Thursday, October 23, 2014

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Anti-Seasonal Outlook, Seasonal Outlook: Part IV

Dr. Seasonal or: How I learned to stop worrying and love the planet

            Why should you not concern yourself with seasonal (or longer) forecasts of the Earth system? Quite simply, it all comes down to the fact that we are operating in a complex, nonlinear system that is highly dependent on the initial conditions. We know a few, but since we don’t know what each molecule of air or water vapor is doing we are just guessing.
            Edward Lorenz clearly demonstrated this in the late 1960s, shortly after John von Neumann and Jules Charney produced the first numerical weather forecasts. While state of the art models have made impressive progress in forecast lead times over the past 50 years, at longer forecast times the problems of numerical error growth (floating point and truncation) results in diverging solutions as does the failure to accurately represent the physical mechanisms at various, interacting scales. As the equations of fluid motion have no analytical solution, numerical approximations must suffice and thus are susceptible to the aforementioned numerical errors.
            Turbulence in the atmosphere and ocean are critical components involved in the transfer of energy both up and down scales, and are not closed mathematical systems. Unclosed mathematical systems have more unknowns in the set of equations than known equations. This problem has been haunting physicists since initial recognition of the problem in 1924 by Keller and Friedman. Approximations are the only way around this, and out the window goes long-term skill. The list of issues goes on, from poor resolution of terrain that exerts a tremendous influence on the regional and global circulations (see Broccoli and Manabe 1992) to the formation of clouds in all environments.

Figure 1: Global averaged annual sea surface temperature from the MERRA ERA-Interim reanalysis model and observational data assimilation product.

            Global climate models do a phenomenal job of recreating physically reasonable features predictability with skill continues to disappoint. This is likely due to the issues listed above (turbulence, not knowning the states of all molecules) as well as significant biases in key fields, such as sea surface temperatures (SSTs; see Figures 1 and 2). Thus I see virtually no use, unless your interest is in wasting time, to make a seasonal, let alone multiple-season (i.e., extended winter NDJFMA) forecast, as an educated guess versus a random guess will likely demonstrate the same skill.

Figure 2: Global averaged annual sea surface temperature hindcast (1870-2013) and forecast (2013-2100) output from the CCSM4 global climate model. Note the ~3°C cold bias of CCSM4 and the linear increase in SSTs. Few natural systems are so linear, and this is cause for concern both in the modeling approach and the potential system responses (abrupt climate change anyone?).

            Relationships between predictor variables are demonstrably nonstationary (Ramage 1983). This means that the relationships change over time. For example, for some period of time the negative phase of ENSO leads to less than average precipitation but then for some other period the opposite is true. Big trouble! The use of stationary assumptions developed over a finite period of time will only confound the prediction process. Relationships do exist, of course, but the interactive nature of the forcing terms greatly complicates the matter as these relationships change as boundary conditions change and are subject to variance in higher frequency forcing terms which also perturbs the 'known' relationships. Even if we did know all of the conditions, we still can’t solve the equations analytically!
            It should be easy to see why forecasting at lead times longer than 7-10 days will only lose you money. That said, GCMs are excellent tools for examining sensitivities to the climate system, such as how the hydrologic cycle will respond to a warmer planet (warning, not good! See Held and Soden 2006 and Trenberth 2011 for depressing news). The bottom line is just wait and see! Spend your time training, visualizing, and planning for radness. This way, your season will be awesome no matter what the outcome.


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