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African Journal of Range & Forage Science
ISSN: 1022-0119 (Print) 1727-9380 (Online) Journal homepage: http://www.tandfonline.com/loi/tarf20
Estimating evapotranspiration in semi-arid
rangelands: connecting reference to actual
evapotranspiration and the role of soil
evaporation
Onalenna Gwate, Sukhmani K Mantel, Andiswa Finca, Lesley A Gibson, Zahn
Munch & Anthony R Palmer
To cite this article: Onalenna Gwate, Sukhmani K Mantel, Andiswa Finca, Lesley A Gibson,
Zahn Munch & Anthony R Palmer (2018): Estimating evapotranspiration in semi-arid rangelands:
connecting reference to actual evapotranspiration and the role of soil evaporation, African Journal
of Range & Forage Science, DOI: 10.2989/10220119.2018.1505779
To link to this article: https://doi.org/10.2989/10220119.2018.1505779
Published online: 23 Nov 2018.
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African Journal of Range & Forage Science 2018: 1–9
Printed in South Africa — All rights reserved
Copyright © NISC (Pty) Ltd
AFRICAN JOURNAL OF
RANGE & FORAGE SCIENCE
ISSN 1022-0119 EISSN 1727-9380
https://doi.org/10.2989/10220119.2018.1505779
African Journal of Range & Forage Science is co-published by NISC (Pty) Ltd and Informa UK Limited (trading as Taylor & Francis Group)
This is the nal version of the article that is
published ahead of the print and online issue
Evapotranspiration (ET) is one of the most important
components of the hydrological cycle in terms of global
change studies but remains one of the most difficult to
determine. Evapotranspiration comprises water loss from
various surfaces and transpiration through plant leaves.
Transpiration (T) is closely coupled with plant produc-
tion, while Es reflects the so-called ‘unproductive’ loss of
water to the atmosphere (Kool et al. 2014). As many parts
of the world are increasingly becoming water limited, the
need to account for ET and its various components cannot
be overemphasised. More importantly, the increasing
world population requires improvements in water produc-
tivity, especially in water-limited environments (Molden et
al. 2010; Kool et al. 2014). Water productivity is the ratio of
the net benefits from agricultural activities to the amount of
water consumed to yield those benefits (Molden et al. 2010).
Therefore, it is prudent to enhance productive water use and
reduce the so-called ‘unproductive’ evaporation. Partitioning
of ET into its various components such as Es, and T
provides a sound starting point for enhancing water produc-
tivity. Consequently, several algorithms, ranging from data
intense to parsimonious ones exist to account for total ET.
In data scarce areas, simple models using readily available
input data are useful for ET modelling. Models have been
developed that are based on empirical relationships between
observed ET and another independent variable, such as
the leaf area index (LAI) or vegetation indices (VIs) that are
known to correlate with ET, for example, the normalised
difference vegetation index (NDVI) and the enhanced
vegetation index (EVI) (Nagler et al. 2005a, 2013; Palmer et
al. 2014). Consequently, models have been developed trying
to link water vapour fluxes to canopy attributes. These have
mainly revolved around connecting ET0 to actual evapotrans-
piration (AET) by using crop coefficients, or using LAI or VI
as scalars (Allen et al. 1998; Nagler et al. 2013; Palmer et al.
2014). The empirical relations take the following forms:
ET = KcET0 (1)
where Kc is the crop coefficient and ET0 is the reference
evapotranspiration.
Alternatively, vegetation indices could be used to connect
ET0 to AET, whereby Kc is replaced by VIs:
ET = f (VI)*ET0 (2)
These approaches of determining ET have been widely
applied in crops and natural ecosystems (Allen et al.
1998; Nagler et al. 2013). However, there are a number
of challenges and uncertainties related to the use of LAI
or VIs approaches to determine ET. For example, they
are unable to detect changes in stomatal behaviour. The
Estimating evapotranspiration in semi-arid rangelands: connecting
reference to actual evapotranspiration and the role of soil evaporation
Onalenna Gwate1* , Sukhmani K Mantel1 , Andiswa Finca2, Lesley A Gibson3 , Zahn Munch4 and Anthony R
Palmer1,2
1 Institute for Water Research, Rhodes University, Grahamstown, South Africa
2 Agricultural Research Council–Animal Production Institute, Grahamstown, South Africa
3 School of Engineering, University of Edinburgh, Edinburgh, EH9 3JL, UK
4 Department of Geography and Environmental Studies, Stellenbosch University, Stellenbosch, South Africa
* Corresponding author, email: onalennag37@gmail.com
In a context of water scarcity, efforts to increase landscape production should focus on improving water
productivity. This requires an appreciation of the various components of evapotranspiration (ET), including
soil evaporation (Es) because the latter reflects ‘unproductive’ water loss. Both complex and simple algorithms
have been developed to determine ET. In data scarce areas, developing and testing parsimonious algorithms is
useful. This study sought to improve a simple single layer ET model by incorporating an Es component. Empirical
methods were also explored to predict ET from vegetation indices (VIs), leaf area index (LAI) and reference
evapotranspiration (ET0). A large aperture scintillometer and an eddy covariance (EC) system were used to validate
the proposed algorithm at three sites over Grasslands and Albany Thicket biomes in the Eastern Cape, South
Africa. There was good agreement between the observed and predicted ET with RMSE of 0.30–0.58 mm d−1 when
average daily observed ET was 0.43–3.24 mm. The VIs had moderate correlations with the observed data due to the
significant role played by Es (65%–84%) across the sites and stomatal conductance at the Albany Thicket site. The
simple algorithms developed would make determining ET easier in data scarce regions.
