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• 1. [Article] On the Observability of Bottom Topography from Measurements of Tidal Sea Surface Height

  of whether features of the ocean bottom topography can be identified from measurements of water level is investigated using a simplified one-dimensional barotropic model. Because of the nonlinear dependence ...

  Citation × Citation Citation Abstract Copy Title: On the Observability of Bottom Topography from Measurements of Tidal Sea Surface Height Author: Zaron, Edward D. Year: 2016 of whether features of the ocean bottom topography can be identified from measurements of water level is investigated using a simplified one-dimensional barotropic model. Because of the nonlinear dependence of the sea surface height on the water depth, a linearized analysis is performed concerning the identification of a Gaussian bump within two specific depth profiles, (1) a constant depth domain, and, (2) a constant depth domain adjoining a near-resonant continental shelf. Observability is quantified by examining the estimation error in a series of identical-twin experiments varying data density, tide wavelength, assumed (versus actual) topographic correlation scale, and friction. For measurements of sea surface height that resolve the scale of the topographic perturbation, the fractional error in the bottom topography is approximately a factor of 10 larger than the fractional error of the sea surface height. Domain-scale and shelf-scale resonances may lead to inaccurate topography estimates due to a reduction in the effective number of degrees of freedom in the dynamics, and the amplification of nonlinearity. A realizability condition for the variance of the topography error in the limit of zero bottom depth is proposed which is interpreted as a bound on the fractional error of the topography. Appropriately designed spatial covariance models partly ameliorate the negative impact of shelf-scale near-resonance, and highlight the importance of spatial covariance modeling for bottom topography estimation. Title: On the Observability of Bottom Topography from Measurements of Tidal Sea Surface Height Author: Zaron, Edward D. Year: 2016 of whether features of the ocean bottom topography can be identified from measurements of water level is investigated using a simplified one-dimensional barotropic model. Because of the nonlinear dependence of the sea surface height on the water depth, a linearized analysis is performed concerning the identification of a Gaussian bump within two specific depth profiles, (1) a constant depth domain, and, (2) a constant depth domain adjoining a near-resonant continental shelf. Observability is quantified by examining the estimation error in a series of identical-twin experiments varying data density, tide wavelength, assumed (versus actual) topographic correlation scale, and friction. For measurements of sea surface height that resolve the scale of the topographic perturbation, the fractional error in the bottom topography is approximately a factor of 10 larger than the fractional error of the sea surface height. Domain-scale and shelf-scale resonances may lead to inaccurate topography estimates due to a reduction in the effective number of degrees of freedom in the dynamics, and the amplification of nonlinearity. A realizability condition for the variance of the topography error in the limit of zero bottom depth is proposed which is interpreted as a bound on the fractional error of the topography. Appropriately designed spatial covariance models partly ameliorate the negative impact of shelf-scale near-resonance, and highlight the importance of spatial covariance modeling for bottom topography estimation. Close

• 2. [Article] A macroscale measurement and modeling approach to improve understanding of the hydrology of steep, forested hillslopes

  The dominant controls on flow generation in steep, forested hillslopes are poorly understood. This dissertation examined the dominant flow processes operating at the hillslope scale, using a combined ...

  Citation × Citation Citation Abstract Copy Title: A macroscale measurement and modeling approach to improve understanding of the hydrology of steep, forested hillslopes Author: Graham, Christopher Brian The dominant controls on flow generation in steep, forested hillslopes are poorly understood. This dissertation examined the dominant flow processes operating at the hillslope scale, using a combined macroscale measurement and model development and analysis framework. Irrigation experiments at two steep forested hillslopes were conducted to isolate individual hillslope flow components and reveal the dominant controls on flow routing to the stream. A new perceptual model of flow processes at the hillslope scale was developed from these field experiments that included three key components: 1) A connected preferential flow network located at the soil/bedrock interface controls lateral water and solute transport, 2) The bedrock surface controls the subsurface flow routing, and 3) Bedrock is permeable, and acts as a sink for precipitation at the hillslope scale. These components formed the basis of a new, low dimensional numerical model that was used to represent, quantitatively, qualitative experimental findings. A multiple criteria calibration using hydrometric and tracer experimental data was conducted to evaluate the model and determine parameter identifiability. The model was able to adequately reproduce both hydrometric response to precipitation, and a tracer application breakthrough. The model was then used within a virtual experiment framework to test the dominant controls on the whole storm precipitation / discharge threshold relationship at the catchment scale. The modeling experiments showed that the macroscale precipitation / discharge threshold was controlled by a balance between antecedent evaporation (evaporation rate times antecedent drainage time), and geologic factors (bedrock permeability and subsurface storage volume). Overall, these findings suggest that making measurements at the scale of the processes one wishes to understand, and constructing numerical models based on the dominant processes at the same scale may be a first step towards the development of macroscale laws of hillslope behavior. Title: A macroscale measurement and modeling approach to improve understanding of the hydrology of steep, forested hillslopes Author: Graham, Christopher Brian The dominant controls on flow generation in steep, forested hillslopes are poorly understood. This dissertation examined the dominant flow processes operating at the hillslope scale, using a combined macroscale measurement and model development and analysis framework. Irrigation experiments at two steep forested hillslopes were conducted to isolate individual hillslope flow components and reveal the dominant controls on flow routing to the stream. A new perceptual model of flow processes at the hillslope scale was developed from these field experiments that included three key components: 1) A connected preferential flow network located at the soil/bedrock interface controls lateral water and solute transport, 2) The bedrock surface controls the subsurface flow routing, and 3) Bedrock is permeable, and acts as a sink for precipitation at the hillslope scale. These components formed the basis of a new, low dimensional numerical model that was used to represent, quantitatively, qualitative experimental findings. A multiple criteria calibration using hydrometric and tracer experimental data was conducted to evaluate the model and determine parameter identifiability. The model was able to adequately reproduce both hydrometric response to precipitation, and a tracer application breakthrough. The model was then used within a virtual experiment framework to test the dominant controls on the whole storm precipitation / discharge threshold relationship at the catchment scale. The modeling experiments showed that the macroscale precipitation / discharge threshold was controlled by a balance between antecedent evaporation (evaporation rate times antecedent drainage time), and geologic factors (bedrock permeability and subsurface storage volume). Overall, these findings suggest that making measurements at the scale of the processes one wishes to understand, and constructing numerical models based on the dominant processes at the same scale may be a first step towards the development of macroscale laws of hillslope behavior. Close