Uncertainty can also arise from issues with measurement representativity. Errors associated with representativeness more often appear as random errors except in cases where the correlation between a specific feature (e.g., large upwind body of water) and the measurement (wind direction, for example) introduces a systematic effect in the measurement. In this example, the directional persistence of the wind moving over the body of water will bring cooler and more moist conditions which would reveal a directional bias in the data.
Representativeness requires an interpretation of the natural spatial-temporal variability of the measurand. For example, where was an air parcel earlier, what changes occurred during its advection to the observation site, and how is the value of the measurand correlated with its values at other times and locations? Such correlations must be considered when estimating uncertainty because measurements cannot be considered independent in the presence of such correlations.
Exploratory statistical correlations for paired data can be very useful in determining correlations arising from representativity. The Ordinary or Pearson Correlation coefficient is given by
where Cov(x,y) is the covariance of x and y and sx and sy are the sample standard deviations. For testing temporal representativity, the autocorrelation function can be used to compute correlations for various lags. The autocorrelation for a time lag of 𝜏 samples is given by
Where Cov(x,y) = E(x-x̄)(y-ȳ), where E denotes the expected value.
Let’s consider an example in which we measure component winds (u, v, w) for an hour with a sonic anemometer at 20 Hz. This sampling frequency would yield 72,000 measurements. The autocorrelation shows that the measurements have a correlation time of 0.5 minutes, that is, the e-folding time for the autocorrelation coefficient to decrease to 0.37 is 0.5 minutes.
In this situation, how many independent measurements do we have? Select the best answer.
The correct answer is b.
In this situation, we get an independent measurement every 0.5 minutes, so will have 120 independent measurements instead of 72,000.
For measurements to be representative, atmospheric processes in general must be relatively homogeneous, or vary linearly, across the spatial and temporal domains of an instrument network. Representativeness cannot be defined by an observation or a specific parameter, but results from an assessment of the instrumentation, sampling frequency, exposure, and the application.