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- Author or Editor: Jeff Hansen x
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Abstract
A minimum spanning tree (MST) rank histogram (RH) is a multidimensional ensemble reliability verification tool. The construction of debiased, decorrelated, and covariance-homogenized MST RHs is described. Experiments using Euclidean L 2, variance, and Mahalanobis norms imply that, unless the number of ensemble members is less than or equal to the number of dimensions being verified, the Mahalanobis norm transforms the problem into a space where ensemble imperfections are most readily identified. Short-Range Ensemble Forecast Mahalanobis-normed MST RHs for a cluster of northeastern U.S. cities show that forecasts of the temperature–humidity index are the most reliable of those considered, followed by mean sea level pressure, 2-m temperature, and 10-m wind speed forecasts. MST RHs of a Southwest city cluster illustrate that 2-m temperature forecasts are the most reliable weather component in this region, followed by mean sea level pressure, 10-m wind speed, and the temperature–humidity index. Forecast reliabilities of the Southwest city cluster are generally less reliable than those of the Northeast cluster.
Abstract
A minimum spanning tree (MST) rank histogram (RH) is a multidimensional ensemble reliability verification tool. The construction of debiased, decorrelated, and covariance-homogenized MST RHs is described. Experiments using Euclidean L 2, variance, and Mahalanobis norms imply that, unless the number of ensemble members is less than or equal to the number of dimensions being verified, the Mahalanobis norm transforms the problem into a space where ensemble imperfections are most readily identified. Short-Range Ensemble Forecast Mahalanobis-normed MST RHs for a cluster of northeastern U.S. cities show that forecasts of the temperature–humidity index are the most reliable of those considered, followed by mean sea level pressure, 2-m temperature, and 10-m wind speed forecasts. MST RHs of a Southwest city cluster illustrate that 2-m temperature forecasts are the most reliable weather component in this region, followed by mean sea level pressure, 10-m wind speed, and the temperature–humidity index. Forecast reliabilities of the Southwest city cluster are generally less reliable than those of the Northeast cluster.
Measuring a Rogue? An Investigation into an Apparent Giant WaveAbstract
An apparent giant wave event having a maximum trough-to-crest height of 21 m and a maximum zero-upcrossing period of 27 s was recorded by a wave buoy at a nearshore location off the southwestern coast of Australia. It appears as a group of waves that are significantly larger both in height and in period than the waves preceding and following them. This paper reports a multifaceted analysis into the plausibility of the event. We first examine the statistics of the event in relation to the rest of the record, where we look at quantities such as maximum-to-significant wave height ratios, ordered crest–trough statistics, and average wave profiles. We then investigate the kinematics of the buoy, where we look at the relationship between the horizontal and vertical displacements of the buoy, and also attempt to numerically reconstruct the giant event using Boussinesq and nonlinear shallow water equations. Additional analyses are performed on other sea states where at least one of the buoy’s accelerometers reached its maximum limit. Our analysis reveals incompatibilities of the event with known behavior of real waves, leading us to conclude that it was not a real wave event. Wave events similar to the one reported in our study have been reported elsewhere and have sometimes been accepted as real occurrences. Our methods of forensically analyzing the giant wave event should be potentially useful for identifying false rogue wave events in these cases.
Abstract
An apparent giant wave event having a maximum trough-to-crest height of 21 m and a maximum zero-upcrossing period of 27 s was recorded by a wave buoy at a nearshore location off the southwestern coast of Australia. It appears as a group of waves that are significantly larger both in height and in period than the waves preceding and following them. This paper reports a multifaceted analysis into the plausibility of the event. We first examine the statistics of the event in relation to the rest of the record, where we look at quantities such as maximum-to-significant wave height ratios, ordered crest–trough statistics, and average wave profiles. We then investigate the kinematics of the buoy, where we look at the relationship between the horizontal and vertical displacements of the buoy, and also attempt to numerically reconstruct the giant event using Boussinesq and nonlinear shallow water equations. Additional analyses are performed on other sea states where at least one of the buoy’s accelerometers reached its maximum limit. Our analysis reveals incompatibilities of the event with known behavior of real waves, leading us to conclude that it was not a real wave event. Wave events similar to the one reported in our study have been reported elsewhere and have sometimes been accepted as real occurrences. Our methods of forensically analyzing the giant wave event should be potentially useful for identifying false rogue wave events in these cases.
