Type:	Package
Title:	Stochastic Collision Risk Model
Version:	1.1.2
Description:	Collision Risk Models for avian fauna (seabird and migratory birds) at offshore wind farms. The base deterministic model is derived from Band (2012) https://tethys.pnnl.gov/publications/using-collision-risk-model-assess-bird-collision-risks-offshore-wind-farms. This was further expanded on by Masden (2015) <doi:10.7489/1659-1> and code used here is heavily derived from this work with input from Dr A. Cook at the British Trust for Ornithology. These collision risk models are useful for marine ornithologists who are working in the offshore wind industry, particularly in UK waters. However, many of the species included in the stochastic collision risk models can also be found in the North Atlantic in the United States and Canada, and could be applied there.
License:	GPL (≥ 3)
Depends:	R (≥ 4.0)
Imports:	cli, dplyr, glue, logr, magrittr, msm, pracma, purrr, rlang, stats, tibble, tidyr
Suggests:	rmarkdown, knitr, spelling, testthat (≥ 3.0.0), covr
Config/testthat/edition:	3
Encoding:	UTF-8
Language:	en-GB
LazyData:	true
LazyDataCompression:	bzip2
URL:	https://github.com/HiDef-Aerial-Surveying/stochLAB, https://hidef-aerial-surveying.github.io/stochLAB/
BugReports:	https://github.com/HiDef-Aerial-Surveying/stochLAB/issues
RoxygenNote:	7.2.2
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2022-12-21 19:18:54 UTC; humph
Author:	Grant Humphries [aut, cre], Bruno Caneco [aut], Aonghais Cook [aut], Elizabeth Masden [aut], Marine Scotland [fnd, cph], HiDef [cph], DMPstats [cph], Kelly Street [rev] (GITHUB: @kstreet13)
Maintainer:	Grant Humphries <grwhumphries@blackbawks.net>
Repository:	CRAN
Date/Publication:	2022-12-22 08:50:07 UTC

Pipe operator

Description

See ⁠magrittr::[\%>\%][magrittr::pipe]⁠ for details.

Usage

lhs %>% rhs

Arguments

Value

The result of calling rhs(lhs).

Total day and night hours per month

Description

Taken from Forsythe et al.(1995) A model comparison for daylength as a function of latitude and day of year. Ecological Modelling. 80: 87 - 95

Usage

Day_Length(wf_latitude)

Arguments

Value

data frame with total number of daylight hours and night hours in each month at the specified latitude.

Examples

    x <- Day_Length(54.6)

Summarized flight height profiles from Johnston et al (2014)

Description

A dataframe containing flight height profiles for all species in Johnston et al. (2014). Values are expressed as the proportion of birds in 1 metre height intervals.

Usage

Johnston_Flight_heights_SOSS

Format

A data frame object with 3 columns containing the maximum likelihood, the median, and Upper/Lower confidence limits of flight height distributions. Flight height bands go from 1 - 300m ASL.

height

Height above sea level, in metres. First element represents the 0-1 meters height band, and height interval is 1 metre.

variable

The species name and variable from Johnston et al 2014 estimates. E.G., ArcticSkua.est is the maximum likelihood estimate from those models. .est = maximum likelihood, .lcl and .ucl are the lower and upper 95% CLs, and .med is the median estimate.

prop

The proportion of birds within the 1m flight height bands.

Source

https://www.bto.org/our-science/wetland-and-marine/soss/projects

Collision risk model, for a single species and one turbine scenario

Description

Core function of the Collision Risk Model (CRM). Calculates the expected number of in-flight collisions per month of a seabird species on a given offshore windfarm, for a choice of model options.

Calculations are equivalent to those performed on the original CRM spreadsheet, as per Band (2012), providing backward compatibility with the original outputs.

Usage

band_crm(
  model_options = c("1", "2", "3", "4"),
  flight_speed,
  body_lt,
  wing_span,
  flight_type,
  avoid_rt_basic = NULL,
  avoid_rt_ext = NULL,
  noct_activity,
  prop_crh_surv = NULL,
  dens_month,
  prop_upwind,
  site_fhd = NULL,
  gen_fhd = NULL,
  rotor_speed,
  rotor_radius,
  blade_width,
  blade_pitch,
  n_blades,
  hub_height,
  chord_prof = chord_prof_5MW,
  n_turbines,
  turb_oper_month,
  wf_width,
  wf_latitude,
  tidal_offset,
  lrg_arr_corr = TRUE,
  xinc = 0.05,
  yinc = 0.05,
  ...
)

Arguments

Details

Collision risk can be calculated under 4 options, specified by model_options:

• Option 1 - Basic model with proportion at collision risk height derived from site survey (prop_crh_surv).

• Option 2 - Basic model with proportion at collision risk height derived from a generic flight height distribution (gen_fhd).

• Option 3 - Extended model using a generic flight height distribution (gen_fhd).

• Option 4 - Extended model using a site-specific flight height distribution (site_fhd).

Where,

• Basic model - assumes a uniform distribution of bird flights at collision risk height (i.e. above the minimum and below the maximum height of the rotor blade).

• Extended model - takes into account the distribution of bird flight heights at collision risk height.

Value

Returns the expected number of bird collisions per month, for each of the chosen CRM Options. Returned months are those shared between dens_month and turb_oper_month. Output format is specific to how the function is called:

• data frame object, if called as a stand-alone function.

• list object, if called inside stoch_crm().

Validation and pre-processing of inputs

band_crm() requirements and behaviour are dependent on how it is called:

As a stand-alone function

• All arguments are expected to be specified as describe above

• Input validation and pre-processing are carried out.

Inside stoch_crm()

• Assumes inputs have already been pre-processed and validated, and thence it skips those steps.

• Additional arguments rotor_grids and wf_daynight_hrs_month need to be passed to the function. Under the stochastic context, these quantities can be calculated ahead of the simulation loop to maximize performance.

• Furthermore, gen_fhd, site_fhd, dens_month and turb_oper_month can be provided as numeric vectors

Code revision and optimization

Core code performing Band calculations in Masden (2015) implementation was substantially re-factored, re-structured and streamlined to conform with conventional R packages requirements.

Furthermore, previous code underpinning key calculations for the extended model was replaced by an alternative approach, resulting in significant gains in computational speed over Masden's approach. This optimization is particularly beneficial under a stochastic context, when Band calculations are called repeatedly, potentially thousands of times. See generate_rotor_grids() for further details.

Examples

# ------------------------------------------------------
# Run with arbitrary parameter values, for illustration
# ------------------------------------------------------

# Setting a dataframe of parameters to draw from
params <- data.frame(
  flight_speed = 13.1,         # Flight speed in m/s
  body_lt = 0.85,              # Body length in m
  wing_span = 1.01,            # Wing span in m
  flight_type = "flapping",    # flapping or gliding flight
  avoid_rt_basic = 0.989,      # avoidance rate for option 1 and 2
  avoid_rt_ext = 0.981,        # extended avoidance rate for option 3 and 4
  noct_activity = 0.5,         # proportion of day birds are inactive
  prop_crh_surv = 0.13,        # proportion of birds at collision risk height (option 1 only)
  prop_upwind = 0.5,           # proportion of flights that are upwind
  rotor_speed = 15,            # rotor speed in m/s
  rotor_radius = 120,          # radius of turbine in m
  blade_width = 5,             # width of turbine blades at thickest point in m
  blade_pitch = 15,            # mean radius pitch in Radians
  n_blades = 3,                # total number of blades per turbine
  hub_height = 150,            # height of hub in m above HAT
  n_turbines = 100,            # number of turbines in the wind farm
  wf_width = 52,               # width across longest section of wind farm
  wf_latitude = 56,            # latitude of centroid of wind farm
  tidal_offset = 2.5,          # mean tidal offset from HAT of the wind farm
  lrg_arr_corr = TRUE          # apply a large array correction?
)

# Monthly bird densities
b_dens <- data.frame(
  month = month.abb,
  dens = runif(12, 0.8, 1.5)
)

# flight height distribution from Johnston et al
gen_fhd_dat <- Johnston_Flight_heights_SOSS %>%
  dplyr::filter(variable=="Gannet.est") %>%
  dplyr::select(height,prop)


