Commonly used methods fail to detect known propagation speeds of simulated signals from time–longitude (Hovmöller) diagrams

Yair De-Leon,Nathan Paldor

doi:10.5194/os-15-1593-2019

Abstract

Abstract. This work examines the accuracy and validity of two variants of Radon transform and two variants of the two-dimensional fast Fourier transform (2-D FFT) that have been previously used for estimating the propagation speed of oceanic signals such as sea surface height anomalies (SSHAs) derived from satellite-borne altimeters based on time–longitude (Hovmöller) diagrams. The examination employs numerically simulated signals made up of 20 or 50 modes where one, randomly selected, mode has a larger amplitude than the uniform amplitude of the other modes. Since the dominant input mode is known ab initio, we can clearly define “success” in detecting its phase/propagation speed. We show that all previously employed variants fail to detect the phase speed of the dominant input mode when its amplitude is smaller than 5 times the amplitude of the other modes and that they successfully detect the phase speed of the dominant input mode only when its amplitude is at least 10 times the amplitude of the other modes. This requirement is an unrealistic limitation on oceanic observations such as SSHA. In addition, three of the variant methods detect a dominant mode even when all modes have the exact same amplitude. The accuracy with which the four methods identify a dominant input mode decreases with the increase in the number of modes in the signal. Our findings are relevant to the reliability of phase speed estimates of SSHA observations and the reported “too fast” a phase speed of baroclinic Rossby waves in the ocean.

Highlights

Time–longitude (Hovmöller) diagrams at a given latitude of an oceanic variable, η(x, t), that represents, for example, temperature, sea surface height, chlorophyll, obtained for example by satellite observations are often used for estimating the propagation rate of the oceanic variable
The dominant propagation speed calculated by the Radon transform does not match the propagation speed of the dominant input mode
None of the methods can identify a dominant input mode unless its amplitude is significantly larger than the others and most of them erroneously detect a dominant mode when there is no such input mode

Summary

Introduction

Time–longitude (Hovmöller) diagrams at a given latitude of an oceanic variable, η(x, t), that represents, for example, temperature, sea surface height, chlorophyll, obtained for example by satellite observations are often used for estimating the propagation rate of the oceanic variable. All methods have successfully filtered out the high-amplitude white noise from the three-harmonic signal and accurately detected the main mode (some of them detected the secondary modes). Such a signal is too synthetic/ideal and cannot be compared to real oceanic observations that include tens, if not hundreds, of modes with different frequencies and propagation speeds and not just three modes compounded by white noise. Paldor: Commonly used methods fail to detect known propagation speeds In this short study we simulate oceanic observations and examine whether the methods detect a single dominant propagation speed out of many (20 or 50) speeds.

Generating the simulated observations

Methods for estimating the observed propagation speed

Examining the accuracy of dominant mode detection

Results

Discussion