J. Geogr. Sci. 2013, 23(2): 359-369
DOI: 10.1007/s11442-013-1015-9
© 2013 Science Press Springer-Verlag
1,2
*
3,1
4
1
5
6
1. Key Laboratory of Water Cycle & Related Land Surface Processes, Institute of Geographic Sciences and
Natural Resources Research, CAS, Beijing 100101, China;
2. Graduate University of Chinese Academy of Sciences, Beijing 100049, China;
3. State Key Lab. of Water Resources & Hydropower Engineering Science, Wuhan University, Wuhan 430072,
China;
4. Department of Geosciences, University of Oslo, Oslo, Norway;
5. Department of Hydrology and Water Management, Institute of Physical Geography and Environmental
Planning, Adam Mickiewicz University, Poznan, Poland;
6. Puyang Water Conservancy Bureau, Puyang 457000, Henan, China
Abstract: Actual evapotranspiration is a key process of hydrological cycle and a sole term that links land surface water balance and land surface energy balance. Evapotranspiration plays a key role in simulating hydrological effect of climate change, and a review of evapotranspiration estimation methods in hydrological models is of vital importance. This paper firstly summarizes the evapotranspiration estimation methods applied in hydrological models and then classifies them into the integrated converting methods and the classification gathering methods by their mechanism. Integrated converting methods are usually used in hydrological models and two differences exist among them: one is in the potential evaporation estimation methods, while the other in the function for defining relationship between potential evaporation and actual evapotranspiration. Due to the higher information requirements of the Penman-Monteith method and the existing data uncertainty, simplified empirical methods for calculating potential and actual evapotranspiration are widely used in hydrological models.
Different evapotranspiration calculation methods are used depending on the complexity of the hydrological model, and importance and difficulty in the selection of the most suitable evapotranspiration methods is discussed. Finally, this paper points out the prospective development trends of the evapotranspiration estimating methods in hydrological modeling.
Keywords: hydrological model; actual evaporation; potential evaporation; function of soil moisture
Evapotranspiration is a key process of water balance and also an important element of energy balance. Its precise estimation is not only of vital importance for the study of climate
Received: 2012-11-05 Accepted: 2012-12-10
Foundation: CAS-CSIRO Cooperative Research Program, No.CJHZ1223; National Basic Research Program of China,
No.2010CB428406
Author: Zhao Lingling, Ph.D, specialized in hydrological cycle simulation. E-mail: linglingzhao@foxmail.com
* Corresponding author: Xia Jun, Professor, President of IWRA, E-mail: xiaj@igsnrr.ac.cn
www.geogsci.com springerlink.com/content/1009-637X

360 Journal of Geographical Sciences change and evaluation of water resources, but also has much application value in crop water requirement management, drought forecasting and monitoring, effective water resources development and utilization etc. Land evapotranspiration process is invisible and difficult to measure, and needs to be determined by measurement and estimation (Lu et al ., 2010). In
1694 E. Halley (Halley, 1694) for the first time applied evaporator to determine water surface evaporation, initiating measurements of the basin evaporation. J. Dalton integrated the influence of wind, air temperature and humidity to evapotranspiration and proposed the
Dalton’s Law of Evaporation in 1802 (Dalton, 1802), which provided clear physical meaning to the basin evaporation theory.
Evaporation measurement methods include the hydrological method, micro-meteorological method, plant physiology law-based method and scintillometer method. The hydrological method is based on the principle of water balance to determine the whole basin or sub-basin evapotranspiration. In this method evapotranspiration is measured either in a large time scale, usually in years (water balance method) or measured in a small regional scale, cell scale or point scale (lysimeter method, water flux method). The micro-meteorological method is based on the energy balance equation or aerodynamic equations to determine evapotranspiration in a selected part of the analyzed area. However, assumptions of the micro-meteorological method are difficult to achieve in reality, causing large errors (Bowen ratio energy balance method, aerodynamic method), in addition, it requires complex instrument manufacturing, causing maintenance difficulties and high costs. All these problems make this method difficult to be popularized. The plant physiology law-based methods through the determination of the plants’ water consumption determine their transpiration in the basin, so its representativeness of the watershed is poor. So is the case of the scintillometer method (Zuo et al ., 1988).
