Quantifying hydraulic roughness coefficients is commonly required in order to calculate flow rate in open channel applications. An assumption typically coupled with the use of Manning’s equation is that a roughness coefficient (n) that is solely dependent upon a boundary roughness characteristic (k) may be applied. Even though Manning reported unique values of n and x’ (the exponent of the hydraulic radius in Manning’s equation) for each of the different boundary roughness materials he tested, he chose x’ = 2/3 as representative, assumed a constant n value, and suggested that it was sufficiently accurate. More recent studies have suggested that in addition to k; Rh, Se, and Fr can influence n. While research points to situations where n may vary, it is always a temptation to simply apply the constant n assumption especially in the case of more complicated channels such as composite channels where different roughness materials line different parts of a channel cross section. This study evaluates the behavior of n as a function of Re, Rh, k, So, and Fr for four different boundary roughness materials ranging from smooth to relatively rough in a rectangular tilting flume. The results indicate that for the relatively rough materials n is best described by its relationship with Rh where it varies over a lower range of Rh but approaches and at a point maintains a constant value as Rh increases. The constant value of n is attributed to both the physically smooth boundary materials and a quasi-smooth flow condition in the rougher boundary materials. The study shows that an x’ = 2/3 (the basis of Manning’s equation) correlated to the assumption of a constant n value only applies to smooth boundary roughness materials and a quasi-smooth flow condition in the rougher boundary materials; otherwise, either n or x’ must vary. These findings are then applied to compare 16 published composite channel relationships. The results identify the importance of applying a varying n where applicable due to the potential for error in assuming and applying a constant n. They also indicate that the more complicated predictive methods do not produce more accurate results than the simpler methods of which the most consistent is the Horton method.

Conventional coastal ocean models solve the shallow water equations, which describe the conservation of mass and momentum when the horizontal length scale is much greater than the vertical length scale. In this case vertical pressure gradients in the momentum equations are nearly hydrostatic. The outputs of coastal ocean models are thus sensitive to the bottom stress terms defined through the formulation of Manning’s n coefficients. This thesis considers the Bayesian inference problem of the Manning’s n coefficient in the context of storm surge based on the coastal ocean ADCIRC model. In the first part if the thesis, we apply an ensemble-based Kalman filter, the singular evolutive interpolated Kalman (SEIK) filter to estimate both a constant Manning’s n coefficient and a 2-D parameterized Manning’s coefficient on one ideal and one of more realistic domain using observation system simulation experiments (OSSEs). We study the sensitivity of the system to the ensemble size. we also access the benefits from using an inflation factor on the filter performance. To study the limitation of the Guassian restricted assumption on the SEIK filter, we also implemented in the second part of this thesis a Markov Chain Monte Carlo (MCMC) method based on a Generalized Polynomial chaos (gPc) approach for the estimation of the 1-D and 2-D Mannning’s n coefficient. The gPc is used to build a surrogate model that imitate the ADCIRC model in order to make the computational cost of implementing the MCMC with the ADCIRC model reasonable. We evaluate the performance of the MCMC-gPc approach and study its robustness to different OSSEs scenario. we also compare its estimates with those resulting from SEIK in term of parameter estimates and full distributions. we present a full analysis of the solution of these two methods, of the contexts of their algorithms, and make recommendation for fully realistic application.

