A simplistic view of a dataset is that it is collection of numbers. In fact data are much more than that and all data are collected at a set place and time. Often either the location, or the time, is fixed within the dataset and one or both are disregarded. When the place and time of the collection are incorporated into the analysis, the result is a spatio-temporal model. Spatio-temporal data are the focus of this thesis. The majority of the datasets used are radio tracking studies of animals where the objective is to measure the habitat use. Observations are made over a long period of time and a large area. The largest dataset analysed tracks over a hundred animals, in an area larger than 40 square miles, for multiple years. In this context understanding the spatio-temporal relationships between observations is essential. Even data that do not have an obvious spatial component can benefit from spatio-temporal analysis. For example, the data presented on volatility in the stock market do not have an obvious spatial component. The spatial component is the location in the market, not a physical location. Two different methods for measuring and correcting bias are presented. One method relies on direct modelling of the underlying process being observed. The underlying process is animal movement. A model for animal movement is constructed and used to estimate the missing observations that are thought to be the cause of the bias. The second method does not model the animal movement, but instead relies on a Bayesian Hierarchical Model with some simple assumptions. A long running estimation is used to calculate the most likely result without ever directly estimating the underlying equations. In the second section of the thesis two methods for measuring change from shifts in both spatial and temporal location are presented. The methods, Large Diffeomorphic Deformation Metric Mapping (LDDMM) and Diffeomorphic Demons (DD), were originally developed for anatomical data and are adapted here for nonparametric regression surfaces. These are the first applications of LDDMM and DD outside of computational anatomy.

In epidemiological studies of an exposure-response association, often only a mismeasured exposure is taken on each individual of the population under study. If ignored, exposure measurement error can bias the estimated exposure-response association in question. A reliability study may be carried out to estimate the relation between the mismeasured and true exposure, which could then be used to adjust for measurement error in the attenuated exposure-response relationship. However, taking repeated exposure measurements may be expensive. Given a fixed total study cost, a two-stage design may be a more efficient approach for regression parameter estimation compared to the traditional single-stage design since, in the second-stage, repeated measurement is restricted to a sample of first-stage subjects. Sampling the extremes of the first-stage exposure distribution has been shown to be more efficient than random sampling.

Soil moisture is an essential climate variable and provides critical state information for hydrological applications. The state of soil moisture influences the exchange of water and energy between the earth surface and the atmosphere, partitions infiltration and runoff, can limit the net primary productivity of a region and govern the dynamics of geochemical processes. Satellite observations can be used to provide information about this important variable but are often available at a scale that is far greater than most hydrological processes. The scope of the research presented in this dissertation was to identify practical methods to facilitate the use of coarse scale satellite soil moisture information in higher resolution hydrological and land-surface modelling applications. Research was primarily conducted in the Hamilton-Halton watershed of Southern Ontario, Canada, although other watersheds and datasets were periodically used in some chapters. A comprehensive review was conducted on the use of high resolution soil moisture information for hydrological applications, and data assimilation was identified as the most common method for integrating soil moisture information into a hydrological model. It was also identified that most watersheds displayed the property of temporal persistence and that root-zone soil moisture was of greater importance than surface soil moisture (Appendix B). In light of this information, the focus of this research was the downscaling of soil moisture and brightness temperature (TB) observations from the Soil Moisture and Ocean Salinity (SMOS) passive microwave satellite. Satellite observations are sensitive to surface soil moisture, while rootzone soil moisture provides the greatest benefit to hydrological and land surface applications. To overcome this discrepancy, artificial neural networks (ANN) were evaluated as a method to estimate rootzone soil moisture from surface observations that accounted for the known non-linearities of soil moisture processes. The ANN model was trained with a numerical soil moisture physics model and validated using in situ observations from the McMaster Mesonet and USDA SCAN sites. The ANN was capable of accurately depicting the rootzone soil moisture based on its training data at multiple sites, but was limited when the temporal distribution of soil moisture at a particular site was considerably different than the training data. Therefore, with the appropriate training data, ANNs are a viable method for predicting rootzone soil moisture from surface observations such as those available from satellites. To provide high resolution soil moisture information from coarse resolution satellite data, bias correction was proposed and evaluated as a downscaling method for both soil moisture and TB. Using in situ data from two well instrumented USDA watersheds and a hydrological land-surface scheme (HLSS), it was found that temporal evolution of both soil moisture and TB at fine scale (~1 km) could be well characterized by the temporal evolution of the coarse scale (~20 km) soil moisture and TB. The fine scale spatial distribution of soil moisture could be predicted with a high degree of skill by correcting the bias between the coarse and fine scale soil moisture/TB. In studying the correction of biases, it was found that naïve application of bias correction methods could result in the introduction of multiplicative biases in the bias corrected dataset. The theoretical implications of this for a data assimilation system were discussed although not yet evaluated. A bootstrap resampling approach was evaluated as a solution to this problem and it was found that resampled data could result in a robust bias correction that eliminated additive bias in most instances while limiting the induction of multiplicative bias. This new method was found to significantly outperform the standard bias correction techniques. / Thesis / Doctor of Philosophy (PhD) / Soil moisture is an important hydrological variable. The state of soil moisture controls the partition between the runoff and infiltration as well as the exchange of heat from the surface to the atmosphere. Therefore, an accurate depiction of the state of soil moisture is important for producing accurate flood and drought forecasts, numerical weather prediction and agricultural forecasts. The state of soil moisture can be observed from space using microwave remote sensing measurements. However, the resolution of most passive microwave observations, such as those from the European Space Agency Soil Moisture and Ocean Salinity (SMOS) satellite are at a resolution of approximately 40 km which is far more coarse than the approximately 1 km resolution of most hydrological processes. The work in this thesis presented bias correction methods as a mean to match the spatial scale of the satellite observations to high resolution hydrological and land surface models. These data were generated and compared using an advanced land surface hydrological scheme under development at Environment Canada. It was found that simple bias correction methods were capable of effectively downscaling SMOS observations to the a scale of 1 km without the loss of information from the satellite. A new bias correction method was also presented that was found to significantly outperform standard techniques.

