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
5.1. Modelling strategy The modelling strategy was to first assess the per-
formance of the model using, as far as possible, the parameters used routinely in the Hadley Centre GCM
Cox et al., 1999. In order to make meaningful com- parisons and to limit the number of optimised param-
eters in subsequent stages the soil parameters θ
sat
, and θ
wilt
and roughness length were specified from independent, site specific measurements see Sections
4.1 and 4.3. Other soil parameters within the model were adjusted to be consistent with θ
sat
and θ
wilt
fol- lowing Cosby et al., 1984. The vegetation parame-
ters were taken as typical for the site: leaf area index, LAI = 2, vegetation height was 0.2 m, the root depth
was set at 1.0 m, and the vegetation fraction was 0.95. Soil moisture was initialised by equating to the initial
1 January measurement and the deep soil tempera- tures were initialised as 9.0
◦
C.
316 R.J. Harding et al. Agricultural and Forest Meteorology 100 2000 309–322
A second stage was to compare the perfor- mance of the model containing untuned transpira-
tionphotosynthesis parameters with that of a model containing a very simple transpiration description, i.e.
constant value for the conductance.
The third stage was to optimise parameters within the transpiration module against evaporation mea-
surements. The calibration was made by maximising the percentage of variance explained by the model,
σ
PVE
of measured hourly evaporation. This statistics also provides an assessment of model performance.
A range of optimisations were undertaken using dif- ferent sets of optimised parameters. Parameters were
optimised for one year 1995 and then these values applied in subsequent years 1996–1997 to test the
predictive capability. This was an excellent test be- cause the years were very different, with large deficits
developing in 1996 but not 1997. Model performance was also addressed by comparing the measured and
modelled soil moisture changes, although this was done by eye and with no formal statistic.
5.2. The initial model run An initial model run using standard parameters de-
scribed in Section 3 reveals that the model system- atically underestimated evaporation at high tempera-
tures. This behaviour was also found by Blyth et al. 1999 for Sahelian vegetation. To correct this error,
T
1
was reset to 55
◦
C, essentially removing any mod- elled upper temperature limitation on photosynthesis
and transpiration at this site. With this correction, statistic σ
PVE
increased for 1995 from 68.7 to 72.3 with equivalent improvements in the other years, see
Table 1. 5.3. Comparison with simpler models for 1995
To clarify the impact of increasing complexity of the description of the transpiration on the model fit,
Table 1 The effect upon percentage of variance explained of changing T
1
from 36
◦
C to 55
◦
C T
1
= 36
◦
C T
1
= 55
◦
C 1995
68.7 72.3
1996 69.2
70.2 1997
79.7 81.8
two additional runs were made with very simple tran- spiration equations:
i with a constant conductance 0.0143 m s
− 1
with no soil moisture control.
ii with a constant conductance 0.0143 m s
− 1
but with soil moisture control.
The value of 0.0143 m s
− 1
for conductance is rec- ommended for grassland by Allen et al. 1989 and
was derived from experimental generally lysimeter studies. The goodness of fit of these runs was com-
pared with those using using the MOSES transpiration model in Table 2. The first run, i, gave a poor sim-
ulation with low σ
PVE
and a systematic overestimate of the evaporation. Run ii gave a reasonable model
fit σ
PVE
= 70.8 but was not as good as using the
MOSES routines without optimisation. 5.4. The optimisation of parameters within the model
runs for 1995 A variety of optimisations were performed and com-
pared to the value of 72.3 for the standard parame- ters with T
1
= 55
◦
C. First, all three variables V
max
, D
∗
and f were varied see Table 2 for new parameter
values, and in this optimisation 79.6 of the variance was explained. However, there was significant inter-
play between variable values due to collinearity, result- ing in predictions of ‘best fit’ parameters which were
many orders of magnitude away from their literature values. The three parameters were then optimised indi-
vidually, with the other parameters fixed at the values prescribed in Section 5.2. This exercise showed that
some improvement can be achieved by the optimisa- tion of f
, but comparatively little improvement from the individual optimisation of V
max
and D
∗
. The best fit value of f
= 0.88 yielded a fit of 76.1 variance
explained; this run was adopted as the best estimate. This was a compromise between the best model fit,
with full optimisation, but with unrealistic parameters and a slightly less good fit but with realistic param-
eter values and less optimisation. The results of this model run are presented graphically in Fig. 5. It is ob-
served that though there was considerable scatter be- tween the hourly measured and modelled evaporation
values, they were clustered arround the 1 : 1 line as may be expected following an optimisation exercise,
except for the very high measured fluxes.
