R.J. Harding et al. Agricultural and Forest Meteorology 100 2000 309–322 313
et al. 1994 and set to a value of 0.4 × 10
− 5
mol CO
2
m
− 2
s
− 1
. This parameter appears within the description of the temperature dependent rubisco
capacity of the top leaf level of C
3
plants thus: V
T
= V
max
2
0.1T
s
− 25
[1 + e
0.3T
s
− T
1
] 3
where T
s
is the surface temperature. Parameter T
1 ◦
C represents stomatal closure at higher temperatures and
an initial value of T
1
= 36
◦
C e.g. Sellers et al., 1996 is prescribed. Except in strongly light-limited condi-
tions, net leaf photosynthesis a
n
mol CO
2
m
− 2
s
− 1
is broadly proportional to V
T
Cox et al., 1999 with all other factors invariant. Parameters f
and D
∗
in Eqs. 1 and 2 were also used in the optimisation.
The equations for g
s
were derived from observa- tions on individual leaves. A scaling up procedure is
adopted in MOSES to calculate the whole canopy con- ductance, g
c
. It is assumed that all limiting factors for photosynthesis decay within the canopy, follow Beer’s
Law, and so by integration of the canopy and noting that g
s
is linear in a
n
, then g
c
= 1 − e
− kL
c
k g
s
4 where k is an extinction coefficient set to 0.5 and L
c
is the local leaf area index.
Fig. 2. Values of measured total soil moisture within the top 1.4 m of soil for 1995–1997.
4. Data analysis
4.1. Soil moisture The time series of total water contents in the top
1.4 m for the 3 years showed important differences be- tween the years Fig. 2. The summer of 1995 was dry,
particularly through July and August, and the maxi- mum soil moisture deficit developed at the end of Au-
gust. The summer of 1996 was dry, but wetter than 1995, however this year had a very dry autumn which
caused an extended period of deficit during September and October although the extreme values of deficits
observed in 1995 were not reached. 1997 had a dry spring but frequent rain periods through the summer,
leading to only moderate soil moisture deficits. From visual inspection of the soil moisture profiles in the
drier years, it was evident that the seasonal summer drying extended down to 1.4 m.
The values of soil moisture at saturation, θ
sat
= 0.400 m
3
H
2
O m
− 3
, and wilting point, θ
wilt
= 0.128 m
3
H
2
O m
− 3
, were inferred from the wettest and dryest soil moisture measured over the entire record Finch
and Harding, 1998. The value of a third soil param- eter, θ
crit
, was set to be consistent with the values of θ
sat
and θ
wilt
using the underlying assumption that θ
crit
is equivalent to a soil water potential of −
0.033 MPa, itself inferred from the soil properties
314 R.J. Harding et al. Agricultural and Forest Meteorology 100 2000 309–322
Fig. 3. A cumulative plot for a 1995, b 1996 and c 1997 of measurements of net radiation, R
n
, evaporative flux, λE, sensible heat flux, H and R
n
–λE–H where such data exists. Tick marks on the time axis correspond to approximately two monthly periods.
Cosby et al., 1984; Cox et al., 1999. This returned a value of θ
crit
= 0.211 m
3
H
2
O m
− 3
. 4.2. The energy closure
The cumulative energy components for the mea- sured data for each year are shown in Fig. 3a–c. It
should be noted that these are not totals for the en- tire year but for the hours when all three fluxes λE,
H and R
n
are available approximately half the time. The figures show the partitioning of energy and the
energy closure. It can be seen that over the year ap- proximately 80 of the radiation went into latent heat
flux, this proportion was reduced slightly during the summer months thus in July and August the propor-
tion was 71 in 1995 and 76 in 1997. In the win- ter the evaporation often exceeded the net radiation.
The energy closure was excellent in 1995 and 1997, when the net radiation was within 5 of the sum of
the turbulent fluxes. In 1996 the sum of the turbulent
R.J. Harding et al. Agricultural and Forest Meteorology 100 2000 309–322 315
fluxes was 10 greater than the net radiation, how- ever this is still well within the errors expected from
net radiometers Halldin and Lindroth, 1992 and tur- bulent flux measurements Lloyd et al., 1997. There
was, as expected, some variation through the year due to changes in soil heat storage.
4.3. Roughness length A value of the roughness length for momentum
transport was calculated by inverting the logarithmic wind profile equation with a Monin–Obukov stabil-
ity correction using the hourly measured momentum fluxes see, for example, Paulson, 1970. To avoid
errors inherent in wind speed measurements at low speeds, calculations were only made when the wind
speed exceeded 1 m s
− 1
. There was considerable scat- ter in the hourly calculated values of roughness length.
There was some evidence of a seasonal dependence, rising from 0.03 m in winter to 0.07 m in the late sum-
mer Fig. 4. This was almost certainly related to the growth of the grass modified by the impact of reg-
ular grazing. There was also a dependence on wind direction; the roughness was less from the west, the
direction for which there was the largest fetch over the pasture. The median value of roughness length for
momentum, z
0m
m, was 0.038 m. This was greater than the 10 of vegetation height which is generally
assumed Monteith and Unsworth, 1990, p. 117 and it seems very likely that the surrounding trees and
buildings were increasing the momentum transport and hence the effective roughness length. However the
Fig. 4. A plot of inferred values of momentum roughness length, z
0m
log axis, against day number for year 1996 tick marks correspond to approximately two monthly intervals. Also plotted the continuous line are mean values for each period.
exposure of this field was fairly typical of the south of England so this measured value was used in the
analysis following. The closure of the energy balance, despite the limited fetch and evidence of the effect of
the nearby trees on the momentum exchange, may be partial as a result of the predominantly grass fields be-
yond the trees. The roughness length for heat was as- sumed to be one tenth of that of momentum, see, for
example, Garratt 1992 Figure 4.4, pp. 93–94.
5. Modelling and optimisation
