Comparative Evaluation of IDF Equation Types in Southern Nigeria

This paper evaluates four types of non-Probability Density Function {nonPDF} IDF equations mostly
used in engineering practice for design of urban hydraulic structures. The empirical models employed
for comparison on the development of standard IDF equations using historic data for Benin, Calabar,
Port Harcourt, and Warri meteorological stations, all in Southern Nigeria were available in literature.
The model evaluation indices were; percent relative error, Nash – Sutcliffe efficiency (NSE), LogNSE,
percent volume error(PerErr), total accuracy and RMSE - observations standard deviation ratio
(RSR). The percent relative error and total accuracy being the product of NSE, LogNSE, and PerErr
(Equation 5) were used to evaluate each IDF equation form against each station. The values of the
combination of the three accuracy measures range from 0 to 1 with the perfect fit at 1. RSR varies
from the minimal value of 0, to a large positive value. The application of the three numerical
assessment measures: percent relative error, total accuracy and RSR across each stations show that
Equation 1 is rated best at Benin City, Equation 2 at Calabar, Equation 3 at Port Harcourt and
Equation 1 at Warri. On the basis of relative percent error, the IDF equations were evaluated for
return periods ranging from 5 to 40 years and for storm durations ranging from 15 to 30 minutes. The
strength and weakness of the different models were assessed using the mean ± standard deviation as
range between intensities estimated for 5 and 40 years, and percent relative error between the
observed and predicted rainfall intensities as performance criteria. The results obtained show that IDF
type-1 and 2 equations displayed lower range of intensities for all returned periods. Also IDF type-1
and 2 equations predicted the lowest relative error of less than or equal to 6% in all stations
considered. Finally, we recommend IDF equation type 1 and 2 best for design of storm water
management facilities at Benin City, Calabar and Warri while equation 2 and 3 at Port Harcourt. The
study has advanced the understanding of the equations and further insight in their utility as hydrologic
design tools.