Spatial variability of rainfall is a significant factor in hydrologic and water quality modeling. In recent years, characterizing and analyzing the effect of spatial variability of rainfall in hydrologic applications has become vital with the advent of remotely sensed precipitation estimates that have high spatial resolution. In this study, the effect of spatial variability of rainfall in hourly runoff generation was analyzed using the Soil and Water Assessment Tool (SWAT) for Big Sandy Creek and Walnut Creek Watersheds in North Central Texas. The area of the study catchments was 808 km2 and 196 km2 for Big Sandy Creek and Walnut Creek Watersheds respectively. Hourly rainfall measurements obtained from raingauges and weather radars were used to estimate runoff for the years 1999 to 2003. Results from the study indicated that generated runoff from SWAT showed enormous volume bias when compared against observed runoff. The magnitude of bias increased as the area of the watershed increased and the spatial variability of rainfall diminished. Regardless of high spatial variability, rainfall estimates from weather radars resulted in increased volume of simulated runoff. Therefore, weather radar estimates were corrected for various systematic, range-dependent biases using three different interpolation methods: Inverse Distance Weighting (IDW), Spline, and Thiessen polygon. Runoff simulated using these bias adjusted radar rainfall estimates showed less volume bias compared to simulations using uncorrected radar rainfall. In addition to spatial variability of rainfall, SWAT model structures, such as overland flow, groundwater flow routing, and hourly evapotranspiration distribution, played vital roles in the accuracy of simulated runoff.

In the context of the SERVIR-Africa project, the SERVIR Arizona Team is developing streamflow forecast systems on African basins using Satellite Precipitation Products (SPP) to drive the models. These products have errors that need to be addressed before using them to drive hydrologic models. An analysis of the errors of the Satellite Precipitation Products TMPA-3B42RT, CMORPH, and PERSIANN over Africa is presented, followed by bias correction and error reduction methods to improve the remote sensed estimates. The GPCP 1-degree-day reanalysis product was used as the rainfall truth dataset. The Bias Correction Spatial Downscaling (BCSD) method developed by Wood et al., was used successfully to reduce the errors of SPP. The original and bias corrected estimates from the three SPP are used to calibrate and simulate three catchments of the Senegal River basin using HYMOD, finding that the use of bias corrected estimates produces a significant improvement in streamflow simulation.

Affine term structure models (ATSMs) are one set of popular models for yield curve modeling. Given that the models forecast yields based on the speed of mean reversion, under what circumstances can we distinguish one ATSM from another? The objective of my dissertation is to quantify the benefit of knowing the “true” model as well as the cost of being wrong when choosing between ATSMs. In particular, I detail the power of out-of-sample forecasts to statistically distinguish one ATSM from another given that we only know the data are generated from an ATSM and are observed without errors. My study analyzes the power and size of affine term structure models (ATSMs) by evaluating their relative out-of-sample performance. Essay one focuses on the study of the oneactor ATSMs. I find that the model’s predictive ability is closely related to the bias of mean reversion estimates no matter what the true model is. The smaller the bias of the estimate of the mean reversion speed, the better the out-of-sample forecasts. In addition, my finding shows that the models' forecasting accuracy can be improved, in contrast, the power to distinguish between different ATSMs will be reduced if the data are simulated from a high mean reversion process with a large sample size and with a high sampling frequency. In the second essay, I extend the question of interest to the multiactor ATSMs. My finding shows that adding more factors in the ATSMs does not improve models' predictive ability. But it increases the models' power to distinguish between each other. The multiactor ATSMs with larger sample size and longer time span will have more predictive ability and stronger power to differentiate between models.

