## Description

This dissertation solves two important problems in the modern analysis of big climate data. The first is the efficient visualization and fast delivery of big climate data, and the second is a computationally extensive principal component analysis (PCA) using spherical harmonics on the Earth’s surface. The second problem creates a way to supply the data for the technology developed in the first. These two problems are computationally difficult, such as the representation of higher order spherical harmonics Y400, which is critical for upscaling weather data to almost infinitely fine spatial resolution. For the first problem, the 4D Visual Delivery (4DVD) software technology has been created as a web application to provide appealing visualizations of climate data and to easily deliver big climate data to end users quickly and efficiently. The need for such an application is first discussed and is followed up with the initial design requirements. From here, a novel interconnected system is designed that seamlessly integrates a database, web server, and front-end computing. WebGL and JavaScript are used to generate feature rich maps and time series of global climate data. The delivered data can be sorted and their statistical properties can be easily computed. All this is done with minimal processing from the server because the computations are moved instead to the end user’s web browser, taking a heavy burden off of the back-end. The second topic is the calculation of an annual mean global climate of surface air temperature anomalies through the use of optimal interpolation of existing weather stations by using the eigenvalues and vectors calculated via a spherical harmonics representation of the global climate field. An optimal interpolation is made for the weather station data by using a multivariate regression built on these eigenvalues and vectors which is calculated via an SVD algorithm in the spectral space. The background, mathematics, and code logic are explored for three of the main difficulties: transform of the high order spherical harmonic functions, the calculation of eigenvalues and vectors in complex space in Java, and the calculation of the optimal weights when involving large complex matrices. In the research, code optimizations and numerical verifications of the statistical theory are made and a novel cloud computing approach was explored to find optimal weights over Apache Spark, which is a distributed computing library. Cloud computing was carried out to generate many results of this research, and the cloud computing procedure is documented in this dissertation for other researchers.