Error and Uncertainty in Precipitation
Measurements
The answers
to questions such as:
1) What is 6
x 7?
2) What were the key events leading to the American Declaration
of Independence in 1776?
3) What is the current temperature?
have different
types of true values. For 1), a simple mathematical equation, the
answer 42, is known exactly. For 2), a historical question, the
answer is a matter of opinion, though in grading such a test question
teachers can deduct points for answers that are obviously wrong,
such as “the Louisiana Purchase,” since this event did
not occur until 1803. For 3), the measurement of a geophysical quantity,
the value can be estimated but is not known exactly; there is always
some uncertainty in the measurement.
Error is the
difference between a measured or calculated value and the true value.
Uncertainty is a quantitative estimate of the error that exists
in the measurement or calculated result. Scientists are taught that
an uncertainty should always accompany any measurement result. Even
values for physical constants, like the speed of light and the mass
of the electron, have some uncertainty and are provided with an
estimate of error. For example, the speed of light in a vacuum may
be quoted as: c = 2.99793 ± 0.0000001 × 108 m/sec,
so that the true value of the speed of light is expected to be somewhere
within ± 10 m/sec of 299,793,000 m/sec.
The concepts
of error and uncertainty also apply to rainfall measurements, whether
you are measuring the amount of rain that falls in your backyard,
or making global observations of precipitation from GPM's constellation
of satellites. For a backyard measurement, you might use a simple
rain gauge, such as a graduated tube for collecting rainwater. Measurements
from the gauge will represent estimates of the true value, but will
not be the true value since the gauge will be subject to measurement
errors. For example, calibration errors, human errors in reading
the gauge, resolution between the lines on the gauge’s scale,
wind diverting drops away from the gauge opening, evaporation, a
leaf obstructing the opening, or even a thirsty sparrow may all
affect the measurement. Any result quoted from the backyard rain
gauge should be accompanied with an uncertainty that estimates the
errors from these varied sources.
Furthermore,
you might ask, “How representative is the backyard measurement
of the areal average rainfall in my neighborhood, town, or county?”
Driving in a car during a rainstorm, you can observe the variability
of rainfall over short distances; the sizes and numbers of drops
hitting the windshield can vary rapidly. Therefore, it would be
nearly impossible to accurately estimate rainfall for large areas
from a single backyard measurement.
For water resource
applications such as flood forecasting and reservoir management,
a key parameter of interest is the areal average rainfall over a
watershed—a relatively large area of land that drains into
a river system, lake, or the like. To determine rainfall for an
area of this size, it is necessary to collect data at numerous points
in the region. In fact, the goal of GPM is to provide estimates
of rainfall for areas ranging down to the size of a large town (~10
km x 10 km) all over the entire globe! As you might guess, these
global rainfall rates must be accompanied by uncertainty estimates.
GPM’s Ground Validation program is responsible for providing
values of uncertainty for these satellite-derived estimates, and
when possible diagnosing sources of error to aid in improving the
satellite estimates. (Click
here to view an article on GPM Ground Validation in the October
2002 issue of The GPM Monitor)
But the methods
for estimating uncertainty in data obtained from spaceborne instruments
undoubtedly must differ from those discussed in our backyard example,
above. How will scientists estimate uncertainty for GPM measurements?
A common method of estimating uncertainty is to make repeated measurements
under the same conditions. This method cannot be applied to measurements
of precipitation, however, since the atmosphere is chaotic and the
same exact conditions are never repeated. In Ground Validation,
we must resort to another method. Often we compare two rainfall
estimates obtained for the same region at the same time to examine
the discrepancies between the reported results and to estimate a
relative error. Ideally the two estimates are independent and one
has greater accuracy and higher precision than the other. The closer
we get to this ideal in our choice of what kinds of estimates to
use, the more valuable is the comparison between the two estimated
values in determining how close we are to the true value.
By way of illustration,
Figure 1 provides a comparison between two independent measurements
of precipitation near Kwajalein Atoll in the western Pacific Ocean—one
using satellite-derived estimates, and the other from ground-based
estimates. [Kwajalein is a ground validation site for the Tropical
Rainfall Measurement Mission (TRMM) program and will continue in
an upgraded capacity as a ground validation site for GPM.] The first
estimate (Panel a) is derived from the ground-based Kwajalein S-band
radar (KR), and the second (Panel b) is derived from data processed
from the TRMM satellite’s passive microwave sensor called
the TRMM Microwave Imager, or TMI. So we can compare the two measurements
on the same scale, we have rescaled the resolution of the two graphs
so that each pixel represents about 0.1 degree or 10 km. While generally
similar, the patterns, in detail, exhibit several types of differences
that can provide us with clues in diagnosing the sources of error.
