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.

Final Review

Random error is the variation between measurements, also known as noise.

Unpredictable Zero arithmetic meanRandom error is caused by (a) unpredictable fluctuations of a measurement apparatus, (b) the experimenter's interpretation of the instrumental reading;

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.

A common method to minimize random error is to make multiple observations.

How to express errors

CC oo 5.010

ee

%)100(ee

e (unit) ± Δe, e.g.,

Unit Error: Percent Error:

Averaging

n

ttx

nnxxx

nx

1)(

1)](...)2()1([(

1

yxyxf

Variance 22 'xx Standard deviation 2'xx

n

iiyix

nyx

1)(')('

1Covariance

yx

)yx(xy Correlation coefficient

Estimating Errors of derived variables/Propagation of Errors

CC

BB

AA

XX

Max error:

Significant figures

1. 37.76 + 3.907 + 226.4 = 2. 319.15 - 32.614 = 3. 104.630 + 27.08362 + 0.61 = 4. 125. - 0.23 + 4.109 = 5. 2.02 x 2.5 = 6. 600.0 / 5.2302 = 7. 0.0032 x 273 = 8. (5.5)3 = 9. 0.556 x (4x101 - 32.5) =

10. 45. x 3.00 = 11. 3.00 x 105 - 1.5 x 102 = 12. What is the average of 0.1707, 0.1713, 0.1720, 0.1704, and 0.1715?

Temperature measurements

Absolute temperature (Kelvin) 15.273 Ck oTT

Thermometer Calibrations

Three reference points Ice Triple Point

Steam

Kelvin 273.15 273.16 373.15

Celsius 0.00 0.01 100.00

1. Liquid in glass thermometer

VV 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

wT

T

TTT wD

Absolute pressure, Gage pressure,Differential pressure

Two types of fluid systems: static and dynamic

Static pressure Dynamic pressure Total (or Stagnation) pressure

Atmospheric pressure measurement

Barometers

Mercury barometer zzHg hgP ,,

Temperature correction

Gravity correction

Fortin Barometer

Aneroid Barometer Barographs

Precipitation

Precipitation rate (R): rain water falling on ground per unit area per unit time

hmm

sm 6106.31

Ordinary rain gauge

Tipping bucket rain gauge

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

Polar coordinate

x

y

U

V

W

O OEast

NorthUp

M speed Wind

direction Wind

P, z,

Dynamic force anemometerscup anemometers, vane windmill, and gill-type anemometers

Pressure pulse frequency anemometers (sonic anemometer )

It measures the variation of speed of sound with wind

)(

222 uc

ut

3-D sonic anemometer2-D sonic anemometerThe 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 ShiftrV

df 2

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).

Frequency 50 MHz 405 MHz 915 MHzWavelength 600 cm 74 cm 33 cmAntenna 100 m 13 m 2 m

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.

RadiosondeRadiosonde 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.

angleazimuthal

angleelevation

sin;cos;cos SySxRS

vty

utx

;

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.

Transmitter operates on a frequency from 1668.4 to 1700.0 MHz

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

Energy flux- 22 m

W

sm

J

Laws of blackbody radiation

1. Plank’s law

2. Wien’s displacement law

TK)(2898 m

.K Wm5.7x10 ,T E :lawBoltzman -Stefan 3. 4-2--84

Gray body: 10;4 TE

E

absorbedEa

)(

Absorbtivity Reflectivity

Transmissivity

E

reflectedEr

)(

E

transmitedEt

)( 1 tra

Electronic excitationPhotoionization

M Me

overlap

Interaction between radiation and atmosphere

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 KLongwave LTotal Q = K + L

Spectral Radiation Instruments: LKQ ;;

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

2. Active remote sensing technique

1. EM waves that fall into the microwave (1 mm < λ < 75 cm)

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.

Reflectivity

dBZ

ZdBZ 10log10

Z-R Relationship Z aR b R is the rainfall rate (mmh-1)

v

DNZ

k

iii

1

6

Frequencies WEATHER RADAR BANDS

BandFrequency (GHz) Wavelength

(cm)

L (precipitation) ~ 1 ~20.0

S (precipitation) 2.0 – 4.0 ~10.0

C (precipitation) 4.0 – 6.0 ~6.0

X (precipitation) 8.0 – 12.0 ~3.0

K (cloud) 12.0–18.0(Ku);18.0–40.0 (Ka) ~1.0

W (cloud) 90.0 – 100.0 ~0.1High 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

Precipitation 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.

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 ModeThe 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 airdrymass

liquidmasswl

Liquid water density of clouds airdryofvolume

liquidmassl

airll w

Cloud droplet distribution

Number density N (D):the number of droplets per unit volume (concentration) in an interval D + ΔD

He-Ne Hybrid Laser

Airflow

Dump spot

Prism

Scattering PhotodetectorModule

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.

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

Altitudes are typically at 850 km. Orbital periods are about 98-102

minutes. Hence, each satellite will complete

about 14 orbits in one day.

Polar orbit satellite

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 constant viewing angles. Gravitational force = Centrifugal force