AOSC 634
Air Sampling and Analysis
Lecture 1
Measurement Theory
Performance Characteristics of instruments
Nomenclature and static response
Copyright Brock et al. 1984; Dickerson 2015
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Static Response
Output
Sensor output in response to unchanging input.
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bias or zero offset
Input
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Static Response
I = input, atmospheric, oceanic, or other environmental signal.
O = Output, sensor response voltage, current, counts, etc.
Nomenclature varies but concepts are fundamental.
Sensitivity – slope of I/O diagram.
Bias (zero offset) – Y intercept. Mass flow controllers are a
good example.
Range – max to min measureable.
Span – max minus min.
Linearity – how well the calibration curve fits a straight line.
Resolution – the smallest change in the input that can
produce a change in the output.
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Primary vs. secondary variables
Example - a pressure transducer sensitive to temperature
.
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UV absorption instruments
• The [O3] indicated is actually a molecular number
density. The mixing ratio (ppb) has to be corrected
for air temperature and pressure.
[O3 ]indicated
æ 298 ö æ P(hPa) ö
= [O3 ]real × ç
÷
÷×ç
è T(K) ø è 1013 ø
• The ozone instrument has sensitivity to a secondary
input – air density.
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6
Indicated wind speed
Example of threshold
a cup anemometer with static friction.
Input - Actual wind speed
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Additional Nomenclature
I don't like the traditional definitions of
"precision" and "accuracy" given in Brock’s book,
but they are in common use among
meteorologists. Here are alternative definitions
in common use by analytical chemists and
meteorologists.
Precision - The standard deviation of a series of
measurements made under constant conditions.
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Accuracy - This is a slippery concept that can only be determined
if the "true" value of the variable of interest is known. For
example, the "accuracy" of a thermometer can be determined at
0°C with an ice water bath. If we measure air temperature with the
same thermometer we might be able to determine the "accuracy" of
the measurement with a second, much better thermometer, but
what about state-of-the-art instruments measuring unknown
quantities? For the most interesting questions in atmospheric
science, "accuracy" must be estimated.
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Uncertainty - The combined effect of all the sources of noise or
other error in a measurement. Usually expressed as some range of
values at some confidence level; for example 25.03 ± 0.04°C. If
the sources of error or uncertainty are "normal" or Gaussian, (and
often they are not) these ranges might represent confidence of 68%
(+/- σ), 95% (+/- 2 σ), or 99% (+/- 2.5 σ).
y=
1
2ps
e
- [(x - x) / s ] / 2
2
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Detection limit- Also called lowest detectable level, this is the concentration or
amount below which an instrument cannot provide meaningful information.
Because several definitions are common use, a good paper will define the detection
limit used. Consider an atomic emission spectrometer that produces a net output of
2 V for an aqueous solution of 2.0 μM Na+, and a background signal with Gaussian
noise with a standard deviation of 0.25 V when the signal integration time is 1 s. The
signal-to-noise ratio is 2:1 for [Na+] of 2.0 μM for ±2σ. For a rainwater or aerosol
sample then, the detection limit for sodium is 1.0 μM at a signal-to-noise ratio of 1:1
with a 95% confidence interval for a 1 s integration time. Again the detection limit
might be better for longer sampling times, but the experimenter must prove this.
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Summary
• There are may “figures of merit” for an
instrument or measurement.
• The best ones depend on the application at
hand.
• For example do you want an instrument that
is fast and sensitive for flux measurements of
aircraft observations or one that is stable and
insensitive to temperature and pressure for
monitoring?
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