Transcript Student-Determined Z-R Relationship for North Dakota

Radar Meteorology Laboratory
Rain from Doppler Radar data
Prof. LEE, Dong-In
23 November 2000
Object: To get rainfall from radar
data
Theory:
 Add
appropriate theory from text or other
sources.
Radar reflectivity factor
z   Ni D
6
i
where z is radar reflectivity factor (mm6/m3),
Ni is the number of drops per unit volume
(m-3) and Di is diameter (mm) for drops in
the ith size category.
Rain Rate
 Rain
rate is the rate at which water volume
accumulates over a unit area and is given by
R

3
 N i Di
6
At
where A is the area involved and t is time.

This equation actually calculates the volume
of water per unit area per unit time.
Liquid Water Content
 Liquid
water content is the mass of liquid
water in a volume in space, given by
r w  N i Di3 


M

6 At i  vi 
where vi is the terminal velocity of the ith
diameter raindrop, and rw is the density of
water.
Z-R Relationship
z (mm6/m3) R (mm/h) z (mm6/m3) R (mm/h)
562.3
478.6
501.2
1023.3
1.254 Z=200R 1.6 MP
1.720
10 0.153765
1.200
100000 48.62462
1.610
398.1
851.1
1122.0
2238.7
1.460 Z=300R 1.5 J-W
2.480
10 0.103574
4.300
100000 48.07499
4.570
138.0
1.138 Z=429R 1.59 RADAR7
Procedure:
 Get
Radar data during rain situation
 Trace contours of reflectivity from each
time onto a single image.
 “Connect the dots” and draw swaths of the
path of the storm at each reflectivity level.
 Convert Z to R
 Get rain at each time by integrating amount
over each location at each time.
(Ex.) NEXRAD images of rain
 Get
data at hourly intervals.
 One possible way is to get it from:
 http://wxp.atms.purdue.edu/radar/previous/rad_
comp-X.gif where X can be 1, 2, 3, 4, 5, or 6.
 Alternatively,
specific site.
get more detailed data from a
We can combine these into a
single image.
You may want to select a single
region for your analysis.
Transfer Z data from each image
to a common image.
 Draw
outlines of each reflectivity level onto
a single piece of acetate or a separate image.
 Then combine these.
Now combine individual images
into a single image.
“Connect the dots” to produce
rain swaths.
Fill the contours if you like.
Convert Z to R
 Use
Z-R relationship.
= 300 R1.5 where R is rainrate in mm/h and z
is radar reflectivity factor in mm6/m3
z
Draw new contours of R (parallel to
the Z contours already on image)
Razzelfratz!!!
 After
spending an hour or so generating all
the (ugly) images before this, it finally
dawned on me that this is not necessarily
going to answer the question: “How much
did it rain at point X?”
 How can we answer that question?
Questions:
 Define
“rainfall”
 How do we go from radar data to rainfall
accumulations?
 What points (on the ground) are good ones
to use?
 How much time resolution in the radar data
is needed? Does it depend on the kind of
rain falling?
Rainfall total
RTotal 
t end
t end
t start
t start
 Rdt   RDt
where R is the rainrate (mm/h) at a given
place and time, Dt is the time interval
between consecutive radar data sets.
Rtotal = the total depth of rain at the location
over the entire time interval.
How do we get R?
 Radar
give radar reflectivity factor Z (or z).
 From a z-R relationship, we can convert z
into R.
 z = ARb where A and b are empirical
constants, R is rainrate in mm/h, and z is the
linear radar reflectivity factor in mm6/m3.
 Use: z = 200R1.6, the Marshall-Palmer z-R
relationship.