Rangeland Plant Growth Model - Crop Growth Assessment and Modelling, Crop Production | Crop Production Notes- Agricultural Engineering PDF Download

 Page 1


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
8.4 Rangeland Plant Growth Model
Initiation and growth of above- and below- ground biomass for range plant communities are
estimated by using a potential growth curve. The potential growth curve can be de?ned with either an
unimodal or a bimodal distribution (Fig. 8.4.1 and 8.4.2). The potential growth curve (Eq. [8.4.1]) is
described by a modi?cation of the generalized Poisson density function (Parton and Innis, 1972; and
Wight, 1987). The potential growth curve should be de?ned to represent the aggregate total production
for the plant community. The ?exibility of the potential growth curve allows for description of either a
warm or cool season plant community or for a combination of the two communities.
For a unimodal potential growth curve:
g
i
= G
1
I L a e
d
c
h hh (1-ß) M O [8.4.1]
where
a=
I J L P
d
- G
b
t
i
- G
b
h hhhhhhh M J O c
[8.4.2]
 
Page 2


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
8.4 Rangeland Plant Growth Model
Initiation and growth of above- and below- ground biomass for range plant communities are
estimated by using a potential growth curve. The potential growth curve can be de?ned with either an
unimodal or a bimodal distribution (Fig. 8.4.1 and 8.4.2). The potential growth curve (Eq. [8.4.1]) is
described by a modi?cation of the generalized Poisson density function (Parton and Innis, 1972; and
Wight, 1987). The potential growth curve should be de?ned to represent the aggregate total production
for the plant community. The ?exibility of the potential growth curve allows for description of either a
warm or cool season plant community or for a combination of the two communities.
For a unimodal potential growth curve:
g
i
= G
1
I L a e
d
c
h hh (1-ß) M O [8.4.1]
where
a=
I J L P
d
- G
b
t
i
- G
b
h hhhhhhh M J O c
[8.4.2]
 
 
ß=
I J L P
d
- G
b
t
i
- G
b
h hhhhhhh M J O d
[8.4.3]
g
i
is the increment of growth expressed as a fraction of 1.0, G
1
is the fraction of maximum live biomass
at the ?rst peak, P
d
is the Julian day peak live biomass occurs, G
b
is the Julian day the growth curve
begins, c is the shape parameter for the ascending side of the curve, d is the shape parameter for the
descending side of the curve, and t
i
is the current Julian day.
1 50 99 148 197 246 295 344
0.0
0.2
0.4
0.6
0.8
1.0
Day of Year
Potential Plant Growth (unitless)
Year 1
Year 2
Year 3
Year 4
Year 5
Variables:
cf1               
cf2               
rgcmin         
gtemp        
tempmn       
pscday       
scday         
ffp     
1.00
0.00
0.00
5.00
-5.00
240.00
0.00
320.00
Figure 8.4.1. Unimodal potential plant growth for a ?ve year period.
Variables:
cf1               
cf2               
rgcmin         
gtemp        
tempmn       
pscday       
scday         
ffp     
0.25
0.75
0.00
5.00
-5.00
60.00
250.00
320.00
1 50 99 148 197 246 295 344
0.0
0.2
0.4
0.6
0.8
1.0
Day of Year
Potential Plant Growth (unitless)
Year 1
Year 2
Year 3
Year 4
Year 5
Figure 8.4.2. Bimodal potential plant growth for a ?ve year period.
 
Page 3


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
8.4 Rangeland Plant Growth Model
Initiation and growth of above- and below- ground biomass for range plant communities are
estimated by using a potential growth curve. The potential growth curve can be de?ned with either an
unimodal or a bimodal distribution (Fig. 8.4.1 and 8.4.2). The potential growth curve (Eq. [8.4.1]) is
described by a modi?cation of the generalized Poisson density function (Parton and Innis, 1972; and
Wight, 1987). The potential growth curve should be de?ned to represent the aggregate total production
for the plant community. The ?exibility of the potential growth curve allows for description of either a
warm or cool season plant community or for a combination of the two communities.
For a unimodal potential growth curve:
g
i
= G
1
I L a e
d
c
h hh (1-ß) M O [8.4.1]
where
a=
I J L P
d
- G
b
t
i
- G
b
h hhhhhhh M J O c
[8.4.2]
 
