Dynamic response of the thermometric net radiometer
J.D. Wilson
a,
*
, W.J. Massman
b
, G.E. Swaters
c
a
Department of Earth & Atmospheric Sciences, University of Alberta, 1-26 Earth Sciences Building, Edmonton, Alberta, Canada T6G 2E3
b
U.S. Forest Service, Fort Collins, CO, USA
c
Department of Mathematics and Statistics, University of Alberta, Edmonton, Alberta, Canada
1. Introduction
Several authors have considered the possibility that the net
radiation measurement may be the seat of the widely reported
energy balance closure problem, often presupposing that time
variation of the radiative fluxes on turbulence timescales need not
be considered. However by virtue of the boundary conditions on its
upper and lower planes, the equations governing the response of a
thermometric radiometer are non-linear, raising the possibility
that, if either or both of the upward and downward longwave flux
densities (L
"
; L
#
) do vary in time on frequencies f that are rapid
compared to the reciprocal of the thermal time constant of the
device (roughly, d
2
=
k
$ 10 s;
k
is the thermal diffusivity and d is the
thickness of the substrate), a mean signal may be produced even in
the absence of a mean net longwave flux density
L
Ã
¼ L
"
À L
#
.
Since the longwave fluxes certainly do fluctuate on rapid time-
scales, in response to the spectrum of air temperature fluctuations,
the passage of clouds, and possible variation of plant canopy and
ground temperatures, such a bias (if significant in magnitude)
would compromise use of this type of instrument, or at least
demand a correction. Laboratory and field studies of a range of net
radiometers led Smith et al. (1997) to conclude there is ‘‘a
fundamental deficiency in the two-sided thermopile design used in
most net pyrradiometers under non-equilibrium conditions.’’
Where measurements fail to close the energy balance, it is
generally found that the sum Q
H
þ Q
E
of the convective fluxes (of
sensible and latent heat, respectively) underestimates the avail-
able energy Q
Ã
À Q
G
À
D
Q
S
(where Q
Ã
is the net radiation, Q
G
is the
soil heat flux density, and
D
Q
S
any storage term). Accordingly,
many authors have considered that the seat of the problem lies
with estimation of the convective fluxes
1
. However Kohsiek et al.
(2007) focused on the radiative fluxes (as measured by thermo-
metric radiometers), and indicate a possibility that the radiation
term may lie at the root of the problem (though these authors
assumed that error in Q
Ã
, if present, would have arisen from spatial
inhomogeneity of the site, or from radiometer calibration
inaccuracy; they did not question the principle of the thermometric
radiometer). Mauder et al. (2007), participants in the same
experiment (EBEX-2000), recommend that ‘‘net radiation is
preferably to be inferred from its four components, rather than
measured directly.’’ Echoing Brotzge and Duchon (2000) they note
that ‘‘no international agreement exists on a radiation standard
and calibration procedure’’ for the pyrgeometer (i.e. hemispheric
longwave radiometer) and that ‘‘there is no agreement on the
mathematical description of the physics of the instrument.’’ As
regards the latter, according to Mauder et al. the World Radiation
Agricultural and Forest Meteorology 149 (2009) 1358–1364
ARTICLE INFO
Article history:
Received 3 September 2008
Received in revised form 7 March 2009
Accepted 15 March 2009
Keywords:
Net radiometer
Pyrgeometer
Thermal radiometer
Thermometric radiometer
ABSTRACT
We computed the dynamic response of an idealized thermometric net radiometer, when driven by an
oscillating net longwave radiation intended roughly to simulate rapid fluctuations of the radiative
environment such as might be expected during field use of such devices. The study was motivated by
curiosity as to whether non-linearity of the surface boundary conditions implies the existence of a non-
vanishing mean signal even when mean forcing (i.e. mean net radiation) vanishes. These simulations do
not prove (and owing to discretization and roundoff error, cannot prove) such a bias is absolutely non-
existent, however they establish that the bias is of negligible practical importance, even for
unrealistically large fluctuations in the net radiation. Other aspects of net radiometer design must
account for the serious errors known to sometimes result (in the case of many devices), from field
application of steady-state calibration factors.
ß 2009 Elsevier B.V. All rights reserved.
* Corresponding author. Tel.: +1 780 492 0353.
E-mail address: jaydee.uu@ualberta.ca (J.D. Wilson).
1
On the basis of Large Eddy Simulations Huang et al. (2008) reported, as have
earlier authors, that the underlying cause of the energy balance closure problem is
(or can be) inadequate spatial representativity of point measurements of the
vertical fluxes.
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Agricultural and Forest Meteorology
journal homepage: www.elsevier.com/locate/agrformet
0168-1923/$ – see front matter ß 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.agrformet.2009.03.007