2
Development and Testing of Model Parameterizations: Some Examples
Workshop participants discussed the importance of having the physical basis of large-system models firmly established by process studies based on field and laboratory measurement programs, theory, and numerical modeling. Based on the workshop participants’ expertise—including the workshop discussions and written input from the participants (see Appendix B for extended abstracts written by workshop invitees as requested by the organizing committee)—several key processes needing improved model parameterizations were discussed. In this chapter, a specific example of how parameterizations ought to be developed and tested is discussed, followed by a few examples of parameterizations that clearly need more work.
In many ways the research on fluxes between the atmosphere and oceans provides a nearly ideal example of how progress can be made in the representation of physical processes in large-scale models. A body of theory was developed, based mostly on dimensional reasoning, and field and laboratory experiments were designed to carefully and rigorously test the theoretical predictions. Field measurements led, in turn, to refinement of existing theory and, in some cases, to the development of new approaches. These were then once again tested in the field and in the lab, and further refinements were made. Even the very difficult problem of air-sea fluxes at the extreme wind speeds encountered in hurricanes has been addressed this way, with a number of laboratory and
field projects under way to test theoretical predictions. This has led to the desirable outcome that there is very little variation in representations of surface fluxes over the oceans in large-scale models.
At the other end of the spectrum is the representation of clouds and convection in regional and global models. Parameterizations of clouds and convection purport to describe the higher-order statistics of ensembles of clouds (e.g., the variance of relative humidity or the vertical flux of energy due to cloud-scale motions) in terms of lower-order statistics (e.g., mean temperature, humidity, vertical velocity). Here all statistics are assumed to be based on averages over scales that are large relative to individual clouds.
Parameterizing clouds and moist convection in models presents several unique challenges to modelers. Layer clouds may span many grid cells horizontally, but may be thin compared to typical vertical layer thicknesses; conversely, convective clouds usually occupy only a small fraction of a grid cell, yet span many model levels. Convective clouds represent major local sources of enthalpy and water vapor, and layer clouds have large effects on both shortwave and longwave radiative transfer. Representing both is crucial to most atmospheric and climate models, yet doing so has proven notoriously difficult. Transfer of enthalpy and water substance by convective clouds is sensitive to very small-scale processes such as turbulent entrainment and cloud microphysics, but evaluating parameterizations of clouds and moist convection against direct observations of these processes is a formidable undertaking. As discussed in Chapter 3, the difficulty of directly testing cumulus and cloud parameterizations has led to some undesirable practices in developing and testing such schemes. However, a new U.S. Climate Variability and Predictability (CLIVAR)-based activity, Climate Process and Modeling Teams (CPTs1), was established in 2003 to provide a thorough, efficient forum for improving model parameterizations by bringing together theoreticians, field observationalists, process modelers, and scientists at the large modeling centers (Bretherton et al., 2004; http://www.usclivar.org/CPT/index-newcpt.html). Three pilot CPTs are
being funded currently, one of which is examining cloud-feedback parameterizations.
The development of parameterizations of land-surface processes presents another set of difficulties. Correct representation of fluxes of heat, moisture, and momentum between the land surface and the atmosphere is critical to successful simulation of climate and weather. Progress in developing high-quality representations is impeded by the difficulty of making representative measurements of key land-surface properties and processes, such as soil moisture and evapotranspiration. Point measurements of many of these are difficult, and even if high-quality measurements could be made, the inhomogeneity and temporal variability of the land surface can render such measurements unrepresentative of the area- and time-average fluxes needed for input into regional and global models.
In the case of unresolved internal gravity waves, different parameterization methods can give very different results, and observations do not constrain these different methods well enough to distinguish among them. There is an abundance of data in which gravity waves are detected, but only rare datasets provide the needed informationthat is, momentum flux as a function of at least two wave characteristics and the propagation direction. It is a substantial observational challenge to characterize these intermittent and highly variable phenomena on a global scale using available measurements that were not designed to observe gravity waves.
Progress is being made using models to aid in the interpretation of global datasets and model studies of wave sources constrained by local observations. Early papers that described applications of gravity-wave parameterizations in global models used to commonly omit details on the momentum flux spectrum input into the parameterizations that were needed to understand the effects of the parameterized waves on the results, but this has been remedied in recent years (Manzini and McFarlane, 1998; Scaife et al., 2000, 2002; Giorgetta et al., 2002).
The representation of small-scale physical and biological processes in the oceans also presents several unique challenges. Oceanic general circulation models make severe compromises in their representation of many of the controlling dynamical processes. On scales smaller than oceanic basins, significant fluxes of momentum and dissolved materials are effected by mesoscale eddies; inertial, internal gravity, and surface gravity waves; double-diffusive mixing; and small-scale turbulent
motions in the surface and bottom boundary layers. And, of course, the fluxes also are effected by the possible interactions among all of these phenomena and in their relationships with the large-scale circulation and stratification. In the general circulation models, these fluxes are represented by parameterizations of well-known equations, and they are designed and evaluated on the basis of theory, measurement, and fine-scale simulation. To further improve ocean parameterizations, there are two ocean mixing CPTs in addition to the aforementioned cloud-feedbacks CPT—one studies the interaction of eddies and the surface boundary layer, and the other studies the bottom boundary layer as a gravity current. A recent essay (Schopf et al., 2003) commissioned by U.S. CLIVAR in developing a plan for these CPTs surveys the relevant processes and the status of their understanding and parameterization.
The oceanic and terrestrial ecosystems are important functional elements of Earth’s system. For instance, the ocean’s biogeochemical cycling of nitrogen, carbon, oxygen, and so forth is carried out by the lower trophic levels from viruses through plankton. In large-scale models this is represented as transport, reaction, and population dynamics. For the most part, the model rules for these ecosystem dynamics are acts of imagination, usually involving abstraction of actual organisms to hypothesized generic forms but guided by overall conservation principles. Such constructs are exceedingly difficult to evaluate except at the gross level of chemical distributions and fluxes, both because of their organismic unreality and the technical measurement challenges of highly variable compositions with quite heterogeneous distributions.