Climate change is one of the most challenging and defining issues that has resulted in substantial societal, economic, and environmental impacts across the world. To assess the potential climate change impact, climate projections are generated with General Circulation Models (GCMs). However, the climate change signals remain uncertain and GCMs have difficulty in representing regional climate features. Therefore, comprehensive knowledge of climate change signals and reliable high-resolution climate projections are highly desired. This dissertation aims to address such challenges by developing climate projections with multi-model ensembles for climate impact assessment. This includes: i) developing multi-model ensembles to analyze global changes in all water components within the hydrological cycle and quantify the uncertainties with GCM projections; ii) development of bias correction models for generating high-resolution daily maximum and minimum temperature projections with individual GCMs and multi-model ensemble means over Canada; iii) proposing bias correction models with individual GCMs and multi-model ensemble means for high-resolution daily precipitation projections for Canada. The proposed models are capable of developing high-resolution climate projections at a regional scale and exploring the climate change signals. The reliable climate projections generated could provide valuable information for formulating appropriate climate change mitigation and adaptation strategies across the world. / Thesis / Doctor of Philosophy (PhD)

Uncertainty surrounds the understanding of natural variability in hydrologic extremes such as droughts and floods and how these events are projected to change in the future. This thesis leverages Global Climate Model (GCM) data to analyse 738 year streamflow scenarios in the Nelson-Churchill River Basin. Streamflow scenarios include a 500 year stationary period and future projections forced by two forcing scenarios. Fifty three GCM simulations are evaluated for performance in reproducing observed runoff characteristics. Runoff from a subset of nine simulations is routed to generate naturalized streamflow scenarios. Quantile mapping is then applied to reduce volume bias while maintaining the GCM’s sequencing of events. Results show evidence of future increases in mean annual streamflow and evidence that mean monthly streamflow variability has decreased from stationary conditions and is projected to decrease further into the future. There is less evidence of systematic change in droughts and floods. / May 2016

We develop and test a probabilistic real-time streamflow-forecasting platform, Multimodel and Multiproduct Streamflow Forecasting (MMSF), that uses information provided by a suite of hydrologic models and satellite precipitation products (SPPs). The SPPs are bias-corrected before being used as inputs to the hydrologic models, and model calibration is carried out independently for each of the model-product combinations (MPCs). Forecasts generated from the calibrated models are further bias-corrected to compensate for the deficiencies within the models, and then probabilistically merged using a variety of model averaging techniques. Use of bias-corrected SPPs in streamflow forecasting applications can overcome several issues associated with sparsely gauged basins and enable robust forecasting capabilities. Bias correction of streamflow significantly improves the forecasts in terms of accuracy and precision for all different cases considered. Results show that the merging of individual forecasts from different MPCs provides additional improvements. All the merging techniques applied in this study produce similar results, however, the Inverse Weighted Averaging (IVA) proves to be slightly superior in most cases. We demonstrate the implementation of the MMSF platform for real-time streamflow monitoring and forecasting in the Mara River basin of Africa (Kenya & Tanzania) in order to provide improved monitoring and forecasting tools to inform water management decisions.

We present an evaluation of daily estimates from three near real-time quasi-global Satellite Precipitation Products-Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA), Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN), and Climate Prediction Center (CPC) Morphing Technique (CMORPH)-over the African continent, using the Global Precipitation Climatology Project one Degree Day (GPCP-1dd) as a reference dataset for years 2001 to 2013. Different types of errors are characterized for each season as a function of spatial classifications (latitudinal bands, climatic zones and topography) and in relationship with the main rain-producing mechanisms in the continent: the Intertropical Convergence Zone (ITCZ) and the East African Monsoon. A bias correction of the satellite estimates is applied using a probability density function (pdf) matching approach, with a bias analysis as a function of rain intensity, season and latitude. The effects of bias correction on different error terms are analyzed, showing an almost elimination of the mean and variance terms in most of the cases. While raw estimates of TMPA show higher efficiency, all products have similar efficiencies after bias correction. PERSIANN consistently shows the smallest median errors when it correctly detects precipitation events. The areas with smallest relative errors and other performance measures follow the position of the ITCZ oscillating seasonally over the equator, illustrating the close relationship between satellite estimates and rainfall regime.