Drying-out simulation
Root water uptake pattern: De Jong van Lier (2013) model
Time–depth root water uptake (RWU, d-1) pattern, leaf pressure
head (hl, dashed line), and relative transpiration (Tr,
continuous line) simulated by the SWAP model together with the
model for clay soil, two levels of potential transpiration
Tp: 1 and 5 mm d-1 (first and second lines of the plots,
respectively), and three levels of root length density R: low, medium, and
high (indicated at the top of the figure).
In this section we first focus on the behaviour of the model
in predicting RWU for the evaluated scenarios in the drying-out experiment.
Figure shows the RWU patterns for the case of the clay soil for
the three evaluated root length densities R and the two levels of potential
transpiration Tp. It can be seen how R and Tp affect RWU distribution
and transpiration reduction as the soil dries out. The onset and shape of
transpiration reduction is affected by the RWU pattern. For low R, the low
number of roots in deeper layers is not sufficient to supply high RWU rates.
When the upper layers become drier, transpiration reduction follows
immediately. Under medium and high R, the RWU front moves gradually
downward as water from the upper layers is depleted. Comparing from high to
medium R, the RWU front goes even deeper, and transpiration is maintained
at potential rates for a longer time (Fig. ). Accordingly, the
plant exploits the whole root zone and little water is left when
transpiration reduction onsets, causing an abrupt drop in transpiration.
Regarding Tp, the RWU patterns are very similar for both evaluated rates,
differing only in time scale: for high Tp the onset of transpiration
reduction and the shift in RWU front occur earlier. The uptake patterns for
the sand and loam soil (not shown here) are very similar. However, for the
sand soil potential transpiration is maintained a little longer and more
water is extracted from deeper layers. For the loam soil, the onset of
transpiration reduction occurred earlier.
The leaf pressure head hl over time shown in Fig.
illustrates how the model adapts hl to R and Tp levels in a drying
soil. Initially all scenarios have the same water content distribution and
lower hl values are required for low R or high Tp scenarios to supply
potential transpiration rates. As soil becomes drier, hl is decreased to
increase the pressure head gradient between bulk soil and root surface, thus
maintaining RWU corresponding to the demand. Therefore, uptake in wetter
layers becomes more important. Transpiration reduction only onsets when hl
reaches the limiting leaf pressure head hwl (=-200 m), after
significant changes in the RWU patterns, characterized by increased uptake
from deeper layers.
Optimal parameters of each empirical model for all
scenarios in the drying-out experiment.
FM
FMm
JMf
JMm
PM
PMm
Soil
Tp
R
h3
Mc
h3
ωc
Mc
ωc
h3
lm
Mc
lm
mm d-1
cm cm-3
cm
cm2 d-1
cm
–
cm2 d-1
–
cm
–
cm2 d-1
–
clay
1
0.01
-1968.7
0.213
-284.5
0.711
0.366
0.494
-1615.7
1.322
0.227
1.290
clay
1
0.10
-1211.0
0.329
-132.4
0.196
0.944
0.024
-7579.9
0.869
0.076
0.884
clay
1
1.00
-1.7
0.950
-0.0
1.000
5.971
0.004
-10673.7
0.354
0.022
0.342
loam
1
0.01
-7588.1
0.334
-5.0
0.457
22.483
0.016
-6927.6
1.086
0.408
1.084
loam
1
0.10
-6085.6
0.487
-93.9
0.126
25.721
0.002
-11795.6
0.911
0.113
0.917
loam
1
1.00
-17.0
5.014
-48.0
1.000
106.223
0.000
-10878.8
0.561
0.058
0.553
sand
1
0.01
-1014.0
0.146
-291.6
0.942
0.288
0.436
-621.2
1.262
0.149
1.252
sand
1
0.10
-1122.6
0.115
-113.6
0.407
1.925
0.005
-2351.3
1.179
0.024
1.159
sand
1
1.00
-3.9
0.338
-0.0
1.000
25.887
0.000
-3158.0
0.717
0.005
0.706
clay
5
0.10
-1397.7
0.334
-218.4
0.325
0.395
0.271
-5537.2
1.512
0.196
1.449
clay
5
1.00
-260.6
0.792
-135.3
0.148
1.212
0.013
-6745.0
0.672
0.088
0.687
loam
5
0.10
-5236.5
0.784
-0.0
0.277
2.306
0.100
-8322.9
1.165
0.488
1.157
loam
5
1.00
-1249.5
2.563
-292.9
0.161
28.143
0.001
-8630.0
0.833
0.224
0.838
sand
5
0.10
-918.0
0.190
-556.2
0.432
4.154
0.018
-1273.9
1.612
0.083
1.510
sand
5
1.00
-582.3
0.533
-342.5
0.193
4.888
0.001
-3582.3
1.272
0.012
1.240
Maximum possible transpiration Tp,max as a function of
root hydraulic conductivity Kroot for some values of the overall
conductance over the root-to-leaf pathway Ll computed by the
model for a rooting depth of 0.5 m, low root length
density, and a constant soil pressure head over depth equal to -1 m for
sandy soil. The
dashed vertical line highlights the value of Kroot= 3.5 ⋅ 10-8 m d-1 that was used in our simulations.