# monthly operational time of the wind farm
turb_oper <- data.frame(
  month = month.abb,
  prop_oper = runif(12,0.5,0.8)
)


band_crm(
  model_options = c(1,2,3),
  flight_speed = params$flight_speed,
  body_lt = params$body_lt,
  wing_span = params$wing_span,
  flight_type = params$flight_type,
  avoid_rt_basic = params$avoid_rt_basic,
  avoid_rt_ext = params$avoid_rt_ext,
  noct_activity = params$noct_activity,
  prop_crh_surv = params$prop_crh_surv,
  dens_month = b_dens,
  prop_upwind = params$prop_upwind,
  gen_fhd = gen_fhd_dat,
  site_fhd = NULL,  # Option 4 only
  rotor_speed = params$rotor_speed,
  rotor_radius = params$rotor_radius,
  blade_width = params$blade_width,
  blade_pitch = params$blade_pitch,
  n_blades = params$n_blades,
  hub_height = params$hub_height,
  chord_prof = chord_prof_5MW,
  n_turbines = params$n_turbines,
  turb_oper_month = turb_oper,
  wf_width = params$wf_width,
  wf_latitude = params$wf_latitude,
  tidal_offset = params$tidal_offset,
  lrg_arr_corr = params$lrg_arr_corr
  )

Parameter values and outputs from Band's Collision Risk spreadsheet ("Final_Report_SOSS02_BandSpreadSheetWorkedExampl1.xlsm")

Description

A list object comprising parameter values and outputs from Band's worked example for testing the consistency of package functions with the original model and its implementation.

Usage

band_spreadsheet_dt

Format

A list object containing:

flight_speed

Bird flight speed, in m/s

rotor_radius

rotor radius, in meters

...

Parameter values and outputs from Band's Collision Risk spreadsheet, example nr. 2

Description

A list object comprising parameter values and outputs from Band's worked example for testing the consistency of package functions with the original model and its implementation.

Usage

band_spreadsheet_dt_2

Format

A list object containing:

flight_speed

Bird flight speed, in m/s

rotor_radius

rotor radius, in meters

...

Example of bird parameters stored in wide format

Description

A data frame of (fake) data on biological parameters of three seabird species.

Usage

bird_pars_wide_example

Format

A 3 x 16 data frame, with the biological parameters (columns) for each of the 3 species (rows). Columns include:

Species

Species name

AvoidanceBasic

Mean of basic avoidance rate

AvoidanceBasicSD

SD of basic avoidance rate

AvoidanceExtended

Mean of extended avoidance rate

AvoidanceExtendedSD

SD of extended avoidance rate

Body_Length

Mean body length

Body_LengthSD

SD of body length

...

Details

Intended to illustrate the application of stoch_scrm() to a multiple scenario setting, where parameter data is available from tables in wide format.

Rotor blade chord profile

Description

A data.frame giving the blade's chord width profile, i.e. the chord width along the length of the blade, provided as a proportion of its maximum width.

Usage

chord_prof_5MW

Format

A dataframe

pp_radius

radius at bird passage point, as a proportion of rotor radius (R)

chord

chord width at pp_radius, as a proportion of the maximum chord width

...

Details

This is a generic profile for a typical modern 5MW turbine used for offshore generation. Due to commercial sensitivities by blade manufacturers, some of this detailed information may not be readily available for each make/model of blade and hence generic information may have to be used.

Note

"chord_prof_5MW" is numerically identical to "coverC". "coverC" should become deprecated in future versions of the code

Number of collisions under model option 1

Description

Wrapper function to run CRM calculations under option 1:

• Basic model, i.e. flights across collision risk height are uniformly distributed.

• Proportion at collision risk height derived from site survey.

Usage

crm_opt1(
  flux_factor,
  prop_crh_surv,
  avg_prob_coll,
  mth_prop_oper,
  avoidance_rate,
  lac_factor
)

Arguments

Value

A numeric vector, the expected number of collisions per month based on model option 1

See Also

get_flux_factor() for calculating the flux factor

Examples

 flux_fct <- get_flux_factor(
      n_turbines = 100,
      rotor_radius = 120,
      flight_speed = 13.1,
      bird_dens = c(1.19,0.85,1.05,1.45,1.41,1.45,1.12,1.45,0.93,0.902,1.06,1.23),
      daynight_hrs = Day_Length(52),
      noct_activity = 0.5
      )

turb_oper <- data.frame(
   month = month.abb,
   prop_oper = runif(12,0.5,0.8)
   )
turb_oper_month <- turb_oper$prop_oper

crm_opt1(
 flux_factor = flux_fct,
 prop_crh_surv = 0.13,
 avg_prob_coll = 0.1494609,
 mth_prop_oper = turb_oper_month,
 avoidance_rate = 0.989,
 lac_factor = 0.9998287)

Number of collisions under model option 2

Description

Wrapper function to run CRM calculations under option 2, i.e.:

• Basic model, i.e. flights across collision risk height are uniformly distributed

• Proportion at collision risk height derived from a flight height distribution (Q'_2R)

Usage

crm_opt2(
  d_y,
  flux_factor,
  avg_prob_coll,
  mth_prop_oper,
  avoidance_rate,
  lac_factor
)

Arguments

Value

A numeric vector, the expected number of collisions per month based on model Option 2.

See Also

get_fhd_rotor(), get_flux_factor()

Examples

avg_collision_risk <-
 get_avg_prob_collision(
   flight_speed = 13.1,
   body_lt = 0.85,
   wing_span = 1.01,
   prop_upwind = 0.5,
   flap_glide = 1,
   rotor_speed = 15,
   rotor_radius = 120,
   blade_width = 5,
   blade_pitch = 15,
   n_blades = 3,
   chord_prof = chord_prof_5MW
 )


 gen_fhd_dat <- Johnston_Flight_heights_SOSS %>%
      dplyr::filter(variable=="Gannet.est") %>%
      dplyr::select(height,prop)

 gen_fhd <- gen_fhd_dat$prop

 gen_fhd_at_rotor <-
    get_fhd_rotor(
      hub_height = 150,
      fhd = gen_fhd,
      rotor_radius = 120,
      tidal_offset = 2.5,
      yinc = 0.05)


 flux_fct <- get_flux_factor(
      n_turbines = 100,
      rotor_radius = 120,
      flight_speed = 13.1,
      bird_dens = c(1.19,0.85,1.05,1.45,1.41,1.45,1.12,1.45,0.93,0.902,1.06,1.23),
      daynight_hrs = Day_Length(52),
      noct_activity = 0.5
      )

turb_oper <- data.frame(
   month = month.abb,
   prop_oper = runif(12,0.5,0.8)
   )
turb_oper_month <- turb_oper$prop_oper

crm_opt2(
    flux_factor = flux_fct,
    d_y = gen_fhd_at_rotor,
    avg_prob_coll = avg_collision_risk,
    mth_prop_oper = turb_oper_month,
    avoidance_rate = 0.989,
   lac_factor = 0.9998299)

Number of collisions under model Option 3

Description

Wrapper function to run CRM calculations under option 3, i.e.:

• Using the extended model, which takes into account the distribution of bird flight heights at risk height (above the minimum and below the maximum height of the rotor blade)

• Using generic flight height distribution data

Usage

crm_opt3(
  rotor_grids,
  d_y_gen,
  rotor_radius,
  blade_width,
  rotor_speed,
  blade_pitch,
  flight_type,
  wing_span,
  flight_speed,
  body_lt,
  n_blades,
  prop_upwind,
  avoidance_rate,
  flux_factor,
  mth_prop_oper,
  lac_factor
)

Arguments

Value

A numeric vector, the expected number of collisions per month based on model option 3

