- VMBE = (VCL - VLLJ).
This simple model will be used as a framework upon which to test our hypotheses.
Figure 1. Conceptual model of MBE movement (VMBE) as the vector sum of the mean flow in the cloud layer (VCL) and the propagation component (VPROP). The magnitude and direction of VPROP are assumed to be equal and opposite to those of the low-level jet (VLLJ). The angles f and j are used in (3) and (4) to calculate VMBE given observed values of VCL and VLLJ. Dashed lines (labeled THKNS) indicate a typical relationship of the 850-300 mb thickness pattern to the environmental flow and MBE movement during MCC events.
Section 2 describes the data and methods used in the empirical analysis and section 3 presents the results. A brief summary with concluding remarks is given in section 4.
2. DATA AND METHODOLOGY
An empirical approach requires, of course, a sizable sample of events. To this end, 103 mesoscale convective systems, 99 of which met MCC criteria, were selected for study. The events occurred during the four-year period 1980-83 and were identified from the annual MCC summaries of Maddox et al. (1982) and Rodgers et al. (1983) and from inspection of geostationary satellite imagery. Standard surface and upper-air sounding data along with hourly manually-digitized radar (MDR) composite charts were compiled for each event.
Because the standard sounding data are only available at 0000 and 1200 UTC, criteria had to be established for selecting the time most representative of the MBE environment. Also, since the point of this paper is to develop a tool that will aid in forecasting, it is of most interest to examine whether or not knowledge of VCL and VLLJ near the time of MCC genesis is sufficient to produce a successful short-term forecast. Therefore, the sounding time within six hours of MCC genesis, as defined by Maddox (1980), was selected as representative of the MBE environment.
As indicated in (1), a forecast of VMBE requires estimates of the mean flow in the cloud layer and the low-level jet. Based upon the analyses of Maddox (1983) and McAnelly and Cotton (1986), it is assumed that the cloud layer is well-represented by the 850 to 300 mb layer. The mean flow in this layer is determined in a manner following Fankhauser (1964), i.e.,
(2)
- VCL = (V850 + V700 + V500 + V300)/4,
where the direction and magnitude of the wind at each level on the right hand side is taken to be representative of the 900-800 mb, 800-600 mb, 600-400 mb and 400-200 mb layers, respectively. Fankhauser justified allocating equal weight to the lowest layer despite its smaller depth by noting that most of the air entering a thunderstorm originates at low levels. Estimates of the winds in the vicinity of the MCCs were obtained using the objective analysis system documented in Cahir et al. (1981) .
Estimates for the speed and direction of the low-level jet are obtained following the strict criteria of Bonner (1968), i.e.,
- criterion 1: the wind speed at the level of maximum wind is
over 12 ms-1 and decreases by at least 6 ms-1 to the next higher
minimum or the 3 km level, whichever is lower.
criterion 2: the wind speed at the level of maximum wind is
over 16 ms-1 and decreases by at least 8 ms-1 to the next higher minimum or the 3 km level, whichever is lower.
criterion 3: the wind speed at the level of maximum wind is over 20 ms-1 and decreases by at least 10 ms-1 to the next higher minimum or the 3 km level, whichever is lower.
Only wind maxima at or below 1.5 km above ground level were considered low-level jets since the thunderstorm cells of developing MCCs are most likely to ingest air from near the surface. For five cases where pre-MCC convection formed in the overrunning zone above a frontal surface, however, data from the 2.5 or 3.0 km level were used. In the absence of a low-level maximum in the vertical distribution of the wind, the inflow wind at 850 mb (or at 700 mb over the elevated area between the Rockies and 100 degrees west longitude) that exhibits a maximum in the horizontal wind speed distribution is used as the low-level jet.