 
ß=
I J L P
d
- G
b
t
i
- G
b
h hhhhhhh M J O d
[8.4.3]
g
i
is the increment of growth expressed as a fraction of 1.0, G
1
is the fraction of maximum live biomass
at the ?rst peak, P
d
is the Julian day peak live biomass occurs, G
b
is the Julian day the growth curve
begins, c is the shape parameter for the ascending side of the curve, d is the shape parameter for the
descending side of the curve, and t
i
is the current Julian day.
1 50 99 148 197 246 295 344
0.0
0.2
0.4
0.6
0.8
1.0
Day of Year
Potential Plant Growth (unitless)
Year 1
Year 2
Year 3
Year 4
Year 5
Variables:
cf1               
cf2               
rgcmin         
gtemp        
tempmn       
pscday       
scday         
ffp     
1.00
0.00
0.00
5.00
-5.00
240.00
0.00
320.00
Figure 8.4.1. Unimodal potential plant growth for a ?ve year period.
Variables:
cf1               
cf2               
rgcmin         
gtemp        
tempmn       
pscday       
scday         
ffp     
0.25
0.75
0.00
5.00
-5.00
60.00
250.00
320.00
1 50 99 148 197 246 295 344
0.0
0.2
0.4
0.6
0.8
1.0
Day of Year
Potential Plant Growth (unitless)
Year 1
Year 2
Year 3
Year 4
Year 5
Figure 8.4.2. Bimodal potential plant growth for a ?ve year period.
 
 
An optimization routine was developed to predict the shaping parameters c and d based on G
b
, f
p
,
and P
d
, where f
p
is the frost-free period in Julian days.
c = 8.515 - 22.279 a + 16.734 a
2
[8.4.4]
d = 12.065 - 63.229 a + 87.34 a
2
[8.4.5]
where
a =
I J L G
1
+ G
2
G
1
f
p
h hhhhhhh M J O P
d
- G
b
h hhhhhhhhhhh .
[8.4.6]
The user must enter the potential maximum live above-ground biomass (P
mx
). This value can be
obtained from the USDA Natural Resource Conservation Service Range Site guide as total annual
production for the site (section 5) with favorable growing season precipitation. The user can adjust the
total annual potential production to re?ect the condition of the site based on its current range condition
(ecological status). The initiation of growth and senescence for the plant community for the growth curve
are predicted based on air temperature. The physiological information necessary to de?ne the growth
curve is the minimum temperature necessary for initiation of growth in the spring (GTEMP) and a critical
sustained minimum temperature which will induce dormancy (TEMPMN). Where the average daily
temperature (T
a
) is calculated as T
a
= (T
mx
+ T
mn
)/2. T
mx
and T
mn
are de?ned as the maximum and
minimum daily temperature (°C), respectively.
Plant growth is initiated when g
i
is greater than 0.001. Once g
i
has reached 1.0, plant growth stops
for that growth period. Change from standing live biomass (L
t
) to standing dead biomass (R
a
)is a
function of the decay rate of the growth curve, a minimum temperature which induces dormancy, and
drought stress. Once a 5 day average minimum temperature is equal to a minimum temperature
(TEMPMN) all standing live biomass is transferred to standing dead.
The drought stress (D
s
) transfers old standing live to standing dead biomass as a function of actual
evapotranspiration, potential evapotranspiration, and a plant speci?c available soil water variable
(PLTOL). D
s
has been de?ned such that the maximum single day reduction in old standing live biomass
is 3%. The daily water stress (W
a
) is calculated as a running four day average of the calculated water
stress (WST).
D
s
= 1 - e
-3.5W
a
[8.4.7]
Increments of new growth are calculated as:
L
i
= g
i
P
mx
[8.4.8]
where L
i
is the new plant growth on day of simulation, g
i
is the positive increment between today’s and
yesterday’s g
i
, and P
mx
is the potential maximum live biomass (kg
.
m
-2
).
Water stress is calculated as the ratio of actual transpiration to potential transpiration. If available
soil water is limiting then W
a
is utilized to kill standing live biomass and transfer the recently killed
biomass to standing dead biomass. W
a
is only calculated when the actual soil water content is below a
 