Examples

 rotor_grids <- generate_rotor_grids(yinc = 0.05, xinc = 0.05, chord_prof_5MW)

 gen_fhd_dat <- Johnston_Flight_heights_SOSS %>%
      dplyr::filter(variable=="Gannet.est") %>%
      dplyr::select(height,prop)

 gen_fhd <- gen_fhd_dat$prop

 gen_fhd_at_rotor <-
    get_fhd_rotor(
      hub_height = 150,
      fhd = gen_fhd,
      rotor_radius = 120,
      tidal_offset = 2.5,
      yinc = 0.05)


 flux_fct <- get_flux_factor(
      n_turbines = 100,
      rotor_radius = 120,
      flight_speed = 13.1,
      bird_dens = c(1.19,0.85,1.05,1.45,1.41,1.45,1.12,1.45,0.93,0.902,1.06,1.23),
      daynight_hrs = Day_Length(52),
      noct_activity = 0.5
      )

turb_oper <- data.frame(
   month = month.abb,
   prop_oper = runif(12,0.5,0.8)
   )
turb_oper_month <- turb_oper$prop_oper

crm_opt3(
  rotor_grids = rotor_grids,
  d_y_gen = gen_fhd_at_rotor,
  rotor_radius = 120,
  blade_width = 5,
  rotor_speed = 15,
  blade_pitch = 15,
  flight_type = "flapping",
  wing_span = 1.01,
  flight_speed = 13.1,
  body_lt = 0.85,
  n_blades = 3,
  prop_upwind = 0.5,
  avoidance_rate = 0.981,
  flux_factor = flux_fct,
  mth_prop_oper = turb_oper_month,
  lac_factor = 0.9998299
  )

Number of collisions under model Option 4

Description

Wrapper function to run the CRM calculations under option 4, i.e.:

• Using the extended model, which takes into account the distribution of bird flight heights at risk height (above the minimum and below the maximum height of the rotor blade)

• Using site-specific flight height distribution of the species obtained from site survey data

Usage

crm_opt4(
  rotor_grids,
  d_y_surv,
  rotor_radius,
  blade_width,
  rotor_speed,
  blade_pitch,
  flight_type,
  wing_span,
  flight_speed,
  body_lt,
  n_blades,
  prop_upwind,
  avoidance_rate,
  flux_factor,
  mth_prop_oper,
  lac_factor
)

Arguments

Value

A numeric vector, the expected number of collisions per month based on model option 4

Examples

 rotor_grids <- generate_rotor_grids(yinc = 0.05, xinc = 0.05, chord_prof_5MW)

 site_fhd_dat <- Johnston_Flight_heights_SOSS %>%
      dplyr::filter(variable=="Gannet.est") %>%
      dplyr::select(height,prop)

 site_fhd <- site_fhd_dat$prop

 surv_fhd_at_rotor <-
    get_fhd_rotor(
      hub_height = 150,
      fhd = site_fhd,
      rotor_radius = 120,
      tidal_offset = 2.5,
      yinc = 0.05)


 flux_fct <- get_flux_factor(
      n_turbines = 100,
      rotor_radius = 120,
      flight_speed = 13.1,
      bird_dens = c(1.19,0.85,1.05,1.45,1.41,1.45,1.12,1.45,0.93,0.902,1.06,1.23),
      daynight_hrs = Day_Length(52),
      noct_activity = 0.5
      )

turb_oper <- data.frame(
   month = month.abb,
   prop_oper = runif(12,0.5,0.8)
   )
turb_oper_month <- turb_oper$prop_oper

crm_opt4(
  rotor_grids = rotor_grids,
  d_y_surv = surv_fhd_at_rotor,
  rotor_radius = 120,
  blade_width = 5,
  rotor_speed = 15,
  blade_pitch = 15,
  flight_type = "flapping",
  wing_span = 1.01,
  flight_speed = 13.1,
  body_lt = 0.85,
  n_blades = 3,
  prop_upwind = 0.5,
  avoidance_rate = 0.981,
  flux_factor = flux_fct,
  mth_prop_oper = turb_oper_month,
  lac_factor = 0.9998299
  )

Example of Truncated Normal parameters for monthly estimates of bird density

Description

A data frame of (fake) monthly bird density parameters for three seabird species.

Usage

dens_tnorm_wide_example

Format

A 3 x 25 data frame, with the monthly density parameters (columns) for each of the 3 species (rows). Columns include:

Species

Species name

Jan

January mean density

JanSD

SD of density in January

Feb

February mean density

FebSD

SD of density in February

...

Details

Intended to illustrate the application of stoch_scrm() to a multiple scenario setting, where parameter data is available from tables in wide format.

Format any month name to three letter code

Description

Format any month name to three letter code

Usage

format_months(months)

Arguments

Value

a character string. The three letter name of the month

Examples

  format_months("January")

Geometric attributes at equidistant points within the rotor's unit circle

Description

Generates a list of grids containing geometric attributes of the rotor disk at equidistant locations, taking the center of the rotor as the reference point and overlaying the left-half of the rotor disk. The size of grid cells are determined by xinc and yinc, and their values map properties of the rotor at the cell's location.

Usage

generate_rotor_grids(yinc = 0.05, xinc = 0.05, chord_prof)

Arguments

Details

These grids are required for an alternative approach to the calculation of probability of collision under the extended model (i.e. non-uniform flight distribution at risk height).

Functions xrisksum2, pcollxy and pcoll used in Masden & Cook implementation (PCollFunctions.r script) were based on Visual Basic computations available in the original Band worksheet. This Visual Basic code was devised under a deterministic context, i.e. for one single set of collision calculations for one given species and turbine scenario. However, in a stochastic context, where potentially thousands of collision calculations are performed per species and turbine scenario, it became clear that xrisksum2 and associated functions were highly inefficient for the task at hand.

The alternative approach streamlines computations by calculating (relative) rotor geometric attributes outside the stochastic sampling loop, which remain constant over iterations. These elements, calculated via generate_rotor_grids, are then applied to sampled parameters via vectorized operations. The number of calculations per iteration are thence substantially reduced, leading to significant gains in computational speed over Masden's implementation for a 1000 iterations run.

Value

A list with the following elements, taking the center of the rotor as the origin in the rotor's plane:

• x_grid, a 2D array of horizontal distances from the rotor's horizontal axis, as proportion of rotor radius, at each grid point

• y_grid, a 2D array of vertical distances from the rotor's vertical axis, as proportion of rotor radius, at each grid point

• r_grid, a 2D array of radial distances from rotor center, as proportion of rotor radius, at each grid point

• phi_grid, a 2D array of angles, relative to vertical, at each grid point

• chord_grid, a 2D array of blade chord width at each grid point

All elements are representative of the left-half of the rotor circle

See Also

get_x_grid(), get_y_grid(), get_phi_grid()

Examples

rotor_grids <- generate_rotor_grids(yinc = 0.05, xinc = 0.05, chord_prof_5MW)

Bootstrap samples of generic FHDs of 25 seabird species

Description

A list object comprising bootstrap samples of the generic flight height distribution (FHD) of 25 seabird species. FHD is expressed as the proportion of bird flights at 1 metre height intervals.

Usage

generic_fhd_bootstraps

Format

A list object with 25 elements, one for each species, containing a data frame with 500 bootstrap samples of the distribution of bird flights with height. Each nested data frame contains:

height

Height above sea level, in metres. First element represents the 0-1 meters height band, and height interval is 1 metre.

bootId_1

First bootstrap sample of the proportion of birds flights within each height interval

...

bootId_200

200th bootstrap sample of the proportion of birds flights within each height interval

Source

https://besjournals.onlinelibrary.wiley.com/doi/full/10.1111/1365-2664.12191

Average single transit collision risk with no avoidance

Description

Calculate the average probability of collision for a single bird transit at any point across the rotor, assuming no avoidance action. Required for the Basic model calculations, where flights at collision risk height are assumed to be uniformly distributed.

Usage

get_avg_prob_collision(
  flight_speed,
  body_lt,
  wing_span,
  prop_upwind = 0.5,
  flap_glide,
  rotor_speed,
  rotor_radius,
  blade_width,
  blade_pitch,
  n_blades,
  chord_prof = chord_prof_5MW
)

Arguments

Details

Methodology and assumptions underpinning get_avg_prob_collision are described in "Stage C" of Band (2012).

Value

A numeric value. The average collision probability (risk) for a bird flying through any point of the rotor circle area.

