Background

This R Markdown documents the preparation of the observed buoy data recorded off the Florida Panhandle. The available record from 3 buoys were downloaded from the National Data Buoy Center (https://www.ndbc.noaa.gov/):

The text files were brought into Excel for cleaning. Date-Time gaps were filled in with empty cells in order to create a continuous time-series. Cells with error flags (i.e., 99, 999, 9999, as appropriate) were replaced with empty cells so as not to interfere with later analyses. The final cleaned Excel files were then brought into R for further analysis.

This analysis uses the following libraries:

library(dplyr)
library(knitr)
library(plotrix)
library(spatstat)
## [1] "This RMarkdown and the included analyses were built using R version 4.0.4 (2021-02-15)"

All Available Hourly Data

Following Stockdon et al. (2006) and the procedure utilized in Ware et al. 2019, the dominant wave periods were first transformed into wavelengths at each buoy location using linear wave theory:

\(L_0 = 9.8\frac{T^2}{2\pi}tanh(\frac{2\pi D}{L_0})\)

where \(L_0\) is the deep-water wavelength, \(T\) is the wave period, and \(D\) is the buoy depth.

Wave heights for intermediate-depth waves were then reverse shoaled to deep-water equivalents:

\(\kappa = \frac{2\pi}{L_i}\) (\(\kappa\) - wave number, \(L_i\) - intermediate wavelength)

\(K_s = \sqrt\frac{2cosh(\kappa D)^2}{sinh(2 \kappa D) + 2\kappa D}\) (\(K_s\) - shoaling coefficient, \(\kappa\) - wave number, \(D\) - buoy depth)

\(H_0 = \frac{H_i}{K_s}\) (\(H_0\) - deep-water wave height, \(H_i\) - intermediate wave height, \(K_s\) - shoaling coefficient)

Stockdon et al. (2006) Empirical parameterization of setup, swash, and runup. Coastal Engineering 53: 573-588
Ware et al. (2019) Using wave runup modeling to inform coastal species management: An example application for sea turtle nest relocation. Ocean and Coastal Management 173: 17-25.

Below is a visualization of the available oceanographic data from the respective buoys. Note that there are several small and a few large gaps in the various records. Most waves reported by the 3 buoys are 0.824-1.016 m high with a mean wave period of 5.275-5.647 sec. Median values are lower than mean values (0.70-0.83 m high, 5.26-5.56 sec long) due to the effect of large wave height/period observations during storms. There are also distinctive peaks in the tail of the wave period distribution. These peaks most likely correspond to various storm events.

Below is a summary of the available oceanographic data from each buoy. Though most waves are between 0.46-0.52 m and 1.020-1.310 m high (25th to 75th percentile) and 4.0-4.55 sec and 6.25-6.67 sec long (25th to 75th percentile), the maximum values reported were highly variable between buoys (6.0-12.0 m high and 23.53-25.00 sec long).

Orange Beach Buoy - Hourly, 2009 to 2019
Wave Height (m) Wave Period (sec) Wave Direction (deg) Water Temp (deg C)
Mean 0.824 5.275 162.793 23.93
SE 0.002 0.006 NA 0.02
Median 0.700 5.260 NA 24.40
N 79597.000 79616.000 79611.000 76213.00
Min 0.240 2.150 NA 8.00
Max 6.260 23.530 NA 33.70
25th Percentile 0.460 4.000 122.260 19.60
75th Percentile 1.020 6.250 194.910 28.70
2.5th Percentile 0.280 2.740 22.840 14.30
97.5th Percentile 2.150 8.330 326.450 31.00
Pensacola Buoy - Hourly, 1998 to 2019
Wave Height (m) Wave Period (sec) Wave Direction (deg) Water Temp (deg C)
Mean 1.016 5.647 180.382 25.24
SE 0.002 0.004 NA 0.01
Median 0.830 5.560 NA 25.10
N 167637.000 167637.000 98744.000 174477.00
Min 0.000 0.000 NA 8.20
Max 12.050 23.530 NA 34.40
25th Percentile 0.520 4.550 112.030 22.10
75th Percentile 1.310 6.670 229.690 28.70
2.5th Percentile 0.260 3.130 17.420 19.29
97.5th Percentile 2.790 9.090 345.760 30.80
West Tampa - Hourly, 1998 to 2019
Wave Height (m) Wave Period (sec) Wave Direction (deg) Water Temp (deg C)
Mean 0.938 5.406 148.263 24.50
SE 0.002 0.004 NA 0.01
Median 0.750 5.260 NA 24.50
N 152215.000 152351.000 150920.000 164456.00
Min 0.000 0.000 NA 10.00
Max 8.020 25.000 NA 33.80
25th Percentile 0.470 4.350 98.120 21.00
75th Percentile 1.200 6.250 248.730 28.30
2.5th Percentile 0.240 2.940 12.060 17.70
97.5th Percentile 2.710 9.090 344.020 30.50