Keywords: Grassland, leaf area index, Thicket, vegetation indices
Introduction
Gwate, Mantel, Finca, Gibson, Munch and Palmer2
dynamics in stomatal behaviour greatly influence the carbon
and water vapour exchanges over canopies, which in turn
affect the partitioning of total ET into Es and T. In addition,
approaches employing LAI and VIs to connect potential
ET and actual ET are not able to determine Es. However,
it is well established that Es is significant in drylands with
LAI < 2.5 and can contribute ~80% of total ET (Leuning et
al. 2008; Mu et al. 2011; Morillas et al. 2013). Therefore, in
such systems, there is a need for algorithms that can also
capture Es in order to accurately characterise total ET.
Other approaches tend to combine these VIs with other
meteorological data, such as air temperature and net
radiation (Rn), in simple or non-linear and multiple linear
regressions in order to develop predictive equations (see
review by Glenn et al. 2008). These empirical relations are
very crucial in data scarce areas and where there is no ET
validation equipment. In South Africa, there are relatively few
micrometeorological observation towers, although scientific-
grade weather stations are becoming common. Therefore,
the development of such simple empirical algorithms may be
useful in deriving ET for all biomes of the country.
The main aim of this study was to explore an improved
Penman–Monteith-based model formulation over the
grasslands and Albany Thicket vegetation by advancing
the preliminary work of Palmer et al. (2014), conveniently
called the Penman–Monteith–Palmer (PMP) algorithm.
Palmer et al. (2014) reckoned the need for developing and
testing parsimonious ET models in data scarce areas such
as rangelands of southern Africa. This study adds an Es
component to the preliminary work of Palmer et al. (2014)
in order to improve ET estimation in semi-arid rangelands
characterised by short and open canopies. The proposed
algorithm has the advantage of using widely available
weather data, surface albedo as well as LAI and it does not
require observed ET to calibrate some parameters and this
is crucial in data scarce areas. Secondly, this study sought
to develop simple empirical algorithms for predicting ET in
rangelands using observed ET on one hand and ET0 as
well as LAI on the other. Such empirical relations may help
in scaling up ET from point observations to the landscape
across the biomes of interest.
Theory
Based on the resource optimisation theory (Glenn et al.
2008), plants have evolved to scale foliage density in line
with resources availability. Hence, in vegetated surfaces,
AET approaches ET0 under ideal conditions of plentiful soil
moisture and soil fertility when plant root systems are able
to supply water to the atmosphere via stomata at a rate
almost corresponding to demand. Details of the PMP model
can be found in Palmer et al. (2014).
Modelling Es is quite a delicate issue because a good
model should be able to reproduce the rate of soil moisture
changes over time. However, it is well established that the
link between groundwater and the upper soil moisture is
one of the least understood hydrological processes (Wilcox
2010) and this exacerbates the problem. It is recognised
that the rate of Es follows three stages as a result of soil
physical and atmospheric characteristics (Kool et al. 2014).
Stage 1 denotes a period where Es is limited by available
energy (A) to drive ET and stage 2 where water loss is
strongly coupled with soil characteristics such as soil
moisture, soil hydraulic properties on one hand, and vapour
pressure deficit on the other. Stage 3 relates to a context
where Es is nil due to unavailable soil water (Morillas et
al. 2013). In order to capture these dynamics, the ratio of
equilibrium evaporation to precipitation method was adopted
(Zhang et al. 2010; Morillas et al. 2013). Many studies have
demonstrated that this approach was able to capture the
soil drying process (Zhang et al. 2010; Morillas et al. 2013;
Zhang et al. 2016). The approach has the advantage that
it simply uses rainfall and equilibrium evaporation data to
parameterise the fraction (f) of Es and there is no need for
parameter fine-tuning. Therefore, such simple models are
relevant in data scarce areas and can be used with sparsely
distributed weather stations to enable accounting for ET.
The proposed improved algorithm is presented as:
(3)
s
0
max
LAI
ET ET
LAI 1
A
f
ε
= ∗+
ε+
15
Zhang
eq, ,
15
min ,1
i
i
i
i
si
i
P
f
E
−
−
=
∑
∑
NIR red
NIR red
NDVI ρ −ρ
=ρ +ρ
NIR red
NIR red blue
EVI 2.5 6 7.5 1
ρ −ρ
=ρ +ρ − ρ +
where As is energy available to the soil, and the logistics of
its derivation can be found in Allen et al. (1998) and Morillas
et al. (2013); LAImax is the maximum leaf area index, ε is
the slope (∆) of the curve relating saturation water vapour
pressure to temperature divided by the psychrometric
constant (γ), and f is a factor modulating potential evapora-
tion from the soil and ranges between 0 and 1.
