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Sensitivity analysis of the evaporation module of the E-DiGOR model

aerodynamic resistance (s m–1), λ is the latent heat of vaporisation (MJ kg–1), γ is the psychrometric constant (kPa °C–1), and 86.4 is the factor for conversion from kJ s–1 to MJ day–1.

The formulas calculating the relative sensitivity coefficients of the variables in Equation (1) are as follows:

a) Sd =

2Ep 2d

#

d Ep

=

1+

1 86.4#t#cp # d / ra d#(Rn - Gs)

-

1 1+

c d

b) SRn

=

2Ep 2Rn

#

R

n

E

p

=

d# R n d#(Rn - Gs) + 86.4#t#cp #d / ra

c) SGs

=

2Ep 2Gs

#

G E s p

=

  • -

    d# G s

d#(Rn - Gs) + 86.4#t#cp #d / ra

d) S2 =

2Ep

2d

#

d

Ep

=

1

d#(Rn - Gs) ra 86.4 # t # cp # d

+1

e) Sra =

2Ep 2ra

#

r E a p

=

  • -

    1

d#(Rn - Gs)# ra 86.4 # t # cp # d

+1

Actual evaporation rates were computed using Aydın’s equation (Aydın et al. 2008):

Ea =

Log } - Log }ad Log }tp - Log }ad

#Ep

(2)

w h e r e E a a n d E p a r e a c t u a l a n d p o t e n t i a l e v a p o r a t i o n r a t e s ( m m d a y - 1 ) , r e s p e c t i v e l y , | ψ t p | i s t h e a b s o l value of soil water potential (matric potential) at u t e

500

which actual evaporation starts to drop below potential one, |ψad| is the absolute values of soil water potential at air-dryness, and |ψ| is the absolute values of soil water potential. The values of all ψ are in centimetres of water.

The sensitivity coefficients based on the partial derivatives for Equation (2) are as follows:

a) S} =

2Ea 2}

#

} Ea

=

}

ln 10 # } #(Log } - Log }tp )

b) S}ad

2E

a

2}

ad

=

#

}ad Ea

=

1 ln 10

#

e

  • -

    1

Log } - Log }ad

  • +

    Log }tp

1

  • -

    Log }ad

o

c) SEp =

E E E E p a p a # 2 2

=1

2E

a

2}

tp

d) S}tp

=

#

  • -

    1

}tp Ea

=

ln 10#_Log }tp - Log }ad i

To estimate |ψ|, Aydın and Uygur’s equation can be used (Aydın 2008; Aydın et al. 2008):

ψ

=

  • -

    [(1/α)

(10∑Ep)3 /

2 ( θ f c

θ a d

)

(Dav

t/π)1/2]

(3)

w h e r e ψ i s s o i l w a t e r p o t e n t i a l ( c m o f w a t e r ) a t t h e t o p s u r f a c e l a y e r , α i s a s o i l - s p e c i f i c p a r a m e t e r ( c m ) r e l a t e d t o f l o w p a t h t o r t u o s i t y i n t h e s o i l , E p i s c u m u l a t i v e p o t e n t i a l s o i l e v a p o r a t i o n ( c m ) , a n d θ f c a n d θ a d a r e a v e r a g e - v o l u m e t r i c w a t e r c o n t e n t ( cm−3) at field capacity and air-dryness, respectively. c m D a v i s a v e r a g e h y d r a u l i c d i f f u s i v i t y ( c m 2 d a y 1 ) , t i s t h e t i m e s i n c e t h e s t a r t o f e v a p o r a t i o n ( d a y s ) , a n d π 3.1416. i s 3

The relative sensitivity of |ψ| to input variables in Equation (3) is as follows:

a) SEp =

2} 2Ep

#

Ep }

=

30Ep 10/Ep

b) SDav

=

2} 2Dav

#

Dav }

= - 1/2

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