# Evaluation of three complementary relationship evapotranspiration

Journal of Hydrology 308 (2005) 105–121 www.elsevier.com/locate/jhydrol

# Evaluation of three complementary relationship evapotranspiration models by water balance approach to estimate actual regional evapotranspiration in different climatic regions

C.-Y. Xu a,b,

*, V.P. Singh c a

Department of Earth Sciences, Hydrology, Uppsala University, Villava¨gen 16, Uppsala S-75236, Sweden b

Nanjing Institute of Geography and Limnology, Chinese Academy of Sciences, Nanjing, Jiangsu Province, People’s Republic of China c

Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA 70803-6405, USA

Received 29 July 2003; revised 3 September 2004; accepted 1 October 2004

Abstract

Three evapotranspiration models using the complementary relationship approach for estimating areal actual evapotranspiration were evaluated and compared in three study regions representing a large geographic and climatic diversity: NOPEX region in Central Sweden (cool temperate, humid), Baixi catchment in Eastern China (subtropical, humid), and the Potamos tou

Pyrgou River catchment in Northwestern Cyprus (semiarid to arid). The models are the CRAE model of Morton, the advection– aridity (AA) model of Brutsaert and Stricker, and the GG model proposed by Granger and Gray using the concept of relative evapotranspiration (the ratio of actual to potential evapotranspiration). The calculation was made on a daily basis and comparison was made on monthly and annual bases. The study was performed in two steps: First, the three evapotranspiration models with their original parameter values were applied to the three regions in order to test their general applicability. Second, the parameter values were locally calibrated based on the water balance study. The results showed that (1) using the original parameter values all three complementary relationship models worked reasonably well for the temperate humid region, while the predictive power decreases in moving toward regions of increased soil moisture control, i.e. increased aridity. In such regions, the parameters need to be calibrated. (2) Using the locally calibrated parameter values all three models produced the annual values correctly. For the monthly values there was a time shift for the appearance of maximum monthly values between the evapotranspiration model estimations and water balance calculations, and the drier the region, the larger the difference.

Further examination of the water balance components showed that while the actual evapotranspiration is controlled by several hydrometeorological factors in warmer and drier months the soil moisture is the dominating factor.

q

2004 Elsevier B.V. All rights reserved.

Keywords: Actual evapotranspiration; Potential evapotranspiration; Complementary relationship; Regional evapotranspiration; Water balance

* Corresponding author. Address: Department of Earth Sciences, Hydrology, Uppsala University, Villava¨gen 16, Uppsala S-75236, Sweden.

E-mail addresses: [email protected] (C.-Y. Xu), [email protected] (V.P. Singh).

0022-1694/$ - see front matter q

2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.jhydrol.2004.10.024

106

## 1. Introduction

Evapotranspiration is the only term that appears in both a water balance equation and a land surface energy balance equation. Evapotranspiration estimates are needed in a wide range of problems in hydrology, agronomy, forestry and land management, and water resources planning, such as water balance computation, irrigation management, river flow forecasting, investigation of lake chemistry, ecosystem modeling, etc. Reliable estimates of evapotranspiration are also essential for the improvement of

atmospheric circulation models ( Yates, 1997

). Due to complex interactions amongst the components of the land–plant–atmosphere system evapotranspiration is perhaps the most difficult of all the components of the hydrologic cycle.

Several methods have been proposed in the literature for calculating actual evapotranspiration.

introduced resistance terms into the well-known method of

and derived at an equation for evapotranspiration from surfaces with either optimal or limited water supply. This method, often referred to as Penman–Monteith method, has been successfully used to estimate evapotranspiration from different land covers. The method requires data on aerodynamic resistance and surface resistance which are not readily available, so that the Penman–Monteith method for estimating actual evapotranspiration has been limited in practical use.

Another approach is the complementary relationship proposed by

Bouchet (1963) . For areal estimation,

this method is usually preferred because it requires only standard meteorological variables and does not require local parameter calibration. Different models have been derived using the complementary relationship concept, which include the advection–aridity

(AA) model proposed by

, the complementary relationship areal evapotranspiration (CRAE) model derived by

, and the complementary relationship model proposed by

using the concept of relative evapotranspiration (the ratio of actual to potential evapotranspiration). In this study this model is named as GG model. Although the above three models are derived using the complementary relationship concept, the assumptions and derived model

C.-Y. Xu, V.P. Singh / Journal of Hydrology 308 (2005) 105–121 forms are different. Besides the above cited references, there are a number of studies on evaluating the validity of the complementary relationship model (e.g.

1990; Lemeur and Zhang, 1990; Chiew and McMahon,

1991; Granger and Gray, 1990; Hobbins et al.,

2001a,b; Xu and Li, 2003 ). A comparative study that

evaluates the performance of these three models

(i.e. CRAE, AA, and GG) in terms of different climate regions and calculation seasons using the same data sets has not been done.

The primary objective of this study is to evaluate and compare the performance of the above three evapotranspiration models in three study areas: one in

Central Sweden representing a seasonally snowcovered boreal region, one in Eastern China representing a subtropical humid monsoon region and one in Northwestern Cyprus representing a semiarid region. This study differs from those reported in the literature in the following respects: (1) This study compares three complementary relationship-based models, which does not appear to have been done before. (2) The study includes the regions that have large geographic and climatic diversity. (3) The results of these evapotranspiration models are compared with both a long-term water balance study and a monthly water balance model. This permits comparison of not only the annual evapotranspiration values but also the monthly dynamic values.

The paper is organized as follows: Introducing the theme of the paper in Section 1, the models are described in Section 2. The study regions and data are described in

Section 3. The results are given in Section 4, followed by a general discussion in Section 5. Summary and conclusions are given in Section 6.