Bin wave height and direction conditions by buoy

Wave height and direction observations were combined into variable-width bins to classify the most common combinations at each buoy, following Long et al. (2014). For wave height, bins were separated every 0.5 m up to 2.0 m, then a catch-all bin up to 12.0 m. For direction, bins were separated every 22.5 degrees up to 360 degrees. This results in 80 bins overall. The most populous bin for Orange Beach (7.7%) was Bin 37 (0.5 <= Wave Height (m) < 1.0 & 157.5 <= direction (degrees) < 180.0). For Pensacola and West Tampa, Bin 41 (0 <= Wave Height (m) < 0.5 & 180.0 <= direction (degrees) < 202.5) was the most populous (5.3% and 4.7%, respectively).

Long et al. (2014) A probabilistic method for construction wave time-series at inshore locations using model scenarios. Coastal Engineering 89: 53-62

Proportion of Observations - Orange Beach #42012
0 0.5 1 1.5 2
0 0.005 0.015 0.004 0.000 0.000
22.5 0.006 0.015 0.004 0.000 0.000
45 0.008 0.015 0.003 0.000 0.000
67.5 0.015 0.028 0.009 0.001 0.000
90 0.016 0.033 0.016 0.007 0.003
112.5 0.019 0.047 0.029 0.012 0.008
135 0.041 0.070 0.034 0.013 0.010
157.5 0.051 0.077 0.035 0.012 0.007
180 0.038 0.049 0.018 0.006 0.003
202.5 0.024 0.024 0.005 0.002 0.002
225 0.025 0.026 0.004 0.001 0.001
247.5 0.020 0.019 0.005 0.002 0.001
270 0.009 0.009 0.003 0.001 0.000
292.5 0.004 0.004 0.001 0.000 0.000
315 0.002 0.006 0.002 0.000 0.000
337.5 0.004 0.010 0.003 0.000 0.000
Proportion of Observations - Pensacola #42039
0 0.5 1 1.5 2
0 0.006 0.012 0.008 0.003 0.002
22.5 0.005 0.010 0.007 0.003 0.002
45 0.006 0.012 0.006 0.003 0.002
67.5 0.011 0.028 0.019 0.011 0.009
90 0.014 0.034 0.022 0.012 0.008
112.5 0.011 0.028 0.017 0.008 0.005
135 0.019 0.038 0.021 0.010 0.008
157.5 0.036 0.049 0.027 0.011 0.009
180 0.053 0.047 0.021 0.007 0.007
202.5 0.020 0.020 0.009 0.003 0.003
225 0.012 0.016 0.006 0.002 0.003
247.5 0.010 0.018 0.008 0.004 0.007
270 0.010 0.016 0.008 0.004 0.008
292.5 0.008 0.014 0.008 0.005 0.006
315 0.007 0.014 0.010 0.007 0.006
337.5 0.006 0.012 0.010 0.007 0.005
Proportion of Observations - West Tampa #42036
0 0.5 1 1.5 2
0 0.012 0.015 0.010 0.006 0.003
22.5 0.009 0.019 0.011 0.006 0.004
45 0.011 0.023 0.015 0.008 0.005
67.5 0.013 0.029 0.017 0.008 0.003
90 0.012 0.024 0.012 0.004 0.002
112.5 0.009 0.019 0.008 0.002 0.002
135 0.020 0.034 0.012 0.004 0.003
157.5 0.023 0.036 0.017 0.007 0.006
180 0.047 0.044 0.021 0.007 0.005
202.5 0.041 0.033 0.012 0.004 0.003
225 0.016 0.019 0.007 0.003 0.003
247.5 0.015 0.023 0.012 0.006 0.010
270 0.018 0.025 0.013 0.007 0.012
292.5 0.015 0.017 0.008 0.005 0.005
315 0.009 0.009 0.005 0.003 0.003
337.5 0.006 0.010 0.007 0.005 0.004

Nesting Season Only - Hourly Data

Below are visualizations of wave height and dominant wave period only during the nesting season (May through October). Mean wave heights (0.724-0.841 m) were depressed compared to full-year averages while wave periods were largely unaffected (5.215-5.553 sec). Median values are lower than mean values (0.590-0.650 m high, 5.00-5.26 sec long) due to the effect of large wave height/period observations during storms. Note that the maximum observed wave height and wavelengths were recorded during the nesting season.

