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DRAFT REPORT ON POTENTIAL EVAPOTRANSPIRATION
MODELS
PREPARED BY:
Nicolette Taylor 1, John Annandale 1, Edossa Etissa 1 and Mark Gush 2 1University of Pretoria, 2CSIR
Deliverable submitted to the Water Research Commiss ion – Project K5/1770
March 2008
0
CONTENTS……………………………………………………………………PAGE
1. INTRODUCTION ......................................................................................1
2. POTENTIAL EVAPOTRANSPIRATION MODELS ................ ..................3 2.1 Generic crop models .........................................................................3
2.1.1 FAO56 ........................................................................................3 2.1.2 SAPWAT and SAPWAT3 ...........................................................8 2.1.3 Soil Water Balance (SWB) .......................................................15 2.1.4 Penman-Monteith calculations of evapotranspiration ...............18 2.1.5 The Priestley-Taylor formula ....................................................21
2.2 Remote Sensing ..............................................................................22
2.2.1 Surface Energy Balance Algorithm for Land (SEBAL)..............22
3 POTENTIAL GROWTH MODELS............................ ..............................24 3.1 Generic Growth Models ...................................................................27
3.1.1 MAESTRA ................................................................................27 3.2 Specific crop growth models............................................................29
3.2.1 Pecan tree growth model..........................................................29 3.2.2 PEACH.....................................................................................32 3.2.3 ‘CITROS’ – A Dynamic Model of Citrus Productivity.................34
4. DISCUSSION AND CONCLUSIONS ......................... ............................35
5. REFERENCES .......................................................................................47
6. APPENDIX A - FLOW DIAGRAM INDICATING THE PROCEDURE FOR THE ESTIMATION OF CROP EVAPOTRANSPIRATION (ET C)...........55
7. APPENDIX B - FLOW CHART OF THE VARIOUS SUB-MODELS WITHIN THE SWB-2D MODEL............................ .................................56
8. APPENDIX C - FLOW CHART OF THE VARIOUS OBJECTS WITH IN THE PECAN TREE GROWTH MODEL (ANDALES ET AL. 2006).. .....60
1
1. INTRODUCTION
The need to improve irrigation scheduling and water use efficiency of fruit tree
crops in the summer and winter rainfall areas of South Africa, where water
stress is increasing, has been identified (Roux 2006). Existing models in
South Africa cannot confidently simulate water use of fruit trees for different
climate, soil, water and management conditions. This information is absolutely
essential when drawing up on-farm water management plans for fruit
production and for issuing licenses for water use. Many models have been
developed for field crops which have a one-dimensional canopy radiation
interception and water redistribution procedure. Fruit tree orchards are more
complex and this complexity needs to be taken into account when developing
evapotranspiration models for fruit trees. Process-based research on the
water use of fruit tree orchards is therefore required to provide accurate site
specific information, which can be extrapolated across regions, soils and
management practices in South Africa.
Most horticultural species have discontinuous canopies which results in
complex light interception dynamics, aerodynamics and gas exchange (Gary
et al. 1998). As a result of planting fruit trees in hedgerows, and allowing for
large spaces between rows for vehicle movement, distribution of energy is not
uniform across these widely spaced rows (Annandale et al. 2002). The
distribution of energy across rows will therefore depend on a number of
factors including, solar and row orientation, tree size and shape, as well as
slope and land aspect (Annandale et al. 2002). In addition, localised irrigation
(micro- or drip) used in orchards only wets a limited area under the canopy of
the trees, so evaporation from the surface is not uniform. The tree canopy
intercepts and channels precipitation down the stem, so even rainfall will not
be evenly distributed at the surface. All this makes traditional soil water
balance approaches to determining water use of fruit trees problematic. It is
hoped that with field measured sap flow rates, together with soil water content
(in at least a 2-D profile), total evaporation and the driving weather variables
2
for atmospheric demand, an ideal data set will be generated for calibrating
and verifying evapotranspiration models. Nicolas et al. (2005), Rana et al.
(2005) and Pereira et al. (2007b) have all used sap flow data to validate their
model.
It has been suggested that models fall within two broad categories: 1)
mechanistic models developed for scientific understanding of the processes in
nature and 2) functional or empirical models developed to solve management
problems (Passioura et al. 1996). Mechanistic models are based on
hypotheses, which may or may not be correct, on how plants grow. These
models are often difficult to parameterise, require large numbers of inputs and
as a result are not favoured by users due to their complexity. On the other
hand, models based on empirical relationships established in a given
environment are unlikely to apply outside that environment. These models
should only be used within the range over which they were calibrated. The
overall aim of a model should be accurate prediction on which to base sound
advice. As we would like to extrapolate to a range of management practices,
soil types and growing regions in South Africa, it is very important to use a
more mechanistic approach in order to gain an understanding of the system
and the driving variables for water use in the various fruit trees.
Prior to setting up a particular model the appropriateness of using the model
must be gauged. Numerous aspects need to be considered including the
availability of required input data, ability of the model to simulate the desired
processes and complexity of operation (ease of use / user support) among
others. We must be able to differentiate between water-supply- or
evaporative-demand-limited water uptake. A mechanistic model would
therefore be preferable, as empirical models often assume that water loss is
demand-limited. For real-time decisions the model should include a daily time
step, however, for planning purposes a monthly time step should be
adequate. The models proposed for evaluation in this project are the SWB
model, the FAO56 model and SAPWAT. These are general or generic crop
models that are applied to a wide range of crops. In addition to these, crop
specific growth models are available, e.g. pecan (Andales et al. 2006) and
3
peach (Grossman and Dejong 1994). It should be kept in mind that growth
models are often difficult to parameterise and a large number of variables will
have to be quantified as a result. More generic growth models are also
available such as MAESTRA (Medlyn 2004), which is a development of the
earlier MAESTRO model (Wang and Jarvis 1990) and is a three dimensional
model of forest canopy radiation absorption, photosynthesis and transpiration.
A different approach is the use of remote sensing to estimate the spatially
distributed surface energy balance in composite terrains, such as that found in
SEBAL (Surface Energy Balance Algorithm for Land) (Bastiaanssen et al.
1998). Possible collaboration with these authors could be invaluable when
considering the water use of fruit trees on a broader scale. The project team
are also aware of the drafting of new FAO33 yield response to water
guidelines for fruit trees and vines, which will deal particularly with how to
manage water during times of limited supply.
2. POTENTIAL EVAPOTRANSPIRATION MODELS
2.1 Generic crop models
2.1.1 FAO56
The FAO56 model (Allen et al. 1998) provides a means of calculating
reference and crop evapotranspiration from meteorological data and crop
coefficients. The effect of climate on crop water requirements is given by the
reference evapotranspiration (ETo), and the effect of the crop by the crop
coefficient Kc. Actual crop evapotranspiration (ETc) is calculated by multiplying
ETo by Kc :
ETc = Kc x ETo (1)
The calculation of ETo is based on the Penman-Monteith combination method,
and represents the evapotranspiration of a hypothetical reference crop (short
grass). The equation is as follows (Allen et al. 1998):
4
)34.01(
)(273
900)(408.0
2
2
u
eeuT
GRET
asn
o ++∆
−+
+−∆=
γ
γ (2)
where ETo reference evapotranspiration [mm day-1], Rn net radiation at the crop surface [MJ m-2 day-1], G soil heat flux density [MJ m-2 day-1], T mean daily air temperature at 2 m height [°C], u2 wind speed at 2 m height [m s-1], es saturation vapour pressure [kPa], ea actual vapour pressure [kPa], es - ea saturation vapour pressure deficit [kPa], ∆ slope of the vapour pressure curve [kPa °C -1], γ psychrometric constant [kPa °C -1].
The reference crop has the following unambiguous definition “A hypothetical
reference crop with an assumed height of 0.12 m, a fixed surface resistance
of 70 s m-1 and an albedo of 0.23, closely resembling the evaporation of an
extensive surface of green grass of uniform height, actively growing and
adequately watered.” The technique uses standard climatic data that can be
easily measured or derived from commonly collected weather station data (air
temperature, humidity, radiation and wind speed) and takes into account the
location (altitude above sea level and latitude).
Differences in the canopy and aerodynamic resistances of the crop being
simulated, relative to the reference crop, are accounted for within the crop
coefficient (Kc). Kc serves as an aggregation of the physical and physiological
differences between crops and takes into account canopy properties and the
aerodynamic resistance of the crop. Two calculation methods to derive ETc
from ETo are possible. The first approach integrates the relationships between
evapotranspiration of the crop and the reference surface into a single
coefficient (Kc). This is used for normal irrigation planning and management
purposes, for the development of basic irrigation schedules and for most
hydrological water balance studies. The second approach splits Kc into two
factors that separately describe the evaporation (Ke) and transpiration (Kcb)
components. This allows Kc to be calculated on a daily time step. There is an
attempt to simulate supply-limited water use by introducing a water stress co-
5
efficient (Ks) (Allen et al. 1998). The threshold point at which soil water
content is low enough to limit evapotranspiration takes into account the
atmospheric evaporative demand. In this case crop evapotranspiration will be
calculated as follows:
ETcadj = [KsKcb + Ke] x ETo (3)
A flow chart for the calculation of ETc is presented in Appendix A.
The FAO56 publication lists crop coefficients for numerous crops under
“standard conditions”, which implies that no limitations are placed on crop
growth or evapotranspiration from soil water and salinity stress, crop density,
pests and diseases, weed infestations or low fertility. The season is also split
into 4 distinct growth phases, viz. an initial phase, a development phase, a
mid-season phase and finally an end phase, each with its own associated Kc
value (Figure 1).
Figure 1: Crop coefficient curve for the four growth stages (Allen et al. 1998).
0.00
0.20
0.40
0.60
0.80
1.00
1.20
Time of season (days)
Kc
Kc ini
Kc mid
Kc end
initial mid-season late season
crop developmentt
6
The list includes several deciduous and woody species such as certain fruit
and nut trees. Table 1 lists the crop factors for the selected species in this
study. Data for macadamia could not be found. Crop factors could be utilised
for the specific species they represent, or modified to better represent crop
development stages (and associated dates) for additional species not yet
represented. Multiplication of the reference evaporation by the basal crop
coefficient represents the upper envelope of crop transpiration where no
limitations are placed on plant growth or evapotranspiration. The option to
split the crop coefficient (Kc) into two factors that separately describe the
evaporation (Ke) and transpiration (Kcb) components is particularly suited to
this particular study because the field data that will be collected will yield
values of transpiration (excluding soil evaporation), and are consequently
directly comparable to the simulated values of Kcb. In addition, wetted areas
and frequency of wetting will have a big effect on water use. Another major
advantage of FAO56 is that all the necessary data to successfully run the
model will be collected at site and will be sufficient to use as input into the
model. This includes weather data, stage of growth and leaf area index.