Abstract
High-resolution observations from a 55-m-long wave flume were used to investigate the dynamics of wave setup over a steeply sloping reef profile with a bathymetry representative of many fringing coral reefs. The 16 runs incorporating a wide range of offshore wave conditions and still water levels were conducted using a 1:36 scaled fringing reef, with a 1:5 slope reef leading to a wide and shallow reef flat. Wave setdown and setup observations measured at 17 locations across the fringing reef were compared with a theoretical balance between the local cross-shore pressure and wave radiation stress gradients. This study found that when radiation stress gradients were calculated from observations of the radiation stress derived from linear wave theory, both wave setdown and setup were underpredicted for the majority of wave and water level conditions tested. These underpredictions were most pronounced for cases with larger wave heights and lower still water levels (i.e., cases with the greatest setdown and setup). Inaccuracies in the predicted setdown and setup were improved by including a wave-roller model, which provides a correction to the kinetic energy predicted by linear wave theory for breaking waves and produces a spatial delay in the wave forcing that was consistent with the observations.
Abstract
High-resolution observations from a 55-m-long wave flume were used to investigate the dynamics of wave setup over a steeply sloping reef profile with a bathymetry representative of many fringing coral reefs. The 16 runs incorporating a wide range of offshore wave conditions and still water levels were conducted using a 1:36 scaled fringing reef, with a 1:5 slope reef leading to a wide and shallow reef flat. Wave setdown and setup observations measured at 17 locations across the fringing reef were compared with a theoretical balance between the local cross-shore pressure and wave radiation stress gradients. This study found that when radiation stress gradients were calculated from observations of the radiation stress derived from linear wave theory, both wave setdown and setup were underpredicted for the majority of wave and water level conditions tested. These underpredictions were most pronounced for cases with larger wave heights and lower still water levels (i.e., cases with the greatest setdown and setup). Inaccuracies in the predicted setdown and setup were improved by including a wave-roller model, which provides a correction to the kinetic energy predicted by linear wave theory for breaking waves and produces a spatial delay in the wave forcing that was consistent with the observations.
Abstract
The effect of bottom roughness on setup dynamics was investigated using high-resolution observations across a laboratory fringing reef profile with roughness elements scaled to mimic the frictional wave dissipation of a coral reef. Results with roughness were compared with smooth bottom runs across 16 offshore wave and still water level conditions. The time-averaged and depth-integrated force balance was evaluated from observations collected at 17 locations along the flume and consisted of cross-shore pressure and radiation stress gradients whose sum was balanced by quadratic mean bottom stresses. The introduction of roughness had two primary effects. First, for runs with roughness, frictional wave dissipation occurred on the reef slope offshore of the breakpoint, reducing wave heights prior to wave breaking. Second, offshore-directed mean bottom stresses were generated by the interaction of the combined wave–current velocity field with the roughness elements. These two mechanisms acted counter to one another. Frictional wave dissipation resulted in radiation stress gradients that were predicted to generate 18% (on average) less setup on the reef flat for rough runs than for smooth runs when neglecting mean bottom stresses. However, mean bottom stresses increased the predicted setup by 16% on average for runs with roughness. As a result, setup on the reef flat was comparable (7% mean difference) between corresponding rough and smooth runs. These findings are used to assess prior results from numerical modeling studies of reefs and also to discuss the broader implications for how large roughness influences setup dynamics in the nearshore zone.
