Spectral Fit Module

Compute spectral and directional model fit parameters for wave system data

 

Spectral Fit Module

The  Spectral Fit Module computes a variety of 1D fit and 2D fit parameters suitable for engineering design applications.  Specific features include:

  • JONSWAP, Gaussian, Lognormal and Ochi-Hubble 1D partition fits
  • Windsea, swell, and Cos2n directional distributions
  • Composite full-spectrum fit parameters
  • Interactive Fit Selection Window
  • User-guided display of fit results
  • User-selected export of partition statistics and fit parameters

 

Spectral Fit operates on the wave spectral partitions computed by the Wave Systems Module. Processing options for Spectral Fit are set in the Spectral Fit Parameters Table, which opens upon selecting Spectral Fit from the Module pull-down menu.  Spectral Fit results can be fine-tuned using the Spectral Fit Selection Tool.

 

The Data View Module includes several features to support the display and export of Spectral Fit results.  A Spectral Fit Plot Library allows the comparison of fit results to original data.  A Data Export Utility allows the user to design a custom table of fit results to export.

 

The Spectral Fit Module computes a variety of 1D (non-directional) and 2D (Directional) fit parameters for the spectral partitions computed by the Wave Systems Module.  The user can select the type of fits applied to both wind sea and swell partitions.  Furthermore, Spectral Fit will linearly combine these fits to compute a composite fit for the full (parent) spectrum.  A variety of display options allow the user to compare fit results to actual data.

 

Launching the Spectral Fit Module

Spectral Fit is launched by selecting the Spectral Fit command on the Module pull-down menu.  The Wave Systems Module must be run before spectral fitting can performed.  The Spectral Fit Parameters Table is then used to set processing options.

 

1D Spectrum Fitting

Once the user selects Run in the Spectral Fit Parameters Table, a sequence of fitting operations is performed.  The first step is the computation of variance density (1D) spectrum fits.  An efficient multivariate nonlinear optimization approach (Lagarias et al., 1998) is employed to optimize model fits to partitioned spectra.  The following 1D fits are computed for each wave partition:

  • JONSWAP- Least squares fit of a JONSWAP variance density spectrum.  There are two options here:

1. Default – Uses a modified form of JONSWAP that is based on significant wave height (Hs), peak period (Tp), and peak enhancement factor (Gamma, γ).  Sigma A and Sigma B are held constant at 0.07 and 0.09, respectively.  Alpha is then computed independently based on Hs, Tp and γ.

2. Advanced JONSWAP – A traditional JONSWAP fit of Alpha, peak period, and gamma.  Peak period is based on a 3-point parabolic fit to the spectral peak.  Sigma A and Sigma B are held initially held constant at 0.07 and 0.09, respectively.  Several post-processing options for Sigma A and Sigma B are available in the Spectral Fit Selection Tool.

  • Gaussian – Least squares fit to a Gaussian variance density spectrum.  The significant wave height (Hs), peak period (Tp), and standard deviation of the Gaussian (σ) are computed.
  • Lognormal – Least squares fit to a variation of the Gaussian spectral form, allowing for some asymmetry in shape.  The significant wave height (Hs), peak period (Tp), and standard deviation of the Gaussian (σ) are computed.
  • Ochi-Hubble – Least squares fit to the Ochi-Hubble spectral form for a single peak.  The significant wave height (Hs), peak period (Tp), and spectral shape parameter (λ) are computed.

 

Directional Distributions

Once all of the 1D fits are completed, the user-selected directional distributions for wind sea and swell are computed.  Directional distributions provide mean direction and spread values that are based on standard model forms.

The following directional distributions are available:

 

Ewans Swell – Based on supplied Tp and peak direction (θp) computes a wrapped normal directional distribution Q (f,θ) for swell (Ewans, 2001).

 

Ewans Windsea - Based on supplied Tp and peak direction (θp) computes a symmetric double Gaussian directional distribution Q(f,θ) for wind sea (Ewans, 1998)

 

Cos^2n – A least squares fit of a cos2n(θ) distribution to the wave directions.  Here the resulting value of n is saved as a directional fit parameter.

 

Composite Fits

Once all of the individual partition 1D and 2D fits are generated, a set of composite fit results are computed based on the user-selected fit options in the Spectral Fit Parameters Table.  Composite fits are generated from a linear summation of the individual 1D and 2D partition fits for each record.

 

After the composite fits are computed the spectral fit plot page opens up in Data View.  Available plot types are listed in the Plot Library.

 

Fit Selection Tool

Once Spectral Fit data processing is complete, the interactive Spectral Fit Selection Tool can be used to modify the fits applied to each wave system.  A variety of fit performance data and plots are included, as well as tools to modify the computation of Sigma A and Sigma B in advanced JONSWAP fits.

 

Fit Data Export

The Data Export Utility is used to save Spectral Fit data fields to external ASCII-, EXCEL- and MATLAB-formatted data files.  The user can select specific data fields to write to these files.

 

Additional Help

An overview of spectral fitting appears in the tutorial Spectral Fitting.