For the f value, this study adopted the precipitation and
equilibrium evaporation ratio method conveniently called the
fZhang (Zhang et al. 2010; Morillas et al. 2013):
s
0
max
LAI
ET ET
LAI 1
A
fε
= ∗+
ε+
15
Zhang
eq, ,
15
min ,1
i
i
i
i
si
i
P
f
E
−
−
=
∑
∑
NIR red
NIR red
NDVI ρ −ρ
=ρ +ρ
NIR red
NIR red blue
EVI 2.5 6 7.5 1
ρ −ρ
=ρ +ρ − ρ +
(4)
where pi is the accumulated daily precipitation and Eeq,s,i is
the daily soil equilibrium evaporation rate for day i over a
number of days (N); this study used N = 16 days (day i and
15 preceeding days).
Materials and methods
Study site
Three study sites were selected for testing and validating
the algorithm. These included two sites in the grassland
biome, one in the Southern Drakensberg Highland
Grassland (Truro farm) and the other in the East Griqualand
Grassland (Mucina et al. 2006), i.e. Somerton farm in the
northern Eastern Cape province, South Africa (Figure 1,
Table 1). The two grassland sites are situated approxi-
mately 14 km apart on freehold land where mixed farming is
practised. Extensive cattle and sheep production as well as
rainfed crop cultivation are key farming activities. The third
study site is situated in the Great Fish Thicket in the Albany
Thicket (AT) Biome on the eZulu Game Reserve (EGR) in
the south-western Eastern Cape. The succulent Thicket
vegetation at this study site has been used to support
extensive livestock farming (sheep and goats) since the
early 1800s and has since 1998 been converted to wildlife
ranching. There is no dryland crop cultivation, but irrigated
cultivation does occur along the Great Fish River.
African Journal of Range & Forage Science 2018: 1–9 3
Measurement of ET and micrometeorological variables
At the EGR site, ET was measured by an Integrated CO2/
H2O Open-Path Gas Analyser and 3D Sonic Anemometer
(IRGASON, Campbell Scientific Inc., Logan, UT, USA). The
EC system and details of instrumentation and data analysis
can be found in Gwate et al. (2016). At the grassland sites,
a Large Aperture Scintillometer (LAS; LAS MkII, Kipp and
Zonen BV, Delft, The Netherlands) was used for validating
the new algorithm. Details of the instrumental set up, data
processing and quality checks can be found in Gwate
(2018). Given that the proposed algorithm does not require
any calibration, the measurement and modelling periods
were similar at each study site (Table 1).
Meteorological data
To test the utility of sparsely located weather stations in ET
estimation over wide areas, daily meteorological data were
obtained from an automatic weather station (AWS) to derive
ET0 and As (Table 2). At Truro farm, there was no weather
station and as such the Agricultural Research Council’s
Somerton station was used, which was approximately
14 km away. However, a rainfall data set combining ground
and remotely sensed data called Tropical Applications
of Meteorology Using Satellite Data and Ground-Based
Observations (TAMSAT; Maidment et al. 2014; Tarnavsky
et al. 2014) was used in the calculation of the f values at
the Truro farm site since there was no weather station.
Gwate (2018) showed that TASMSAT rainfall data were
similar with those from an AWS at Somerton farm. Details
for deriving other meteorological data, such as atmospheric
pressure, vapour pressure and the procedures for gap-filling
meteorological data, can be found in Gwate (2018).
MOD 15A2 FPAR/ LAI product
The MODerate-resolution Imaging Spectroradiometer
(MODIS) provides 1 km spatial resolution data every day
in 36 spectral bands and these have been used to develop
several products. The MOD15A2 (FPAR/LAI) product
was acquired from the Oak Ridge National Laboratory
Distributed Active Archive Center (ORNL DAAC) website
(https://lpdaac.usgs.gov/dataset_discovery/modis/modis_
products_table/mod15a2). The 8-day average LAI was
extracted for the three areas of interest from the year 2000
to day of year (DoY) 318 in 2016. This provided the LAI
values used in the algorithm (Equation 3) to derive the ET.
MODIS vegetation indices (MOD13A2)
Vegetation indices are empirical measures of vegeta-
tion performance and include NDVI and EVI. Vegetation
indices are essentially indicative of the integrative
functions of a vegetated surface (Huete et al. 2002). The
16-day MOD13A2 product with a spatial resolution of
1 km was also used during this study and was acquired
from the ORNLP DAAC website (https://lpdaac.usgs.
gov/data_access/data_pool). The NDVI and EVI values
coinciding with the study period were extracted. The NDVI
is a normalised transform of the near infrared (NIR) to red
reflectance ratio, designed to standardise VI values to
between −1 and +1 and is expressed as:
s
0
max
LAI
ET ET
LAI 1
A
fε
= ∗+
ε+
15
Zhang
eq, ,
15
min ,1
i
i
i
i
si
i
P
f
E
−
−
=
∑
∑
NIR red
NIR red
NDVI ρ −ρ
=ρ +ρ
NIR red
NIR red blue
EVI 2.5 6 7.5 1
ρ −ρ
=ρ +ρ − ρ +
(5)
where ρ is the full or partially atmospheric-corrected
(for Rayleigh scattering and ozone absorption) surface
reflectance.