There are many methods to estimate evapotranspiration, from those taking into account evaporation from water surface to a variety of potential evapotranspiration and actual evapotranspiration estimations, but most of them just consider evapotranspiration from a single underlying surface, such as water, bare soil, and vegetation at the same time neglecting water balance. These methods regard evapotranspiration not as an important process of the hydrological cycle, but as a static quantity to estimate. Recent development of remote sensing methods can estimate the basin scale evapotranspiration, but due to the technological limitations, that estimation is difficult to meet the time scale requirements, usually being instantaneous, besides it is susceptible to external conditions, so its accuracy is not high.
Estimations of actual evapotranspiration based on hydrological models consider influence of water and energy, and can be calculated in different spatial and temporal scales, so results of such estimations are able to meet the demand of water resources assessment and water resources management (Xu et al ., 2001; Xu et al ., 2003). There are many kinds of evapotranspiration estimation methods based on existing hydrological models, and their data input requirements are different. At the same time, the accuracy of their output results is rarely compared. In the following sections evapotranspiration estimation modules based on the existing hydrological models are reviewed, then their differences are analyzed to be classified in accordance with their estimation principles. Finally, the prospective development trends of evapotranspiration estimation methods based on hydrological models are forecasted.

ZHAO Lingling et al .: Evapotranspiration estimation methods in hydrological models 361
There are two groups of evapotranspiration estimation methods in hydrological models: one first estimates separately water surface evaporation, soil evaporation and vegetable transpiration, and then integrates them to get the basin evapotranspiration depending on the land use pattern. The other one first estimates potential evapotranspiration (ETp) and then converts it into actual evapotranspiration (ETa) applying the Soil Moisture Extraction Function.
In this paper the first type methods are called the classification gathering methods, while the second – the integrated converting methods.
Table 1 lists some evapotranspiration estimation methods usually used in hydrological models. It can be clearly seen that lumped conceptual models, system models and distributed models commonly apply the integrated converting methods, while physically based hydrological models usually use the classification gathering methods to estimate basin evapotranspiration.
Table 1 Selected evapotranspiration estimation methods applied in hydrological models (HM)
Type
Integrated Converting Methods
Classification
Gathering Methods
Name of HM
Xin’anjiang (Zhao, 1984)
SWMM (Xu, 2009)
HSPF (Xu, 2009)
Kind of input ETp
Input
Evapotranspiration rate
Input
PRMS Jensen-Haise
HBV (Gardelin, 1997) Penman; Priestley-Taylor
TOPMODEL (Beven et al ., 1984) Water surface ETp
DTVGM (Xia et al ., 2005a; 2005b)
WASMOD (Sigh et al ., 2002)
TOPKAPI (Liu, 2002)
PDTANK (Xu, 2009)
Hargreaves; Water surface ETp
Input
Hargreaves; Water surface ETp
Penman-Monteith; Priestley-Taylor;
Water surface ETp
Thornthwaite
Penman-Monteith
SHE (Abbott et al ., 1986a; 1986b)
VIC (Liang et al ., 1994)
VIP (Mo et al ., 2004)
WEP (Jia et al ., 2001)
Penman-Monteith
Penman-Monteith
Penman-Monteith
Penman-Monteith
The integrated converting methods have following advantages in estimating evapotranspiration: they are easy to use, require few input variables and have strong adaptive ability.
So they are widely used in hydrological models. As to the hydrological models, we found two differences among them: one is different method of estimation of potential evapotranspiration, usually applied by the researchers depending on the data availability; the other is different soil moisture extraction function, which complexity differs significantly despite the same basic format. These two differences are discussed in the following parts.

362 Journal of Geographical Sciences
3.1 Soil moisture extraction function
In conceptual hydrological models actual evapotranspiration is the function of potential evapotranspiration and water availability in soil. The degree of soil humidity is expressed by actual soil moisture divided by field capacity soil moisture.
When actual soil moisture content is larger than evapotranspiration-limited soil moisture content, evapotranspiration is just limited by climate conditions and water will evaporate at the largest rate. With decreasing soil moisture, evapotranspiration rate also decreases until actual soil moisture content is smaller than withering soil moisture content, or in other words soil water reaches the largest deficit. At that time, evapotranspiration is just limited by the water supply conditions, and evapotranspiration rate trends to zero. The basic formula of the soil moisture extraction function is given below:
SMT
SMC
(1) where SMT is actual soil moisture; SMC is field capacity soil moisture.
Dyck (1985), Mintz and Walker (1993) summarized the soil moisture extraction functions in commonly used hydrological models; these functions are shown in Table 2. The ratios of actual evapotranspiration and potential evapotranspiration change with water availability in soil. Their relationship is demonstrated in Figure 1a; its format is related to the soil type and the Leaf Area Index (LAI), which has close relationship with the growth stage of vegetables, but is hard to define (Mintz et al ., 1993). Figure 1b shows several curves of soil moisture extraction functions drawn according to equations (7)–(12) given in Table 2.
