Search USGSSearch

Geology topics

Mark L. Buckley

Publications and source records attributed to Mark L. Buckley.

At least 19 recordsLinked to original sources

Wave runup and total water level observations from time series imagery at several sites with varying nearshore morphologies

Coastal imaging systems have been developed to measure wave runup and total water level (TWL) at the shoreline, which is a key metric for assessing coastal flooding and erosion. However, extracting quantitative measurements from coastal images has typically been done through the laborious task of hand-digitization of wave runup timestacks. Timestacks are images created by sampling a cross-shore array of pixels from an image through time as waves propagate towards and run up a beach. We utilize over 7000 hand-digitized timestacks from six diverse locations to train and validate machine learning models to automate the process of TWL extraction. Using these data, we evaluate two deep learning model architectures for the task of runup detection. One is based on a fully convolutional architecture trained from scratch, and the other is a transformer-based architecture trained using transfer learning. The deep learning models provide a probability of each pixel being either wet or dry. When contoured at the 50% level (equal chance of being wet or dry), the deep learning models more accurately identified TWL maxima than minima at all sites. This resulted in accurate predictions of 2% exceedance runup, but under predictions of significant swash and over predictions of wave setup. Improved agreement with the complete TWL time series was obtained through post-processing by utilizing the wet/dry probability of each pixel to weight the contouring toward lower dryness probabilities for runup minima (maxima agreed well with observations without tuning). Overall, a transformer-based model using transfer learning provided the best agreement with wave runup statistics, including a) the 2% exceedance runup, b) significant swash, and c) wave setup at the shoreline. For a random subset of images, the model was found to be within the uncertainty range of hand-digitization. The relative success of the transfer learning model suggests that fine-tuning a large model has advantages compared to training a smaller model from scratch. Models provide per-pixel probabilistic estimates in less than 10 s per timestack on a single computational unit, versus the more than 5 min required for hand-digitization. The model is therefore well-suited for near real-time applications, allowing for the development of early warning systems for difficult to forecast events. Real-time wave runup and total water level observations can also be incorporated into coastal hazards forecasts for data assimilation and continual model validation and improvement.

Coastal Engineering

Developing a decision tree model to forecast runup and assess uncertainty in empirical formulations

The coastal zone is a dynamic region that can change rapidly and significantly with respect to the morphology of the beach and incoming wave conditions. Runup forecasts may be improved by adapting a dynamic approach that allows for different runup models to be implemented in response to changes in beach state. Accurately forecasting wave runup is critical to characterize exposure to coastal hazards and provide an early warning against potential erosion and inundation. Here, we developed a decision tree model to produce a weighted ensemble of existing runup models to predict 1.25 years of runup at Duck, North Carolina, USA. We then applied the calibrated decision tree model to reproduce observed runup during the DUNEX experiment in Pea Island, North Carolina, USA. We found that the decision tree approach yielded a prediction that was comparable or greater in accuracy (i.e. higher r2, lower RMSE) than the individual runup models. We also interrogated the decision tree predictions to determine how the individual models perform relative to each other and why certain models perform better than others under the same observed wave and beach conditions. We found that the decision tree approach drew on the processes represented in the individual models in the ensemble to produce a forecast that is accurate and explainable without relying on prior knowledge of the study site(s) or requiring manual adjustments beyond the initial model training.

North Carolina

Modeling total water level and coastal change at Pea Island, North Carolina, USA

The DUring Nearshore Event eXperiment (DUNEX) was carried out on Pea Island, North Carolina, USA between September-October 2021. We use a coupled numerical model (Windsurf) to hindcast the evolution of the DUNEX transect and produce a time series of hourly water levels at the shoreline from the model output. In addition to assessing the ability of Windsurf to reproduce TWL, we use model output paired with an ensemble of empirical models to assess how TWL forecasts can be improved by incorporating dynamic morphology. The morphological hindcast achieved an RMSE of 0.10 m and a BSS of 0.47, while the total water level (TWL) time series from the model correlates with the U.S. Geological Survey forecast (r 2 = 0.61) for the study period but with a 0.47 m bias that is primarily due to the much steeper beach slope used to produce the forecast compared to that surveyed at the start of the study period. We find that using dynamic morphology provides a small but statistically significant (α = 0.05) improvement in predicting TWL versus applying the pre-storm beach slope to the whole time series.

