Aerial Survey Analysis with tidycreel

Introduction

Aerial creel surveys estimate total angler effort by conducting an instantaneous count of anglers on the water from a low-flying aircraft. Because the aircraft captures a snapshot of angler activity at a single moment, the count must be expanded to total effort using the hours the fishery is open (h_open) and the mean trip duration of anglers on the water (L_bar). The basic estimator is:

$\hat{E} = N_{obs} \times \frac{h_{open}}{v}$

where $N_{obs}$ is the observed (instantaneous) angler count, $h_{open}$ is the number of hours the fishery is open per day, and $v$ is the detection probability — the proportion of anglers present that are detected from the aircraft. The mean trip duration $\bar{L}$ is estimated from ground interviews and enters the catch rate estimation step rather than the effort expansion step.

When not all anglers are visible from the air — for example, anglers fishing under tree cover or in enclosed shelters — a visibility correction adjusts the count upward. If observers detect only 85% of anglers present, the corrected effort estimate is scaled by $1 / 0.85 \approx 1.18$ , yielding a higher and more accurate total. The visibility_correction argument to creel_design() carries $v$ , and is required for an aerial design: pass "none" to state explicitly that no correction applies.

$v$ is the reciprocal of the published ratio

Field studies do not report $v$ directly. The standard ground-truthing method reports the ratio

$r = \frac{\text{ground count}}{\text{aerial count}}$

which is greater than 1 whenever the aircraft undercounts — Smucker et al. (2010) report $r = 2.69$ for shore anglers. Because visibility_correction is a probability, convert before supplying it:

$v = 1 / r \qquad\text{so}\qquad r = 2.69 \;\longrightarrow\; v = 0.372$

Passing $r$ directly is rejected by the (0, 1] check rather than silently accepted, because the two parameterisations differ by a factor of $r^2$ in the effort estimate.

The correction is estimated, so it carries uncertainty

$v$ is estimated from paired air–ground counts, and the standard field method reports its standard error as routine output. Supply it as visibility_se — on the same probability scale — and that uncertainty is propagated into the effort SE. For an SE published on the ratio scale, convert with $SE(v) = SE(r) / r^2$ .

Because one estimate of $v$ divides every scaled count, it is a shared multiplier: its contribution enters once at the total and does not shrink as more flights are flown. Omitting visibility_se reports the component as absent rather than as zero — a zero would be indistinguishable from never having propagated it at all.

Example Data

This vignette uses two built-in datasets representing a hypothetical summer walleye and bass fishery at a Nebraska reservoir in June-July 2024.

library(tidycreel)

data(example_aerial_counts)
data(example_aerial_interviews)

head(example_aerial_counts)
#>         date day_type n_anglers
#> 1 2024-06-03  weekday        39
#> 2 2024-06-05  weekday        32
#> 3 2024-06-07  weekday        29
#> 4 2024-06-08  weekend        45
#> 5 2024-06-09  weekend        51
#> 6 2024-06-10  weekday        34
head(example_aerial_interviews)
#>         date day_type trip_status hours_fished walleye_catch walleye_kept
#> 1 2024-06-03  weekday    complete          3.4             3            2
#> 2 2024-06-03  weekday    complete          3.2             0            0
#> 3 2024-06-03  weekday    complete          2.5             0            0
#> 4 2024-06-05  weekday    complete          4.9             1            0
#> 5 2024-06-05  weekday    complete          2.2             1            0
#> 6 2024-06-05  weekday    complete          2.3             1            0
#>   bass_catch bass_kept
#> 1          0         0
#> 2          0         0
#> 3          0         0
#> 4          1         0
#> 5          0         0
#> 6          1         1

example_aerial_counts contains 16 sampling days (one overflight per day), each recording an instantaneous count of anglers on the water. Weekday counts range from 15 to 40 anglers; weekend counts range from 40 to 80. The example_aerial_interviews dataset contains 48 angler interviews (3 per sampling day) with trip duration in hours_fished and catch by species.

Design Construction

Build an aerial survey design with creel_design(). The h_open argument is required for aerial surveys — it specifies the number of hours the fishery is open each day, which sets the expansion factor for the instantaneous count.

