# Time Series Analysis

filter1d.m

## Filter1D: Time Series Analysis Tool

• The Matlab utility provides users of the SMS, a one-stop package for preparing model input time series and allows users to interpolate, resample, filter, and transform any type of model forcing and supports SMS compatible file formats for ease of data transfer.
• The main feature of the software is the ability to apply high-pass, low-pass, band-pass, and band-stop filters to time series.
• Filter1D uses a windowed sinc filter which is a non-recursive finite impulse response filter.
• Wiki Manual Filter1d
• PDF User Guide filter1d_user-guide.pdf

TAP Interface

## TAP: Tidal Analysis and Prediction software

• TAPtides is the ideal package to explore and develop preliminary or finalized tidal predictions from serial records spanning several weeks to several months.
• Designed to be easy to use, its Graphical User Interface permits quick separation of a time series of water level measurements into its tidal and non-tidal components using a selective least squares harmonic reduction employing up to 35 tidal constituents.
• After saving the tidal constants for the constituents selected during analysis, the user can generate predictions of the astronomical tide, the water level that varies at known tidal frequencies attributable to gravitational interactions between the earth, moon, and sun.

# Matlab scripts

## Read CMS-Flow Grid File (*_grid.h5)

• Description:
Reads a CMS grid file and creates a structure variable containing the grid variables
• Usage:

• Input:
filename - Input file name including full path (e.g. 'Flow_grd.h5')
• Output:
grd - structure variable containing the following variables
nx - Grid size in x direction [-]
ny - Grid size in y direction [-]
x0 - Grid origin in x direction [m]
y0 - Grid origin in y direction [m]
angle - Grid angle [deg]
x(1:nx) - Cell-center coordinates in x direction [m]
y(1:ny) - Cell-center coordinates in y direction [m]
depth(1:ny,1:nx) - Cell-centered depth [m]
active(1:ny,1:nx) - Cell activity (1-active and 0-inactive) [logical]
Plus other optional datasets such as mannings, d50, etc.
• Author: Alex Sanchez, USACE-ERDC-CHL

## Read CMS-Flow Tel File (*.tel)

• Description:
Reads a CMS telescoping grid file and output all variables to a structure array.
• Usage:

• Input:
telfile - Telescoping grid file including path (*.tel)
• Output:
tel - Structure including the following fields
ncells - Number of cells
x0 - Grid origin in x-direction [m]
y0 - Grid origin in y-direction [m]
angle - Grid angle [deg]
id - Cell ID number
x - Grid cell-centered coordinate in x-direction [m]
y - Grid cell-centered coordinate in y-direction [m]
dx - Grid cell resolution in x-direction [m]
dy - Grid cell resolution in y-direction [m]
iloc - Cell connectivity
depth - Cell-centered depths (-999 = inactive cell) [m]
• Author: Alex Sanchez, USACE

• Description:
Reads a CMS solution file and creates a structure variable containing the solution datasets values and times
• Input:
filename - input file name including full path
grd - Grid structure containing the following fields
nx - Grid size in x direction
ny - Grid size in y direction
varargin - dataset names
• Output:
sol - structure variable containing dataset values and times
varargout - variable length datasets corresponding to varargin
• Usage:

filename = 'test_sol.h5';
'points',pts,'cells',ids,'polygon',poly,'steps',nstep,'times',t)

• Author: Alex Sanchez, USACE-ERDC-CHL

## Read SMS Time Series Data File

• Description: Reads the Surface-water Modeling System time-series data (*.tsd) file.
• Usage:

## Read a CMS Save Point File

• Description:
Reads a CMS Save Point file
• Usage:

• Input:
filename - CMS Save Point file name
• Output:
sp - Structure with the following fields
variable - Name of output variable
reference_time_str - Reference time string in the following format 'yyyy-mm-dd HH:MM:SS'
reference_time - Reference time
label - Save point label
creation_date - Creation date
horizontal_projection - Horizontal projection
vertical_datum - Vertical datum
time_units - Time units
output_units - Units of output variable
cms_version - CMS version number
number_points - Number of points in time series
names - Names of output points
xy - Coordinates of output points
time - Output times
scalar - Output scalar
vector - Output vector
• Author: Alex Sanchez, USACE-CHL

