Measurement Theory

Intro to measurementDiscussion of standards & traceabilityPrac exampleUncertaintyExamples of measurementExercisesCautions

Measurement

The process of determining the value of

some quantity in terms of a

standard unit.

Standards

There is a hierarchy of standards – that is agreed unitsSome of these are artifacts ie the kgSome are “realised” eg temperatureAt the top of the hierarchy are Primary standardsRIC currently hold Primary standards for P, T and Radiation

True Temperature Scale

Agreed international scale of temperature – ITS-90Comprised of points on the scale that are realized – that is made up temporarily using physical systems

Interpolation between the points is via Pt resistance thermometers

Pt resistance thermometers are approximately linear between points on the true temperature scale

  

Substance Temperature K Temperature °C State

Mercury, Hg 234.3156 -38.8344 Triple Point

Water, H20 273.16 0.01 Triple Point

Gallium, Ga 302.9146 29.7646 Melting Point

Indium, In 429.7485 156.5985 Freezing Point

Tin, Sn 505.078 231.928 Freezing Point

Zinc, Zn 629.677 419.527 Freezing Point

Aluminium, Al 933.473 660.323 Freezing Point

Silver, Ag 1234.93 961.78 Freezing  

Water Triple Point Cell

Ultra pure water is sealed under vacuum into a glass vesselThe apparent air gap above the liquid is entirely composed of water vapour whose pressure is determined by the temperatureIt forms a sealed system at equilibrium

Contd.WTP defined to be at 0.01oCThe ice must be as a moveable mush ie. It must freely rotate in the cellThe WTP maintenance bath can keep the cell at this temperature for daysThe kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

Gallium Melting Point

Defined to be at 29.7646 degrees C

As can be seen in the graph it is a plateau

Energy is going into breaking bonds – hence no temperature rise until all of the Ga has melted

Can be drawn out for about 30 hours 5 6 7 8 9 10

29.765

29.766

29.767

29.768

29.769

Te

mp

era

ture

(o C

)

Time (hours)

0 5 10 15 20 2527.0

27.5

28.0

28.5

29.0

29.5

30.0

30.5

31.0

End of Melt

Start of Melt

Te

mp

era

ture

(o C

)

Time (hours)

Traceability

Traceability is the unbroken chain of calibration/verification from a primary standard to the device in questionThis chain may have one link or several depending on the deviceAt each stage of must be fully documented

Pressure TraceabilityInternational

HO Transfer

Regional Kew

Regional Transfer

Station

0.03 hPa

0.07 hPa

0.10 hPa

0.15 hPa

0.20 hPa

National

RA V (WMO)

Dimensional

Pressure

Total 0.27 hPa

• The degree of doubt about a measurement!

• Parameter, associated with the result of a measurement, that characterises the dispersion of the values that could reasonably be attributed to the measurand. (International Vocabulary of Basic and General Terms of Metrology)

Uncertainty

Uncertainty

Low AccuracyHigh Precision

xxx

x

xxx xxx

xxx

x

x

x

xxx

x

x

x

x x

Medium AccuracyLow Precision

AccuracyThe closeness of the experimental mean

value to the true value.

High accuracy = Small systematic error.

PrecisionThe degree of scatter in the results.

High precision = Small random error.

1

High Repeatability / Low Reproducibility

Golfer OneGolfer One

Drift in an instrument

2

Low Repeatability / Low Reproducibility

Golfer TwoGolfer Two

Low Precision

3

High Repeatability / High Reproducibility

Golfer ThreeGolfer Three

Low Uncertainty

What’s Normal?

The outcome of most natural processes is normally distributedThis results from the central limit theorem

Significance of Differences

Xa Xb

U95

Not Significant

Significant

Xa Xb

Confidence

How many samples do you have to take to be “confident” you have estimated the mean value correctly?The mean we determine will have an expected value – in this case the mean of the population and a varianceHow well we estimate the mean depends on how many samples we take.

Xa

Temperature Prac

Use the two IR thermometers to take the victims temp.Take 7 measurements with each deviceForm an averageMax and Min

Making a measurement

Any single measurement is a “selection” from a distribution of possible valuesMore measurements give you greater “confidence” in estimating population parametersCan’t make an infinite amount of measurements because the system being tested may not be stable

Test Uncertainty Ratio (TUR)

It is intuitive that in order to measure something you need to measure it with something more accurateThis is the TUR – the ratio of the uncertainty in your reference to the uncertainty of the device under testUsually a TUR value of 4 or better is used

Xa

Xa

Contd.

