Soil erosion is widespread with spatio-temporal variability and is central to the determination of sediment yield, which is vital to proper management of watersheds. We propose a relation between the Curve Number (SCS 1956) and the Sediment Yield Index (SYI) using cubic, quadratic and quintic splines in this research. Using Mohgaon watershed (part of Narmada Basin) data, the relation between observed and computed SYI is found to have a coefficient of determination (R2) value of 0.87, 0.40 and 0.10 corresponding cubic, quadratic and quintic splines suggesting that such a relation can be used to determine SYI from the available CN value. The cubic spline was found to be the best method with respect to Absolute Prediction Error (APE), Integral Square Error (ISE), Coefficient of Efficiency (CE), Coefficient of Correlation (CC) and degree of agreement (d) (i.e., APE = 1.35, ISE = 3.09, CE = 62.08, CC = 79.60 and d = 0.99). The quintic spline (with an average value of APE = 19.59, ISE = 7.84, CE =  − 165.73, CC = 19.30 and d = 0.26) and the quadratic spline (with an average value of APE = 20.99, ISE = 8.92, CE =  − 199.90, CC = 8.95 and d = 0.15) ranked as the 2nd and the 3rd best methods, respectively.

Soil erosion modeling of watershed using cubic, quadratic and quintic splines

The spread of communicable diseases, such as COVID-19, has a detrimental effect on our socio-economic structure. In a dynamic log-run world, socio-economic and environmental factors interact to spread communicable diseases. We investigated the long-term interdependence of communicable disease spread, economic prosperity, greenhouse gas emissions, and government health expenditures in India's densely populated economy using a variance error correction (VEC) approach. The VEC model was validated using stationarity, cointegration, autocorrelation, heteroscedasticity, and normality tests. Our impulse response and variance decomposition analyses revealed that economic prosperity (GNI) significantly impacts the spread of communicable diseases, greenhouse gas emissions, government health expenditures, and GNI. Current health expenditures can reduce the need for future increases, and the spread of communicable diseases is detrimental to economic growth. Developing economies should prioritize economic growth and health spending to combat pandemics. Simultaneously, the adverse effects of economic prosperity on environmental degradation should be mitigated through policy incentives. 

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The long-term dynamic relationship between communicable disease spread, economic prosperity, greenhouse gas emissions, and government health expenditures: preparing for COVID-19-like pandemics

Cubic spline interpolation is a very popular curve fitting method since it is easy to implement and produces a smooth curve. This article discusses the development of the cubic spline interpolation method for a clamped boundary condition taken from finite-difference explicit formulas with higher-order accuracy. The development of this method is applied to an object tracking problem. In particular, this problem is examined for second-order clamped cubic spline, and the interpolated results are compared with those for natural and first-order clamped cubic splines. From the simulation of trajectory data generated from the Archimedean spiral curve, the total error values for natural, first-order, and second-order clamped cubic splines are respectively E1 tot = 0.14290, E2 tot = 0.22614 and E3 tot = 0.09007. Based on these results, it is concluded that the second-order clamped cubic spline interpolation developed in this article can produce a more accurate object trajectory than the natural and firstorder clamped cubic splines.

Development of a clamped cubic spline interpolation method and its application in object tracking problem

In this chapter, a comprehensive review is made on the application of cubic spline interpolation techniques in the field of power systems. Domains like available transfer capability (ATC), electric arc furnace modeling, static var. compensation, voltage stability margin, and market power determination in deregulated electricity market are taken as samples to illustrate the significance of cubic spline interpolation.

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Prabhakar Karthikeyan Shanmugam

Papers

Application of Cubic Spline Interpolation Technique in Power Systems: A Review