Examples

       get_avg_prob_collision(
           flight_speed = 13.1,
           body_lt = 0.85,
           wing_span = 1.01,
           prop_upwind = 0.5,
           flap_glide = 1,
           rotor_speed = 15,
           rotor_radius = 120,
           blade_width = 5,
           blade_pitch = 15,
           n_blades = 3,
           chord_prof = chord_prof_5MW
           )

Get expected collisions based on the basic model

Description

Provides the number of collisions expected to occur by month. The basic model assumes a uniform distribution of bird flights at risk height (i.e. between min and max rotor height).

Usage

get_collisions_basic(
  n_transits,
  avg_prob_coll,
  mth_prop_oper,
  avoidance_rate,
  lac_factor = 1
)

Arguments

Value

A numeric vector. The expected number of collisions at each time periods

Examples

turb_oper <- data.frame(
 month = month.abb,
 prop_oper = runif(12,0.5,0.8)
 )
 mth_oper_month <- turb_oper$prop_oper

 flux_factor <- get_flux_factor(
   n_turbines = 100,
   rotor_radius = 120,
   flight_speed = 13.1,
   bird_dens = c(1.19,0.85,1.05,1.45,1.41,1.45,1.12,1.45,0.93,0.902,1.06,1.23),
   daynight_hrs = Day_Length(52),
   noct_activity = 0.5
 )

 prop_crh_surv <- 0.13

 n_transits_opt1 <- flux_factor * prop_crh_surv

 get_collisions_basic(
   n_transits = n_transits_opt1,
   avg_prob_coll = 0.1494609,
   mth_prop_oper = mth_oper_month,
   avoidance_rate = 0.989,
   lac_factor = 0.9998287
 )

Number of collisions based on the extended model

Description

Calculates the expected number of collisions under the extended model, i.e. taking into account the distribution of bird flight heights at risk height (above the minimum and below the maximum height of the rotor blade)

Usage

get_collisions_extended(
  rotor_grids,
  d_y,
  rotor_radius,
  blade_width,
  rotor_speed,
  blade_pitch,
  flight_type,
  wing_span,
  flight_speed,
  body_lt,
  n_blades,
  prop_upwind,
  avoidance_rate,
  flux_factor,
  mth_prop_oper,
  lac_factor
)

Arguments

Value

Numeric vector with the expected number of collisions per month based on the extended model

Note

The original Masden code for extendend model (Option 3) included the calculation of the "Flux Integral" and "Average collision risk for single rotor transit". These quantities are not required for the calculation of collisions under the extended model, nor are used anywhere else in the package. Therefore, those calculations were dropped from the current implementation to keep computations to a minimum required.

See Also

generate_rotor_grids()

Examples

 rotor_grids <- generate_rotor_grids(yinc = 0.05, xinc = 0.05, chord_prof_5MW)

 gen_fhd_dat <- Johnston_Flight_heights_SOSS %>%
      dplyr::filter(variable=="Gannet.est") %>%
      dplyr::select(height,prop)

 gen_fhd <- gen_fhd_dat$prop

 gen_fhd_at_rotor <-
    get_fhd_rotor(
      hub_height = 150,
      fhd = gen_fhd,
      rotor_radius = 120,
      tidal_offset = 2.5,
      yinc = 0.05)


 flux_fct <- get_flux_factor(
      n_turbines = 100,
      rotor_radius = 120,
      flight_speed = 13.1,
      bird_dens = c(1.19,0.85,1.05,1.45,1.41,1.45,1.12,1.45,0.93,0.902,1.06,1.23),
      daynight_hrs = Day_Length(52),
      noct_activity = 0.5
      )

turb_oper <- data.frame(
   month = month.abb,
   prop_oper = runif(12,0.5,0.8)
   )
turb_oper_month <- turb_oper$prop_oper

get_collisions_extended(
  rotor_grids = rotor_grids,
  d_y = gen_fhd_at_rotor, # ... with generic FHD = Option 3, with site FHD = Option 4
  rotor_radius = 120,
  blade_width = 5,
  rotor_speed = 15,
  blade_pitch = 15,
  flight_type = "flapping",
  wing_span = 1.01,
  flight_speed = 13.1,
  body_lt = 0.85,
  n_blades = 3,
  prop_upwind = 0.5,
  avoidance_rate = 0.981,
  flux_factor = flux_fct,
  mth_prop_oper = turb_oper_month,
  lac_factor = 0.9998299
  )

Returns the proportion of birds at height bands along the rotor

Description

Derive the expected proportion of bird flights at equidistant height bands between the lowest and highest points of the rotor. In other words, returns the flight height distribution at collision risk (d(y)).

Usage

get_fhd_rotor(hub_height, fhd, rotor_radius, tidal_offset, yinc = 0.05)

Arguments

Value

A numeric vector, the flight height distribution at collision risk, i.e. between minimum and maximum rotor height.

Examples

 gen_fhd_dat <- Johnston_Flight_heights_SOSS %>%
       dplyr::filter(variable=="Gannet.est") %>%
       dplyr::select(height,prop)
 if(is.data.frame(gen_fhd_dat)) gen_fhd <- gen_fhd_dat$prop

 get_fhd_rotor(
   hub_height = 150,
   fhd = gen_fhd,
   rotor_radius = 120,
   tidal_offset = 2.5,
   yinc = 0.05)

Flux factor

Description

Returns the flux factor, expressing the total number of bird flights through the rotors of the wind farm per month if all flights occurred within the rotor's circle area of all turbines, i.e. before the proportion at risk height and avoidance level are taken into account.

Usage

get_flux_factor(
  n_turbines,
  rotor_radius,
  flight_speed,
  bird_dens,
  daynight_hrs,
  noct_activity
)

Arguments

Details

The flux factor is used for other model calculations. Methodology and assumptions underpinning get_flux_factor are described in "Stage B" of Band (2012)

Value

The number of bird flights potentially transiting through rotors at each time period (assuming no avoidance), if all flights occur within the rotor's circular area.

Examples

  get_flux_factor(
      n_turbines = 100,
      rotor_radius = 120,
      flight_speed = 13.1,
      bird_dens = c(1.19,0.85,1.05,1.45,1.41,1.45,1.12,1.45,0.93,0.902,1.06,1.23),
      daynight_hrs = Day_Length(52),
      noct_activity = 0.5
      )

Large array correction factor

Description

A correction factor for large windfarms with a large array of turbines, to take into account the depletion of bird density in later rows of the site.

Usage

get_lac_factor(
  n_turbines,
  rotor_radius,
  avoidance_rate,
  avg_prob_coll,
  avg_prop_operational,
  wf_width
)

Arguments

Value

The large array correction factor to be applied

Examples

  get_lac_factor(
     n_turbines = 100,
     rotor_radius = 120,
     avoidance_rate = 0.989,
     avg_prob_coll = 0.1494609,
     avg_prop_operational = 0.6388292,
     wf_width = 52
     )

Migration Flux factor

Description

Returns the migratory flux factor, expressing the total number of bird flights through the rotors of the wind farm per month, if all flights occur within the rotor's circle area of all turbines, and assuming birds take no avoiding action.

Usage

get_mig_flux_factor(n_turbines, rotor_radius, wf_width, popn_est)

Arguments

Details

The flux factor is used for other model calculations. Methodology and assumptions underpinning get_mig_flux_factor are described in "Stage B" of Band (2012)

Value

The number of bird flights potentially transiting through rotors at each time period (assuming no avoidance), if all flights occur within the rotor's circular area

Examples

get_mig_flux_factor(
     n_turbines = 100,
     rotor_radius = 120,
     wf_width = 51,
     popn_est = 10000
)

Grid of probabilities of single transit collision at points in rotor circle

Description

Calculates single transit collision risk at grid points (X, Y) inside the left-half of the rotor circle, for a given flight direction (upwind or downwind), and assuming no avoidance action. The origin of the (X, Y) coordinates is the rotor center

Usage

get_pcoll_grid(
  rotor_grids,
  direction,
  rotor_radius,
  blade_width,
  rotor_speed,
  blade_pitch,
  flight_type,
  n_blades,
  flight_speed,
  wing_span,
  body_lt
)

Arguments

Details

Methodology and assumptions underpinning get_pcoll_grid are described in section "Extended Approach Taking Account Of Flight Heights" of Band (2012). Note that collision risk calculations are based on equation (3) in "Stage C" section, but using (X, Y) coordinates to reference transit points instead of the equivalent (r, phi) coordinates.