## Write SMS Time Series Data File

• Description: Writes a Surface-water Modeling System time-series data (*.tsd) file.
• Usage:

sms_write_tsd(filenamet,dat,curvename,curvetype);

## Read SMS XY Series File

• Description: Reads the Surface-water Modeling System xy series (*.xys) file.
• Usage:

## Write SMS XY Series File

• Description: Writes a Surface-water Modeling System xy series (*.xys) file.
• Usage:

sms_write_xys(file,x,y,name)

## Bin scatter data

Example of xyzbin.m application to multibeam data with 5-m bins.
• Description: Averages the x, y, and z values of points within the same bin. The grid used to define the bins may be user specified are calculated based on the extent of the scatter points. The routine is useful for thinning/smoothing large scatter sets such as multibeam or LIDAR data. The binning method is less accurate then the search radius method, but is much faster.
• Usage:

[x,y,z] = xyzbin(...);
[x,y,z] = xyzbin('infile',infile,'outfile',outfile,'dx',dx);
[x,y,z] = xyzbin('x',xin,'y',yin,'z',zin,'dx',dx);
[x,y,z] = xyzbin('x',xin,'y',yin,'z',zin,'dx',dx,'dy',dy);
[x,y,z] = xyzbin('infile',infile,'dx',dx,'x0',x0,'y0',y0,'theta',theta);

## Interpolation of CMS-Wave Spectra

• Description: Interpolates the energy spectra in the CMS-Wave *.eng file to a specified output interval which may be specified in intervals or time units (hours). For example, an output interval of 0.5 index units, interpolates the spectra at half intervals. This subroutine is useful for filling small gaps in CMS spectra.
• Usage:

interp_eng('Wave.eng','New.eng',1,0.5) %interpolates to every half interval
interp_eng('Wave.eng','New.eng',1,2) %resamples every two spectra
interp_eng('Wave.eng','New.eng',2,1) %hrs

• Input:
engin = Input eng file
engout = Output eng file
mode = 1 - Index, 2 - Time
dtout = Output steering interval in hours for mode=2 or index for mode 1 (can be less than 1)

## Principle Component Analysis

Example of a principle component analysis.
• Description: Calculates the principle axes of vector time series data. This subroutine is useful for determining the main direction of fluid flow and extracting the velocity component along the major axis. The principle axes are determined by solving the eigenvalue problem for two-dimensional scatter data.
• Usage:

s = pca2d(u,v)

• Output:
s = Structure with the following fields:
center = Ellipse center (centroid)
area = Ellipse area
axes = Ellipse axes
eigen_values = Eigen values
eigen_vectors = Eigen vectors
total_variance = Total variance
percentage_variance = Percentage variance for each axes
angles = Angles for each axes in degrees
eccentricity = Ellipse eccentricity
slope = Slope of the linear fit which goes through the origin
• Note: An alternative simple way of determining the principle axes of vector time series is
 ${\displaystyle \phi _{p}={\frac {1}{2}}\arctan ^{-1}{\biggl (}{\frac {2{\big \langle }u'v'{\big \rangle }}{{\big \langle }u'^{2}{\big \rangle }-{\big \langle }v'^{2}{\big \rangle }}}{\biggr )}+\pi /2}$ (1)

where ${\displaystyle u'=u-{\bar {u}}}$ and ${\displaystyle v'=v-{\bar {v}}}$.

## Data Density Scatter Plot

Example of a data density plot.
• Description: datadensity Computes and plots the data density (points/area) of scattered points
• Usage:

• Input:
(x,y) - coordinates of points
method - either 'squares','circles', or 'voronoi'
default = 'voronoi'
radius - Equal to the circle radius or half the square width

## Spectral Analysis

Example of Power Spectrum for an idealized water level time series with white noise and a large gap.
• Description: Calculates the spectrum for a scalar time series using Welch's method. The confidence intervals are calculated with the inverse of chi-square distribution. Also includes a filtering option using the butterworth filter to see the effect of the filter on the spectrum.
• Usage:

q = specwelch(x,dt,w,Nsg,pnv,Wn,ftype,n);
[psdf,f] = specwelch(x,dt,w,Nsg,pnv,Wn,ftype,n);
[psdf,conf,f] = specwelch(x,dt,w,Nsg,pnv,Wn,ftype,n);

