Measurement Errors 2 atmospheric errors Geraint Vaughan How

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Measurement Errors 2: atmospheric errors Geraint Vaughan

Measurement Errors 2: atmospheric errors Geraint Vaughan

How accurate is this wind measurement? How accurate is the wind measurement? 1 minute

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

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

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

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

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

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’?

10 -point running average Still a bit ‘noisy’?

50 -point running average ‘Better’, but smooth enough? Are the excursions really noise? End

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

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

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

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

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

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

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. •

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

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

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

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.