Lab 4
Physics 171
Radar-derived Rainfall
Introduction
The National Weather Service Doppler radar network consists of 158 radar stations that are spread
across the country. This network is best tool that meteorologists have for detecting and predicting
imminent precipitation and severe weather. These expensive and complex devices were first deployed
in 1988 and were all completed by 1997.
A radar system works by emitting electromagnetic radio waves with a wavelength of 10 cm. This
radiation goes outward from the radar dome in all directions. If it encounters any objects in the air,
some small fraction of that radiation will be reflected back toward the receiving antenna in the radar
dome. A computer can then calculate where the reflecting object is located based on how long it took
for the emitted radiation to return (since it travels at a known speed) and the angle at which it returned
from. As the radar antenna scans radiation coming in at all angles, the fraction of received radiation is
(termed radar reflectivity, Z) is measured and displayed on a radar map. In addition to locating the
position of the reflecting object and measure its strength, we can determine that the amount of
returned radiation is related to the size of the reflecting object and how many separate objects are
contained within the radar beam. It turns out that the reflected radiation is proportional to the radius
of the drop raised to the 6th power. Thus the radar is an extremely sensitive detector of raindrop size.
The number of drops is also extremely important in determining the strength of the reflected radiation,
but somewhat less than the drop size.
Because both raindrop size and raindrop concentration are measured by the radar, it becomes possible
to combine this information to make a direct conversion between the radar reflectivity and the rate of
rainfall. This finding has become one of the most powerful uses of radar. It allows us to integrate the
rainfall rate to determine the amount of rain that falls everywhere, and not just at the widely scattered
positions of actual rain gauges on the ground. This is important because rainfall can vary by a great
amount in a small distance, particularly in strong storms. Knowing exactly what locations have received
a lot of rainfall and what locations have not is absolutely critical for forecasts and emergency responses
to flash flooding as well as agricultural responses to drought and irrigation decisions.
Different types of precipitation events contain a different profile of raindrop sizes due to differences in
updraft speeds, CCN concentrations, and drop growth mechanisms. For this reason, 3 primary
equations are used:
Z = 300R1.4 for convective precipitation including thunderstorms
Z = 250R1.2 for tropical storms and hurricanes
Z =200R1.6 for continental stratiform rainfall not including thunderstorms
In radar images, the reflectivity Z is usually displayed in decibels (dbZ). A decibel is really just a
logarithmic way of expressing a ratio of the amount of energy reflected back to the antenna. The ratio is
expressed in logarithmic terms because it routinely varies by many orders of magnitude. To use these
equations, we’ll need to undo “undo” the decibel and return the reflectivity to the non-logarithmic
ratio Z. This is very similar to working with a natural logarithm, except that is based on powers of 10
rather than e.
Z = 10(dbZ/10)
In the 3 equations above, R stands for the rainfall rate in mm/hr.
Procedure
Part I
In this lab, you will be applying one of the Z-R relationships to a recent rainfall event.
To begin, go to the following webpage:
www.rap.ucar.edu/weather/radar
We are going to looking at the radar images from the brief, but fairly heavy thunderstorm that passed
over Central New Jersey on Monday, Sept. 28, 2008. The thunderstorm occurred between about 5 and
630 pm EDT. Use the webpage to download these 2 hours of radar data (make sure you are
downloading the .5 degree reflectivity maps). Note that the time entered on the page will be the end of
the loop and is entered in Z, not local time. When done correctly, 25 total images will be displayed at
about 4.5 minute intervals in a java loop.
1.
For these two hours, record the time and each value of radar reflectivity in dBZ that was located
over TCNJ. I’ll help you zoom in on the correct spot for TCNJ.
2.
Open Microsoft Excel and enter your 25 values of reflectivity for this thunderstorm in the
second column.
3.
In the first column, enter the local hour your measurement was made. In the second column,
enter the minutes, in the third column, enter the seconds.
4.
Next, you will need to choose which of the 3 Z-R equations to use. Once you have chosen, solve
this equation algebraically for the rainfall rate, R. Show this solution below:
5.
Enter your solution for R in the 4rd column and use it to calculate the local rainfall rate in mm/hr
for each of the 26 measurements.
5.
In the 5th column, calculate the elapsed time between the previous image and this time of the
current image, entered in decimal hours.
6.
In the 6th column, covert mm/hr to in/hr and multiply by the time interval (in hrs) to get the
total amount of rain fallen in each 5 minute interval.
7.
In the 7th column, calculate the cumulative rainfall (in inches) over the course of the storm.
8.
Open the course website and look into the 1 week data archive of our TCNJ weather station.
Enter the amount of rainfall at the closest time in column 8 and a column of cumulative rain gauge data
in column 9.
9.
Create a plot of the two cumulative precipitation totals against the time.
10.
How good was the radar estimate? What factors could have caused errors?
Part II
The variability in drop size distributions often means that Z-R relationships can’t be used as an absolute
measure of precipitation. Instead, their results must calibrated based on the “ground-truth” of real rain
gauges, much as you’ve just done. Nevertheless, they are critical for understanding the geographical
distribution of rainfall. The following website displays the results of these Z-R calculations that have
been applied to the entire country after adjustment and calibration to ground truth.
http://water.weather.gov/
Use this website to answer the following questions:
1.
So far this year, what exact location in the United States has received the greatest percent
amount of excess precipitation in comparison to normal.
2.
What location in the United States has received the least precipitation relative to normal?
3.
In the last 30 days, which location has received the most rain, and what was that amount?