North Carolina

Wave-scale observations of sediment resuspension and subsequent transport across a fringing reef flat

During a 3-month deployment on a broad, fringing reef flat in Moloka’i, Hawai’i, we observed over 28,000 wave-driven resuspension (WDR) events of coarse-grained sediment in order to identify major factors. These events were short-lived (2-11 s) and distinct from the longer-duration patterns of water-column backscatter. The wave-driven transport of WDR events was onshore, but the net cross-shore transport was ultimately controlled by water levels. Higher water levels produced larger reef-flat waves, which were requisite for these events to occur. But rising water levels also drove stronger offshore flows. Consequently, onshore net transport of WDR events only occurred within a narrow water-level range, when waves were sufficiently large, but the offshore flow was still weak. Our observations demonstrate how cross-shore transport of coarse-grained material over reef flats is sensitive to changing water levels. Rising sea levels will likely alter transport patterns, which will in turn affect cross-shore delivery of carbonate sand to adjacent shorelines.

Hawaii

Carbonate sediment transport across coral reefs: A comparison of fringing vs. barrier reefs

Considerable uncertainty remains in the budgets of carbonate sediment on reef lined coasts, particularly with respect to the supply of sediment to a reef flat that is then transported throughout a reef system. In this study, we re-examine two recent studies, one on a barrier reef bounded by channels that incise the reef, and one on a fringing reef without channels. Results indicate that the presence of channels results in a circulation regime that promotes not only the onshore sediment flux across the reef flat, but also upslope transport of sediment from the fore reef onto the reef flat. Data from these experiments suggest that when channels are present in the reef flat, the hydrodynamics of these reef systems favor the transport the transport of sediment up the fore reef. This outcome has implications for the design of potential reef restoration efforts intended to protect shorelines.

Conference Paper

Dynamics of the wave-driven circulation in the lee of nearshore reefs

Nearshore rocky reefs with scales of order 10–100 m are common along the world's coastline and often shape wave-driven hydrodynamics and shoreline morphology in their lee. The interaction of waves with these reefs generally results in either two or four-cell mean circulation systems (2CC and 4CC, respectively), with diverging flows behind the reefs and at the shoreline in the 2CC case and flows that diverge in the lee and converge at the shoreline in the 4CC case. By applying a phase-resolving wave-flow model to conduct a detailed analysis of mean momentum balances for waves interacting with nearshore reefs, we develop an understanding of the drivers of 2CC and 4CC flow dynamics and how they vary for different reef geometries and wave and water level conditions. The 2CC or 4CC patterns were primarily driven by alongshore pressure gradients toward the exposed (nonreef fronted) or reef-fronted beach. These alongshore pressure gradients were dependent on the cross-shore setup dynamics governed by the balance between pressure (i.e., related to the setup) and radiation stress gradients, and mean bottom stresses exerted on the water column. If shoreline wave setup in the lee of the reef was less than the exposed beach, a 4CC pattern developed with convergent flow at the shoreline in the lee of the reef; otherwise, a 2CC emerged with divergent flow at the shoreline. Across the parameter space investigated, reef roughness, distance to the shoreline, and beach slope were the three parameters most likely to change the flow patterns between 2CC and 4CC.