You can work with TURs less than 4The barometers are calibrated with a TUR of approximately 1!You need to take a lot of samples! Xa

Xb

Instrument Properties

Linearity – Accuracy of response over measurement rangeStability – short and long term (drift)Response time – how fast it respondsPrecision Hysteresis

Linearity

Opposite are plots of True versus probe temperature for AWS Temp probesNote they are all approximately linear in responseThey each have a slightly different line

-10 0 10 20 30 40 50 60-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08 RTDs

Cor

rect

ion

(o C)

Temperature (oC)

Stability

Humidity probe short term drift (2 hrs)Humidity Probe medium term drift (20 days)

0 5 10 15 200.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Probe 1 Probe 2 Probe 3 Probe 4

80 % RH

Co

rrec

tion

(%

RH

)

Day

40 60 80 100 12049.5

49.6

49.7

49.8

49.9

50.0

50.1

50.2

% R

H

Time (Min)

Response Time

Opposite are plots of RH versus time for a humidity probe.RH was changed “instantaneously” “Response time” is defined as the time taken for the instrument to read 63% of the step change

410 420 430 440 450 460 470

30

40

50

60

70

80

% R

H

Time (sec)

1980 1990 2000 2010 2020 2030 2040

30

40

50

60

70

80

% R

H

Time (sec)

Precision

Opposite are the plots Temp versus time for two probesThe two probes have differing systematic errors (y axis shift)The two probes have different precisions (y axis spread) 200 300 400

21.90

21.95

22.00

22.05

22.10

22.15

22.20

Tem

per

atur

e (o C

)

Time (sec)

Probe 1 Probe 2

Contd.

The probes exhibit a systematic error – offset or biasBoth probes have approximately the same precision

0 500 1000 1500 2000 2500 3000 3500

55.13

55.14

55.15

55.16

55.17

55.18

55.19

55.20

55.21

Tem

pera

ture

(o C

)

Time (sec)

Probe 1 Probe 2

2000 2500 300055.1700

55.1725

55.1750

55.1775

55.1800

55.1825

55.1850

55.1875

55.1900

55.1925

55.1950

Oceanus 6

Tem

pera

ture

(o C

)

Time (sec)

Quantization

0 20 40 60 80 1002.6

2.7

2.8

2.9

3.0

3.1

3.2

3.3

Pe

rio

d B

twn

Tip

s (s

ec)

Sample No.

Pump System Gravity System

Quantised measurements take discrete levelsImportant to know how they were quantizedWere they rounded or truncated?No necessarily less accurate than analogue data

Hysteresis & Linearity

100 200 300 400 500

100

200

300

400

500

0

Hysteresis

Linearity

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

-15 -5 5 15 25 35 45 55

Temperature °C

Cor

rect

ion

to r

efer

ence

hP

a

PA11a Increasing Temperature

PA11a Decreasing Temperature

PTB220B Increasing Temperature

PTB220B Decreasing Temperature

PA11a & PTB220B Hysterisis

GoodGoodClean Mercury Rising Pressure

BadBadPossibly Dirty MercuryFalling Pressure

Very BadVery BadDirty MercuryFalling Pressure

Mercury Barometers

Response Versus Temperature

Opposite is a plot of the corrections required for HMP45D probes versus TempNote – response is quite consistent – but not linear

5 10 15 20 25 30 35 40 45 50

0.0

0.5

1.0

1.5

2.0

2.5

3.0Response versus TemperatureVaisala HMP45D Humidity Probes

Cor

rect

ion

(o C)

Temperature (oC)

With-in run precision.

Variability on an occasion

Reproducibility

Variability on different occasions

Between-run precision

Repeatability

Contd.

Opposite is a plot of the RH reached by the humidity generator versus timeSystem was cycled between 3 RH levelsRepeatability is the closeness of the match in RH achieved

2000 4000 6000 8000 100000

20

40

60

80

100

% R

H

Time (sec)

Reproducibility

Reproducibility is the “between trial” variabilityOpposite is a plot of the long term error for a barometer

Calibration Errors

Co

rrec

tio

n (

hP

a)Jun-65 May-70 May-75 May-80 May-85 May-90

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Populations

0 20 40 60 80 100

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Original probes tested Probes from other batches

Temp = 25oC

Err

or

(Re

f -

Pro

be

) %

RH

Reference % RH

Opposite is a plot of the offset errors for a batch of humidity probes.The error for any particular probe for any measurement will be approximately normally distributedThe offset or bias of the all probes is also expected to be normally distributed!

Resolution

Resolution is the smallest increment in value the instrument can returnResolution will affect the precision of the instrumentResolution will not ordinarily affect the accuracy of an instrument

Resolution = Uncertainty

Half of the least significant digit on an analogue instrument

The least significant digit on a digital instrument.