 

References

Lagarias, J.C., A. Reeds, M.H. Wright and P.E. Wright, 1998.  Convergence properties of the Nelder-Mead Simplex Method in low dimensions, SIAM Journal of Optimization, 9(1), 112-147.

 

Adjustable parameters in the Spectral Fit Parameter Table allow the user to select processing options for the Spectral Fit Module.

 

 

The Spectral Fit Parameter Table is very similar to the Wave Systems Parameter Table.  It is divided into 3 main sections:

 

1. Commands (Left column of buttons)

2. Parameters (center column of inputs)

3. Interactive Display (right column).

 

The features in each of these sections are described below.

 

1.  Commands

The commands appearing on the left side of the Spectral Fit Parameters Table control the saving and use of selected parameters.  The following commands and options are available:

 

Named Settings – Select from a list of pre-existing parameter settings.  Parameter values will automatically update.  To see the results of these new parameters in the plot, click Update Plot.

Update – Update the displayed parameters to the current named parameter set.

Save New – Save the displayed parameters to a new named parameter set.  User will be prompted to provide a name for the new parameter set.

Reset – Reset displayed parameters to saved values

Delete – Delete the current named parameter set

Run – Process the data set using the current named parameter set

Cancel – Exit the Spectral Fit Parameter Table without processing any data

 

2.  Parameters

The processing parameters allow the user to specify the type of fits to apply to wind sea and swell partitions.

 

1D Energy Fits

The following 1D fits can be selected:

 

  • JONSWAP- Least squares fit of a JONSWAP variance density spectrum.  There are 2 options for this fit, Default or Advanced.  See JONSWAP Fit Type parameter in the Fit Controls section below.

 

  • Gaussian – Least squares fit to a Gaussian variance density spectrum.  The significant wave height (Hs), peak period (Tp), and standard deviation of the Gaussian (σ) are computed.

 

  • Lognormal – Least squares fit to a variation of the Gaussian spectral form, allowing for some asymmetry in shape.  The significant wave height (Hs), peak period (Tp), and standard deviation of the Gaussian (σ) are computed.

 

  • Ochi-Hubble – Least squares fit to the Ochi-Hubble spectral form (single peak).  The significant wave height (Hs), peak period (Tp), and spectral shape parameter (λ) are computed.

 

 

2D Directional Fits

Directional distributions provide mean direction and spread values that are based on standard model forms.

 

The following directional distributions are available:

 

  • Ewans Swell – Based on supplied Tp and peak direction (θp) computes a wrapped normal directional distribution Q (f,θ) for swell (Ewans, 2001).

 

  • Ewans Windsea - Based on supplied Tp and peak direction (θp) computes a symmetric double Gaussian directional distribution Q(f,θ) for wind sea (Ewans, 1998)

 

  • Cos^2n – a least squares fit of a cos2n(θ) distribution to the wave directions.  Here the resulting value of n is saved as a directional fit parameter.

 

 

Fit Controls

The user has the option of turning on two Fit Conservation options:

 

  • Wave Height Conservation – The fitted wave heights are replaced with the input data wave heights

 

  • Wave Period Conservation – If the fitted peak wave periods fall outside the user-specified tolerance, they are replaced with the input data wave periods

 

Furthermore the user can select between Default or Advanced JONSWAP fit types:

 

  • Default – Uses a modified form of JONSWAP that is based on significant wave height (Hs), peak period (Tp), and peak enhancement factor (Gamma, γ).  Sigma A and Sigma B are held constant at 0.07 and 0.09, respectively.  Alpha is then computed independently based on Hs, Tp and γ.

 

  • Advanced JONSWAP – A traditional JONSWAP fit of Alpha, peak period, and gamma.  Peak period is based on a 3-point parabolic fit to the spectral peak.  Sigma A and Sigma B are initially held constant at 0.07 and 0.09, respectively.  Several post-processing options for Sigma A and Sigma B are available in the Spectral Fit Selection Tool.

 

 

3.  Interactive Display

The plot window on the right side of the Wave Systems Parameter Table can be used to view the results of various parameter settings prior to processing data.  The following user-controls are provided:

 

Plot Title – Right click on the plot title to select from several display options:

 

  • Wave System 1D Fits –Compares the partition 1D spectra to the computed 1D spectral fits in the current record

 

  • Composite 1D Fit –Compares the full 1D spectrum with the composite 1D fit computed from linear summation of the partition 1D fits in the current record

 

  • System Directional Fits – Compares the system 1D direction spectrum to the computed 1D direction spectra fit for each partition in the current record

 

  • Composite Directional Fit - Compares the composite 1D direction spectra to the computed 1D direction spectral fit for the entire spectrum in the current record

 

  • Composite Directional Distribution – A 2D plot of the composite directional distribution computed from the 2D partition fits in the current record

 

  • Observed Directional Distribution – A 2D plot of the observed directional distribution from the current record

 

  • Fit Error Table – Presents the least squares correlation coefficient (r) for each fit in the current record

 

Change Plot Date and Time – Navigate through the data file records using the Previous and Next buttons or by clicking on the scroll-down arrow in the date-time box under the plot.