The EVI is an improvement on NDVI and it incorporates
an algorithm to reduce the effects of atmospheric scattering,
canopy background reflection and does not saturate in high
biomass areas as opposed to the NDVI (Huete et al. 2002).
The EVI formula is expressed as:
s
0
max
LAI
ET ET
LAI 1
A
fε
= ∗+
ε+
15
Zhang
eq, ,
15
min ,1
i
i
i
i
si
i
P
f
E
−
−
=
∑
∑
NIR red
NIR red
NDVI ρ −ρ
=ρ +ρ
NIR red
NIR red blue
EVI 2.5 6 7.5 1
ρ −ρ
=
ρ +ρ − ρ +
(6)
AFRICA
South
Africa
SOUTH
AFRICA
24° E
33° S
31° S
29° S
26° E 28° E 30° E
170 km
Truro
Somerton
eZulu
Queenstown
Grahamstown
Eastern
Cape
INDIAN OCEAN
Site name Latitude/Longitude ET data period Instrument Vegetation type Elevation (m) MAR (mm)
Somerton 31°09′02″ S, 28°23′03″ E DoY 309, 2015–
DoY 101, 2016
LAS East Griqualand Grassland 1 257 756
Truro 31°04′10″ S, 28°17′25″ E DoY 265–
DoY 308, 2015
LAS Southern Drakensberg
Highland Grassland
1 471 786
eZulu Game Reserve 33°01′08″ S, 26°04′47″ E DoY 283, 2015–
DoY 318, 2016
EC Great Fish Thicket (Albany
Thicket biome)
554 400
Table 1: Location and characteristics of study sites. MAR = mean annual rainfall
Figure 1: Location of the study sites at eZulu Game Reserve, Truro
farm and Somerton farm in Eastern Cape province, South Africa
Gwate, Mantel, Finca, Gibson, Munch and Palmer4
Nadir Bidirectional Reflectance Distribution Function
Adjusted Reflectance (NBRDF) product (MCD43B4)
The MCD43B product (Strahler and Muller 1999) was
used to obtain the surface albedo. This product provides
1 km reflectance data adjusted using the bidirectional
reflectance distribution function of MCD43B1 to model
values as if they were acquired from a nadir view (Strahler
and Muller 1999). Shortwave albedo is required in the
calculation of net radiation when the new algorithm is
applied. Hence, the MCD43B4 product was acquired
from the ORNL DAAC website (https://lpdaac.usgs.gov/
data_access/data_pool) and average 8-day albedo values
that coincided with the study period were extracted.
Subsequently, the equation developed by Liang (2001)
was applied to compute surface albedo.
Model evaluation
The mean absolute error (MAE) and root mean square
error (RMSE) were chosen as metrics to evaluate the
new algorithm. These indices indicate the extent of the
error in the simulated and measured ET and they have
the advantage of using units similar to variables under
consideration. The MAE is suitable for uniformly distributed
errors as it gives the same weight to all errors, whereas
the RMSE gives errors with larger absolute values more
weight, and hence it is necessary for evaluating data that
are normally distributed such as model errors (Chai and
Draxler 2014).The RMSE-observations standard deviation
ratio (RSR), which standardises RMSE using the observa-
tions standard deviation, was also used in order to give
insights as to what should be considered as low RMSE
(Moriasi et al. 2007). The percent bias (PBIAS) was
also computed to help decipher model over- and under-
estimation bias. Finally, simple linear regression using the
ordinary least square regression method was prepared
between the observed and predicted ET. The r 2, slope and
intercept of the linear regression between the observed
and modelled ET were also reported. These were chosen
because they are reflective of the extent to which simulated
ET reproduces the measured ET, while the r 2 shows the
proportion of variance in measured ET that is explained by
the model (Moriasi et al. 2007).
Development of predictive equations
Vegetation indices have been widely used to predict ET
over wide areas (Nagler et al. 2005b; Glenn et al. 2010;
Nagler et al. 2013). Data from the two grassland sites
were combined and the EGR data were used separately
in developing regressions to explore the possibility of
estimating ET in these biomes using VIs, LAI and ET0.
Simple linear, non-linear regression and the linear correla-
tion (r) of VIs (NDVI and EVI) against ET were also
generated to explore the nature of the relationship between
the observed ET and VIs. In this case 16-day ET was
summed in order to coincide with the availability of VI.
This relationship enabled the study to make a determi-
nation as to whether VIs can be used to predict ET in
rangelands similar to the study site. Furthermore, multiple
linear regressions of measured ET0 and LAI against ET
were developed for the grassland and the AT sites, respec-
tively, to develop simple algorithms for estimating ET in
data scarce areas.
