lag()`

. The dataset `Q`

needs to
contain three variables:

`ID`

Character string which refers to the identifier of the gauging station (in Austria: HZBCODE).`Time`

Character string with date-time information of measurements.`Q`

Numeric, flow measurements.

The combination of `ID`

and `Time`

must be
unique. Functions that use the dataset `Q`

assume that these
variables are contained in this order with exactly these names. If this
is not the case, i.e., if the columns have different names or are not in
this order, the order can be specified in these functions with argument
`cols`

. The columns are then renamed internally to make the
data processable. Also the date-time format must be specified if it is
different from the function’s default format used.

The following code loads the sample dataset `Q`

and shows
the first few rows:

```
<- system.file("testdata", "Q.csv", package = "hydroroute")
Q_path <- read.csv(Q_path)
Q head(Q)
#> ID Time Q
#> 1 200000 2014-01-01 00:00:00 4.07
#> 2 200000 2014-01-01 00:15:00 4.06
#> 3 200000 2014-01-01 00:30:00 4.05
#> 4 200000 2014-01-01 00:45:00 4.04
#> 5 200000 2014-01-01 01:00:00 4.03
#> 6 200000 2014-01-01 01:15:00 4.01
```

The sample dataset `Q`

is a data frame with 22656 rows and
3 variables as described above. The station ID’s along the flow path are
`100000, 200000, 300000, 400000`

. The time ranges from
`"2014-01-01 00:00:00"`

to
`"2014-02-28 23:45:00"`

.

`relation`

The dataset `relation`

provides information about the
gauging stations of neighboring hydrographs. It contains:

`ID`

Character string which refers to the identifier of the gauging station (in Austria: HZBCODE).`Type`

Character string which characterizes the source hydrograph (`Turbine flow`

,`Gauge`

,`Basin outflow`

).`Station`

Character string which indicates the order of the`n`

hydrographs in`relation`

in downstream direction (`Si`

with`i = 1, ..., n`

).`fkm`

Numeric, position of hydrograph in km relative to the source.`LAG`

Character string which contains the cumulative mean translation time (or estimated cumulative lag) between the source and a specific gauging station in the format`HH:MM`

. For`S1`

this is either indicated as missing (`NA`

) or always given as`00:00`

. It is either already provided in`relation`

or can be estimated from the corresponding dataset`Q`

with`get_lag()`

.

The following code loads an example dataset:

```
<- system.file("testdata", "relation.csv", package = "hydroroute")
relation_path <- read.csv(relation_path)
relation
relation#> ID Type Station fkm LAG
#> 1 100000 Gauge S1 0.01 00:00
#> 2 200000 Gauge S2 9.16 01:00
#> 3 300000 Gauge S3 17.02 02:15
#> 4 400000 Gauge S4 29.27 03:30
```

The dataset `relation`

contains 4 adjacent gauging
stations.

The output files from **hydropeak**’s
`get_events_*()`

function are used to identify AEs. The
naming scheme of the output files is
`ID_event-type_date-time-from_date-time-to.csv`

. Event types
are defined as follows:

- 0: Constant event after an NA event (i.e., a missing event) or as first event in the time series.
- 1: Constant event after a decreasing event.
- 2: Increasing event (IC).
- 3: Constant event after an increasing event.
- 4: Decreasing event (DC).
- 5: NA event.

The most important event types for the following analysis are
`2`

(increasing event; IC) and `4`

(decreasing
event; DC).

Package **hydroroute** includes 8 sample
`Event`

files for each gauging station ID contained in the
sample dataset `Q`

and event type `2`

(IC) and
`4`

(DC) between `"2014-01-01 00:00:00"`

and
`"2014-02-28 23:45:00"`

. The increasing events for the
station with ID `100000`

are thus loaded using:

```
<- system.file("testdata", "Events", "100000_2_2014-01-01_2014-02-28.csv",
Sx package = "hydroroute")
<- read.csv(Sx)
Sx head(Sx)
#> ID EVENT_TYPE Time AMP MAFR MEFR DUR RATIO
#> 1 100000 2 2014-01-01 00:15:00 0.01 0.01 0.01000000 1 1.003546
#> 2 100000 2 2014-01-01 01:00:00 27.07 12.20 6.76750000 4 10.565371
#> 3 100000 2 2014-01-01 10:15:00 29.38 15.50 7.34500000 4 11.801471
#> 4 100000 2 2014-01-01 13:30:00 0.16 0.03 0.02666667 6 1.060837
#> 5 100000 2 2014-01-01 17:30:00 30.91 16.90 7.72750000 4 12.490706
#> 6 100000 2 2014-01-01 20:45:00 0.02 0.01 0.01000000 2 1.007812
```

