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Radar-rainfall uncertainty quantification has been recognized as an intricate problem due to the complexity of the multi-dimensional error structure, which is also associated with space and time scale. The error structure is usually characterized by two moments of the error distribution: bias and error variance. Despite numerous efforts to investigate radar-rainfall uncertainties, many questions remain unanswered. This dissertation uses two statistical descriptions (mean and variance) of the error distribution to highlight and describe some of the remaining gaps in representing radar-rainfall uncertainties. The four central issues addressed in this dissertation include:
1. Investigation of radar relative bias caused by radar calibration.
2. Statistical modeling of range-dependent error arising from the radar beam geometry structure.
3. Scale-dependent variability of radar-rainfall and rain gauge error covariance.
4. Scale-dependence of radar-rainfall error variance.
The first two issues describe systematic features of main error sources of radar-rainfall. The other two are associated with quantifying radar error variance using the error variance separation (EVS) method, which considers the spatial sampling mismatch between radar and rain gauge data.
This study captures the main systematic features (systematic bias arising from radar calibration and range-dependent errors) of radar measurements without using ground reference data and the error variance structure with respect to the spatio-temporal transformation of the measurements for further applications to hydrologic fields. Such consideration of radar-rainfall uncertainties represented by error mean and variance can enhance the characterization of the uncertainty structure and yield a better understanding of the physical process of precipitation.