tag:blogger.com,1999:blog-7729093380675162051.post2129730517698235496..comments2024-03-28T13:56:47.604+11:00Comments on moyhu: Cubing the sphereNick Stokeshttp://www.blogger.com/profile/06377413236983002873noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-7729093380675162051.post-56704589210438748962017-06-19T07:04:53.071+10:002017-06-19T07:04:53.071+10:00Follow on to this post http://contextearth.com/201...Follow on to <a href="http://contextearth.com/2017/06/03/enso-forcing-validation-via-lod-data/" rel="nofollow">this post http://contextearth.com/2017/06/03/enso-forcing-validation-via-lod-data/</a><br /><br />If one thinks that wind is the forcing agent for ENSO and not angular momentum variations, consider the following physics of tidal forcing: Imparting a 1 millisecond slowdown (or speedup) on the rotation of the earth with a surface velocity of almost 500 meters/second over the course of a couple of weeks (a fortnight) will result in an inertial lateral movement of ~ 1/2 a meter in the volume of the Pacific ocean due to Newton's first law.<br /><br />This does not seem like a big deal until you realize that the thermocline can absorb this inertial impulse as a vertical sloshing, since the effective gravity is reduced by orders of magnitude due to the slight density differences above and below the thermocline. This is reflected as an Atwood number and shows up in Rayleigh-Taylor instability experiments, e.g. <a href="http://rsta.royalsocietypublishing.org/content/roypta/368/1916/1663.full.pdf" rel="nofollow">SEE THIS PAPER</a><br /><br />With an Atwood number less than 0.001 which is ~0.1% density differences in a stratified fluid, the 0.5 meter displacement that occurs over two weeks now occurs effectively over half an hour, or alternately is 1000X more sensitive than an unstratified volume. Either way, its an elementary scaling exercise to evaluate the impact.<br /><br />So intuitively, one has to ask the question of what would happen if the ocean was translated laterally by 1/2 a meter over the course of a 1/2 an hour? We know what happens with earthquakes in something as basic as a swimming pool or as threatening as a tsunami. But this is much more subtle because we can't obviously see it, and why it has likely been overlooked as a driver of ENSO.<br /><br />All that math modeling of ENSO described in the first link works backwards to this point. The actual forcing working on the earth's rotation can lead to the response shown, both in the dynamic sense of precisely tracking the measured ENSO time-series and now in terms of a physical order-of-magnitude justification.<br /><br />This effect is real and not imagined, and so should be accommodated in ENSO models.<br />@whuthttps://www.blogger.com/profile/18297101284358849575noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-84481989090616123502017-06-19T03:21:58.383+10:002017-06-19T03:21:58.383+10:00This paper "Recent progress and review of iss...This paper "Recent progress and review of issues related to Physics Dynamics Coupling in geophysical models"<br />https://arxiv.org/pdf/1605.06480.pdf<br /><br />They say at the end <i>"Probably the most sensitive parameter is the time step."</i><br /><br />That is true if the forcing is not strong and the problem relies on uncertain initial conditions. If the forcing is strong and the response is stable and converges, that forcing flows through to the response as clear as a bell irrespective of the chosen time step. For example, allowing a 60 Hz hum to enter an amplifier's input stages will certainly result in a 60 Hz hum visible in the output.<br /><br />So what do they recommend?<br /><i>"One option is to reduce the equation set, as in section 5, which then renders the generation of a reference solution more straight forward and allows for more rigorous mathematical analysis. Another option, as discussed in section 6, is to reduce the complexity of the GCM. Obviously the balance has to be right. Oversimplification does not challenge the coupling as the real model would, overly complex setups make the analysis intractable."</i><br /><br />So why don't we do this? <br /><br />And that coupling may not be coupling but a common mode response to other external factors, such as a gravitational forcing. I have shown how the ocean (via ENSO) and atmosphere (via QBO) respond to precisely the same lunar forcing.<br /><br />Contrary to what Mr.Browning says, it appears that the consensus climate science community is well aware of the issues. I really think there will be a path forward if we start with the obvious candidates to model, i.e. ENSO and QBO.<br />@whuthttps://www.blogger.com/profile/18297101284358849575noreply@blogger.comtag:blogger.com,1999:blog-7729093380675162051.post-47283262033322356062017-06-18T01:25:00.044+10:002017-06-18T01:25:00.044+10:00Elsewhere Olof questions whether Gerald Browning i...Elsewhere Olof questions whether Gerald Browning is a talker or a doer.<br /><br />The issue with scientists such as Browning is that they create these complex worlds of math that they live in during the course of their career and are surprised that nothing ever comes of it. In his case, Browning doesn't ride into the sunset but instead stirs the pot by claiming :<br /><br /><i>"Climate Models<br /><br />1. the climate models are based on the wrong set of differential equations, i.e., the hydrostatic equations instead of the well posed multi-scale hyperbolic system or the well posed reduced system (Browning and Kreiss 2002).<br /><br />2. The use of the hydrostatic system leads to columnar heating for the vertical velocity. In order to reduce the noise introduced by the point wise (lat,lon) heating, an unrealistically large dissipation must be applied and this reduces the numerical accuracy of the spectral method by two orders of magnitude (Browning, Hack and Swarztrauber and ECMWF plots shown on this site).<br /><br />3. For a model based on the hydrostatic system the accuracy of the numerical approximation is destroyed by the boundary layer parameterization within a matter of days (Sylvie Grsvel et al. on this site).<br /><br />4. There are no mathematical or numerical justifications for running a numerical model beyond the point where numerical accuracy is lost, let alone when it is based on the wrong equations and inaccurate parameterizations.<br />"</i><br /><br />Who knows, maybe he is right about all this. Yet, I doubt anything will come of it even if he is listened to. All the correct math in the world won't matter if one hasn't set down the right premise and that it can be applied, as in applied math leading to applied physics. <br /><br />Pierre-Simon Laplace was probably more responsible than anyone for Browning's consternation when he created his set of hydrostatic tidal equations in 1776. These equations are a reduced form of the complete set of primitive equations that go into every GCM developed, but also can be simplified to the extent that they can be used for applied physics. The ultimate example of this is how the tidal equations reduce to almost nothing (i.e. input forcing => scaling transform => output) when applied for straightforward tidal analysis.<br /><br />Something slightly more advanced than the reduced complexity of tidal analysis is likely what goes into ENSO and QBO analysis. We don't have to listen to Browning, but take the path of Laplace and iterate from there. Browning was likely down in the weeds from when he started decades ago and never really emerged.<br /><br /><br /><br />@whuthttps://www.blogger.com/profile/18297101284358849575noreply@blogger.com