Value

a matrix. The probability of collisions at different flight height bands

See Also

generate_rotor_grids

Examples

  rotor_grids <- generate_rotor_grids(yinc = 0.05, xinc = 0.05, chord_prof_5MW)

  get_pcoll_grid(
    rotor_grids = rotor_grids,
    direction = 1,
    rotor_radius = 120,
    blade_width = 5,
    rotor_speed = 15,
    blade_pitch = 15,
    flight_type = "flapping",
    n_blades = 3,
    flight_speed = 13.1,
    wing_span = 1.01,
    body_lt = 0.85)

Grid with angles between points (x, y) and the rotor's vertical axis

Description

Given grids of vertical and horizontal distances from rotor axes at points (x, y) inside the rotor circle, get_phi_grid calculates the associated radial angles, relative to the rotor vertical axis.

Returned grid represents the left-half of the rotor's circle.

Usage

get_phi_grid(x_grid, y_grid)

Arguments

Value

A 2D array, giving a grid of angles (in radians) between points (x, y) inside the rotor circle and the rotor center, for the left-half of the rotor circle area.

See Also

get_x_grid(), get_y_grid()

Examples

 x_grid <- get_x_grid(yinc=0.05, xinc=0.05)
 y_grid <- get_y_grid(x_grid,yinc=0.05)
 get_phi_grid(x_grid,y_grid)

Calculate the total proportion of bird flights at collision risk based on a flight height distribution

Description

Calculate the expected proportion of bird flights at collision risk height (i.e. at rotor height, between bottom and top of the rotor) based on the bird's flight height distribution (Q'_{2R}).

Usage

get_prop_crh_fhd(d_y)

Arguments

Value

The total proportion of birds at collision risk height derived from a flight height distribution

Examples

 gen_fhd_dat <- Johnston_Flight_heights_SOSS %>%
      dplyr::filter(variable=="Gannet.est") %>%
      dplyr::select(height,prop)

 gen_fhd <- gen_fhd_dat$prop

 d_y <-
    get_fhd_rotor(
      hub_height = 150,
      fhd = gen_fhd,
      rotor_radius = 120,
      tidal_offset = 2.5,
      yinc = 0.05)

 prop_chr_fhd <- get_prop_crh_fhd(d_y)

Single transit collision risk along the chord of the rotor at height band y

Description

Calculates the single transit collision risk/probability along the horizontal chord of the rotor at height y via numerical integration.

Usage

get_risk_y(x_at_y, pcoll_doty)

Arguments

Value

a numeric value, the single transit collision risk along the whole horizontal chord of the rotor circle at height band y

See Also

get_x_grid(), get_pcoll_grid()

Examples

  rotor_grids <- generate_rotor_grids(yinc = 0.05, xinc = 0.05, chord_prof_5MW)

  y_lt <- dim(rotor_grids$r_grid)[1]

  pcollxy_grid_up <- get_pcoll_grid(
    rotor_grids = rotor_grids,
    direction = 1,
    rotor_radius = 120,
    blade_width = 5,
    rotor_speed = 15,
    blade_pitch = 15,
    flight_type = "flapping",
    n_blades = 3,
    flight_speed = 13.1,
    wing_span = 1.01,
    body_lt = 0.85)

    risk_up <- rep(NA, y_lt)
    for(i in 1:y_lt){
      risk_up[i] <- get_risk_y(rotor_grids$x_grid[i, ], pcollxy_grid_up[i, ])
    }

Grid of horizontal distances from points in the rotor circle to its vertical axis

Description

Taking the center of the rotor circle as the origin, get_x_grid generates a grid containing horizontal distances x (by xinc increments) from the y-axis up to the outer edge of the rotor circle, at equidistant height bands y (by yinc increments) between minimum and maximum rotor height.

Distances are expressed as proportion of rotor radius (i.e. x is dimensionless).

Returned grid represents the left-half of the rotor's circle.

Usage

get_x_grid(xinc = 0.05, yinc = 0.05)

Arguments

Value

A 2D array giving a grid of horizontal distances x from rotor's vertical axis, expressed as the proportion of rotor radius (i.e. [0, 1]), for the left-half of the rotor circle area.

Examples

get_x_grid(xinc=0.05,yinc=0.05)

Grid of vertical distances from points in the rotor circle to its horizontal axis

Description

Taking the center of the rotor circle as the origin, get_y_grid generates a grid of vertical distances y (by yinc increments) from the x-axis to the outer edge of the rotor circle, across width intervals x (by xinc increments) between the center and maximum rotor width.

Returned grid represents the left-half of the rotor's circle.

Distances are expressed as proportion of rotor radius (i.e. y is dimensionless).

Usage

get_y_grid(x_grid, yinc = 0.05)

Arguments

Value

2D array giving a grid of vertical distances y from the rotor's horizontal axis, expressed as the proportion of rotor radius, for the left-half of the rotor circle area. Negative values represent distances from the bottom half of the rotor circle.

Examples

 x_grid <- get_x_grid(yinc=0.05, xinc=0.05)
 get_y_grid(x_grid,yinc=0.05)

Stochastic migration collision risk model

Description

Run migration stochastic collision risk model for a single species and one turbine scenario

Usage

mig_stoch_crm(
  wing_span_pars,
  flt_speed_pars,
  body_lt_pars,
  prop_crh_pars,
  avoid_bsc_pars,
  n_turbines,
  n_blades = 3,
  rtn_speed_pars,
  bld_pitch_pars,
  rtr_radius_pars,
  bld_width_pars,
  wf_width,
  wf_latitude,
  flight_type,
  prop_upwind = 0.5,
  popn_estim_pars,
  season_specs,
  chord_profile = chord_prof_5MW,
  trb_wind_avbl,
  trb_downtime_pars,
  n_iter = 10,
  LargeArrayCorrection = TRUE,
  log_file = NULL,
  seed = NULL,
  verbose = TRUE
)

Arguments

Details

This function is an adaption of code from Masden(2015) used for estimating the collision risk of seabirds in offshore windfarm sites and is a further adaptation from Band(2012). It is a further adaptation of the stoch_crm function.

The collision risk model evaluates risk for each defined migratory period where flux rate is simply the number of birds travelling through the windfarm.

Changes in relation to previous top-line function stoch_crm

• function will run only option 1 for migratory species

Value

Estimates of number of collisions per migratory season for the n number of iterations specified

Examples

# ------------------------------------------------------
# Run with arbitrary parameter values, for illustration
# ------------------------------------------------------
season_specs <- data.frame(
  season_id = c("PrBMigration", "PoBMigration","OMigration"),
  start_month = c("Mar", "May", "Oct"), end_month = c("Apr", "Sep", "Feb")
)

# wind availability
windavb <- data.frame(
  month = month.abb,
  pctg = runif(12, 85, 98)
)
head(windavb)

# maintenance downtime
dwntm <- data.frame(
  month = month.abb,
  mean = runif(12, 6, 10),
  sd = rep(2, 12))
head(dwntm)


mig_stoch_crm(
  # Wing span in m,
  wing_span_pars = data.frame(mean = 1.08, sd = 0.04),
  # Flight speed in m/s
  flt_speed_pars = data.frame(mean = 7.26, sd = 1.5),
  # Body length in m,
  body_lt_pars = data.frame(mean = 0.39, sd = 0.005),
  # Proportion of birds at CRH
  prop_crh_pars = data.frame(mean = 0.06, sd = 0.009),
  # avoidance rate
  avoid_bsc_pars = data.frame(mean = 0.99, sd = 0.001),
  n_turbines = 150,
  n_blades = 3,
  # rotation speed in m/s of turbine blades
  rtn_speed_pars = data.frame(mean = 13.1, sd = 4),
  # pitch in degrees of turbine blades
  bld_pitch_pars = data.frame(mean = 3, sd = 0.3),
  # sd = 0, rotor radius is fixed
  rtr_radius_pars = data.frame(mean = 80, sd = 0),
  # sd = 0, blade width is fixed
  bld_width_pars = data.frame(mean = 8, sd = 0),
  wf_width = 100,
  wf_latitude = 54.1,
  prop_upwind = 0.5,
  flight_type = "flapping",
  # population flying through windfarm,
  popn_estim_pars = data.frame(mean = 21584, sd = 2023),
  season_specs = season_specs,
  chord_profile = chord_prof_5MW,
  trb_wind_avbl = windavb,
  trb_downtime_pars = dwntm,
  n_iter = 1000,
  LargeArrayCorrection = TRUE,
  log_file = NULL,
  seed = 1234,
  verbose = TRUE)

