Calculate observed flights / time / area from point transects

This function converts the uncorrected encounter rate, the effective detection radius (see for example Buckland et al. (2001) ) and the effective detection height into an estimate of flight flux per unit time per unit area of vertical airspace (Smales et al. 2013) .

Usage

obs_flux(encounter_rate, eff_detection_width, eff_detection_height)

Arguments

encounter_rate: numeric; number of flights observed per unit time of survey as output by encounter_rate() or similar.
eff_detection_width: numeric; Allows you to manually specify the effective detection width, which is usually 2 x effective detection radius or 2 x effective strip (half) width. Must be in the same units as eff_detection_height.
eff_detection_height: numeric; The effective detection height. Because the density of flights typically decreases with increasing height, the assumption of uniform density required for traditional distance correction doesn't hold. So the observer's detection function is effectively convolved with the flight height distribution of the bird. Therefore, in most cases we recommend using the maximum tip height of the turbine as the "effective detection height" and desktop truncating the observations to that height. This is the simplest way to avoid artificially inflating or deflating the flux through the turbine. It is possible to use another method to estimate an effective detection height but we leave this to the analyst's judgement. Must be in the same units as eff_detection_width.

Value

numeric; number of flights through a vertical plane of unit area per unit time. Area units are defined by the units of the width and height, and time interval is the same as referenced by the encounter_rate input.

Details

Observed flux from point counts

Given an encounter rate (encounter_rate()), a distribution of flight heights and a related distance model (fit using the Distance package (Miller et al. 2019) ) we calculate the flight flux through a rectangle with a width of 2 x (effective detection radius) and a height equal to the effective detection height (typically set to the tip height of the proposed turbine) in one unit of observation time.

Note the function accepts only single valued inputs, so stochastic inputs must be sampled from prior to calling this function. For more information, see vignette("simple-simulation-example", package = "collision").

References

Buckland S, Anderson D, Burnham K, Laake J, Borchers D, Thomas L (2001). Introduction to Distance Sampling: Estimating Abundance of Biological Populations, volume xv. Oxford University Press. ISBN 978-0-19-850649-2. doi:10.1093/oso/9780198506492.001.0001 .

Miller DL, Rexstad E, Thomas L, Marshall L, Laake JL (2019). “Distance Sampling in R.” Journal of Statistical Software, 89, 1–28. ISSN 1548-7660. doi:10.18637/jss.v089.i01 .

Smales I, Muir S, Meredith C, Baird R (2013). “A Description of the Biosis Model to Assess Risk of Bird Collisions with Wind Turbines.” Wildlife Society Bulletin, 37(1), 59–65. ISSN 19385463. doi:10.1002/wsb.257 .

Examples


## A simple example of calculating flux from a point count and
## using this to generate the number of flights through a turbine 
## in a year
## 
## # Step by step
## 

# four surveys
# Note the observation data should include observations within max rotor swept height
df_obs <- data.frame(
  size = c(0, 2 , 3, 0), #individuals observed per survey (below max rotor swept height)
  survey_duration = c(20, 20, 18, 20), # minutes
  # Optional survey weights to deal with stratification etc
  survey_weight = c(1,1,1,1)
)

rotor_diameter <- 300
hub_height <- 200
edr <- 800 # derive from distance model
max_rsh <- hub_height + rotor_diameter/2

# flights observed per minute of survey
flights_per_min <- encounter_rate(
  df_obs_summary = df_obs,
  wilson_correction = TRUE # Default
)

# observed flights through vertical plane of one metre squared in one minute
flights_per_m2_per_min <- obs_flux(
  encounter_rate = flights_per_min,
  eff_detection_width = 2*edr,
  eff_detection_height = max_rsh
)

# scale to turbine width and height
flights_turbine_min <- turbine_flights(
  obs_flux = flights_per_m2_per_min,
  rotor_diameter = rotor_diameter,
  hub_height = hub_height
)

# scale to annual flights through area of rotor_diameter x turbine height 
flights_turbine_year <- flights_per_year(
  flights_per_time = flights_turbine_min,
  time_units = "min", # Default
  prop_day = 0.5,  #diurnal species
  prop_year = 1    # present all year
)

## Alternate calc using a wrapper function
## to go from observations to turbine flights per year
## 
flights_turbine_year2 <- turbine_flights_year(
  survey_type = "point", # only supported option currently
  encounter_rate = flights_per_min,
  time_units = "min",
  eff_detection_width = 2*edr,
  eff_detection_height = max_rsh,
  rotor_diameter = rotor_diameter,
  hub_height = hub_height,
  prop_day = 0.5,  #diurnal species
  prop_year = 1   # present all year
)

#They are the same
flights_turbine_year
#> [1] 3160.817
flights_turbine_year2
#> [1] 3160.817