A common occurrence with crop factors is that inaccuracies occur due to
assumptions made about the plant-soil system. Crop factor curves assume
that plant growth and development is dependent on calendar days, but
thermal time (degree days) and water supply play a more important role in
canopy development (Ritchie and NeSmith 1991). This limits the “universality”
of a particular crop factor. In addition, crop factors do not always take into
account processes that are taking place in the soil which impact on water
uptake by the plant. This includes infiltration, soil water potential and rooting
density, all of which vary with soil depth and distance from the tree row
(Annandale et al. 2000).
7
Table 1: Crop coefficients, Kc, for non stressed, well-managed cops in
subhumid climates (RHmin≈ 45%, u2 ≈ 2 m s-1) for use with FAO Penman-
Monteith (Allen et al. 1998). Values for Macadamia could not be found in the
guidelines.
* The midseason value is lower than the initial and ending values due to the effects of stomatal closure during periods of peak ET (Allen et al. 1998). For humid and subhumid environments, where there is less control of stomates by citrus, the values can be increased by 0.1-0.2.
Fruit tree specie K c ini Kc mid Kc end Maximum crop height (m)
Apples
-no ground cover, killing frost
0.45 0.95 0.7 4
- no ground cover, no frost
0.60 0.95 0.75 4
- active ground cover, killing frost
0.50 1.20 0.95 4
-active ground cover, no frost 0.80 1.20 0.85 4
Peaches
-no ground cover, killing frost
0.45 0.90 0.65 3
- no ground cover, no frost 0.55 0.90 0.65 3
- active ground cover, killing frost 0.50 1.15 0.90 3
-active ground cover, no frost 0.80 1.15 0.85 3
Citrus , no ground cover
- 70% canopy 0.70 0.65* 0.70 4
- 50% canopy 0.65 0.60 0.65 3
- 20% canopy 0.50 0.45 0.50 2
Citrus , with active ground cover or weeds
- 70% canopy 0.75 0.70 0.75 4
- 50% canopy 0.80 0.80 0.80 3
- 20% canopy 0.85 0.85 0.85 2
8
2.1.2 SAPWAT and SAPWAT3
SAPWAT is a user-friendly computer programme whose primary function is to
estimate crop evapotranspiration for planning purposes in a user-friendly
format (Crosby and Crosby 1999). In this way irrigation requirements for
application in planning, design and management can be deduced. It was not
designed as a real-time irrigation management tool. SAPWAT links to and is a
development of the FAO planning model CROPWAT, which has been derived
from several FAO irrigation and drainage papers. SAPWAT does not attempt
to model crop growth but is rather a management and planning aid that is
supported by extensive South African climate and crop databases. Some of
the major innovations incorporated into SAPWAT include (SAPWAT 2008):
1) the replacement of the American Class A evaporation pan with
reference evaporation from a short grass surface calculated from
climatic data by means of the standardised Penman-Monteith
procedure. The short grass surface has the characteristics of a
growing crop and this automatically compensates for regional
climatic differences
2) the use of FAO four stage methodology whereby crop factors
compatible with the short grass reference evaporation can be
developed and modified by applying simple and understandable
procedures
3) the facility to differentiate between soil evaporation and plant
transpiration, making it possible to cater for field crops, orchards
and vegetables in conjunction with a full range of irrigation methods
and strategies.
This is in accordance with FAO56.
For predictive purposes, SAPWAT uses average climatic data from weather
stations throughout South Africa (locally obtained weather data can be
inserted into the model) and crop factors which are specific for a geographic
region, planting date and time of year. According to the user manual, when
calculating crop factors and determining the crop factor curve for a particular
location provision is made for selecting the percentage cover at full growth.
9
Figures of less than 100% are usually found in the case of permanent crops,
such as orchards, where young trees will have a final cover of as low as 10%
in a given season and even when mature seldom reach 100%. In such an
instance, where a final cover of less than 100% is entered, a leaf area index is
calculated by the program. The percentage wetted area is also accounted for
when determining the crop factor curve, which is particularly important in
orchard crops where localised irrigation is used, in the form of micro- or drip
irrigation. From here the crop evapotranspiration is calculated, which allows
the estimation of crop water requirements and therefore irrigation. If
significant, rainfall can be included in the irrigation requirement calculations,
otherwise rainfall is ignored and irrigation requirements are calculated as if all
crop water requirements will be derived from irrigation alone. Irrigation
requirements are calculated according to the system used, the efficiency of
the irrigation, the target yield and the uniformity of distribution of the irrigation.
SAPWAT is a valuable tool for Water User Associations for registration and
licensing purposes, for macro-planning and for water demand management
strategies. The crop specific transpiration data generated by this particular
study will be very useful in validating the current selection of crop factors for
the selected fruit tree species as shown in Figures 2 to 5. We are confident
that this study will, at least, improve on the estimated crop factors for the
selected fruit tree species in South Africa.
10
Figure 2: Crop factors for early/short, medium and late/long apples in South
Africa. Data obtained from http://www.sapwat.org.za.
11
Figure 3: Crop factors for citrus in South Africa. Tables for “above average”,
“average” and “below average” citrus do not differ. Data obtained from
http://www.sapwat.org.za.
Figure 4: Crop factors for macadamia in South Africa Data obtained from
http://www.sapwat.org.za.
12
Figure 5: Crop factors for short/early, medium and long/late peaches in South
Africa. Data obtained from http://www.sapwat.org.za.
The information contained in the above tables is interpreted as follows:
St.1 to St. 4 indicates the number of days per growth cycle, which is in
accordance with the four-stage crop factor curve. It should be noted that
SAPWAT uses a 360 day year. The initial stage in perennial crops starts at
13
the onset of full or semi-dormancy until re-growth has started. The second
phase is the crop development stage which lasts until effective full ground
cover is reached, during that particular season. The mid-season stage lasts
from reaching full effective ground cover, till the beginning of maturity, as
indicated by a change in leaf colour and leaf abscission. The final stage is the
late season stage and lasts from the end of the mid-season stage until full
maturity. In fruit trees harvesting takes place before the onset or at the
beginning of this stage. Kc is the maximum crop factor value expected and
therefore maximum transpiration. This usually varies between 1.1 and 1.2 for
crops at full cover. When determining crop factors, crops that do not give full
cover at maturity e.g. orchards, can be accounted for by adjusting the
percentage cover at full growth. Maximum Fv (foliage value) lies between 0.1
and 1.0 and accounts for those instances where transpiration is suppressed
(supply limited) e.g. in stressed or diseased plants. A value of 0.8 implies that
even though full canopy has been reached, crop transpiration is at an 80%
level of efficiency. Fv end (foliage value at harvest or at onset of dormancy) is
a value between 1 and 100. For crops that are harvested at full maturity this
would be 1, for those that are harvested at the end of stage 3, for example,
this value could be 100. Fv start (foliage value at the end of the dormancy
period for perennial crops) is a value between 1 and 100. This value is usually
1 for perennial crops that restart growth from bare branches and increases for
semi-dormant crops, such as subtropical fruit species. There is also provision
made for perennial crops. Within the months column, the onset of the fullest
level of dormancy is marked for perennial crops with a ‘Y’.
Water / irrigation requirements are estimated in SAPWAT by making use of
general approaches to root development, rooting depth and soil water holding
capacity. However, when using the management module, provision is made to
adjust these parameters according to the specific area and crop. In terms of
soil, characteristics can be changed by the user, this includes total available
water (total water holding capacity of the soil), maximum rain infiltration rate
(total amount of rain that the soil can absorb in the course of a day), initial soil
depletion (level which soil moisture is beneath field capacity at the beginning
of the cycle) and soil rooting depth (rooting depth of the crop or soil depth in
14
the case of an impermeable layer). Rainfall can be included or excluded in
water management calculations.
Crop characteristics for application by SAPWAT were mainly collected by
means of surveys of researchers, technicians and farmers and where possible
evaluated against existing published data (van Heerden 2008). It is therefore
unlikely that the majority of crop factors and growth stages derived for fruit
tree species would have been validated. There is therefore concern that the
currently available crop factors for fruit tree species in South Africa are not
robust enough to be applicable to all regions in South Africa where the fruit
trees are grown. In addition the four stage canopy growth descriptors may not
be sufficient to predict the changes that occur in evergreen canopies
throughout the year.
SAPWAT is currently being upgraded to SAPWAT3 (van Heerden et al.
2008). SAPWAT3 integrates an upgraded version of PLANWAT with the latest
SAPWAT crop irrigation requirement engine. This allows for data to be stored,
which was not possible for SAPWAT. SAPWAT3 also uses an internationally
accepted climate system, the Köppen-Geiger Climate System, in order to
standardize regions that form the background of the update of the crop factor
data. This system is based on a combination of temperature and precipitation
and is computed in terms of monthly or annual values. This makes SAPWAT
universally applicable. In addition, 50 years of calendar weather data,
including ETo has been incorporated into SAPWAT3 on a quaternary basis.
SAPWAT3 also makes provision for adjusting the slope of the crop factor
curve for the dominant third stage, as it is believed that a horizontal curve is
an over-simplification, particularly for fruit tree crops. This is achieved by
including a start and end entry for the 3rd growth phase when setting up the
growth factor curve in SAPWAT3. The dual crop coefficient approach is used
in SAPWAT3, where crop transpiration and evaporation from the soil surface
are calculated separately (Allen e al. 1998, van Heerden et al. 2008). Crop
water requirements are therefore calculated as follows
ETc = (Kcb + Ke)ETo (1)
15
Although this is a more complex approach it gives a better understanding of
the role of soil evaporation as part of crop irrigation requirement estimation
and how different irrigation strategies can increase or reduce this loss (van
Heerden et al. 2008)
2.1.3 Soil Water Balance (SWB)
SWB is a mechanistic, real-time, generic crop growth / soil water balance
model, which was developed by Annandale et al., (1999), as an irrigation
management tool. From soil, weather and crop inputs it simulates crop growth
and provides insights into the one-dimensional biophysical links between the
atmosphere (environment), plant systems and the soil system. It has been
calibrated and tested under a range of conditions and crops and has proven
to be very helpful, with reliable correctness. Canopy growth and crop water
uptake is well simulated under both water-supply- and energy-demand-limited
conditions (Annandale et al. 2000). Subsequent to the development of the
original SWB model, a new version that performs energy interception and
water balance modelling in two dimensions, by trees planted in hedgerows
(SWB-2D), was developed and verified as an extension of the former model.