`get_lag()`

For the identification of AEs, the translation time between
neighboring hydrographs and the event amplitude have to be considered.
For the first criterion, the mean translation time (`LAG`

)
between hydrographs has to be estimated and the cumulative values
appended to the `relation`

data for further processing, if
not available yet.

Function `get_lag_file()`

uses:

`Q_file`

A path to a file that contains the`Q`

data from several stations or a data frame that contains this information.`relation_file`

A path to a`relation`

file. The`ID`

s of the stations must be in`Q`

.

If the argument `save`

is `TRUE`

, the
`relation`

data with appended `LAG`

column is
written to a file specified in `outfile`

. If a
`LAG`

column already exists, argument `overwrite`

has to be set to `TRUE`

to overwrite the existing column. The
function can be applied to several `relation`

files by
iterating over file paths or if a single `Q`

data file is
available, `get_lag_dir()`

can be used. `relation`

files can be selected from a directory using regular expressions
(argument `relation_pattern`

).

The following code shows this for single file names:

```
<- system.file("testdata", "Q.csv", package = "hydroroute")
Q_file <- system.file("testdata", "relation.csv", package = "hydroroute")
relation get_lag_file(Q_file, relation, inputsep = ",", format = "%Y-%m-%d %H:%M",
(save = FALSE, overwrite = TRUE))
#> ID Type Station fkm LAG
#> 1 100000 Gauge S1 0.01 00:00
#> 2 200000 Gauge S2 9.16 01:15
#> 3 300000 Gauge S3 17.02 02:45
#> 4 400000 Gauge S4 29.27 04:00
```

This code indicates the use with `get_lag_dir()`

where the
directory is specified:

```
<- system.file("testdata", "Q.csv", package = "hydroroute")
Q_file <- file.path(tempdir(), "testdata")
relations_path dir.create(relations_path)
file.copy(list.files(system.file("testdata", package = "hydroroute"),
full.name = TRUE),
recursive = FALSE, copy.mode = TRUE)
relations_path, #> [1] FALSE FALSE TRUE TRUE TRUE TRUE TRUE
get_lag_dir(Q_file, relations_path, inputsep = ",",
(inputdec = ".", format = "%Y-%m-%d %H:%M", overwrite = TRUE))
#> [[1]]
#> ID Type Station fkm LAG
#> 1 100000 Gauge S1 0.01 00:00
#> 2 200000 Gauge S2 9.16 01:15
#> 3 300000 Gauge S3 17.02 02:45
#> 4 400000 Gauge S4 29.27 04:00
```

`estimate_AE()`

Greimel et al. (2022) propose the following algorithm to identify AEs:

“For every event `x`

at the upstream hydrograph, the mean
translation time between the neighboring hydrographs (calculated by an
autocorrelation analysis) is subtracted from the downstream hydrograph.
This then captures several events from the downstream hydrograph within
a time slot +/- the translation time. Among those matches only those
events are retained where the relative difference in amplitude is +/-
one. In the following, a potential AE is the event `y`

detected with the smallest time difference to `x`

after
accounting for the mean translation time meeting the time and amplitude
criteria. […]

The relative difference in amplitude is then determined for these
events, and parabolas are fitted to the histograms obtained for the
relative difference data binned into intervals from -1 to 1 with a width
0.1 by fixing the vertex at the inner maximum of the histogram […]. The
width of the parabola is determined by minimizing the average squared
distances between the parabola and the histogram data along arbitrary
symmetric ranges from the inner maximum. Based on the fitted parabola,
cut points with the `x`

-axis are determined so that only
those potential AEs whose relative difference is within these cut points
are retained. If this automatic scheme does not succeed in determining
suitable cut points, e.g., because the estimated cut points are outside
the defined intervals, a strict criterion for the relative difference in
amplitude is imposed to identify AEs considering only deviations of at
most 10%.”

