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Fig. 2 | Earth, Planets and Space

Fig. 2

From: Ionospheric electron density modelling using B-splines and constraint optimization

Fig. 2

2D tensor product B-spline representation of a key parameter \(\kappa _r\), as introduced in Eq. (11). The endpoint-interpolating B-splines (top left panel) and the trigonometric B-splines (bottom left panel) are shown for the selected level values \(J_1 = 4\) and \(J_2 = 3\), respectively. Accordingly, there are \(K_{J_1} = 2^{J_1} + 2 = 18\) B-splines \(N_{4,k_1}^2(\varphi )\) with \(k_1 = 0,1,\ldots , 17\) defined along the latitude and \(K_{J_2} = 3 \cdot 2^{J_2} = 24\) trigonometric B-splines \(T_{3,k_2}^2(\lambda )\) with \(k_2 = 0,1,\ldots , 23\) defined along longitude between \(-180^{\circ }\) and \(180^{\circ }\). As one of altogether \(432 = 18 \cdot 24\) 2D tensor product B-splines functions the right panel shows exemplarily the function \(N_{4,11}^2(\varphi ) \cdot T_{3,2}^2(\lambda )\); the non-zero region is referred to as its influence zone. Both the polynomial and trigonometric B-splines basis functions are unitless and hence their product also remains unitless in this figure

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