Two types of observations

In situ measurement: refers to measurements obtained through direct contact with the respective object. Remote sensing measurement: acquisition of information of an

object or phenomenon, by the use of either recording or real-time sensing devices that are wireless, not in physical or intimate contact with the object.

Active remote sensing Passive remote sensing

Mid-term review

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.

Pro

babi

lity

den

sity

Ref

eren

ce v

alue

Ave

rage

Measured value

Accuracy

Precision

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;

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.

Random error can be reduced or removed by taking many measurements

Expression of Measures: e (unit) ± Δe, e.g.,

ee

%)100(ee

Unit Error:

Percent Error:

Averaging

n

ttx

nnxxx

nx

1)(

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

1

Variance 22 'xx

Standard deviation 2'xx

Simple statistics

n

iiyix

nyx

1)(')('

1covariance

yx

)yx(xy Correlation coefficient

Sensible heat flux 22 mW

smJ:unit

Specific heat at constant pressure KkgJ

p 1004C

K ,shsm

CSH

kgKJ

3m

kgs2m

J

p

Kinematic sensible heat flux, sh

flux ,Tu ,Tv ,Tw

Sensible heat flux, SH TuC ,TvC ,TwC ppp

z

T

0T

0w

0T

0w

0Twflux

z

T

0T

0w

0T

0w

0Twflux

daytime nighttime

11

22

Estimating Errors of derived variables/Propagation of Errors

Consider a quantity CAB

X where A, B, C are measured quantities,

The error associated with each of them is CBA &,,

.

What is the error of the derived variable X?

CBACAB

X lnlnlnlnln

)ln()ln(lnln CdBdAdXd

CC

BB

AA

XX

CC

BB

AA

XX

Max error:

Significant figures

1. All non-zero digits are significant.2. In a number without a decimal point, only zeros BETWEEN non-

zero digits are significant (unless a bar indicates the last significant digit--see below).

3. In a number with a decimal point, all zeros to the right of the first non-zero digit are significant. A decimal point may be placed after the number; for example "100." indicates specifically that three significant figures are meant

For multiplication and division, the result should have as many significant figures as the measured number with the smallest number of significant figures.

For addition and subtraction, the result should have as many decimal places as the measured number with the smallest number of decimal places.

Rule of arithmetic computation

1. 37.76 + 3.907 + 226.4 = 268.1 2. 319.15 - 32.614 = 286.54 3. 104.630 + 27.08362 + 0.61 = 132.32 4. 125. - 0.23 + 4.109 = 129. 5. 2.02 x 2.5 = 5.0 6. 600.0 / 5.2302 = 114.7 7. 0.0032 x 273 = 0.87 8. (5.5)3 = 1.7 x 102

9. 0.556 x (4.x101 - 32.5) = 4.10. 45. x 3.00 = 1.4 x 102

11. 3.00 x 105 - 1.5 x 102 = 3.0 x 105 12. What is the average of 0.1707, 0.1713, 0.1720, 0.1704, and 0.1715?Answer = 0.1712

Temperature scales

FTT oCF oo 32

59 15.273 Ck oTTbaTT CF oo

Thermometer Calibrations

Three reference points Ice Triple Point

Steam

Kelvin 273.15 273.16 373.15

Celsius 0.00 0.01 100.00

baxT

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 air1. 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.

Thermometer Response Time

inversely proportional to heat transfer rate. proportional to the heat capacity

Moisture Measurement

TRe vv 2vTR

E LTE

K 16.273T ,kg J X105.2L hPa, 11.6E

),TT

T-T

RL

exp(EE

01-6

0

0

0

v0

Mixing ratio, r 622.0R

R ,

pe

e-pe

r v

dMM

d

v

Specific humidity, q pe

)e-(1-pe

qvd

v

MMM

Relative humidity, h %qq

rr

Ee

hss

Dew-point

For isobaric process QTC p

Enthalpy pVUTCH p

Wet bulb temperature

)( wv

pTofs TT

crr

w

)(622.0 w

v

pTofs TT

pcee

w

Since )( Ds tee )( ws Tee

TTT wD

)()( rrTTc wvwp

wT

T

Sling psychrometer

Theory

How to operate sling psychrometer

Atmospheric pressure measurement

Barometers

Mercury barometer zzHg hgP ,,

Temperature correction

Gravity correctionFortin Barometer

Aneroid Barometer

BarographsA barograph, which records a graph of some atmospheric pressure, uses an aneroid barometer mechanism to move a needle on a smoked foil or to move a pen upon paper, both of which are attached to a drum moved by clockwork.

An evacuated medal capsule supported by a spring. The expansion and contraction drives mechanical levers such that the tiny movements of the capsule are amplified and Displayed.

Precipitation

Precipitation refers to any product of the condensation of atmospheric water vapour that is deposited on the Earth's surface.

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

sm

kg2

w

R s

m

Mass flux

hmm

sm 6106.31

Ordinary rain gauge

Tipping bucket rain gauge

Optical rain gauge (ORG)

Disdrometer

Precipitation radar

Relationship between the intensity echo and precipitation

6.1200RZ

Echo strength is measured in units of DBZ (decibels).

)(log10 10 ZdBZ

Measuring the drop size distribution and velocity of falling droplets.

)()( 36 iiil DVDDNR

dBZRainrate

(inches per hour)Description

65 16+ Extreme thunderstorms, possible hail

60 8.00Very heavy thunderstorms, possible

hail55 4.00 Heavy thunderstorms52 2.50 Thunderstorms47 1.25 Very heavy rain or sleet41 0.50 Heavy rain or sleet36 0.25 Moderate rain or sleet30 0.10 Light rain or moderate snow20 Trace Very light rain or snow