## 2. Description of models

Utilizing an analysis based on energy balance,

corrected the misconception that a larger potential evapotranspiration necessarily signified a larger actual evapotranspiration by demonstrating that as a surface dried from initially moist conditions the potential evapotranspiration, i.e. evaporative capacity increased, while the actual evapotranspiration decreased as the available water decreased. The relationship that he derived has come to be known as the complementary relationship

2.1. The AA model

C.-Y. Xu, V.P. Singh / Journal of Hydrology 308 (2005) 105–121 between actual and potential evapotranspiration; it states that as the surface dries the decrease in actual evapotranspiration is accompanied by an equal, but opposite, change in the potential evapotranspiration; the potential evapotranspiration thus ranges from its value at saturation to twice this value. This relationship is described as

ET a

C

ET p

Z

2ET w

(1) where ET a

, ET p and ET w are actual, potential and wet environment evapotranspiration, respectively.

The complementary relationship has formed the basis for the development of some evapotranspiration

models ( Morton, 1983; Brutsaert and Stricker, 1979;

Granger and Gray, 1989 ), which differ in the

calculation of ET p and ET w

. ET a is usually calculated as a residual of (1). For the sake of completeness, the model equations are briefly summarized in what follows using the same notations as used by the original authors. For a more complete discussion, the reader is referred to the cited literature.

107

This formulation of f ( U

2

) was first proposed by

for use in the AA model operating at a temporal scale of a few days.

Substituting (3) and the wind function (4) into the

Penman equation (2) yields the expression for ET p used by

in the original

AA model:

ET

AA p

D

Z

D

C g

R n l g

C

D

C g f

ð

U

2

Þð e s

K e a

Þ

(5)

The AA model calculates ET w

partial equilibrium evapotranspiration equation

ET

AA w

D

Z a

D

C g

R n l

(6) where a

Z

1.26. Different values for a have been reported in the literature, the original value was first tested in this study. Substitution of (5) and (6) into (1) results in the expression for ET a

(7) in the AA model:

ET

AA a

D

Z

ð

2 a

K

1

Þ

D

C g

R n l g

K

D

C g f

ð

U

2

Þð e s

K e a

Þ

(7)

In the AA model, the ET p is calculated by combining information from the energy budget and water vapour transfer in the

equation

ET p

D

Z

D

C g

R n l g

C

D

C g

E a

(2) where R n is the net radiation near the surface, D is the slope of the saturation vapour pressure curve at the air temperature, g is the psychrometic constant, l is the latent heat, and E a is the drying power of the air which in general can be written as

E a

Z f

ð

U z

Þð e s K e a

Þ

(3) where f ( U z

) is some function of the mean wind speed at a reference level z above the ground; and e a and e s are the vapour pressure of the air and the saturation vapour pressure at the air temperature, respectively. In this study,

originally suggested an empirical linear approximation for f ( U z

) which was used here f

ð

U z

Þ z f

ð

U

2

Þ

Z

0

:

0026

ð

1

C

0

:

54 U

2

Þ

(4) which, for wind speeds at 2-m elevation in m/s and vapour pressure in Pa, yields E a in mm/day.

2.2. The GG model

showed that an equation similar to

Penman could also be derived following the approach of

complementary relationship.

derived a modified form of Penman’s equation for estimating the actual evapotranspiration from different non/saturated land covers (Eq. (8))

ET

GG a

D G

Z

D

G

C g

R n

= l g G

C

D

G

C g

E a

(8) where G is a dimensionless relative evapotranspiration parameter and other notations have the same meaning as in (2).

showed that the relative evapotranspiration, the ratio of actual to potential evapotranspiration, G

Z

ET a

/ET p is a unique parameter for each set of atmospheric and surface conditions. Based on daily estimated values of actual evapotranspiration from water balance,

showed that there exists a unique relationship between G and a parameter which

108

2.3. The CRAE model

C.-Y. Xu, V.P. Singh / Journal of Hydrology 308 (2005) 105–121 they called the relative drying power, D , given as

D

Z

E a

E a

C

R n

(9) and

G

Z

1

1

C

0

:

028 e

8

:

045 D

Later on,

modified (10) to:

G

Z

0

:

793

C

1

0

:

20 e

4

:

902 D

C

0

:

006 D

(10)

(11) to account for the temperature dependence of both the net radiation term and the slope of the saturated vapour pressure curve D . The Priestley–Taylor factor a is replaced by a smaller factor b

2

Z

1.20, while the addition of b

1

Z

14 W m

K

2

(or 0.49 mm/day) accounts for large-scale advection during seasons of low or negative net radiation and represents the minimum energy available for ET w but becomes insignificant during periods of high net radiation

ET

CRAE w

Z b

1

Z b

1

C b

2

C b

2

D

P

D

P

C g

R

TP

D

P

D

P

C g

½

R n

K

4 3s T

3 p

ð

T p

K

T a

Þ ð

14

Þ where D p and R

TP are the slope of the saturated vapor pressure curve and the net available energy adjusted to the equilibrium temperature T p

, respectively. Other symbols are as defined previously. Actual evapotranspiration is calculated as a residual of (1).

Different forms of the CRAE model have been reported in the literature; in this study the original form presented by

was used. To calculate ET p in the CRAE model,

decomposed the Penman equation into two separate parts describing the energy balance and vapour transfer process. A refinement was developed by using an ‘equilibrium temperature’ T p

, which is defined as the temperature at which

energy budget method and mass transfer method for a moist surface and plants yield the same result for ET p

.

