Transcript Slide 1

Final Review
Two types of observations
In situ measurement:
Remote sensing measurement:
Active remote sensing
Passive remote sensing
Accuracy is the difference between what we measured and the true
(yet unknown) value.
Precision (also called reproducibility or repeatability) describes the
degree to which measurements show the same or similar results.
Random error is the variation between measurements, also
known as noise.
Unpredictable
Zero arithmetic mean
Random error is caused by
(a) unpredictable fluctuations of a measurement apparatus,
(b) the experimenter's interpretation of the instrumental reading;
A common method to minimize random
error is to make multiple observations.
Systematic errors are biases in measurement which lead to the
situation where the mean of many separate measurements differs
from the actual value of the measured attribute.
A common method to remove systematic error is through
Calibration of the measurement instrument.
How to express errors
e (unit) ± Δe, e.g.,
10o C  0.5o C
e
Unit Error:
Percent Error:
e
Averaging
e
(100%)
e
1
1 n
x  [( x(1)  x(2)  ...  x(n)]   x(t )
n
n t 1
f  x y  x y
Variance
Covariance
 x2  x'2
Standard deviation
1 n
xy   x' (i ) y ' (i )
n i 1
( x y)
Correlation coefficient  xy   x y
 x  x '2
Estimating Errors of derived variables/Propagation of Errors
Max error:
X A B C



X
A
B
C
Significant figures
1.
2.
3.
4.
5.
6.
7.
8.
9.
37.76 + 3.907 + 226.4 =
319.15 - 32.614 =
104.630 + 27.08362 + 0.61 =
125. - 0.23 + 4.109 =
2.02 x 2.5 =
10. 45. x 3.00 =
11. 3.00 x 105 - 1.5 x 102 =
600.0 / 5.2302 =
12. What is the average of 0.1707, 0.1713,
0.0032 x 273 =
0.1720, 0.1704, and 0.1715?
3
(5.5) =
0.556 x (4x101 - 32.5) =
Temperature measurements
Absolute temperature (Kelvin)
Tk  ToC  273.15
Thermometer Calibrations
Ice
Three reference points
Kelvin 273.15
Celsius 0.00
Triple
Point
273.16
0.01
Steam
373.15
100.00
1. Liquid in glass thermometer
V
V
Volume expansion of glass:1.2-2.7x10-5 per 1.00oC,
Volume expansion of Hg:18x10-5 per 1.00oC
2. Maximum thermometer
3. Minimum thermometer
Making temperature measurements in the atmosphere
1. Air is a poor conductor, thus, a good flow over the sensor
should be maintained.
2. Sensor to be thermally insulated from the mounting.
3. To prevent radiation, sensors can be polished or coated to
reflect solar radiation and to reduce the absorption of infrared
radiation. A shield can also be used to shelter the sensor, but it
needs to be aspirated to ensure proper ventilation.
4. Heating by adiabatic compression may occur when a sensor is
exposed to air moving at very high rates, e.g., aircraft
measurements. Adiabatic heating needs to be corrected.
5. Wetting of a temperature sensor will lower the measured
temperature due to evaporative cooling. Upper air measurements
can be affected as a sensor goes though a cloud. A special device is
needed to prevent sensor wetting. For surface measurements,
the radiation shield should keep the sensor dry.
Moisture Measurement
Mixing ratio, r
Relative humidity, h
Dew-point, TD
Wet bulb temperature, TW
T
TD  Tw  T
Tw
Atmospheric pressure measurement
Absolute pressure,
Gage pressure,
Differential pressure
Two types of fluid systems: static and dynamic
Static pressure Dynamic pressure Total (or Stagnation) pressure
Barometers
Mercury barometer
P   Hg g , z h , z
Temperature correction
Gravity correction
Fortin Barometer
Aneroid Barometer
Barographs
Precipitation
Precipitation rate (R):
rain water falling on ground per unit area per unit time
Ordinary rain gauge
Tipping bucket
rain gauge
m
6 mm
1  3.6 10
s
h
Optical rain gauge (ORG)
A ORG measures the scintillation in an optical beam produced by
raindrops falling between a light source and an optical receiver.
