Models in Irrigation andWater Management - Practices of Irrigation and On-farm Water Management - page 392

(i) Bias (i.e., error) or Mean Bias:

N

1
N

Bias = ( S i − M i ) (10.1)

i = 1

where S and M are the simulated (or predicted) and measured (or observed)
values for the i th observation and N is the number of observations.
(ii) Mean absolute bias:

i = N

1
N

=

MAE I. S i − M i I (10.2)

i = 1

(iii) Root mean square error (RMSE), which quantifies the dispersion between
simulated and measured (or observed) data:

1
N

N

2

RMSE =

1 (

S i − M i ) (10.3)

i =

Ideally, the value of Bias, MAE, and RMS should be zero.
(iv) Relative error (RE):

RMSE
y

RE = 100 (10.4)

where y is the mean of observed values. RE indicates the percentage deviation
with respect to mean observed value.
(v) Model efficiency (EF): Model efficiency is calculated as

( M

− ( S

− M ) 2 M ) 2 −

EF = ( M (10.5)

− M ) 2

where
M

measured mean
An ideal value of EF is unity.
(vi) Index of agreement (IA):

=

i = 1 ( o i

N

s i ) 2

−

IA = 1 − , 0 ≤ IA ≤ 1 (10.6)

i = 1

N

( O i + S i ) 2

where O i =| , S i =|

O i − S | S i − S | , O i is the observed value, S i is the simulated

value, S is the simulated mean.
(vii) Coefficient of residual mass (CRM):