This dissertation investigates the use of remotely sensed data in coastal tide and inundation models, specifically how these data could be more effectively integrated into model construction and performance assessment techniques. It includes a review of numerical wetting and drying algorithms, a method for constructing a seamless digital terrain model including the handling of tidal datums, an investigation into the accuracy of land use / land cover (LULC) based surface roughness parameterization schemes, an application of a cutting edge remotely sensed inundation detection method to assess the performance of a tidal model, and a preliminary investigation into using 3-dimensional airborne laser scanning data to parameterize surface roughness. A thorough academic review of wetting and drying algorithms employed by contemporary numerical tidal models was conducted. Since nearly all population centers and valuable property are located in the overland regions of the model domain, the coastal models must adequately describe the inundation physics here. This is accomplished by techniques that generally fall into four categories: Thin film, Element removal, Depth extrapolation, and Negative depth. While nearly all wetting and drying algorithms can be classified as one of the four types, each model is distinct and unique in its actual implementation. The use of spatial elevation data is essential to accurate coastal modeling. Remotely sensed LiDAR is the standard data source for constructing topographic digital terrain models (DTM). Hydrographic soundings provide bathymetric elevation information. These data are combined to form a seamless topobathy surface that is the foundation for distributed coastal models. A three-point inverse distance weighting method was developed in order to account for the spatial variability of bathymetry data referenced to tidal datums. This method was applied to the Tampa Bay region of Florida in order to produce a seamless topobathy DTM. Remotely sensed data also contribute to the parameterization of surface roughness. It is used to develop land use / land cover (LULC) data that is in turn used to specify spatially distributed bottom friction and aerodynamic roughness parameters across the model domain. However, these parameters are continuous variables that are a function of the size, shape and density of the terrain and above-ground obstacles. By using LULC data, much of the variation specific to local areas is generalized due to the categorical nature of the data. This was tested by comparing surface roughness parameters computed based on field measurements to those assigned by LULC data at 24 sites across Florida. Using a t-test to quantify the comparison, it was proven that the parameterizations are significantly different. Taking the field measured parameters as ground truth, it is evident that parameterizing surface roughness based on LULC data is deficient. In addition to providing input parameters, remotely sensed data can also be used to assess the performance of coastal models. Traditional methods of model performance testing include harmonic resynthesis of tidal constituents, water level time series analysis, and comparison to measured high water marks. A new performance assessment that measures a model's ability to predict the extent of inundation was applied to a northern Gulf of Mexico tidal model. The new method, termed the synergetic method, is based on detecting inundation area at specific points in time using satellite imagery. This detected inundation area is compared to that predicted by a time-synchronized tidal model to assess the performance of model in this respect. It was shown that the synergetic method produces performance metrics that corroborate the results of traditional methods and is useful in assessing the performance of tidal and storm surge models. It was also shown that the subject tidal model is capable of correctly classifying pixels as wet or dry on over 85% of the sample areas. Lastly, since it has been shown that parameterizing surface roughness using LULC data is deficient, progress toward a new parameterization scheme based on 3-dimensional LiDAR point cloud data is presented. By computing statistics for the entire point cloud along with the implementation of moving window and polynomial fit approaches, empirical relationships were determined that allow the point cloud to estimate surface roughness parameters. A multi-variate regression approach was chosen to investigate the relationship(s) between the predictor variables (LiDAR statistics) and the response variables (surface roughness parameters). It was shown that the empirical fit is weak when comparing the surface roughness parameters to the LiDAR data. The fit was improved by comparing the LiDAR to the more directly measured source terms of the equations used to compute the surface roughness parameters. Future work will involve using these empirical relationships to parameterize a model in the northern Gulf of Mexico and comparing the hydrodynamic results to those of the same model parameterized using contemporary methods. In conclusion, through the work presented herein, it was demonstrated that incorporating remotely sensed data into coastal models provides many benefits including more accurate topobathy descriptions, the potential to provide more accurate surface roughness parameterizations, and more insightful performance assessments. All of these conclusions were achieved using data that is readily available to the scientific community and, with the exception of the Synthetic Aperture Radar (SAR) from the Radarsat-1 project used in the inundation detection method, are available free of charge. Airborne LiDAR data are extremely rich sources of information about the terrain that can be exploited in the context of coastal modeling. The data can be used to construct digital terrain models (DTMs), assist in the analysis of satellite remote sensing data, and describe the roughness of the landscape thereby maximizing the cost effectiveness of the data acquisition.