Customised sampling functions for the Beta distributions

Description

generate random samples from a beta distribution, parameterized as mean and sd, and returning NAs if conditions are not met

Usage

rbeta_dmp(n, p, sd)

Arguments

Value

a vector of samples values from the beta distribution

Examples

    rbeta_dmp(n=100,p=0.9,sd=0.01)

Sample rotor grids for generated_rotor_grids unit test

Description

Sample rotor grids for generated_rotor_grids unit test

Usage

rotor_grids_test

Format

list of data frames

Customised sampling of Truncated Normal distribution

Description

Wrapper of the msm::rtnorm() function, improving on outputs management and user feedback on edge cases

Usage

rtnorm_dmp(n, mean = 0, sd = 1, lower = -Inf, upper = Inf)

Arguments

Value

a vector of samples values from the truncated normal distribution

Examples

rtnorm_dmp(n=10,mean=0.4,sd=0.2)

Parameter sampling whiz

Description

Generates the random samples of all the stochastic CRM parameters. For internal use.

Usage

sample_parameters(
  model_options,
  mod_mths,
  n_iter = 10,
  flt_speed_pars,
  body_lt_pars,
  wing_span_pars,
  avoid_bsc_pars,
  avoid_ext_pars,
  noct_act_pars,
  prop_crh_pars,
  bird_dens_opt = "tnorm",
  bird_dens_dt,
  gen_fhd_boots = NULL,
  site_fhd_boots = NULL,
  rtr_radius_pars,
  air_gap_pars,
  bld_width_pars,
  rtn_pitch_opt = "probDist",
  bld_pitch_pars,
  rtn_speed_pars,
  windspd_pars,
  rtn_pitch_windspd_dt,
  trb_wind_avbl,
  trb_downtime_pars,
  lrg_arr_corr
)

Arguments

Details

Collision risk can be calculated under 4 options, specified by model_options:

• Option 1 - Basic model with proportion at collision risk height derived from site survey (prop_crh_surv).

• Option 2 - Basic model with proportion at collision risk height derived from a generic flight height distribution (gen_fhd).

• Option 3 - Extended model using a generic flight height distribution (gen_fhd).

• Option 4 - Extended model using a site-specific flight height distribution (site_fhd).

Where,

• Basic model - assumes a uniform distribution of bird flights at collision risk height (i.e. above the minimum and below the maximum height of the rotor blade).

• Extended model - takes into account the distribution of bird flight heights at collision risk height.

Value

A list object with each element comprising sampled values of given CRM parameter

Examples

  bird_dens_dt <- data.frame(
    month = month.abb,
    mean = runif(12, 0.8, 1.5),
    sd = runif(12, 0.2, 0.3)
  )

 # wind availability
  trb_wind_avbl <- data.frame(
    month = month.abb,
    pctg = runif(12, 85, 98)
  )

  # maintenance downtime
  trb_downtime_pars <- data.frame(
    month = month.abb,
    mean = runif(12, 6, 10),
    sd = rep(2, 12))

  # Wind speed relationships
  wind_rtn_ptch <- data.frame(
    wind_speed = seq_len(30),
    rtn_speed = 10/(30:1),
    bld_pitch = c(rep(90, 4), rep(0, 8), 5:22)
    )


  bird_dens_opt <- "tnorm"
  ### extract and standardize month format from monthly data sets
  b_dens_mth <- switch (bird_dens_opt,
                        tnorm = bird_dens_dt$month,
                        resample = names(bird_dens_dt),
                        qtiles = names(bird_dens_dt)[names(bird_dens_dt) != "p"]
  ) %>% format_months()
  dwntm_mth <- format_months(trb_downtime_pars$month)
  windav_mth <- format_months(trb_wind_avbl$month)
  ### Set months to model: only those in common amongst monthly data sets
  mod_mths <- Reduce(intersect, list(b_dens_mth, dwntm_mth, windav_mth))
  ### Order chronologically
  mod_mths <- mod_mths[order(match(mod_mths, month.abb))]

  param_draws <- sample_parameters(
    model_options = c(1,2,3),
    n_iter = 10,
    mod_mths = mod_mths,
    flt_speed_pars = data.frame(mean=7.26,sd=1.5),
    body_lt_pars = data.frame(mean=0.39,sd=0.005),
    wing_span_pars = data.frame(mean=1.08,sd=0.04),
    avoid_bsc_pars = data.frame(mean=0.99,sd=0.001),
    avoid_ext_pars = data.frame(mean=0.96,sd=0.002),
    noct_act_pars = data.frame(mean=0.033,sd=0.005),
    prop_crh_pars = data.frame(mean=0.06,sd=0.009),
    bird_dens_opt = "tnorm",
    bird_dens_dt = bird_dens_dt,
    gen_fhd_boots = generic_fhd_bootstraps[[1]],
    site_fhd_boots = NULL,
    rtr_radius_pars = data.frame(mean=80,sd=0),
    air_gap_pars = data.frame(mean=36,sd=0),
    bld_width_pars = data.frame(mean=8,sd=0),
    rtn_pitch_opt = "windSpeedReltn",
    bld_pitch_pars = NULL,
    rtn_speed_pars = NULL,
    windspd_pars = data.frame(mean=7.74,sd=3),
    rtn_pitch_windspd_dt = wind_rtn_ptch,
    trb_wind_avbl = trb_wind_avbl,
    trb_downtime_pars = trb_downtime_pars,
    lrg_arr_corr = TRUE
    )

Generate random draws based on empirical c.d.f.

Description

Generate random draws from a set of quantiles, based on the empirical cumulative density function

Usage

sample_qtls(n, probs, qtls)

Arguments

Details

Based on the Inverse Transform Sampling technique, by sampling random probabilities from a uniform distribution and interpolate (cubic) the count samples from the percentiles provided by the user (taken as the empirical cumulative density function)

Value

a numeric vector, with random draws of the approximated distribution underpinning the provided quantiles

Examples

 sample_qtls(10,c(0.1,0.2,0.3),qtls=c(0.05,0.1,0.95))

Sampling function for a single turbine in the mCRM

Description

Samples and aggregates appropriate data for a single wind turbine

Usage

sample_turbine_mCRM(
  rtn_speed_pars,
  bld_pitch_pars,
  rtr_radius_pars,
  bld_width_pars,
  season_specs,
  n_iter = 10,
  trb_wind_avbl,
  trb_downtime_pars
)

Arguments

Value

A data frame of all the information sampled for the turbine with nrow = n_iter

Examples

season_specs <- data.frame(
  season_id = c("PrBMigration", "PoBMigration","OMigration"),
  start_month = c("Mar", "May", "Oct"), end_month = c("Apr", "Sep", "Feb")
  )

  windavb <- data.frame(
    month = month.abb,
    pctg = runif(12, 85, 98)
  )

  dwntm <- data.frame(
    month = month.abb,
    mean = runif(12, 6, 10),
    sd = rep(2, 12))

  sample_turbine_mCRM(rtn_speed_pars = data.frame(mean = 13.1, sd = 4),
                      bld_pitch_pars = data.frame(mean = 3, sd = 0.3),
                      rtr_radius_pars = data.frame(mean = 80, sd = 0),
                      bld_width_pars = data.frame(mean = 8, sd = 0),
                      season_specs = season_specs,
                      n_iter = 10,
                      trb_wind_avbl = windavb,
                      trb_downtime_pars = dwntm)

Customised sampling function wrapper

Description

Samples a dataset based on inputs for either the rtnorm, rbeta or 'rnorm' distributions

Usage

sampler_hd(
  dat,
  mode = "rtnorm",
  n = NULL,
  mean = NULL,
  sd = NULL,
  lower = 0,
  upper = NULL
)

Arguments

Value

a vector of samples values from the distribution

Examples

  sampler_hd(dat=0.1,
       mode='rtnorm',
       n=100,
       mean=9,
       sd=0.1)

Generate sequence of months

Description

Generate sequence of months

Usage

seq_months(start_month, end_month)

Arguments

Value

character vector. The list of months that falls in between two months

Examples

   seq_months("Jan", "Apr")

stochLAB: Stochastic Collision Risk Model

Description

stochLAB is a tool to run stochastic (and deterministic) Collision Risk Models (CRM) for seabirds on offshore wind farms.