The energy-balance and vapour transfer equations can be expressed, respectively, as

ET

CRAE p

Z

R

T

K

½ g f

T

C

4 3s

ð

T

P

C

273

Þ

3

ð

T

P

K

T

Þ

(12)

ET

CRAE p

Z f

T

ð e

P

K e d

Þ

(13) in which ET p is the potential evapotranspiration in the units of latent heat; T p and T are the equilibrium and air temperatures, respectively, in 8 C; R

T is the net radiation for soil–plant surfaces at the air temperature; g is the psychrometric constant; s is the Stefan–

Boltzmann constant;

3 is the surface emissivity; f

T the vapour transfer coefficient; e p is is the saturation vapour pressure at T p

; and e d is the saturation vapour pressure at the dew-point temperature. The potential evapotranspiration estimate is obtained by using in

(12) the value of T p

(

).

obtained by an iterative process

In calculating the wet-environment evapotranspiration,

modified the Priestley–

Taylor equilibrium evapotranspiration equation (6)

2.4. The monthly water balance model

NOPEX-6 (

b t

. Parameter a

3

water and snow balance model. It was originally developed for investigation of water balance of the

NOPEX (A NO rthern hemisphere climate P rocesses land-surface EX periment) area (

The prototype of the model system was defined by

Van der Beken and Byloos (1977) . The principal equations

of the NOPEX-6 are presented in

data to the model are monthly values of areal precipitation, long-term monthly average potential evapotranspiration and air temperature. Precipitation p t is first divided into rainfall r t and snowfall s t by using a temperature index function. Snowfall is added to the snowpack sp t fraction m t at the end of the month, of which a melts and contributes to the soil moisture storage sm t

. Parameters a

1 and a

2 are threshold temperatures which determine the form of precipitation and the rate of snowmelting. Before rainfall contributes to the soil storage as ‘active’ rainfall, a small part is subtracted and added to evapotranspiration. The latter storage contributes to evapotranspiration e t

, to the fast component of flow f t

, and to slow flow is used to convert long-term average monthly potential evapotranspiration to actual values of monthly potential evapotranspiration.

C.-Y. Xu, V.P. Singh / Journal of Hydrology 308 (2005) 105–121 109

Table 1

Principal equations of the NOPEX-6 monthly snow and water balance model

Snow fall

Rainfall

Snow storage

Snowmelt

Potential evapotranspiration

Actual evapotranspiration

Slow flow

Fast flow equation

Total computed runoff

Water balance equation s t

Z p t f

1

K exp

½

K

ð c r t

Z p t K s t t

K a t

Þ

=

ð a

1

K a

2

Þ

2 g

C

; a

1

R a

2 sp t

Z sp t

K

1 C s t K m t m t

Z sp t f

1

K exp

½ð c t

K a

2

Þ

=

ð a

1

K a

2

Þ

2 ep e t t

Z

ð

1

C a

3

Z min

½ ep t

ð

ð c t

1

K

K a c w t

4 m

ÞÞ

= ep t ep

Þ

; m w t

; f b t t

Z

Z a a

5

6

ð

ð sm

C t

K

1 sm C t

K

1

Þ

Þ

2

2

;

ð m t a

C

5

R n t

Þ

;

0 a

6

R

0

0

% a

4 g

C

% 1 d t

Z b t C f t sm t

Z sm t

K

1 C r t C m t K e t K d t where and c t w t

Z r t C sm

C t

K

1 is the available water; sm

C t

K

1

Z max

ð sm t

K

1

;

0

Þ is the available storage; n are monthly precipitation and air temperature, respectively; ep m and c m t

Z r t K ep t

ð

1

K e

K r t

= ep t

Þ is the active rainfall; p t are long-term monthly average potential evapotranspiration and air temperature, respectively; a i

( i

Z

1,2,

.

,6) are model parameters.

It can be eliminated from the model if potential evapotranspiration data are available or calculated using other methods. Parameter a

4 determines the value of actual evapotranspiration that is an increasing function of potential evapotranspiration and available water. The smaller the values for a

4

, the greater the evapotranspiration losses at all moisture storage states.

The slow flow parameter a

5 controls the proportion of runoff that appears as ‘base flow’ and higher values of a

5 produce a greater proportion of ‘base flow’. It seems likely then that higher values are expected in forest areas than in open field and in sandy soil than in clayey soil. The fast flow parameter a

6 will increase with the degree of urbanisation, average basin slope, and drainage density, and lower values should be expected for catchments that are dominated by forest. In case snowfall and frost are not a significant factor, the

NOPEX-6 model as described in

can be simplified by eliminating the snow routine part.

## 3. Study area and data

Three regions representing a large geographical and climatic diversity were chosen in this study to evaluate the selected evapotranspiration models. The first study region is located in central Sweden

(

Fig. 1 C). Uppsala Flygplats (59

8 53

0

N, 17 8 35

0

) is a national standard meteorological station maintained by the Swedish Meteorological and Hydrological

Institute (SMHI). It is the only national standard station in the NOPEX area (

central Sweden. Hourly meteorological data are available since the early 1980s, which include air temperature, dew point temperature, relative humidity, wind speed, solar radiation, sun shine hour, precipitation, etc. The mean monthly meteorological variables are shown in

There are 10 hydrological catchments in the

NOPEX area ranging in size from 6 to about

1000 km

2

. In order to evaluate the performance of the selected evapotranspiration models by using water balance calculations, two catchments nearest to the

Uppsala Flygplats station were selected in the study, namely, Ha˚gaa˚n at Lurbo (in short, LU) located on the west of the station, and Sa¨vjaa˚n at Sa¨vja (SA) located on the east of the station (see

). The LU catchment has an area of 124 km

2 and its altitude ranges from 15 to 75 m-above-sea-level. Landuse of the catchment includes 0.3% lake, 68.2% forest and

31.5% agricultural land. The SA catchment has an area of 727 km

2 and altitude ranges from 5 to

75 m-above-sea-level. The landuse of the catchment includes 2.0% lake, 64% forest and 34% agricultural land. An earlier investigation (

) has shown that the distribution of soil type is quite similar to the distribution of landuse, i.e. areas with forest consist of sandy soil, whereas agricultural areas consist of clay soil. The soil type and landuse are the main factors that affect the runoff coefficient in the region, since topography does not vary appreciably.

