Mulgor Logo Long Wave Extraction at GeoNet Sites:  Methodology

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In this webpage, I describe the steps involved in extracting the long waves from GeoNet tsunami data files of sea level.

The methods are described in more detail in:

Goring, D. G. 2008: Extracting long waves from tide-gauge records. Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 134, No. 5: 306-312.

Preliminary Data Preparation

Preliminary data processing involves the following steps:


Removing the tide from the signal involves forecasting the tide and subtracting it from the record. The tide consists of a number of constituents (up to 600). Each of these constituents is related to a particular astronomical phenomenon. This governs the constituent's period, but each constituent also has an amplitude and phase, corresponding to its strength and timing. We determine the amplitude and phase of each tidal constituent by analysing a long period of historical tide gauge data. Once we have the constituents, we can forecast the tide within a few cm for anytime in the future or the past.


Tide gauge records occasionally have gaps from a few minutes up to a few days, caused by instrument malfunction or downtime during maintenance. These gaps are undesirable, but unfortunately they are inevitable. We try to minimise them as much as possible. For many data processing routines, we need a continuous record with no gaps. Therefore, we must do something about the gaps, at least for the calculations. Oftentimes, we remove the gaps, do the calculations, then reintroduce the gaps so that we do not misinterpret the results. The procedure for degapping sea-level records is to remove the tide from the record (see detiding ) and linearly interpolate across the gap. If necessary, the tide can be added back in again later.


Spikes occur as a result of instrument error: either of the sensor, or the telemetry system that transmits the data. In sea-level records, spikes usually are a single point. The record will be going along nicely when suddenly it registers a zero or a large number. A single spike in a record can completely mask the waves of interest. Detecting spikes by eye is easy. In fact, the human eye is the best spike-detecting instrument there is. Detecting spikes automatically and robustly requires sophisticated mathematical methods such as those described here (187 KB). For sea-level records, the algorithm we have found works best uses wavelet analysis to decompose the detided residual, then looks for points that exceed a threshold within a particular time window. The spikes are replaced by gaps, and later we remove the gaps by degapping. Determination of the threshold and the length of the window differs from site to site and must be estimated from historical data.


Noise occurs in a tide gauge record as a result of instrument errors and improper sampling of swell waves (aliasing). Usually, noise only affects long waves; however, the methods described here can be applied to any process.

A detailed report on denoising sea-level records is available from here (239 KB).

In brief, denoising involves first of all analysing the sea-level record to determine the background noise that occurs in a quiescent period when there are no significant waves, then using the information from that period to estimate how much of the signal is noise, and removing that proportion of the signal at times when there are significant waves. The technique uses new technology called "wavelet analysis" to decompose the sea-level record and separate the noise from real data.

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Extracting the Long-Wave Record

Once the detided, degapped, despiked, denoised residual has been evaluated, we can derive the long-wave record by high-pass filtering. This removes any left-over tide after detiding, as well as long-period effects like storm surge and long-term variations in sea level.

For the records shown here, we used orthogonal wavelet decomposition . This has the advantage over other high-pass filter methods that it is a localised filtering method, thus accommodating non-stationary data (i.e., data with changing variance).

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Wave Parameters

The long-wave record can be processed as if it were a wind-wave record, except that it is continuous rather than in bursts. Waves were reckoned as occurring between downward zero-crossings.

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Continuous Wavelet Plot

The long wave record was first decomposed using the continuous wavelet method described by Torrence and Compo(1998). We used the Mexican Hat mother wavelet and four intervals within each dyadic scale. We then reconstituted the signal to give a series of continuous wave records at various dilation scales. At this point, we had a very complicated array of sea levels as a function of time and dilation scale. The original long wave record could be obtained from this array by integrating over the dilation scales at each time interval. In order to display the distributed data, we smoothed the wave records over time by calculating the significant wave height using a 6-hour moving window with a 4-hour overlap (significant wave height is the average of the highest third of the waves). This gave a set of data at two-hour intervals for each dilation scale. To obtain a representative period for each of these scales, we calculated the average period of the significant waves over the timespan. The results of these calculations are presented in the Figures 1 B in the form of a contour map of significant wave height as a function of time and period (equivalent to dilation scale).

Torrence, C.; Compo, G.P. 1998: A practical guide to wavelet analysis. Bulletin of the American Meteorological Society, 79(1): 61-78.

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Enquiries: Derek Goring

Mulgor Consulting Ltd

24 Brockworth Place

Riccarton, Christchurch

New Zealand

Phone: 64 3 343 5400

Fax: 64 3 343 5403