Static stability is the classical measure of convective activity. However, this static parameter quantifies the potential for, but not the strength of, actual convection. A useful dynamical parameter is the correlation between equivalent temperature u and w:
The quantities cp, L, g, T q have their standard meaning. h is governed by the:
This is a first-order linear differential equation for the function h = h(p) with boundary condition h(ps) = LH + SH. Eq. (2) is driven by the quantity:
-, V, Rad are the del-operator, the wind vector (both 3D) and the net radiation flux (1D, positive downwards), respectively; the overbar refers to gridscale quantities. bud represents the sum of all gridscale terms and corresponds to Yanai's quantity Q1-Q2-QR; it is calculated from gridscale analysed data. The imbalance imb in (2) carries all model and data inconsistencies. It is determined from the misfit between the vertical mean of bud and the surface fluxes LH and SH. The size of imb is about 25% of bud in the rms-mean. The function 1/b(p) generalizes the classical Bowen ratio to free atmosphere levels. The 1/b(p)-profile is externally specified; its impact upon the solution h(p) is quite limited. Haimberger et al. (1995) have shown that the extremum of h is largely controlled by the mean slope of bud in the vertical.
After solving (2) the sub-gridscale vertical flux h(p)-profile quantifies the strength of actual convection in the atmospheric column considered. For details of the theory just sketched see Dorninger et al. (1992), Hantel et al. (1993) and Haimberger et al. (1995).
We now consider the regional flash flood over Piedmont of November 1994; the case has been described, e.g., by Buzzi et al. (1995). Fig. 1 shows the measured gridscale bud-profiles (solid curves, lower panel) together with the diagnosed h-profiles (solid curves, upper panel) for a convectively active column (TORINO) and for an inactive column (LYON). The profile of bud in the column TORINO represents strong cooling in the lowest troposphere caused mainly by moisture convergence (not shown) and heating in the layers above. This leads to heavy convection in the lower troposphere, indicated by the upward directed h-flux which exceeds -1200 W/m2. On the other hand, the column LYON shows a weak budget and thus a weak flux. The dashed curves demonstrate that the mean vertical derivative of bud controls the size of h in a first approximation.
Figure 1. Vertical profiles of h-flux (upper panel) and bud (lower panel) for convectively active column TORINO (left) and inactive column LYON (right) for 5 Nov.1994 12UTC pm +/-6h; profiles valid for area of (100x100)km2; negative fluxes are upward directed; shaded area indicates area mean orography. Solid curves: h-fluxes diagnosed by measured bud; dashed curves: h-profiles calculated from linear slope of bud.
Figure 2. Sequence of column mean of h (curves, left axis) and observed precipitation (bars, right axis) for column TORINO (left) and LYON (right) for period 3 Nov. 1994 12 UTC to 7 Nov. 1994 12 UTC. TORINO: strong correlation between convective activity and precipitation; LYON: moderate precipitation without convection.
Fig. 2 exhibits the time evolution of the vertical mean of the h-flux and the observed surface precipitation at the locations above. Due to eq. (2) the h-flux is independent upon precipitation. The 4-day sequence of Fig. 2 shows a strong correlation between the h-flux and precipitation for TORINO. This is different for LYON, which is a case of moderate rain but no convection for the entire period. Visual inspection of the SYNOP data for the same day indicates that the atmosphere over TORINO was characterized by convection (Cb's) while over LYON it was not (exclusively Sc's).
Buzzi, A., N. Tartaglione, C. Cacciamani, T. Pacagnella and P. Patruno, 1995: Preliminary meteorological analysis of the Piedmont flood of November 1994, MAP Newsletter 2, 2-6.
Dorninger, M., et al. 1992: A thermodynamic diagnostic model for the atmosphere. Part I: Analysis of the August 1991 rain episode in Austria. Meteorol. Zeitschrift, N.F. 1, 87-121.
Haimberger, L.,et al. 1995: A thermodynamic diagnostic model for the atmosphere. Part III: DIAMOD with orography and new error model. (in press)
Hantel, M., et al. 1993: A thermodynamic diagnostic model for the atmosphere. Part II: The general theory and its consequences. Meteorol. Zeitschrift, N.F. 2, 255-271.
This project is being funded by the Austrian Fonds zur Förderung der Wissenschaftlichen Forschung (P/8863-GEO). Dr. F. Rubel analysed the precipitation fields. ECMWF and the Zentralanstalt für Meteorologie und Geodynamik provided data and computer facilities.
MAP Data Centre - April '05 - MAP WebMaster