Dose calculations in proton therapy need to be computed as fast as possible for successful cancer treatment planning and execution. The dose calculation algorithms that provide enough accuracy for treatment planning, takes too much time to utilise; therefore there is a need for faster alternatives. One of the alternatives is using a deterministic semi-analytic numerical algorithm for EM interactions. This alternative in its current state is not accurate enough, and therefore it is sought to include the effects of secondary protons on the total dose distribution of the deterministic semi-analytic numerical algorithm, using convolutional methods. In this thesis an attempt is made to find a kernel that, when convoluted with a primary proton flux, produces the desired secondary proton dose. The parameters of two different types of kernels, the Gaussian kernel and Fractional Filter kernel, are optimised and their resulting shapes are presented. Furthermore, the secondary proton dose through the convolution of the primary proton flux and the different kernels are presented. The doses obtained from the optimal kernels are compared with the target dose on the shape and a measure of quality: the gamma index passing rate. Found was that the Fractional Filter kernel can produce both asymmetric doses and symmetric doses, while the Gaussian kernel can only produce symmetric doses. The passing rate was found to be 29.41% for the Fractional Filter kernel and 17.65% for the Gaussian kernel. Thus, the Fractional Filter is better for estimating secondary proton dose distribution through convolutional methods than using a Gaussian kernel. but insufficient due to the low passing rate. A suggestion for improvement is applying skew-Gaussians in the Fractional Filter kernel or by applying other asymmetric kernels.

This thesis delves into glacier dynamics using the 2D Shallow Ice Approximation enriched by satellite remote sensing data on glacier surface velocities and ice thickness, aiming to refine empirical laws for better predicting glacier movements. The integration of such data has been pivotal, markedly enhancing model calibration despite challenges like steady-state assumptions necessitated by data scarcity. This underscores the critical role of high-quality, temporally resolved data in modeling glacier dynamics accurately. A significant advancement was the implementation of spatial stratification, which notably improved model performance—reducing Root Mean Square Error (RMSE) by up to 30% and elevating the coefficient of determination (R²) by 0.2 to 0.4 across different regions. This highlights the potential of fully distributed inversions to capture the complex variability of glaciers. Employing Julia for its computational efficiency proved effective for large-scale modeling tasks, setting a promising foundation for future research aimed at understanding and predicting glacier responses to climate change. It is recommended to utilize geostatistical interpolation methods for inverting glacier characteristics from sparse data, in order to acquire these characteristics across the entire glacier area.

This thesis delves into glacier dynamics using the 2D Shallow Ice Approximation enriched by satellite remote sensing data on glacier surface velocities and ice thickness, aiming to refine empirical laws for better predicting glacier movements. The integration of such data has been pivotal, markedly enhancing model calibration despite challenges like steady-state assumptions necessitated by data scarcity. This underscores the critical role of high-quality, temporally resolved data in modeling glacier dynamics accurately. A significant advancement was the implementation of spatial stratification, which notably improved model performance—reducing Root Mean Square Error (RMSE) by up to 30% and elevating the coefficient of determination (R²) by 0.2 to 0.4 across different regions. This highlights the potential of fully distributed inversions to capture the complex variability of glaciers. Employing Julia for its computational efficiency proved effective for large-scale modeling tasks, setting a promising foundation for future research aimed at understanding and predicting glacier responses to climate change. It is recommended to utilize geostatistical interpolation methods for inverting glacier characteristics from sparse data, in order to acquire these characteristics across the entire glacier area.

This thesis delves into glacier dynamics using the 2D Shallow Ice Approximation enriched by satellite remote sensing data on glacier surface velocities and ice thickness, aiming to refine empirical laws for better predicting glacier movements. The integration of such data has been pivotal, markedly enhancing model calibration despite challenges like steady-state assumptions necessitated by data scarcity. This underscores the critical role of high-quality, temporally resolved data in modeling glacier dynamics accurately. A significant advancement was the implementation of spatial stratification, which notably improved model performance—reducing Root Mean Square Error (RMSE) by up to 30% and elevating the coefficient of determination (R²) by 0.2 to 0.4 across different regions. This highlights the potential of fully distributed inversions to capture the complex variability of glaciers. Employing Julia for its computational efficiency proved effective for large-scale modeling tasks, setting a promising foundation for future research aimed at understanding and predicting glacier responses to climate change. It is recommended to utilize geostatistical interpolation methods for inverting glacier characteristics from sparse data, in order to acquire these characteristics across the entire glacier area.