• Input:
x - Time series, [vector]
dt - Sampling Rate, [scalar]
win - Window, one of: 'hanning', 'hamming', 'boxcar'
Nsg - Number of Segments (>=1)
pnv - Percentage Noverlap of Segments (0-100)
Nb - Band Averaging, number of bands to average
P - Probability for confidence intervals, (e.g. 0.95)
Wn - Cut-Off frequencies, used for filtering
ftype - Type of filter, 'high', 'low' or 'stop'
n - Number of coefficients to use in the Butterworth filter
• Output:
q - structure with the following fields:
xp - detrended x
f - Frequencies
T - Periods
m - Magnitude
a - Amplitude
s - Power spectrum, Sxx(win), [Power]
psdw - Power Spectrum Density, Pxx(win), [Power/rad/sample]
psdf - Power Spectrum Density, Pxx(f), [Power/sample-freq]
psdT - Power Spectrum Density, Pxx(T), [Power*time-unit]
conf - Upper and Lower Confidence Interval multiplication factors using chi-squared approach

## Vector Plot

Example comparisons between feater.m, quiver.m, and vecplot.m
• Description: Plots directionally correct vectors. Both of matlab subroutines feather.m and quiver.m do not preserve the correct vctor angles.
• Usage:

h = vecplot(x,y,u,v,'PropertyName',PropertyValue,...)
h = vecplot(u,v,'PropertyName',PropertyValue,...)

• Input:
x,y = Position Coordinates
u,v = Vector Componentes
• Optional Properties
'DataAspectRatio' = Scaling factor between x and y axes. This is set as the second element of the property 'DataAspectRatio'
'LengthScale' = Length scaling factor for the barbs or arrows
'LineSpec' = Line specification string syntax (default '-k^') (e.g. '^k' - plots black arrows, 'k' - plots black sticks)
'Linewidth' = Linewidth
'Marker' = '^' for triangle arrows, 'v' for angled arrows,
and for stick plots (default stick)
'MarkerFaceColor' = Arrow fill color (default none)
'MarkerEdgeColor' = Arrow edge color (default line color)
'MarkerSize' = Marker size
'LegendLength' = Sets the length of the legend vector
'LegendUnits' = Sets the units for the legend vector
'legendPosition' = Sets the legend position (normalized units 0-1)
• Output:
h = handles for plot objects

Example using vecplot to plot wave conditions.

## Tidal Harmonic Analysis

Example tidal harmonic analysis results for Crescent City, CA
• Description: Simple program which performs a tidal harmonic anlaysis of scalar (e.g. water level) or vector (current velocity) time series. The script is only applicable for relatively short time series of a few months.
• Usage:

out = tha(in);

• Input:
in - Structure array with the following fields
x - real or complex vector [arbitrary units]
t - time in hrs from zero [hours startin from zero]
start_time - starting time as [yyyy,mm,dd,HH,MM,SS]
constituents - optional input constituent names
rayleigh - optional rayleigh criteria (<=1)
secular - optional secular correction. Either 'linear' or 'none'. If set to 'linear', the slope is included as a correction to the time series.
• Output:
out - Structure array with different fields depending on whether the input time series in real or complex.
amplitudes - Tidal constituent amplitudes (real time series)
constituents - Tidal constituent names
equilibrium_arguments - Equilibrium arguments (v+u) for each constituent and starting time
frequencies - Tidal constituent frequencies
frequency_units - 'cycles/hour'
nodal_factors - Nodal factors for each constituent and year.
phases - Tidal constituent phases
phase_units = 'degrees'
percent_variance_explained - Percent variance explained of the measured time series by the fitted time series.
residuals - difference between measured and fit time series
slope - fitted slope(s)
speeds - Tidal constituent speeds in degrees/hour
speed_units = 'degrees/hour'
time - Julien time in hours from start of year
time_units = 'hours'
(variables bewlow are only for complex time series only)
major_amplitude - Semi-major axis amplitude
minor_amplitude - Semi-minor axis amplitude
positive_amplitude - Positive axis amplitude (a+)
negative_amplitude - Negative axis amplitude (a-)
positive_phase - Positive axis phase (phase+) [deg]
negitive_phase - Negative axis phase (phase-) [deg]
ellipse_inclination - Ellipse orientation or inclination [deg]
eccentricity