The mean annual precipitation, runoff and runoff coefficients calculated using the observed data for the period of 1981–1991 are 720 mm, 302 mm and 0.41

for LU and 716 mm, 234 mm and 0.33 for SA, respectively. Since these two catchments have similar

110 C.-Y. Xu, V.P. Singh / Journal of Hydrology 308 (2005) 105–121

Fig. 1. Map of the three countries with the location of the study regions.

quantities and temporal variations of precipitation, as can be seen in the results section, the runoff coefficient is the main factor that determines the difference in the calculated areal evapotranspiration of the two catchments.

The second study region is the Baixi catchment located in Zhejiang province (29 8 15

0

N and 121 8 10

0

E)

B). The catchment has an area of 254 km

2

, and more than 90% of the land-use is forest and the rest is farming land. The climate of the area is a subtropical monsoon one with mild temperatures. The long-term average annual precipitation is around 1800 mm, of which 65% falls between April and September. The annual evapotranspiration is about 790 mm resulting in a runoff coefficient of 0.56. The warmest month is June with a mean temperature of 28 8 C and the coldest month is December with a temperature of 4.0

8 C.

C.-Y. Xu, V.P. Singh / Journal of Hydrology 308 (2005) 105–121 111

Fig. 2. Comparison of the mean monthly climatological variables for the three study regions.

The mean monthly values of the major climatic parameters in the Pinghu station near the Baixi catchment are given in

The third study region is located in northwestern part of the Greek Cypriot area of the Cyprus island

(

Fig. 1 C). The catchment of the river is approximately

42 km

2

. The land cover consists of hilly forest, grass and bedrock. Both the bedrock and the soil are rather homogenous in the area and consist of Gabbro and

Eutric cambisol. The average elevation of the catchment is about 675 m-above-sea-level. The national discharge station Q12830 and the two meteorological stations record daily values of meteorological and hydrological variables from 1980. The most complete data period is from 1989 to 1993 and it is used in the study. The climate of the region is semiarid with annual precipitation of about 645 mm and annual potential evapotranspiration about

1250 mm. The mean runoff coefficient is 0.3, but the seasonal variation of both precipitation and runoff are extremely high. About 90% of the annual precipitation and annual runoff are measured in the rainy months from December to March. The dry months are really dry which is very much different from the other two study regions.

shows the mean monthly values of the major climatic parameters.

## 4. Results

The study was performed in two steps. First, the three complementary relationship evapotranspiration models with their original parameter values were applied to the three study regions in order to test their

112 C.-Y. Xu, V.P. Singh / Journal of Hydrology 308 (2005) 105–121 validity in different climatic regions. Second, the parameter values were calibrated based on water balance calculations in order to see how much the results can be improved. In this section, the results obtained using the original parameter values for the three regions are first presented, followed by the results obtained with locally calibrated parameter values. Common features and differences are compared. A general discussion will be given in Section 5.

4.1. Results obtained using original parameters

4.1.1. Central Sweden

Calculations were made on a daily basis for the period of 1983–1991 using meteorological data taken from station Uppsala Flygplats. The mean monthly evapotranspiration computed from the three models are shown in

(columns 2–4) and plotted in

Fig. 3 A. It is seen that (1) all three models gave close

estimates of evapotranspiration for summer months from June to August. (2) Larger differences existed between the CRAE model and the other two models in winter months. This is due to the b

1 included in ET

CRAE

W

(14 W m K

2

) term

. Similar results were reported by

Hobbins et al. (2001a) . (3) As for the long-term annual

averages, the CRAE model yielded closest value to the water balance model estimation, while the AA models gave about 100 mm smaller. (4) The peak values estimated by the water balance models appeared one month earlier than the evapotranspiration models did; this phenomenon will be explained in Section 4.2.

4.1.2. East China

For the Chinese catchment, calculations were made on a daily basis for the period of 1989–1998. The mean monthly actual evapotranspiration calculated from three models are compared in

(columns

2–4) and

Fig. 3 B. It is seen that using the original

parameter values, larger differences existed between the complementary relationship models. For this catchment, the GG produced closest agreement with water balance estimates, while the CRAE and AA methods produced much higher values especially for warmer months. This means that the parameter values must be locally tuned in order to determine which method gives the more correct results. The peak values estimated by the water balance models appeared one month later than the evapotranspiration models did; this phenomenon will be explained in

Section 4.2.

4.1.3. Northwestern Cyprus

Calculations were made on a daily basis for the period of 1989–1993. The mean monthly actual evapotranspiration calculated from three models using the original parameter values are compared in

(columns 2–4) and

C. The results show that using original parameter values, larger differences existed between the three methods.

Table 2

Mean monthly actual evapotranspiration calculated by the monthly water balance model and evapotranspiration models with original and tuned parameter for the Swedish catchment (1983–1991)

Month

5

6

7

8

3

4

1

2

9

10

11

12

Total

With original parameters

ET

AA

A

0

0.8

7.9

26.1

58.9

89.9

98.1

56.7

16.8

2.1

0.1

0

357

ET

CRAE

A

7.1

11.1

23.5

39.4

66.8

90.9

96.3

65

32

18.4

8.7

7

466

ET

GG

A

0.7

3.1

17.6

44

76.4

91.5

94.6

61

26.5

5.5

0.7

0.4

422

With tuned parameters

ET

AA

A

10.2

10.4

21.5

37.3

65.4

94

101.9

65.3

28.4

10.9

8.7

9.4

463

ET

CRAE

A

6

8.6

19

37.5

70.7

97.1

103.2

66.6

28

12.7

7.2

6.1

463

ET

1.1

3.9

20

48.1

84.5

96.8

100.6

67.2

31.2

8.1

1.3

0.6

463

GG

A

Water balance

ET

WB

A

2.1

3.9

13.8

46.7

89

99.5

87.8

66.2

38.8

14.1

1

0

463

C.-Y. Xu, V.P. Singh / Journal of Hydrology 308 (2005) 105–121 113

Fig. 3. Comparison of the mean monthly actual evapotranspiration calculated by the water balance model and the three complementary relationship evapotranspiration models using the original parameter values for the three study regions.

