Skip to content

Latest commit

 

History

History
237 lines (155 loc) · 6.46 KB

estimation_methods.md

File metadata and controls

237 lines (155 loc) · 6.46 KB

Estimation Methods

DIWASP provides five different methods for estimating directional wave spectra. Each method has different characteristics in terms of accuracy, speed, and suitability for different data types.

Method Overview

Method Speed Accuracy Noise Tolerance Best For
DFTM Very Fast Low Poor Quick overview
EMLM Fast Medium Poor Narrow spectra
IMLM Medium Good Medium General use
EMEP Variable Very Good Good Noisy data
BDM Slow Excellent Excellent Best accuracy

DFTM: Direct Fourier Transform Method

Reference: Barber (1961)

The DFTM is the simplest and fastest method. It directly integrates the cross-spectra with transfer functions.

Algorithm:

S(f, theta) ~ sum_n sum_m [H_n * H_m* * C_nm * exp(i * kx_nm)]

Characteristics:

  • Very fast, non-iterative
  • Good for initial overview of spectral shape
  • Poor directional resolution
  • Can produce negative energy (unphysical)
  • Poor tolerance of errors in data

When to use:

  • Quick sanity check of data
  • Initial exploration before using better methods
  • When computation speed is critical

EMLM: Extended Maximum Likelihood Method

Reference: Isobe et al. (1984)

The EMLM inverts the cross-spectral density matrix to improve directional resolution.

Algorithm:

E(theta) = 1 / sum_nm [H_n * H_m* * C_inv_nm * exp(i * kx_nm)]

Characteristics:

  • Fast method
  • Good accuracy with narrow unidirectional spectra
  • Can provide excellent accuracy per computation time in ideal cases
  • Poor tolerance of errors can lead to negative energy or failure
  • Sensitive to noise due to matrix inversion

When to use:

  • Clean data with narrow directional spreading
  • When moderate speed is needed with better resolution than DFTM

IMLM: Iterated Maximum Likelihood Method

Reference: Pawka (1983)

The IMLM iteratively refines the EMLM estimate.

Algorithm:

  1. Start with initial estimate (e.g., from EMLM)
  2. Iteratively update using weighted likelihood
  3. Apply relaxation to ensure convergence

Parameters:

  • max_iter: Number of improvement iterations (default 100)
  • gamma: Step size relaxation (default 0.1)
  • alpha: Convergence factor (default 0.1)

Characteristics:

  • Computation time directly depends on iteration count
  • Reduces anomalies like negative energy from EMLM
  • Can overestimate peaks by overcorrecting
  • Quality depends on initial EMLM solution

When to use:

  • General purpose estimation
  • When EMLM gives reasonable but imperfect results
  • Good balance of speed and accuracy

EMEP: Extended Maximum Entropy Principle

Reference: Hashimoto et al. (1993)

The EMEP uses model selection based on the Akaike Information Criterion (AIC).

Algorithm:

  1. Separate co- and quadrature components from cross-spectra
  2. Use cosine/sine basis expansion with unknown coefficients
  3. Iteratively fit models of increasing order
  4. Select best model using AIC

Characteristics:

  • Good all-round method that accounts for errors
  • Computation time is highly variable
  • Can be as fast as IMLM with superior results
  • Low energies at spectral tails can slow computation
  • Automatic model order selection provides robustness

When to use:

  • Default recommended method
  • Data with significant noise or errors
  • When robustness is more important than speed
  • Multi-modal spectra

BDM: Bayesian Direct Method

Reference: Hashimoto and Kobune (1987)

The BDM uses Bayesian inference with Tikhonov regularization.

Algorithm:

  1. Log-transform spectral density: x = log(S)
  2. Solve inverse problem with Tikhonov regularization
  3. Use QR decomposition for numerical stability
  4. Select regularization via Akaike Bayesian IC (ABIC)

Characteristics:

  • Overall best accuracy
  • Very computationally intensive
  • Natural smoothing via Laplacian regularization
  • Robust to noise
  • Can have problems with three-quantity measurements (PUV, heave-roll-pitch)

When to use:

  • When accuracy is paramount and time permits
  • Noisy or complex data
  • Research applications requiring best estimates

Choosing a Method

Decision Flowchart

Is this a quick sanity check?
├── Yes → DFTM
└── No → Is the data clean with narrow spreading?
         ├── Yes → EMLM or IMLM
         └── No → Is computation time critical?
                  ├── Yes → EMEP
                  └── No → BDM

Tips for Each Method

All methods:

  • Reduce frequency resolution to increase speed

EMEP/BDM:

  • Reduce directional resolution (dres) to increase speed
  • Optimal iteration count before relaxation varies by dataset

Testing: Use synthetic data from makespec to test methods for your specific instrument configuration before processing real data.

Resolution Parameters

EP.nfft - FFT Length

Controls frequency resolution. Higher values give finer frequency bins but require more data and computation.

frequency_resolution = fs / nfft

EP.dres - Directional Resolution

Number of directional bins covering 360 degrees. Default is 180 (2-degree bins).

Reducing this value dramatically improves speed for EMEP and BDM.

EP.iter - Iterations

For IMLM: Number of improvement corrections at each frequency. Directly affects computation time.

For EMEP/BDM: Limit before computation "relaxes" the iterative calculation. Reducing doesn't necessarily improve speed if the algorithm converges before reaching the limit.

EP.smooth - Smoothing

Applies 2D smoothing to remove unphysical spikes. Recommended to keep enabled (default).

Troubleshooting

Garbage Output

If you get nonsensical results:

  1. Try DFTM first - it rarely fails completely
  2. If DFTM gives garbage, check your inputs
  3. Verify sensor positions and types are correct
  4. Check data quality and synchronization

Slow Computation (EMEP/BDM)

Low spectral energies at high/low frequencies can cause slow convergence:

  1. Reduce directional resolution
  2. Limit frequency range to energetic portion
  3. Reduce iteration limit (may reduce quality)

Negative Energy

If you see negative spectral values:

  1. Switch from DFTM/EMLM to EMEP or BDM
  2. These methods naturally prevent negative values
  3. Check data for errors or contamination

Matrix Warnings

Warnings about matrix conditioning during EMLM or IMLM:

  1. Usually handled internally
  2. Switch to EMEP or BDM for more robust handling
  3. May indicate too few sensors or poor geometry