Improving the Accuracy Of MEPDG Climate Modeling Using Radial Basis Function

In this paper, the accuracy of two mesh-free approximation approaches, the Gravity model and Radial Basis Function, are compared. The two schemes’ convergence behaviors prove that RBF is faster and more accurate than the Gravity model. As a case study, the interpolation of temperature at different locations in Tennessee, USA, are compared. Delaunay mesh generation is used to create random points inside and on the border, which data can be incorporated in these locations. 49 MERRA weather stations as used as data sources to provide the temperature at a specific day and hour. The contours of interpolated temperatures provided in the result section assert RBF is a more accurate method than the Gravity model by showing a smoother and broader range of interpolated data. INTRODUCTION In current data driven world, maintaining the quality of data and its derivatives is of most importance. Complete data sets are necessary to properly understand, interpret and use data for 1 Ghasemi, February 17, 2021 ar X iv :2 10 2. 07 89 0v 1 [ cs .L G ] 1 5 Fe b 20 21 various applications; however, gaps do exist in data. One of the methods employed to fill data gaps is data interpolation. The purpose of this study was to assesses the two common methods used in data interpolation; gravity model and radial basis function model. Both models are still used in different applications, but their output accuracies are yet to be compared. When comparing both interpolation models’ outputs to the actual analytical outputs, the radial basis function model achieved faster, and higher accuracy as compared to the gravity model. To illustrate the effects of these interpolated output differences, temperature contour maps were produced for the state of Tennessee considering; 49 MERRA weather stations as data sources and, 3881 data interpolation points. The interpolated temperature contours were much smoother, and well defined with the RBF model and it’s output ranges were wider than the gravity model. When dealing with , being a small data set or big data, quality is the most important factor to consider. In the growing demand of tools and methods to deal with the vast daily or periodic data, it is important to consider tools and methods that will provide desired data quality. For cases where data gap(s) are experienced, different methods can be employed to fill these gaps. Filling of data gaps is necessary for multiple tasks such as; accurate data interpretations, model calibrations and realistic presentation of information. One common method used in filling empty gaps while considering existing data quantities is data interpolation. Many interpolation methods have been developed throughout the years with different applications in various fields of study. Common to these widely used interpolation methods include the gravity model and the radial basis function (RBF) model. Being the common methods for data interpolation, it is vital to determine the accuracy offered by each method. GRAVITY MODEL Inspired by the Newton’s universal law of gravity that relates the gravitational force between two bodies to the product of their masses and being inversely proportional to the square of the distance between them, the gravity model also applies the same principle. The gravity model has different applications throughout multiple disciplines including the transportation industry, civil engineering, data and computer science fields. Some application of the gravity model includes data 2 Ghasemi, February 17, 2021 classification (Cano et al. 2013). Gravity model algorithms have been used for multi-label lazy learning, by treating instances of data as particles of the data. The use of gravity model in multilabel lazy learning reported better performance than the state-of-the-art multi-label lazy methods (Reyes et al. 2016). The gravity models in combination with cognitive laws have been used for small noisy data classification (Wen et al. 2013). Gravity models have been employed to improve the local weighted learning regression method for multi-target data (Reyes et al. 2018). For data interpolation purposed, the gravity model is being used in the formation of Visual Weather Station (VWS) for the mechanistic-empirical pavement design procedures (Schwartz et al. 2015). Gravity Model Interpolation theory The gravity interpolation model also known as 1/R method considers distances in establishing weights for its final interpolated output. During the interpolation, closest points to the interpolation point of interest, contributes more weight to the final output. The gravity model uses the equation as seen below. Where Dint is the gravity interpolation output, D is the data that is obtained from the different neighboring points at distance, (Eq. 1) (Schwartz et al. 2015). Dint = ∑n i=1 Di d2 i ∑n i=1 1 d2 i (1) RADIAL BASIS FUNCTION The general linear governing equation for RBF can be expressed as