The horizontal dashed line highlights the value of potential
transpiration.
For the high Tp–low R scenarios, transpiration reduction starts
on the first day of simulation, although the soil is relatively wet. This is
a case of transpiration reduction under non-limiting soil hydraulic
conditions due to high atmospheric demand . For such
conditions, the high water flow within the plant required to meet the
atmospheric demand cannot be supported by the root system with a low R and
hydraulic parameters given in Table . Higher atmospheric
demand (here represented by Tp) leads to faster reduction of
hl caused by the hydraulic resistance to water flow within the
plant, and the transpiration rate and RWU are a function of hl. The
physical model assumes a parsimonious relationship (Eq. )
between transpiration and hl: transpiration rate is only reduced
when hl reaches a limiting value hwl, which corresponds
to a maximum transpiration rate Tp,max allowed by the plant for
the current soil hydraulic and atmospheric conditions. Under non-limiting
soil hydraulic conditions, root system properties and plant hydraulic
parameters (Table ) are the major determining factors for
Tp,max, whereas soil hydraulic conditions play a minor role.
Figure shows Tp,max as a function of
Kroot for some values of Ll with a constant soil pressure
head of -1 m in the root zone for low R in the sandy soil. In this
scenario, Kroot limits the crop transpiration and Ll
becomes important only when Kroot increases. The potential
transpiration can be achieved by raising Kroot to about
10-7 m d-1. This can also be achieved by decreasing hwl
(not shown in Fig. ).
In the field, transpiration rate and root length density are related to each
other: a high transpiration rate only occurs in a high leaf area, and a high
leaf area implies a high root length density. Thus, even under very dry and
hot weather conditions, a crop with a low R may not be able to realize a
high transpiration rate. Furthermore, crop transpiration depends on the
stomatal conductance. In the model, this is
implicitly taken into account by the simple relationship between hl
and Ta. However, stomatal conductance is relatively complex and
depends on several environmental factors such as air temperature, solar
radiation, and CO2 concentration. Therefore, high potential transpiration
rates may not be achieved because of the stomatal conductance reduction due
to temperature or solar radiation. This behaviour could be simulated by the
coupling of the model to stomatal conductance models, such
as the model.
Root water uptake pattern predicted by the empirical models
In this section, we evaluate the empirical RWU models (models and their
abbreviations are listed in Table ) based on the
comparison of RWU patterns and transpiration reduction over time with the
respective predictions from the model (VLM). All empirical
model predictions were obtained with respective optimized parameters as shown
in Table and are discussed in Sect. ,
and therefore represent the best fit with VLM.
Time–depth root water uptake (RWU) pattern and relative
transpiration (Tr) simulated by the SWAP model in combination with
the reduction function and the empirical models, for the
sand soil at high root length density and Tp=1 mm d-1.
The RWU patterns simulated by VLM and the empirical models for the sandy soil
and high R scenario are shown in
Figs. and for low and high
Tp, respectively. Both versions of the Feddes model (FM and FMm)
predicted enhanced RWU from the upper soil layers. When the soil pressure
head (hs for FM) or soil matric flux potential [Ms for
FMm] is greater than the threshold value for uptake reduction, these uptake
patterns are equivalent to the vertical R distribution. For conditions
drier than the threshold value (when αf and αm are
less than 1), the predicted RWU patterns by the models become different
(Figs. and ).