This method of comparing ground-based measurements with those obtained
from satellites will allow scientists to estimate the uncertainty
of GPM rainfall measurements, thereby increasing the value of the
remotely-sensed rainfall data.
|
Figure 1. Rain rates
estimates for 0.1 deg pixels from a) Kwajalein S-band
Ground Validation Radar and b) TRMM overpass at 2103 UTC 25
July 1999. |
If you desire
to learn more about error and uncertainty estimation, the following
sources provide further information:
Bevington, P.
R., and D. K. Robinson, 1992: Data reduction and error analysis
for the physical sciences. McGraw Hill, Boston, 328 pp.
National Institute
of Standards and Technology NIST Technical Note 1297, Guidelines
for Evaluating and Expressing Uncertainty of NIST Measurement Results,
Barry N. Taylor and Chris E. Kuyatt, 1994 Edition.
By Sandra
Yuter, Min-Jeong Kim, and Robert Wood/Department of Atmospheric
Sciences, University of Washington and Steven Bidwell/GSFC
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Kwajalein: A Good Place To Measure
Rain
When we think about GPM, we often envision an international constellation
of satellites that will provide remotely obtained global rainfall
data to scientists. While this scenario will undoubtedly come about,
there will be certain important elements of GPM that are not space-based.
One of these elements—the Ground Validation (GV) site network—will
provide an independent means of evaluation, diagnosis, and improvement
of the GPM measurements from space. The GV site network will consist
of a number of stations on Earth collecting rainfall and other meteorological
data. Data from these ground sites will be compared with coincident
data from the GPM constellation spacecraft to help determine bias
and uncertainty, improving the value of the remotely collected data.
But where should GPM place these GV sites? Not surprisingly, the
answer to this question is quite complex. We can only afford to
operate a certain number of sites on Earth; we must choose their
locations wisely. First GV sites must be placed where significant
precipitation can be easily measured, and they must be globally
distributed to maximize their usefulness. Most of the globe is covered
by ocean, and so islands are often considered prime candidates for
GV sites. It takes manpower to staff ground sites, however, and
these ocean islands are often sparsely populated and lack basic
resources that humans require to live comfortably. Also, an island’s
governing nation must agree to host the GV site. Thus, precipitation
rate, distribution, logistics, infrastructure, and political stability
all play a part in the decision of where to place GV sites.
In the effort to determine the locations of its GV sites, GPM is
currently analyzing the advantages and disadvantages of numerous
potential sites. One strong contender is Kwajalein Atoll, located
in the Pacific Ocean, half way between Hawaii and Papau New Guinea.
Kwajalein Atoll is part of the Republic of the Marshall Islands,
and is home to the U.S. military’s Kwajalein Missile Range.
The southernmost island in the atoll—Kwajalein Island—is
less than 15 square km in size. Other than a few equipment towers,
the atoll has no topographical features that would interfere with
ground-based meteorological instruments. In fact, Kwajalein Atoll
is already the site of a GV facility for the Tropical Rainfall Measuring
Mission (TRMM), a program that uses space-based remotely sensed
data to investigate precipitation in Earth’s tropical regions.
 |
Kwajalein in the Marshall
Islands
A good location to monitor precipitation |
Because of the military presence on Kwajalein Island, the U.S.
government assures that island residents have access to reliable
energy sources, safe food and water supplies, and communications
services. An American school, commissary, infirmary, post office,
and recreational facilities exist on the island. Currently, two
commercial airlines provide round-trip passenger service between
Kwajalein and Hawaii. Consequently, the living conditions on Kwajalein
Island, while not perfect, are relatively tolerable considering
it is such a remote, small island.
Meteorologically speaking, Kwajalein is in a good location to monitor
precipitation. The atoll receives significant rainfall (2,600 mm
per year). Kwajalein Island, however, lies just north of a zone
where even heavier precipitation typically occurs, and many times
very intense storms pass just out of range of Kwajalein-based instruments.
Overall, these factors (precipitation rate, physical location,
logistics considerations, living conditions, political stability,
and available labor source) combine to make Kwajalein Atoll a quality
location for a GPM GV site.
Information for this article was obtained from:
Global Precipitation Measurement – Report 5
Potential Tropical Open Ocean Precipitation Validation Sites
By W. Adkins and S. Yuter
Edited by: E.A. Smith and W.J. Adams
For more information on other locations being considered for
GPM GV sites, GPM Report 5 is available online at http://gpm.gsfc.nasa.gov/library.html.
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