PhD Thesis Emmanuel Obeng Bekoe - Cranfield University

N
∑
t = 1
124
N
sim obs 2
obs obs
( q − q ) ( q − q )
∑
PME = 1− --------------------------------------------(5.5)
t
t
t = 1
t
t −1
where qt sim , qt obs and qm obs are respectively the daily simulated, observed and mean
flow of the observed flows and N is the number of data points.
They have the ability to assess aspects of the model performance/hydrograph
that are relevant to the aims and objectives i.e. the PBIAS function assesses
overestimation or underestimation of streamflows and the PME statistic
evaluates whether the ACRU model will be suitable for prediction when the
objective to simulate the impacts of scenarios of future change is undertaken.
The Daily Root Mean Square (DRMS) and Root Mean Square (RMS) error
compute the standard deviation of the model prediction error; where a smaller
value indicates a better model performance, and are measured in millimetres.
The Performance Bias (PBIAS) measures the average tendency of the
simulated flows to be larger or smaller than their observed counterparts; the
optimal value is zero (0); positive values indicate a model bias toward
underestimation, whereas negative values indicate a bias toward
overestimation. Its units are in percentages.
The Nash and Sutcliffe Efficiency (NSE) measures the relative magnitude of the
residual variance (“noise”) to the variance of the flows (“information”); the
optimal value is 1.0 and the values should be larger than zero (0.0) to indicate
“minimally acceptable” performance (Gupta et al., 1999). A value equal to zero
indicates that the mean observed flow is as good as the model. Henrikson et al.
(2003) categorised NSE into five classes namely; excellent, very good, good,
poor and very poor and defined the limits of the classes for each of the
efficiency indexes. They proposed a limit of 0.5 for a result between good and
poor performance. Liden and Harlin, (2000) and Andersen et al. (2001) also
state that a good simulation should have an NSE between 0.5 and 0.95.
Emmanuel Obeng Bekoe Phd Thesis Chapter 5 Hydrological modelling of Densu
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