The Earth's surface is a complex landscape that is essential for a wide range of applications, from urban planning to environmental monitoring. Digital models of the Earth's surface are generated through mathematical calculations using elevation data collected from various sources and the Digital Terrain Model (DTM) which captures the bare earth's surface topography in 2.5D. The creation of DTM is an approximation of terrain in unsample locations, by using x-y coordinates and one z value. Traditionally, terrain interpolation uses deterministic or geo-statistical methods to calculate elevation. This research would use random forest regression as an alternative method and to compare the results against traditional interpolation. Comparing different locations against traditional interpolation yields similar results overall. Feature importance, within the the points that are closest to the sampled ICESat-2 data point are more significant than other features used in Random Forest model. The correlation between these datasets and the spatial relationship established would impact on the results of the elevation. The improvement overall of using traditional interpolation compared to random forest regression is limited depending on the location and using model trained with local datasets. For model trained on other geographical locations, which shows similar differences.

With the increasing pressure on global forests due to deforestation and habitat loss, it is more important than ever to understand our forest ecosystems on a larger scale. Canopy gap fraction is an indicator used for estimating forest biomass and better understanding of ecosystem functioning. For decades there have been research on computing canopy gap fraction using ground measurements as well as Airborne Laser Scanning (ALS). These approaches, however, are limited by the data available. A global coverage of data on canopy gap fraction could be made available by space-based laser altimetry mission Ice, Cloud and land Elevation Satellite (ICESat-2). Although its main scientific objectives are focused on polar areas, it has already proven to facilitate broader scientific disciplines. The ATL08 data product is focused on land-vegetation and already provides global data on canopy heights. However, there is ongoing research for using ATL08 data for canopy gap fraction estimation. Although some approaches have been suggested in the literature, a tested workflow to achieve this goal has not been published.

This thesis tests two methods for estimating canopy gap fraction from ICESat-2 ATL08 data and evaluates the results against openly available ALS data. First, a simple method of using canopy to total photon ratio is used. Then, an alternative method that aims to correct for the surface reflectivity is tested. The results from both methods are similar, therefore the computationally less expensive method is recommended. Although this thesis does not achieve to present a sufficiently accurate approach for using ICESat-2 ATL08 data for canopy structure estimation, it is shown that further research is needed and the results are promising. Furthermore, it is demonstrated that annual trends in canopy gap fraction can be seen in ATL08 data. Considering the global coverage of ICESat-2 data, it is concluded that despite the accuracy not meeting the expectations, using ATL08 for studying canopy gap fraction on a global scale and through time has high value and great potential for environmental research.

Digital Surface Models (DSMs) are commonly employed to investigate topographical characteristics and processes; however, the presence of canopy and infrastructure in urban and forested areas can lead to height biases and inaccuracies. In this study, I aim to correct such biases by applying a deep learning approach known as Residual U-Net to remove the selected pixels and generate Digital Terrain Models (DTMs) that accurately represent the Earth's surface without canopy and infrastructure influence.

The Residual U-Net model was trained and tested on a dataset of DSM and DTM pairs, which were acquired from resampled AHN4. The model was evaluated on its ability to predict DTMs from DSMs, and its performance was compared with other existing methods. Additionally, the model was tested on different resolutions and the Copernicus DEM to assess its adaptability and generalization capabilities.

The results indicate that the Residual U-Net model outperforms conventional techniques, effectively reducing the influence of canopy and infrastructure, and resulting in DTMs with enhanced precision. The study also explores the errors in detail and identifies the model's error causes, highlighting its limitations and areas for potential improvement.

This study concludes by demonstrating the efficacy of applying deep learning techniques, such as Residual U-Net, to correct global elevation models for canopy and infrastructure. The results indicate that the model is a promising tool for topographical investigation in both urban and woodland situations, offering a versatile solution for generating accurate DTMs from DSMs.

In the past 15 years the field of general purpose computing on graphics processing units, or GPUs, has become well developed and the practice is becoming more mainstream. Computational demands of simulation software are continuously increasing. As such for many applications traditionally computed on the central processing unit the question arises of whether moving to GPU computing is a possible cost effective way of meeting these demands.
The fundamental nature of GPU architecture that makes it so cost effective at doing bulk computation also poses restrictions on which applications are suitable for it. The shallow water equations are a simplified form of the Navier-Stokes equations and describe water levels and flow currents in suitably shallow water such as rivers, estuaries and the North sea. The main research goal of this thesis project was to determine whether the shallow water equations are suitable for implementation on a GPU. Two options exist, the equations may be solved with either an explicit or implicit time integration method. First, a literature study was conducted to familiarize with the tools required to build explicit and implicit shallow water models on a GPU. Then both an explicit and implicit shallow water solver were developed first in the MATLAB programming language and later in CUDA C++ on both CPU and GPU. The main findings are that both explicit and implicit methods are well suited for GPU implementation. Both methods proved to be compatible with a wetting and drying mechanism of numerical cells. The Cuda C++ implementation was in the order of 10 times as fast as a MATLAB implementation for both CPU and GPU. For the benchmark cases tested, the Cuda C++ GPU implementation was in the order of 50 times faster than the equivalent multithreaded CPU implementation.
The implicit implementation was benchmarked using the conjugate gradient method to solve the linear system. Various preconditioners were tested and a Repeated Red Black preconditioner was found to be the most effective. The computation time of the RRB preconditioned implicit method was compared with the explicit method and it was found that the two methods reached parity in computation time when the implicit time step was taken roughly 50 times as large as the explicit time step. For implicit time steps smaller than that the explicit method was faster and when the implicit time step was larger the implicit method was faster. For the benchmark cases tested, the implicit method using a time step 50 times larger than the explicit method was found to be less accurate and less stable than the explicit method. The conclusion is that for cases similar to the benchmark cases an explicit method is the fastest, most stable and most accurate method and thus the preferred choice.