Once values for VCL and VLLJ are determined, then a forecast of the magnitude of VMBE can be obtained from:
(3)
- VMBE = {(VCL)2 + (-VLLJ)2 - 2((VCL)(-VLLJ))cos@}1/2,
where @ is the angle between the mean cloud-layer wind and the low-level jet (see Fig. 1). Similarly, MBE direction can be determined using an elementary relationship for the angle $ between the direction of MBE movement and the mean cloud-layer wind:
(4)
- $ = arcsin{(-VLLJ)sin@/VMBE)},
where MBE speed is given by (3).
The final set of data necessary to examine whether of not there are useful predictive relationships among VCL , VLLJ , and MBE movement is the observed movement of the MBEs. The MBEs were defined as areas of VIP (video integrator and processor) level 3 or greater on the manually digitized radar (MDR) charts. A VIP value of three or more implies an hourly precipitation rate in excess of 25.4 mm (generally thunderstorm precipitation). Their movement was determined by plotting the centroid of their hourly positions throughout the lifecyle of each MCC. A mean speed and direction of MBE movement was determined by subjectively constructing a straight line of best fit from the beginning to the end of each event. Because precipitation intensity is digitized on a grid with only one VIP value allotted for each approximately 40 by 40 km area, the resolution of areal intensity is compromised. Such resolution problems are lessened somewhat since the positions and movements of the deepest cells are noted as part of the MDR summary. Additionally, detailed precipitation analyses of all 1982-83 MCCs (available from Kane et al. 1987), using hourly rain gauge data, were examined to corroborate the MDR data, i.e., the heaviest precipitation was found to be colocated in general with the MBEs.
3. RESULTS
The first step in developing the forecasting technique was to investigate whether or not the advective component of MBE movement, defined as the mean motion of the cells comprising the system, is proportional to the mean flow in the cloud layer. Figure 2 presents scatter plots of a) observed cell speeds vs. the magnitude of VCL, and b) observed cell directions vs. the direction of VCL. These plots clearly indicate that much of the cell motion is dictated by the mean cloud layer flow. These results agree with the early radar studies of Brooks (1946) and Byers and Braham (1949) who found that cells move downwind in the direction of the mean cloud layer flow.
Figure 2. Scatter plot of a) mean 850-300 mb wind speed vs. cell speed and b) mean wind direction vs. cell direction. Speeds rounded to the nearest 2.5 ms-1 and directions to the nearest 5 degrees. Cell movements were available for 74 of the 103 events during the MCC genesis stage. Dashed lines denote perfect (one-to-one) relationship.
A substantially more questionable part of the forecast technique is whether or not the speed and direction of the low-level jet are indicative of the propagation component of MBE movement. If true, this would be a rather sweeping relationship since propagation can be influenced by many factors such as convective available potential energy, convective inhibition, orographic influences, gravity waves, outflow boundaries, etc. In order to examine this issue, we have plotted the direction of the observed propagation component vs. the direction of the low-level jet (Fig. 3). The observed propagation component is defined as the departure of the MBE movement from the mean flow in the cloud layer. Clearly, there is a strong tendency for the propagation direction to be approximately 180 degrees out of phase with the direction of the corresponding low-level jet. Although the correlation coefficient is only 0.65, this value increases to 0.84 upon omission of the two outliers in the upper left part of the graph. Thus, in spite of all the factors that influence propagation, it is evident that there is an overwhelming tendency for MBEs to propagate toward or "into" the low-level jet.
Figure 3. Scatter plot of MBE propagation direction vs. the direction of the low-level jet for 103 events. Propagation direction defined as the layer (850-300 mb) wind. Systems with propagation vectors between 0 and 120 degrees have been plotted between 360 and 480. Directions in degrees azimuth. Dashed line denotes perfect anti-parallel relationship between direction of MBE propagation and that of the low-level jet.
The final component of the conceptual model that needs to be investigated is whether or not the speed of the low-level jet is an important factor in determining the magnitude of VPROP. If this is the case, then it should be true in most cases that the difference between VLLJ and VCL will provide a skillful forecast of VMBE, the vector movement of the meso-beta scale elements.
