MT23E Handout
Dr Mike Pedder
HANDOUT
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
Rn  G0  H  E  A ,
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 eddycorrelation 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
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MT23E Handout
Dr Mike Pedder
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 K 
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
K  tends to be larger than u*kz by a fraction that depends on the lapse rate. Hence the
aerodynamic method tends to under-estimate fluxes under these conditions if we assume
K   u*kz . (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 u* / k  as the slope of a
straight line ‘fitted’ to measurements of U plotted against ln z  .
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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