Page 4


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
8.4 Rangeland Plant Growth Model
Initiation and growth of above- and below- ground biomass for range plant communities are
estimated by using a potential growth curve. The potential growth curve can be de?ned with either an
unimodal or a bimodal distribution (Fig. 8.4.1 and 8.4.2). The potential growth curve (Eq. [8.4.1]) is
described by a modi?cation of the generalized Poisson density function (Parton and Innis, 1972; and
Wight, 1987). The potential growth curve should be de?ned to represent the aggregate total production
for the plant community. The ?exibility of the potential growth curve allows for description of either a
warm or cool season plant community or for a combination of the two communities.
For a unimodal potential growth curve:
g
i
= G
1
I L a e
d
c
h hh (1-ß) M O [8.4.1]
where
a=
I J L P
d
- G
b
t
i
- G
b
h hhhhhhh M J O c
[8.4.2]
 
 
ß=
I J L P
d
- G
b
t
i
- G
b
h hhhhhhh M J O d
[8.4.3]
g
i
is the increment of growth expressed as a fraction of 1.0, G
1
is the fraction of maximum live biomass
at the ?rst peak, P
d
is the Julian day peak live biomass occurs, G
b
is the Julian day the growth curve
begins, c is the shape parameter for the ascending side of the curve, d is the shape parameter for the
descending side of the curve, and t
i
is the current Julian day.
1 50 99 148 197 246 295 344
0.0
0.2
0.4
0.6
0.8
1.0
Day of Year
Potential Plant Growth (unitless)
Year 1
Year 2
Year 3
Year 4
Year 5
Variables:
cf1               
cf2               
rgcmin         
gtemp        
tempmn       
pscday       
scday         
ffp     
1.00
0.00
0.00
5.00
-5.00
240.00
0.00
320.00
Figure 8.4.1. Unimodal potential plant growth for a ?ve year period.
Variables:
cf1               
cf2               
rgcmin         
gtemp        
tempmn       
pscday       
scday         
ffp     
0.25
0.75
0.00
5.00
-5.00
60.00
250.00
320.00
1 50 99 148 197 246 295 344
0.0
0.2
0.4
0.6
0.8
1.0
Day of Year
Potential Plant Growth (unitless)
Year 1
Year 2
Year 3
Year 4
Year 5
Figure 8.4.2. Bimodal potential plant growth for a ?ve year period.
 
 
An optimization routine was developed to predict the shaping parameters c and d based on G
b
, f
p
,
and P
d
, where f
p
is the frost-free period in Julian days.
c = 8.515 - 22.279 a + 16.734 a
2
[8.4.4]
d = 12.065 - 63.229 a + 87.34 a
2
[8.4.5]
where
a =
I J L G
1
+ G
2
G
1
f
p
h hhhhhhh M J O P
d
- G
b
h hhhhhhhhhhh .
[8.4.6]
The user must enter the potential maximum live above-ground biomass (P
mx
). This value can be
obtained from the USDA Natural Resource Conservation Service Range Site guide as total annual
production for the site (section 5) with favorable growing season precipitation. The user can adjust the
total annual potential production to re?ect the condition of the site based on its current range condition
(ecological status). The initiation of growth and senescence for the plant community for the growth curve
are predicted based on air temperature. The physiological information necessary to de?ne the growth
curve is the minimum temperature necessary for initiation of growth in the spring (GTEMP) and a critical
sustained minimum temperature which will induce dormancy (TEMPMN). Where the average daily
temperature (T
a
) is calculated as T
a
= (T
mx
+ T
mn
)/2. T
mx
and T
mn
are de?ned as the maximum and
minimum daily temperature (°C), respectively.
Plant growth is initiated when g
i
is greater than 0.001. Once g
i
has reached 1.0, plant growth stops
for that growth period. Change from standing live biomass (L
t
) to standing dead biomass (R
a
)is a
function of the decay rate of the growth curve, a minimum temperature which induces dormancy, and
drought stress. Once a 5 day average minimum temperature is equal to a minimum temperature
(TEMPMN) all standing live biomass is transferred to standing dead.
The drought stress (D
s
) transfers old standing live to standing dead biomass as a function of actual
evapotranspiration, potential evapotranspiration, and a plant speci?c available soil water variable
(PLTOL). D
s
has been de?ned such that the maximum single day reduction in old standing live biomass
is 3%. The daily water stress (W
a
) is calculated as a running four day average of the calculated water
stress (WST).
D
s
= 1 - e
-3.5W
a
[8.4.7]
Increments of new growth are calculated as:
L
i
= g
i
P
mx
[8.4.8]
where L
i
is the new plant growth on day of simulation, g
i
is the positive increment between today’s and
yesterday’s g
i
, and P
mx
is the potential maximum live biomass (kg
.
m
-2
).
Water stress is calculated as the ratio of actual transpiration to potential transpiration. If available
soil water is limiting then W
a
is utilized to kill standing live biomass and transfer the recently killed
biomass to standing dead biomass. W
a
is only calculated when the actual soil water content is below a
 