Table 3

Mean monthly actual evapotranspiration calculated by the monthly water balance model and evapotranspiration models with original and tuned parameter for the Chinese catchment (1989–1998)

Month

7

8

5

6

1

2

3

4

9

10

11

12

Total

With original parameters

ET

AA

A

20.8

30.8

57.5

87.9

121.9

141.9

180.8

162.1

111.4

70.8

33

20

1039

ET

CRAE

A

33.7

36.1

53.5

82.8

124.9

140.3

184

169

118.8

84

54

39.8

1121

ET

GG

A

25.8

34

53

73.4

96.1

104.7

129.1

117.1

83.7

58.4

33.8

24.8

834

With tuned parameters

ET

AA

A

25.9

30.4

48.6

66.4

86.6

101.2

123.9

111.7

81.6

56.7

31.7

25

790

ET

CRAE

A

28.8

26.7

35.4

52.9

81.2

93.3

125.9

118.6

84.6

62.2

45

35.1

790

ET

25.2

33

51.3

70.1

90.3

98.3

119.8

108.8

78.1

55

31.9

23.8

786

GG

A

Water balance

ET

WB

A

27.6

29.4

40.8

58.8

78.3

94.2

108.7

119.8

89.1

62.5

47.1

33.8

790

114 C.-Y. Xu, V.P. Singh / Journal of Hydrology 308 (2005) 105–121

Table 4

Mean monthly actual evapotranspiration calculated by the monthly water balance model and evapotranspiration models with original and tuned parameter for the Cypriot catchment (1989–1993)

Month

7

8

5

6

1

2

3

4

9

10

11

12

Total

With original parameters

ET

AA

A

16.8

28.1

58.7

90.4

123.3

141.6

144.4

126

79.3

37.9

22.8

17.6

887

ET

CRAE

A

29.2

35.8

53.9

65.7

89.1

85

72.6

54.1

40.1

30.3

27.2

28.6

612

ET

GG

A

22.3

31.3

56.8

80.7

100.6

111.2

112.6

100.1

70.9

45.4

26.9

19.9

779

With tuned parameters

ET

AA

A

16.1

21.4

36.9

50.3

69

75.3

74

62.9

38.9

20.4

17.5

17.9

501

ET

CRAE

A

21.9

29.2

45.2

56.2

78.4

72.9

60.4

43.1

30.7

22.3

19.5

21.6

501

ET

14.4

20.8

37.6

53.2

67.1

72.3

72.3

63.8

44.9

28.8

17.2

13

505

GG

A

Water balance

ET

WB

A

22

26.3

56.2

78.5

76.7

67.2

49

32.5

19.7

20.4

29.5

22.3

500

For this catchment, the CRAE models produced closest agreement with the water balance estimates, while the GG and AA methods produced much bigger values especially for warmer months. As for the

Chinese catchment, the parameter values must be locally calibrated in order to determine which method gives the more correct results. Again there is a mismatch problem for the time appearance of the peak values between the complementary evapotranspiration estimations and the water balance model calculations. For this arid catchment, this phenomenon becomes more pronounced and an explanation will be given in Section 4.2.

4.2. Results obtained using locally calibrated parameters based on water balance studies

In order to verify the results obtained from different methods, two calculations were performed.

First, the mean annual actual evapotranspiration was calculated from the long-term water balance equation

ET

Z

PT

K

QT. Second, the monthly actual evapotranspiration was computed using the monthly water balance model. Although one cannot guarantee that the monthly water balance model would yield true values, it is interesting to compare the results and discuss the difference, especially when the observed areal actual evapotranspiration data are not available.

In tuning the parameters of the evapotranspiration model, two factors were considered to be important, i.e. they should be able to produce the yearly total values correctly and they should produce total values for summer months as close as possible. Two criteria were used in tuning the parameter values: First, the mean annual actual evapotranspiration calculated from the long-term water balance equation was used to tune the parameters so that the three evapotranspiration methods would produce correct results for yearly totals. Second, the mean monthly evapotranspiration for summer months calculated from the monthly water balance model was used to tune the parameters to make them produce closer results for the growing season.

4.2.1. Central Sweden

Using the areal precipitation and discharge data of two catchments, LU and SA, the average annual actual evapotranspiration was calculated from the long-term water balance equation ET

Z

PT

K

QT as

463 mm. Using the monthly water balance model, the monthly water balance components, including runoff and actual evapotranspiration, were simulated for these two catchments, and the average of the two was used for comparison with the evapotranspiration models. The parameter values tuned using the two criteria are as follows: for the AA model, the a value of 1.26 in (6) was replaced by a smaller factor 1.18, with an addition of b

Z

8.5 W m K

2

(i.e. 0.3 mm/day) which accounts for large-scale advection during seasons of low or negative net radiation and represents the minimum energy available for ET w

. Eq. (6) was

C.-Y. Xu, V.P. Singh / Journal of Hydrology 308 (2005) 105–121 modified to ET

AA w

Z

0

:

3

C

1

:

18

ð

D

=

D

C g

Þð

R n

= l

Þ

. For the GG model, it was found necessary to change the parameter values 0.793 and 0.20 in (11) to 0.55 and

0.15, respectively. For the CRAE model, the parameter values of 14 and 1.20 in (14) were changed to

8.8 and 1.30, respectively.

