CEE514 Tidal Harmonic Analyzer Coastal engineering

NOAA Parser, Multi-Axis Zooming, Dual-Unit Pipeline & Harmonic Solver

Time Axis:
Units:
Drag & Drop NOAA / CSV Data File Here

Supports 100,000+ rows (6-min or 1-hr annual datasets)

Active Dataset Synthetic
Rows Count: 336
Time Step (Δt): 60.0 min
Start: t = 0.0 h
End: 14.0 days

CSV Auto-Detection & Mapping

Auto Units

10 Tidal Constituents

h(t) = Z0 + ∑ Ai cos(ωi t - φi)
Preset Sets:
Mode ω (°/h) Amp Ai (m) Phase φi (°)
M2 28.9841
S2 30.0000
N2 28.4397
K2 30.0821
K1 15.0411
O1 13.9430
P1 14.9589
Q1 13.3987
M4 57.9682
M6 86.9526
Rayleigh Resolution Status

Record length = 14 days. Minimum required to resolve S2 vs K2 is 182.6 days.

CEE514 Preset Profiles

Form Factor (F)
0.27 Mixed
Spring Range 2(M2 + S2)
3.20 m Est. Max
Shallow Distortion (M4 / M2)
0.042 Symmetric
Max Velocity Proxy (dh/dt)
0.61 m/h RMSE: 0.04m

Water Level Elevation Time-Series h(t)

Observed vs Least-Squares Reconstructed Fit & Residual Error

Observed Solved Fit Residual
Zoom Presets:
0h 336h

Harmonic Spectrum Decomposition

Derived Amplitudes (Ai) vs Target Values

Tidal Velocity Proxy (dh/dt)

Flood vs. Ebb duration asymmetry & Peak current proxy

Least-Squares Decomposition Solved Parameters

Constituent Angular Speed ωi (°/h) Target Amp (m) Solved Amp Ai (m) Target Phase (°) Solved Phase φi (°) Amp Error (%)

Estuary & Tidal Hydrodynamics Reference

1. Form Factor (F) Classification

F = (AK1 + AO1) / (AM2 + AS2)

  • Semidiurnal (F < 0.25): Two nearly equal high/low tides per day.
  • Mixed, semidiurnal (0.25 < F < 1.5): Significant diurnal inequality.
  • Mixed, diurnal (1.5 < F < 3.0): Diurnal dominant, occasional semidiurnal.
  • Diurnal (F > 3.0): One high and one low tide per day.

2. Shallow Water Distortion & Asymmetry

Distortion Ratio = AM4 / AM2 | Relative Phase = 2φM2 - φM4

  • Non-linear momentum terms (u · ∂u/∂x) transfer energy into overtides (M4, M6).
  • 2φM2 - φM4 ≈ 0° to 180°: Flood dominant (shorter, stronger flood tide).
  • 2φM2 - φM4 ≈ 180° to 360°: Ebb dominant (shorter, stronger ebb tide).

3. Rayleigh Criterion for Frequency Resolution

To separate two constituents with angular speeds ω1 and ω2, record duration T must satisfy:
T ≥ 360° / |ω1 - ω2|
For example, separating S2 (30.0000°/h) and K2 (30.0821°/h) requires T ≥ 182.6 days (6 months) to avoid matrix ill-conditioning.

4. Least-Squares Matrix Mechanics

Model: h(t) = a0 + ∑ [ai cos(ωi t) + bi sin(ωi t)]
Normal equations: (XTX) C = XT Y
Amplitude Ai = √(ai2 + bi2), Phase φi = atan2(bi, ai).

Tidal Asymmetry & Sediment Transport Dominance Engine

θ = 2φM2 - φM4
Relative Phase Difference (θ)
-90.0°

Distortion metric governing ebb/flood asymmetry duration

Shallow Distortion Ratio (AM4 / AM2)
0.0417

Values > 0.05 indicate significant shallow water distortion

Sediment Transport Regime
Flood-Dominant (Bedload Import)

Shorter flood duration yields stronger peak flood currents and net landward sediment transport.