Why isn’t the SEB equation satisfied



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These notes are intended to help you to interpret some of the results obtained from the field experiments, and need to be considered when writing your reports.

Why isn’t the SEB equation satisfied?

Given independent measured values of net radiation, ground heat flux, surface sensible heat flux and surface latent heat flux, we would expect that the measured values sum to zero (see equation 1.2 in Keynotes). However, that is rarely if ever the case in practice, due to various sources of error in the measured parameters. The result is that from independent measurements we obtain

[pic],

where A is either a positive or negative number which we recognise is significantly different from zero and is therefore likely to be due to errors of measurement. Also we may find that different methods of measuring the same parameter, e.g. H, give very different answers. Again, this implies that one or both of the methods are subject to large errors of measurement. The following considers some important sources of error which may affect measurements on the University field site.

1. Instrument error

There is an obvious source of error associated with uncertainties in the calibration characteristics of the instruments. Associated values of probable error on measurements can be estimated provided we know the accuracy of the instruments, and the notes for the experiments give you guidance on how to estimate such errors. However, there are other sources of instrument error which may have affected our measurements. Examples are the effect of stalling in the case of anemometers operated in light-wind conditions and the effect of instrument lag when measuring turbulent fluctuations. Both lead to an under-estimation of mean wind speed and mean fluxes.

2. Sampling error

This type of error arises when we try to measure the mean value of a parameter from a finite number of measurements. It is probably not too important in the case of our experiments, though it might be significant in the case of the eddy-correlation measurements and when measuring the offset between sensors in the case of the Bowen Ratio experiment. Sampling error can be reduced by averaging over longer time periods. However, data may then be affected significantly by the diurnal variation of sensed parameters. This leads to another type of sampling error which can be serious in the case of eddy-correlation measurments, because the analysis tends to associate temperature trend with the turbulent variation about a fixed mean value, whereas that is obviously not the case in practice.

3. Representativeness error

This is an important source of error in field measurements. A simple example is the measurement of Go using just one soil heat-flux plate: this measures the flux averaged over a few square cm, whereas other measurements (such as that of Rn) are effectively averaged over several square metres. Also, it is necessary to bury the plate a cm or two below the surface, so it will tend to measure a value less than Go when the latter is positive. Another example is that both the eddy-correlation and profile measurements are effectively sensing fluxes which are associated with turbulence generated up-wind of the field site, where the value of Rn may be rather different to that actually measured on the field site. (This problem would be reduced if we could make measurements at a location surrounded by a rather uniform, flat surface.)

4. Model error

This is an error that arises because some theoretical assumption which we use when analysing data is not valid for the conditions actually sampled. A simple example is the assumption that the heat flux measured by the eddy-correlation method is the same as the surface sensible heat flux H on the field site. However, suppose it is cloudy most of the time, but the sun comes out towards the end of a sampling period. Then the ground starts to heat up rapidly, and some of this heat is transferred to a shallow layer of air near the ground. So H increases rapidly. However, the vertical heat flux at the height of the instruments will not tend to change until a ‘new’ boundary layer has developed to beyond the height of the instruments. Hence the eddy correlation method would tend to under-estimate H in this situation.

Another example is that the observed mean wind-speed profile can be used to determine [pic] under the conditions of the experiment. However, the theory in section 8 of the Keynotes only applies accurately if the potential temperature lapse rate is near neutral. For higher lapse rates [pic] tends to be larger than [pic] by a fraction that depends on the lapse rate. Hence the aerodynamic method tends to under-estimate fluxes under these conditions if we assume [pic]. (It is possible to correct for the effect of lapse-rate, and this problem is covered in a more advanced module on surface layer processes.) If the nature of the surface changes near the area of measurement, then it is unlikely that the observed profile will be truly logarithmic, even under neutral conditions. Consequently, errors arise when estimating [pic] as the slope of a straight line ‘fitted’ to measurements of U plotted against [pic].

Further Reading

Some useful secondary source material may be found in the following textbooks, which are held in the Departmental library.

McIlveen, R., 1991, Fundamentals of Weather and Climate.

Monteith, J.L., and M.H. Unsworth, 1990, Principles of Environmental Physics.

Oke, T.R., 1978, Boundary Layer Climates.

Arya, S.P., 1988, Introduction to micrometeorology.

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