 
plant speci?c critical soil water content (PLTOL). If PLTOL is not known for a speci?c plant community
then set PLTOL to 0.0 and the model will use a default value of 25% of the soil water content at ?eld
capacity. After 20 consecutive days of water stress development of new phytomass ceases. Initiation of
growth is reactivated after 80 mm of precipitation.
1 50 99 148 197 246 295 344
0.0
0.1
0.2
0.3
0.4
0.5
Day of Year
Leaf Area Index (unitless)
Figure 8.4.3. Bimodal plant growth depicted to illustrate leaf area index over time with a minimum
evergreen function initialized (RGCMIN).
For plant communities with an evergreen component the RGCMIN parameter can be initialized to
maintain the live biomass at a given fraction of maximum live biomass for the entire year. When the
calculated value of g
i
is less than RGCMIN, g
i
is set to RGCMIN. This modi?cation allows for a daily
leaf area index value for evergreen communities like sagebrush, and creosote bush which may actively
transpire water throughout the entire year (Fig. 8.4.3).
For a bimodal potential growth curve two potential growth curves are calculated and then spliced
together. To describe the second peak in potential live biomass, the user must de?ne two additional
parameters, G
2
and P
2
. G
2
is the fraction of maximum live biomass at the second peak. P
2
is the Julian
day the second peak in live biomass occurs. The shaping coef?cients e and f for the second growth curve
are calculated in a similar manner as c and d for the ?rst growth curve. For the second growth curve the
coef?cient, a, is calculated as:
a =
f
p
-
G
1
+ G
2
G
1
f
p
h hhhhhhh P
2
-
I J L G
1
G
2
G
1
f
p
h hhhhhh + G
b
M J O h hhhhhhhhhhhhhhhhhh [8.4.9]
The user must initialize both above ground standing dead biomass and litter and organic residue on
the soil surface. The transfer of standing live biomass (L
t
)to R
a
is calculated as a function of the rate of
decline in the potential growth curve. The transfer (d)of R
a
to R
g
is a function of daily rainfall, R (m). d
has been de?ned such that the maximum single day reduction in old standing dead is 5%.
 
Page 5


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
8.4 Rangeland Plant Growth Model
Initiation and growth of above- and below- ground biomass for range plant communities are
estimated by using a potential growth curve. The potential growth curve can be de?ned with either an
unimodal or a bimodal distribution (Fig. 8.4.1 and 8.4.2). The potential growth curve (Eq. [8.4.1]) is
described by a modi?cation of the generalized Poisson density function (Parton and Innis, 1972; and
Wight, 1987). The potential growth curve should be de?ned to represent the aggregate total production
for the plant community. The ?exibility of the potential growth curve allows for description of either a
warm or cool season plant community or for a combination of the two communities.
For a unimodal potential growth curve:
g
i
= G
1
I L a e
d
c
h hh (1-ß) M O [8.4.1]
where
a=
I J L P
d
- G
b
t
i
- G
b
h hhhhhhh M J O c
[8.4.2]
 