JGR-Oceans

Wave runup and inundation dynamics on a perched beach

Sandy beaches perched over rocky shore platforms are common globally, yet their mixed sand and rocky morphology present challenges for quantifying and predicting wave runup and inundation. For typical linear beach profiles, simple relationships can be made between vertical runup and horizontal inundation based on beach slope. However, as topographic irregularities increase, substantial deviations from these relationships can occur. Shore platforms often experience a range of beach states, from full sand coverage (accreted) to complete shore platform erosion (exposed). As a result, existing methods for quantifying runup and inundation on purely sandy beaches are generally not directly applicable to these coastlines. To advance our understanding of runup and inundation on perched beaches, the aim of this work is three-fold: (1) to provide a method for quantifying beach slope and runup across a range of perched beach profiles, (2) to assess the relationship between vertical runup and horizontal inundation observations, and (3) to understand how different hydrodynamic mechanisms (i.e., setup, swash) contribute to runup during different beach states. To achieve this, we conducted an 8-month field study along a perched beach in southwestern Australia that experiences large seasonal variations in beach state and wave climate. A method was developed to measure runup and beach slope when only the topography shoreward of the shore platform edge was known. Using this method, an approximately linear relationship between inundation and runup was identified by incorporating beach slope. Our observations suggest that the components that dominate runup on perched beaches were primarily dependent on beach state (i.e., accreted versus exposed). Runup was dominated by swash in the infragravity band when in an accreted beach state, and setup when in an exposed beach state. These results aid our understanding of coastal processes on perched beaches, while providing new methods applicable to a range of perched beach profiles.

Geomorphology

Free long wave transformation in the nearshore zone through partial reflections

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.

Journal of Physical Oceanography

Wave-driven hydrodynamic processes over fringing reefs with varying slopes, depths, and roughness: Implications for coastal protection

Wave breaking on the steep fore-reef slopes of shallow fringing reefs is effective at dissipating incident sea-swell waves prior to reaching reef shorelines. However, wave setup and free infragravity waves generated during the sea-swell breaking process are often the largest contributors to wave-driven water levels at the shoreline. Laboratory flume experiments and a multi-layer phase-resolving nonhydrostatic wave-flow model, which includes a canopy model to predict drag forces generated by roughness elements, were used to investigate the wave-driven water levels on fringing reefs. Though the model is capable of three dimensional simulations, consistent with the laboratory study, a two-dimensional vertical mode was used. In contrast to many previous studies, both the laboratory experiment and the numerical model account for the effects of large bottom roughness. The numerical model reproduced the observations of the wave transformation and runup over both smooth and rough reef profiles. The numerical model was then extended to quantify the influence of reef geometry and compared to simulations of plane beaches lacking a reef. For a set offshore forcing condition, the fore-reef slope controlled wave runup on reef fronted beaches, whereas the beach slope controlled wave runup on plane beaches. As a result, the coastal protection utility of reefs is dependent on these slopes. For our examples, with a fore-reef slope of 1/5 and a 500 m prototype reef flat length, a beach slope of ~1/30 marked the transition between the reef providing runup reduction for steeper beach slopes and enhancing wave runup for milder slopes. Roughness coverage, spacing, dimensions, and drag coefficient were investigated with results indicating the greatest runup reductions were due to tall roughness elements on the reef flat.

JGR Oceans

The influence of submerged coastal structures on nearshore flows and wave runup

Engineered and natural submerged coastal structures (e.g., submerged breakwaters and reefs) modify incident wave fields and thus can alter hydrodynamic processes adjacent to coastlines. Although submerged structures are generally assumed to promote beach protection by dissipating waves offshore and creating sheltered conditions in their lee, their interaction with waves can result in mean wave-driven circulation patterns that may either promote shoreline accretion or erosion. Here, we analyse the mean flow patterns and shoreline water levels (wave runup) in the lee of idealised impermeable submerged structures with a phase-resolved nonhydrostatic numerical model. Waves propagating over submerged structures can drive either a 2-cell mean (wave-averaged) circulation, which is characterised by diverging flows behind the structure and at the shoreline, or 4-cell circulation, with converging flows at the shoreline and diverging flows in the immediate lee of the structure. The numerical results show that the mode of circulation can be predicted with a set of relationships depending on the incoming wave heights, the structure crest level, and distance to the shoreline (or structure depth). Qualitative agreement between the mean flow and proxies for the sediment transport using an energetics approach suggest that the mean flow can be a robust proxy for inferring sediment transport patterns. For the cases considered, the submerged structures had a minimal influence on shoreline wave setup and wave runup despite the wave energy dissipation by the structures due to alongshore wave energy fluxes in the lee. Consequently, these results suggest that the coastal protection provided by the range of impermeable submerged structures we modelled is primarily due to their capacity to promote beach accretion.