Time–depth root water uptake (RWU) pattern and relative
transpiration (Tr) simulated by the SWAP model in combination with
the reduction function and the empirical models, for the
sand soil at high root length density and Tp=5 mm d-1.
When reducing RWU for a period depending on R, Tp, and h3, RWU
from the upper soil layers predicted by FM rapidly decreases to zero. This
zero-uptake zone expands downward as soil dries out. On the other hand, the
uptake predicted by FMm is substantially reduced right after the onset of
transpiration reduction, proceeding at lower rates and for a much longer time
until approaching zero. These features become evident by comparing the shapes
of both reduction functions (Fig. ). αm is
linear with M after M>Mc, but it is concavely shaped as a function of
h – as also shown by and . This makes
αm
decrease abruptly for M>Mc, causing a substantial decrease in RWU even when h is slightly below
the threshold value. Therefore, RWU proceeds at low rates for a longer time.
In contrast and due to the linear shape of αf, RWU predicted by FM
remains higher for a longer time after h<h3. FM does not predict an
abrupt change in RWU patterns, especially when Tp is low
(Fig. ). When h approaches h4, αf is still
relatively high and RWU makes h decrease rapidly. Another diverging feature
between αf and αm, also shown in
Fig. , is that the shape of αm varies with
soil type (regardless of the value of its threshold parameter Mc), whereas
αf does not. These different features of the reduction functions also
affect the matching values of the parameters, as discussed below. Although
the choice of the reduction function affects transpiration over time only
slightly, RWU patterns are strongly affected (Figs.
and ).
(αf, grey lines) and proposed
(αm, black lines) water uptake reduction functions
as a function of soil pressure head h using their respective optimized parameters for the scenario of high root length
density, three types of soil, and two potential transpiration
levels.
The RWU patterns predicted by the JMf and JMm models can be very different,
as shown by Fig. for the high R–low Tp
scenario. In this scenario, the JMf model did not predict any compensation
because the optimal ωc equalled 1 (Table ) – thus
becoming identical to FM – and the optimal h3 values for JMf and FM were
similar. In Fig. , although h3 values for FM and JMf
(ωc=1) are close to zero, the plant transpiration is near
Tp for a prolonged time due to a small reduction of α. These
high R–low Tp scenarios with a high R in deep soil layers
allow RWU at higher rates when surface soil layers become drier (as predicted
by VLM). Then, the reduction of ωc, an attempt to numerically predict
compensation with JMf, makes the RWU pattern deviate even more from the VLM
pattern. This is illustrated in Fig. and by the optimal
h3 and ωc values shown in Table . In order to
mimic the VLM uptake patterns, the value of h3 for all soil types in this
scenario was equal or close to zero. Decreasing h3 or ωc to
simulate compensation makes JMf predict higher uptake from upper layers,
increasing the discrepancy between the models. The optimal ωc for all
soil types was equal to 1 (in other words: there was no compensation). RWU in
the upper layers predicted by VLM is substantially reduced within a few days,
whereas reducing ωc in the JMf model to predict compensation has the
side effect of causing an increase in uptake from upper layers. The model,
therefore, is not able to adequately mimic the scenarios with compensation
evaluated here. On the other hand, the JMm model was able to reproduce
considerably well the VLM pattern for the evaluated scenarios due to the
shape of αm as discussed above. As soon as M<Mc in the
upper layers, RWU decreased at a higher rate, compensated for by increasing
uptake from the wetter, deeper layers. This agrees more closely with VLM
predictions.
For high Tp (Fig. ), the JMf model can predict
compensation (ωc<1); however, its predicted RWU pattern is quite
different from JMm and VLM. JMf predicts a higher longer-lasting RWU near the
soil surface than the other models that account for compensation. This makes
soil water depletion more intense and RWU from these layers to cease sooner when
hs becomes lower than h4. At this point, Ta is
predicted to continue to be equal to Tp because of the low optimal
ωc (=0.19), which increases RWU from the deeper layers where h
is close or equal to h4. JMm performed very differently, predicting uptake
over the first few days (when Ms>Mc) in accordance with R
distribution. After M<Mc in the upper soil layers, the RWU pattern
started to change gradually and RWU increased at lower depths.