The main functions of stochLAB are:

• stoch_crm(): Stochastic Collision Risk Model,

• band_crm(): Deterministic Collision Risk Model,

• mig_stoch_crm(): Stochastic Migration Collision risk Model

Overview

The {stochLAB} package is an adaptation of the R code developed by Masden (2015) to incorporate variability and uncertainty in the avian collision risk model originally developed by Band (2012).

Code developed under {stochLAB} substantially re-factored and re-structured Masden's (heavily script-based) implementation into a user-friendly, streamlined, well documented and easily distributed tool. Furthermore, this package lays down the code infrastructure for easier incorporation of new functionality, e.g. extra parameter sampling features, model expansions, etc.

Previous code underpinning key calculations for the extended model has been replaced by an alternative approach, resulting in significant gains in computational speed over Masden's code. This optimization is particularly beneficial under a stochastic context, when Band calculations are computed repeatedly. See generate_rotor_grids() for further details.

Function stoch_crm()

stoch_crm() is essentially a replacement function for script BandModel.r in Masden's approach. Main changes in terms of user interface include:

• Collision model runs for one single scenario (i.e. one species for one turbine scenario) at each stoch_crm() call. Apart from gains in development code structure, this unit-based approach was considered to offer greater end user flexibility for setting up and managing multiple scenarios (including parallel computation).

• Input parameters now entered explicitly into feature-specific arguments, instead of bundled together into wide-column tables. This improves code readability and reduces the quantity of hard-coded parameter names, therefore making referencing errors less likely.

• Outputs no longer saved automatically to external files.

Seasonal Outputs

stoch_crm() now provides an option for user-defined seasonal outputs, allowing for country/region specific seasonal definitions.

Currently implemented CRM calculations produce collision estimates on a monthly basis to reflect changing bird abundance within the windfarm area. Seasonal estimates are obtained by aggregating monthly estimates over each season definition, with uncertainty in collision estimates being suitably propagated to seasonal outputs.

Sampling distributions

Masden's implementation used Normal and Truncated Normal distributions to generate random parameter values. However, the Normal distribution is unbounded, and so there was the risk of randomly drawing inappropriate values in some cases.

stoch_crm() extends the use of bounded probability distributions to all model parameters. Strictly positive features (e.g. bird densities, body length, turbine downtime, etc.) are sampled from Truncated Normal distributions, while features constrained between 0 and 1 (e.g. nocturnal activity, proportion of flights at collision risk height, etc) are assumed to follow Beta distributions.

In addition, new functionality has been incorporated to allow the use of bird density resamples (e.g. bootstrap samples) or quantile estimates from density estimation models in the simulations.

Function band_crm()

band_crm() performs the core CRM calculations required to estimate the number of collisions, as per Band (2012). While being the computing workhorse of the stoch_crm() function, it can also be used alone, providing backward compatibility with the original Band spreadsheet outputs.

See Also

Useful links:

• https://github.com/HiDef-Aerial-Surveying/stochLAB

• Report bugs at https://github.com/HiDef-Aerial-Surveying/stochLAB/issues

Examples

# ------------------------------------------------------
# Run with arbitrary parameter values, for illustration
# ------------------------------------------------------

# Setting a dataframe of parameters to draw from
params <- data.frame(
  flight_speed = 13.1,         # Flight speed in m/s
  body_lt = 0.85,              # Body length in m
  wing_span = 1.01,            # Wing span in m
  flight_type = "flapping",    # flapping or gliding flight
  avoid_rt_basic = 0.989,      # avoidance rate for option 1 and 2
  avoid_rt_ext = 0.981,        # extended avoidance rate for option 3 and 4
  noct_activity = 0.5,         # proportion of day birds are inactive
  prop_crh_surv = 0.13,        # proportion of birds at collision risk height (option 1 only)
  prop_upwind = 0.5,           # proportion of flights that are upwind
  rotor_speed = 15,            # rotor speed in m/s
  rotor_radius = 120,          # radius of turbine in m
  blade_width = 5,             # width of turbine blades at thickest point in m
  blade_pitch = 15,            # mean radius pitch in Radians
  n_blades = 3,                # total number of blades per turbine
  hub_height = 150,            # height of hub in m above HAT
  n_turbines = 100,            # number of turbines in the wind farm
  wf_width = 52,               # width across longest section of wind farm
  wf_latitude = 56,            # latitude of centroid of wind farm
  tidal_offset = 2.5,          # mean tidal offset from HAT of the wind farm
  lrg_arr_corr = TRUE          # apply a large array correction?
)

# Monthly bird densities
b_dens <- data.frame(
  month = month.abb,
  dens = runif(12, 0.8, 1.5)
)

# flight height distribution from Johnston et al
gen_fhd_dat <- Johnston_Flight_heights_SOSS %>%
  dplyr::filter(variable=="Gannet.est") %>%
  dplyr::select(height,prop)


# monthly operational time of the wind farm
turb_oper <- data.frame(
  month = month.abb,
  prop_oper = runif(12,0.5,0.8)
)


band_crm(
  model_options = c(1,2,3),
  flight_speed = params$flight_speed,
  body_lt = params$body_lt,
  wing_span = params$wing_span,
  flight_type = params$flight_type,
  avoid_rt_basic = params$avoid_rt_basic,
  avoid_rt_ext = params$avoid_rt_ext,
  noct_activity = params$noct_activity,
  prop_crh_surv = params$prop_crh_surv,
  dens_month = b_dens,
  prop_upwind = params$prop_upwind,
  gen_fhd = gen_fhd_dat,
  site_fhd = NULL,  # Option 4 only
  rotor_speed = params$rotor_speed,
  rotor_radius = params$rotor_radius,
  blade_width = params$blade_width,
  blade_pitch = params$blade_pitch,
  n_blades = params$n_blades,
  hub_height = params$hub_height,
  chord_prof = chord_prof_5MW,
  n_turbines = params$n_turbines,
  turb_oper_month = turb_oper,
  wf_width = params$wf_width,
  wf_latitude = params$wf_latitude,
  tidal_offset = params$tidal_offset,
  lrg_arr_corr = params$lrg_arr_corr
  )

Stochastic collision risk model for a single species and one wind farm scenario

Description

Runs a Stochastic Collision Risk Model (SCRM) for estimating the number of in-flight collisions with offshore windfarm turbines, for given species and windfarm scenario. Core calculations follow the work developed by Masden (2015). See Background and Updates section below for more details.

Usage

stoch_crm(
  model_options = c("1", "2", "3", "4"),
  n_iter = 1000,
  flt_speed_pars,
  body_lt_pars,
  wing_span_pars,
  avoid_bsc_pars = NULL,
  avoid_ext_pars = NULL,
  noct_act_pars,
  prop_crh_pars = NULL,
  bird_dens_opt = c("tnorm", "resample", "qtiles"),
  bird_dens_dt,
  flight_type,
  prop_upwind,
  gen_fhd_boots = NULL,
  site_fhd_boots = NULL,
  n_blades,
  air_gap_pars,
  rtr_radius_pars,
  bld_width_pars,
  bld_chord_prf = chord_prof_5MW,
  rtn_pitch_opt = c("probDist", "windSpeedReltn"),
  bld_pitch_pars = NULL,
  rtn_speed_pars = NULL,
  windspd_pars = NULL,
  rtn_pitch_windspd_dt = NULL,
  trb_wind_avbl,
  trb_downtime_pars,
  wf_n_trbs,
  wf_width,
  wf_latitude,
  tidal_offset,
  lrg_arr_corr = TRUE,
  xinc = 0.05,
  yinc = 0.05,
  out_format = c("draws", "summaries"),
  out_sampled_pars = FALSE,
  out_period = c("months", "seasons", "annum"),
  season_specs = NULL,
  verbose = TRUE,
  log_file = NULL,
  seed = NULL
)

Arguments

Details

Collision risk can be calculated under 4 options, specified by model_options:

• Option 1 - Basic model with proportion at collision risk height derived from site survey (prop_crh_surv).