Coastal Engineering

Smoothed Particle Hydrodynamics simulations of reef surf zone processes driven by plunging irregular waves

As waves interact with the slopes of coral reefs and other steep bathymetry profiles, plunging breaking usually occurs where the free surface overturns and violent water motion is triggered. Resolving these surf zone processes pose significant challenges for conventional mesh-based hydrodynamic models, due to the rapidly-deforming nature of the free surface and associated flows. Yet the accurate prediction of these surf zone hydrodynamics is critical for predicting a wide range of nearshore processes driven by wave breaking (e.g., wave dissipation and energy transfers; mean water levels and currents; and wave runup). In this study we assess the ability of the mesh-free, Lagrangian particle-based numerical modelling approach Smoothed Particle Hydrodynamics (SPH) based on DualSPHysics, to simulate the fine-scale hydrodynamic processes driven by irregular wave transformation over a fringing reef profile, by comparing results against detailed experimental observations from a physical modelling study. To greatly improve the computational efficiency, the SPH model was coupled to the mesh-based multi-layer nonhydrostatic wave-flow model SWASH. With this coupled approach, SWASH was used to efficiently simulate the evolution of non-breaking waves from the wavemaker up to the fore reef slope, with the SPH model then used to simulate the detailed hydrodynamic processes over the reef from just offshore of the breakpoint to the shoreline . The SPH model was able to accurately reproduce the complex free surface deformations during plunging breaking, the spectral evolution of waves across the reef flat (including nonlinear wave shape), the mean water levels and currents, and wave runup at the shoreline. Using the long duration simulations (>400 wave periods), the model was able to reproduce the full range of wave motions over the reef (from sea-swell to infragravity frequencies), including the increasing dominance of low frequency waves towards the shoreline and the large cross-reef standing wave motions excited by the reef geometry.

Ocean Modelling

Predicting coastal impacts by wave farms: A comparison of wave-averaged and wave-resolving models

Wave energy converters (WECs) will have to be arranged into arrays of many devices to extract commercially viable amounts of energy. To understand the potential coastal impacts of WEC arrays, most research to date has relied on wave-averaged models given their computational efficiency. However, it is unknown how accurate wave-averaged model predictions are given a lack of validation data and their inherent simplifications of various hydrodynamic processes (e.g., diffraction). This paper compares the predictions of coastal wave farm impacts from a coupled wave-averaged and flow model (Delft3D-SNL-SWAN), to a wave-resolving wave-flow model (SWASH) that intrinsically accounts for more of the relevant physics. Model predictions were compared using an idealized coastal bathymetry over a range of wave conditions and wave farm geometries. Both models predicted the largest impacts (changes to the nearshore hydrodynamics) for large and dense wave farms located close to the shore (1 km) and the smallest impacts for the small and widely spaced farm at a greater offshore distance (3 km). However, the wave-resolving model generally predicted somewhat larger impacts (i.e., changes to the nearshore wave heights, mean velocities and mean water levels). We also found that coupling the wave-averaged model to a flow model resulted in more realistic downstream predictions than the stand-alone wave-averaged model.

Renewable Energy

A numerical study of wave-driven mean flows and setup dynamics at a coral reef-lagoon system

Two-dimensional mean wave-driven flow and setup dynamics were investigated at a reef-lagoon system at Ningaloo Reef, Western Australia, using the numerical wave-flow model, SWASH. Phase-resolved numerical simulations of the wave and flow fields, validated with highly detailed field observations (including >10 sensors through the energetic surf zone), were used to quantify the main mechanisms that govern the mean momentum balances and resulting mean current and setup patterns, with particular attention to the role of nonlinear wave shapes. Momentum balances from the phase-resolved model indicated that onshore flows near the reef crest were primarily driven by the wave force (dominated by radiation stress gradients) due to intense breaking, whereas the flow over the reef flat and inside the lagoon and channels was primarily driven by a pressure gradient. Wave setup inside the lagoon was primarily controlled by the wave force and bottom stress. The bottom stress reduced the setup on the reef flat and inside the lagoon. Excluding the bottom stress contribution in the setup balance resulted in an over prediction of the wave-setup inside the lagoon by up to 200–370%. The bottom stress was found to be caused by the combined presence of onshore directed wave-driven currents and (nonlinear) waves. Exclusion of the bottom stress contribution from nonlinear wave shapes led to an over prediction of the setup inside the lagoon by approximately 20–40%. The inclusion of the nonlinear wave shape contribution to the bottom stress term was found to be particularly relevant in reef regions that experience a net onshore mass flux over the reef crest.