Figure 4 shows plots of the "forecast" MBE speed and direction vs. the observed values; Table 1 summarizes the forecast errors. It is evident that the forecasting technique possesses considerable skill; correlation coefficients are 0.80 and 0.78 for MBE speed and direction, respectively. The scheme tends to overforecast the speed of slow systems (those with speeds less than 12.5 ms-1) but, overall, provides a good estimate of the rate of movement.
Figure 4. Scatter plot of a) forecast MBE speed vs. observed and b) forecast MBE direction vs. observed for 103 events. Speeds rounded to the nearest 2.5 ms-1; directions rounded to the nearest 5 degrees azimuth. Dashed lines denote perfect forecasts.
Table 1. Comparison of forecast MBE speed and direction to the observed values. Speeds in ms-1; directions in degrees azimuth. Standard deviations in parentheses. Average absolute error is the sum of the absolute variance for all events divided by the total number of events.
Directional forecasts, however, are somewhat more problematic. Considering that the typical MCC in the U.S. persists for about 9.5 h (Velasco and Fritsch 1987), the average directional error shown in Table 1 would result in a 100-150 km error in the location of the center of the MBE activity at the time the system dissipates. Nevertheless, for most of the systems life cycle, the typical location error would be less than 100 km which is well within the approximately 300 km width of the heavy rain band (greater than 13 mm) of most MCCs (Kane et al. 1987).
4. SUMMARY AND CONCLUDING REMARKS
A procedure for operationally predicting the movement of the meso-beta scale convective elements (MBEs) responsible for the heavy rain in most MCCs was developed. The procedure is based on the well known concept that the motion of convective systems can be considered as the sum of an advective component, given by the mean motion of the cells comprising the system, and a propagation component, defined by the rate and location of new cell formation relative to existing cells. The advective component was found to be correlated to the mean flow in the cloud layer. The propagation component was shown to be directly proportional (but opposite in sign) to the speed and direction of the low-level jet.
Application of the procedure to 103 mesoscale convective systems (99 of which were MCCs) yielded correlation coefficients of 0.80 and 0.78 for predictions of the speed and direction, respectively, of the MBEs. Mean absolute errors in forecasts of MBE speed and direction were 2.0 ms-1 and 17 degrees, respectively. For the typical MCC, these errors are sufficiently small so that the forecast path of the center of the MBE activity would be well within the heavy rain swath during most of a given system's lifecycle.
The forecast procedure has several advantages that make it well-suited to operational use: 1) it only requires knowledge of the speed and direction of the mean cloud-layer wind and the low-level jet, 2) the procedure can be used with all types of environmental wind configurations, and 3) it is capable of "recognizing" quasi-stationary or upstream-propagating systems which are known for producing extremely heavy rainfalls.
Finally, it is important to note that these results, while encouraging, are built upon radar and sounding observations that, by today's standards, are relatively crude. Thus, they should be considered preliminary and subject to validation with more detailed data and/or rigorous operational application. Of course, as the resolution of operational numerical models increases, the formation and movement of MCCs eventually will be predicted explicitly. Thus, forecasting procedures such as the one presented here will be replaced by explicitly predicted MCC paths. In the meantime, however, this procedure can provide quick and useful guidance for improving short-term quantitative precipitation forecasts.
ACKNOWLEDGEMENTS
Sincere appreciation is extended to George Young who provided many helpful suggestions and often lent a helping hand. Special thanks are reserved for Harry Henderson for his willing and able computer-related support, and to Dennis Rodgers and Rod Scofield for their help in acquiring the necessary satellite imagery. Thanks also go to Joann Singer and Delores Corman for providing able technical support.
The authors wish to especially acknowledge Louis Uccellini of National Weather Service Headquarters in Washington, DC, without whose support this study would not have been completed. The first author would also like to express appreciation to David A. Olson, Ronald D. McPherson, James Howcroft, and his National Meteorological Center colleagues for allowing him to pursue full-time graduate study at Penn State.
This research was supported by NSF Grant ATM-92-22017.
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