(a) α of the JMII model (Eq. ) as a
function of soil pressure head hs, (b) ωc
parameter (Eq. ) for different soil types (the three soil types
used in the simulations and soils from ), expressed by
Mmax, and (c) the normalized root length density β
computed by Eqs. () (JMf) and () (JMII) as a function
of root length density R, given by Eq. () with
Ravg=1.0 cm cm-3 and b=2.
The proposed models (PM and PMm) are capable of predicting RWU patterns
similar to VLM. For the low Tp–high R scenario
(Fig. ), RWU is more uniformly distributed over depth than
in the VLM model for the first days and uptake from upper layers is lower
than that predicted by the VLM model. For high Tp
(Fig. ), these models better represent RWU patterns and, in
general, differences in predictions of RWU between the proposed models are
small. The shape of the transpiration reduction over time, however, is
smoother than predicted by the VLM model. Concerning the relative transpiration curve, the
proposed models appear to be less precise than the other models that account
for RWU compensation.
JMII does not mimic well the RWU pattern predicted by VLM for the high
R–low Tp scenarios. It overestimates uptake from surface layers
during the first days. Before the onset of transpiration reduction, uptake
from upper layers reaches zero, but it is compensated for by a higher uptake
from deeper layers. The model is very sensitive to both R and M. For the
high R–high Tp scenarios, JMII provides better uptake pattern
predictions (Fig. ). However, the model does not perform
well in the other scenarios with low and medium R (data not shown here).
Comparing RWU predictions from JMf and JMII, the Jarvis-type
models are affected by the definition of α. This becomes clear from
Fig. , which shows the α of JMII
(Eq. ) as a function of hs and ωc
(Eq. ) for different soil types, expressed by Mmax.
The α function shows that even though the soil resistance increases as
the soil becomes drier, defining α by Eq. () does not
seem plausible. In this case, α is suddenly reduced when the soil is
still near saturation. When hs=1 m, for instance, α is much
lower than 0.5. Such behaviour is not reasonably compatible with for the α
concept. The ωc values are also extremely low. The low α
values are, however, balanced by high α2 values (due to low ω
and ωc values), leading to suitable values of RWU in a given soil
layer. Nevertheless, the magnitudes of α and ωc are
conceptually questionable. Therefore, we conclude that (i) the ωc
value in Jarvis-type models, which sets the compensation level, depends on
the definition of α. For instance, for the original
model, ωc=0.5 corresponds to a moderate level of compensation.
Surely, this would not hold if α were defined by
Eq. (); (ii) comparing the to the
model led to a rather unrealistic α function, and its
behaviour does not properly represent the α concept. This may be
caused by the fact that the model does not take into
consideration the plant hydraulic resistances. This might explain the rapid
decline of α near saturation. The threshold-type functions seem to be
more feasible.
Box plot of the coefficient of determination r2 and model efficiency coefficient E for
the comparison of root water uptake (RWU) and actual transpiration (Ta) predicted by the empirical
models and the model for the drying-out simulations at three levels of root length density
for three types of soil and two potential transpiration levels. The symbols ∗ and ∘ represent the
average and outliers, respectively.
The fact that JMII is more sensitive to both R and M, as stated above,
when compared to the other M-based models is attributed to the α
function and the derived equations to express their parameters
(Eqs. and ). It can be seen from
Fig. c that β defined by Eq. () (β
of JMII) tends to be higher when R increases and lower when R decreases
compared to the β of JMf and JMm. Thereby, for the first days of
simulations when the soil hydraulic conditions tend to be rather uniform over
depth, JMII overestimates RWU compared to VLM predictions. This becomes more
important for the high R–low Tp scenarios. For such conditions,
the RWU over depth predicted by the VLM tends to be more uniform, which seems
reasonable as the low transpiration demand can be met by any small R in
deeper soil depths. After some time, the discrepancies between VLM and JMII
tend to increase, since the higher RWU in the upper layers reduces h; thus,
because of the α shape of JMII, RWU in the upper layers is suddenly
reduced towards zero. These are the main reasons for JMII not to predict
well in the high R–low Tp scenarios.