Journal of Geophysical Research-Oceans

The contribution of currents, sea-swell waves, and infragravity waves to suspended-sediment transport across a coral reef-lagoon system.

Coral reefs generate substantial volumes of carbonate sediment, which is redistributed throughout the reef‐lagoon system. However, there is little understanding of the specific processes that transport this sediment produced on the outer portions of coral reefs throughout a reef‐lagoon system. Furthermore, the separate contributions of currents, sea‐swell waves, and infragravity waves to transport, which are all strongly influenced by the presence of a reef, is not fully understood. Here, we show that in reef‐lagoon systems most suspended sediment is transported close to the seabed and can, at times, be suspended higher in the water column during oscillatory flow transitions (i.e., near slack flow) at sea‐swell wave frequencies, and during the peak onshore oscillatory velocity phase at infragravity wave frequencies. While these wave frequencies contribute to the transport of suspended sediment offshore and onshore, respectively, the net flux is small. Mean currents are the primary transport mechanism and responsible for almost 2 orders of magnitude more suspended‐sediment flux than sea‐swell and infragravity waves. Whilst waves may not be the primary mechanism for the transport of sediment, our results suggest they are an important driver of sediment suspension from the seabed, as well as contributing to the partitioning of sediment grain sizes from the reef to the shoreline. As the ocean wave climate changes, sea level rises, and the composition of reef benthic communities change, the relative importance of mean currents, sea‐swell waves, and infragravity waves is likely to change, and this will affect how sediment is redistributed throughout reef‐lagoon systems.

Ningaloo Reef

An efficient method to calculate depth-integrated, phase-averaged momentum balances in non-hydrostatic models

Analysis of the mean (wave-averaged) momentum balance is a common approach used to explain the physical forcing driving wave set-up and mean currents in the nearshore zone. Traditionally this approach has been applied to phase-averaged models but has more recently been applied to phase-resolving models using post-processing, whereby model output is used to calculate each of the momentum terms. While phase-resolving models have the advantage of capturing the nonlinear properties of waves propagating in the nearshore (making them advantageous to enhance understanding of nearshore processes), the post-processing calculation of the momentum terms does not guarantee that the momentum balance closes. We show that this is largely due to the difficulty (or impossibility) of being consistent with the numerical approach. If the residual is of a similar magnitude as any of the relevant momentum terms (which is common with post-processing methods as we show), the analysis is largely compromised. Here we present a new method to internally calculate and extract the depth-integrated, mean momentum terms in the phase-resolving non-hydrostatic wave-flow model SWASH in a manner that is consistent with the numerical implementation. Further, we demonstrate the utility of the new method with two existing physical model studies. By being consistent with the numerical framework, the internal method calculates the momentum terms with a much lower residual at computer precision, combined with greatly reduced calculation time and output storage requirements compared to post-processing techniques. The method developed here allows the accurate evaluation of the depth-integrated, mean momentum terms of wave-driven flows while taking advantage of the more complete representation of the wave dynamics offered by phase-resolving models. Furthermore, it provides an opportunity for advances in the understanding of nearshore processes particularly at more complex sites where wave nonlinearity and energy transfers are important.