For comparison purpose, the mean monthly evapotranspiration and yearly totals calculated using the three evapotranspiration models with locally tuned parameters are shown in

(columns 5–7) together with the values computed using the water balance model (column 8). These values are also plotted in

Fig. 4 A. The results showed the following:

(1) All three models produce mean annual values correctly as expected. (2) The CRAE model follows best the variation with the water balance model for mean monthly values. (3) Compared with

June. To explain this phenomenon better,

115

(columns 2–4), a relatively big change is found for the AA model since the original parameter value underestimated the yearly total value, while only minor changes are made for the other two methods. (4) Evapotranspiration estimated based on the routine climatological observations gives a peak in

July, while the water balance model gives the peak in

used, where the areal mean monthly precipitation, potential evapotranspiration and soil moisture content computed by the water balance model together with the mean monthly actual evapotranspiration are plotted. It is seen that for this region the available water for evapotranspiration as measured by the soil moisture content in July is the smallest. This causes

Fig. 4. Comparison of the mean monthly actual evapotranspiration calculated by the water balance model and the three complementary relationship evapotranspiration models using the locally tuned parameter values for the three study regions.

116 C.-Y. Xu, V.P. Singh / Journal of Hydrology 308 (2005) 105–121

Fig. 5. Comparison of the mean monthly water balance components for the three study regions.

evapotranspiration in July to be slightly lower than that in June for the water balance model. The complementary relationship models do not directly use the soil moisture information and hence produce the highest evapotranspiration rate in July. As will be shown later in this paper, this time shift phenomenon becomes more pronounced for the Chinese and

Cypriot catchments where the soil moisture plays a more important role.

In order to have a dynamic comparison, the monthly values of ET a calculated by these three models were regressed against the water balance model values. The results are shown in

seen from the figure that (1) the results from the three evapotranspiration models were closely correlated with the water balance model, resulting in high R

2 values (

O

0.87 in all cases). (2) The correlation between the CRAE model and the water balance model was the best for this region, although the other two were also good. The monthly evapotranspiration values calculated from the three models were also regressed against each other (plot is not shown), and the R

2 values are higher (0.98 for AA-CRAE, 0.97 for

GG-CRAE, and 0.94 for AA-GG) than when they were regressed against water balance calculations.

4.2.2. Eastern China

Using the areal precipitation and discharge data of the Baixi catchment, the average annual actual evapotranspiration was calculated from the longterm water balance equation ET

Z

PT

K

QT as

790 mm. Using the monthly water balance model, the monthly water balance components, including runoff and actual evapotranspiration, were simulated for the catchment. The parameter values tuned using the two criteria are as follows: for the AA model, the a

C.-Y. Xu, V.P. Singh / Journal of Hydrology 308 (2005) 105–121 117

Fig. 6. Correlation between monthly actual evapotranspiration calculated by the three complementary relationship evapotranspiration models and the water balance model for NOPEX region in Central Sweden.

value of 1.26 in (6) is replaced by a smaller factor 1.0, with an addition of b

Z

8.2 W m K

2

(i.e. 0.29 mm/day) which accounts for large-scale advection during seasons of low or negative net radiation and represents the minimum energy available for ET w

. For the GG model, it was found necessary to change the parameter value 0.793 in (11) to 1.03. For the

CRAE model, the parameter values of 14 and 1.20

in (14) were changed to 17 and 0.95, respectively.

Comparison between actual evapotranspiration calculated by the three evapotranspiration models with locally tuned parameters and the water balance model is shown in

(columns 5–8). These values are also plotted in

showed that (1) all three models produced mean annual values correctly as expected; (2) again CRAE model followed closest the water balance model for mean monthly values; (3) compared with

(columns 2–4), it is seen that original values used in the AA and CRAE models gave overestimation for the study region. For the GG model, the original parameter values worked reasonably well for the region and a very minor improvement was obtained with the recalibrated parameter; and (4) as shown in

A for the Swedish catchment, there is a time shift in the peak values calculated using evapotranspiration model based on the routine climatological observations and the water balance model for this catchment. The difference is that for the

Chinese catchment, the water balance model gives the peak one month later than the evapotranspiration models, while for the Swedish catchment the opposite is true. To explain this phenomenon better,

used, where the areal mean monthly precipitation, potential evapotranspiration and soil moisture content computed by the water balance model and mean monthly actual evapotranspiration are plotted. It is seen that for this region, although the evaporationability as measured by the potential evapotranspiration is slightly higher in July than in August, the available water for evapotranspiration as measured by precipitation and soil moisture content in August is the highest. This causes evapotranspiration in July to be slightly lower than that in August for the water balance model. The complementary relationship models do not use directly the soil moisture information and hence produce the highest evapotranspiration rate in July.

The ET a values calculated by these three models were regressed against water balance model values.

The results are shown in

. It is seen that (1) the results from three models were closely correlated with the water balance calculations, resulting in high R

2 values ( O 0.85 in all cases). (2) The correlation between the CRAE model and the water balance model is the best in R

2 value and the other two models give similar results.

4.2.3. North-western Cyprus

Using the areal precipitation and discharge data of the catchment, the average annual actual evapotranspiration was calculated from the long-term water balance equation ET

Z

PT

K

QT as 500 mm. Using the monthly water balance model, the monthly water balance components, including runoff and actual evapotranspiration, were simulated for the catchment.

In tuning the parameters involved in the evapotranspiration models for the semi-arid catchment with sparse vegetation, an extra fact was considered.

That is soil heat flux, G , cannot be considered as

118 C.-Y. Xu, V.P. Singh / Journal of Hydrology 308 (2005) 105–121

Fig. 7. Correlation between monthly actual evapotranspiration calculated by the three complementary relationship evapotranspiration models and the water balance model for Baixi catchment in Eastern China.

negligible (e.g.

Clothier et al., 1986; Kustas et al.,

1993 ). Field observations show that

G / R n can range from 0.05 to 0.30, and is dependent on the time, soil moisture and thermal properties, and vegetation amount and height (

). In this study an arbitrary value of G

Z

0.15

R n was subtracted from the net radiation, R n

. Parameter values were then tuned using the two criteria as before: for the AA model, the a value of 1.26 in (6) is replaced by a smaller factor 1.04, with an addition of b

Z

5.9 W m

K

2

(i.e.