Abstract
The effect of bottom roughness on setup dynamics was investigated using high-resolution observations across a laboratory fringing reef profile with roughness elements scaled to mimic the frictional wave dissipation of a coral reef. Results with roughness were compared with smooth bottom runs across 16 offshore wave and still water level conditions. The time-averaged and depth-integrated force balance was evaluated from observations collected at 17 locations along the flume and consisted of cross-shore pressure and radiation stress gradients whose sum was balanced by quadratic mean bottom stresses. The introduction of roughness had two primary effects. First, for runs with roughness, frictional wave dissipation occurred on the reef slope offshore of the breakpoint, reducing wave heights prior to wave breaking. Second, offshore-directed mean bottom stresses were generated by the interaction of the combined wave–current velocity field with the roughness elements. These two mechanisms acted counter to one another. Frictional wave dissipation resulted in radiation stress gradients that were predicted to generate 18% (on average) less setup on the reef flat for rough runs than for smooth runs when neglecting mean bottom stresses. However, mean bottom stresses increased the predicted setup by 16% on average for runs with roughness. As a result, setup on the reef flat was comparable (7% mean difference) between corresponding rough and smooth runs. These findings are used to assess prior results from numerical modeling studies of reefs and also to discuss the broader implications for how large roughness influences setup dynamics in the nearshore zone.
Abstract
Long waves are generated and transform when short-wave groups propagate into shallow water, but the generation and transformation processes are not fully understood. In this study we develop an analytical solution to the linearized shallow-water equations at the wave-group scale, which decomposes the long waves into a forced solution (a bound long wave) and free solutions (free long waves). The solution relies on the hypothesis that free long waves are continuously generated as short-wave groups propagate over a varying depth. We show that the superposition of free long waves and a bound long wave results in a shift of the phase between the short-wave group and the total long wave, as the depth decreases prior to short-wave breaking. While it is known that short-wave breaking leads to free-long-wave generation, through breakpoint forcing and bound-wave release mechanisms, we highlight the importance of an additional free-long-wave generation mechanism due to depth variations, in the absence of breaking. This mechanism is important because as free long waves of different origins combine, the total free-long-wave amplitude is dependent on their phase relationship. Our free and forced solutions are verified against a linear numerical model, and we show how our solution is consistent with prior theory that does not explicitly decouple free and forced motions. We also validate the results with data from a nonlinear phase-resolving numerical wave model and experimental measurements, demonstrating that our analytical model can explain trends observed in more complete representations of the hydrodynamics.
Abstract
Long waves are generated and transform when short-wave groups propagate into shallow water, but the generation and transformation processes are not fully understood. In this study we develop an analytical solution to the linearized shallow-water equations at the wave-group scale, which decomposes the long waves into a forced solution (a bound long wave) and free solutions (free long waves). The solution relies on the hypothesis that free long waves are continuously generated as short-wave groups propagate over a varying depth. We show that the superposition of free long waves and a bound long wave results in a shift of the phase between the short-wave group and the total long wave, as the depth decreases prior to short-wave breaking. While it is known that short-wave breaking leads to free-long-wave generation, through breakpoint forcing and bound-wave release mechanisms, we highlight the importance of an additional free-long-wave generation mechanism due to depth variations, in the absence of breaking. This mechanism is important because as free long waves of different origins combine, the total free-long-wave amplitude is dependent on their phase relationship. Our free and forced solutions are verified against a linear numerical model, and we show how our solution is consistent with prior theory that does not explicitly decouple free and forced motions. We also validate the results with data from a nonlinear phase-resolving numerical wave model and experimental measurements, demonstrating that our analytical model can explain trends observed in more complete representations of the hydrodynamics.