`estimate_AE()`

estimates suitable settings for the
amplitude based on the method developed in Greimel et al. (2022) based
on potential associated events identified using the specified time and
metric deviations allowed for a match.

It performs this procedure for two neighboring hydrographs, i.e., it
takes a subset of `relation`

and the two corresponding
`Event`

files as input. The gauging station `ID`

s
in the subset of `relation`

and in the `Event`

files must match. Suitable settings for the amplitude are estimated as
follows:

`Sy$Time`

is shifted by the optimal mean translation time between`Sx`

and`Sy`

.Based on the specified time lags, matches between

`Sx`

and`Sy`

are captured.Relative differences in

`AMP`

are computed, e.g.,`(Sy$AMP - Sx$AMP) / Sx$AMP`

, and only matches are retained where these relative differences are within the range specified.Matched events are iteratively filtered to retain those where the time lag is most similar leading to the potential AEs.

The relative differences of potential AEs are binned into intervals of length 0.1 from -1 to 1. The created relative frequency table of the binned relative differences is passed to function

`get_parabola()`

where either suitable cut points with the x-axis are determined or a strict criterion is returned.The table of the relative differences is visualized in a plot where the fitted parabola and the cut points with the x-axis are also shown.

The estimated settings for amplitude, a data frame of “real” AEs, i.e., associated events within the estimated cut points, and the plot are returned.

Note that the metric flow ratio (RATIO) does not make sense for
`S1`

if the hydrograph is not of type `Gauge`

. So
metric `RATIO`

is set to `NA`

internally in this
case.

The following code shows this procedure for two `Event`

files:

```
# file paths
<- system.file("testdata", "Events", "100000_2_2014-01-01_2014-02-28.csv",
Sx package = "hydroroute")
<- system.file("testdata", "Events", "200000_2_2014-01-01_2014-02-28.csv",
Sy package = "hydroroute")
<- system.file("testdata", "relation.csv", package = "hydroroute")
relation
# read data
<- utils::read.csv(Sx)
Sx <- utils::read.csv(Sy)
Sy <- utils::read.csv(relation)
relation <- relation[1:2, ]
relation
# estimate AE, exact time matches
<- estimate_AE(Sx, Sy, relation, timeLag = c(0, 1, 0)) results
```

```
$settings
results#> station.x station.y bound lag metric
#> 1 S1 S2 lower 0 0.9286046
#> 2 S1 S2 inner 1 1.0500000
#> 3 S1 S2 upper 0 1.1713954
```

Column `bound`

represents the lower, inner and upper
bounds that are used to subset potential AEs. `lag`

represents the time lag. Only exact matches are used in this examples,
which is specified by argument `timeLag = c(0, 1, 0)`

, which
refers to 0 deviation at the lower and upper bound and 1 at the inner
bound, meaning, that the mean translation time from
`relation`

is not altered when time matches are computed.

`$plot_threshold results`

```
head(results$real_AE)
#> id.x event_type.x time.x amp.x mafr.x mefr.x dur.x ratio.x
#> 1 100000 2 2014-01-11 17:15:00 39.01 20.4 13.00333 3 12.177650
#> 2 100000 2 2014-01-14 12:30:00 15.00 6.0 2.50000 6 1.262238
#> 3 100000 2 2014-01-15 06:15:00 77.14 38.3 12.85667 6 27.060811
#> 4 100000 2 2014-01-15 20:15:00 10.20 5.1 2.55000 4 1.312883
#> 5 100000 2 2014-01-19 06:45:00 74.41 23.7 9.30125 8 30.883534
#> 6 100000 2 2014-01-27 15:45:00 0.10 0.1 0.10000 1 1.001391
#> station.x id.y event_type.y time.y amp.y mafr.y mefr.y dur.y
#> 1 S1 200000 2 2014-01-11 18:15:00 39.06 20.3 6.510 6
#> 2 S1 200000 2 2014-01-14 13:30:00 14.40 5.3 2.400 6
#> 3 S1 200000 2 2014-01-15 07:15:00 77.49 33.2 15.498 5
#> 4 S1 200000 2 2014-01-15 21:15:00 10.20 4.0 2.040 5
#> 5 S1 200000 2 2014-01-19 07:45:00 76.36 28.9 9.545 8
#> 6 S1 200000 2 2014-01-27 16:45:00 0.10 0.1 0.100 1
#> ratio.y station.y diff_metric
#> 1 7.804878 S2 1.281723e-03
#> 2 1.231140 S2 -4.000000e-02
#> 3 14.111675 S2 4.537205e-03
#> 4 1.280992 S2 0.000000e+00
#> 5 16.457490 S2 2.620616e-02
#> 6 1.001311 S2 1.469658e-13
```