## Extract Time Series from NOAA World Blended Sea Winds

Blended Surface Sea Winds for a section of the North-West US coast.
Extracted sea winds
Extracted sea winds

## Image Digitization Tool

Example digitization of an earthquake rupture zone.
• Description: digitize is a user interfase that allows to import image files (.bmp, etc) into MatLab to digitize data from. Previous sessions can also be loaded. It is useful for digitizing plots%and making world files for images. The utility can be used for digitizing time series plots, geographic features such as coastlines, or elevation contours.
• Instructions:
1. To start a new session, click on the "Load" menu and select "Image File".
• Reference the image
2. Left-click on the points reference points and Right-click when finished.
3. Right-click on any reference point and select "Reference" to enter the points "true" coordinate.
4. When the coordinated for all the reference points have been entered the "Reference Data Complete" item under the "Transformation" menu will be checked.
5. To delete Transformation points, right-click on a point and select "Delete".
• Digitize Points
1. Click on the "Digitization" menu and select "Add Points". The digitized points may be entered at any time, but their transformed coordinated are not calculated until the reference data is complete.
2. To see a digitized point's transformed coordinate, right-click on a point and select "Coordinates".
• Export the Digitized Points
1. Click on "Export" and select one of the output options including variables to the workspace and an ASCII file.

## Create Spectra Generation Import file with WIS datafiles

• Description: This function creates the .txt file used in the spectra generator of CMS Wave. It prompts the user to select all the desired WIS output files, specify the depth of the station, and whether or not to average the data series. The data and user inputs are manipulated into the format used by CMS Wave file import for spectra generation. Currently the output file is saved in the active directory of matlab.
• Usage: Type mfile name in Matlab command window

CMS_WIS_to_txt_for_spectragen

## Read an SMS Super ASCII data file (*.dat)

• Description: This function reads an SMS Super ASCII data file (*.dat). These files are part of the SMS Super ASCII format and is an output option for global solution datasets in CMS. The SMS Super ASCII format also includes a coordinates file (*.xy) and a super file (*.sup) which contains the names of the coordinate file and dataset files.
• Usage:

## Read an SMS xy file (*.xy)

• Description: This function reads an SMS xy file (*.xy). These files are used in the SMS Super ASCII in conjuction with the by CMS as an ASCII output option for global solution datasets. The SMS Super ASCII format also includes dataset files (*.dat) and a super file (*.sup) which contains the names of the coordinate file and dataset files.
• Usage:

## Wave Number Calculation

• Description: Simple program which solves the wave dispersion relation sig^2 = g*k*tanh(k*h).
• Usage:

wk = wavenumber(g,wa,wd,h,u,v,tol)
[wk,err] = wavenumber(g,wa,wd,h,u,v)

# TextPad Syntax File for CMS-Flow Card File

Example cmcards file viewed in Textpad
• Color codes the CMS-Flow card file (*.cmcards) so that it is easier to read and avoids misspelling of keywords.
• To setup the file:
1. Open Textpad and click on the menu Configure and go to Preferences.
2. Click on folder on the left hand side and note the path to the syntax files.
3. Copy-paste the .syn to the path noted in step 2.
4. Click on Configure | New Class Document.
5. Enter CMS-Flow as the document name and click next.
6. Enter *.cmcards in Class members and click next.
7. Enable the syntax highlighting and select the CMS-Flow_V4.syn file.
8. Click on Finish and your done!

# Notepad++ Syntax File for CMS-Flow Card File

Example cmcards file viewed in Notepad++
• Color codes the CMS-Flow card file (*.cmcards) so that it is easier to read and avoids misspelling of keywords.
• Version 4.1 and earlier: CMS-Flow_v4p1.xml.

# UltraEdit Syntax File for CMS-Flow Card File

Example cmcards file viewed in UltraEdit
• Color codes the CMS-Flow card file (*.cmcards) so that it is easier to read and avoids misspelling of keywords.
• Version 4.1 and earlier: CMS-Flow_v4p1.uew.

# HDFview

• HDFview is a free visualization tool for browsing and editing HDF4 and HDF5 files.