3.2 Potential evapotranspiration estimation methods
Potential evapotranspiration is an important input in hydrological cycle simulations.
There are many kinds of potential evapotranspiration estimation methods; however, the use of different methods to estimate potential evapotranspiration influences the simulation accuracy of a given hydrological model. In 1997 Gardelin and Lindstrom analyzed the effect of different potential evapotranspiration calculation methods on the simulation accuracy of the HBV model. They found that the temperature-corrected Penman method improved the simulation accuracy; nevertheless, with the Priestley-Taylor method the obtained results were better. Consequently, the best method was the Priestley-Taylor method, which improved the negative potential evapotranspiration in winter by considering the soil heat flux.
The potential evapotranspiration estimation methods can be divided into the energy-based, temperature-based and mass transfer-based methods, depending on their mechanisms. The energy based method applies the energy balance concept to estimate potential evapotranspiration. In 2000 Xu and Singh compared 8 energy-based methods, including those described by Turc (1961), Makkink (1957), Jensen and Haise (1963), Hargreaves (1975), Doorenbos and Pruitt (1977), McGuinness and Bordne (1972), Abtew (1996) and Priestley and Taylor
(1972). He found that: applying the Penman-Monteith method, Makkink, Priestley and Taylor and Abtew got better results than the other methods. Under limited climate data conditions many researchers proposed some temperature-based methods. In 2001 Xu et al . analyzed seven types of temperature-based methods; the results show that the Blaney-Criddle method, the Hargreaves method and the Thornthwaite method give better simulation results

ZHAO Lingling et al .: Evapotranspiration estimation methods in hydrological models
Table 2 Examples of relationships between actual and potential evaporation
363
Minhas et al . (1974)
Norero (1969)
Baier, Robertson (1966)
Koitzsch and Golf (1983)
Roberts
1 2exp
1 exp( − γ SMT)
( − γ SMC
) + exp( γ SMT)
⎢
⎢
⎡
1
⎣
+
SMT ⎞ b.k
SMC
⎤
⎥
− 1
(3)
− 0.62
(4)
(2) n
k j
⎜
⎝
SMT
SMC j
SMT
⎠
Z j
(5)
(6)
RAT / (RAT 2
(
RAT
) 2
(7)
(8)
RAT (9)
1/2
Daily
Daily
Daily
Daily
Daily
Xu et al . (1996,1998)
HBV
Renger et al . (1974)
Budyko and Zubenok (1961)
Glugla (1980)
Bagrov (1953)
RAT (12) min
( (
− α
(
− −
[
SMT/max(ETp,1
]
α ETp
)
, ETp )
)
,SMT
)
(13)
SMT
LP SMC
(14)
2 (15)
RAT (16)
⎡
−
S
+ Δ
⎤ 1/ns
(17)
⎡
−
⎤ 1/n
(18)
Daily or monthly
Daily or monthly
5-day
Monthly
Monthly
Long term
Eagleson (1978) m
V
α
[ − ]
β
S
+ MK v
(19) Long term
Note: RAT=SMT/SMC , SMT is actual soil moisture, SMC is field capacity soil moisture, SMT
j
, i –1 is the previous day j -layer soil moisture, Z j
is available soil moisture considering root suction when actual evapotranspiration is smaller than potential evapotranspiration, K j is available soil moisture in j -layer, r is free coefficient. B is constant soil coefficient; M is vegetable canopy density. than the other ones. The mass transfer-based method is one of the oldest one, which estimates free water surface potential evaporation and mainly considers the effect of air pressure deficit and wind speed (Singh et al ., 1997). In 1802 Dalton proposed the first method of estimation of potential evaporation, while in 1948 Penman introduced his method based on the mass transfer principles.