`peaktrace()`

Function `peaktrace`

combines the identification of
potential AEs and the estimation of suitable amplitude settings for a
whole river section as specified in a `relation`

file. In
addition, the flow metrics of the AEs are pictured by scatter plots and
the translation and retention process between the hydrographs is
described by linear models.

In the following, the input arguments of function
`peaktrace()`

are described:

`relation_path`

: Is the path where the whole relation file from a river section is to be read from.`events_path`

: Is the path of the directory where the`Event`

files are located. These files must correspond to the format described earlier in the section discussing the input data.`initial_values_path`

: Is the path where initial values for predicting the metric at the neighboring stations are to be read from. It should not contain missing values. But missing values can be imputed with a method specified in argument`impute_method`

, which is by default`max`

. An example for such a file is:

```
<- system.file("testdata", "initial_value_routing.csv",
initial_values_path package = "hydroroute")
<- read.csv(initial_values_path)
initials
initials#> Station Metric Value Name
#> 1 S1 AMP 93.00000 Q_max
#> 2 S1 AMP 69.75000 Q_0.75
#> 3 S1 AMP 46.50000 Q_0.5
#> 4 S1 AMP 23.25000 Q_0.25
#> 5 S1 MAFR 93.00000 Q_max
#> 6 S1 MAFR 69.75000 Q_0.75
#> 7 S1 MAFR 46.50000 Q_0.5
#> 8 S1 MAFR 23.25000 Q_0.25
#> 9 S1 MEFR 93.00000 Q_max
#> 10 S1 MEFR 69.75000 Q_0.75
#> 11 S1 MEFR 46.50000 Q_0.5
#> 12 S1 MEFR 23.25000 Q_0.25
#> 13 S1 DUR 1.00000 N
#> 14 S2 RATIO 19.90099 Max
```

The columns must be identical to this example. The content may vary. The initial values used for prediction must not contain any missing values.

`Station`

refers to the gauging station of the hydrograph. Here, all initial values correspond to gauging station`S1`

except for metric`RATIO`

, which starts at gauging station`S2`

.`Metric`

corresponds to the metric. This is used to pick the corresponding fitted predictive model.`Value`

can be chosen arbitrarily or estimated with a data-driven approach. A unique`Name`

is assigned which can be used to characterize the curve obtained from this initial value used to predict the metrics in downstream direction. E.g., for this example the initial values are set to certain quantiles of the metrics at station`S1`

.

The return value of function `peaktrace()`

is structured
as follows:

A named list with one list element for each

`event_type`

.For each

`event_type`

:One element that contains the estimated settings from

`estimate_AE()`

for all gauging stations.Plot of relative differences of

`AMP`

with cut points from settings_AE()` for all pairs of neighboring gauging stations.Real AEs according to the estimated settings from

`estimate_AE()`

for all pairs of neighboring gauging stations and a column`diff_metric`

that contains the relative difference in`AMP`

.A grid of scatter plots containing the AEs for neighboring hydrographs and for each metric with the fitted regression line.

Results of model fitting. Each row contains the corresponding stations and metric, the model type (default: “lm”), formula, coefficients, number of observations and \(R^2\).

