Introduction to Radar
Iwan Holleman / Hans Beekhuis
Contents:
- Introduction
- Rainfall product (pCAPPI)
- Echotop product
- Vertically Integrated Liquid (VIL)
- Doppler Radar
Introduction:
The KNMI operates two Doppler Radars built by
Gematronik , one in De Bilt and one in Den Helder,
which are used for measurement of precipitation over The Netherlands and the
surrounding area. These C-band Radars emit and receive Radio-waves with a
frequency of about 6 GHz and with a wavelength close to 5 cm. The Doppler Radar
Radars can be used in two different ways: as a convetional Radar where the
intensity of the received, scattered Radio-waves is measured and as a genuine
Doppler Radar where the velocity distribution of the scattering particles is
measured. For the conventional Radar measurements the received, scattered
signal is, after some calibration and correction for the distance, converted to
the quantity Z, the so-called Radar reflectivity.
Assuming that the diameters (D_i) of the scattering precipitation particles is
(much) smaller than the wavelength of the Radar radiation, then Rayleigh
scattering will be dominant, the Radar reflectivity can be written as:
Z = SUM(n_i . D_i^6)
Where n_i is the number of particle per unit volume having diameter D_i. So the
Radar reflectivity is the sum over the product of the number of particles and
their diameters to the power six, and therefore it is very sensitive for the
diameters of the particles. When the diameters of the precipitation particles
are equal or larger than the wavelength of the Radar radiation, the reflectivity
Z is proportional with the square of the diameters. Because of the larger spread
of possible values of Z a decibel-unit is commonly used:
Z[dBZ] = 10 . 10log(Z [mm^6/m^3])
Using a standard precipitation-diameter distribution-function and a certain
dependence of the terminal vertical velocity with the diameter, the reflectivity
Z can be converted to precipitation rate R. At KNMI the following formula is
used to convert radar reflectivity into precipitation rate:
Z[mm^6/m^3] = 200 . R[mm/h]^1.6
There is still quite some discussion within the radar community on which
formula is best: common values for the pre-factor are between 150 and 300 and
common values for the exponential are between 1.4 and 2. The differences are
small, however, and errors from other sources are generally more important. The
formula can also be rewritten in terms of the decibel-unit commonly used for
Z:
Z[dBZ] = 23 + 16 . 10log(R[mm/h])
In the following table a few examples of reflectivity values and corresponding
precipitation rates are given:
| Z [dBZ] | 7 | 15 | 23 | 31 | 39 | 47 |
| R [mm/h] | 0.1 | 0.3 | 1 | 3 | 10 | 30 |
The reflectivity is measured at a large distance from the Radar site (0-320 km) and at moderate altitude (0.8-3 km) above surface of the earth, and therefore discrepancies can occur between the precipitation rates as determined using the Radar and those determined by the on-ground observers. This can be caused by, for instance, evaporation or generation of precipitation just above the earth surface or by anomalous propagation (Anaprop) of the Radar beam. From results of the radar verification, however, by Rudolf van Westrhenen it can be concluded that up to a distance of 150~km the KNMI Radars produce a rather good quantitative view of the precipitation above The Netherlands.
Rainfall product (pCAPPI):
During a scan the antenna of the Radar performes at a few elevations
(tilting with respect to the horizontal plane) a full turn about his vertical
axis (azimuth). To be more accurate, the azimuth is the clockwise angle of the
Radar antenna with respect to the direction of North. At every position of the
Radar antenna the reflectivity is measured as a function of the distance. All
information together delivers a view of the three-dimensional distribution of
reflectivity in the atmosphere. The Radars of the KNMI perform a small scan
over just 4 low elevations every 5 minutes and a large scan over 14 elevations
up to 12 degrees every 15 minutes. The well-known radar precipitation images
are just a horizontal cross-section at constant altitude above the earth
surface through the three-dimensional data of the small scan. These
precipitation images are actually called pCAPPI's, or pseudo-Constant-Altitude
Plan-Position Indicator. An example of such a pCAPPI product can be viewed
below:
Echotop product:
Via the large, 14-elevation radar scans a more complete picture of the
three-dimensional distribution of the precipitable-water-content of the
atmosphere is obtained. This three-dimensional distribution can, for instance,
be used to calculate a the heights of the Radar echotops. The echotops are
defined as the highest altitude at which a Radar reflectivity strength
equivalent to a rainfall rate of 0.1 mm/h is still found. The echotop product,
which has recently been introduced on the Meteorological Work Stations (MWS),
is an important product for aviation meteorology. An example of such an echotop
product can be viewed below (zoomed).
Vertically Integrated Liquid (VIL):
Another quantity that can be calculated from the large 14-elevation radar scan
is the so-called Vertically-Integrated-Liquid (VIL). The VIL-value at a certain
location is the sum of all observed radar reflectivities (converted to liquid
watercontent) in a vertical column above this location. The unit of VIL is
kg/m2 or mm, and it can be regarded as a measure for the potential rainfall.
The rate at which precipitable waterdroplets are formed is proportional to the
updraft-speed, and therefore the VIL-value is both a function of updraft-speed
and cloud thickness. It has been noted already by others that observations of
high VIL-values and the occurrences of severe thunderstorms correlate quite
well. An example of a VIL-image, recorded at the same date and time as the
echotop product shown above, is given below (also zoomed).
In stratiform clouds a VIL-value of 10 kg/m2 is rarely exceeded. In areas with strong convection, however, a VIL-value of 10 kg/m2 is easily exceeded and VIL-values of 25 kg/m2 or higher are not exception. In the Radar severe-weather-product that is currently under development, the VIL-product will probably play an important role in identifying areas with strong updrafts.
Doppler Radar:
Apart from these new Radar products that are based on measurements of reflectivity, the new KNMI Radars have also the possibility to run in Doppler-mode. In the Doppler-mode the velocity-component of the waterdroplets in the direction of the Radar site can be measured. The value of product of the maximum detectable velocity and the maximum distance is fixed, however, and only determined by the wavelength of radiation used by the Radar. It is, therefore, relatively easy to operate a Doppler Radar at short distances, but to operate a Doppler Radar over an area as large as the Netherlands is quite painstaking. There are ways to circumvent this "velocity * distance" limit by using a different pulse sequence (dual PRF). Currently, these techniques introduce (additional) errors in the Doppler signal. Carefull analysis of these errors, development of error correction methods and optimizing of the pulse sequences have to be performed before reliable Doppler products can be produced.
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Hans Beekhuis