Mesoscale Dynamics and Predictability

Goal: The skill of precipitation forecasts is limited by both fundamental and practical constraints. The practical constraints include the accuracy of the forecast model and the accuracy of its initial conditions. This is in turn determined by the available observations and their quality and by the scheme used to assimilate those observations. The fundamental constraint is the finite limit of predictability, which arises even for an accurate model and initial conditions from the influence of unresolved scales.

Dynamics

Understanding the relation between meso- and synoptic-scale flows involves, in part, understanding how atmospheric dynamics change as the Rossby number increases. At small Rossby number, virtually all dynamical theories rest upon the foundation of quasigeostrophy (QG), which is the leading-order theory in Rossby number. David Muraki (Simon Fraser University, Canada), Chris Snyder and Richard Rotunno have introduced a convenient technique for extending QG to an additional order in Rossby number; they call this extended theory "QG+1."

Greg Hakim (University of Washington), Snyder and Muraki have applied QG+1 to simulations of quasi-two-dimensional, balanced, decaying turbulence to understand the observed preference for cyclonic vortices on the tropopause at subsynoptic scales. These simulations produce numerous small cyclonic vortices with sharp edges, while the anticyclones are infrequent, relatively large scale and diffuse. These asymmetries appear to arise not from corrections to the basic geostrophic balance (e.g., gradient wind balance) but through the action of the horizontally divergent component of velocity during frontogenesis; in essence, the asymmetries are tied to the fact that on average warm air rises and cold air sinks during frontogenesis, thus leading to a mean cooling at the surface.

Prediction and Predictability

Fuqing Zhang (USWRP postdoc, now Texas A&M University), Snyder and Rotunno have explored the limits of predictability for precipitation within the context of the "surprise" snowstorm that paralyzed Washington, D.C. on 25 January, 2000. Their work began by analyzing a number of practical influences on the skill of the 36-h forecast of this storm, such as the model resolution and the initial conditions. They found that reducing the horizontal resolution from 10 km to 30 km, or using another, equally plausible initial analysis, can significantly degrade the precipitation forecast. In both cases, the degradation of the forecast is intimately tied to moist processes, which result in the growth of forecast differences at horizontal scales of a few hundred to a few tens of kilometers. These experiments have led Zhang et al. to consider more explicitly how initial errors of small scale and small amplitude can alter the subsequent forecast. Using an embedded, 3-km grid, they have shown that initial differences with scales of less than 100 km and amplitudes of less than 1 K, grow rapidly by altering the position and timing of individual convective elements (in this case, in a region of negative lifted index over Louisiana). The differences then contaminate larger scales, altering the mature cyclone and the precipitation over the East coast 36 h later. It is clear that this growth from small to large scales places an upper bound of a few tens of hours on skillful, deterministic precipitation forecasts.

Thomas Hamill (NOAA-CIRES Climate Diagnostics Center), Snyder and Rebecca Morss have also used a quasi-geostrophic model, along with a three-dimensional variational assimilation (3DVAR) scheme, to explore the characteristics of forecast and analysis errors at synoptic scales. They find that both forecast and analysis errors reflect the influence of the dynamics: The errors have significant projection on the subspace of leading Lyapunov vectors. Their time-mean vertical distribution in both energy and potential enstrophy is similar to that in the "true" state, and error variance in potential vorticity is typically confined to regions in which the true state has large gradients of potential vorticity. A consequence of this dynamical influence is that the spectrum of the covariance matrix for both forecast and analysis errors is steep and small samples (or ensembles, of a few 10's of members) can provide much information about the errors.

The fact that a small ensemble can provide useful information about forecast errors provides potential for improving data assimilation schemes, thereby decreasing the practical limitations on forecast skill. The resulting assimilation schemes are typically referred to as ensemble Kalman filters (EnKF). Hamill, Snyder and Jeff Whitaker (NOAA-CIRES Climate Diagnostics Center) have examined the use of distance-dependent truncation of the ensemble information in the EnKF. Snyder and Zhang have applied the EnKF to the analysis and prediction of convective scale motions using the simple cloud model developed by Juanzhen Sun. They have shown that a 50-member EnKF is able to estimate tangential and vertical velocity and temperature, given simulated Doppler-radar observations of radial velocity alone (extracted from a reference simulation of a supercell thunderstorm). Typically, about 4 volume scans (or 20 minutes) of observations are required to produce a good estimate of the unobserved variables. These results hold substantial promise for the application of the EnKF to meso- and convective scales, where more traditional assimilation schemes such as 3DVar can be problematic.

Given the location and uncertainty of an observation, the EnKF can provide a quantitative estimate of the impact of that observation on the analysis uncertainty. This provides a basis for adaptive observational strategies, which seek improved forecasts by reallocating observational resources to improve the analysis. Hamill and Snyder completed a study within the quasi-geostrophic model that tests the use of the EnKF in the adaptive design of observing networks. They have developed a simple and efficient algorithm to choose the locations of observations: using the ensemble Kalman filter, they find the location at which the impact of an observation is estimated to be largest. They then find the next best location given the first observation and continue the process up to the desired number of observations. In these tests, they find that as few as half as many adaptive observations are required to produce analyses with the same uncertainty as those obtained for a given fixed observation network.

Expected fractional reduction of analysis error variance from application of adaptive observation algorithm based on an ensemble Kalman filter. Results are shown for Day 14 of the 90-day test in a quasigeostrophic model (see Figure 1).

The Antarctic Mesoscale Prediction System (AMPS)

In response to the need for improved forecasting capabilities to support the United States Antarctic Program at McMurdo Station MMM has developed and implemented an experimental, MM5-based NWP system for Antarctica. The system, known as AMPS (Antarctic Mesoscale Prediction System), has operated since the 2000-2001 field season. AMPS employs the Polar MM5, a version of the model containing parameterizations and features aimed to better capture polar conditions. These features encompass packages such as modified radiation schemes and the inclusion of sea ice. AMPS provides higher resolution over the regions of key forecast concern than other available Antarctic guidance, with 10-km horizontal grids over the Western Ross Sea/McMurdo Station and the South Pole areas. AMPS has served to assist the daily forecasting for McMurdo and the South Pole performed by the Space and Naval Warfare Systems Center (SPAWAR) for NSF, and was also employed in the successful medical rescue of Dr. Ronald Shemenski from the South Pole in April, 2001. An AMPS forecast archive is maintained to support the research of modelers, polar meteorologists and grad students.