Two types of models are included in SWB-2D for hedgerow crops. Firstly, a
mechanistic two-dimensional energy interception and finite difference,
Richard’s equation based soil water balance model and secondly, an FAO-
based crop factor model, with a quasi-2D cascading soil water balance model
(Annandale et al. 2002). The first model calculates the two-dimensional
energy interception for hedgerow crops based on solar and row orientation,
tree size and shape, and leaf area density. A two-dimensional water
redistribution is also calculated with a finite difference solution. Some of the
input parameters for this model, such as leaf area density and soil saturated
hydraulic conductivities, are not always easy to obtain, which affects the ease
with which this model can be used. This prompted the development of the
second model which is based on the FAO crop factor approach and allows for
the prediction of crop water requirements with limited input data. This model,
16
includes a semi-empirical approach for partitioning above-ground energy, a
cascading soil redistribution that separates the wetted and non-wetted portion
of the ground and a prediction of crop yield according to the CROPWAT
model develop by the FAO (Smith 1992a). The two-dimensional model was
incorporated into the original SWB model (Annandale et al., 1999; Annandale
et al., 2002; Annandale et al., 2003; Annandale et al., 2004).
Input data to run the two dimensional canopy interception model are: day of
year, latitude, standard meridian, longitude, daily solar radiation, row width
and orientation, canopy height and width, stem height and distance to the
bottom of the canopy, extinction coefficient, absorptivity and leaf area density
(Annandale et al. 2002). A flow diagram for the energy interception model is
shown in Appendix B.
Spatial distribution of evaporation at the soil surface is calculated by the
model in two steps (Annandale et al. 2002):
1) potential evaporation at each node is estimated by applying the
Penman-Monteith equation (Allen et al. 1998), using radiation
estimated locally as an input, and
2) evaporation from the soil surface at each node is calculated as a
function of potential evaporation, air humidity and humidity of the soil
surface.
In order to simulate two dimensional water movement in the soil the following
inputs are required: altitude, rainfall and irrigation water amounts and
minimum and maximum daily temperature. The following soil measurements
are required for each soil layer (after establishing a grid of nodes): two points
on the water retention function (normally field capacity and permanent wilting
point), initial volumetric soil water content and bulk density. Row distance,
wetted diameter of micro-jets or drippers, fraction of roots in the wetted
volume of soil and distance of the nodes from the tree row are also required
as inputs. The flow diagram of the two-dimensional soil water balance for
hedgerow crops is shown in Appendix B.
17
Potential transpiration from the trees is calculated as follows (Annandale et al.
2002): potential evapotranspiration (PET) is partitioned between potential
evaporation from the soil and potential transpiration from the canopy. PET is
calculated using the Penman-Monteith equation (Allen et al. 1998) using
locally obtained weather data and the maximum crop factor after rainfall
occurs (Jovanovic and Annandale 1999). Local potential evaporation
calculated at each radiation node are weighted according to the surface and
are accumulated over the whole surface to calculate overall potential
evaporation (PE). Potential transpiration is then taken as the difference
between PET and PE. Root densities at different soil depths are accounted for
in the calculation of root water uptake using the approach of Campbell and
Diaz (1998). This allows for differentiation between atmospheric-limited and
supply-limited water demand. Root depth and the root fraction in the wetted
and non-wetted volume of the soil can also be entered by the user. Due to the
complexity of this model it has not been widely implemented as an irrigation
scheduling tool, but it may be a useful mechanistic approach to generating
orchard specific crop factors.
The FAO-based crop factor model does not attempt to grow the canopy
mechanistically and therefore the impact of water stress on canopy growth is
not simulated (Annandale et al. 2002). This model will, however, still perform
satisfactorily if the estimated canopy cover closely resembles that found in the
field. The following crop parameters need to be known in order to calculate
the crop factor: Kcb for the initial, mid- and late stages; crop growth periods in
days for initial, development, mid- and late stages; initial and maximum root
depth and initial crop height and maximum crop height. The following inputs
are required to run the FAO-type crop factor model: planting date (before
flowering for evergreen trees and bud burst for deciduous trees), latitude,
altitude and maximum and minimum air temperatures. In the absence of the
preferred measured data SWB estimates solar radiation, vapour pressure and
wind speed according to FAO recommendations (Smith 1992b, Smith et al.
1996). A flow diagram of the FAO-type crop factor model included in SWB is
included in Appendix B.
18
The soil water balance under localised irrigation is also calculated in SWB
(crop factor approach) using a simplified procedure for the calculation of non-
uniform wetting of the soil surface, evaporation and transpiration (Annandale
et al. 2002). The data input required to run the two-dimensional cascading
model are rainfall and irrigation amounts, volumetric soil water content at field
capacity and permanent wilting point and initial soil water content for each
layer. Row spacing, wetted diameter, distance between micro-jets or drippers,
and the fraction of roots in the wetted volume are also required. A flow
diagram of the cascading soil water balance for fruit tree crops under localised
irrigation is included in Appendix B.
2.1.4 Penman-Monteith calculations of evapotranspiration
Evapotranspiration from a Clementine (Citrus reticulate Blanco) orchard in
Southern Italy, with a Mediterranean climate, was estimating using a modified
Penman-Monteith formula (Rana et al. 2005). The authors compared the sap
flow method for quantifying actual evapotranspiration with eddy covariance (a
micrometeorological method) and then examined the effectiveness of the crop
coefficient method to determine the water requirements of the orchard. Finally
a model of actual evapotranspiration on an hourly scale was developed
following the Penman-Monteith approach and simple standard meteorological
variables as inputs for determination of the canopy resistance. Good
correlation was found between sap flow and eddy covariance measurement of
transpiration, indicating that sap flow is a valid method for estimating field
scale evapotranspiration. Rana et al. (2005) found that the generic citrus crop
factor given by Allen et al. (1998) did not correspond well with the calculated
crop factor during a 105 day period during bud swelling and flowering. During
this time the calculated crop factor was considerably higher than the
prescribed factor given by Allen et al. (1998). This was probably due to it
being a period of active growth, with associated high stomatal conductance,
high wind speeds and high vapour pressure deficits (Rana et al. 2005). The
evaporation (E) modelling used a simple formulation based on the Penman-
Monteith model.
19
)/1(
/)(
ac
ap
rr
rDcAE
++∆+∆
=γ
ρλ (1)
where A = Rn – G is the available energy in W m-2, ρ is the air density in kg
m-3, ∆ is the slope of the saturation pressure deficit versus temperature
function in kPa °C -1, γ is the psychrometric constant in kPa °C -1, cp is the
specific heat of moist air in J kg-1 °C -1, D the vapour pressure deficit of the air
in kPa, rc is the bulk canopy resistance in s m-1 and ra is the aerodynamic
resistance in s m-1.
For irrigated crops the canopy resistance rc is not constant and varies
according to the available energy and the vapour pressure deficit. Katerji and
Perrier (1983) proposed to calculate rc as
br
ra
r
r
aa
c +=*
(2)
where a and b are empirical calibration coefficients which require
experimental determination. r* (s m-1) is given as:
A
Dcr pρ
γγ
∆+∆=* (3)
The resistance r* is linked to the isothermal resistance (ri = ρcpD/γH) (Monteith
1965) and can be considered as “climatic” resistance as it is dependent on
weather variables.
The canopy resistance (rc) was calculated from Eq. (1) by using E values
calculated from the eddy covariance method, together with the measured
values of vapour pressure deficit and available energy and the estimated
value for ra (Eq. (4)). These values of rc were combined with Eq. (2) to
estimate the parameters a and b. The model input variables are air
20
temperature and humidity, wind speed and direction, global radiation, rainfall
and mean height of the orchard.
*
)/()ln(
ku
dhdzr c
a
−−= (4)
where, z is a reference point sited in the boundary layer above the canopy, d
(m) is the zero plane displacement, hc is the mean height of the orchard, k is
the von Kármán constant and u* is the friction velocity (m s-1).
The canopy resistance of irrigated crops is therefore considered a function of
radiation and vapour pressure deficit (Eq. (3)). The final expression of the
model, on an hourly scale is:
)/(226.00042.0(
)/(*
a
ap
rr
rDcAE
++∆+∆
=γ
ρλ (5)
The model was tested for a year and compared with E measured by the sap
flow method. These two methods were found to agree closely. The model was
therefore shown to be preferable for calculating the water requirement of the
Clementine orchard, over an approach based on a crop coefficient which is
considered constant during the different growth stages.
Pereira et al. (2006) demonstrated that well irrigated canopy transpiration can
be accurately estimated using the conventional grass reference evaporation
and the Penman-Monteith formula described by FAO56 (Allen et al. 1998) in a
number of different species in New Zealand. These authors did not use the
recommended crop factors, but rather the computed reference evaporation
was corrected using the ratio between the canopy leaf area and the 2.88 m2
of the leaf area assumed for the hypothetical reference grass surface. A good
correlation was found between estimates using this method and sap flow
determined by the compensation heat-pulse technique (Pereira et al. 2006).
No other empirical correction or adjustment factor was required, but a reliable
21
method for estimating canopy leaf area is needed. This was tested in normal
apples, dwarf apples, olives, walnuts, grapevines and kiwifruit and it was
evident that under the same Eo conditions the sap flow of irrigated trees is a
positive function of the total canopy leaf area. In addition, when sap flow was
converted to per unit leaf area (L M-2 leaf d-1) an empirical function indicated
that sap flow corresponded, on average, to 35% of Eo. It is, however, unlikely
that this empirical relationship will be universally applicable.