 
ß=
I J L P
d
- G
b
t
i
- G
b
h hhhhhhh M J O d
[8.4.3]
g
i
is the increment of growth expressed as a fraction of 1.0, G
1
is the fraction of maximum live biomass
at the ?rst peak, P
d
is the Julian day peak live biomass occurs, G
b
is the Julian day the growth curve
begins, c is the shape parameter for the ascending side of the curve, d is the shape parameter for the
descending side of the curve, and t
i
is the current Julian day.
1 50 99 148 197 246 295 344
0.0
0.2
0.4
0.6
0.8
1.0
Day of Year
Potential Plant Growth (unitless)
Year 1
Year 2
Year 3
Year 4
Year 5
Variables:
cf1               
cf2               
rgcmin         
gtemp        
tempmn       
pscday       
scday         
ffp     
1.00
0.00
0.00
5.00
-5.00
240.00
0.00
320.00
Figure 8.4.1. Unimodal potential plant growth for a ?ve year period.
Variables:
cf1               
cf2               
rgcmin         
gtemp        
tempmn       
pscday       
scday         
ffp     
0.25
0.75
0.00
5.00
-5.00
60.00
250.00
320.00
1 50 99 148 197 246 295 344
0.0
0.2
0.4
0.6
0.8
1.0
Day of Year
Potential Plant Growth (unitless)
Year 1
Year 2
Year 3
Year 4
Year 5
Figure 8.4.2. Bimodal potential plant growth for a ?ve year period.
 
 
An optimization routine was developed to predict the shaping parameters c and d based on G
b
, f
p
,
and P
d
, where f
p
is the frost-free period in Julian days.
c = 8.515 - 22.279 a + 16.734 a
2
[8.4.4]
d = 12.065 - 63.229 a + 87.34 a
2
[8.4.5]
where
a =
I J L G
1
+ G
2
G
1
f
p
h hhhhhhh M J O P
d
- G
b
h hhhhhhhhhhh .
[8.4.6]
The user must enter the potential maximum live above-ground biomass (P
mx
). This value can be
obtained from the USDA Natural Resource Conservation Service Range Site guide as total annual
production for the site (section 5) with favorable growing season precipitation. The user can adjust the
total annual potential production to re?ect the condition of the site based on its current range condition
(ecological status). The initiation of growth and senescence for the plant community for the growth curve
are predicted based on air temperature. The physiological information necessary to de?ne the growth
curve is the minimum temperature necessary for initiation of growth in the spring (GTEMP) and a critical
sustained minimum temperature which will induce dormancy (TEMPMN). Where the average daily
temperature (T
a
) is calculated as T
a
= (T
mx
+ T
mn
)/2. T
mx
and T
mn
are de?ned as the maximum and
minimum daily temperature (°C), respectively.
Plant growth is initiated when g
i
is greater than 0.001. Once g
i
has reached 1.0, plant growth stops
for that growth period. Change from standing live biomass (L
t
) to standing dead biomass (R
a
)is a
function of the decay rate of the growth curve, a minimum temperature which induces dormancy, and
drought stress. Once a 5 day average minimum temperature is equal to a minimum temperature
(TEMPMN) all standing live biomass is transferred to standing dead.
The drought stress (D
s
) transfers old standing live to standing dead biomass as a function of actual
evapotranspiration, potential evapotranspiration, and a plant speci?c available soil water variable
(PLTOL). D
s
has been de?ned such that the maximum single day reduction in old standing live biomass
is 3%. The daily water stress (W
a
) is calculated as a running four day average of the calculated water
stress (WST).
D
s
= 1 - e
-3.5W
a
[8.4.7]
Increments of new growth are calculated as:
L
i
= g
i
P
mx
[8.4.8]
where L
i
is the new plant growth on day of simulation, g
i
is the positive increment between today’s and
yesterday’s g
i
, and P
mx
is the potential maximum live biomass (kg
.
m
-2
).
Water stress is calculated as the ratio of actual transpiration to potential transpiration. If available
soil water is limiting then W
a
is utilized to kill standing live biomass and transfer the recently killed
biomass to standing dead biomass. W
a
is only calculated when the actual soil water content is below a
 