Plot of predicted values based on the initial values.

```
<- system.file("testdata", "relation.csv", package = "hydroroute")
relation_path <- system.file("testdata", "Events", package = "hydroroute")
events_path <- system.file("testdata", "initial_value_routing.csv",
initial_values_path package = "hydroroute")
<- peaktrace(relation_path, events_path, initial_values_path) res
```

The first list object refers to event type 2 (IC event).

```
$`2`$settings
res#> station.x station.y bound lag metric
#> 1 S1 S2 lower 1 0.7388856
#> 2 S1 S2 inner 1 0.9500000
#> 3 S1 S2 upper 1 1.1611144
#> 4 S2 S3 lower 1 0.8818457
#> 5 S2 S3 inner 1 1.0500000
#> 6 S2 S3 upper 1 1.2181543
#> 7 S3 S4 lower 1 0.8267117
#> 8 S3 S4 inner 1 0.9500000
#> 9 S3 S4 upper 1 1.0732883
```

The `settings`

data frame contains the estimated time lag
and metric settings computed with `estimate_AE()`

. In this
example with 4 stations, it contains nine rows where three rows describe
the relation between two neighboring stations. Since only exact time
matches were allowed, the `lag`

values are 0 for
`lower`

and `upper`

bound and 1 for
`inner`

. `metric`

contains the range of relative
values of the amplitude allowed.

Events, where the relative difference in amplitude and the relative
difference in time are within these settings, are considered as “real”
AE and therefore events caused by disruptive factors are excluded as far
as possible.

The following plot shows the histograms obtained for the relative differences in amplitude for each pair of neighboring gauging stations binned into intervals from -1 to 1 of width 0.1. The dashed line shows the fitted parabola and the cut points of the parabola with the x-axis are indicated. Potential AEs where the relative difference is within these cut points are considered as “real” AEs.

`::grid.draw(res$`2`$plot_threshold) grid`

The “real” AEs can be inspected using:

```
head(res$`2`$real_AE)
#> id.x event_type.x time.x amp.x mafr.x mefr.x dur.x ratio.x
#> 1 100000 2 2014-01-01 01:00:00 27.07 12.2 6.767500 4 10.565371
#> 2 100000 2 2014-01-01 10:15:00 29.38 15.5 7.345000 4 11.801471
#> 3 100000 2 2014-01-01 17:30:00 30.91 16.9 7.727500 4 12.490706
#> 4 100000 2 2014-01-02 17:30:00 26.88 14.1 4.480000 6 8.636364
#> 5 100000 2 2014-01-03 05:00:00 27.34 12.9 9.113333 3 10.559441
#> 6 100000 2 2014-01-03 16:00:00 27.16 14.8 3.017778 9 10.912409
#> station.x id.y event_type.y time.y amp.y mafr.y mefr.y dur.y
#> 1 S1 200000 2 2014-01-01 02:15:00 25.83 13.11 5.166000 5
#> 2 S1 200000 2 2014-01-01 11:30:00 28.49 14.54 5.698000 5
#> 3 S1 200000 2 2014-01-01 18:45:00 29.15 14.98 7.287500 4
#> 4 S1 200000 2 2014-01-02 19:00:00 26.43 11.49 3.303750 8
#> 5 S1 200000 2 2014-01-03 06:15:00 26.69 13.70 5.338000 5
#> 6 S1 200000 2 2014-01-03 17:30:00 27.03 12.20 3.861429 7
#> ratio.y station.y diff_metric
#> 1 7.506297 S2 -0.045807167
#> 2 8.679245 S2 -0.030292716
#> 3 8.379747 S2 -0.056939502
#> 4 6.427105 S2 -0.016741071
#> 5 7.655860 S2 -0.023774689
#> 6 7.808564 S2 -0.004786451
```

The scatter plots of the metrics at the neighboring gauging stations
for the “real” AEs are contained in `plot_scatter`

. The
scatter plots are arranged in a grid where each row contains scatter
plots for a specific metric and each colums contains a different pair of
neighboring gauging stations. The x-axis is the upstream hydrograph
`Sx`

, the y-axis is the downstream hydrograph
`Sy`

. A linear regression line and the corresponding \(R^2\) value are added to each plot. By
default the aspect ratio is fixed and the axis limits are equal within
each plot.

