Old Rocks
Diamond Member
Equatorial wave expansion of instantaneous flows for diagnosis of equatorial waves from data: Formulation and illustration
Equatorial wave expansion of instantaneous flows for diagnosis of equatorial waves from data: Formulation and illustration
Abstract
This paper presents a method for expanding horizontal flow variables in data using the free solutions to the shallow-water system as a basis set. This method for equatorial wave expansion of instantaneous flows (EWEIF) uses dynamic constraints in conjunction with projections of data onto parabolic cylinder functions to determine the amplitude of all equatorial waves. EWEIF allows us to decompose an instantaneous wave flow into individual equatorial waves with a presumed equivalent depth without using temporal or spatial filtering a priori.
Three sets of EWEIF analyses are presented. The first set is to confirm that EWEIF is capable of recovering the individual waves constructed from theoretical equatorial wave solutions under various scenarios. The other two sets demonstrate the ability of the EWEIF method to derive time series of individual equatorial waves from instantaneous wave fields without knowing a priori exactly which waves exist in the data as well as their spatial and temporal scales using outputs of an equatorial β-channel shallow-water model and ERA-Interim data. The third set of demonstrations shows, for the first time, the continuous evolutions of individual equatorial waves in the stratosphere whose amplitude is synchronized with the background zonal wind as predicted by quasi-biennial oscillation theory.
1. Introduction Rossby waves, named after the seminal work of (Rossby, 1939), play a fundamental role in large-scale atmospheric and oceanic motions that affect weather and climate. An equally seminal work on Rossby waves is Yeh (1949), who discovered the downstream development mechanism of weather systems in the midlatitudes via the dispersion relation of Rossby waves. In the extratropics, more than 90% of wave fields at any given instance are in the form of Rossby waves. In the equatorial region, on the other hand, all types of waves can co-exist for a relatively longer time after their excitations owing to the much longer inertial time scale for horizontal motions near the equator. A theoretical as well as practical question is whether we can isolate these individual equatorial waves from the total wave flow field observed at a given instance, which is the subject of this study.
Should have gone to the original paper right off the bat. Rather than contradicting present climate science, this is just another paper that verifies and enforces what the scientists have been trying to tell us. That Anthony Watts gets it all wrong is just the what he does.
Equatorial wave expansion of instantaneous flows for diagnosis of equatorial waves from data: Formulation and illustration
Abstract
This paper presents a method for expanding horizontal flow variables in data using the free solutions to the shallow-water system as a basis set. This method for equatorial wave expansion of instantaneous flows (EWEIF) uses dynamic constraints in conjunction with projections of data onto parabolic cylinder functions to determine the amplitude of all equatorial waves. EWEIF allows us to decompose an instantaneous wave flow into individual equatorial waves with a presumed equivalent depth without using temporal or spatial filtering a priori.
Three sets of EWEIF analyses are presented. The first set is to confirm that EWEIF is capable of recovering the individual waves constructed from theoretical equatorial wave solutions under various scenarios. The other two sets demonstrate the ability of the EWEIF method to derive time series of individual equatorial waves from instantaneous wave fields without knowing a priori exactly which waves exist in the data as well as their spatial and temporal scales using outputs of an equatorial β-channel shallow-water model and ERA-Interim data. The third set of demonstrations shows, for the first time, the continuous evolutions of individual equatorial waves in the stratosphere whose amplitude is synchronized with the background zonal wind as predicted by quasi-biennial oscillation theory.
1. Introduction Rossby waves, named after the seminal work of (Rossby, 1939), play a fundamental role in large-scale atmospheric and oceanic motions that affect weather and climate. An equally seminal work on Rossby waves is Yeh (1949), who discovered the downstream development mechanism of weather systems in the midlatitudes via the dispersion relation of Rossby waves. In the extratropics, more than 90% of wave fields at any given instance are in the form of Rossby waves. In the equatorial region, on the other hand, all types of waves can co-exist for a relatively longer time after their excitations owing to the much longer inertial time scale for horizontal motions near the equator. A theoretical as well as practical question is whether we can isolate these individual equatorial waves from the total wave flow field observed at a given instance, which is the subject of this study.
Should have gone to the original paper right off the bat. Rather than contradicting present climate science, this is just another paper that verifies and enforces what the scientists have been trying to tell us. That Anthony Watts gets it all wrong is just the what he does.
