Introduction to hydroroute

In hydroroute: Trace Longitudinal Hydropeaking Waves

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.align = 'center'
)
old <- options(useFancyQuotes = FALSE)
library("hydroroute")

Introduction

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.

Input data

Several data files are required to perform the analysis.

Dataset 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:

1. ID Character string which refers to the identifier of the gauging station (in Austria: HZBCODE).
2. Time Character string with date-time information of measurements.
3. 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:

Q_path <- system.file("testdata", "Q.csv", package = "hydroroute")
Q <- read.csv(Q_path)
head(Q)

The sample dataset Q is a data frame with r nrow(Q) rows and r ncol(Q) variables as described above. The station ID's along the flow path are r paste(sort(unique(Q$ID)), collapse = ", "). The time ranges from r dQuote(min(Q$Time)) to r dQuote(max(Q$Time)).

Dataset relation

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

1. ID Character string which refers to the identifier of the gauging station (in Austria: HZBCODE).
2. Type Character string which characterizes the source hydrograph (Turbine flow, Gauge, Basin outflow).
3. Station Character string which indicates the order of the n hydrographs in relation in downstream direction (Si with i = 1, ..., n).
4. fkm Numeric, position of hydrograph in km relative to the source.
5. 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:

relation_path <- system.file("testdata", "relation.csv", package = "hydroroute")
relation <- read.csv(relation_path)
relation

The dataset relation contains r nrow(relation) adjacent gauging stations.

Event files

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:

Sx <- system.file("testdata", "Events", "100000_2_2014-01-01_2014-02-28.csv",
                  package = "hydroroute")
Sx <- read.csv(Sx)
head(Sx)

Get mean translation time between hydrographs with 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 IDs 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:

Q_file <- system.file("testdata", "Q.csv", package = "hydroroute")
relation <- system.file("testdata", "relation.csv", package = "hydroroute")
(get_lag_file(Q_file, relation, inputsep = ",", format = "%Y-%m-%d %H:%M",
              save = FALSE, overwrite = TRUE))

This code indicates the use with get_lag_dir() where the directory is specified:

Q_file <- system.file("testdata", "Q.csv", package = "hydroroute")
relations_path <- file.path(tempdir(), "testdata")
dir.create(relations_path)
file.copy(list.files(system.file("testdata", package = "hydroroute"),
                     full.name = TRUE),
          relations_path, recursive = FALSE, copy.mode = TRUE)
(get_lag_dir(Q_file, relations_path, inputsep = ",",
             inputdec = ".", format = "%Y-%m-%d %H:%M", overwrite = TRUE))

Estimate settings with 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 IDs 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
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

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.

results$plot_threshold

head(results$real_AE)

Combine everything with 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:

initial_values_path <- system.file("testdata", "initial_value_routing.csv",
                                   package = "hydroroute")
initials <- read.csv(initial_values_path)
initials

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.

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

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

res$`2`$settings

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

The "real" AEs can be inspected using:

head(res$`2`$real_AE)

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

The fitted regression models may also be inspected:

res$`2`$models

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:

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

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:

initials[1, ]
res$`2`$models[1, ]

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.

res$`2`$models[6, ]

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.

res$`2`$models[11, ]

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.

res$`4`$settings

head(res$`4`$real_AE)

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

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

res$`4`$models

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

Extract AEs and perform routing with existing settings

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.

Extract AEs

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().

relation_path <- system.file("testdata", "relation.csv", package = "hydroroute")
events_path <- system.file("testdata", "Events", package = "hydroroute")
settings_path <- system.file("testdata", "Q_event_2_AMP-LAG_aut_settings.csv",
                             package = "hydroroute")
initials_path <- system.file("testdata", "initial_value_routing.csv",
                             package = "hydroroute")
real_AE <- extract_AE(relation_path, events_path, settings_path)
head(real_AE)

Routing

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().

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

This produces the same scatter plot as before when peaktrace() was called as the events and the settings are the same.

grid::grid.draw(res$plot_scatter)

res$models

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

Use peaktrace() with existing settings

It the automatically determined settings using peaktrace() are not suitable, the settings files can be edited to insert manual settings. In the following we use a path to a settings file for event type 2 where between S2 and S3 the settings were modified to 0.75, 1 and 1.5 and no settings are provided for subsequent pairs of stations. Function peaktrace() is called again providing also the path to this settings file and the resulting settings for event type 2 are inspected:

settings_path <- system.file("testdata", package = "hydroroute")
res <- peaktrace(relation_path, events_path, initial_values_path,
                 settings_path)
res$`2`$settings

The procedure is then applied without determining the settings in an automatic way, but using those specified. The settings files can also only provide settings for some relations between neighboring stations which are then used, while for those relations between neighboring stations where no settings are provided, these are again determined using the automatic procedure.

options(old)

References

Greimel F, Zeiringer B, Höller N, Grün B, Godina R, Schmutz S (2016). "A Method to Detect and Characterize Sub-Daily Flow Fluctuations." Hydrological Processes, 30(13), 2063-2078. doi: 10.1002/hyp.10773

Greimel F, Grün B, Hayes DS, Höller N, Haider J, Zeiringer B, Holzapfel P, Hauer C, Schmutz S (2022). "PeakTrace: Routing of Hydropower Plant-Specific Hydropeaking Waves Using Multiple Hydrographs - A Novel Approach." River Research and Applications, 1-14. doi: 10.1002/rra.3978

hydroroute documentation built on Feb. 16, 2023, 10:29 p.m.