Below is a summary of the available oceanographic data from each buoy. Though most waves are between 0.40-0.42 m and 0.88-1.03 m high (25th to 75th percentile) and between 4.00-4.55 sec and 6.25 sec long (25th to 75th percentile), the maximum values reported were highly variable between buoys (6.0-12.0 m high and 23.53-25.00 sec long).

Orange Beach Buoy - Hourly, 2009 to 2019 Nesting Season
Wave Height (m) Wavelength (m) Wave Direction (deg) Water Temp (deg C)
Mean 0.724 5.215 167.272 28.12
SE 0.002 0.008 NA 0.01
Median 0.590 5.260 NA 28.50
N 41058.000 41066.000 41063.000 40016.00
Min 0.240 2.150 NA 20.60
Max 6.260 23.530 NA 33.70
25th Percentile 0.420 4.000 132.560 26.70
75th Percentile 0.880 6.250 204.300 29.70
2.5th Percentile 0.270 2.740 44.620 23.40
97.5th Percentile 1.910 9.090 286.840 31.40
Pensacola Buoy - Hourly, 1998 to 2019 Nesting Season
Wave Height (m) Wavelength (m) Wave Direction (deg) Water Temp (deg C)
Mean 0.841 5.553 184.359 28.22
SE 0.002 0.006 NA 0.01
Median 0.650 5.260 NA 28.60
N 84627.000 84627.000 49433.000 88633.00
Min 0.000 0.000 NA 8.20
Max 12.050 23.530 NA 34.40
25th Percentile 0.430 4.550 120.160 26.90
75th Percentile 1.030 6.250 217.650 29.70
2.5th Percentile 0.250 3.030 30.600 23.70
97.5th Percentile 2.500 9.090 335.740 31.20
West Tampa - Hourly, 1998 to 2019 Nesting Season
Wave Height (m) Wavelength (m) Wave Direction (deg) Water Temp (deg C)
Mean 0.795 5.276 197.995 27.86
SE 0.002 0.006 NA 0.01
Median 0.610 5.000 NA 28.30
N 76060.000 76155.000 75108.000 83224.00
Min 0.000 0.000 NA 19.80
Max 8.020 25.000 NA 33.80
25th Percentile 0.400 4.170 110.020 26.60
75th Percentile 0.980 6.250 241.180 29.40
2.5th Percentile 0.220 2.940 17.250 22.90
97.5th Percentile 2.430 9.090 330.760 30.90

Bin wave height and direction conditions by buoy within the nesting season

Wave height and direction observations were combined into variable-width bins to classify the most common combinations at each buoy, as above for the full year. During the nesting season, the most populous bin for Orange Beach (7.7%) was Bin 32 (0.5 <= Wave Height (m) < 1.0 & 132.0 <= direction (degrees) < 157.5). For Pensacola and West Tampa, Bin 41 (0 <= Wave Height (m) < 0.5 & 180.0 <= direction (degrees) < 202.5) was the most populous (8.5% and 6.8%, respectively).

