Page 175 - IJES Special Issues for AIEC2016
P. 175
International Journal of Environment and Sustainability, 2016, 5(2): 72-88 75
al., 1988). Kriging has also been implemented in two variables, and it was chosen to get an indica-
several other studies (Beelan et al., 2009; Zou, et tion of the correspondence of timing and evolu-
al., 2011; Shad et al., 2009). tion between observed and interpolated concen-
tration values. The coefficient of efficiency (NSE)
Natural Neighbor interpolation finds the closest indicates the normalized fit of the model, the
subset of input samples to a query point and ap- value ranges from -∞ to 1. It compares the mean
plies weights to them based on proportionate ar- square error generated by a particular model
eas to interpolate a value. It is also known as simulation to the variance of the output se-
Sibson or "area-stealing" interpolation. quence; a value of 1 indicates a perfect fit (Nash
and Sutcliffe, 1970). Ross, 1996 proposed a sim-
2.2 Performance Measures ple multiplicative factor called accuracy factor
(ACFT) that represents the spread of the results
A statistical error is the amount by which an ob- of the modelled data. A value of one indicates
servation differs from its expected value. The that there is perfect agreement between all the
statistical indices selected to measure perfor- predicted and modelled values and values larger
mance are Root Mean Square Error (RMSE), than one indicate the less accurate average esti-
Mean Absolute Percentage Error (MAPE), Nash- mate.
Sutcliffe equation (NSE) (Nash and Sutcliffe,
1970) and Accuracy Factor (ACFT) (Ross, 1996) Several studies have used error statistics to com-
given by equations 1 to 4, respectively. The Pear- pare observed and predicted meteorology and
son correlation coefficient (r) was also measured air quality data. RMSE was used by Shad et al.
to check the strength and direction of the linear (2009) to compare the observed data with the
relationship between the observed and interpo- predicted air pollution using fuzzy genetic linear
lated values. Kriging. Monteiro et al., (2013) used it in bias
correction techniques to improve air quality en-
= ∑( − ) [1] semble predictions, and Son et al., (2010) used it
in a study of individual exposure to air pollution
=( ) [2] and lung function in Korea. EU-wide maps were
prepared based on the predictor variables and
=1− ( ) [3] the modelled air pollution concentrations were
( ∗) selected on the predefined performance
measures r2 and RMSE. A value of RMSE <10 and
|( )| [4] r2 >0.5 was considered a good performance
measure (Beelan et al., 2009). Singh et al., (2012)
= 10( ∈ ) used RMSE, ACFT and NSE as performance
measures of different linear and nonlinear mod-
Where Intri = Interpolated value; Obsi = Ob- eling approaches for predicting urban air quality.
served value; n = number of observations Solar radiation and the air pollution index were
estimated based on linear, exponential and loga-
RMSE is the frequently used measure of the dif- rithmic models, and similar indices were used to
ferences between values predicted by a model or check the performance index in China (Zhao et
an estimator and the values actually observed. It al., 2013). In the current study, RMSE, MAPE and
basically represents the sample standard devia- r2 were primarily used as performance
tion of the differences between predicted and measures. RMSE <8 MAPE <25% and r2>0.5 was
observed values. RMSE gives important infor- considered a good measure.
mation in predicting the magnitude of a pollutant
concentration, a measure close to zero repre- 2.3 Station Elimination Process
sents good predictions. The absolute mean per-
centage error denoted by MAPE is calculated by The main objective of this optimization process
dividing the sum of percentage error by the num- is to eliminate as many stations as possible and
ber of observations, and a value equal or close to fill in the missing information through the inter-
zero is considered ideal. The correlation coeffi- polated values. The steps involved in this process
cient is a measure of linear dependence between
Science Target Inc. www.sciencetarget.com
