Noise as Glue for a Broken Climate Vase ✎

Original: "Climate dynamics and fluid mechanics: Natural variability and related uncertainties"
arXiv:1006.2864 · 2010-06-15 · arXiv non-exclusive · independent analysis · 3 min
Random perturbations can lump disparate climate models into classes, erasing subtle differences between them.

For thirty years, climatologists have been gathering the shards of a broken vase. Each climate model is its own shard, and they all promise different warming by 2100, from 1.5 to nearly 6 degrees. The spread does not shrink no matter how much the models are improved. Inside this vase lives the ocean, which by itself oscillates with periods of 7 and 14 years, like a pendulum that no one pushes but that never stops. And the equations describing climate are such that the slightest change in the description of clouds or turbulence can flip the behavior of the whole system upside down. It is as if the vase shattered not into large pieces but into the finest dust, where every shard is unique.

The researchers studied a simple model of ocean circulation where wind drives water in a loop. As the wind strengthens, the current first stays still, then begins to pulse, and then transitions into chaos.

The sequence of bifurcations, qualitative rearrangements of the system's behavior, leads from stationary states to periodic ones and then to chaos.

In this chaos, a curious pattern emerged: new regimes arise not randomly but with specific wavenumbers, as if the ocean picks only certain notes from a huge range. But even such quantization does not save from spread: slightly change the viscosity or wind stress, and the entire bifurcation picture changes. The vase shards continue to splinter.

So the scientists changed tactics. Instead of trying to glue the vase exactly along the fracture lines, they decided to add glue that fills all the gaps. That glue was noise, random perturbations that are always present in the real ocean due to turbulence and weather systems. In a simple mathematical model, the Arnold circle map family, which describes the competition of two periodicities, noise destroys the narrow synchronization tongues, leaving only a finite number of wide ones.

Outside the tongues, the random attractor becomes a random fixed point, and the devil's staircase is smoothed.

Two models that behaved completely differently without noise become indistinguishable under its influence. The glue fills the cracks, and the shards merge into large pieces.

This result offers hope for a new way to classify climate models. Instead of comparing models by mean fields or sensitivity to carbon dioxide, one can look at how they respond to random perturbations. Models that differed deterministically may fall into the same stochastic class. This is like two different people who may behave alike in a noisy crowd, although in silence their personalities are dissimilar. So far the idea has been tested only on simple models, but it provides a theoretical basis for developing stochastic parameterizations in climate models. Perhaps noise itself will help assemble the climate vase into a whole, albeit with rough seams.

The Arnold circle map family describes the competition between two periodicities, such as the internal rhythm of El Niño and the annual cycle. In El Niño models, steps of the devil's staircase are indeed observed, corresponding to periods of 4 years, 2 years, and 16 months.

q_t + J(\psi,q) - \nu\Delta^2\psi + \mu\Delta\psi = -\tau\sin\frac{2\pi y}{L_y}, \quad q = \Delta\psi - \lambda_R^{-2}\psi + \beta y
Evolution of potential vorticity under wind, viscosity, and friction
x_{n+1} = x_n + \tau - \epsilon\sin(2\pi x_n) \mod 1
Model of interaction between two frequencies with nonlinear coupling
Concepts
natural variability ENSO El Niño seasonal cycle fluid flow interannual variability tropospheric biennial oscillation El Niño-Southern Oscillation Jin-Timmermann model ocean current TAO/TRITON moorings ocean-atmosphere coupling climate fluid dynamics in porous media spring predictability barrier monsoon wind stress Multivariate ENSO Index La Niña seasonal forcing