Results
Environmental characteristics across the study sites
The environmental conditions varied greatly at each experi-
mental site (Table 3). The LAI was < 2 across the sites but
differed significantly, as the Kruskal–Wallis test revealed (p
< 0.05), with the lowest LAI being observed at the EGR site
(Table 3).
Model performance
The improved PMP algorithm resulted in a RMSE of
0.58 mm d−1 at Somerton and 0.39 mm d−1 at Truro in
a context where the observed daily mean ET was 3.24
and 2.23 mm, respectively. At the EGR the RMSE was
0.50 mm d−1 and this was largely unsystematic (Table 4) in
a context of a daily mean of 0.76 mm. The RSR was similar
(0.08–0.13) across sites (Table 4). The model tended to
slightly overestimate and underestimate observed ET at the
Truro and Somerton sites, respectively, as shown by the
PBIAS (Table 4). The unsystematic RMSE was relatively
higher than the systematic RMSE across the sites. When
data from the two grassland sites were combined, the
RMSE was within 18% of the observed mean daily ET
(3.01 ± 1.23 mm) against the modelled value of 3 ± 1.55 mm
(Table 4). Modelled soil evaporation accounted for 69%,
65% and 84% of the total modelled ET at Truro, Somerton
and EGR, respectively. At the EGR the growing season
(August–April) and non-growing season (May–July) RMSE
were 0.51 and 0.3 mm d−1, respectively, and the PBIAS was
negative for both seasons (Table 5). In the non-growing
season, the average EC ET was 0.43 ± 0.49, whereas in the
growing season it was 0.85 ± 0.66.
At the Somerton site, the improved algorithm under-
estimated ET at the beginning of the validation period but
intermittently overestimated ET after DoY 21, 2016. The
model also underestimated ET between DoY 89 and 94
(Figure 2a and b). A similar pattern was observed at the
Truro farm (Figure 2c and d). The underestimation coincided
with periods of reduced rainfall, whereas the overestimation
bias occurred during periods after rainfall events. A similar
pattern was observed at the EGR site (Figure 2e and f).
Weather parameter Instrument
Solar radiation (MJ m−2) Pyranometer (LI-200SA)
Relative humidity (%) and air temperature(°C) Vaisala HMP60 Temp/Humidity probe (HMP60)
Wind speed (m s−1) and direction (°) RM Young wind sentry wind set (10FT LEAD, Model 03001)
Rainfall (mm) TE525MM-L Texas Electronics Rain Gage 0.1 mm (0.00394 inch)
Table 2: Summary of instruments at the automated weather station
African Journal of Range & Forage Science 2018: 1–9 5
The linear regression between the observed and modelled
ET was significant (p < 0.001). The combined grassland
data set yielded a slope of 1.04 (r 2 = 0.73), whereas at
the EGR site a slope of 1.02 was obtained (r 2 = 0.52). At
both sites there was no positive autocorrelation (p > 0.05).
When the EGR data were separately analysed by seasons,
a slope of 1.02 and intercept of 1.1 mm were obtained for
the growing season (r 2 = 0.49). For the non-growing season,
a slope of 0.92 and intercept of 1.1 mm (r 2 = 0.49) were
obtained. The scatter plots of the relationships between the
observed and predicted ET over the entire validation periods
for the grasslands and EGR sites are presented (Figure 3).
The ET data were accumulated over 8-day periods to
coincide with each new MODIS 8-day LAI.
Predicting ET from vegetation indices and LAI
Using linear and non-linear regression, the relationship
between VIs and ET was weak (r 2 ≤ 0.3). The correla-
tion between ET and VI at the study sites is presented
(Table 6). The NDVI had a better correlation with ET
(p < 0.05), whereas the relationship between EVI and ET
was non-significant at EGR (p > 0.05). Using multiple
linear regressions, the 8-day average LAI and 8-day
accumulated ET0 were regressed against the observed
8-day accumulated ET. At the EGR, strong relations were
observed (r 2 = 0.35, F = 11.92, p < 0.001, N = 51, 8-day
periods). The equation is expressed as:
ET = 16*LAI + 0.004*ET0 − 0.17 (7)
Using the combined data from the grassland sites, signifi-
cant relationships were also found (r 2 = 0.65, F = 16.73,
p < 0.001, N = 20, 8-day periods) and the equation was:
ET = 14.19*LAI + 0.58*ET0 − 14.1 (8)
Discussion
Validity of observed ET
This study sought to advance the work of Palmer et al.
(2014) in order to accurately estimate total ET in semi-arid
rangelands. Although the two grassland sites were adjacent
to each other, environmental conditions differed during the
respective validation periods. Owing to the field campaign
approach adopted and logistical constraints, micrometeoro-
logical measurements could not be conducted across
the growing and non-growing season over the grassland
sites. Suffice to note that rainfall predominantly occurs
during the growing season months in the grasslands
study sites and much of ET takes place during this period.
