Geoscience Reference
In-Depth Information
Downward integration requires observations at the storm top; however, typical radar scan
geometries are configured for operational monitoring of low-level precipitation and severe
low-level wind phenomena (e.g., downburst and tornado). Such configurations do not often
provide detailed observations of the storm top, where the vertical velocities may be
significantly different from zero during storm development (Mewes & Shapiro, 2002).
Several studies have used low pass filters, such as the Leise filter (Leise, 1981), to apply high
wavenumber adjustments to the lower boundary conditions prior to upward integration of
the mass continuity equation. Such adjustments reduce noise in estimates of upper-level
winds (Parsons & Kropfli, 1990, Wakimoto et al., 2003).
One alternative is to apply the anelastic mass conservation equation as a weak constraint
(Gao et al., 1999, hereafter G99; Gao et al., 2004, hereafter G04). This method is based on a
three-dimensional variational approach, and removes the need to explicitly integrate the
anelastic continuity equation. This prevents the accumulation of severe errors in the vertical
velocity and ensures that uncertainties in the upper and lower boundary conditions do not
propagate vertically. Furthermore, multiple Doppler radar analysis is usually performed in
a Cartesian coordinate system; Doppler velocity data are often interpolated into this
Cartesian coordinate system using a Cressman filter (Cressman, 1959). The scheme
introduced by G99 bypasses this step by allowing reverse linear interpolation (from the
regularly spaced Cartesian grid to the irregularly spaced radar observation points) during
calculation of the cost function. This reverse interpolation procedure preserves the radial
nature of radar observations; however, as noted above, operational radar networks are often
incapable of providing dense observations, especially at upper levels. In such cases, the G99
scheme requires accurate background information, such as sounding data, to fill in the data-
void regions between successive elevation angles. It is frequently difficult to obtain accurate
background information in these cases, due in part to the coarse temporal resolution of
sounding data. If spatially continuous Doppler velocity data could be obtained in Cartesian
coordinates through the careful use of Cressman filters, accurate vertical velocity could be
obtained from operational radar scans without the need for additional information.
Otherwise, additional information regarding upper-level winds is necessary to reduce errors
in estimates of vertical velocity near the storm top.
This chapter presents a simplified version of the G99 scheme that applies a three-
dimensional variational approach on a regular Cartesian grid. The accuracy of calculated
winds and the dependence of this accuracy on the density of upper-level radar
observations are investigated using a set of idealized data sampled from a simulated
supercell storm. A detailed description of the structure of this simulated supercell has
been provided by Shimizu et al. (2008). The objective of this chapter is to propose an
optimal method for analyzing severe thunderstorms using typical configurations of
current operational radar data (less than 20 Plan Position Indicators, or PPIs, within 5-6
minutes).
2. Analysis method and variational scheme
This section briefly reviews the variational scheme for multiple Doppler radar analysis; a
detailed description has been provided by Gao et al. (1999). The variational technique
minimizes a cost function (J), which is defined as the sum of squared errors due to
discrepancies between observations and analyses and additional constraint terms:
