E. Lamaud et al. Agricultural and Forest Meteorology 106 2001 187–203 191
Fig. 1. Climatic conditions during the March–April 1998 experiment in the Landes forest.
3. Validation of eddy flux measurements
3.1. Energy balance closure When many runs are lumped together and averaged,
eddy fluxes measured above a forest appear gener- ally valid, as proved by the energy balance closure on
a daily basis Jarvis et al., 1997 or an hourly basis Baldocchi and Vogel, 1997; Berbigier et al., 1998.
Of course, at such short time scales this requires reli- able estimates of the storage terms in the soil G and
in the different compartments of the canopy J, over- storey, litter, trunks, and the air layer below the flux
measurement level.
In the lower part of the canopy two problems arise. First, the eddy covariance method is subject to crit-
icism because the underlying requirements are not always fulfilled: low wind speed, strong heterogene-
ity and intermittent turbulence contribute to making the convergence of the statistical moments difficult.
Second, the relative importance of the storage terms in the understorey energy balance is substantially
higher than in the previous case. At canopy scale in day-time conditions, the sum F of the sensible H
and latent LE heat fluxes corresponds to about 90 of the incident net radiation, whereas at the under-
storey level this proportion is on average only about 60 of the transmitted net radiation R
n,b
, and can be as low as 40. Altogether, it is more difficult in these
conditions to obtain a correct energy balance closure. As an example, Baldocchi and Vogel 1997 ob-
tained a relatively poor closure over the understorey, whereas their results were rather good above the
forest.
In Fig. 2, we plotted the sum of turbulent fluxes F = H + LE measured above the forest floor di-
rectly against the transmitted net radiation R
n,b
, for the whole data set. Three main features can be seen: i for
day-time data R
n,b
0 there is a large discrepancy between F and R
n,b
the slope of the linear regression for day-time data is 0.63, ii there is a large scat-
ter r
2
is only 0.76 for day-time data, iii during the night F is about zero, whereas R
n,b
is negative down to −30 W m
− 2
.
192 E. Lamaud et al. Agricultural and Forest Meteorology 106 2001 187–203
Fig. 2. Sum of eddy fluxes F vs. net radiation R
n,b
, below the forest canopy. The straight line represents the linear regression for
day-time data R
n,b
0.
In Fig. 3, the sum of storage terms S = G + J was added to the sum of turbulent fluxes. The sum
of storage terms and turbulent fluxes, S + F , is noted T. The residual difference between R
n,b
and T is fur- ther noted R. The results are remarkable: the whole
set of points is now centered around the 1:1 line. Table 1 shows that the slope of the regression line for
the whole data set is 0.99, that the intercept is negligi- ble 0.49 W m
− 2
and that the scatter has substantially decreased. In other words a careful evaluation of the
various storage terms allow us to obtain a satisfac- tory closure of the energy balance. Incidentally, these
results show that at night the turbulent fluxes at the understorey level are negligible, R
n,b
being only com- pensated by the storage terms. This is an important
difference with what is currently observed above a forest canopy.
It must be mentioned that the ratio FR
n,b
varies to a large extent from about 0.4 to 0.8 during the
Table 1 Regressions of the sum of storage terms and eddy fluxes versus net radiation R
n,b
estimated just above the understorey Whole data set
Day-time data R
n,b
Regression not forced through 0
Regression forced through 0
Regression not forced through 0
Regression forced through 0
Slope 0.99
0.99 0.97
0.99 intercept W m
− 2
0.49 1.96
r
2
0.94 0.94
0.88 0.88
Fig. 3. Sum of eddy fluxes and storage terms T vs. net radiation R
n,b
, below the forest canopy. The slope of the linear regression for day-time data not illustrated is 0.99, with r
2
= 0.88 see
Table 1. The straight lines other than 1:1 correspond to the selection thresholds defined in Section 3.3, using the “a” slope
and “b” intercept coefficients. The two examples given here correspond to a, b = 0.1, 10 and 0.15, 0, respectively.
experiment, in response to the evolution of climatic conditions. From 14 to 26 March, turbulent fluxes
represent about 60 of the net radiation. From 27 to 31 March, they represent only 40 to 50 of R
n,b
. At the end of the experiment, from 1 to 6 April, they
are largely dominant in the energy balance 70 to 80 of R
n,b
. As mentioned above, this third period corresponds to a strong decrease in Bowen ratio, the
latent heat flux being twice or three times larger than the sensible heat flux. The ratio LER
n,b
rises from about 0.3 to 0.4–0.5, while the ratio HR
n,b
remains unchanged. Of course, as for nocturnal data, this
evolution of the ratio FR
n,b
is compensated by an equivalent evolution of the ratio SR
n,b
. Table 1 also shows the statistics of the regressions
performed over day-time data only. As nocturnal
E. Lamaud et al. Agricultural and Forest Meteorology 106 2001 187–203 193
turbulent fluxes were found to be close to zero, the good closure of the energy balance at night is essen-
tially a validation of the storage terms. Thus, day-time data give a better idea of the quality of the energy bal-
ance closure from the point of view of the validation of turbulent fluxes. The regression coefficients remain
high 0.88 over the whole period and the slopes of the regressions are close to the previous values 0.97 or
0.99 when the intercept is forced through the origin.
Fig. 4 shows 3 single days of the experiment, which correspond to the three periods just mentioned. The
main features presented by net radiation are fairly well reproduced by the turbulent fluxes. The day-to-day
variation of the ratio FR
n,b
is well compensated by the variation of the storage terms. Whatever the rela-
tive contributions of F and S, the energy balance clo- sure is correct i.e. T = F + S ≈ R
n,b
, except for occasional half-hourly values. At night, the sum of the
storage terms is close to net radiation and follows its variations even at short time scales. This is particu-
larly well illustrated before sunrise on 27 March and confirms that the near-zero values of the nocturnal tur-
bulent fluxes, observed on Fig. 2, are real.
3.2. Variability of eddy flux measurements Fig. 4 also shows that non-zero values of turbulent
fluxes on 5 April before sunrise are not compensated by any concomitant variation in R
n,b
or S. These peaks result from errors in the measurement of latent heat
fluxes due to the rain events illustrated in Fig. 1. Also, a few peaks in the time series of the eddy fluxes, not
matching net radiation, appear during fine days e.g. 25 March in the early afternoon, 27 March in the late
morning.
Such occasional excursions, not validated by the energy balance, are not specific to the data recorded
in the lower part of the forest, and have also been ob- served frequently on measurements performed above
vegetation canopies Lamaud et al., 1994; Blanken et al., 1997. It is indeed a common fact that turbulent
flux measurements exhibit noticeable run-to-run vari- ability. This variability is sometimes compatible with
the variation of net radiation due to passing clouds but it can also be observed in the absence of any
perturbation in the diurnal evolution of R
n,b
. Blanken et al. 1997 noticed that a “saw-tooth” pattern is
often observed in both H and LE, especially in clear
Fig. 4. Diurnal variation of net radiation R
n,b
, the sum of eddy fluxes F, the total storage S and the sum of eddy fluxes and
storage terms T, below the forest canopy, for 25 and 27 March and 5 April 1998.
sky conditions when R
n,b
varies smoothly throughout the day. After a series of checks on their data set
stationarity, homogeneity, high-frequency cut-off, footprints, Blanken et al. 1997 concluded that,
even after such a quality assessment procedure, many suspect flux values could not be objectively removed.
Part of the residual scatter observable in our data set is another example of such variability. Even if the good
closure of the energy balance guarantees, on a mean
194 E. Lamaud et al. Agricultural and Forest Meteorology 106 2001 187–203
basis, the validity of turbulent flux measurements in the lower part of the forest canopy, Fig. 3 shows that
the residual term of the energy balance R = |R
n,b
− T | is larger than 15 of R
n,b
for a large amount of data. Only 40 of day-time data and 35 of nocturnal
data are included in the area defined by the slopes 0.85–1.15. Depending on the intended use of the data
set, a more or less severe selection should then be operated on the basis of the residue of the energy
balance. This is the object of the next section.
3.3. Data selection As mentioned in the introduction, ecophysiological
and turbulence studies do not require the same de- gree of accuracy in eddy flux measurements. In the
first case, we suggest to compare the residual term of the energy balance to net radiation, which amounts
to expressing the selection threshold as a fraction of R
n,b
. In the second case, the selection threshold will be expressed as a fraction of the sum of the turbulent
fluxes, F. 3.3.1. Selection for ecophysiological studies
In ecophysiological studies it is necessary to keep a reasonable amount of data from night, early morning
and late afternoon, even if the accuracy on both storage and eddy flux measurements is relatively low during
these periods. Thus, the selection threshold should al- low a larger latitude for data at small positive R
n,b
, as well as for negative R
n,b
. Indeed, Fig. 3 shows that a selection threshold defined as a fraction of R
n,b
0.15 in this example would reject many samples at low
Table 2 Fraction of selected data for various “a” and “b” coefficients
a
Nocturnal data R
n,b
681 samples Day-time data with R
n,b
60 W m
− 2
259 samples Day-time data with R
n,b
60 W m
− 2
199 samples a = 0.15, b = 10
94 82
82 a = 0.1, b = 10
93 80
77 a = 0.05, b = 10
92 77
65 a = 0.15, b = 5
78 65
75 a = 0.1, b = 5
74 59
63 a = 0.05, b = 5
68 54
51 a = 0.15, b = 0
35 26
59 a = 0.1, b = 0
23 18
46 a = 0.05, b = 0
13 9
25
a
See Section 3.3.1.