These methods could prove very useful in improving estimation of water use
of fruit trees for growers, as they are relatively simple and take into account
local conditions and management practices. The major stumbling block,
however, remains the simple and reliable estimation of leaf area. If this can be
adequately addressed these types of models should prove to be extremely
useful. However, more mechanistic approaches, that include soil
measurements, need to be followed in order to ensure the accurate estimation
and then simulation of water use of fruit trees in various regions of South
Africa.
2.1.5 The Priestley-Taylor formula
Pereira et al. (2007b) describe a simple method for estimating daily sap flow
from well-irrigated orchards by using empirical relationships between radiation
absorbed by the canopy and daily sap flow measurements. This approach
was validated in an apple orchard consisting of large trees, an apple orchard
consisting of dwarf trees, an olive orchard and an isolated walnut tree. These
authors adapted the Priestley-Taylor formula to estimate daily sap flow of a
tree (T, L tree-1 day-1), using only net all-wave radiation, average air
temperature and tree leaf area. This is viewed as a simpler approach than the
traditional Penman-Monteith FAO56 model (Allen et al. 1998) which requires
local climate data, which is not always available from a standard climate
station.
22
The adapted Priestley-Taylor formula is as follows
λγα A
s
sT
+= (1)
where, s (kPa °C -1) is the slope of the saturation vapour pressure curve at
average daily temperature, γ is the psychrometric constant (= 0.066 kPa °C -1),
λ (=2.45 MJ L-1) is the latent heat of vaporization, A (MJ tree-1 day-1) is the
total amount of net (all-wave) radiation absorbed by the leaf canopy and α is
the Priestley-Taylor parameter. A was estimated from a measurement of the
net radiation over grass (RN, MJ m-2 day-1) and the trees total, one-sided, leaf
area (LA, m2 tree-1). According to Pereira et al. (2007a) the relationship is A =
0.303 (±0.032) RN LA. However using a fixed value of 0.32 for A, regardless of
the tree species, and α = 1.26, the authors were able to get a good estimate
of the daily sap flow recorded in the trunks of fully irrigated orchard trees
(Pereira et al. 2007b). The fixed value for A was determined previously for
citrus (Pereira et al. 2001). By determining leaf area, a more accurate
estimation can be obtained, but obtaining reliable leaf area measurements is
problematic and the authors are still trying to develop a rapid way of
assessing leaf area. Pereira et al. (2007b) found that empirically, sap flow per
unit tree leaf area is one quarter of the net radiation over a grass sward. This
is a very simple method for estimating the water use of orchards. The
applicability of this empirical relationship to different locations is questionable.
These two approaches were considered by the authors to be a simple working
alternative to the traditional crop-coefficient approach which relates crop water
use to potential evapotranspiration. Once again the lack of soil measurements
is a concern.
2.2 Remote Sensing
2.2.1 Surface Energy Balance Algorithm for Land (SEBAL)
SEBAL uses surface temperature To, hemispherical surface reflectance ro and
Normalized Difference Vegetation Index (NDVI), as well as their
23
interrelationships to infer surface fluxes for a wide spectrum of land types
(Bastiaanssen et al. 1998). Actual satellite data is inserted in the derivation of
the regression coefficients. Figure 6 illustrates the principal components of
SEBAL which converts remotely measured spectrally emitted and reflected
radiances into the surface energy balance and land wetness indicators. It
provides an opportunity to monitor energy balances from individual lands to
scheme level. Comparisons of predicted ET by SEBAL to lysimeter
measurements indicate a relatively good accuracy and show promise for
application in river basin planning and water rights management (Allen et al.
2001).
Figure 6: Principle components of SEBAL which converts remotely measured
spectrally emitted and reflected radiances into the surface energy balance
and land wetness indicators (Bastiaanssen et al. 1998).
Advantages of the SEBAL model include: minimal collateral data is required; it
is a physical concept and is therefore applicable for various climates; there is
no need for land use classification or the involvement of data demanding
hydrological models; evaporation is retrieved directly without the use of crop
factors; the method is suitable for all visible, near-infrared and thermal-
infrared radiometers, which implies it can be applied at different spatial and
temporal resolutions; for high resolution images, the results can be verified
with in-situ fluxes and soil water measurements; and it is a modular approach
(Bastiaanssen et al. 1998). The disadvantages include: the requirement for
Surface resistance
Visible
Near infrared
Thermal- infrared
Surface albedo
Vegetation
Surface temperature
Conversion
Net radiation flux density
Soil heat flux density
Sensible heat flux density
Latent heat flux density
Bowen-ratio
Evaporation fraction
SEBAL
Satellite radiances
Surface parameters
Land surface parameterization
Surface energy balance
Wetness indicator
24
cloud-free conditions; the presence of both drylands (Λ=0) and wetlands
(Λ=1); surface roughness is poorly described; it is only suitable for flat terrain
(Bastiaanssen et al. 1998) and it does not explain the causes, it only
measures the net effects of land surface processes (Stevens et al. 2005).
3 POTENTIAL GROWTH MODELS
Crop modelling is just one step in the process of designing better
management tools. Physical yield of a crop is determined by dry matter (DM)
production, DM distribution and DM content of the harvestable organ
(Marcelis et al. 1998). Dry matter production is largely driven by
photosynthesis, whilst photosynthesis is largely dependent on intercepted
radiation. Intercepted radiation in turn is determined by leaf area. Most crop
growth models are deterministic, which implies that in a given context, defined
by the set of variables, a unique output is calculated (Gary et al. 1998). In this
instance the variability in the system is ignored. In contrast, stochastic models
take uncertainty into account. In some instances these models are used to
reduce possible variability in the marketable product. These models are,
however, generally, not mechanistic and they are based on probability density
functions (Gary et al. 1998). Plant morphology is considered an important
input into growth models to simulate light interception and photosynthesis.
The dynamics of the spatial organisation of shoot and root systems has been
the main characteristic addressed in fruit trees to date (Gary et al. 1998). It is
also important to remember when modelling perennial fruit tree growth that
there will be an interaction between the current and subsequent growth cycle
(Monselise and Goldschmidt 1982).
Two basic frameworks have been adapted for modelling growth and
development. Firstly, those models which analyse growth, and secondly,
models which are photosynthesis-driven (Gary et al. 1998). Growth analysis
models attempt to represent key features of crop behaviour without a detailed
account of the respective mechanisms. In some instances the relative growth
rate is determined in terms of the changes in size and activity of the canopy
25
i.e. the leaf area ratio (m2 g-1) and the net assimilation rate (g m-2 d-1). These
models have proven to be highly effective in studying the reaction of the plant
to environmental conditions and comparisons between species. However,
they have proved ineffectual in modelling mutual shading of leaves (Marcelis
et al. 1998). Development of photosynthesis-based models has been the
dominant strategy in horticulture and agriculture in general. For a comparison
of empirical and mechanistic growth models see Figure 7. These models are
based on fairly detailed descriptions of the fate of carbon in the crop, from the
production to the storage and/or assimilation of photoassimilates. These
models allow for long term prediction of biomass accumulation and they can
also simulate short term (hourly) responses to the environment. They
calculate the interception of radiation by the leaf area in order to simulate the
production of photosynthates (Marcelis et al. 1998). The use of
photosynthates for respiration, conversion into structural dry matter and the
partitioning to different plant organs is calculated and finally fresh mass can
be estimated from dry mass. In order to simulate crop photosynthesis in detail
Figure 7: Comparison of A) empirical and B) mechanistic approaches to yield
prediction. The empirical model describes the basic processes which may
limit yield. In a mechanistic approach a more realistic description is possible,
provided the more numerous parameters can be estimated (Gary et al. 1998).
26
the calculation of total radiation interception and spatial variation in radiation
interception is required (Marcelis et al. 1998). These models also need to take
into account stomatal resistance, as this might limit photosynthesis especially
under high light conditions (Marcelis et al. 1998). This is achieved by
simulating a negative influence of stomatal resistance on the maximum rate of
leaf photosynthesis. Strong features of photosynthesis-based models are the
simulation of light interception and gross photosynthesis and weak features
are the simulation of leaf area development, maintenance respiration, organ
abortion, DM content and product quality (Marcelis et al. 1998).
Growth models must also model respiration, which is most often divided into
two components, viz. growth and maintenance (Amthor 1989). Maintenance
respiration is assumed to have priority over growth. The amount of assimilates
required for maintenance (Rm) are therefore subtracted from gross
photosynthesis (Pg) and the remaining assimilates are available for dry mass
increase (dw/dt)
dw/dt = Yg x (Pg - Rm) (1)
where, Yg is the growth conversion efficiency, which is the weight of dry mass
formed per unit weight of assimilates. The amount of assimilates used for
maintenance respiration as a fraction of the gross assimilate production has
been estimated to be 33% for peach (Grossman and DeJong 1994) and
depending on latitude and harvest date it varied between 30-80% for apple
(Wagenmakers 1995). It is important for fruit crops that assimilates partitioned
to the fruit should not be too high or an alternate bearing cycle will be initiated.
Thus thinning of fruits is often practiced in deciduous fruit orchards and on
occasion in citrus to avoid the entry into severe alternate bearing cycles. The
partitioning of this dry matter at the crop level is still poorly understood and
there seems to be great diversity in the manner in which crops partition
assimilates (Marcelis et al. 1998). As a result current available models are
fairly species specific.
27
The definition of morphological types and the adoption of some standards are
necessary in order to model the diversity of horticultural crops (Gary et al.
1998). The difficulty in modelling fruit tree species lies partly in the
heterogeneity found in orchard situations. Variability may be found in the
genetic make-up of the plants, the root and shoot environment and plant
management strategies (e.g. pruning). Attempts to include variability around
each parameter will result in unrealistic noise in the model (Gary et al. 1998)
and thus it is considered best to characterise variability in the environment,
e.g. the spatial variability in soil.
The modelling of sink strength has found numerous applications in
reproductive crops, including peach and citrus. Effects of environmental
conditions, pruning strategies and plant densities can be simulated through
their effects of sink strengths of individual organs, number of organs, or
indirectly through effects of source strength on organ formation (Marcelis et al.
1998).
By modelling photosynthesis and assimilate partitioning and therefore growth,
it is possible to mechanistically grow a canopy. Changes in canopy size
during a season can therefore be accurately estimated in a number of
different locations for use in evapotranspiration calculations.