The uncertainty of this thermometer is ± 2°C.

If the scale has 10°C divisionsThe resolution is 5°C

If the scale has 2°C divisions

The resolution is 1°C

20

30

10

0

40

50

Contd

Both probes have the same resolutionRed probes has approx four times the uncertainty

200 300 40021.90

21.95

22.00

22.05

22.10

22.15

22.20

Tem

per

atur

e (o C

)

Time (sec)

Probe 1 Probe 2

Confidence

100%95%65%<1%

± 0.5°C± 5°C

± 10°C± 30°C

20

30

10

0

40

50

Errors Vs Blunders

By definition most measurements will not be exactly “right” they will be in error to some degreeA blunder is when a human is in the loop and produces a mistakeIe. Misreads a thermometer as 35.25oC instead of 25.25oC

Calibration

Comparing the reading of an instrument when it is exposed to a known artifact or conditionEither the instrument is adjusted to read “correctly” orA table of corrections is produced so that the operator can “correct” the instrument reading to the true readingMay need to interpolate

VerificationMost of the work of the RIC involves verifying that an instrument/probe etc is in specificationThis is not a calibration since corrections etc are not suppliedHence equipment sent to the field is within spec but may lie anywhere within the specification - two humidity probes could differ in readings by 4% RH and both could still be in spec

0 20 40 60 80 100

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

HMP45D HMP45A

Temp = 23oC

Co

rre

ctio

n (

Re

f - P

rob

e)

% R

H

Reference % RH

Field TolerancesSensor

ComparisonMethod

UncertaintyField

Tolerance

Pressure Standard 0.3hPa 0.5hPa

TemperatureWithin ScreenPsychrometer

0.3°C0.4°C

0.5°C0.6°C

RelativeHumidity

Within ScreenPsychrometer

4%5%6%

Wind Speed ? 10% N/A

Wind Direction Compass 5% 10%

RainfallWith Syphon

Without Syphon

3% (<250mm/h)

4% (250 – 350mm/h)

8%8%

Exercise 1Currently the inspection handbook “checks” an AWS RTD with an Inspection grade Mercury in glass thermometerRTD accurate to 0.2oC – MIG accurate to?Single measurement after 1 hour of stabilisationWhat is are the flaws in this procedure?Come up with some alternatives alternatives

Exercise 2

Currently the inspectors check an AWS humidity probe with an wet/dry bulb thermometersOne wet/dry measurement after 1 hour of stabilisationWhat is are the flaws in this procedureSuggest alternatives

Exercise 3

NCC alerted RIC to anomalous readings from manual sites (red) and AWS humidity probes (black)The manual obs (wet/dry bulb) appear to over-estimate the dew point

0 20 40 60 80 100 120

-6

-4

-2

0

2

4

6

8

10

12

14

De

w P

oint

(o C

)

Time

AWS Data Manual Obs

Contd.Plotted opposite is the DP from manual obs (x-axis) versus the AWS derived DP (y-axis)In a perfect world the data would lie along the line y = xPostulate a model as to what has gone wrongAssume humidity probe was checked and found to be in-spec within previous 6 months.

-6 -4 -2 0 2 4 6 8 10 12-4

-2

0

2

4

6

8

10

12

14

Slope = 0.75

Man

ual O

bs D

ew P

oint

(o C

)

AWS Dew Point (oC)

Scatter Plot Linear Fit of Data1_B

Hypotheses

1 – The humidity probe is stuft!2 – The manual observers were drunk!3 – Both 1 & 24 – Both sets of data are correct!Come up with some others –Also assume all measurements made were correct!

Best GuessIt is troubling that the line of best fit does not have a slope of 1 and this suggests there may be a problem with the algorithms used to calculate DP.Having said that, it is most likely that both sets of data are essentially “correct”.RH probes (currently in use) measure RH Wet/dry bulb measurements really measure evaporation rate – not really the same thingWet/dry measurements over-estimate humidity by up to 20% in still air conditions.A useful comparison would be RH from each technique after selecting data obtained when the wind speed was greater than 2 m/s

Data Quality

Site Selection and Installation

Measurements

Quality Assurance

Quality Control

Data

Instrument Selection

Final Product

Meteorologists & Climatologists

PMAs

Observers

ROMs & Engineers

Lab

Training Double checkUse Calibrated instrumentsMinimises the number of variablesUse standard test procedures“If it is not broken don’t fix it”Document, document, document

How to improve the Data Quality

Field Adjustment

Don’tJust DON’T!An adjustment in the field will remove all traceabilityIf it is out of spec – remove and return

Questions?