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Wilfred von Dauster

June 2002 FSL Forum Flow Imbal By Steven E. Koch and Fernando Caracena


When was the last time you had a smooth airplane ride? If you fly frequently in and out of Denver International Airport, you may say, "Never!" The snow-capped Rockies that rise majestically west of the airport disturb the air currents, resulting in turbulent flying in the area.

Pilots report turbulence when strong inhomogeneities in the airflow cause the aircraft to pitch, yaw, rattle and roll. For passengers and crew alike, turbulence is more than a nuisance causing temporary discomfort; it is a serious air safety hazard that pilots need to avoid. A good turbulence forecast would certainly help, but, unfortunately, turbulence is difficult to forecast. As discussed below, the search for a good turbulence forecasting scheme leads in different directions, because of the variety of physical mechanisms that produce turbulence.

Physical Causes of Turbulence

Much of the Earth's atmosphere flows smoothly in layers — the atmosphere is stably stratified. At the ground the wind may be calm, but at 30,000 feet the wind speed may be over 100 miles per hour. Mountains disturb the layers of wind, producing vertical undulations (mountain waves) sometimes seen as stacks of lens-shaped (lenticular) clouds downwind from the ridges (as shown in Figure 1). Some mountain waves may steepen, overturn, and cascade into turbulence.

Flow Imbal - Fig. 1

Figure 1. Lenticular clouds are formed in mountainous areas
when layers of wind produce vertical undulations (mountain
waves) in the airflow downwind from the ridges.
Photo by Fernando Caracena

Obviously, thunderheads disturb the smooth, stratified airflow. Time-lapse videos show cloud towers billowing up, withering, and collapsing — a lot of vertical motion. Surging cloud towers strike, flatten out and reverberate on the tropopause, generating gravity waves in the upper troposphere and stratosphere that move out in all directions beyond and above the cloud. Rain-cooled air falls to earth beneath these towers, rushing out, rolling, and twisting. Thunderstorms fill a volume of the atmosphere larger than themselves with turbulence.

Clear-air turbulence (CAT) is generally believed to be caused by a subtle mechanism referred to as the Kelvin-Helmholtz instability. The change in wind vector with height (vertical wind shear) may approach a critical strength, beyond which it overcomes atmospheric stability and begins to turn over the layer. The degree of this type of shear instability is portrayed by a parameter called the Richardson number.

Another kind of wave, the "mesoscale gravity wave" (MGW), is generated by a dynamical imbalance within the jet stream. Case studies (some described below) suggest that MGWs may be another source of turbulence. The existence of MGWs has been documented from the time-evolution of surface pressure, as analyzed from 5-minute data from the National Weather Service Automated Surface Observing System (ASOS), and from wind profiler analyses. These analyses suggest that MGWs have horizontal wavelengths greater than 50 kilometers and can last 1 – 3 hours.

Difficulties in Forecasting Turbulence

Turbulence forecasting is tantamount to determining where the smooth, vertically stratified airflow will break down into strong vertical circulations having large height-to-width ratios capable of disturbing the smooth flight of an aircraft. These turbulent eddies are much smaller than the resolution of current numerical weather prediction (NWP) models, and they exist in part because of the circulations that are happening on still smaller scales. In the real atmosphere, these whirls are part of a linked series of whirls that cascade energy from the largest scales of atmospheric motion down to the molecular dissipation scale. By their very nature, NWP models truncate the series of interlocked circulations involved in the energy cascade. In the model atmosphere, subgrid circulations that affect resolvable circulations are parameterized. Different parameterization schemes, of course, give different results. For the above reasons, turbulence forecasts currently are diagnosed from the larger-scale conditions forecast by NWP models.

For several years, diagnostic algorithms for predicting CAT have been applied to the Rapid Update Cycle (RUC) model forecasts and incorporated into a fuzzy logic process known as the Integrated Turbulence Forecast Algorithm (ITFA). The forecast skill of ITFA and its component algorithms has been evaluated both objectively and by forecasters. These studies show that the best of the algorithms display similar probability of detection (POD) curves (Figure 2), and that there is considerable room for improvement. [The optimum scheme would display PODy=1.0 with a value of (1-PODn)=0.0, since PODy (PODn) is the proportion of Yes (No) observations correctly forecasted.] FSL developed one set of algorithms most used in ITFA, the DTF (Diagnostic TKE Function) series. [See the February 1999 and June 1997 issues of the FSL Forum.]

