As the forecasting models become more sophisticated in their physics and possible depictions of the nearshore hydrodynamics, they also become increasingly sensitive to errors in the inputs. These input errors include: mis-specification of the input parameters (bottom friction, eddy viscosity, etc.); errors in input fields and errors in the specification of boundary information (lateral boundary conditions, etc.). Errors in input parameters can be addressed with fairly straightforward parameter estimation techniques, while errors in input fields can be somewhat ameliorated by physical linkage between the scales of the bathymetric information and the associated model response. Evaluation of the errors on the boundary is less straightforward, and is the subject of this thesis. The model under investigation herein is the Delft3D modeling suite, developed at Deltares (formerly Delft Hydraulics) in Delft, the Netherlands. Coupling of the wave (SWAN) and hydrodynamic (FLOW) model requires care at the lateral boundaries in order to balance run time and error growth. To this extent, we use perturbation method and spatio-temporal analysis method such as Empirical Orthogonal Function (EOF) analysis to determine the various scales of motion in the flow field and the extent of their response to imposed boundary errors. From the Swirl Strength examinations, we find that the higher EOF modes are affected more by the lateral boundary errors than the lower ones.

The heavily developed Long Key is located in Pinellas County in west-central Florida. The structured Blind Pass at the north end of the barrier island interrupts the southward longshore sediment transport, resulting in severe and chronic beach erosion along the northern portion of the island. Frequent beach nourishments were conducted to mitigate the erosion. In this study, the performance of the most recent beach nourishment in 2010 is quantified through time-series beach profile surveys. Over the 34-month period, the nourished northern portion of the island, Upham Beach, lost up to 330 m3/m of sand, with a landward shoreline retreat of up to 100 m. The middle portion of the island gained up to 25 m3/m of sand, benefiting from the sand lost from Upham Beach. The southern portion of Long Key lost a modest amount of sediment, largely due to Tropical Storm Debby, which approached from the south in June 2012. The severe erosion along Upham Beach is induced by a large negative longshore transport gradient. The beach here has no sand bar and retreated landward persistently over the 34-month study period. In contrast the profiles in the central section of the island generally have a sand bar which moved landward and seaward in response to seasonal and storm-induced wave-energy changes. The sand volume across the entire profile in the central portion of the island is mostly conserved. Two typical example beach profiles, LK3A and R157, were selected to examine the ability of the commonly used principal component analysis (PCA), also commonly known as empirical orthogonal function analysis (EOF), to identify beach profile ix changes induced by longshore and cross-shore sediment transport gradients. For the longshore-transport driven changes at the non-barred profile LK3A, the principal eigenvector accounted for over 91% of the total variance, with a dominant broad peak in the cross-shore distribution. At the barred R157, the profile changes were caused mainly by cross-shore transport gradients with modest contribution from longshore transport gradient; eigenvalue one only accounted for less than 51% of the total variance, and eigenvalues two and three still contributed considerably to the overall variance. In order to verify the uniqueness of the PCA results from LK3A and R157, five numerical experiments were conducted, simulating changes at a barred and non-barred beach driven by longshore, cross-shore, and combined sediment transport gradients. Results from LK3A and R157 compare well with simulated beach erosion (or accretion) due to variable longshore sediment transport gradients and due to both cross-shore and longshore sediment transport gradients, respectively. Different PCA results were obtained from different profile change patterns.

Estuaries are vital environmental and economic resources, providing habitat for thousands of species, absorbing runoff, and supporting recreation and commerce. Yet, despite their importance, estuaries are threatened by human activities. Empirical Orthogonal Function (EOF) analysis and Cross Spectral techniques were used in the analysis and prediction of estuarine morphology. The estuaries selected for study were Suisun Bay, CA and Mobile Bay, AL. It was found that EOF is an effective and efficient technique to analyze morphology, a coupling with cross spectral methods such as Fourier Transformation (FFT) resulted in determination of forcing functions responsible for imparting variance to the bathymetry. In both the estuaries it was found that the first two eigenvalues represented almost 80% of the morphological/bathymetric dataset. The second eigenfunction was found to be closely dependent on the freshwater inflows to the estuaries. EOF analysis on Suisun Bay revealed that the bay is depositional particularly in the shallow bays of Honker and Grizzly, whereas the main channels as well as Carquinez Straits maintained their depths throughout the period studied. Utilizing a Cross spectral technique, Amplitude Response Function (ARF), temporal eigenfunctions for the bay were determined for year 2100. The temporal eigenfunctions were predicted for cases where river inflows to the bay were varied by 1 standard deviation unit. These predicted eigenfunction values combined with the eigenvalues resulted in the recovery of predicted depths for year 2100. It was found that Suisun Bay remains depositional through the year 2100 and maintains depths in the main channels as well as Carquinez Straits. This depositional behavior results in the decrease of bay volume to almost 40% of the volume in 1989. EOF analysis on Mobile Bay revealed that the bay is predominantly depositional except in the navigation channel and the shoreline of the Bay. The navigation channel maintaining it depth is attributed to the regular dredging carried to facilitate shipping. The second temporal eigenfunction showed a close correlation with river inflows as in the case of Suisun Bay. However, a cross correlation performed on the second temporal eigenfunction and inflows revealed that the response of the eigenfunction is perturbed by almost 9 years, as opposed to 6 to 9 years for Suisun Bay. An ARF on the temporal eigenfunctions combined with a reverse EOF resulted in the formation of bathymetric datasets for the year 2100 for inflows variation of 1 standard deviation. It was revealed that increasing the flows results in an increase of bay volume by approximately 30% and a decrease in flows results in a loss of volume by approximately 20%.