The data collected were essentially for the wet growing
season although environmental conditions varied. For the
EGR site, data were collected for an entire year and as
such the experiment captured the seasonal water vapour
fluxes over the study area. The environmental conditions
at the grassland sites and the EGR site are different. For
example, long-term modelled mean annual rainfall are
756–786 and 400 mm y−1 at the grassland and the EGR
sites (Schulze 1997), respectively. Therefore, the valida-
tion took place under varied environmental conditions
and the improved model was largely able to capture the
dynamics of measured ET. In addition, uncertainties
associated with the inputs, especially MOD15A2 LAI and
MCD43B surface albedo, may have influenced the fluxes
derived. For example, errors in the MOD15A2 LAI introduce
uncertainties in the modelled ET and the tendency by
MOD15A2 LAI to overestimate LAI by up to 0.25 units has
been recognised (Huemmrich et al. 2005).
Model performance and evaluation
The model performed better over grassland as shown by
the RMSE, but the RSR was low across the grassland
and AT, suggesting that the model simulation was good in
both biomes. At the grassland sites, validation was done
during a generally wet period and the improved model
Environmental
parameter
Somerton
(N = 104)
Truro
(N = 29)
EGR
(N = 401)
Air temperature (°C) 20.22 ± 3.68 18.2 ± 2.5 19.5 ± 4.7
Relative humidity (%) 67.5 ± 29.4 58.2 ± 16.3 62.24 ± 12.84
Wind speed (m s−1) 1.41 ± 0.37 3.2 ± 0.78 1.73 ± 0.75
Net radiation (W m−2) 127.3 ± 55.6 99.3 ± 35 71.8 ± 52
ET (mm) 3.24 ± 1.24 2.23 ± 0.85 0.76 ± 0.65
ET0 (mm) 4.5 ± 2.1 4.8 ± 1.3 3.24 ± 1.48
SWC (m3 m−3) 0.22 ± 0.11 0.14 ± 0.02 0.09 ± 0.02
Rainfall (mm) 2.95 ± 5.86 1.7 ± 3.2 0.78 ± 2.5
LAI (m2 m−2) 1.32 ± 0.23 0.77 ± 0.14 0.39 ± 0.14
Table 3: Environmental conditions during the experiments at
Somerton and Truro farms and eZulu Game Reserve (EGR). Values
are the mean ± SD. ET = Evapotranspiration, ET0 = reference
evapotranspiration, SWC = soil water content, LAI = leaf area index
Statistic Somerton Truro Grassland
Combined EGR
MAE 0.50 0.19 0.45 0.32
RMSE 0.58 0.39 0.55 0.5
RSR 0.08 0.11 0.08 0.13
PBIAS 0.11 –0.38 0.04 –2.6
Systematic RMSE 20 14 24 18
Unsystematic
RMSE
31 13.5 31 63
Modelled ET
(mean ± SD)
3.21 ± 2.7 2.28 ± 0.62 3 ± 1.55 0.9 ± 0.77
Table 4: Model evaluation at Somerton farm (N = 104 d), Truro
farm (N = 29 d) and eZulu Game Reserve (EGR; N = 401 d).
MAE = Mean absolute error, RMSE = root mean square error,
RSR = RMSE-observations SD ratio, PBIAS = percent bias, ET =
evapotranspiration
Statistic Summer Winter
MAE 0.30 0.23
RMSE 0.51 0.30
RSR 0.13 0.08
PBIAS −2.3 −2.5
Systematic RMSE 19 22
Unsystematic RMSE 58 61
Modelled ET (mean ± SD) 1.03 ± 0.8 0.45 ± 0.38
Table 5: Model performance in summer (N = 312 d) and winter
(N = 89 d) at eZulu Game Reserve. MAE = Mean absolute error,
RMSE = root mean square error, RSR = RMSE-observations SD
ratio, PBIAS = percent bias, ET = evapotranspiration
Gwate, Mantel, Finca, Gibson, Munch and Palmer6
1
2
3
4
5
6
7
309
104
316
323
330
337
344
35
42
49
56
69
76
83
90
97
ET (mm)
2015 2016 2015
2015 2015
2016
(a)
LAS ET
Improved PM P ET
LAS ET
Improved PM P ET
5
10
15
20
25
30
35
309
316
323
330
337
344
35
42
49
56
69
76
83
90
97
RAINFALL (mm)
2015 20162015 2016
(b)
0.5
1
1.5
2
2.5
3
3.5
4
266
268
270
272
274
276
278
280
282
284
286
288
290
292
294
(c)
Improved PM P ET
2
4
6
8
10
12
266
268
270
272
274
276
278
280
282
284
286
288
290
292
294
(d)
1
2
3
0
4
283
309
335
361
22
48
74
100
126
152
178
204
230
256
282
308
(e) EC ET
5
0
10
15
20
283
309
335
361
22
48
74
100
126
152
178
204
230
256
282
308
(f)
DAY OF THE YEAR
Figure 2: Variation in measured evapotranspiration (ET), modelled ET and rainfall at (a and b) Somerton Farm, (c and d) Truro farm and
(e and f) eZulu Game Reserve. LAS = Large Aperture Scintillometer, PMP = Penman–Monteith–Palmer algorithm, EC = eddy covariance
was largely able to reproduce observed ET. However,
the underestimation bias at the beginning of the valida-
tion period could possibly be due to low modelled f values.