R
n,b
for which the T, R
n,b
pairs are fairly close to the 1:1 line. To avoid this we can define the rejection
threshold as a linear function of R
n,b
with a non-zero value of the intercept
R a|R
n,b
| + b
Fig. 3 shows two examples of selection thresholds using respectively the values 0.1, 10 and 0.15, 0 for
the selection coefficients a, b. While both approaches allow us to reject the most doubtful data, the first one
preserves a reasonable amount of data at negative and small positive R
n,b
, which is obviously not the case for the second one.
Table 2 presents in a quantitative way the conse- quences of the selection with different a, b pairs.
This table distinguishes three categories of data: nocturnal data, day-time data with R
n,b
less than 60 W m
− 2
and day-time data with R
n,b
larger than 60 W m
− 2
. Concerning day-time data, the fraction of selected data is of the same order for R
n,b
higher or lower than 60 W m
− 2
, provided that b is not zero. This gives a fairly good description of the daily and
day-to-day evolution of turbulent fluxes, as illustrated in Fig. 5 with a, b = 0.1, 10. Indeed, the most
spurious data are rejected, while the main tendencies in the evolution of the turbulent fluxes are preserved. A
comment must be made concerning nocturnal data. It was noticed in Section 3.1 that the near-zero values of
nocturnal turbulent fluxes were validated by the mean energy balance closure. In other words, the nocturnal
energy balance can be written as R
n,b
≈ S. Conse-
quently, the analysis of the energy balance residue on a run-to-run basis cannot be used as a criterion for
E. Lamaud et al. Agricultural and Forest Meteorology 106 2001 187–203 195
Fig. 5. Times series of net radiation R
n,b
, the total storage S and the sum of eddy fluxes F, below the forest canopy, for the period from 14 March to 7 April 1998. Filled circles represent the values of F rejected with a = 0.1 and b = 10.
selecting nocturnal eddy flux data, except for the case of strongly spurious values like on 5 April during rain
events. For illustrative purpose, the nocturnal data pre- sented in Table 2 give an idea of the quality of the
storage estimates, but this point will not be further discussed in this paper dedicated to the validation of
eddy flux measurements.
3.3.2. Selection for turbulence studies If the data set is to be used for specific analyses of
turbulent transfer, a data selection like that illustrated in Fig. 5 is clearly not adequate. Indeed, the relative
uncertainty on the values of the eddy fluxes is much too high. For example, with a, b = 0.1, 10, the
absolute uncertainty is 16 W m
− 2
when R
n,b
equals 60 W m
− 2
. As eddy fluxes were found to represent only about 60 of R
n,b
see Section 3.1, the rela- tive uncertainty represents in this case nearly 50 of
the value of F. Furthermore, this relative uncertainty increases for lower values of R
n,b
. For this second kind of studies, we suggest using a selection criterion based
on the ratio of the energy balance residue to the sum of the turbulent fluxes themselves, i.e.
R α|F | or
R
′
= R
| F |
α Table 3 shows how the current data set is qualified us-
ing this criterion with different values of α. The qua- lity of the eddy flux measurements may seem poor as,
for example, only 53 of the data corresponding to R
n,b
higher than 60 W m
− 2
and 16 of data from the other category are validated with a relative error less
than 20. However, it must be emphasized that this selection criterion is very harsh as all errors, includ-
ing those resulting from storage terms and net radia- tion estimations, are carried over to the eddy fluxes.
Thus, this may lead to the rejection of accurate eddy flux data. Nevertheless, for studies requiring a high
196 E. Lamaud et al. Agricultural and Forest Meteorology 106 2001 187–203
Table 3 Fraction of selected data for various thresholds of the relative residue R
′
= R|F | see Section 3.3.2
a
R
′
50 R
′
40 R
′
30 R
′
20 R
′
10 Day-time data with R
n,b
60 W m
− 2
88 89 82 86
72 76 53 59
34 38 Day-time data with R
n,b
60 W m
− 2
42 48 33 40
24 30 16 22
9 15
a
The values within brackets refer to the clear days 120 samples for R
n,b
60 W m
− 2
, 88 samples for R
n,b
60 W m
− 2
and the others to the whole data set 199 samples and 259 samples, respectively.
degree of confidence, this type of selection is more adapted, even if the data set is to be considerably
reduced. Furthermore, it must be noted that a large part of the data rejected with this criterion come from
overcast for instance 2 April where R
n,b
is less than 60 W m
− 2
for the whole day or partially cloudy days like 5 April. In the latter case, because of the vari-
ability in both R
n,b
and F, it is more difficult to get a good energy balance closure on a run-to-run ba-
sis. As presented in Table 3, the fraction of selected data increases appreciably when only clear days are
considered, which corresponds to about 50 of our current data set. A characterization of turbulent trans-
fer in the lower part of the forest canopy, based on a spectral or statistical analysis of turbulent variables,
should only be performed, at least in a first step, on this data subset.
4. Modelling the storage terms