The goal of this research was to improve ocean colour chlorophyll a (Chla) retrievals in the coastal Case 2 waters of the Salish Sea by characterizing the main drivers of optical variability and using this information to parameterize empirical algorithms based on an optical classification. This was addressed with three specific objectives: (1) build a comprehensive spatio-temporal data set of in situ optical and biogeochemical parameters, (2) apply a hierarchical clustering analysis to classify above-water remote sensing reflectance (Rrs) and associated bio-optical regimes, (3) optimize and validate class-specific empirical algorithms for improved Chla retrievals. Biogeochemical and optical measurements, acquired at 145 sites, showed considerable variation; Chla (mean=1.64, range: 0.10 – 7.20 µg l-1), total suspended matter (TSM) (3.09, 0.82 – 20.69 mg l-1), and absorption by chromophoric dissolved organic matter (a_cdom (443)) (0.525, 0.007 – 3.072 m-1), thus representing the spatial and temporal variability of the Salish Sea. A comparable range was found in the measured optical properties; particulate scattering (b_p (650)) (1.316, 0.250 – 7.450 m-1), particulate backscattering (b_bp (650)) (0.022, 0.005 – 0.097 m-1), total beam attenuation coefficient (c_t (650)) (1.675, 0.371 – 9.537 m-1), and particulate absorption coefficient (a_p (650)) (0.345, 0.048 – 2.020 m-1). Empirical orthogonal function (EOF) analysis revealed 95% of the Rrs variance was highly correlated to b_p (r = 0.90), b_bp (r = 0.82), and TSM concentration (r = 0.80), suggesting a strong influence from riverine systems in this region. Hierarchical clustering on the normalized Rrs revealed four spectral classes. Class 1 is defined by high overall Rrs magnitudes in the red, indicating more turbid waters, Class 2 showed high Rrs values in the red and well defined fluorescence and absorption features, indicated by a high Chla and TSM presence, Class 3 showed low TSM influence and more defined Chla signatures, and Class 4 is characterized by overall low Rrs values, suggesting more optically clear oceanic waters. Spectral similarities justified a simplification of this classification into two dominant water classes – (1) estuarine class (Classes 1 and 2) and (2) oceanic class (Classes 3 and 4) – representing the dominant influences seen here. In situ Chla and above-water remote sensing reflectance measurements, used to validate and parameterize the OC3M/OC3S3, two-band ratio, FLH and, modified FLH (ModFLH) empirical algorithms, showed a systematic overestimation of low Chla concentrations and underestimation of higher Chla values for all four algorithms when tuned to regional data. FLH and ModFLH algorithms performed best for these data (R2 ~ 0.40; RMSE ~ 0.32). Algorithm accuracy was significantly improved for the class-specific parametrizations with the two-band ratio showing a strong correlation to the Chla concentrations in the estuarine class (R2 ~ 0.71; RMSE ~ 0.33) and the ModFLH algorithm in the oceanic class (R2 ~ 0.70; RMSE ~ 0.26). These results demonstrated the benefit of applying an optical classification as a necessary first step into improving Chla retrievals from remotely sensed data in the contrasted coastal waters of the Salish Sea. With accurate Chla information, the health of the Salish Sea can be viably monitored at spatial and temporal scales suitable for ecosystem management. / Graduate / 0416 / stephen.uvic@gmail.com

We study the space-time characteristics of global tropical rainfall. The data used is from the Tropical Rainfall Measuring Mission (TRMM) and spans the years 2000-2009. Using anomaly fields constructed by removing a single mean and by subtracting the climatology of the ten year dataset, we extract the dominant modes of variability of tropical rainfall from an Empirical Orthogonal Function (EOF) analysis. To our knowledge, this is the first attempt at applying the EOF formal-ism to high spatio-temporal resolution global tropical rainfall. Spatial patterns and temporal indices obtained from the EOF analysis with single annual mean removed show large scale patterns associated with the seasonal cycle. Even though the seasonal cycle is dominant, the principal component (PC) time series show fluctuations at subseasonal scales. When the climatological mean is removed, spatial patterns of the dominant modes resemble features associated with tropical intraseasonal variability (ISV). Correspondingly, the signature of a seasonal cycle is relatively suppressed, and the PCs have prominent fluctuations at subseasonal scales. The significance of the leading EOFs is demonstrated by means of a novel ratio plot of the variance captured by the leading EOFs to the variance in the data. This shows that, in regions of high variability (which go hand in hand with high rainfall), the EOF/PC pairs capture a fair amount of the variance (up to 20% for the first EOF/PC pair) in the data. We then pursue an EOF analysis of the finest data resolution available. In particular, we per-form a regional analysis (a global analysis is beyond our present computational resources) of the tropics with 0.25◦×0.25◦, 3-hourly data. The regions we focus on are the Indian region, the Maritime Continent and South America. The spatial patterns obtained reveal a rich hierarchical structure to the leading modes of variability in these regions. Similarly, the PCs associated with these leading spatial modes show variability all the way from 90 days to the diurnal scale. With the results from EOF analysis in hand, we quantify the multiscale spatio-temporal structures encountered in our study. In particular, we examine the power spectra of the PCs and EOFs. A robust feature of the space and time spectra is the distribution of energy or variance across a range of scales. On the temporal front, aside from a seasonal and diurnal peaks, the variance scales as a power-law from a few days to the 90 day period. Similarly, below the planetary scale, from approximately 5000 km to 200 km the spatial spectrum also follows a power-law. Therefore, when trying to understand the variability of tropical rainfall, all scales are important, and it is difficult to justify a focus on isolated space and time scales.