Statistical indices
The performance of the empirical models was analysed by the coefficient of
determination r2 and the model efficiency coefficient E
calculated by comparing to the RWU and relative
transpiration predicted by VLM. For the low R–high Tp scenarios, the
VLM predicts water stress (Ta<Tp) from the beginning of the simulation
as discussed in Sect. . The empirical models (except for JMf and
JMm by setting ωc>1) are not able to reproduce these results, thus
these scenarios were not considered when analysing the performance of the
models.
Statistical indices for the evaluated scenarios of each model are concisely
shown by the boxplots in Fig. . The width of whiskers
indicates the range of the statistical indices for each model used in the
evaluated scenarios. The outliers indicate whether a model had different
performance at some scenarios than its overall performance. Focusing first on
RWU, the figure shows that the proposed models performed better. The performance of PM
was just a bit poorer than PMm's, shown by the presence of an outlier and
lower median. JMm performed as good as the proposed models, and only in two
scenarios it had a bad performance as shown by the outliers in
Fig. . The wider whiskers and presence of outliers of the
others models confirm their poorer performance.
Among the models that account for RWU compensation, JMf and JMII performed
worst, especially in the high R–low Tp scenarios. In general their
performances were poorer for medium R scenarios, especially for low Tp.
Thus, the use of αm in Jarvis-type models promotes substantial
improvements, especially from medium to high R scenarios. For low R
scenarios all models performed well and the highest values of the boxes in
Fig. usually refer to this scenario.
Best models for the evaluated scenarios (root length density R,
soil type, and potential transpiration Tp)
based on Akaike's information criteria AIC through comparison of root water uptake (RWU) and relative transpiration (Tr)
predicted by the physical model in the drying-out
experiment.
Low Tp
High Tp
R
Clay
Loam
Sand
Clay
Loam
Sand
Low
JMm
JMf
JMm
JMm
JMm
JMm
RWU
Medium
PMm
PMm
JMII
JMm
PM
PMm
High
PMm
PMm
PM
PM
PMm
PM
Low
JMm
JMm
JMm
JMm
JMm
JMm
Tr
Medium
JMm
JMm
JMII
JMm
PM
JMf
High
PMm
PMm
PMm
JMII
JMm
JMm
In predicting transpiration, all models accounting for compensation performed
well, except JMf. It can be noticed that JMII performed much better in
predicting transpiration than RWU. As for the RWU, all models performed worse in high R scenarios than in low R scenarios.
As the evaluated models differ regarding the number of empirical parameters
(from 0 to 2), it is important to use a statistical measure that accounts for
this and penalizes the models with more parameters. The Akaike's information
criteria (AIC) is a suitable measure for such a model comparison. The
selection of the “best” model is determined by an AIC score, defined as
:
AIC=2K-log(L(θ^|y)),
where K is the number of fitting parameters and
L(θ^|y) is the log-likelihood at its maximum point. The
“best” model is the one with the lowest AIC score. Table
lists the best models for every scenario based on the AIC score. Overall, the
AIC supports the above descriptive statistical analyses, indicating that the
proposed models are the best models in predicting RWU estimated by VLM,
especially from medium to high R scenarios. For the low R scenarios JMm
is the best model. On predicting Tr by VLM, the above analyses
indicated that, in general, most models performed similarly. The AIC
indicated comparable results, but overall JMm was the best model. The
proposed models (PM or PMm) were the best models for high R–low
Tp scenarios.
Time–depth root water uptake (RWU) pattern and relative
transpiration (Tr) simulated by the SWAP model in combination with
the reduction function, and evaluated empirical models
optimized performed Tr instead of RWU for loam soil and low (first
line of the plots) and high (second line of the plots) root length density
and Tp=1 mm d-1. The dashed lines indicate Tr
when the models were optimized with RWU.