Disdrometer
1. Measuring the speed
of falling droplets.
2. Droplet size distribution
Wind Measurements
Local right-hand Cartesian coordinate
z, P,  Up
W
y North
x East
O
Polar coordinate
Wind direction 
Wind speed
M
V
O
U
Dynamic force anemometers
cup anemometers, vane windmill, and gill-type anemometers
Pressure pulse frequency anemometers (sonic anemometer )
It measures the variation of speed of sound with wind
t 
2 u
(c 2  u 2 )
2-D sonic anemometer
3-D sonic anemometer
The spatial resolution is given by the path length between
transducers, which is typically 10 to 20 cm
Sonic anemometers can take measurements with very fine
temporal resolution, 20 Hz or better, which make them well
suited for turbulence measurements.
Their main disadvantage is the distortion of the flow itself by the
structure supporting the transducers, which requires a correction
based upon wind tunnel measurements to minimize the effect.
Wind profilers
•A wind profiler is a type of sensitive Doppler radar that uses
electromagnetic waves or sound waves to detect the wind speed
and direction at various elevations above the ground, up to the
troposphere (i.e., between 8 and 17 km above mean sea level)
•Detection of the signal backscattered from refractive
index in-homogeneities in the atmosphere
•In clear air, the scattering targets are the temperature and
humidity fluctuations produced by turbulent eddies
Measuring horizontal winds using three beams
Doppler Shift
f d  2
Vr

where Vr is the radial velocity of the scatterers.
 is wave length
The 915 MHz (33 cm, UHF) profiler measures the wind at low
levels, typically up to 1-3 km above ground level, depending on
atmospheric conditions, especially humidity. The 915 MHz
profiler has fairly small antennas (at most 2x2 or 3x3 m), making
it transportable and less expensive.
A VHF wind profiler (50 MHz or 6 m) measures wind profiles
between 2 and 16, occasionally 20 km above the ground level
(AGL), but the antenna occupies 2 soccer fields (100x100m).
The US NOAA operates a network of 400 MHz wind profilers.
These are smaller (antenna size about 10 x10 m). The higher
the frequency, the smaller the antenna, the smaller the turbulent
flow scale that is resolved.
Frequency
Wavelength
Antenna
50 MHz
600 cm
100 m
405 MHz
74 cm
13 m
915 MHz
33 cm
2m
Radiosonde
Radiosonde is a small,
expendable instrument package
that is suspended below a large
balloon filled with hydrogen or
helium. The radiosonde consists
of sensors used to measure
several meteorological
parameters coupled to a radio
transmitter and assembled in a
lightweight box. The meteorological sensors sample the ambient temperature,
relative humidity, and pressure of the air through which it rises. By tracking the
position of the radiosonde, wind speed and direction aloft are also obtained.
  elevation angle
  azimuthal angle
S  R cos  ; x  S cos  ; y  S sin 
x
y
 u;  v
t
t
Transmitter operates on a frequency from 1668.4 to 1700.0 MHz
The altitude reached by rawinsonde varies for several reasons:
bursting height of the balloon;
faulty receiving equipment;
atmospheric interference.
When the balloon reaches its elastic
limit and bursts, the parachute slows
the descent of the radiosonde,
minimizing the danger to lives and
poperties.
600-gram balloon can rise
approximately 90,000 feet.
The bursting altitude for
larger 1,200-gram balloon
exceeds 100,000 feet.
Launch each day at 00:00 and
12:00 UTC (Greenwich Mean
Time),
GPS Dropsondes
Dropsonde is a weather reconnaissance device created by the
National Center for Atmospheric Research (NCAR), designed to
be dropped from an aircraft at altitude to accurately measure
tropical storm conditions as the device falls to the ground. The
dropsonde contains a GPS receiver, along with pressure,
temperature, and humidity sensors to capture atmospheric
profiles and thermodynamic data and winds.
Driftsondes
It is a new type of observing
system to track weather above
hard-to-reach parts of the
globe, as well as make
soundings that will fill critical
gaps in data coverage over
oceanic and remote arctic and
continental regions. These
areas include (1) relatively
void of in-situ measurements
from radiosondes and
commercial aircraft, such as the remote Pacific and Atlantic oceans,
(2) covered with extensive cloud shields so that satellite measurements
are limited.