Flow Imbal - Fig. 2

Figure 2. Plot of skill in 3-hour RUC forecasts for ITFA, the best four algorithms used by ITFA, and AIRMETs for JanuaryMarch 2001. Line indicates no skill in forecasts of turbulence. Similar statistical behavior occurs at other forecast times.

Our research indicates that these algorithms also typically predict patterns that are similar to one another, and that moderate-or-greater (MOG) pilot reports (PIREPs) of turbulence often fall in the margins of the predicted ITFA regions. One contributing reason for these seeming deficiencies is that PIREPs are used to steer aircraft from areas where pilots have reported turbulence, resulting in an apparent overforecast of the predicted areas.

The shortage of PIREPs in the center of the areas of predicted turbulence makes it very difficult to assess the true performance of turbulence prediction schemes. However, we suggest that there may be another dynamical reason for the imperfect performance of IFTA algorithms.

The best of these algorithms are fundamentally based on the destabilizing dynamics of vertical wind shear. The Richardson Number Ri (Rich in Figure 2) varies inversely with the square of the vertical wind shear. Another algorithm, Brown-1, is a simplification of the Ri tendency equation. DTF3 attempts to account for two major sources of turbulent kinetic energy — shear instabilities and momentum flux. Ellrod-2 is simply the product of the magnitude of the vertical wind shear and the combined horizontal wind deformation plus convergence. This latter algorithm assumes that horizontal deformation will produce frontogenesis, resulting in enhanced vertical wind shear needed to maintain thermal wind balance and sufficient to decrease Ri so that shearing instability will be generated. The tilting term, though recognized as the main contributor to upper-level frontogenesis, is entirely ignored in Ellrod-2.

A New Turbulence Prediction Scheme

FSL has developed a new turbulence prediction scheme based on the knowledge that MGWs displaying wavelengths >50 km are generated as an unbalanced jet streak propagates toward an inflection axis in the upper-level height field (Figure 3). We have diagnosed gravity waves and flow imbalance in several detailed case studies. These analyses show that MOG PIREPs and analyzed MGWs consistently occur directly downstream of the region of diagnosed flow imbalance. Furthermore, this new predictive scheme not only produces patterns systematically different from the current ITFA algorithms but also predicts turbulence regions missed by those methods.

Flow Imbal - Fig. 3

Figure 3. Schematic model showing region of MGW activity (shaded) that occurs as a jet streak (V) advances ahead of the geostrophic wind maximum (Vg) and approaches an axis of inflection in the upper-level height field (dashed) north of a warm or stationary front at the surface. Gravity waves are generated near the inflection axis and propagate downstream to the ridge axis (dotted).

Subjective evaluation of the turbulence prediction algorithms by forecasters at the Aviation Weather Center suggests that MOG turbulence in the winter season is frequently associated with upper troughs and jet streams. Our own research indicates that this happens most frequently on days when well-developed cyclonic storms form in areas affecting the major flight routes. In these cases, nonconvective turbulence encounters (no lightning nearby) tend to cluster in two areas: the anticyclonic upper-level outflow regions of cyclones, and downstream of the dry slot in the area of strong horizontal deformation surrounding the comma head. This is distinctly different from that of the other ITFA algorithms, which typically maximize in the vicinity of the strongest wind shears associated with the jet stream irrespective of the occurrence of cyclogenesis.

