# Demonstration

## Getting Started

Type Spectra', hit <return> and the main Spectra window will appear:

Figure 1a: Main Spectra' window.

There are five pull-down menus, plus a Help' button for a brief description of each.

• File/Data: used for reading in the dataset to be analyzed ('Read Vector',and 'Read Matrix' functions), and for writing out results created by the toolkit ('Write Vector' and Write Matrix' functions). It also enables internal data management operations, such as selecting a column vector from a matrix ('Matrix/Vector'), and selecting a submatrix from a matrix ('Matrix/Matrix'). Please see also the Help' button.
• Analysis Tools:
• Blackman-Tukey Correlogram
• Maximum-Entropy spectrum estimation
• Multi-Taper Method spectrum estimation
• Singular Spectrum Analysis (SSA)
• Multi-Channel Singular Spectrum Analysis (MSSA)

• Plot: provides useful plotting functions. You can plot a selected vector vs. its index using 'Vector''VectorList' creates a plot of a list of vectors of equal length. 'MultiVector' creates a plot of two pairs of vectors ( for x and y axis). 'Matrix' creates a plot of selected matrix columns. Using 'Options' user can change the graphics output for ALL plotting functions inside the Toolkit. Currently the Toolkit supports IDLACE/gr (default!), and Grace (descendant of ACE/gr) plotting packages.

• Logfile: opens the internal logfile containing the detailed output from all tools. It forms an integral part of the Toolkit's output. The Logfile can be saved to a local file 'Logfile' on disk via 'Save' button.

• Credits: Lists members and contributions of SSA-MTM group, which made this Toolkit version possible.

The Exit' button quits all tools, and any results are lost unless they have been explicitly saved. Any open plot windows remain, however. The toolkit creates a number of local files while running. These files will be ALL DELETED !!! after exiting the program.

Before applying any of the Toolkit tools, the file containing the time series to be analyzed must be read in.

Data should be in the form of ascii columns, and can be either a column vector of a single time series, or a matrix of several columns, one for each time series. The 'Read Vector' or 'Read Matrix' functions from the File/Data menu are used to read the data. However, if a multi-column file (matrix ) is read using 'Read Vector', only the second column is read into a vector, while the first column, assumed to be time values, is ignored.

Values in the time series must be equally spaced in time. The sampling interval is assumed to be unity by default. If it is not unity, each tool needs to be told individually what the sampling interval is using the "Sampling Interval" box (see below). The resulting spectra are then plotted accordingly. If, for example, the data are sampled every 2 months instead of monthly, the Nyquist interval on the frequency axis will be labeled from 0 to 0.25 cycles/month.

Throughout the Toolkit the spectrum is calculated per unit time by dividing by the length of the data series in time units N'' (ie, a power spectral density). This is the default convention.

We will work through examples using each tool on a time series of monthly values of the Southern Oscillation Index (SOI), a climatic index that chracterizes El Niño (Bjerknes, 1969). The 690 month series soi' was obtained from monthly mean sea-level pressures at Tahiti and Darwin, Australia, by removing their seasonal cycles, dividing the resulting anomalies by the corresponding standard deviations, and then taking the Tahiti-minus-Darwin difference. The SOI series considered here is for the time interval from January 1942 through June 1999, during which no observations are missing.

It is also included in a source code dsitribution. To read the SOI time series, we use the 'Read Vector' function, which opens the following window:

Figure 1b. Read Vector' window.

This window allows you to browse a list of files, select a file and then read it and store in a named vector. SSA-MTM Toolkit allows you to handle many time series at once; these might typically be a raw input time series and a filtered series derived using the Toolkit. These time series and results of the computation are stored internally as vectors or matrices, each of which needs to be given a name.

To choose the time series soi' for analysis, either:

• scroll down to the name of the input time-series file, select it with the mouse and press the Read File' button, or else
• type the input file name soi' in Selection' and press the Read File' button.

The input vector is given name data', by default. If additional time series are read, the user needs to change this name, or the vector with the name 'data' will be overwritten.

The user has access to vectors and matrices via window lists, which show the names and dimensions (Fig. 1c.), i.e. the number of elements in a vector and number of rows and columns for a matrix. List windows are activated by pressing on the arrow buttons located next to the boxes with the name of the vector or matrix, see Fig. 1.b.

Figure 1c: 'Vector List' and 'Matrix List' windows.

To make a plot of the time-series data, we go to the 'Vector' function in a pull-down Plot menu, which opens the following window:

Figure 1d: 'Plot Vector' window.

This window allows the vector elements to be plotted against their index. The user has to specify the name of the vector from the vector list. By pressing on the 'Plot' button, a new graphics window opens with a plot of SOI time series:

Figure 1e: SOI Time series.

The time series soi' that we have read in is noisy, with no obvious oscillatory components. Our goal is to identify the low-frequency quasi-quadrennial (QQ) and quasi-biennial (QB) components of El Niño (Rasmusson et al., 1990).

When selecting Options in the pull-down menu for Plot on the main panel, the following window will open:

Figure 1f: Graphics options

The user can choose here between IDLACE/gr (default!), and Grace (descendant of ACE/gr) plotting packages. If we choose IDL, and use again Plot of Vector function as described above, the IDLDE (IDL Development Environment) will be started with a following plot:

Figure 1g: SOI plot by IDL.

IDL plots are created with the script files written out by the Toolkit whenever the Plot button is pressed for any of the plotting functions. The name of the script file is given by the variable 'BATCHFILE', (see Fig. 1i below) i.e. 'vector.idl.tmp' for our example. InIDLDE window the user can perform further analysis by starting IDL Insight, or by running their own IDL scripts using the plot data imported into IDLDE (as seen below in Fig. 1i). We can create a postscript file idl.ps of the plot in Fig.1g by entering at IDL propmtSET_PLOT, 'PS', and then @vector.idl.tmp.

Please note that IDLDE and Insight are features of the IDL version 5.0 and later.

Figure 1i: IDLDE window.