Proportion of Observations - Orange Beach #42012
0 0.5 1 1.5 2
0 0.005 0.006 0.001 0.000 0.000
22.5 0.005 0.007 0.001 0.000 0.000
45 0.008 0.008 0.001 0.000 0.000
67.5 0.014 0.017 0.005 0.001 0.000
90 0.016 0.028 0.013 0.006 0.003
112.5 0.023 0.054 0.028 0.009 0.005
135 0.058 0.077 0.029 0.007 0.006
157.5 0.068 0.074 0.024 0.005 0.004
180 0.051 0.056 0.015 0.005 0.003
202.5 0.035 0.032 0.004 0.002 0.001
225 0.040 0.042 0.005 0.000 0.000
247.5 0.030 0.023 0.003 0.000 0.000
270 0.010 0.006 0.001 0.000 0.000
292.5 0.003 0.002 0.000 0.000 0.000
315 0.002 0.004 0.001 0.000 0.000
337.5 0.003 0.005 0.001 0.000 0.000
Proportion of Observations - Pensacola #42039
0 0.5 1 1.5 2
0 0.007 0.007 0.003 0.001 0.001
22.5 0.005 0.006 0.003 0.001 0.002
45 0.007 0.009 0.004 0.002 0.001
67.5 0.013 0.024 0.016 0.009 0.009
90 0.016 0.034 0.022 0.012 0.008
112.5 0.015 0.034 0.016 0.008 0.006
135 0.029 0.045 0.016 0.006 0.006
157.5 0.056 0.048 0.014 0.005 0.005
180 0.085 0.053 0.016 0.006 0.006
202.5 0.031 0.027 0.009 0.003 0.003
225 0.018 0.021 0.006 0.002 0.002
247.5 0.016 0.024 0.008 0.002 0.002
270 0.017 0.023 0.007 0.002 0.001
292.5 0.012 0.014 0.004 0.002 0.001
315 0.008 0.010 0.004 0.002 0.001
337.5 0.007 0.008 0.004 0.002 0.001
Proportion of Observations - West Tampa #42036
0 0.5 1 1.5 2
0 0.014 0.009 0.005 0.002 0.001
22.5 0.010 0.014 0.006 0.004 0.005
45 0.012 0.019 0.012 0.006 0.005
67.5 0.014 0.027 0.018 0.007 0.004
90 0.013 0.027 0.015 0.004 0.003
112.5 0.012 0.023 0.009 0.002 0.003
135 0.032 0.044 0.012 0.003 0.003
157.5 0.035 0.034 0.011 0.003 0.004
180 0.068 0.039 0.012 0.003 0.004
202.5 0.050 0.033 0.009 0.004 0.003
225 0.022 0.024 0.007 0.003 0.003
247.5 0.021 0.028 0.011 0.003 0.003
270 0.028 0.032 0.012 0.002 0.002
292.5 0.024 0.019 0.004 0.001 0.001
315 0.012 0.008 0.002 0.001 0.001
337.5 0.007 0.007 0.003 0.001 0.001

Bin wave height and wave period conditions by buoy within the nesting season

Wave height and wave period observations were combined into variable-width bins to classify the most common combinations at each buoy. For wave height, bins were separated every 0.5 m up to 2.0 m, then a catch-all bin up to 12.0 m. For wave period, bins were separated every 1.0 sec from 3.0 sec to 9.0 sec, with catch-all bins from 0.0-3.0 sec and 9.0-25.0 sec. This results in 24 high-resolution bins to cover the majority of the data and 40 bins overall. The majority of Orange Beach observations (13.6%) fall into Bin 17 (0.5 <= Wave Height (m) < 1.0 & 5.0 <= Wave Period (sec) < 6.0). This is the same for Pensacola (15.2%), but not for West Tampa. West Tampa (15.6%) was predominantly in Bin 12 (0.5 <= Wave Height (m) < 1.0 & 4.0 <= Wave Period (sec) < 5.0).

Proportion of Observations - Orange Beach #42012
0 0.5 1 1.5 2
0 0.052 0.004 0.000 0.000 0.000
3 0.101 0.083 0.001 0.000 0.000
4 0.071 0.116 0.016 0.000 0.000
5 0.078 0.136 0.046 0.008 0.000
6 0.036 0.065 0.040 0.012 0.003
7 0.021 0.027 0.021 0.010 0.007
8 0.006 0.005 0.004 0.003 0.003
9 0.007 0.005 0.003 0.003 0.008
Proportion of Observations - Pensacola #42039
0 0.5 1 1.5 2
0 0.021 0.001 0.000 0.000 0.000
3 0.073 0.041 0.001 0.000 0.000
4 0.083 0.131 0.015 0.000 0.000
5 0.061 0.152 0.085 0.015 0.001
6 0.030 0.036 0.041 0.029 0.010
7 0.027 0.022 0.012 0.013 0.020
8 0.016 0.008 0.003 0.002 0.006
9 0.017 0.010 0.003 0.002 0.013
Proportion of Observations - West Tampa #42036
0 0.5 1 1.5 2
0 0.029 0.001 0.000 0.000 0.000
3 0.096 0.044 0.000 0.000 0.000
4 0.099 0.156 0.018 0.000 0.000
5 0.058 0.127 0.091 0.021 0.002
6 0.034 0.028 0.023 0.019 0.014
7 0.035 0.017 0.011 0.006 0.013
8 0.011 0.006 0.002 0.002 0.005
9 0.009 0.005 0.002 0.002 0.012

Intra-Annual Distributions

Below is the monthly and weekly mean wave height and wave period at each buoy derived from the hourly data. Note the increasing trend in wave height late in the nesting season, corresponding with typical hatchling emergence, and the oscillation in wave period throughout the nesting season.