`::grid.draw(res$`2`$plot_scatter) grid`

The fitted regression models may also be inspected:

```
$`2`$models
res#> station.x station.y metric type formula (Intercept) x n r2
#> 1 S1 S2 amp lm y ~ x -0.5542922 1.0194716 164 0.99658281
#> 2 S1 S2 dur lm y ~ x 1.6520198 0.8453943 164 0.64266715
#> 3 S1 S2 mafr lm y ~ x -0.3694711 1.0066784 164 0.91454377
#> 4 S1 S2 mefr lm y ~ x 0.4813008 0.7150873 164 0.70223571
#> 5 S2 S3 amp lm y ~ x 0.7597112 0.9782935 100 0.99765823
#> 6 S2 S3 dur lm y ~ x 0.7959971 0.7868426 100 0.70537848
#> 7 S2 S3 mafr lm y ~ x -1.0932362 1.5764049 100 0.94356887
#> 8 S2 S3 mefr lm y ~ x 0.5505522 1.0358693 100 0.76774263
#> 9 S2 S3 ratio lm y ~ x 0.5890385 0.6172956 100 0.97341252
#> 10 S3 S4 amp lm y ~ x -0.1251017 0.9485448 30 0.98810523
#> 11 S3 S4 dur lm y ~ x 3.0299519 0.4642539 30 0.09809454
#> 12 S3 S4 mafr lm y ~ x 3.0964565 0.5820430 30 0.87656463
#> 13 S3 S4 mefr lm y ~ x 2.2653366 0.7352544 30 0.56098791
#> 14 S3 S4 ratio lm y ~ x 1.2112368 0.3257644 30 0.44545302
```

The `models`

data frame contains the fitted (linear)
models for each pair of neighboring stations and each metric.

`station.x`

is the upstream hydrograph`Sx`

.`station.y`

is the downstream hydrograph`Sy`

.`metric`

is the name of the corresponding metric.`type`

is the model class, by default`lm`

.`formula`

is the expression that is used to fit the model.`(Intercept)`

,`x`

are the extracted coefficients (called with`coef`

).`n`

is the number of events used to fit the model.`r2`

is the extracted or computed \(R^2\) for each model.

Finally the fitted regression models are used to predict the values of the metrics along the longitudinal flow path given the initial values:

`::grid.arrange(grobs = res$`2`$plot_predict$grobs, nrow = 3, ncol = 2) gridExtra`

If a file with initial values is passed to `peaktrace()`

,
predictions along the longitudinal flow path are made and visualized in
a plot. Each line in the plot represents a different scenario, e.g., the
uppermost solid lines for AMP, MAFR and MEFR represent the values of
`Q_max`

in the initial file. Starting from these initial
values, predictions are made with the corresponding models, e.g., the
first value of the initial valus file is passed to the model that
describes the relationship of AMP between `S1`

and
`S2`

to predict the value at `S2`

.

The initial value and the first fitted model are:

```
1, ]
initials[#> Station Metric Value Name
#> 1 S1 AMP 93 Q_max
$`2`$models[1, ]
res#> station.x station.y metric type formula (Intercept) x n r2
#> 1 S1 S2 amp lm y ~ x -0.5542922 1.019472 164 0.9965828
```

The resulting predicted value is then passed to the next model along
the flow path, i.e., the model of `S2`

and `S3`

to
predict the value at `S3`

.

```
$`2`$models[6, ]
res#> station.x station.y metric type formula (Intercept) x n r2
#> 6 S2 S3 dur lm y ~ x 0.7959971 0.7868426 100 0.7053785
```

Finally, this predicted value is passed to the last model along this
river section: the model between `S3`

and `S4`

to
predict the value at `S4`

.

```
$`2`$models[11, ]
res#> station.x station.y metric type formula (Intercept) x n r2
#> 11 S3 S4 dur lm y ~ x 3.029952 0.4642539 30 0.09809454
```

This procedure is repeated for all metrics according to the initial
values file. Note that in this initial values file metric RATIO starts
at station `S2`

. Therefore the first value of RATIO to
predict is at station `S3`

.