The tendency to overestimate ET at the EGR site was
due to overestimated Es and possibly the underestimated
latent heat flux as shown by the poor energy balance
closure reported in Gwate (2018). In addition, the LAI that
is used to connect ET0 to T in the model was relatively
stable. However, in the AT on the EGR it is suggested that
the dominant shrub, Portulacaria afra, exercises greater
stomatal control, resulting in high water use efficiency
(Mills and Cowling 2006). Admittedly, grasslands may
also exercise great stomatal control over ET (Snyman et
al. 2013; Favaretto et al. 2015), but P. afra has a higher
water use efficiency and hence its widespread environ-
mental plantings in South Africa under the auspices of the
Clean Development Mechanism (Mills and Cowling 2006).
Therefore, the available leaf area may not necessarily
be reflective of ET taking place as changes in stomatal
behaviour greatly influence the water vapour flux. This
African Journal of Range & Forage Science 2018: 1–9 7
result was not surprising because the LAI, which represents
the phenological characteristics of the vegetation in the
model, cannot detect variations in stomatal behaviour that
influence the total flux over vegetated surfaces. Glenn et al.
(2010) observed that ET models based on VIs are not able
to estimate Es and stomatal conductance, which affect total
ET. Hence, the overestimation bias could be indicative of the
model’s limitations in reproducing the stomatal behaviour.
The overestimation by the model can be reduced by
a careful choice of the number of days (N) to be used in
the determination of the f value. Sensitivity analysis of
such approaches has shown that increasing N reduces
overestimation and the optimum N lies between 16 and
20 days (Morillas et al. 2013). However, despite the
overestimation, on an annual basis, the model reproduced
the measured ET with a relatively low RMSE from the EGR
site despite the complex nature of the environment. In
addition, across sites, the RMSE was largely unsystematic
and this suggests that the proposed algorithm is robust
(Willmott 1981; Leuning et al. 2008). Willmott (1981) warned
that models that had a relatively high systematic RMSE
were not good enough and should not be accepted despite
a seemingly good fit. Therefore, the results from this study
confirm that the improved algorithm is robust. Using similar
approaches of modelling Es, good agreement between
flux tower observed ET and modelled ET across many
catchments have been recorded (Zhang et al. 2010; Morillas
et al. 2013; Zhang et al. 2016). The good performance of
the proposed algorithm is very important particularly for
data scarce areas. The model allows for ET to be calculated
using routine meteorological data, surface albedo and LAI
without the need for fine-tuning with observed data. These
data are readily available in sparsely distributed weather
stations and from remote sensing. This work, therefore,
has advanced the preliminary work by Palmer et al. (2014)
to develop parsimonious models for predicting ET in data
scarce areas at a fine resolution.
Predicting wide-area ET from VIs
In line with the objective of developing simple algorithms for
estimating ET in drylands where data is scarce, the relation-
ship between VIs and ET were investigated. Positive correla-
tions between ET and VIs were observed. However, across
sites, NDVI had better correlations with measured ET than
EVI. These results were consistent with those of Haynes
and Senay (2012), who found even lower correlations
of 0.14 during the winter season in the USA. In addition,
Helman et al. (2015) found that NDVI provided better model
fit than EVI when VIs were regressed against observed ET
in the Mediterranean regions. However, the results from the
present study were in sharp contrast with results from the
USA that found EVI to be a more useful scalar in connecting
potential ET to actual ET (Nagler et al. 2005a, 2007; Glenn
et al. 2008). The results from the present study sites were
probably due to the low VIs and LAI (0.1–1.8). It is well
established that in areas with LAI < 2.5, Es is crucial and
could account for ~80% of total evaporation (Leuning et al.
2008; Morillas et al. 2013). This suggests that much of the
water is consumed through the so-called ‘unproductive’ or
‘white’ evaporation and hence there is scope for improving
water productivity across the study sites. At the same
time, VIs can neither estimate Es nor dynamics in stomatal
conductance (Glenn et al. 2010). Therefore, results from
this study are not surprising since Es accounted for between
65% and 84% of total ET across sites. This is consistent
with literature values of between 30% and 80% reported in
rangelands (Kool et al. 2014). Thus, the moderate relation-
ship was likely caused by the influence of Es and stomatal
control of ET in the study sites. Owing to these moderate
relations, the study could not go on to develop predictive
0 5 10 15
0
5
10
15
20
EC ET (mm)
10 15 20 25 30 35
10
15
20
25
30
35
LAS ET (mm)
IMPROVED PMP ET (mm)
(a) (b)
y = 1.0 4x − 0.88
r2 = 0.73
p < 0.001
y = 1.0 2x + 1.04
r2 = 0.52
p < 0.001
Figure 3: Relationship between a) accumulated 8-day observed ET from the large aperture scintillometer (ET LAS) and the improved
algorithm over the grassland (N = 20, 8-day periods) and b) accumulated 8-day observed ET from the eddy covariance system (ET EC) and
the improved algorithm over the Albany Thicket (N = 51, 8-day periods)
Study site EVI NDVI
Somerton and Truro farm 0.47 0.53
EGR 0.31 0.47
Table 6: Correlation coefficients between ET and vegetation
indices.