0.21 mm/day). For the GG model, it was found necessary to change the parameter values 0.793 in

(11) into 0.91 and 0.20 into 0.3. For the CRAE model, the parameter values of 14 and 1.20 in (14) were changed to 10 and 1.18, respectively.

The actual evapotranspiration calculated by the three evapotranspiration models with locally tuned parameters and the water balance model is shown in

(columns 5–8) and

C. It is seen that (1) all three models produced mean annual values correctly as expected; and (2) all three models failed to follow the pattern of variation of the water balance model calculated monthly evapotranspiration, although the CRAE model did relatively better. A two-month time shift was found between the water balance model results and the AA and GG models, while one month-time delay existed between the

CRAE model and the water balance model estimations. Again, this phenomenon is explained using

C, where the areal mean monthly precipitation, potential evapotranspiration and soil moisture content computed by the water balance model and mean monthly actual evapotranspiration are plotted. It is seen for this region that although the evaporationability as measured by the potential evapotranspiration is the highest in July, the available water for evapotranspiration as measured by precipitation and soil moisture content in July is very low. Already from

May, the amount of monthly precipitation becomes very small resulting in a rapid decrease in soil moisture. This causes the actual evapotranspiration to reach its peak in April and then decreases as the available water decreases.

The ET a values calculated by these three models were regressed against water balance model values. The results are shown in

Fig. 8. Correlation between monthly actual evapotranspiration calculated by the three complementary relationship evapotranspiration models and the water balance model for Potamos tou Pyrgou river catchment in North-western Cyprus.

with

,

shows that (1) in arid region, the correlations between monthly evapotranspirations calculated by complementary evapotranspiration models and the water balance models are much worse than that in humid regions. (2) The correlation between the CRAE model and the water balance model is the best in R

2 value and the other two models give similar results.

## 5. Discussion

C.-Y. Xu, V.P. Singh / Journal of Hydrology 308 (2005) 105–121

The fact that the complementary relationship models evaluated in this study use only the standard meteorological observations has both advantages and disadvantages as compared with the Penman–

Monteith method and the water balance approaches.

The main advantage of these models is that the models bypass the complex and poorly understood soil–plant processes and thus do not require data on soil moisture, stomatal resistance properties of the vegetation, which are difficult to obtain. The disadvantage is that the models rely only on the routine climatological observations, while local variations, such as properties of vegetation, soil type, basin slope, etc. affect the runoff coefficient, which, in turn, influence the local evapotranspiration.

Before a general discussion is made about the results, a brief review of the conclusions made from earlier studies is useful. According to the study made by

Hobbins et al. (2001a,b) , the predictive power of

both the CRAE and AA models increases in moving toward regions of increased climate control (i.e.

humid regions) of evapotranspiration rates and decreases in moving toward regions of increased soil control (i.e. arid regions). Increased climate/soil control in this context refers to increased and decreased moisture availability, respectively. The studies made by

Xu and Li (2003) and Lemeur and

confirmed the conclusion made by

.

studied two humid regions in Japan by using the CRAE and

AA models and found the results are reasonable as compared with other methods. In the study made by

Lemeur and Zhang (1990) , the CRAE and AA model

were applied to a semiarid region in Northwestern

China and larger errors were found as compared with the water balance approach. In this study we found that using the original parameter values all three complementary models, i.e. CRAE, AA and GG gave acceptable results for the Swedish catchment where the climate variables are a controlling factor for evapotranspiration, since the soil never gets really dry all year around. The results for the Swedish catchment showed that all three models give equally good results for the warmer months, the main difference is found between the AA model and the CRAE model for winter and cool months where the AA model gives lower values than does the CRAE model. That is the snow cover period in Sweden. The main reason is that the AA model, as for many other evapotranspiration models which utilize a form of the Penman equation, does not work (well) for those conditions in which period the available energy ( R n

) is negative or very near to zero. This problem is corrected in the CRAE model by adding a constant b

1 that accounts for largescale advection during seasons of low or negative net radiation and represents the minimum energy available for ET w

. When the models are used with the original parameter values on the Chinese catchment where both climate and soil are controlling evapotranspiration, the results became worse. The worst results were found for the semiarid region in Cyprus where the soil moisture is the main control factor.

Using locally calibrated parameter values all three models were forced to give correct yearly estimates as compared with water balance estimations. As for the monthly estimations, all three models gave acceptable results for the Swedish and Chinese catchments which are relatively humid. For the semiarid region in

Cyprus where the soil moisture is the dominating factor rather than the climate variables for evapotranspiration, all three models failed to gave monthly values that follow the monthly variation pattern of the water balance estimates, although the CRAE model worked better than the other two. This aspect needs further study by including more study regions from the arid climate; unfortunately no more data is available at this time.

## 6. Concluding remarks

119

The performance of the three complementary relationship evapotranspiration models with both original parameter values and recalibrated parameters

120 were tested in three regions representing a large geographic and climatic diversity. One region in

Central Sweden represents a seasonally snow covered humid boreal climate, second study region in eastern

China represents a subtropical humid monsoon climate and the third region in north-western Cyprus represents a semiarid region.

The main conclusions of the study are (1) using the original parameter values all three complementary relationship models worked reasonably well for temperate humid region as represented by the

Swedish catchment (a recent study done by

on German catchments supported this statement), while the predictive power decreases in moving toward regions of increased soil moisture control, i.e. increased aridity. In such regions, the parameters need to be calibrated. (2) Using recalibrated parameter values, all models produced correct yearly values for all the three study regions, as the calibration was carried out to force the parameters that produced close water balance. The recalibrated models produced acceptable monthly values for the Swedish (temperate humid) and the Chinese catchment (subtropical, humid), but failed to produce the monthly variation pattern for the Cypriot catchment (semiarid to arid). (3) In all the three studies regions, the CRAE model produced slightly better results when the recalibrated model parameters are used. The results are supported by those studies already published in the literature. A future study will be carried out by including case studies in different climatic regions such that the conclusions drawn from this study can be generalized.

