The behavior of complex systems, particularly in fluid dynamics, is traditionally described by high-dimensional systems of equations like the Navier-Stokes equations. While providing practical applications as is, these models can obscure the underlying, simplified mechanisms at play. It is notable that ocean modeling already incorporates dimensionality reduction built in, such as through Laplace's Tidal Equations (LTE), which is a reduced-order formulation of the Navier-Stokes equations.

AMO trained on region outside of dashed line, so that's the cross-validated region, using Descent optimized LTE annual time-series, Python python3 ts_lte.py amo.dat --cc --plot --low 1930 --high 1960 using the following JSON parameters file amo.dat.p { "Aliased": [ 0.422362756, 0.38861749700000003, 0.23562139699999995, 0.259019747, 0.33201584700000003, 0.165274488, 0.262765007, 0.385761106, 0.07374525999999999, 0.215992198, 0.192246939, 0.528757205, 0.112996099, 0.03714361, 0.10034691, 0.07660165, 0.501613596, 2.0, 1.0 ], "AliasedAmp": [ 0.03557922624939592, 0.09988731513671248, 0.07106292426402241, 0.1202147059011645, -0.16310647366824904, -0.21099766009700224, 0.3178250739779875, -0.034763054040409205, -0.26973831298426476, -0.13417117453373803, 0.33741450649520405, 0.14844747522132112, 0.38176481941684715, -0.24512757533159843, 0.17007002069621968, -0.3175673142831867, -0.0801663078936891, 0.0410641305028224, 0.15648561320675802 ], "AliasedPhase": [ 12.907437383830702, 9.791011963532627, 20.894959747239227, 11.230932614457465, 24.106215317177334, 14.921596063027563, 11.928445369162157, 14.76066439534825, 9.307516552468496, 6.238399781667854, 4.78878496205605, 19.328424226102666, 4.1510957254818255, 24.986414787848002, 3.764292351659264, 7.899565162852414, 10.701455186458222, 6.575719630634085, 4.603123916071089 ], "DeltaTime": 7.217156366226141e-06, "Hold": 0.001560890374528988, "Imp_Amp": 36.03147961053978, "Imp_Stride": 1, "Initial": 0.023119471463386495, "LTE_Amp": 1.2149052076222568, "LTE_Freq": 232.0780473685175, "LTE_Phase": -1.98155204056087, "Periods": [ 27.2122, 27.3216, 27.564500000000002, 13.63339513, 13.69114014, 13.5961, 13.6708, 13.72877789, 6795.015773000002, 1616.2951719999999, 2120.013852999989, 13.78725, 3232.690344000001, 9.142931547, 9.108450374, 9.120674533, 27.0926041 ], "PeriodsAmp": [ 0.22791356815287772, 0.03599719419115529, 0.18676833431961723, 0.03956128728097599, -0.2649706920257545, 0.10022074474351093, 0.10436992221139457, 0.14430534046016136, 0.07102249228279979, 0.11758452315976271, 0.04510213195702457, 0.06361160068822835, 0.05674788795284906, -0.043657524764462274, 0.07791151774412787, 0.019631216465477552, -0.14009026634971397 ], "PeriodsPhase": [ 13.451016651034463, 7.371101643819357, 18.44011357432109, 6.802030606034782, 21.120997888353294, 9.616514380782336, 5.715489866748063, 10.809731364754402, 9.031554832315345, 7.401459819968337, 5.9383444499771105, 14.60402121854254, 5.541215399062276, 8.44043335583645, 1.6019323722385819, 7.500513005887212, 7.860442540394975 ], "Year": 365.2520198, "final_state": { "D_prev": 0.04294 } }

RealClimate: Here we go again. An obscure, methodologically poor, paper published with little to no review makes a convenient point and gets elevated into supposedly 'blockbusting' science by the merc...

... continued from last post. The last set of cross-validation results are based on training of held-out data for intervals outside of 0.6-0.8 (i.e. training on t<0.6 and t>0.8 of the data, which extends from t=0.0 to t=1.0 normalized). This post considers training on intervals outside of 0.3-0.6 -- a narrower training interval and correspondingly wider test interval. Stockholm, Sweden…

... continued from last post. Each fitted model result shows the cross-validation results based on training of held-out data -- i.e. training on only the intervals outside of 0.6-0.8 (i.e. training on t<0.6 and t>0.8 of the data, which extends from t=0.0 to t=1.0 normalized). The best results are for time-series that have 100 years or more worth of monthly data, so the held-out data is typically 20 years.

The influence of planetary orbital changes on Earth’s temperature has been poorly quantified and subject to speculation. Here, we delineated the effects of greenhouse gases and planetary orbital ch...

This article in MIT News: "New research shows the natural variability in climate data can cause AI models to struggle at predicting local temperature and rainfall." ... "While deep learning has become increasingly popular for emulation, few studies have explored whether these models perform better than tried-and-true approaches. The MIT researchers performed such a study. They compared a traditional technique called…