3.1 Generic Growth Models
3.1.1 MAESTRA
The MAESTRA model (Medlyn 2004) is a development of the earlier
MAESTRO model (Wang and Jarvis 1990) and is a generic three dimensional
crop growth model that was initially developed for forestry. It predicts radiation
absorption, photosynthesis and transpiration of individual crowns of trees in a
stand and by the stand as a whole. It has proved useful in scaling up leaf
measurements to the whole canopy and whole stand. Each crown is divided
into 6 horizontal layers with each layer divided into 12 grid points of equal
volume. A number of physical and physiological properties are specified for
28
each layer, which includes radiation, temperature, leaf area index and leaf
nitrogen content. Environmental variables that drive model simulations are
radiation, air temperature, wind speed and atmospheric CO2 concentration
above the canopy. It is assumed that air humidity, temperature and CO2
concentration are uniform within the canopy.
The radiation penetrating to each point is calculated for three wavebands
(PAR, near infrared and thermal or longwave) and direct diffuse and scattered
radiation are considered separately (Wang and Jarvis 1990). This also takes
into account the hourly position of the sun in the sky and the daylength for a
specified date and latitude. The amount of absorbed radiation by the leaves
considers leaf inclination and the distribution of leaf ages.
Leaf boundary layer and stomatal conductance estimations require reference
height, wind speed, air temperature and water vapour saturation deficit at that
height, crown dimensions of all trees within the plot and PAR flux density
incident normal to the leaf surface. Photosynthesis and transpiration at each
grid point is calculated from absorbed radiation. Transpiration is calculated by
applying the Penman-Monteith equation (Jarvis and McNaughton 1986) to
each grid point and then summing over all grid points. The inputs are the net
radiation flux density absorbed by the leaf surface, the water vapour
saturation deficit of the ambient air, atmospheric pressure, leaf boundary layer
and stomatal conductances (Wang and Jarvis 1990).
Photosynthesis is estimated through a mechanistic C3 photosynthesis model
developed by Farquhar and Von Caemmerer (1982) and stomatal
conductance is estimated through a more empirical formulation, described by
Ball et al. (1987). Inputs for photosynthesis include leaf temperature, the leaf
boundary and stomatal and mesophyll conductances. Respiration is
calculated for leaves, branches and the stem/trunk.
Importantly MAESTRA does not attempt to simulate changes in soil water
content which is very important for micro-irrigated fruit tree orchards. In
addition, this model is unnecessarily complex for our purposes due to its
29
three-dimensional nature. Whilst young orchards are three-dimensional, as
they mature and form hedgerows the orchard becomes two-dimensional and,
as we will be quantifying water use in mature canopies, it will not be
necessary to use a three dimensional model.
3.2 Specific crop growth models
In a literature search conducted by Gary et al. (1998) they found that apple,
peach and kiwifruit represent half of the references on modelling of fruit crops.
Although difficult to parameterise these models are often very accurate due to
the species specific nature of carbon partitioning to various organs.
3.2.1 Pecan tree growth model
A simulation model of pecan growth and yield was developed by Andales et
al. (2006) based on an existing growth-irrigation scheduling model (GISM) (Al-
Jamal et al. 2002) as a tool for managing irrigation and the amount of pruning
required and the timing thereof. Modelling yield in fruit trees is complicated by
the alternate bearing habit of many fruit tree species, which is often a carry-
over from the previous season’s growth, as carbohydrate reserves from the
previous season impact flowering and yield in the current season. This model
simulates irrigation, alternate bearing, shoot biomass allocation and growth on
a daily basis. Figure 8 illustrates a flow chart of the model.
The irrigation object simulates pecan evapotranspiration, using the equation
developed by Samani and Pessarakli (1986) or Penman (Snyder and Pruitt
1992) and an adjusted crop coefficient, soil water balance and water stress.
The calculated non-stressed ET for a closed canopy is reduced by soil
moisture stress (Ks) and a canopy scale factor (Kca). The canopy scale factor
decreases ET from a closed canopy to an amount associated with the percent
cover at each simulation time interval (Andales et al. 2006). The soil moisture
stress function is dependent on the water holding capacity of the soil, the
30
rooting depth and the soil moisture at each time interval. The soil moisture
level at each particular interval takes into account precipitation.
Figure 8: Overall flow chart of the pecan model (Andales et al. 2006).
The biomass allocation object calculates the potential biomass allocation
ratios to different branches and the trunk. The model determines crown
distribution by separating the canopy into levels through successive
numbering of branching i.e. the trunk is level 1 and branches originating from
the trunk are level 2. The branches are distributed uniformly among north,
east, south, west and top side, i.e. 20% of the total number of branches is
located in each sector. The potential yearly growth is calculated according to
the original cross-section area of each branch and trunk, new growth cross-
section area, branch length, number and density. From this, the biomass
allocation ratio is determined.
The pruning object simulates removal of branches and affects the objects of
irrigation, biomass allocation ratios and alternate bearing. Shoot biomass
allocation ratios are adjusted according to pruning inputs. Nut yield and bud
growth rate are adjusted according to the calculated pruning coefficient (Kp).
31
The alternate bearing object simulates carbohydrate reserve amount in the
roots in order to determine fluctuations in yield from year-to-year. This object
also takes into account pruning. Finally, the growth object simulates tree and
nut growth and allocates the biomass components to the tree components
according to ET, WUE, water stress, allocation ratios, pruning effects and the
carbohydrate reserve amount. The allocation of aboveground dry matter is
allocated in the following order: leaves, nuts, reserve carbohydrate pools,
branches and the trunk. The leaf area per tree (m2 tree-1) is modelled by
multiplying total leaf biomass per tree by the specific leaf area (m2 kg-1).
Seasonal growth of each organ is controlled by critical growth stages
expressed as thermal time. Flow diagrams for the various objects included in
this model are shown in Appendix C.
Inputs to the model include daily maximum and minimum temperature and
humidity, solar radiation, wind speed, rainfall and soil temperature. In addition,
irrigation time and amount, pruning time, maximum diameter of branches to
be pruned and sides to be pruned are also included. The growth simulation
requires several initial conditions including tree trunk radius, root depth, root
carbohydrate reserve amount and soil water. To illustrate the difficulty in
parameterising these crop specific growth models a complete list of
parameters for the pecan growth model is as follows: wood density (kg m-3),
lateral outermost branch angle from the horizontal (degrees); maximum LAI
(m-2 m-2); specific leaf area (m2 kg-1); root:shoot biomass ratio; number of
trees per hectare; tree spacing (m); soil water holding capacity (m m-1); initial
trunk radius (m); initial root depth (m); initial carbohydrate reserve (kg tree-1);
initial soil water (m m-1); maximum root depth (m); optimum carbohydrate
reserve in mid winter (kg tree-1); reserve ratio (RR) lower limit; equilibrium RR,
RRe (0-1); maximum leaf growth rate (kg tree-1 GDD-1, where GDD is growing
degree days); maximum bud growth rate in spring (kg tree-1 GDD-1); maximum
shell growth rate (kg tree-1 GDD-1); maximum kernel growth rate (kg tree-1
GDD-1); maximum husk growth rate (kg tree-1 GDD-1); root growth rate (mm
GDD-1); growing degree days (GDD) to bud break; GDDs of leaf
photosynthesis beginning; GDDs to pollination; GDDs to shell hardening;
32
GDDs to leaf fall; GDDs to shuck split (Andales et al. 2006). These
parameters were either measured by the authors or taken from literature.
The growth component of this model is too complex for our purposes, whilst
the irrigation object, which estimates transpiration, is not mechanistic enough
for our purposes. Note should, however, be made of the manner in which
potential yearly cross section can be calculated from the original cross-section
area and how reserve starch levels can be used to estimate alternate bearing.
3.2.2 PEACH
PEACH describes the daily and seasonal carbon balance of peach trees
(Grossman and DeJong 1994a), which is driven by competition amongst
individual, semiautonomous plant organs based on the organ’s growth
potential. Carbon assimilation, maintenance respiration and the growth of
vegetative and reproductive organs of peach trees are all simulated by the
model. Photosynthetic carbon assimilation is simulated using daily minimum
and maximum temperatures and solar radiation as inputs. Carbohydrate
partitioning is simulated based on sink strength, proximity to sources, and the
quantity of carbohydrate available (Grossman and DeJong 1994a). The sink
strength of an organ is based on its genetically determined organ growth
potential, i.e. the maximum rate at which the organ can accumulate dry matter
per unit time. This is closely related to the ability to unload assimilates from
the phloem (DeJong and Grossman 1992). Carbon is partitioned first to
maintenance respiration, then to leaves, fruits, stems and branches and finally
the trunk (Figure 9). Residual carbohydrate from aboveground growth is used
to support root growth. Sink strength can be altered by suboptimal
environmental conditions and/or insufficient available resources e.g.
temperature and water availability.
PEACH is a state-variable model where fruit (number at full bloom, number at
thinning and weight), leaf weight, current-year stem weight, branch weight,
trunk weight and root weight are the state variables, and minimum and
33
maximum air and soil temperature, degree days and solar radiation are the
driving variables. The rate variables that characterise carbohydrate
assimilation and utilization were derived from previous in depth studies of
photosynthesis, respiration and growth potential in peach trees (DeJong and
Goudriaan 1989, DeJong et al. 1990, Grossman 1993, Grossman and
DeJong 1994b).
Figure 9: Flow diagram indicating the partitioning of carbon by the PEACH
model (Grossman and DeJong 1994). Boxes are state variables and valves
are rate variables. Solid lines represent carbon flows and dashed lines
represent information flows.
This brief description of the model illustrates the in-depth physiological studies
that are required in order to accurately parameterise the model. This includes
studies of photosynthesis, respiration and growth potential. These kinds of
34
studies are beyond the scope of this project. A detailed account of the
phenology of the species to be studied, together with accurate determinations
of leaf area should be sufficient to account for changes that occur in the
canopy during any season. However, as this model has been parameterised it
could be included in an evapotranspiration model in order to accurately
simulate canopy growth.