Case Studies – The two-area clustering nature of MOG PIREPs is demonstrated at 1200 UTC 7 February 1999 (Figure 4). MOG PIREPs are superposed on the corresponding enhanced GOES water vapor image (4a). The corresponding 300-hPa analysis is shown in (4b). The first cluster of MOG PIREPs stretches from western Wisconsin to eastern Ohio in the anticyclonic outflow region of the well-developed cyclone centered over southern Illinois. This cluster of turbulence reports is fairly well predicted by the DTF3 algorithm (and ITFA, not shown), though the predicted region (4c) is centered north of the cluster. The second dense MOG PIREPs cluster, over the Ohio Valley region in an arc extending from central Illinois to northern Kentucky, occurs precisely at the tip of the dry slot in the water vapor image. This cluster is essentially missed by the DTF3 and ITFA predictors, but is predicted by our imbalance diagnostic algorithm (4d).

Flow Imbal - Fig. 4a

Flow Imbal - Fig. 4b

Flow Imbal - Fig. 4c

Flow Imbal - Fig. 4d

Figure 4. Analyses and 3-hour RUC-2 forecast diagnostics valid at 1200 UTC 7 February 1999: a) enhanced water vapor imagery and time-space converted MOG PIREPs over a 2-hour interval, b) heights and winds at 300 hPa, ridge axis (thick curve), and jet isotachs (kt), c) DTF3 prediction of turbulence and MOG PIREPs overlay, and d) unit streamwise advection of the residual of the nonlinear balance equation.

What is meant by "imbalance"? We define the flow to be unbalanced when there is a pronounced residual in the computed sum of the terms in the nonlinear balance equation (NBE) from the model, that is, from the RUC model. Imbalance typically occurs in an area where a jet streak propagates toward the inflection axis in a highly diffluent 300-hPa height field (essentially the same region as that where MGWs typically develop (Figure 3)). This is occurring over western Kentucky and southeastern Missouri (4b), where a large residual in the NBE field is diagnosed. The turbulence predictor scheme (4d) is calculated as the unit streamwise advection of the residual. This field displays a pronounced maximum downstream of the residual, namely from central Illinois to Northern Kentucky, coinciding precisely with the second cluster of MOG PIREPs missed by the other IFTA algorithms. This ability of this new scheme, and others based on the concept of unbalanced flow, to add value to the existing methods is characteristic of all the cases we have examined.

Algorithm Testing and Modification

Further refinement of the forecast region can be obtained by adding the requirement that an efficient wave duct must be present downstream of the region of diagnosed flow imbalance to retard the vertical leakage of wave energy, thus allowing coherent MGW to persist. While mesoscale models like RUC can be useful for diagnosing the flow imbalance regions, they do not reliably predict the details of the gravity waves themselves. The next example uses an automated surface mesoanalysis system applied to 5-minute ASOS data to analyze observed MGWs, and compares the existence of diagnosed waves to both PIREPs and various turbulence predictor fields.

A plot of 3-hour accumulated MOG PIREPs for 09001200 UTC 11 March 2000 shows that a coherent area of turbulence centered over the mid-Mississippi Valley region before 1400 UTC progressed steadily eastward to Ohio and eastern Kentucky in the ensuing 12 hours (Figure 5a). The ITFA product based on a 3-hour RUC model forecast valid at 1800 UTC (5b) predicts the strongest turbulence to occur in a broad anticyclonic arc extending from eastern Missouri to Quebec, considerably west and north of the actual region of turbulence. Consideration of the NBE residual field (yellow shading in Figure 5c) together with the duct factor field (blue shading) shows that the region shaded in red would be where gravity waves and associated turbulence would be predicted. In particular, this region is downstream of the maximum diagnosed imbalance, upstream of a region of large duct factor over the Great Lakes, and limited by the ridge in the 300-hPa height field. This field differs as a potential turbulence predictor from the first case, in that we are here considering the presence of a wave duct as an additional prerequisite for coherent MGW occurrence. The predicted turbulence region encompasses the entire swath of MOG PIREPs over the Ohio Valley missed by ITFA. Finally, the surface mesoanalyses (5d) indicate that a very coherent train of gravity waves did indeed propagate from the region of diagnosed imbalance northeastward toward the ridge axis in Ohio and Indiana.