 
plant speci?c critical soil water content (PLTOL). If PLTOL is not known for a speci?c plant community
then set PLTOL to 0.0 and the model will use a default value of 25% of the soil water content at ?eld
capacity. After 20 consecutive days of water stress development of new phytomass ceases. Initiation of
growth is reactivated after 80 mm of precipitation.
1 50 99 148 197 246 295 344
0.0
0.1
0.2
0.3
0.4
0.5
Day of Year
Leaf Area Index (unitless)
Figure 8.4.3. Bimodal plant growth depicted to illustrate leaf area index over time with a minimum
evergreen function initialized (RGCMIN).
For plant communities with an evergreen component the RGCMIN parameter can be initialized to
maintain the live biomass at a given fraction of maximum live biomass for the entire year. When the
calculated value of g
i
is less than RGCMIN, g
i
is set to RGCMIN. This modi?cation allows for a daily
leaf area index value for evergreen communities like sagebrush, and creosote bush which may actively
transpire water throughout the entire year (Fig. 8.4.3).
For a bimodal potential growth curve two potential growth curves are calculated and then spliced
together. To describe the second peak in potential live biomass, the user must de?ne two additional
parameters, G
2
and P
2
. G
2
is the fraction of maximum live biomass at the second peak. P
2
is the Julian
day the second peak in live biomass occurs. The shaping coef?cients e and f for the second growth curve
are calculated in a similar manner as c and d for the ?rst growth curve. For the second growth curve the
coef?cient, a, is calculated as:
a =
f
p
-
G
1
+ G
2
G
1
f
p
h hhhhhhh P
2
-
I J L G
1
G
2
G
1
f
p
h hhhhhh + G
b
M J O h hhhhhhhhhhhhhhhhhh [8.4.9]
The user must initialize both above ground standing dead biomass and litter and organic residue on
the soil surface. The transfer of standing live biomass (L
t
)to R
a
is calculated as a function of the rate of
decline in the potential growth curve. The transfer (d)of R
a
to R
g
is a function of daily rainfall, R (m). d
has been de?ned such that the maximum single day reduction in old standing dead is 5%.
 
 
d= e
-3.5R
[8.4.10]
The decomposition of litter and organic residue on the soil surface is a function of antecedent
rainfall, average daily temperature, and the carbon-nitrogen ratio of the residue and was based on the
work of Ghidey et al. (1985).
R
g
= (R
g
?
L
) - B
c
[8.4.11]
?
L
= 1 - (a
f
t)
2
[8.4.12]
t=
C
n
S
mi
T
a
h hhhhh [8.4.13]
where ?
L
is the fraction of litter after decay, a
f
is the litter decay coef?cient, and B
c
is a daily
disappearance of litter as a function of insects and rodents. t is a function of the antecedent moisture
index, average daily temperature, and the carbon-nitrogen ratio of dead leaves and roots (C
n
). S
mi
is the
amount of rainfall recorded in the last 5 days (mm). S
mi
values greater than 100 millimeters are set to 100
millimeters to reduce the decomposition rate of litter and organic residue during high rainfall periods.
For woody plant communities the trunks, stems, branches, and twigs (W
n
) of the plants are
considered to be nondecomposable but are important components in the calculation of foliar cover and
ground surface cover. W
n
is estimated on day one of the simulation as the product of N
a
and R
a
. W
n
is
held constant until management changes.
Plant characteristics that the model currently calculates are plant height (H
c
), projected plant area
(P
a
), foliar canopy cover (C
c
), ground surface cover (C
g
), and leaf area index (LAI). The height of the
plant canopy is calculated as the weighted average of coverage between the woody and the herbaceous
plant components. The canopy height for the woody component (H
t
and H
s
) are input by the user and are
held constant for duration of the simulation or until management changes.
H
c
=
A/P
a
(H
t
E
t
) + (H
s
E
s
) + (H
g
E
g
)
h hhhhhhhhhhhhhhhhhhhhhh [8.4.14]
A is the representative total vertical surface area of the overland ?ow plane (m
2
), P
a
is the effective
projected plant area (m
2
.
m
-2
), H
t
, H
s
, and H
g
are canopy heights for the tree, shrub, and herbaceous plant
components (m), respectively, and E
t
, E
s
, and E
g
are the vertical area of the tree, shrub, and herbaceous
components (m
2
), respectively.
The canopy height for the herbaceous community, H
g
(m), is estimated with an exponential
function and is updated daily. The parameters necessary to estimate herbaceous plant height are the live
standing biomass, L
t
(kg
.
m
-2
), dead standing biomass, R
a
(kg
.
m
-2
), maximum herbaceous plant height,
H
cm
(m), and a shaping coef?cient, B
h
(m
2
.
kg
-1
). Plant canopy height is de?ned not as the uppermost
extension of the canopy, but where the maximum amount of rainfall interception occurs.
H
g
= H
cm
(1 - e
-B
h
L
t
+ R
a
)
[8.4.15]