# Build the survey calendar from the unique count dates
aerial_cal <- data.frame(
  date = example_aerial_counts$date,
  day_type = example_aerial_counts$day_type,
  stringsAsFactors = FALSE
)

design <- creel_design(
  aerial_cal,
  date        = date,
  strata      = day_type,
  survey_type = "aerial",
  visibility_correction = "none",
  angler_ratio = 1,
  angler_ratio_se = 0,
  h_open      = 14
)

print(design)
#> 
#> ── Creel Survey Design ─────────────────────────────────────────────────────────
#> Type: "aerial"
#> Date column: date
#> Strata: day_type
#> Calendar: 16 days (2024-06-03 to 2024-07-06)
#> day_type: 2 levels
#> Counts: "none"
#> Interviews: "none"
#> Sections: "none"
#> 
#> ── Aerial Survey Design ──
#> 
#> Hours open (h_open): 14
#> Visibility correction: "none" (declared; SE is "NA")
#> Angler-to-people ratio: 1
#> Angler ratio SE: 0

The printed design confirms the survey type, h_open, and the number of sampling days in each stratum.

Adding Count Data and Estimating Effort

Attach the aerial count data with add_counts(). The n_anglers column is auto-detected as the count variable.

design <- add_counts(design, example_aerial_counts)
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability

Aerial effort estimation requires interview data to be attached before calling estimate_effort(), because the estimator uses the mean trip duration ( $\bar{L}$ ) from ground interviews to confirm the expansion factor. Attach the interview data with add_interviews(), then estimate total effort.

design <- suppressWarnings(add_interviews(
  design,
  example_aerial_interviews,
  catch       = walleye_catch,
  effort      = hours_fished,
  trip_status = trip_status
))
#> ℹ Added 48 interviews: 48 complete (100%), 0 incomplete (0%)

effort <- suppressWarnings(estimate_effort(design))
print(effort)
#> 
#> ── Creel Survey Estimates ──────────────────────────────────────────────────────
#> Method: aerial_total
#> Variance: Taylor linearization
#> Confidence level: 95%
#> Effort target: sampled_days
#> Unit: angler-hours
#> Count-sampling SE: 658.3 (known, but se is `NA`)
#> within_day: 0 (known, but se is `NA`)
#> visibility: NA (unknown, so se is `NA`)
#> angler_ratio: 0 (known, but se is `NA`)
#> 
#> # A tibble: 1 × 7
#>   estimate    se se_between se_within ci_lower ci_upper     n
#>      <dbl> <dbl>      <dbl>     <dbl>    <dbl>    <dbl> <int>
#> 1     8918    NA       658.         0       NA       NA    16

The estimate column is the projected total angler-hours over the full survey period, and se_between quantifies between-day variability in the instantaneous counts.

se, ci_lower and ci_upper are NA, and that is the correct output for this design rather than a gap in it. creel_design() above was given visibility_correction = "none", which declares that no detection study was done. The between-day component is known, but a component of the total’s uncertainty is not, and a standard error that silently omitted it would describe a survey more precise than this one. NA says the uncertainty was never propagated; 0 would say it was measured and found to be nothing. The next section supplies a correction and its standard error, and the interval appears.

Visibility Correction

When aerial observers cannot detect all anglers on the water, the raw count underestimates true effort. Supply a visibility_correction to creel_design() to account for this. A value of 0.85 means observers detected 85% of the anglers actually present; the effort estimate is scaled up by $1 / 0.85$ .

Here the correction is accompanied by visibility_se, so the reported effort SE includes the uncertainty in the correction itself rather than treating 0.85 as exactly known.

design_corr <- creel_design(
  aerial_cal,
  date = date,
  strata = day_type,
  survey_type = "aerial",
  h_open = 14,
  visibility_correction = 0.85,
  angler_ratio = 1,
  angler_ratio_se = 0,
  visibility_se = 0.04
)

design_corr <- add_counts(design_corr, example_aerial_counts)
#> Warning in svydesign.default(ids = psu_formula, strata = strata_formula, : No
#> weights or probabilities supplied, assuming equal probability
design_corr <- suppressWarnings(add_interviews(
  design_corr,
  example_aerial_interviews,
  catch       = walleye_catch,
  effort      = hours_fished,
  trip_status = trip_status
))
#> ℹ Added 48 interviews: 48 complete (100%), 0 incomplete (0%)