Relation of the optimal empirical parameters to R and Tp levels
The optimal values of the empirical parameters of all models (except JMII
that has no empirical parameters) for all scenarios but the high Tp–low
R scenario are shown in Table . The threshold reduction
transpiration parameters h3 and Mc (for FM and FMm, respectively) stand
for the soil hydraulic conditions at which the crop cannot meet its potential
transpiration rate. Conceptually, the higher R, the lower is h3 or Mc
due to the larger root surface area for RWU, i.e. the crop can extract water
in drier soil conditions. Similarly, lower h3 and Mc are expected for
low Tp. This can also be deduced from Figs. and by means of the predictions of relative transpiration and
RWU by VLM.
The optimal h3 and Mc values (Table ) for FM and
FMm, respectively, increase with R, contradicting their conceptual
relation to R. For Tp, there is no specific relationship for
these parameters: whether they increase or decrease with Tp depends
on the value of R. In drying-out scenarios, soil water from top layers
depletes rapidly due to the higher initial uptake. Thus, uptake from these
layer starts to decrease, whereas RWU in deeper, wetter layers increases.
This effect becomes stronger at higher R, as seen by the VLM predictions in
Sect. . Because FM and FMm do not account for this mechanism,
decreasing h3 or Mc in search of conceptually meaningful values would
make these models predict higher RWU from upper layers (in accordance with
the R distribution) for a longer period, increasing the discrepancy with
VLM predictions. Therefore, their best fitted values are physically without
meaning due to the model assumptions.
In order to interpret the parameters in Table for JMf,
one should first recall that α in JMf stands for the local RWU
reduction due to soil hydraulic resistance. Thus, its h3 parameter refers
to the local soil pressure head at which RWU starts to decrease. It may be
argued that RWU reduction occurs in drier soil conditions as R increases,
i.e. h3 is more negative for higher R (similarly as for FM and FMm).
However, since JMf accounts for compensation, RWU is interpreted as a
non-local process, and uptake from one layer depends on the water status and
root properties from other layers . Thus, the h3 parameter
from JM is affected by other parts of the root zone. Predictions by VLM show
that RWU reduction from the upper layers starts at less negative pressure
head values as R increases. Therefore, h3 in JMf should increase with
increasing R. The values of h3 for JMf shown in
Table agree with this conceptual meaning. The Mc
parameter from JMm can be interpreted likewise.
Values for ωc from JMf for the high R–low Tp scenarios equal 1,
thus contradicting its conceptual meaning: as in these scenarios the
compensation mechanism is more intense, ωc should be less than one
for the medium and high R scenarios. The reason for ωc=1 was
discussed in Sect. . Conversely, ωc values for
JMm follow the conceptual meaning.
The optimal parameters of the proposed models follow their logical relation
to R and Tp. The lm values for both models are very close. The
optimal lm values are less sensitive to soil types and more sensitive to
R.
High correlation parameters might result in uncertainties and a non-unique
solution of the optimization problem. In general, the correlation parameter
coefficients were low, except for some scenarios in which high correlation
coefficients between ωc and h3 (or Mc) were found. These high
correlations may be due to model structure rather than to the data used for
fitting the models, since the correlations for PM and PMm parameters were
low (absolute correlation coefficient below 0.53).
Optimization using Tr
The empirical models fitted only to RWU, since the primary interest is to
evaluate the model's capability to predict the RWU patterns under different
scenarios. RWU is not easily obtained in real conditions, making the use of
physical RWU models a great advantage. On the other hand, plant
transpiration, one of the main outputs in RWU models, is more easily
measured. Thus, one might consider to fit the models to the temporal course
of (relative) plant transpiration or to fit the models simultaneously to both
plant transpiration and RWU, for which a rather complicated optimization
scheme would be required.
We addressed this issue by fitting the models to the course of relative
transpiration for some scenarios. The procedure was the same as explained in
Sect. , but substituting Si,j in Eq. () by
Tri. The results for some models in two contrasting scenarios of R
are shown in Fig . Models that account for “compensation”
can predict Tr quite reasonably even when fitted to RWU only. The models
that do not account for “compensation” do not mimic the Tr course over
time correctly for the high R scenario predicted by VLM, even when they are
fitted to Tr, and the predictive quality decreases when fitted to RWU. The
most important aspect shown in Fig is that fitting the models
to Tr can improve Tr predictions but impairs their RWU predictions
considerably, especially in high R scenarios. Conversely, if a model fits
well to RWU, it can provide suitable transpiration predictions. This can also
be seen by the analysis of Sect. , when the proposed models
and JMm had good performance in predicting Tr as well.
