Measurement Errors 2 atmospheric errors Geraint Vaughan How
- Slides: 19
Measurement Errors 2: atmospheric errors Geraint Vaughan
How accurate is this wind measurement? How accurate is the wind measurement? 1 minute averages of eastward wind component measured on a tower near the MST radar site, Aberystwyth, 8 Dec 2011
How accurate is this wind measurement? How accurate is the wind measurement? • Systematic errors, e. g. all winds could be 20% too low Instrument intercomparisons and comparison to standards are essential
How accurate is this wind measurement? How accurate is the wind measurement? • Systematic errors • Random errors – Scale resolution – Random variation in measured quantity e. g. photon noise – Noise in the instrument Accuracy – how well does the instrument compare to a standard? – systematic and random errors Precision – how repeatable are the measurements? - random errors only Systematic errors can often be mitigated through use of differences or ratios of measurements
How accurate is this wind measurement? How accurate is the wind measurement? • Systematic errors • Random errors – Scale resolution – Random variation in measured quantity e. g. photon noise – Noise in the instrument • Representativity error – what would the wind look like 100 m away? What are the correlation structures in the data? Accuracy – how well does the instrument compare to a standard? – systematic and random errors Precision – how repeatable are the measurements - random errors only
Representativity error • A major source of error for atmospheric measurements • A real headache for data assimilation – how do you constrain a model using ~20 km grid boxes with point measurements? • Something to think about when you’re on the hill – how representative are the measurements you make of the atmosphere around you?
Reducing random variations We would like a ‘smooth’ time series with the noise removed For wind almost all the noise is due to atmospheric variability – a form of representativity error rather than random noise in the instrument
10 -point running average Still a bit ‘noisy’?
50 -point running average ‘Better’, but smooth enough? Are the excursions really noise? End effect: smoothing only kicks in 25 points into dataset
Are the wind fluctuations Gaussian? Departures from the 50 -point smoothing over the course of a day Pretty good fit to a Gaussian in this case
Take care when averaging What do we do with a feature like this? Instrument problem?
Take care when averaging Passage of a very sharp cold front: this feature is real
Fitted polynomial (quartic) Is the polynomial too smooth? Is there a ‘right’ scale of averaging?
How much averaging? Turbulence theory is based on observations of flow in pipes where you can decompose the instantaneous velocity into two components: v = v + v’ Here, v is a slowly-varying underlying function and v’ the turbulent component. In the atmosphere this concept doesn’t work – the scale of averaging you choose is arbitrary and must be related to what you want to do with the data
Spectra of wind fluctuations over 1 day In a turbulent fluid the variability is fractal – there is no obvious averaging scale. Fractal variations show up as power laws P(k) α k-β in spectra
Are the errors independent and Gaussian? • Instrument random errors – normally yes. • Systematic errors – usually assumed to be though this must be checked for each case • Representativity errors – Gaussian fairly good assumption but independence much more tricky – beware of correlation structures in the data • Be particularly careful if using significance tests (like t-test) on data where the dominant error is representativity.
Autocorrelation of winds Note the very long correlation structures in the full wind data – these are synoptic-scale variations. Much shorter as expected in the wind fluctuations.
Treatment of random variations • Random variations can be reduced by averaging • The standard error in the mean then gives the precision of the averaged measurement • If your measurements are dominated by instrument noise rather than atmospheric variability this approach is easy to implement • But in general, deciding how to average is not trivial – formally this requires the data to be statistically stationary (noise and signal well separated in spectral space). This is seldom the case. • For parameters like wind atmospheric variability is generally greater than the instrument noise
Conclusion • All measurements come with errors • You must always quote the errors as best you can • Systematic errors need to be checked by validation (comparison with another technique) • Noise-like errors can be handled with standard formulae • Representativity errors can be treated as noise if you have enough data – but beware of the nonindependence of data points.
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