## Acknowledgements

C.-Y. Xu, V.P. Singh / Journal of Hydrology 308 (2005) 105–121

The first author thanks VR (The Swedish Research

Council) for providing him research fund year by year which supported his research work. He also gratefully acknowledges CAS (The Chinese Academy of

Sciences) for awarding him with ‘The Outstanding

Overseas Chinese Scholars Fund’. Swedish data were provided by SMHI (the Swedish Meteorological and

Hydrological Institute), the Chinese data were provided by Professor Youpeng Xu at Nanjing University and the Cypriot data were provided by the GIS laboratory at the Department of Earth Sciences of

Uppsala University. The authors gratefully acknowledge their kind support and services.

## References

Bouchet, R.J., 1963. Evapotranspiration re´elle et potentielle, signification climatique. General Assembly Berkeley, Int. Assoc. Sci.

Hydrol., Gentbrugge, Belgium, Publ. No. 62, pp. 134–142.

Brutsaert, W., Stricker, H., 1979. An advection–aridity approach to estimate actual regional evapotranspiration. Water Resour. Res.

15 (2), 443–450.

Chiew, F.H.S., McMahon, T.A., 1991. The applicability of

Morton’s and Penman’s evapotranspiration estimates in rainfall–runoff modeling. Water Resour. Bull. 27 (4), 611–620.

Clothier, B.E., Clawson, K.L., Pinter Jr., P.J., Moran, M.S.,

Reginato, R.J., Jackson, R.D., 1986. Estimation of soil heat flux from net radiation during the Growth of alfalfa. Agric. For.

Meteor. 37, 319–329.

Doyle, P., 1990. Modeling catchment evaporation: an objective comparison of the Penman and Morton approaches. J. Hydrol.

121, 257–276.

Granger, R.J., 1989. An examination of the concept of potential evaporation. J. Hydrol. 111, 9–19.

Granger, R.J., 5–7 March, 1998. Partitioning of energy during the snow-free season at the Wolf Creek Research Basin, In:

Pomeroy, J.W., Granger, R.J. (Eds.), Proceedings of a Workshop held in Whitehorse, Yukon, pp. 33–43.

Granger, R.J., Gray, D.M., 1989. Evaporation from natural nonsaturated surfaces. J. Hydrol. 111, 21–29.

Granger, R.J., Gray, D.M., 1990. Examination of Morton’s CRAE model for estimating daily evaporation from field-sized areas.

J. Hydrol. 120, 309–325.

Halldin, S., Gryning, S.-E., 1999. Boreal forests climate. Agric. For.

Meteorol. 98/99, 1–4.

Hobbins, M.T., Ramirez, J.A., Brown, T.C., 2001. The complementary relationship in estimation of regional evapotranspiration: an enhanced advection–aridity model. Water Resour. Res. 37 (5),

1389–1403.

Hobbins, M.T., Ramirez, J.A., Brown, T.C., Claessens, L.H.J.M.,

2001. The complementary relationship in estimation of regional evapotranspiration: the complementary relationship areal evapotranspiration and advection–aridity models. Water Resour.

Res. 37 (5), 1367–1387.

Kustas, W.P., Daughtry, C.S.T., Van Oevelen, P.J., 1993. Analytical treatment of the relationships between soil heat flux/net radiation ratio and vegetation indices. Remote Sens. Environ.

46, 319–330.

Lemeur, R., Zhang, L., 1990. Evaluation of three evapotranspiration models in terms of their applicability for an arid region.

J. Hydrol. 114, 395–411.

Monteith, J.L., 1963. Gas exchange in plant communities. In:

Environmental Control of Plant Growth.

Monteith, J.L., 1965. Evaporation and environment. Symp. Soc.

Exp. Biol. 19, 205–234.

Morton, F.I., 1978. Estimating evapotranspiration from potential evaporation: practicality of an iconoclastic approach. J. Hydrol.

38, 1–32.

Morton, F.I., 1983. Operational estimates of areal evapotranspiration and their significance to the science and practice of hydrology. J. Hydrol. 66, 1–76.

Penman, H.L., 1948. Natural evaporation from open water, bare and grass. Proc. R. Soc. Lond., Ser. A 193, 120–145.

Priestley, C.H.B., Taylor, R.J., 1972. On the assessment of surface heat fluxes and evaporation using large-scale parameters.

Monthly Weather Rev. 100, 81–92.

Seibert, P., 1995. Hydrological characteristics of the NOPEX research area. MSc Thesis, Division of Hydrology, Uppsala

University, Sweden.

C.-Y. Xu, V.P. Singh / Journal of Hydrology 308 (2005) 105–121 121

Van der Beken, A., Byloos, J., 1977. A monthly water balance model including deep infiltration and canal losses. Hydrol. Sci.

Bull. 22 (3).

Xu, C.-Y., Chen, D., in press. Comparison of seven models for estimation of evapotranspiration and groundwater recharge using lysimeter measurement data in Germany. Hydrol. Process.

Xu, Z.X., Li, J.Y., 2003. A distributed approach for estimating catchment evapotranspiration: comparison of the combination equation and the complementary relationship approaches.

Hydrol. Process. 17, 1509–1523.

Xu, C-Y., Seibert, J., Halldin, S., 1996. Regional water balance modelling in the NOPEX area—development and application of monthly water balance models. J. Hydrol. 180, 211–236.

Yates, D.N., 1997. Approaches to continental scale runoff for integrated assessment models. J. Hydrol. 201, 289–310.

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

### Related manuals

advertisement