3.2.3 ‘CITROS’ – A Dynamic Model of Citrus Productivity
‘CITROS’ is based on a earlier citrus model by Goldschmidt and Monselise
(1977) who suggested that there are three stages in which “a decision should
be taken by the tree” in quantitative terms: how many flowers to produce, how
many fruit to set and how much will the fruit enlarge? Following this, a
mathematical model was developed based on empirical assumptions and
semi-quantitative information, which described alternate bearing and was able
to predict the impact of fruit thinning on final yield. ‘CITROS’ has been
developed to identify and quantify productivity problems, predict yields and
devise methods to optimise citrus production (Bustan et al. 1999). The model
is based on the assumption that when all the needs are optimally managed,
dry matter production and allocation become the fundamental processes that
limit productivity. Parameters that required determination include, the potential
growth rate of the fruit, relative growth rate of fruit under continuous optimum
conditions, conversion coefficient from fresh to dry matter (kDM) and a
conversion factor from dry matter to glucose (I/YG), coefficient of maintenance
respiration response to temperature (Q10), daily carbon exchange rate of the
canopy (estimated to be 340 g glucose by Syvertsen and Lloyd (1994)), and
technical coefficients for the estimation of fruit drop and sensitivity to
deficiencies (Bustan et al 1999).
Temperature was used to estimate physiological time. Effective Heat Units
(EHU) are used and are based on an optimum response curve of citrus to
temperature. This allows the negative effect of high temperature on growth to
be predicted and it accounts for the minimum temperature at which growth is
35
possible. The relative growth rate of the fruit (RGROPT), under continuous
optimal conditions, is related to temperature by dividing the potential relative
growth rate (RGRP, determined under sink-limited growth) by a temperature
coefficient (the ratio of actual accumulated EHU and the maximum EHU).
The potential growth rate function (GRPOT) can then be expressed as the
product of RGROPT, the current fresh weight of the fruit and the current
temperature coefficient (kT).
As with most growth models, ‘CITROS’ distinguishes between growth and
maintenance respiration and gives priority to maintenance respiration (Bustan
et al. 1999). In order to calculate maintenance respiration (rm), growth
respiration is subtracted from total respiration. Growth respiration is calculated
from dry weight composition (McDermitt and Loomis 1981) and the response
to temperature is assumed to be the same as that for growth rate. The
product of fruit dry weight (w), rm and kdTr (temperature response coefficient)
divided by 1.466 (to convert CO2 to glucose) gives the demand for glucose by
fruit maintenance respiration (DEMr). Priority is given to the fulfilment of DEMr
and only the remaining carbohydrates are available for growth. The total
amount of carbohydrates required daily is dependent on the number of fruits
on the tree, which varies greatly during the first few months of fruit
development. The abscission of fruit 80 days after anthesis (DAA) has also
been accounted for in the model, by including a mechanism of self-thinning
which responds to carbohydrate shortages. Photosynthetic rates were
adopted from a previous publication (Syvertsen and Lloyd 1994) and adapted
to local conditions using the EHU method (Bustan et al. 1999). Root demand
for carbohydrates has not been accounted for in this model.
4. DISCUSSION AND CONCLUSIONS
The increasing stress on water resources in South Africa has resulted in the
identification of the need to improve knowledge on water use of fruit tree
species. This will allow the more efficient scheduling of irrigation and the
issuing of water licenses that adequately reflect water requirements of fruit
36
tree orchards. As it is virtually impossible to measure water use under all the
possible combinations of climate, soils and management conditions in South
Africa, it is necessary to develop a model, or verify existing models, which can
accurately simulate water use of fruit trees across all conditions. Modelling
evapotranspiration in orchards is complex due to the discontinuous nature of
the canopy, the localised irrigation (micro- or drip) used in orchards and the
fact that this is a perennial crop, with carryover effects from the previous
season impacting the current season’s growth. It is therefore important that
the correct input variables are chosen and measured in order to accurately
parameterise the model.
As it is vital that the chosen model is able to extrapolate water use of fruit tree
species over a wide range of conditions and management practices it will be
necessary to use a mechanistic approach, where a thorough understanding of
the mechanisms driving transpiration is evident. This largely eliminates
models based on empirical relationships, which can seldom be used in
conditions outside the environment in which they were calibrated. It is also
important that the model should be able to differentiate between water-supply-
or atmospheric-demand-limited water uptake, which implies that
measurements should take into account the soil-plant-atmosphere continuum.
This review has covered both evapotranspiration models and growth models.
Whilst evapotranspiration models attempt to estimate water use of plants,
growth models are largely concerned with carbon assimilation and partitioning
in order to predict yield in many instances. These growth models can be
incorporated into evapotranspiration models in order to accurately “grow the
canopy” over a season, thereby enabling accurate estimations of water use as
the canopy dimensions change. These models can, however, be difficult to
parameterise and as a result the number of input variables needed to be
quantified is drastically increased. Tables 2 to 5 list the variables and
parameters required for each of the evapotranspiration and growth models
included in this review. The number of input variables and difficulty in
parameterising growth models is clearly illustrated in Table 5.
37
Table 2: Variables that must be quantified for the evapotranspiration models
SWB-2D Penman-Monteith FAO 56 SAPWAT Radiation
interception Crop factor Rana et al.
2005 Pereira et al. 2006
Priestley- Taylor
Net radiation Net radiation Day of year Max. and min. air temperature Net radiation Net radiation
Net radiation over a grass reference
Min., max. and mean air temperature
Min., max. and mean air temperature
Daily solar radiation Solar radiation Wind speed Wind speed Average air
temperature
Humidity (saturated vapour pressure deficit)
Humidity (saturated vapour pressure deficit)
Rainfall and irrigation amounts
Humidity Friction velocity Air temperature
Wind speed Wind speed Min. and max. daily temperatures
Wind speed Soil heat flux
Humidity Rainfall and irrigation amounts
Air temperature
Wind speed Vapour pressure deficit
Rainfall
38
Table 3: Parameters required for the evapotranspiration models
SWB-2D Penman-Monteith FAO 56 SAPWAT Radiation
interception Crop factor Rana et al.
2005 Pereira et al. 2006
Priestley- Taylor
Length of crop growth stages
Length of crop growth stages Longitude Length of growth
stages
Empirical calibration coefficients, a and b for the canopy resistance
Canopy leaf area Leaf area
Crop factors Crop factors Standard meridian Crop factors Mean orchard
height
Leaf area of the grass reference surface
Psychrometric coefficient
Threshold point at which soil water limits transpiration
Planting date Latitude Initial max. rooting depth
Psychrometric coefficient Altitude Altitude
Altitude Threshold point at which soil water limits transpiration
Row width & orientation
Initial max. crop height Altitude Atmospheric
pressure Atmospheric pressure
Atmospheric pressure Leaf area index Ellipse height and width Planting date
Atmospheric pressure
Latent heat of vaporization α = 1.26
Latent heat of vaporization Crop height Bare stem
height Altitude Psychrometric coefficient
Psychrometric coefficient Rooting depth Extinction
coefficient Latitude
Leaf resistances Absorptivity
Volumetric water content at field capacity and permanent wilting point
Irrigation type Leaf area density Row spacing
39
Irrigation frequency Bulk density of the soil
Wetted diameter of irrigation
Wetted diameter
Volumetric water content at field capacity and permanent wilting point
Distance between microjets/drippers
Altitude Initial volumetric soil water content
Fraction of roots in the wetted zone
Atmospheric pressure Wetted diameter of irrigation
Latent heat of vaporization Rooting depth
Psychrometric constant
Fraction of roots in the wetted volume of soil
40
Table 4: Variables that must be quantified for SEBAL and the various growth models
SEBAL MAESTRA Pecan PEACH ‘CITROS’
Satellite images Day of year Daily max. and min. temperature
Min. and max. air temperature Days after anthesis
Surface temperature Net radiation flux density absorbed by the leaves Humidity Soil temperature Air temperature
Shortwave atmospheric transmittance PAR flux density Solar radiation Degree-days No. of fruit per tree
Vegetation height Air and leaf temperature Wind speed Solar radiation Fruit weight
Leaf area index Rainfall
Wind speed Soil temperature
Atmospheric CO2 above the canopy Irrigation time and amount
Water vapour saturation deficit Pruning time
Atmospheric pressure Max. diameter of branches to be pruned
Soil surface temperature Side of the tree to be pruned
Tree trunk radius
Root depth
Root carbohydrate reserve amount
41
Table 5: Parameters required for SEBAL and the various growth models
SEBAL MAESTRA Pecan PEACH ‘CITROS’
Thermal infrared emissivity of the atmosphere Hemisphere Wood density Fruit number at bloom Maintenance respiration
Soil heat flux Latitude Lateral outermost branch angle from the horizontal
Fruit number at thinning (defruited, heavily thinned at bloom, thinned at two weeks, thinned at four weeks, thinned at eight weeks, unthinned)
Optimum and minimum temperature for growth
Surface roughness length Longitude Maximum LAI Individual fruit weight Coefficient of maintenance respiration response to temperature
Friction velocity Slope Specific leaf area Leaf weight Max. canopy photosynthesis
Monin-Obukhov length Plot dimensions Root:shoot biomass ratio Current-year stem weight Potential relative growth rate
Total number of trees Number of trees per ha Branch weight Dry weight composition
Transmittance and reflectance of PAR, NIR and thermal radiation of leaves
Tree spacing Trunk weight
Reflectance of PAR, NIR and thermal radiation at the soil surface
Soil water holding capacity Root weight
Inclination angle of leaves Initial trunk radius Rate variables for growth potential
Leaf area density Initial root depth Rate variables for photosynthesis
Leaf age distribution Optimum CHO reserve in mid-winter
Rate variables for respiration
42
Quantum yield Equilibrium reserve ratio (RR) Specific respiration rate
Maximum rate of photosynthesis RR lower limit
Maintenance respiration rate (leaf, current-year stem, branch, trunk, root and fruit)
Empirical approach: convexity of photosynthesis light response curve
Max. leaf growth rate Growth respiration coefficient
Mechanistic approach: max. rate of carboxylation and potential electron transport, effective Michaelis-Menton constant for CO2, initial slope and convexity of the light response curve of the potential electron transport
Max. bud growth rate in spring Relative growth rate
Temperature coefficient of the dark respiration rate Max. shell growth rate Net sink strength of growing
organs
dark respiration at leaf temperature of 0.0°C Max. kernel growth rate
coefficients defining the temperature response of the CO2 compensation point
Max. husk growth rate
Root growth rate
Growing degree days (GGD) to bud break
GDDs of leaf photosynthesis beginning
GDDs to pollination, shell hardening, leaf fall and shuck split
43
In terms of evapotranspiration models, FAO56 (Allen et al. 1998) is the most
widely used in fruit tree orchards due to its physiological and biological basis
(Pereira et al. 2006). The four-stage approach for the canopy size works well
in field crops and is largely applicable to deciduous fruit crops, however, it is
unlikely that such an approach will adequately accommodate evergreen
species, such as citrus and macadamia, which grow in flushes and at any one
stage will have leaves of vastly different ages on the tree, with different
associated resistances. Crop factors also assume that plant growth and
development is dependent on calendar time but thermal time (degree days)
and water supply are important influences on canopy development (Ritchie
and NeSmith 1991). A more mechanistic approach for converting ETo,
estimated using the Penman-Monteith equation, to crop transpiration is
therefore required. Both Rana et al. (2005) and Pereira et al. (2006)
attempted this. Rana et al. (2005) included estimates for canopy resistance,
climatic resistance and aerodynamic resistance in an adapted Penman-
Monteith equation and concluded that this was a more accurate manner to
estimate ET in a Clementine orchard, than a constant crop factor during the
different growth stages. In contrast, Pereira et al. (2006) used the ratio
between canopy leaf area and the leaf area of the reference grass surface to
adjust ETo to ETc in a number of different orchards. While these methods
provide a more accurate manner to convert ETo to ETc for a given orchard,
they are not mechanistic enough and exclude soil conditions. In addition, the
method of Pereira et al. (2006) is based on an empirical relationship which
may not be applicable to all situations.