R.J. Harding et al. Agricultural and Forest Meteorology 100 2000 309–322 317
Table 2 Model fit using 1995 data T
1
= 55
◦
C throughout for runs with either constant surface conductance, or with the MOSES transpiration model Parameters fixed
Constant conductance Constant conductance
Moses or optimised
No soil moisture with soil moisture
Standard Optimising
Optimising Optimising
Optimising parameters
V
max
, f , D
∗
V
max
only f
only D
∗
only variance
53.6 70.8
72.3 79.6
73.8 76.1
72.4 explained
Parameter value V
max
= V
max
= V
max
= f
= D
∗
= 4 × 10
− 5
1.46 × 10
− 4
2.86 × 10
− 5
0.882 D
∗
= 0.08117
f =
0.95 D
∗
= 0.075
Fig. 6 shows that for 1995 the deviation between model prediction and measurement as a function
of time and environmental parameters. The largest and positive deviations i.e. the modelled value
was less than the measurement were at mid-day, in mid-summer, at high temperature, high vapour
pressure deficit and at low soil moisture. All these effects may not be correctly described by this com-
paritively simple model; however, because of corre- lation between these variables it was not possible to
positively identify the root cause of this systematic deviation.
Fig. 5. A scatter diagram of modelled against measured evaporation for the year 1995, with optimisation of model parameter f see Eqs.
1 and 2. Further T
1
= 55
◦
C see Eq. 3.
5.5. Optimised model used predictively for 1996 and 1997
The performance of the model with just f opti-
mised for 1995 revealed statistics σ
PVE
= 74.7 and
σ
PVE
= 78.1 for 1996 and 1997 respectively Table
3. The hourly model errors for 1996 and 1997 not presented here also showed similar dependencies on
the environmental variables as those presented in Fig. 6 for 1995. Although the use of the 1995 parameter
value in 1996 improved the performance of the model, the performance was slightly degraded in 1997.
318 R.J. Harding et al. Agricultural and Forest Meteorology 100 2000 309–322
Fig. 6. A scatter diagram of errors in prediction of evaporation measured–modelled fluxes against a day number, b hour, c soil moisture in top 1.4 m, d temperature, e downward shortwave radiation, f windspeed and g vapour pressure deficit. This corresponds
to year 1995 and for f optimised. Further T
1
= 55
◦
C see Eq. 3.
R.J. Harding et al. Agricultural and Forest Meteorology 100 2000 309–322 319
Fig. 7. A plot of both measurement and model predictions of soil moisture within the top 1.4 m of soil. These are for a 1995, with no optimisation of model paramaters, b 1995 with optimisation of model parameter f
see Eqs. 1 and 2, c 1996 with optimised parameter f
from year 1995 and d 1997 with optimised parameter f from year 1995. For all simulations, T
1
= 55
◦
C see Eq. 3. Also plotted are the soil moisture content values for 1.4 m of soil associated with the model values of saturated, critical and wilting points.
5.6. Soil moisture simulations The soil moisture simulations and observations are
shown in Fig. 7 for the original model for 1995 and with the optimised f
only transpiration parameter for 1995, 1996 and 1997. Optimisation of the transpira-
tion did appear to improve the simulation of soil mois- ture for 1995, particularly during the drying phase in
the spring and early summer. The simulation for 1996 was also very good but that of 1997 was less good. In
particular, the model overestimated the increase in soil moisture following summer rainfall a feature which
320 R.J. Harding et al. Agricultural and Forest Meteorology 100 2000 309–322
Table 3 Percentage of variance explained by the model using original pa-
rameters and with, f =
0.882, the 1995 optimised value T
1
= 55
◦
C throughout
Original parameter 1995 f
value 1996
70.2 74.7
1997 81.1
78.1
occurred regularly in 1997. This is not a failure of the transpiration model, but is a common failure of sim-
ple soil water models see, e.g., Ragab et al., 1997. It is not clear whether it was the underestimation of
evaporation from rain-wetted grass or the neglect of macropore flow through the soil surface runoff was
not observed at this flat site and was not simulated by the model which caused this effect. On the last point
it should be recognised that the soil moisture mea- surement is only at a single point and there may be
some preferential drainage, or systematic local redis- tribution, at this point.
6. Discussion and conclusions
