In dhope/BASSr: Benefit Applied Strategic Sampling

knitr::opts_chunk$set(
  eval=T,
  collapse = TRUE,
  message =F, warning =F,
  fig.width = 8,
  fig.height = 8,
  comment = "#>"
)
library(tidyverse)
library(sf)
library(spsurvey)
library(glue)
library(BASSr)
library(raster)
library(rlang)
library(patchwork)


bcv <- BASSr::cost_vars

Cost model parts

The cost model is comprised of three access types: Truck ATV * Helicopter

The basic cost is based on the number of ARUs to be deployed per study area ($N$). The base rate is 30.

The cost of accessing a site is the sum of the cost of surveying a site by truck, atv and helicopter, each weighted by the proportion that is accessible by that access type. Truck access is assumed to be preffered first, then ATV, then helicopter.

$$ C = \sum p_iC_i = p_TC_T + p_AC_A + p_HC_H $$

Truck access is based on primary roads plus a buffer of 1000m. A truck cost is based on the following formula.

$$ C_{T} = \frac{T_dn_c N}{N_Tn_c} = \frac{T_d N}{N_T} $$ Where $T_d$ is the daily cost of truck usage, set initially to r bcv$truck_cost_per_day. $N_T$ is the number of ARUs a truck crew can deploy (r bcv$truck_arus_per_crew_per_day). This can be changed later to allow for differing daily costs based on the number of truck crews, however as written now, the number of crews ($n_c$) increases deployment rate and cost equivanetly and therefore drops out of the equation.

The cost of ATV deployment is equivalent to truck costs in structure, but the rate of deployment and costs are different between deployment types: $$ C_{A} = \frac{A_dn_c N}{N_An_c} = \frac{A_d N}{N_A} $$

The cost of helicopter deployment has more details. It can be broken down into four pieces: 1. The cost per litre of fuel - $C_l$ 2. The cost of setting up a basecamp - $C_b$ 3. The cost of moving to/from the study area - $C_{f}$ 4. The cost of moving within the study area - $C_{sa}$

The distances between the study area, basecamp and nearest airport drive most of the cost. The distance between the nearest airport and the study area is $D_{s-a}$, between the study area and basecamp $D_{s-b}$, and between basecamp and the airport $D_{a-b}$. If the distance from the airport to the study area is less than a maximum helicopter range $D_{s-a}<D_{max}$ then a basecamp is not needed. If the distance from the basecamp to the study area is greater than $D_{max}$, then a fuel cache is required. Adding a basecamp and fuel cache increase the cost per litre for the helicopter to fly.

$$ C_l = \begin{cases} C_l[1], & \text{if } D_{s-a} < D_{max} \ C_l[2], & \text{else if } D_{s_b} < D_{max}\ C_l[3], & \text{ otherwise} \end{cases} $$

The cost of flying from the airport to the basecamp is as follows:

$$ C_b = \begin{cases} 0,& \text{if } D_{s-a} < D_{max} \ D_{a-b} C^b + 2\frac{D{a-b}}{S_h}l_hC_l, & \text{otherwise} \end{cases} $$ where $C^_b$ is the cost of setting up the basecamp per kilometre from an airport(\$r bcv$helicopter_base_setup_cost_per_km$km^{-1}$), $S_h$ is the helicopter relocation speed in kilometres per hour (r bcv$helicopter_relocation_speed$km/hr$), and $l_h$ is the litres of fuel consumed per hour the helicopter is operational (r bcv$helicopter_l_per_hour$l/hr$).

In the next version we may want to put a cap based on crew size as the cost is capped by weight. So a further flight may require a smaller crew.

The cost of flying to the study area is: $$ C_{f} = \begin{cases} 2D_{s-a}C_D,& \text{if } D_{s-a} < D_{max} \ 2D_{s-b}C_D, & \text{otherwise} \end{cases} $$ where $C_D$ is the cost per kilometre: $$ C_D = \frac{l_hC_l + C_H}{S_h} $$

The cost of operating within the study area is: $$ C_{sa} = N\frac{l_hC_l + C_H}{n_hN_h}H_f $$ where $H_f$ is the hours flying within the study area per day, $n_h$ is the crew size, and $N_h$ is ARUs deployed per day per crew memeber.