Abstract
Long waves play an important role in coastal inundation and shoreline and dune erosion, requiring a detailed understanding of their evolution in nearshore regions and interaction with shorelines. While their generation and dissipation mechanisms are relatively well understood, there are fewer studies describing how reflection processes govern their propagation in the nearshore. We propose a new approach, accounting for partial reflections, which leads to an analytical solution to the free wave linear shallow-water equations at the wave-group scale over general varying bathymetry. The approach, supported by numerical modeling, agrees with the classic Bessel standing solution for a plane sloping beach but extends the solution to arbitrary alongshore uniform bathymetry profiles and decomposes it into incoming and outgoing wave components, which are a combination of successively partially reflected waves lagging each other. The phase lags introduced by partial reflections modify the wave amplitude and explain why Green’s law, which describes the wave growth of free waves with decreasing depth, breaks down in very shallow water. This reveals that the wave amplitude at the shoreline is highly dependent on partial reflections. Consistent with laboratory and field observations, our analytical model predicts a reflection coefficient that increases and is highly correlated with the normalized bed slope (bed slope relative to wave frequency). Our approach shows that partial reflections occurring due to depth variations in the nearshore are responsible for the relationship between the normalized bed slope and the amplitude of long waves in the nearshore, with direct implications for determining long-wave amplitudes at the shoreline and wave runup.
Abstract
Long waves play an important role in coastal inundation and shoreline and dune erosion, requiring a detailed understanding of their evolution in nearshore regions and interaction with shorelines. While their generation and dissipation mechanisms are relatively well understood, there are fewer studies describing how reflection processes govern their propagation in the nearshore. We propose a new approach, accounting for partial reflections, which leads to an analytical solution to the free wave linear shallow-water equations at the wave-group scale over general varying bathymetry. The approach, supported by numerical modeling, agrees with the classic Bessel standing solution for a plane sloping beach but extends the solution to arbitrary alongshore uniform bathymetry profiles and decomposes it into incoming and outgoing wave components, which are a combination of successively partially reflected waves lagging each other. The phase lags introduced by partial reflections modify the wave amplitude and explain why Green’s law, which describes the wave growth of free waves with decreasing depth, breaks down in very shallow water. This reveals that the wave amplitude at the shoreline is highly dependent on partial reflections. Consistent with laboratory and field observations, our analytical model predicts a reflection coefficient that increases and is highly correlated with the normalized bed slope (bed slope relative to wave frequency). Our approach shows that partial reflections occurring due to depth variations in the nearshore are responsible for the relationship between the normalized bed slope and the amplitude of long waves in the nearshore, with direct implications for determining long-wave amplitudes at the shoreline and wave runup.
Abstract
The Australian marine research, industry, and stakeholder community has recently undertaken an extensive collaborative process to identify the highest national priorities for wind-waves research. This was undertaken under the auspices of the Forum for Operational Oceanography Surface Waves Working Group. The main steps in the process were first, soliciting possible research questions from the community via an online survey; second, reviewing the questions at a face-to-face workshop; and third, online ranking of the research questions by individuals. This process resulted in 15 identified priorities, covering research activities and the development of infrastructure. The top five priorities are 1) enhanced and updated nearshore and coastal bathymetry; 2) improved understanding of extreme sea states; 3) maintain and enhance the in situ buoy network; 4) improved data access and sharing; and 5) ensemble and probabilistic wave modeling and forecasting. In this paper, each of the 15 priorities is discussed in detail, providing insight into why each priority is important, and the current state of the art, both nationally and internationally, where relevant. While this process has been driven by Australian needs, it is likely that the results will be relevant to other marine-focused nations.
Abstract
The Australian marine research, industry, and stakeholder community has recently undertaken an extensive collaborative process to identify the highest national priorities for wind-waves research. This was undertaken under the auspices of the Forum for Operational Oceanography Surface Waves Working Group. The main steps in the process were first, soliciting possible research questions from the community via an online survey; second, reviewing the questions at a face-to-face workshop; and third, online ranking of the research questions by individuals. This process resulted in 15 identified priorities, covering research activities and the development of infrastructure. The top five priorities are 1) enhanced and updated nearshore and coastal bathymetry; 2) improved understanding of extreme sea states; 3) maintain and enhance the in situ buoy network; 4) improved data access and sharing; and 5) ensemble and probabilistic wave modeling and forecasting. In this paper, each of the 15 priorities is discussed in detail, providing insight into why each priority is important, and the current state of the art, both nationally and internationally, where relevant. While this process has been driven by Australian needs, it is likely that the results will be relevant to other marine-focused nations.