• Option 2 - Basic model with proportion at collision risk height derived from a generic flight height distribution (gen_fhd).

• Option 3 - Extended model using a generic flight height distribution (gen_fhd).

• Option 4 - Extended model using a site-specific flight height distribution (site_fhd).

Where,

• Basic model - assumes a uniform distribution of bird flights at collision risk height (i.e. above the minimum and below the maximum height of the rotor blade).

• Extended model - takes into account the distribution of bird flight heights at collision risk height.

Value

If out_sampled_pars = FALSE, returns a list with estimates of number of collisions per chosen time periods, with elements containing the outputs for each CRM Option.

If out_sampled_pars = TRUE, returns a list object with two top-level elements:

• collisions, a list comprising collision estimates for each CRM Option,

• sampled_pars, a list with summary statistics of values sampled for stochastic model parameters.

Examples

# ------------------------------------------------------
# Run with arbitrary parameter values, for illustration
# ------------------------------------------------------

# ------------------------------------------------------
# Setting some of the required inputs upfront
b_dens <- data.frame(
  month = month.abb,
  mean = runif(12, 0.8, 1.5),
  sd = runif(12, 0.2, 0.3)
)
head(b_dens)

# Generic FHD bootstraps from Johnson et al (2014)
fhd_boots <- generic_fhd_bootstraps[[1]]
head(fhd_boots)

# wind speed vs rotation speed vs blade pitch
wind_rtn_ptch <- data.frame(
  wind_speed = seq_len(30),
  rtn_speed = 10/(30:1),
  bld_pitch = c(rep(90, 4), rep(0, 8), 5:22)
)
head(wind_rtn_ptch)

# wind availability
windavb <- data.frame(
  month = month.abb,
  pctg = runif(12, 85, 98)
)
head(windavb)

# maintenance downtime
dwntm <- data.frame(
  month = month.abb,
  mean = runif(12, 6, 10),
  sd = rep(2, 12))
head(dwntm)

# seasons specification
seas_dt <- data.frame(
  season_id = c("a", "b", "c"),
  start_month = c("Jan", "May", "Oct"), end_month = c("Apr", "Sep", "Dec")
  )
head(seas_dt)

# ----------------------------------------------------------
# Run stochastic CRM, treating rotor radius, air gap and
# blade width as fixed parameters (i.e. not stochastic)

stoch_crm(
  model_options = c(1, 2, 3),
  n_iter = 1000,
  flt_speed_pars = data.frame(mean = 7.26, sd = 1.5),
  body_lt_pars = data.frame(mean = 0.39, sd = 0.005),
  wing_span_pars = data.frame(mean = 1.08, sd = 0.04),
  avoid_bsc_pars = data.frame(mean = 0.99, sd = 0.001),
  avoid_ext_pars = data.frame(mean = 0.96, sd = 0.002),
  noct_act_pars = data.frame(mean = 0.033, sd = 0.005),
  prop_crh_pars = data.frame(mean = 0.06, sd = 0.009),
  bird_dens_opt = "tnorm",
  bird_dens_dt = b_dens,
  flight_type = "flapping",
  prop_upwind = 0.5,
  gen_fhd_boots = fhd_boots,
  n_blades = 3,
  rtr_radius_pars = data.frame(mean = 80, sd = 0), # sd = 0, rotor radius is fixed
  air_gap_pars = data.frame(mean = 36, sd = 0),    # sd = 0, air gap is fixed
  bld_width_pars = data.frame(mean = 8, sd = 0),   # sd = 0, blade width is fixed
  rtn_pitch_opt = "windSpeedReltn",
  windspd_pars = data.frame(mean = 7.74, sd = 3),
  rtn_pitch_windspd_dt = wind_rtn_ptch,
  trb_wind_avbl = windavb,
  trb_downtime_pars = dwntm,
  wf_n_trbs = 200,
  wf_width = 15,
  wf_latitude = 56.9,
  tidal_offset = 2.5,
  lrg_arr_corr = TRUE,
  verbose = TRUE,
  seed = 1234,
  out_format = "summaries",
  out_sampled_pars = TRUE,
  out_period = "seasons",
  season_specs = seas_dt,
  log_file = NULL
)

Example of turbine and windfarm parameters stored in wide format

Description

A data frame of (fake) data on turbine and wind farm features for 3 scenarios.

Usage

turb_pars_wide_example

Format

A 3 x 51 data frame, with the turbine and windfarm parameters (columns) for each of the 3 development scenarios (rows). Columns include:

TurbineModel

The turbine/windfarm scenario ID

Blades

Nr of blades

RotorRadius

Mean of rotor radius

RotorRadiusSD

SD of rotor radius

HubHeightAdd

Mean of air gap, the distance between sea surface and lowest tip height.

HubHeightAddSD

SD of air gap, as explained above.

...

Details

Intended to illustrate the application of stoch_scrm() to a multiple scenario setting, where parameter data is available from tables in wide format.

Input validator

Description

Input validator

Usage

validate_inputs(
  model_options,
  n_iter = NULL,
  flt_speed_pars = NULL,
  flight_speed = NULL,
  body_lt_pars = NULL,
  body_lt = NULL,
  wing_span_pars = NULL,
  wing_span = NULL,
  avoid_bsc_pars = NULL,
  avoid_rt_basic = NULL,
  avoid_ext_pars = NULL,
  avoid_rt_ext = NULL,
  noct_act_pars = NULL,
  noct_activity = NULL,
  prop_crh_pars = NULL,
  bird_dens_opt = NULL,
  bird_dens_dt = NULL,
  chord_prof = NULL,
  dens_month = NULL,
  turb_oper_month = NULL,
  flight_type = NULL,
  prop_upwind = NULL,
  gen_fhd_boots = NULL,
  site_fhd_boots = NULL,
  n_blades = NULL,
  air_gap_pars = NULL,
  rtr_radius_pars = NULL,
  rotor_radius = NULL,
  blade_width = NULL,
  blade_pitch = NULL,
  hub_height = NULL,
  bld_width_pars = NULL,
  rtn_pitch_opt = NULL,
  bld_pitch_pars = NULL,
  rtn_speed_pars = NULL,
  rotor_speed = NULL,
  n_turbines = NULL,
  windspd_pars = NULL,
  rtn_pitch_windspd_dt = NULL,
  trb_wind_avbl = NULL,
  trb_downtime_pars = NULL,
  wf_n_trbs = NULL,
  wf_width = NULL,
  wf_latitude = NULL,
  tidal_offset = NULL,
  gen_fhd = NULL,
  site_fhd = NULL,
  lrg_arr_corr = NULL,
  xinc = NULL,
  yinc = NULL,
  seed = NULL,
  verbose = NULL,
  out_format = NULL,
  out_sampled_pars = NULL,
  out_period = NULL,
  season_specs = NULL,
  popn_estim_pars = NULL,
  fn = "scrm"
)

Arguments

Value

Nothing returned from this function

Examples

  validate_inputs(model_options=c(1),
               avoid_bsc_pars=data.frame(mean=0.99,sd=0.001),
               prop_crh_pars=data.frame(mean=0.01,sd=0.01),
               air_gap_pars = data.frame(mean=21,sd=0),
               rtr_radius_pars = data.frame(mean=100,sd=0),
               bld_pitch_pars = data.frame(mean=15,sd=0),
               rtn_pitch_opt = "probDist",
               rtn_speed_pars = data.frame(mean=14,sd=5),
               out_period = "months",
               lrg_arr_corr = TRUE,
               fn="scrm")

Example of data with relationship between wind speed, rotation speed and blade pitch

Description

Intended to illustrate the application of stoch_scrm()

Usage

wndspd_rtn_ptch_example

Format

A 30 x 3 data frame with columns:

wind_speed

Wind speed in metres per second.

rtn_speed

Blade rotation speed, in revolutions per minute

bld_pitch

Blade pitch, in degrees