effort_corr <- suppressWarnings(estimate_effort(design_corr))
print(effort_corr)
#> 
#> ── Creel Survey Estimates ──────────────────────────────────────────────────────
#> Method: aerial_total
#> Variance: Taylor linearization
#> Confidence level: 95%
#> Effort target: sampled_days
#> Unit: angler-hours
#> Count-sampling SE: 774.4 (included in se)
#> within_day: 0 (included in se)
#> visibility: 493.7 (included in se)
#> angler_ratio: 0 (included in se)
#> 
#> # A tibble: 1 × 7
#>   estimate    se se_between se_within ci_lower ci_upper     n
#>      <dbl> <dbl>      <dbl>     <dbl>    <dbl>    <dbl> <int>
#> 1   10492.  918.       774.         0    8522.   12462.    16

Comparing the two estimates: the corrected effort is higher than the uncorrected estimate because the visibility correction inflates the count to account for undetected anglers.

cat(
  "Uncorrected effort:", round(effort$estimate[[1]], 0), "angler-hours\n",
  "Corrected effort (v=0.85):", round(effort_corr$estimate[[1]], 0), "angler-hours\n"
)
#> Uncorrected effort: 8918 angler-hours
#>  Corrected effort (v=0.85): 10492 angler-hours

Interview-Based Catch Estimation

Aerial designs use the same interview workflow as other tidycreel designs. The catch rate estimator computes CPUE (walleye per angler-hour) from the complete-trip interviews already attached to the design.

catch_rate <- suppressWarnings(estimate_catch_rate(design))
#> ℹ Using complete trips for CPUE estimation
#>   (n=48, 100% of 48 interviews) [default]
print(catch_rate)
#> 
#> ── Creel Survey Estimates ──────────────────────────────────────────────────────
#> Method: Ratio-of-Means CPUE
#> Variance: Taylor linearization
#> Confidence level: 95%
#> Unit: fish/party-hour
#> 
#> # A tibble: 1 × 5
#>   estimate     se ci_lower ci_upper     n
#>      <dbl>  <dbl>    <dbl>    <dbl> <int>
#> 1    0.413 0.0601    0.295    0.531    48

estimate_total_catch() multiplies the CPUE estimate by the total effort estimate to project total walleye catch over the survey period.

total_catch <- suppressWarnings(estimate_total_catch(design))
print(total_catch)
#> 
#> ── Creel Survey Estimates ──────────────────────────────────────────────────────
#> Method: Total Catch (Effort × CPUE)
#> Variance: Taylor linearization
#> Confidence level: 95%
#> Effort target: sampled_days
#> 
#> # A tibble: 1 × 5
#>   estimate    se ci_lower ci_upper     n
#>      <dbl> <dbl>    <dbl>    <dbl> <int>
#> 1     251.  45.1     160.     341.    48

The delta-method standard error on total catch accounts for variance in both the effort estimate and the CPUE estimate.

Summary

The complete aerial survey workflow in tidycreel consists of four steps:

creel_design(..., survey_type = "aerial", visibility_correction = v, h_open = N) — define the survey with the required h_open expansion factor and the required visibility_correction (a detection probability, or "none" to declare that no correction applies). Add visibility_se to propagate the correction’s own uncertainty.
add_counts(design, counts) — attach the instantaneous angler count data from each overflight.
add_interviews(design, interviews, catch = ..., effort = hours_fished, ...) — attach ground interview data for catch rate estimation.
estimate_effort(), estimate_catch_rate(), estimate_total_catch() — run the estimators.

All estimators return creel_estimates objects with point estimates, standard errors, and 95% confidence intervals. Use print() to display results.

References

Jones, C. M., & Pollock, K. H. (2012). Recreational survey methods: estimation of effort, harvest, and abundance. Chapter 19 in Fisheries Techniques (3rd ed.), pp. 883-919. American Fisheries Society.
Malvestuto, S. P. (1996). Sampling the recreational angler. Chapter 20 in Fisheries Techniques (2nd ed.), pp. 591-623. American Fisheries Society.
Pollock, K. H., Jones, C. M., & Brown, T. L. (1994). Angler Survey Methods and Their Applications in Fisheries Management. American Fisheries Society Special Publication 25. Chapter 12: Aerial counts.