The second list object refers to event type 4 (DC event). The nested objects of this event type are shown below.

```
$`4`$settings
res#> station.x station.y bound lag metric
#> 1 S1 S2 lower 1 0.8168386
#> 2 S1 S2 inner 1 0.9500000
#> 3 S1 S2 upper 1 1.0831614
#> 4 S2 S3 lower 1 0.9202873
#> 5 S2 S3 inner 1 1.0500000
#> 6 S2 S3 upper 1 1.1797127
#> 7 S3 S4 lower 1 0.5814461
#> 8 S3 S4 inner 1 0.8500000
#> 9 S3 S4 upper 1 1.1185539
```

```
head(res$`4`$real_AE)
#> id.x event_type.x time.x amp.x mafr.x mefr.x dur.x ratio.x
#> 1 100000 4 2014-01-01 02:00:00 27.07 13.40 3.867143 7 10.565371
#> 2 100000 4 2014-01-01 11:15:00 29.47 13.90 3.274444 9 12.205323
#> 3 100000 4 2014-01-01 18:30:00 31.04 16.00 3.448889 9 13.125000
#> 4 100000 4 2014-01-02 07:45:00 27.44 13.98 6.860000 4 12.154472
#> 5 100000 4 2014-01-02 20:15:00 27.37 14.20 3.421250 8 10.033003
#> 6 100000 4 2014-01-03 18:15:00 26.87 13.90 5.374000 5 9.867987
#> station.x id.y event_type.y time.y amp.y mafr.y mefr.y
#> 1 S1 200000 4 2014-01-01 03:30:00 26.09 6.5 0.8153125
#> 2 S1 200000 4 2014-01-01 12:45:00 28.09 6.5 1.7556250
#> 3 S1 200000 4 2014-01-01 19:45:00 29.50 7.1 1.2826087
#> 4 S1 200000 4 2014-01-02 08:45:00 26.37 6.2 1.6481250
#> 5 S1 200000 4 2014-01-02 21:00:00 27.26 6.5 0.8793548
#> 6 S1 200000 4 2014-01-03 19:15:00 25.84 6.4 1.9876923
#> dur.y ratio.y station.y diff_metric
#> 1 32 8.032345 S2 -0.036202438
#> 2 16 7.834550 S2 -0.046827282
#> 3 23 9.194444 S2 -0.049613402
#> 4 16 8.069705 S2 -0.038994169
#> 5 31 7.747525 S2 -0.004018999
#> 6 13 6.007752 S2 -0.038332713
```

`::grid.draw(res$`4`$plot_threshold) grid`

`::grid.draw(res$`4`$plot_scatter) grid`

```
$`4`$models
res#> station.x station.y metric type formula (Intercept) x n r2
#> 1 S1 S2 amp lm y ~ x -0.6331382 1.0230064 159 0.9976993
#> 2 S1 S2 dur lm y ~ x 3.4889475 1.1941344 159 0.5660323
#> 3 S1 S2 mafr lm y ~ x 0.3670848 0.6093259 159 0.8288550
#> 4 S1 S2 mefr lm y ~ x 0.3152232 0.5218025 159 0.6858269
#> 5 S2 S3 amp lm y ~ x 0.8889574 0.9860819 89 0.9960296
#> 6 S2 S3 dur lm y ~ x 2.5702522 0.6747927 89 0.8660458
#> 7 S2 S3 mafr lm y ~ x 0.8424465 0.8700683 89 0.9305420
#> 8 S2 S3 mefr lm y ~ x 0.9748893 0.6441977 89 0.7688562
#> 9 S2 S3 ratio lm y ~ x 0.6994949 0.5659408 89 0.9776473
#> 10 S3 S4 amp lm y ~ x -0.4977512 0.8877421 50 0.9569848
#> 11 S3 S4 dur lm y ~ x 1.6421232 0.6351157 50 0.7096118
#> 12 S3 S4 mafr lm y ~ x -0.2972899 0.8213848 50 0.5844032
#> 13 S3 S4 mefr lm y ~ x 0.2811406 1.1317973 50 0.2960442
#> 14 S3 S4 ratio lm y ~ x 0.8553193 0.3178922 50 0.7922559
```

`::grid.arrange(grobs = res$`4`$plot_predict$grobs, nrow = 3, ncol = 2) gridExtra`

If estimated settings are already available, it is possible to use
the settings directly to extract “real” AEs from the `Event`

data. For such an analysis, a path to a `relation`

file must
be provided, as well as a path to the `Event`

data and paths
to `settings`

and initial values.

