Model efficiency performance assessment through a standard triangular diagram (STD)

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ORIGINAL ARTICLE

Model efficiency performance assessment through a standard triangular diagram (STD) Zekâi Şen1,2 Received: 8 July 2020 / Accepted: 3 October 2020 © Springer Nature Switzerland AG 2020

Abstract Model efficiency performance provides reliable and acceptable criteria by comparing the factual data with the model results based on a set of significant parameters’ comparisons. In this paper, a standard triangular diagram (STD) is proposed for such a goal through the comparisons of arithmetic averages, standard deviations, and serial correlation coefficients ratios. It provides also the comparison among different dimensional units. The application of the STD concept is presented for a set of annual rainfall records at different locations based on monthly hydro-meteorological data (rainfall, potential evaporation, soil moisture, and surface runoff) from Salt Lake (in Turkey) region, monthly flow series from trans-boundary Tigris River and autoregressive moving average, ARIMA, and stochastic model ensemble of simulations. Keywords  Diagram · Efficiency · Model · Parameter ratio · Difference · Trilinear

Introduction The modeling concept has started in physical sciences almost 250 years ago, and later, physics and engineering studies started to benefit from modeling approaches with the start of twentieth century extensively. Especially, the entrance of computer software into the scientific domain supported modeling studies in an unprecedented rate. The main idea is to obtain a system of factual data representation through a suitable number of basic equations. In general, the research and simulation models used in practical applications can be viewed in three groups as deterministic (analytical and numerical models) about which Fobes and Priest (1987) provided a comparison of analytical and numerical model solutions on the basis of their model of a unified formulation for steady-state reconnection in which different types of reconnection are produced by varying the input boundary conditions. The second set of modeling is * Zekâi Şen [email protected]; [email protected] 1



Civil Engineering Department, Engineering and Natural Sciences Faculty, Istanbul Medipol University, Beykoz, 34181 Istanbul, Turkey



Department of Meteorology, Center of Excellence for Climate Change Research, King Abdulaziz University, PO Box 80234, Jeddah 21589, Saudi Arabia

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concerned with uncertainty (probabilistic, statistical, and stochastic) in the input variables, which result in uncertain model output. Uncertainty in input and output variables can be represented by convenient probability distribution functions (PDFs). Comparison of a model output with inputs leads to a natural decomposition of the prediction variance and the correlation ratio as a measure of importance (Ayyub and Klir 2006). Another modeling trend is through computer software applications written by a team of experts (Gomaa 2011). In modeling studies, although there are some instances, where several patterns have resemblance to each other visually, it is pr