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)"
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).
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 |
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 |
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 |
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
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 |
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 |
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 |
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).
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 |
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 |
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 |
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).
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 |
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 |
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 |
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).
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 |
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 |
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 |
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.