Supporting Documents:
A quick graphical summary of incremental remapping (pdf or swf)
Link to Lipscomb and Ringler, Monthly Weather Review, vol 133, no 8, pg 2335. (html)
Link to Ringler and Randall, Monthly Weather Review, vol 130, no. 5, pg. 1397. (html)
Regions of the Earth that receive more energy from the sun than is emitted back to space, like the tropics, stay at nearly the same temperature year after year because the excess energy is transported away from that region. The excess energy is transported to regions of energy deficit, like the Arctic.
A key to robust simulation of the climate system is properly modeling the process of transport. In its simplest form, the transport model is
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The equation simply states that a scalar field, such as temperature, moves with the flow velocity. What could be simpler?
This transport operator is deceptive in its
Transport Algorithms: The Core of Climate Models (home)
While the day-to-day weather events certainly give us the impression otherwise, the climate is really a system that is very close to equilibrium. When we average over a period of time (say a year or more) we find extremely small changes in the fields we use to characterize the regional climate (like temperature, precipitation, soil moisture, cloudiness, and so on). We can refer to the near stationarity of regional climate systems as quasi-equilibrium. While the magnitude and rate of human-induced climate change is notable relative to the geologic record, human-induced climate change is, at this point, a small deviation from quasi-equilibrium. Stated another way, in order to do a good job at understanding climate change we need to be able to reproduce the quasi-equilibrium structure of the climate system. Modeling the quasi-equilibrium of climate requires that we pay careful attention to how we model the day-to-day weather events. In order to correctly simulate the long-time scales of climate, we need to do many things right on the short-time scales.
The transport of a tracer field around a large island. The transport model is based on incremental remapping (see Supporting Documents). The transport model is monotone, 2nd-order accurate, and captures the inherently-Lagrangian nature of transport while retaining an Eulerian grid framework.
simplicity. Since the tracers move unchanged as they are advected by the velocity, the process is monotone; new extremes in the tracer field are not created by the transport process. Furthermore, not only is the tracer conserved under the process of transport, all of its higher moments (q^2, q^3, ...,q^n) are also conserved.
For rotating systems, such as our rotating Earth, the difficulty increases even more. Certain fields, such a potential vorticity (PV), are governed by the equation above and, in turn, determine the velocity field; knowing the PV field determines the velocity field that transports the PV field. Errors in PV lead to errors in the velocity field that feed back into even larger errors in the PV field as time progresses. Systematic discrepancies in our transport model, however small, can quickly amplify to the point where the simulation is of no use. Since the PV "tracer" field and the velocity field are so tightly coupled, the emphasis has to be on system transport where we quantify the errors in both the advecting velocity and the tracer transport process.
My work in system transport focuses on how to best capture the inherently-Lagrangian and conservative nature of the transport process while at the same time producing algorithms that are stable over simulation times of years to centuries.