Radiation
J
W
 2
Energy flux2
m s m
Laws of blackbody radiation
1. Plank’s law
2. Wien’s displacement
law

2898( mK)
T
3. Stefan - Boltzman law : E   T 4 ,   5.7x10 -8 Wm -2 K -4 .
Gray body:
E  T 4 ; 0    1
Absorbtivity
Reflectivity
E (absorbed )
a 
E
Transmissivity
E (reflected )
r 
E
E (transmited )
t 
E
Interaction between radiation and atmosphere

M
M
Photoionization
e
Electronic excitation
overlap
a  r  t  1
Atmospheric window.
Oxygen, ozone, carbon dioxide, water vapor are great absorbers
of IR radiation.
Making Radiation Measurements
There are three ways to make radiation measurements.
•Thermal sensitive devise
•Photoelectric cell (photodiode)
•Photochemical sensor
What is the basic operating principle for the photoelectric cell?
A device that converts light into electricity.
What is the basic operating principle for the photochemical sensor?
It utilizes materials that tend to have chemical reaction due to the
absorption of light (including visible, ultraviolet, and infrared).
Broadband Radiation Instruments:
Shortwave K
Longwave L
Total
Q=K+L
Spectral Radiation Instruments: Q ; K  ; L
Pyranometer
measures global-solar shortwave radiation
Shaded Pyranometer measures diffuse solar radiation
Pyrheliometer measures direct beam
Pyrradiometer measures net radiation
Weather radar
Radar:
RAdio Detection And Ranging
1. EM waves that fall into the microwave (1 mm < λ < 75 cm)
2. Active remote sensing technique
Fundamental properties of the emitted beam:
Pulse repetition frequency (PRF): how many pulses of radiation are
transmitted per second; for typical weather radars, typically 325.
Transmission time: the duration of each pulse
Pulse length: the spacing between “range gates”
and is 1 km on average. It determines radial resolution.
Beam width: the angular width of the emitted beam,
and is typically about 1°. It determines angular resolution
Pulse volume: volume determined by pulse length and beam width
Attenuation
Particles will attenuate the energy in two ways:
scattering and absorption, collectively known as attenuation
Particles: raindrop, hail, snow, graupel, insects,…..
Rayleigh Scattering
Scattering from molecules and tiny particles (< 1 /10 wavelength)
Mie Scattering
Scattering from relatively large particles (> 1 wavelength),
which is not strongly wavelength dependent and produces a
sharper and more intense forward lobe
Scan Angle
To keep the beam from hitting objects on the ground, the lowest
scan angle used is 0.5° above horizontal.
Moments
The 0th moment: reflectivity
The 1st moment: radial velocity
The 2nd moment: spectrum width
Distribution of velocities within a pulse volume.
k
Reflectivity
dBZ

Z  i 1
N i Di6
v
dBZ  10 log10 Z 
Z-R Relationship
Z  aR
b
R is the rainfall rate (mmh-1)
Frequencies
WEATHER RADAR BANDS
Frequency (GHz)
Band
L (precipitation)
S (precipitation)
~1
2.0 – 4.0
Wavelength
(cm)
~20.0
~10.0
C (precipitation)
X (precipitation)
K (cloud)
W (cloud)
4.0 – 6.0
8.0 – 12.0
12.0–18.0(Ku);18.0–40.0 (Ka)
90.0 – 100.0
~6.0
~3.0
~1.0
~0.1
High frequency, short-wavelength bands are readily attenuated by
small droplet, making them most useful for detecting clouds and
aerosols. The longer the wavelength, the less attenuation. They
cannot “see” the smaller targets but heavy rain and hail (other like
birds and aircraft). S-band radars are widely used by the NWS.