SAPWAT (Crosby and Crosby 1999) is based on FAO56 and thus encounters
the same shortfalls when trying to estimate water use of fruit tree orchards
over different environmental and management conditions. Although
SAPWAT3 (van Heerden et al. 2008) has tried to improve the prediction of the
crop factor curve, e.g. by allowing the crop factor curve to be sloped during
phase 3 of growth, these improvements need to be validated with
experimental data. As SAPWAT is primarily used as a planning tool it will be
extremely valuable for Water Use Associations, governmental organisations
44
and growers in South Africa to have access to improved crop factors for fruit
trees in order to accurately estimate water use of orchards. This will be
achieved through the accurate estimation of the input variables and the
characterisation of the growth stages required to construct the crop factor
curve (see Table 3 for the required parameters). The need to improve crop
factors stems from the ease with which water use can be estimated using
FAO56 or SAPWAT, which is very attractive to growers. As the accuracy of
estimated transpiration from ETo hinges on the appropriateness of the crop
factor, a more mechanistic approach for crop factor determination should
result in more accurate estimations of crop water use, which should
subsequently improve the efficiency of irrigation scheduling in South Africa.
SWB-2D, on the other hand, allows a more mechanistic approach for the
estimation of water use in fruit tree crops, as it attempts to account for the
complexity associated with hedgerow crops, by modelling radiation
interception across the discontinuous canopy and soil water content in a two
dimensional profile (Annandale et al. 2002). It also provides insight into the
soil-plant-atmosphere continuum, which allows the differentiation between
supply- and demand-limited water uptake. The biggest drawback of this model
is the perceived complexity, but it may be a very useful mechanistic approach
to generating orchard specific crop factors.
The advent of the modern computer and computer programming prompted
the development of numerous crop growth models. Annual crops were the
first to be modelled, followed by the more complex horticultural crops. As
mentioned, these models are difficult to parameterise, largely due to the
required measurements of photosynthesis and respiration that are needed in
order to accurately simulate carbon assimilation and partitioning in the plant.
The incorporation of such growth models in an evapotranspiration model
should allow the accurate estimation of water use over a season, as the
canopy and root system enlarges. However, it has been noted that if soil
water is not limiting, the transpiration will largely be determined by the leaf
area (Pereira et al. 2006). This is reflected in many of the models which
require leaf area as an input variable (see Table 3 and 4). Thus, while
45
modelling tree growth will undoubtedly contribute to a more mechanistic
approach to the estimation of evapotranspiration, it may be more expedient to
develop a reliable and simple method for estimating leaf area. This will
improve the water use estimations considerably without having to quantify
photosynthesis and respiration parameters. Numerous methods have been
used to determine leaf area, which includes Lang and Xiang (1986), Villalobos
et al. (1995), Wünsche and Lakso (1998), Jovanovic and Annandale (1998),
Broadhead et al. (2003) and Jonckheere et al. 2004).
Data needed to calibrate and validate models will be obtained by determining
sap flow rates. In addition, total evaporation will be determined either through
the use of scintillometry or the eddy covariance method (depending on
orchard layout and topography). The scintillometry technique integrates
evaporation rates from the soil and vegetation represented along a bean path.
Together with supporting data on net radiation, soil heat fluxes, wind speed,
air temperature and air pressure, scintillometry allows the calculation of mean
surface sensible heat along the light path. The latent heat fraction that
equates to the evaporation rate is derived from an energy balance equation.
Using the additional sap flow data, the soil evaporation component may be
deduced by subtraction, thereby allowing the different components of
evaporation to be quantified which can be used to compare model estimates
against.
As water use of fruit tree species needs to be estimated over a wide range of
environmental, soil and management conditions, a generic, mechanistic
model of evapotranspiration is required. Of the models reviewed SWB-2D
(Annandale et al. 2002) fits these requirements the best. Importantly, it
includes either an hourly- or daily-time step and can therefore be used in real-
time. The minimum input variables that need to be quantified therefore include
(Table 3): longitude, latitude, standard meridian, row width and orientation,
ellipse height and width, bare stem height, extinction coefficient, absorptivity,
leaf area density, bulk density of the soil, volumetric water content at field
capacity and permanent wilting point, initial volumetric soil water content,
wetted diameter of irrigation, rooting depth and fraction of roots in the wetted
46
zone (Annandale et al. 2002). Variables needed to run the model include day
of year, daily solar radiation, rainfall and irrigation amounts, minimum and
maximum daily temperatures, humidity and wind speed. The inclusion of
rainfall and rooting volumes in the model are very important as it should allow
the grower to make more efficient use of rain and therefore reduce
dependency on available water resources. If a crop specific growth model
exists that has already been parameterised, e.g. PEACH or ‘CITROS’, then
this could be incorporated in SWB-2D in order to mechanistically “grow a
canopy”. However, if unavailable or unsuitable the modelling of leaf area
could prove a far better parameter to accurately estimate water use. The
problem encountered with evergreen crops, such a citrus and macadamia,
where there are leaves of vastly different ages on the tree at any one time
could be partly overcome by including parameters found in the MAESTRA
model which accounts for this variability.
47
5. REFERENCES
AL-JAMAL MS, SAMMIS TW, MEXAL JG, PICCHIONI GA and ZACHRITZ
WH (2002) A growth-irrigation scheduling model for wastewater use in
forest production. Agricultural Water Management 56 57-79
ALLEN RG, PEREIRA LS, RAES D and SMITH M (1998) Crop
evapotranspiration: Guidelines for computing crop water requirements.
FAO Irrigation and Drainage Paper 56. FAO, Rome, Italy
ALLEN RG, MORSE A, TASUMI M, BASTIAANSSEN W, KRAMBER W and
ANDERSON H (2001) Evapotranspiration from Landsat (SEBAL) for
water rights management and compliance with multi-state water
compacts. Geoscience and Remote Sensing Symposium, 2001.
IGARSS '01. IEEE 2001 International 2 830-833
AMTHOR JS (1989) Respiration and Crop Productivity. Springer-Verlag, New
York, pp 215.
ANDALES A, WANG J, SAMMIS TW, MEXAL JG, SIMMONS LJ, MILLER
DR, GUTSCHICK VP (2006) A model of pecan tree growth for the
management of pruning and irrigation. Agricultural Water Management
84 77-88
ANNANDALE JG, BENADÉ N, JOVANOVIC NZ, STEYN JM and DU
SAUTOY N (1999) Facilitating irrigation scheduling by means of the
soil water balance model. Pretoria, South Africa. Water Research
Commission Report No. 753/1/99
ANNANDALE JG, CAMPBELL GS, OLIVIER FC and JOVANOVIC NZ (2000)
Predicting crop water uptake under full and deficit irrigation: an
48
example using pea (Pisum sativum L. cv. Puget). Irrigation Science 19
65-72
ANNANDALE JG, JOVANOVIC NZ, MPANDELI NS, LOBIT, P and DU
SAUTOY N (2002) Two dimensional energy interception and water
balance model for hedgerow crops. Pretoria, South Africa. Water
Research Commission Report No. 945/1/02
ANNANDALE JG, JOVANOVIC NZ, CAMPBELL GS, DU SAUTOY N and
BENADE N (2003) A two-dimensional water balance model for micro-
irrigated hedgerow tree crops. Irrigation Science 22 157 – 170.
ANNANDALE JG, JOVANOVIC NZ, CAMPBELL GS, DU SAUTOY N and
LOBIT P (2004) Two-dimensional solar radiation interception model for
hedgerow fruit trees. Agricultural and Forest Meteorology 121 207 –
225
BALL JT, WOODROW and BERRY JA (1987) A model predicting stomatal
conductance and its contribution to the control of photosynthesis under
different environmental conditions. In: Biggins I (ed) Progress in
Photosynthesis Research, Vol. 1v.5, Proceedings of the VII
International Photosynthesis Congress. Martinus-Nijhoff, Dordrecht,
The Netherlands. Pp 221-224
BASTAIAANSSEN WGM, MENENTI M, FEDDES RA and HOLTSLAG AAM
(1998) A remote sensing surface energy balance algorithm for land
(SEBAL) 1. Formulation. Journal of Hydrology 212-213 198-212
BROADHEAD JS, MUXWORTHY AR, ONG CK and BLACK CR (2003)
Comparison of methods for determining leaf area in tree rows.
Agricultural and Forest Meteorology 115 151-161
49
BUSTAN A, GOLDSCHMIDT EE and ERNER Y (1999) Progress in the
development of ‘CITROS’ – a dynamic model of citrus productivity.
Acta Horticulturae 499 69-80
CAMPBELL GS and DIAZ R (1988) Simplified soil-water balance models to
predict crop transpiration. In: Bidinger FR and Johansen C (eds)
Drought Research Priorities for the Dryland Tropics. ICRISAT, India, pp
15-26
CROSBY CT and CROSBY CP (1999) A computer programme for estimating
irrigation requirements and scheduling strategies in South Africa.
Pretoria, South Africa. Water Research Commission Report No.