The final cost for helicopter is: $$ C_H = C_{sa} + C_{f} + C_b $$

How does this look in practice? Lets look at what deploying an increasing number of ARUs looks like for study areas with just 1 of the three deployment methods. Here I've set up a pretend study area that is intially 250km from the airport, 100km from the basecamp, and with 200km from the airport to the basecamp. I've then compared this to a study area with just roads, just atv roads, a study area not requiring a basecamp, a study area requiring a secondary fuel cache. I've also included a mixed study area that required 30% truck, ATV, and helicopter. We see how the cost changes with the number of ARUs deployed.

maxARUs <- 200
 d_heli <- tibble(StudyAreaID  = "Helicopter", 
        pr= 0,
        sr = 0,
        dist_base_sa = 100,
        dist_dist_airport_sa = 250,
        dsit2airport_base = 200,
        AT = "Highway"
        )
runcost <- function(n,d) {map_df(1:n, estimate_cost_study_area,
                                   StudyAreas =d, 
                                   pr = pr, sr = sr, 
                                   dist_base_sa = dist_base_sa, 
                                   dist_airport_sa = dist_dist_airport_sa,
                                   dist2airport_base = dsit2airport_base, 
                                   vars = cost_vars, AirportType = "Highway")}

cost_heli <-  runcost(maxARUs, d_heli)
 d_heli2 <- mutate(d_heli,
                   StudyAreaID  = "Helicopter - No Base Camp",
        dist_base_sa = 100,
        dist_dist_airport_sa = 130,
        dsit2airport_base = 200,
        AT = "Highway"
        )
cost_heli2 <-  runcost(maxARUs, d_heli2)

 d_heli3 <- tibble(StudyAreaID  = "Helicopter - Fuel Cache", 
        pr= 0,
        sr = 0,
        dist_base_sa = 200,
        dist_dist_airport_sa = 250,
        dsit2airport_base = 200,
        AT = "Highway"
        )
cost_heli3 <-  runcost(maxARUs, d_heli3)
d_truck <- mutate(d_heli, pr = 1, StudyAreaID  = "Truck",
        AT = "Highway" )
cost_truck <- runcost(maxARUs, d_truck)
d_atv <- mutate(d_heli, sr = 1,StudyAreaID  = "ATV" )
cost_atv <- runcost(maxARUs, d_atv)

cost_mixed <- 
  mutate(d_heli, pr = 0.3, sr = 0.3, StudyAreaID = "Mixed", AT = "Highway") %>% 
  runcost(maxARUs,.)

cost_test <- 
bind_rows(cost_heli, cost_truck, cost_atv, cost_heli2,cost_heli3, cost_mixed) %>% 
  group_by(narus) %>% 
  mutate(logcost = log10(RawCost),
         scLogCost = logcost / max(logcost)) %>% ungroup
ggplot(cost_test, aes(narus,RawCost, colour = StudyAreaID )) + geom_line(size = 1) +
  scale_colour_viridis_d(direction = -1) +
  labs(colour = "Access type", x = "Number of ARUs deployed", y = "Raw Cost Value")
  # scale_y_continuous(trans = 'log1p')

ggplot(cost_test, aes(narus,scLogCost, colour = StudyAreaID )) + 
  geom_line(size = 1) +
  scale_colour_viridis_d(direction = -1) +
  labs(colour = "Access type", x = "Number of ARUs deployed", y = "Scaled Log Cost")

---

Baseline variables

BASSr::cost_vars %>% as_tibble() %>% 
  dplyr::select(-helicopter_airport_cost_per_l) %>% 
  pivot_longer(names_to = "Variable", values_to = "Value", cols = everything()) %>% 
  # BASSr::cost_vars$helicopter_airport_cost_per_l
  knitr::kable()

With current version, you can adjust cost of fuel based on airport type

  BASSr::cost_vars$helicopter_airport_cost_per_l %>% 
  knitr::kable()

dhope/BASSr documentation built on April 12, 2024, 9:54 p.m.