Gwate, Mantel, Finca, Gibson, Munch and Palmer8
equations. Hence, the objective of developing robust but
simple algorithms using VIs was not successful.
However, robust relations were developed through
multivariate regression of ET0 and LAI against measured
ET. The r 2 at EGR was relatively lower due to the great
stomatal control of the ET process. Therefore, the study
succeeded in further developing simplified algorithms since
credible strong relations were developed. These algorithms
may be used to predict biome-specific ET, an approach that
is becoming common in ecohydrological studies (Fang et
al. 2016). The strong relationships developed are crucial
particularly for South Africa over the AT because this biome
is critical in global change studies owing to its perceived
high water use efficiency. This makes the task of estimating
ET in such drylands easier by simply using ET0 and LAI in
the empirical relationship developed in this work. However,
such algorithms need further validation.
Model uncertainties
The study improved the PMP model by introducing an Es
component, making it a two-layer model. Model uncertain-
ties stem from the calculation of f values and general
input data. It should be noted that the movement of water
between the upper soil layers and groundwater is not well
understood (Wilcox 2010). Wu et al. (2015) found that even
shallow-rooted plants such as grasses can use ground-
water by exploiting the capillary rise fluxes. The study
sites are underlain by Beaufort Series sandstones of the
Karoo Supergroup (Mucina et al. 2006) and hence the
accompanying shale and mudstones could be creating
peached water tables, causing capillary action to be signifi-
cant and this possibly leads to groundwater becoming
available to even short-rooted vegetation. Therefore, these
factors may introduce minor errors in the subsequent
f values calculated. However, results from this study
and elsewhere (Zhang et al. 2010; Morillas et al. 2013;
Zhang et al. 2016) suggest that the approach is robust in
reproducing dynamics in ET. Other uncertainties are linked
to the MODIS LAI (Myneni et al. 2002) used. For example,
McColl et al. (2011) found that MODIS overestimated LAI
over patchy vegetation (LAI < 0.6) and underestimated
LAI in densely vegetated areas. Serbin et al. (2013) also
reported moderate inconsistency between measured
and MODIS LAI in Manitoba. Therefore, there is a distinct
possibility that these patterns could also be playing out at
the present study sites as LAI was relatively low. Hence,
estimation biases observed in this work could also be linked
to uncertainties in MODIS LAI. The process of selecting
the highest LAI for a particular pixel is also vital and could
result in model uncertainties. In situations where land cover
was not persistent, this could be problematic and great
care should be taken to ensure that maximum LAI relevant
to the particular land-cover type is retrieved. At the Truro
farm, the land was previously invaded by woody invasive
alien species (IAPs) and, hence, a graph of LAI trajectories
since MOD15A became available helped the study in differ-
entiating IAPs signal from that of the grassland. Hence,
the modelled fluxes are a true reflection of dynamics of
ET over the landscape. The use of maximum LAI values
for the same vegetation type found in other areas could
also be useful.
Conclusion
The study developed credible algorithms for estimating
ET in semi-arid areas by advancing the preliminary work
of Palmer et al. (2014). The addition of the soil evapora-
tion component resulted in good agreement between the
observed and modelled ET. The simple two-layer model
described in this study will make it possible to estimate ET
in data scarce areas by using widely available meteoro-
logical data, MODIS LAI and surface albedo without the
need for reverse engineering. This is particularly crucial in
regions where there are no networks of flux tower stations
for validation purposes. However, the model had limitations
in reproducing stomatal behaviour over specific vegeta-
tion species. In semi-arid areas, accounting for Es is crucial
because it contributes a significant proportion to total ET.
Consequently, attempts to develop algorithms based on VIs
were not successful because these indices cannot estimate
Es. The LAI and ET0 were useful predictors of ET across
the sites and this enabled the development of algorithms
for predicting ET on a biome scale and this is vital for data
scarce areas. The empiral algorithms developed in this
study need further refinement once a larger database of ET
has been accumulated.
Acknowledgements — This work was supported by the South
African Water Research Commission (K5/2400/4) and the National
Equipment Programme (Grant 93213). Host farmers in the selected
study sites are also profoundly acknowledged.
ORCID
Onalenna Gwate https://orcid.org/0000-0003-0237-4316
Sukhmani Mantel https://orcid.org/0000-0003-2086-6912
Lesley Gibson https://orcid.org/0000-0002-0824-7927
Zahn Munch https://orcid.org/0000-0003-0691-7920
Anthony Palmer https://orcid.org/0000-0001-9179-2725
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Received 5 October 2017, revised 10 July 2018, accepted 18 July 2018
Associate Editor: Craig Morris