Radar scanning
PPI (Plan Position Indicator)
RHI (Range Height Indicator)
Vertically Pointing
PRODUCT INTERPRETATION
a) Reflectivity
Light snow and rain: 5-20 dBZ,
moderate rain: 30-45 dBZ,
Heavy rain, hail: 60-75 dBZ
b) Radial Velocity
Deduce the lower-tropospheric vertical wind profile
Radar scanning
PPI (Plan Position Indicator)
RHI (Range Height Indicator)
Vertically Pointing
PRODUCT INTERPRETATION
a) Reflectivity
Light snow and rain: 5-20 dBZ,
moderate rain: 30-45 dBZ,
Heavy rain, hail: 60-75 dBZ
b) Radial Velocity
Dual Doppler
Can be used to determine the 3-dimensional wind field (U,V,W)
from the radial velocities obtained from a Doppler radar
Weather radars NEXRAD: WSR-88D
NEXRAD is NEXt-generation RADar, and WSR-88D stands for
Weather Surveillance Radar, the 88 is for 1988 (year the technology
was commissioned and implemented), and D is for Doppler
Clear Air Mode
The radar rotates slower and performs fewer scan angles. This
allows for higher resolution of fine targets such as aerosol particles
(smoke plumes for example), insects, and snow.
Precipitation Mode
The radar rotates faster and performs more scan angles, sacrificing
resolution for more rapid updates. The radar completes 9 different
elevation scans in five minutes.
Severe Mode
The rotation rate is increased even further and more scans are made
at higher angles to capture the full structure of the towering
thunderstorms. It completes 14 elevation scans in five minutes.
Clouds
Liquid water mixing ratio
wl 
Liquid water density of clouds
l  wl  air
Cloud droplet distribution
Number density N (D):
the number of droplets per unit
volume (concentration) in an
interval D + ΔD
mass liquid
mass dry air
l 
mass liquid
volume of dry air
FSSP (forward scattering spectrometer probe)
The FSSP is of the general class of instruments called optical particle counters
(OPCs) that detect single particles and size them by measuring the intensity of
light that the particle scatters when passing through a light beam.
Prism
Scattering
Photodetector
Module
Dump spot
Airflow
He-Ne Hybrid Laser
Optical Array probe
It uses an array of photodiodes to measure the size of hydrometeors
from the maximum width of their shadow as they pass through a
focused He-Ne laser beam. The shadow is cast onto a linear diode
array and the total number of occulted diodes during the airflow's
passage represents the size of droplets. The size is categorized into
one of 60 channels and this information is sent to the data system
where the number of particles in each channel is accumulated over
a preselected time period.
Ceilometer
Ceilometer is an instrument for the measurement of cloud base.
The device works day or night by shining an intense beam of light
(often ultraviolet) at overhead clouds. Reflections of this light
from the base of the clouds are detected by a photocell in the
receiver of the ceilometer. The height can be determined using
the emitted and received light.
Cloud Radar (w band)
Cloud reflectivity and vertical velocity
Satellite Meteorology
Polar orbit satellite
Altitudes are typically at 850 km.
Orbital periods are about 98-102
minutes.
Hence, each satellite will complete
about 14 orbits in one day.
The scan swath is about 3000 km wide.
Note that the orbit is directed to the northwest. The satellites do
not pass directly over the North pole or South Pole creating a
precession in the orbit so that is passes over locations further west
on subsequent orbits.
Factors affecting data resolution
•Subpoint: the location on the earth that is directly below the satellite.
•Satellite footprint: the area being scanned by the satellite, similar to the
area being photographed with a camera.
•Nadir angle: the angle between the footprint and the subpoint.
Accordingly, the resolution gets worse with increasing nadir angle.
•Resolution is a function of: (a) Curvature of the earth. (b) to a lesser
extent, the increasing distance of the footprint from the satellite.
•Data at angles greater than 60° are not very useful
Parallax refers to the displacement
of cloud locations due to increasing
viewing angle.
Geostationary Satellites
•Geostationary satellites orbit in the
earth's equatorial plane at a height of
35,800 km. Note that the typical
space shuttle orbit is only 225-250
km.
•At this height, the satellite's orbital
period matches the rotation of the
Earth, so the satellite seems to stay
stationary over the same point on the
equator. It always view the same
geographical area, day or night.
•This is ideal for making regular
sequential observations of cloud
patterns over a region with visible
and infrared radiometers
•High temporal resolution and
Gravitational force = Centrifugal force
constant viewing angles.