4.1 Sensitivity of potential evapotranspiration estimation methods
There are numerous methods to estimate potential evapotranspiration. Among them the

364 Journal of Geographical Sciences
Figure 1 Nonlinear relationships between Eta and ETp
Penman-Monteith method is widely used in evaluating the influence of climate change on potential evapotranspiration, in the sensitivity analysis of climate (Xie, 2007; Sun et al .,
2009; Zhang et al ., 2010; Liu et al ., 2009; Liu et al ., 2011; Li et al ., 2011) and in simulation of hydrological cycle, because of its physically-based mechanism. However, studies on the sensitivity of the hydrological cycle simulation to the potential evapotranspiration show that the Penman-Monteith method is not the best one to estimate potential evapotranspiration in such simulations. In 1972 Parmele et al . analyzed the effect of error in potential evapotranspiration on the efficiency of hydrological models by testing 3 models in 9 watersheds. The obtained results suggest that the effect of potential evapotranspiration to the runoff modeling can be neglected when the error of potential evapotranspiration is smaller than 20%. Paturel et al . (1995) and Nandakumar et al . (1997) found that the sensitivity to the precipitation error was smaller than the error of potential evapotranspiration. Andersson et al . (1992) compared the sensitivity of the HBV model to 7 potential evapotranspiration methods and found that the temperature-based method slightly improved the accuracy of hydrological model, however, the mean-series Penman-Monteith method gets better accuracy than the time-varying one. Andreassian et al . (2004) also got the same results as Andersson. In 2005
Qudin et al . analyzed the sensitivity of 4 lumped hydrological models to 27 potential evapotranspiration methods in 308 basins of the world. The results suggest that the energy-based and temperature-based methods of the potential evapotranspiration estimation can ensure better efficiency of the hydrological model than the Penman-Monteith method. In
2007 Kannan et al . analyzed the sensitivity of the SWAT-2000 model to the temperature-based Hargreaves method and the Penman-Monteith method, respectively. The results show that application of the Hargreaves method results in better runoff modeling compared with the Penman-Monteith method.
As to the reasons of better hydrological cycle simulations resulting from simplified empirical formulas than from the Penman-Monteith method for the long-term averages, researchers believe that the Penman-Monteith method requires many data, in which many parameters are difficult to obtain. Many conceptual hydrological models are too sensitive to the data input of the Penman-Monteith method, what makes it not suitable for the use in hydrological models (Lu et al ., 2010). Some scientists (Oudin et al.
, 2005; Oudin et al.
, 2006)

ZHAO Lingling et al .: Evapotranspiration estimation methods in hydrological models
Table 3 Some methods for potential evaporation estimating
Type Method
Turc (1961)
Makkink
(1957)
Energy based method
Jensen-Haise
(1963)
Hargreaves
(1975)
Doorenbos-Pruitt
(1977)
Equation
T
(
R s
+ ) >
T (
R s
+ ) +
(1)
ET = α
Δ
Δ +
R s
γ λ
−
α ＝ 0.61, β ＝ 0.12
β (2)
R s x λ
Ct=0.025; T x
= –3
(3)
R s
λ
(4)
ET = α
⎛
⎝
Δ
Δ +
R s
γ λ
⎞
⎠
+ b
(5)
70
(20)
Climate type underlaying surface
Humid; grassland
Humid; grassland
365
Humid and semi-humid; grassland
Arid and semi arid; grassland
Humid; grassland
Abtew (1996)
Priestley-Taylor
(1972)
Thomthwaite
(1948)
Temperature based method
Linacre (1977)
Kharrufa (1985)
Blaney-Criddle
(1959)
ET = α
R s
λ
(6)
α ＝ 0.53
ET = α
Δ
Δ
+
R n
γ λ (7)
α ＝ 1.26
= ' dN
360
ET ' = C
⎛ 10Ta
I
⎞ α i =
⎛ Ta ⎞ 1.51
⎝ 5 ⎠
500T m + 15(T a
− T )
ET =
−
T m
= +
= ρ T a
1.3
(10)
(9)
=
12
j
(8)
ET k ρ + (11)
Humid; wetland
Humid; wet surface
Humid; valley
No limitation; lake surface
Arid; vegetation
Arid and semi arid; vegetation
Hamon (1961)
Mass
Rohwer (1962) transfer method Penman (1948)
Composite method
Penman-Monteith
(Allen et al ., 1998)
Pt =
4.95e
（ 0.062T
a
）
(12)
＝
100
( + U
2
)
(e s
− e ) (13)
＝
( + U
2
)
(e s
− e ) (14)
ET =
0.408
Δ ( − + γ
900
T a
+ 273
)
Δ + γ +
U (e s
− e )
(15)
No limitation; vegetation
Arid and semi arid; free water surface
Humid; free water surface
No limitation; reference vegetation
Note: ET is potential evapotranspiration (mm/ d); R s
/ (m 2 ·d)); T
is short wave radiation (MJ / (m 2 ·d)); R n
is net radiation (MJ a
is mean air temperature ( ℃ ); RH is relative humidity; G is soil flux (MJ / (m 2 ·d)); γ is temperature constant (kPa/ ℃ ); U
2
is wind speed at 2 m height (m/s); e s
is saturation vapor pressure at T a
(kPa); e a
is vapor pressure at T a
(kPa); Δ is slope of saturation vapor pressure curve (kPa/ ℃ ); C t
is temperature constant; in equation
(25) the adjustment factor α = − × − 2 +
2
− × − 3 ×
2
− × − 4 2 − × − 2
2
2 ; k is monthly consumptive use coefficient; p is percentage of total daytime hours for the period used (daily or monthly) out of total daytime hours of the year (365 × 12); T d
is dew point temperature ( ℃ ); h is elevation (m); A is the latitude in degree; D is day time (hours); Pt is saturated water vapor density term.