Growing season simulation
By evaluating the RWU models under real weather conditions during a
relatively dry year and considering the same soil types and crop
characteristics as for the drying-out experiment, it was possible to use the
calibrated parameters for specific soil type and root length density. This
evaluation is important to analyse whether our calibration of the empirical
models with a single drying-out experiment results in consistent predictions
for other circumstances. Models were not evaluated for the low R scenario
because the empirical models (except JMf and JMm) were not able to mimic
those conditions for high Tp (Sect. ).
Time course of actual cumulative plant transpiration Tac
predicted by the model and empirical models for three soils
(clay, loam, and sand) and two levels of root length density
(medium and high), together with rainfall and potential transpiration Tp for the growing season
experiment. The total Tac values predicted by each model for the whole period are shown in the plot aside the model names.
Figure shows the time course of cumulative actual transpiration
simulated by SWAP using all the RWU models, together with rainfall and Tp
throughout the growing season period. Following the first dry spell, Tac
predicted by FM and FMm, not accounting for “compensation”, starts to be
lower than predictions from other models. Two or three more dry spells occur
in the evaluated period. The magnitude of the underestimation, however,
varies with soil type and R. For the medium R–loam soil scenario, for
instance, the Tac for all models are similar. The Tac at the end of
the evaluated period predicted by VLM for low R (not shown in
Fig. ) was much lower and approximately equal for the three soil
types (40.45, 40.05 and 40.08 cm for clay, loam and sand soil, respectively).
In fact, a higher R resulted in an increasing difference of cumulative
transpiration between soil types. Most water is extracted from the clay soil,
followed by sand and loam. Little difference of cumulative transpiration is
found between medium and high R: for sand and clay soil, the cumulative
transpiration was slightly higher for high R; for the loam soil it was and
practically identical.
Comparing cumulative Ta predicted by the empirical models with VLM
predictions shows that the models that do not account for compensation
underestimate cumulative Ta from 2.0 % (medium R – sand soil scenario)
to 13.9 % (high R – clay soil scenario). Overall, the highest
underestimates occurred for high R. All other models predict similar
values. Therefore, for total actual transpiration prediction, any of the
evaluated models accounting for compensation might be suitable after
calibration.
An overall analysis of model performance is shown in Fig. and a
list of the “best” model for each scenario based on AIC is shown in
Table . The best performances are from the models that
account for compensation. An improvement of JMf by using the proposed
reduction function can be observed. Among the models that account for
compensation, JMf had the worst performance. JMII also was poor in predicting
RWU, but showed good performance in estimating plant transpiration. Overall,
the best performances were also obtained by the proposed models (PM and PMm)
and by the modified model (JMm) in predicting RWU. These
results also indicate that the strategy of designing a single drying-out
experiment to calibrate an empirical model is successful.
According to the AIC, PM, PMm and JMm are best in predicting RWU. Regarding
Tr predictions, Fig. shows considerably high statistical
indices (E and r2) for all models that account for “compensation”.
However, the AIC, which penalizes the models with more parameters, indicates
that JMII was the “best” model for most of the scenarios.
In general, the proposed models as well as JMm showed better performance than
the other empirical models. It should be noted, however, that these models
are based on M, making them closer to the physical model.
In this regard, it is important to separately compare JMf and JMm and PM and
PMm. The only difference between JMf and JMm is the α reduction, which
resulted in considerable improvements as discussed. In the proposed models,
M is included in Sp(z) to distribute Tp over depth. In PMm,
αm is used instead of the Feddes reduction function (used in PM).
These simple modifications were sufficient to allow these empirical models to
be fitted too mimic the predictions made by the more complex physical model.
Box plot of the coefficient of determination r2 and model efficiency coefficient E for the comparison of
root water uptake (RWU) and actual transpiration (Ta) predicted by empirical models compared to model
predictions, for the growing season experiment, two levels of root length
density, and three soils. The symbols ∗ and
∘ represent the average and outliers, respectively.