Flow Imbal - Fig. 5a

Flow Imbal - Fig. 5b

Flow Imbal - Fig. 5c

Flow Imbal - Fig. 5d

Figure 5. a) MOG PIREPs for a 12-hour period beginning 1200 UTC 11 March 2000, b) ITFA prediction of turbulence from the 40-km RUC 3-hour forecast valid at 1800 UTC 11 March 2000, c) MGW prediction of turbulence and 300-hPa height field from the 80-km Eta model 6-hour forecast valid at 1800 UTC, and d) diagnosed gravity waves in surface band-pass-filtered objective mesoanalysis or pressure at 1930 UTC (red, positive; blue, negative).

Waves and Convection – While it is true that thunderstorms can generate a wide variety of gravity waves, it has also been established that gravity waves can spawn deep convection, another prevalent source of vigorous turbulence. Thus, finding ways to predict and detect such waves before they trigger thunderstorms would greatly benefit the aviation community. Such an event is shown in Figure 6, in which a gravity wave packet propagated in a coherent fashion from extreme southeastern Colorado at 2300 UTC 17 February to central Kansas by 0300 UTC 18 February 2000. Notice the absence of deep convection in this region at the earlier time, whereas severe thunderstorms have erupted over central Kansas by 0300 UTC (in contrast to the storms in Missouri, which simply persisted throughout this period). The storms erupted as the waves propagated over more unstable air in Kansas. The forecast NBE residual field showed a single maximum over southern Colorado at 1800 UTC and an efficient wave duct over eastern Kansas; a cluster of MOG PIREPs advanced from eastern Colorado to central Kansas and Nebraska at this time. Thus, the area of predicted MGW and CAT activity would be precisely the region in which this activity occurred. Knowledge of the existence and future behavior of the wave packet and diagnosed imbalance would have provided a useful short-term forecast of both the subsequent convection and turbulence.

Flow Imbal - Fig. 6

Figure 6. Comparison of bandpass-filtered surface mesoanalyses of pressure (top left) to enhanced infrared window satellite imagery (top right) at 2300 UTC 17 February 2000, and 0300 UTC 18 February 2000 (bottom). Note the gravity wave packet that propagates from southeastern Colorado at 2300 UTC to central Kansas by 0300 UTC and the formation of severe thunderstorms in Kansas as the waves advanced into more unstable air.

Future Research

Our proposed turbulence prediction scheme is based on the concept that mesoscale gravity waves (MGWs) and clear-air turbulence (CAT) are generated downstream of regions of diagnosed flow imbalance and upstream of regions of appreciable wave duct factor strength. It appears from the case studies presented here and many others not shown that this scheme adds predictive value to existing approaches, by forecasting distinctly different regions of turbulence missed by other ITFA algorithms.

The residual of the nonlinear balance equation and other methods are being investigated to arrive at the optimum method for diagnosing imbalance. Real-time evaluation of these approaches is also being performed in preparation for eventual implementation and full evaluation within ITFA.

Our findings raise the very interesting question: How can CAT be generated by gravity waves with such long wavelengths (>50 km)? The obvious answer is that these waves are not the direct cause of the turbulence, but rather, they are an important predecessor to the generation of Kelvin-Helmholtz instability. Unfortunately, current mesoscale models, while quite useful for diagnosing the conditions in which MGWs develop, cannot reliably predict the characteristics of the waves themselves (phase velocity, amplitude, wavelength), not to mention the ability to predict turbulence intensity. In addition, grid-mean stability, wind shear, and Ri number do not relate well to the patchy, thin-layered nature of turbulence.

We hypothesize that CAT can develop from MGWs as the fronts steepen due to nonlinear advection of the dominant wave in a wave packet. Nonlinearity leads to horizontal wavelength shortening, eventual wave breaking, and resultant turbulent kinetic energy generation. Future idealized modeling studies will be performed to develop a basic understanding of the nonlinear scale contraction process by which MGWs may steepen and saturate, leading to turbulence production.

Note: A complete list of references and more information on this and related topics are available at the main FSL Website www.fsl.noaa.gov, by clicking on "Publications" and "Research Articles."

(Dr. Steven Koch, Chief of the Forecast Research Division, can be reached at koch@fsl.noaa.gov. Dr. Fernando Caracena, a researcher in FRD, can be reached at caracena@fsl.noaa.gov.)

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