The following code shows the extraction of “real” AEs based on the
`settings`

file which is included in the package after having
been generated with `estimate_AE()`

.

```
<- system.file("testdata", "relation.csv", package = "hydroroute")
relation_path <- system.file("testdata", "Events", package = "hydroroute")
events_path <- system.file("testdata", "Q_event_2_AMP-LAG_aut_settings.csv",
settings_path package = "hydroroute")
<- system.file("testdata", "initial_value_routing.csv",
initials_path package = "hydroroute")
<- extract_AE(relation_path, events_path, settings_path)
real_AE head(real_AE)
#> id.x event_type.x time.x amp.x mafr.x mefr.x dur.x ratio.x
#> 1 100000 2 2014-01-01 01:00:00 27.07 12.2 6.767500 4 10.565371
#> 2 100000 2 2014-01-01 10:15:00 29.38 15.5 7.345000 4 11.801471
#> 3 100000 2 2014-01-01 17:30:00 30.91 16.9 7.727500 4 12.490706
#> 4 100000 2 2014-01-02 17:30:00 26.88 14.1 4.480000 6 8.636364
#> 5 100000 2 2014-01-03 05:00:00 27.34 12.9 9.113333 3 10.559441
#> 6 100000 2 2014-01-03 16:00:00 27.16 14.8 3.017778 9 10.912409
#> station.x id.y event_type.y time.y amp.y mafr.y mefr.y dur.y
#> 1 S1 200000 2 2014-01-01 02:15:00 25.83 13.11 5.166000 5
#> 2 S1 200000 2 2014-01-01 11:30:00 28.49 14.54 5.698000 5
#> 3 S1 200000 2 2014-01-01 18:45:00 29.15 14.98 7.287500 4
#> 4 S1 200000 2 2014-01-02 19:00:00 26.43 11.49 3.303750 8
#> 5 S1 200000 2 2014-01-03 06:15:00 26.69 13.70 5.338000 5
#> 6 S1 200000 2 2014-01-03 17:30:00 27.03 12.20 3.861429 7
#> ratio.y station.y diff_metric
#> 1 7.506297 S2 -0.045807167
#> 2 8.679245 S2 -0.030292716
#> 3 8.379747 S2 -0.056939502
#> 4 6.427105 S2 -0.016741071
#> 5 7.655860 S2 -0.023774689
#> 6 7.808564 S2 -0.004786451
```

With the extracted “real” AEs, the routing procedure can be performed to describe the translation and retention processes between neighboring hydrographs.

Therefore, the output from `extract_AE()`

(or similar, the
output `$real_AE`

from `estimate_AE()`

), the
initial values data frame and the `relation`

data frame have
to be passed to function `routing()`

.

```
<- utils::read.csv(relation_path)
relation <- utils::read.csv(initials_path)
initials <- routing(real_AE, initials, relation) res
```

This produces the same scatter plot as before when
`peaktrace()`

was called as the events and the settings are
the same.

`::grid.draw(res$plot_scatter) grid`

```
$models
res#> station.x station.y metric type formula (Intercept) x n r2
#> 1 S1 S2 amp lm y ~ x -0.5542922 1.0194716 164 0.99658281
#> 2 S1 S2 dur lm y ~ x 1.6520198 0.8453943 164 0.64266715
#> 3 S1 S2 mafr lm y ~ x -0.3694711 1.0066784 164 0.91454377
#> 4 S1 S2 mefr lm y ~ x 0.4813008 0.7150873 164 0.70223571
#> 5 S2 S3 amp lm y ~ x 0.7597112 0.9782935 100 0.99765823
#> 6 S2 S3 dur lm y ~ x 0.7959971 0.7868426 100 0.70537848
#> 7 S2 S3 mafr lm y ~ x -1.0932362 1.5764049 100 0.94356887
#> 8 S2 S3 mefr lm y ~ x 0.5505522 1.0358693 100 0.76774263
#> 9 S2 S3 ratio lm y ~ x 0.5890385 0.6172956 100 0.97341252
#> 10 S3 S4 amp lm y ~ x -0.1251017 0.9485448 30 0.98810523
#> 11 S3 S4 dur lm y ~ x 3.0299519 0.4642539 30 0.09809454
#> 12 S3 S4 mafr lm y ~ x 3.0964565 0.5820430 30 0.87656463
#> 13 S3 S4 mefr lm y ~ x 2.2653366 0.7352544 30 0.56098791
#> 14 S3 S4 ratio lm y ~ x 1.2112368 0.3257644 30 0.44545302
```

`::grid.arrange(grobs = res$plot_predict$grobs, nrow = 3, ncol = 2) gridExtra`