estimate_AE function

Estimate Associated Events

For two neighboring stations, potential associated events (AEs) are determined according to the time lag and metric (amplitude) difference allowed. For all potential AEs, parabolas are fitted to the histogram obtained for the relative difference in amplitude binned into intervals from -1 to 1 of width 0.1 by fixing the vertex at the inner maximum of the histogram and the width 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 such that only those potential AEs are retained where the relative difference is within these cut points. If this automatic scheme does not succeed to determine suitable cut points, e.g., because the estimated cut points are outside -1 and 1, then a strict criterion for the relative difference in amplitude is imposed to identify AEs considering only deviations of at most 10%.

estimate_AE(
  Sx,
  Sy,
  relation,
  timeLag = c(1, 1, 1),
  metricLag = c(1, 1),
  unique = c("time", "metric"),
  TimeFormat = "%Y-%m-%d %H:%M",
  tz = "Etc/GMT-1",
  settings = NULL
)

Arguments

• Sx: Data frame that consists of flow fluctuation events and computed metrics (see hydropeak::get_events()) of an upstream hydrograph $S_x$.

• Sy: Data frame that consists of flow fluctuation events and computed metrics (see hydropeak::get_events()) of a downstream hydrograph $S_y$.

• relation: Data frame that contains the relation between upstream and downstream hydrograph. Must only contain two rows (one for each hydrograph) in order of their location in downstream direction. See the appended example data relation.csv or the vignette for details on the structure. See get_lag() for further information about the relation and the lag between the hydrographs.

• timeLag: Numeric vector specifying factors to alter the interval to capture events from the downstream hydrograph. By default it is timeLag = c(1, 1, 1), this refers to matches within a time slot $\pm$ the mean translation time from relation. For exact time matches, timeLag = c(0, 1, 0) must be specified.

• metricLag: Numeric vector specifying factors to alter the interval of relative metric deviations to capture events from the downstream hydrograph. By default. it is metricLag = c(1, 1), such that events are filtered where the amplitude at $S_y$ is at least 0, i.e., amplitude at c("$S_{x} -\n$", "$1 \\cdot$") amplitude at $S_x$, and at most two times the amplitude at $S_x$, i.e., $S_{x} + 1 \cdot$

  amplitude at $S_x$. For exact matches, metricLag = c(0, 0) must be specified.

• unique: Character string specifying if the potential AEs which meet the timeLag and metricLag condition should be filtered to contain only unique events using "time", i.e., by selecting those where the time difference is smallest compared to the specified factor of the mean translation time, or using "metric", i.e., by selecting those where the relative difference in amplitude is smallest (default: "time").

• TimeFormat: Character string giving the date-time format of the date-time column in the input data frame (default: "%Y-%m-%d %H:%M").

• tz: Character string specifying the time zone to be used for the conversion (default: "Etc/GMT-1").

• settings: Data.frame with 3 rows and columns station.x, station.y, bound, lag, metric. lag needs to correspond to the unique value specified in argument timeLag and bound

  needs to contain "lower", "inner", "upper".

Returns

A nested list containing the estimated settings, the histogram obtained for the relative difference data with estimated cut points, and the obtained real AEs.

Examples

# file paths
Sx <- system.file("testdata", "Events", "100000_2_2014-01-01_2014-02-28.csv",
                  package = "hydroroute")
Sy <- system.file("testdata", "Events", "200000_2_2014-01-01_2014-02-28.csv",
                  package = "hydroroute")
relation <- system.file("testdata", "relation.csv", package = "hydroroute")

# read data
Sx <- utils::read.csv(Sx)
Sy <- utils::read.csv(Sy)
relation <- utils::read.csv(relation)
relation <- relation[1:2, ]

# estimate AE, exact time matches
results <- estimate_AE(Sx, Sy, relation, timeLag = c(0, 1, 0))
results$settings
results$plot_threshold
results$real_AE