 

Update Plot – Update the plot to reflect the selected parameter settings.

 

Switch to Linear / Log Plot – Switch plot axes to linear or logarithmic scale.

 

Additional Help

An overview of spectral fitting appears in the tutorial Spectral Fitting.

 

References

 

Ewans, K. C., 1998.  Observations of the Directional Spectrum of Fetch-Limited Waves, J. Phys. Oceanog., v.28, pp.495-512.

 

Ewans, K. C., Directional Spreading in Ocean Swell, WAVES 2001.

 

 

 

The Spectral Fit Selection Tool is used to fine tune the Spectral Fit Module results.  It is launched from the Fit Selection Tool command on the Options pull-down menu, or by selecting the Fit Selection Tool button on the Data View toolbar.  The Spectral Fit Selection Tool provides the user with a variety of fit performance data and plots, as well as the capability to modify the fit types applied to individual wave systems.

 

The Fit Selection Tool has four main features:

 

1. Wave System Fits

Select a wave system to inspect and modify.  A system selection menu allows the user to select between all Systems, Windsea, Windsea segments, All Swells, or a specific system number (System 1, System 2, System 3, etc).  The system numbers correspond to the temporally-tracked systems generated by the Wave Systems Module.  Forward and back arrows allow easy navigation through these wave system options.  Specific wind sea segments can be selected by either (1) typing in the desired start and stop times, or (2) use the mouse to left-click and drag across a segment of the System Height Series plot and then right-click and choose the Set Windsea Segment command.  The plots automatically update to show the selected data.

 

Using the 1D Energy Fit and 2D Directional Fit pull-down menus, the user can change the type of fits applied to each wave system.  1D Fit selections include JONSWAP, Gaussian, Lognormal and Ochi-Hubble.  Directional distribution selections include Ewans Windsea, Ewans Swell, and Cos^2n.  The following push-button commands are available:

 

  • Update Plots - Updates the various plot displays with the selected fit results
  • Accept Fit - Saves the new fit selections to the data file in memory.
  • Cancel All Fits – Restores the data file in memory to the original fit selections
  • Exit – Exit and close the Fit Selection Tool.  The user will be prompted the user to save results if changes have been made.

 

2. Advanced JONSWAP Options

The Advanced JONSWAP options are available for data that have been processed using the Advanced JONSWAP fit option in the Spectral Fit Parameters Table. Right-clicking on the Advanced JONSWAP Options tab will provide access to the advanced fit commands shown in figure below.

 

 

This window allows the user to select from the following sigma processing options (pull-down menu):

 

Default

Sigma A and Sigma B are held constant at 0.07 and 0.09, respectively. The JONSWAP fits are then recomputed using these values.

 

Fitted

Sigma A and Sigma B are fitted along with alpha, peak period, and gamma.

 

User-specified

Sigma A and Sigma B input boxes allow the user to specify the values to use.  The JONSWAP fits are then recomputed using these values.

 

Fetch Estimated

Sigma A and Sigma B are estimated from the input (or computed) wind speed, direction and estimated fetch.  The user is prompted to provide a fetch file that includes a set of directions (from) and fetches (km).  The format of the ascii fetch file is as follows:

 

Direction from

which wind blows

Estimated

Fetch (km)

0

60

45

180

90

200

135

800

180

1000

225

1200

270

80

315

60

360

60

 

The actual fetch used for each record is interpolated from the input values based on the corresponding wind direction.  The Sigma A and Sigma B computations are based on Lewes and Allos (1990).  The non-dimensional fetch χ=gx/u2 is computed, where u is the 10-m elevation wind speed.  Equations 11, 13 and 14 from Lewes and Allos (1990) are then applied for the computation of Sigma A and Sigma B. The JONSWAP fits are then recomputed using these estimated values.

 

Selecting Compute will re-compute all JONSWAP fits using the selected options.  Selecting Exit will return control back to the Wave System Fits window.

 

 

3. Fit Plots

The plot window in the upper right section of the Fit Selection Tool includes scatter plots to compare wave height and period fit results for the selected wave system (or all wave systems).  The scatter plots include a quantification of the RMS error and bias of the fit parameters.  Also included is a JONSWAP Parameters table the lists the computed fit parameters for each wave system for which a JONSWAP Fit has been selected.

 

4. Wide format plots

The lower plot window is used to view the following additional fit performance displays:

 

  • System Height and Period Series - time series comparisons of fit parameters with input data

 

  • Stacked Spectra – The stacked spectra display allows the user to scroll through all the 1D spectra fit comparisons for a selected wave system, with up to 4 records shown at a time.  Use the scroll bar at the bottom of the display to navigate through the wave system records.

 

  • System Height and Period Error Bars – Displays the Root-Mean-Square (RMS) height and period fit errors for all wave systems at a glance

 

An overview of spectral fitting appears in the tutorial Spectral Fitting.

 

Reference

Lewis, A. W. and R. N. Allos, 1990.  JONSWAP’s parameters:  sorting out the inconsistencies, Ocean Engineering, 17, 409-415.