624/1/99
DEJONG TM and GOUDRIAAN (1989) Modeling the carbohydrate economy
of peach fruit growth and crop production. Acta Horticulturae 245 103-
108
DEJONG TM and GROSSMAN YL (1992) Modeling the seasonal carbon
economy of deciduous fruit tree crops. In: Buwalda JG and Atkins TA
(eds) Third International Symposium on Computer Modeling in Fruit
Research and Orchard Management. Acta Horticulturae 313 21-28
DEJONG TM, JOHNSON RS and CASTAGNOLI SP (1990) Computer
simulation of the carbohydrate economy of peach crop growth. Acta
Horticulturae 276 97-104
FARQUHAR GD and VON CAEMMERER S (1982) Modeling of
photosynthetic response to environmental conditions. In; Lange OL,
Nobel PS, Osmond CB and Zeigler H (eds). Encyclopedia of Plant
Physiology, Vol. 12 D. Springer, Berlin. Pp 549-588
GARY C, JONES JW and TCHAMITCHIAN M (1998) Crop modeling in
horticulture: state of the art. Scientia Horticulturae 74 3-20
50
GOLDSCHMIDT EE and MONSELISE SP (1977) Physiological assumptions
toward the development of a citrus fruiting model. Proceedings of the
International Society for Citriculture 2 668-672
GROSSMAN YL (1993) The carbon economy of reproductive and vegetative
growth of a woody perennial, peach (Prunus persica (L.) Batsch):
growth potentials, respiratory demand and a simulation model. Ph.D.
Dissertation, University of California, Davis
GROSSMAN YL and DEJONG TM (1994a) PEACH: A simulation model of
reproductive and vegetative growth in peach trees. Tree Physiology 14
329-345
GROSSMAN YL and DEJONG TM (1994b) Carbohydrate requirements for
dark respiration by peach vegetative organs. Tree Physiology 14 3-48
JARVIS PG and MCNAUGHTON KG (1986) Stomatal control of transpiration:
scaling up from leaf to region. Advanced Ecological Research 15 1-48
JOVANOVIC NZ and ANNANDALE JG (1998) Measurement of radiant
interception of crop canopies with the LAI-2000 plant canopy analyser.
South African Journal of Plant and Soil 15 6-13
JONCKHEERE I, FLECK S, NACKAERTS K, MUYS B, COPPIN P, WEISS M
and BARET F (2004) Review of methods for in situ leaf area index
determination – Part I: theories, sensors and hemispherical
photography. Agricultural and Forestry Meteorology 121 19-35
JOVANOVIC NZ and ANNANDALE JG (1999) An FAO type crop factor
modification to SWB for inclusion of crops with limited data: Examples
for vegetable crops. Water SA 25 181-189
51
KATERJI N and PERRIER A (1983) Modélisation de l’évapotranspiration
réelle ETR d’une parcelled de luzerne: role d’un coefficient cultural.
Agronomie 3 513-521
LANDSBERG JJ and WARING RH (1997) A generalised model of forest
productivity using simplified concepts of radiation-use efficiency,
carbon balance and partitioning. Forest Ecology and Management 95
209-228
LANG ARG and XIANG Y (1986) Estimation of leaf area index from
transmission of direct sunlight in discontinuous canopies. Agricultural
and Forestry Meteorology 37 229-243
MARCELIS LFM, HEUVELINK E and GOUDRIAAN J (1998) Modelling
biomass production and yield of horticultural crops: a review. Scientia
Horticulturae 74 83-111
MCDERMITT DK and LOOMIS RS (1981) Elemental composition of biomass
and its relation to energy content, growth efficiency and growth yield.
Annals of Botany 48 275-290
MEDLYN BE (2004) A MAESTRO retrospective. In: K. McNaughton, Editor,
Forests at the Land–Atmosphere Interface, CAB International (2004),
pp. 105–121.
MONSELISE SP and GOLDSCHMIDT EE (1982) Alternate bearing in fruit
trees. Horticultural Reviews 4 128-173
MONTEITH JL (1965) Evaporation and the environment. In: Fogg GE (ed)
The State and Movement of Water in Living Organism. Proceedings of
the XIX Symposium on Soc. Exp. Biol. Academic Press, New York. Pp
205-234
52
NICOLAS E, TORRECILLAS A, ORTUÑA MF, DOMONGO R and ALARCÓN
JJ (2005) Evaluation of transpiration in adult apricot trees from sap flow
measurements. Agricultural Water Management 72 131-145
PASSIOURA JB (1996) Simulation models: science, snake oil, education or
engineering? Agronomy Journal 88 690-694
PEREIRA AR, ANGELOCCI LR, VILLA NOVA, NA and SENTELHAS PC
(2001) Estimating single tree net radiation using grass net radiation
and tree leaf area. Urban Forestry and Urban Greening 2 19-29
PEREIRA AR, GREEN S and VILLA NOVA NA (2006) Penman-Monteith
reference evapotranspiration adapted to estimate irrigated tree
transpiration. Agricultural Water Management 83 153-161
PEREIRA AR, GREEN SR and VILLA NOVA NA (2007a) Relationships
between single tree canopy and grass net radiations. Agricultural and
Forest Meteorology 142 45-49
PEREIRA AR, GREEN SR and NOVA NAV (2007b) Sap flow, leaf area, net
radiation and the Priestley-Taylor formula for irrigated orchards and
isolated trees. Agricultural Water Management 92 48-52
RANA G, KATERJI N and DE LORENZI F (2005) Measurement and
modelling of evapotranspiration of irrigated citrus orchard under
Mediterranean conditions. Agricultural and Forest Meteorology 128
199-209
RITCHIE JT and NESMITH DS (1991) Temperature and Crop Development.
In: Hanks RJ and Ritchie JT (eds) Modeling plant and soil systems.
(ASA, CSSA and SSSA Agronomy Monograph No. 31) Madison, WI,
USA, pp5-29
53
ROUX AS (2006) Increase in water use efficiency: Western Cape Province,
South Africa. CAB International.
SAMANI ZA and PESSARALI M (1986) Estimating potential crop
evapotranspiration with minimum data in Arizona. Transactions of the
American Society for Agricultural Engineering 29 522-524
SMITH M (1992a) CROPWAT – A computer program for irrigation planning
and management. FAO Irrigation and Drainage Paper 46. FAO, Rome,
Italy
SMITH M (1992b) Expert consultation on revision of FAO methodologies for
crop water requirements. FAO, Rome, Italy, 28-31 May 1990
SMITH M, ALLEN RG and PEREIRA LS (1996) Revised FAO methodology
for crop water requirements. Proceedings of the International
Conference on Evapotranspiration and Irrigation Scheduling, San
Antonio, Texas, USA. Pp 133-140
SNYDER RL and PRUITT WO (1992) Evapotranspiration data management
in California. In: Presented at the American Society for Civil
Engineering Water Forum ‘92’, Baltimore, MD, August 2-6
STEVENS JB, DUVEL GH, STEYN GJ and MAROBANA W (2005) The
range, distribution and implementation of irrigation scheduling models
and methods in South Africa. Pretoria, South Africa. Water Research
Commission Report No. 1137/1/05
SYVERTSEN JP and LLOYD JJ (1994) Citrus. In: Schaffer B and Andersen
PC (eds) Handbook of Environmental Physiology of Fruit Crops. Vol. II:
Subtropical and Tropical Crops. CRC Press Inc., Boca Raton, Florida
VAN HEERDEN P and CROSBY C (2002) SAPWAT User’s manual.
http://www.sapwat.org.za
54
VAN HEERDEN PS, CROSBY CT, GROVÉ B, BENADÉ N, PRETORIUS E,
TEWOLDE MH and NKUMBULE S (2008) Integrating and upgrading of
SAPWAT and PLANWAT to create a powerful and user-friendly
irrigation water planning tool. Concept Final Report to the Water
Research Commission K5/1578//4
VILLALOBOS FJ, ORGAZ F and MATEOS L (1995) Non-destructive
measurement of leaf area in olive (Olea europea L.) trees using a gap
inversion method. Agricultural and Forestry Meteorology 73 29-42
WAGENMAKERS PS (1995) Light relations in orchard systems. Dissertation.
Wageningen Agricultural University, Wageningen
WANG YP and JARVIS PG (1990) Description and validation of an array
model—MAESTRO. Agricultural and Forest Meteorology 51 257–280.
WÜNSCHE JN and LAKSO AN (1998) Comparison of non-destructive
methods for estimating leaf area of apple tree canopies. Acta
Horticulturae 243 175-184
WEBSITES
SAPWAT (2008) http://www.sapwat.org.za (accessed 14.02.2008)
55
6. APPENDIX A - FLOW DIAGRAM INDICATING THE PROCEDU RE
FOR THE ESTIMATION OF CROP EVAPOTRANSPIRATION (ET C)
Calculate Reference ET o
Select stage lengths Verify and supplement locally
Kcb + Ke Dual crop coefficient
Select values for Kcb ini, Kcb mid & Kcb end
Kc
Single crop coefficient
Adjust Kcb min & Kcb end to local climatic conditions
Construct Kcb curve
Determine daily Ke values for surface evaporation
Kc = Kcb + Ke
Select values for Kc ini, Kc mid & Kc end
Adjust Kc ini to reflect wetting frequency
of soil surface
Adjust Kc mid & Kc end to local climatic conditions
Construct Kc curve
ETc = KcETo
56
7. APPENDIX B - FLOW CHART OF THE VARIOUS SUB-MODEL S
WITHIN THE SWB-2D MODEL
Figure 1: Flow diagram of the two-dimensional energy interception model for hedgerow tree crops
57
Figure 2: Flow diagram of the two-dimensional soil water balance model for hedgerow tree crops
58
Figure 3: Flow diagram of the FAO-type crop factor model
59
Figure 4: Flow diagram of the cascading soil water balance for tree crops under localised irrigation
60
8. APPENDIX C - FLOW CHART OF THE VARIOUS OBJECTS W ITHIN
THE PECAN TREE GROWTH MODEL (ANDALES ET AL. 2006)
Figure 1: Flow chart of the irrigation object (Andales et al. 2006).
61
Figure 2: Flow chart of the shoot biomass allocation ratio object (Andales et al. 2006).
62
Figure 3: Flow chart of the pruning object (Andales et al. 2006).
Figure 4: Flow chart of the alternate bearing object (Andales et al. 2006).