From 5cd7f2053f29a8d6a66b2eeda3ecc003ca4a7d4a Mon Sep 17 00:00:00 2001
From: Alexander Barth <barth.alexander@gmail.com>
Date: Thu, 4 Jul 2024 09:38:29 +0200
Subject: [PATCH] add PhysOcean.rayleigh_criterion

---
 src/tides.jl       | 27 +++++++++++++++++++++++++++
 test/test_tides.jl | 12 ++++++++++++
 2 files changed, 39 insertions(+)

diff --git a/src/tides.jl b/src/tides.jl
index 564065e..d5070a8 100644
--- a/src/tides.jl
+++ b/src/tides.jl
@@ -99,3 +99,30 @@ function ep2ap(semimajor, eccentricity, inclination, phase)
 end
 
 export ep2ap
+
+"""
+    Tmin = PhysOcean.rayleigh_criterion(f1,f2)
+
+Compute the minimum duration `Tmin` to separate the frequency `f1` and `f2`
+following the Rayleigh criterion.
+`Tmin` has the inverse of the units of `f1` and `f2`.
+
+For example to resolve the M2 and S2 tides, the duration of the time series has
+to be at least 14.765 days:
+
+```
+using PhysOcean
+f_M2 = 12.4206 # h⁻¹
+f_S2 = 12 # h⁻¹
+Tmin = PhysOcean.rayleigh_criterion(f_M2,f_S2)
+Tmin/24
+# output 14.765
+```
+
+Reference:
+
+Bruce B. Parker, [Tidal Analysis and Prediction](https://web.archive.org/web/20240626033634/https://tidesandcurrents.noaa.gov/publications/Tidal_Analysis_and_Predictions.pdf), NOAA Special Publication NOS CO-OPS 3, page 84
+"""
+function rayleigh_criterion(f₁,f₂)
+    1/abs(1/f₁-1/f₂)
+end
diff --git a/test/test_tides.jl b/test/test_tides.jl
index a4d393f..d85453f 100644
--- a/test/test_tides.jl
+++ b/test/test_tides.jl
@@ -32,3 +32,15 @@ amplitude_u2,phase_u2,amplitude_v2,phase_v2 = ep2ap(semimajor, eccentricity, inc
 @test amplitude_v ≈ amplitude_v2
 @test phase_u     ≈ phase_u2
 @test phase_v     ≈ phase_v2
+
+
+
+# page 82 from
+# https://web.archive.org/web/20240626033634/https://tidesandcurrents.noaa.gov/publications/Tidal_Analysis_and_Predictions.pdf
+
+f_M2 = 12.4206
+f_S2 = 12
+Tmin = PhysOcean.rayleigh_criterion(f_M2,f_S2)
+
+# Table 3.1
+@test Tmin/24 ≈ 14.765 atol=0.001