366 Journal of Geographical Sciences think that the input of the hydrological model and the parameter uncertainty make the model has a certain degree of fault tolerance, which consequently does not enable to take advantage of the Penman-Monteith method.
We think that most conceptual hydrological models describing hydrological processes cannot be compatible with the level of detailed evapotranspiration process in the Penman-Monteith method. Existing soil water function can not accurately estimate soil moisture, so the advantages of the Penman-Monteith method are hampered by less accurate soil moisture extraction functions. On the other hand, the Penman-Monteith method requires detailed weather information, but in reality it is often difficult to find relevant observation data, in order to meet the input needs through a variety of empirical formula transformations, which will inevitably lead to numerous uncertainties. In this situation, the advantages of the less data requirements of simplified empirical formulas along with simplified calculation processes, while achieving the required level of accuracy are indisputable.
4.2 Development trends
Hydrological model simulates interlinkages between the elements of the water cycle and simplifies its complexity. On the one hand, hydrological models are used to study the laws of the hydrological cycle in nature. For this reason, through a variety of experiments and mathematical equations, an attempt to approximate mechanisms of the real hydrological processes and reflect them more accurately, more complex models, such as the SHE model, are constructed. On the other hand, models are built to solve an existing, rooted in specific conditions problem, in order to find convenient and efficient solution, usually reducing complexity of less important processes; such models tend to be more simple and practical.
The development trend of the evapotranspiration estimation methods in hydrological models is consistent with the above-mentioned development directions of these models. While the integrated converting methods focus on the simple relationship between the changes in the process of evapotranspiration, the classification gathering methods develop toward more complex mechanisms, with complex equations to describe the amount of water in all kinds of evapotranspiration and energy conversion processes. Consequently, two main trends in the evaporation estimation methods can be pointed out: first, towards simplification of their practical use, and second, towards their increasing complexity.
Evapotranspiration plays a vital role in water balance. Water from plant interception, surface water and soil water are consumed by evapotranspiration. According to the statistics, in humid areas evapotranspiration accounts for about 50% of the annual precipitation, while in arid regions for about 90%. Observations of actual evapotranspiration are very difficult and vulnerable to the influence of external factors, so indirect estimation methods are commonly used. Estimations of actual evapotranspiration based on hydrological cycle simulations are of great significance to the water resources adaptive management under changing environment. However, there is a wide range of evapotranspiration estimation methods based on hydrological models. These methods are reviewed as follows:
(1) Firstly, this paper reviewed the evapotranspiration estimation methods commonly used

ZHAO Lingling et al .: Evapotranspiration estimation methods in hydrological models 367 in hydrological models. They were divided into two categories, depending on its characteristics, namely the classification gathering methods and the integrated converting methods. The former firstly estimate different kinds of evapotranspiration and then get the basin evapotranspiration depending on the land use pattern. The latter convert potential evapotranspiration into actual evapotranspiration according to the soil moisture content. The differences among the integrated converting methods exist in the way of estimating potential evapotranspiration and in soil moisture extraction functions. This paper summarizes 14 kinds of potential evapotranspiration estimation methods and 12 kinds of soil moisture extraction functions.
(2) There are some uncertainties in hydrological models input, output and model structure and the physically-based Penman-Monteith method has high data requirements. This clearly influences the accuracy of the hydrological cycle simulations. So we need further discussion on how to select compatible potential evapotranspiration estimating equations and soil moisture extraction functions for different hydrological models to reduce their uncertainty.
(3) Regarding the nature of the models, this paper predicts two main directions of their development, which is the increasing complexity of the evapotranspiration estimation methods in hydrological model and the research-driven simplification of their practical use.
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