Ocean Modelling

Physical mechanisms influencing localized patterns of temperature variability and coral bleaching within a system of reef atolls

Interactions between oceanic and atmospheric processes within coral reefs can significantly alter local-scale (< km) water temperatures, and consequently drive variations in heat stress and bleaching severity. The Scott Reef atoll system was one of many reefs affected by the 2015–2016 mass coral bleaching event across tropical Australia, and specifically experienced sea surface temperature anomalies of 2 °C that caused severe mass bleaching (> 60%) over most of this system; however, the bleaching patterns were not uniform. Little is known about the processes governing thermodynamic variability within atolls, particularly those that are dominated by large amplitude tides. Here, we identify three mechanisms at Scott Reef that alleviated heat stress during the marine heatwave in 2016: (1) the cool wake of a tropical cyclone that induced temperature drops of 1.3 °C over a period of 8 days; (2) air–sea heat fluxes that interacted with the reef morphology during neap tides at one of the atolls to reduce water temperatures by up to 2.9 °C; (3) internal tidal processes that forced deeper and cooler water (up to 2.7 °C) into some sections of the shallow reefs. The latter two processes created localized areas of reduced temperatures that led to lower incidences of coral bleaching for parts of the reef. We predict these processes are likely to occur in other similar tide-dominated reef environments worldwide. Identifying locations where physical processes reduce heat stress will likely be critical for coral reefs in the future, by maintaining communities that can help facilitate local recovery of reefs following bleaching events that are expected to increase in frequency and severity in the coming decades.

Coral Reefs

Hydrodynamics of a tidally‐forced coral reef atoll

The hydrodynamics of a tidally forced semi‐enclosed coral reef atoll (North Scott) at the edge of the continental shelf of northwestern Australia were investigated by combining field observations and numerical modeling. The observations revealed that the spring tidal range outside the atoll reaches 4 m, and as the water level drops below mean sea level, the reef rim surrounding the shallow (~10–15 m) lagoon becomes exposed. During this time, the lagoon can only exchange with the open ocean through two narrow channels, resulting in highly asymmetric water levels and velocities that were most pronounced during spring tide. On average, the ebb tide duration was ~2 hr longer than the flood, with rapid flood velocities in the channel reaching 2 m/s. We applied an unstructured grid model Delft3D‐Flexible Mesh to simulate the atoll hydrodynamics and were able to replicate the asymmetric water levels and complex velocities in the lagoon. The results revealed that at higher tidal stages, a dominant momentum balance exists between the pressure gradient (established by the propagation of the tide on the shelf) and the local flow acceleration of water throughout the interior of the atoll. At lower tidal stages, which coincided with a reversal of the offshore tidal pressure gradient, the lagoon became isolated from offshore dynamics and all momentum terms were negligible. This resulted in a tidally averaged residual westward flow within the lagoon that drove an asymmetric flushing pattern within the atoll, which we propose would be a common flushing mechanism within other tide‐dominated atolls worldwide.

Journal of Geophysical Research C: Oceans

Mechanisms of wave‐driven water level variability on reef‐fringed coastlines

Wave‐driven water level variability (and runup at the shoreline) is a significant cause of coastal flooding induced by storms. Wave runup is challenging to predict, particularly along tropical coral reef‐fringed coastlines due to the steep bathymetric profiles and large bottom roughness generated by reef organisms, which can violate assumptions in conventional models applied to open sandy coastlines. To investigate the mechanisms of wave‐driven water level variability on a reef‐fringed coastline, we performed a set of laboratory flume experiments on an along‐shore uniform bathymetric profile with and without bottom roughness. Wave setup and waves at frequencies lower than the incident sea‐swell forcing (infragravity waves) were found to be the dominant components of runup. These infragravity waves were positively correlated with offshore wave groups, signifying they were generated in the surf zone by the oscillation of the breakpoint. On the reef flat and at the shoreline, the low‐frequency waves formed a standing wave pattern with energy concentrated at the natural frequencies of the reef flat, indicating resonant amplification. Roughness elements used in the flume to mimic large reef bottom roughness reduced low frequency motions on the reef flat and reduced wave run up by 30% on average, compared to the runs over a smooth bed. These results provide insight into sea‐swell and infragravity wave transformation and wave setup dynamics on steep‐sloped coastlines, and the effect that future losses of reef bottom roughness may have on coastal flooding along reef‐fringed coasts.

Journal of Geophysical Research C: Oceans