Comparison of Gap Interpolation Methodologies for water Level time Series using perl/PDL

Abstract

Extensive time series of measurements are often essential to evaluate long term changes and averages such as tidal datums and sea level rises. As such, gaps in time series data restrict the type and extent of modeling and research which may be accomplished. The Texas A&M University Corpus Christi Division of Nearshore Research (TAMUCC-DNR) has developed and compared various methods based on forward and backward linear regression to interpolate gaps in time series of water level data.

We have developed a software system that retrieves actual and harmonic water level data based upon user provided parameters. The actual water level data is searched for missing data points and the location of these gaps are recorded. Forward and backward linear regression are applied in relation to the location of missing data or gaps in the remaining data. After this process is complete, one of three combinations of the forward and backward regression is used to fit the results. Finally, the harmonic component is added back into the newly supplemented time series and the results are graphed. The software created to implement this process of linear regression is written in Perl along with a Perl module called PDL (Perl Data Language).

Generally, this process has demonstrated excellent results in filling gaps in our water level time series. The program was tested on existing data under three typesof typical weather conditions: calm summers, frontal passages and extreme weather conditions, such as hurricanes. The parameters varied in order to test the accuracy of the methodology included the number of coefficients utilized in the linear regression processes as well as the size of the gaps to be filled. Results are presented for the different weather conditions and the different gap size and coefficient combinations.