Bottom Bathymetry Research Articles

Quantification of error sources in wave runup estimates on two Mediterranean sandy beaches

Projected future sea level rise and marine storminess is a serious threat for beaches as they induce beach flooding and erosion. Among other factors, wave runup play an important role in beach evolution and must be robustly assessed. However, little attention has been paid to the uncertainties associated to its characterization and how do they compare to other sources of uncertainty. We have quantified the impact of several sources of error in the estimation of wave runup on sandy beaches. Understanding what factors are more influential in the accuracy of the results will help to determine the main sources of uncertainty in beach flooding projections. A calibrated state-of-the-art numerical modelling system has been setup for two beaches in the Mallorca islands (NW Mediterranean). The system has been forced with the best available information of nearshore incoming waves and has been validated against observations to define the benchmark accuracy. To determine the key factors affecting the accuracy of the system's results, different systems configurations have been tested with different degrees of complexity.Our results show that using the most sophisticated modelling system with the best information on boundary conditions, bottom bathymetry, and submerged vegetation leads to a swash RMSE comparable to the standard deviation of the observed swash. We have also found that the choice of lateral boundary conditions (i.e., source of information for the incoming waves) can double the RMSE and induce large biases. Our results also show that using a simple empirical approach usually underestimates the wave runup. However, in locations with vegetated seabed there is a compensation error, and the empirical approach can lead to acceptable results if forced by nearshore waves. In addition, we have compared the error estimates obtained with uncertainties associated to projected sea level rise. Our findings suggest that the uncertainty associated with wave runup modelling should be considered in the assessment of the total uncertainty of future beach flooding, since the analysis performed indicates that this uncertainty can account for between 16% and 60% of the uncertainties linked to mean sea level projections.

The Influence of Bathymetry Over Heat Transport Onto the Amundsen Sea Continental Shelf

AbstractIce streams such as Pine Island and Thwaites Glaciers which terminate at their ice shelves in the eastern Amundsen Sea, West Antarctica, are losing mass faster than most others about the continent. The mass loss is due to basal melting, which is influenced by a deep current that transports warm Circumpolar Deep Water (CDW) from the continental shelf break toward the ice shelves. This current and associated heat transport are controlled by factors such as bottom bathymetry, near‐surface winds and meltwater. Using a realistic regional model as a reference, in this study we use idealized models to examine the role of bathymetric features in determining the shelf‐wide circulation and in enabling heat transport from the deep ocean onto the continental shelf. We find that a ridge that blocks deep westward inflow from the Bellingshausen Sea enables a deep cyclonic circulation on the shelf with an eastward undercurrent immediately south of the shelf break. Inclusion of the ridge enhances heat transport onto the continental shelf; without the ridge the flow features an along‐shelf break westward current that suppresses cross‐shelf break fluxes. We also consider the effects of shifting the prescribed wind forcing profile to the south—a simplified representation of future potential changes to the winds—and we find that the continental shelf is warmer in this scenario. These fundamental investigations will help refine the aims of future fieldwork and modeling.

Soil Erosion and Deposition Rate Inside an Artificial Reservoir in Central Italy: Bathymetry versus RUSLE and Morphometry

This study, using different direct and indirect methodologies, evaluated the sedimentation rate in an artificial reservoir in central Italy. This reservoir is regionally representative and was built in the 1960s for hydroelectric purposes; it has experienced a strong decrease in trap efficiency and a loss of over 70% of the stored water volume. Direct measurements of the lake bottom bathymetry, carried out in 2006 and 2015, and 3D reconstructions performed in a GIS environment, made it possible to calculate the volume of filling material and to verify an increasing trend in the sedimentation rate since 2006. The sample reservoir denudation rate was compared with that obtained using the Revised Universal Soil Loss Equation method to calibrate the fundamental and critical factors of the method itself, and verify the contribution of a hydrological “direct” (through new channels or gullies) or “diffuse” (overland flow) connectivity. Furthermore, the comparison with the results obtained from past studies on ten other artificial regional reservoirs, performed with morphometric analysis, demonstrated a good relationship between soil erosion rate, stream frequency, and contributing area size. The study highlighted how a correct estimate of soil erosion and/or solid transport rates within a hydrographic basin is fundamental for the assessment of the trap efficiency of a reservoir, in a period in which the availability of water resources is becoming more and more vital.

The Role of Sea State to the Morphological Changes of Prasonisi Tombolo, Rhodes Island, Greece

Wave-induced morphodynamic processes that cause formation, preservation, and destruction of the Prasonisi tombolo in Rhodes Island are investigated, based on satellite image analysis and numerical modeling. A new method is developed for extracting wave events that consist of successive wave data of similar characteristics. The wave events refer either to wind seas or swell seas. This process combined with the satellite image analysis is then utilized for the derivation of the most representative wave scenarios that affect tombolo and salient formation. In particular, the main factors that play a significant role in tombolo and salient evolution are the offshore wave conditions, the location and width of the surf zone, the maximum value of the wave breaking index in the study area, and the initial bottom bathymetry before the study area is exposed to a new sea state. In general, the proposed method provides a realistic insight into tombolo morphodynamics and can be used to provide a cost-effective approach and a wave data-reduction technique for coastal engineering studies.

Stages and staging of the study of the seabed for earthmoving systems

The development and development of minerals and building materials in water areas, the laying of underwater communications, planning and dredging underwater are preceded by detailed surveys of soil massifs. They establish the lithology and genesis of deposits, bottom surface bathymetry, physicomechanical, acoustic and other properties of underwater soils. These studies are mainly subordinated to the tasks of geology. At the same time, for the development of the deep-water part of the World Ocean, it is planned to use soil development and transport equipment. The kinematic parameters of the equipment used for engineering and geological research do not correspond to the kinematics of existing or planned underwater systems. Despite some progress in the development of engineering-geological methods for studying the ocean, there are currently no reliable data on the mechanical properties of bottom sediments in natural occurrence. Practically the only way to identify the strength properties of deep-water soils is the sampling method (tubes, grabs, dredges). Soil characteristics are determined from samples brought to the surface in a shore or ship laboratory.
 One of the specific features of the tests being carried out is the consideration of hydrostatic pressure, the effect of which on three-phase soils is especially large. Therefore, it should be expected that the measurement errors of the characteristics of bottom sediments in atmospheric conditions due to the violation of their structural relationships during ascent from great depths can differ by an order of magnitude or more from the true values ​​of the parameters of the soil environment. Thus, in order to determine the operating conditions and set external loads on underwater digging machines, it is necessary to measure the strength, deformation and other characteristics of bottom soils in natural conditions under hydrostatic pressure. This paper considers the methods and technical means used for deep-sea exploration of the seabed. Particular attention is paid to engineering-geological methods, which make it possible at the stage of detailed exploration to obtain not only predictive estimates of the mineral resources of the World Ocean but also to determine the physical and mechanical properties of bottom sediments, on which deep-sea digging machines will have to work.

The Use of the NAMI-DANCE Computational Complex on the Problem of Tsunami Waves

Mathematical models that are applicable to the simulation of the generation and propagation of tsunami waves from different sources, that is, underwater earthquakes, submarine landslides, and meteotsunamis, are described. The models are based on the well-known nonlinear shallow-water theory and its dispersion generalizations in two horizontal dimensions. Long wave dispersion related to the finiteness of water depth increases the order of the initial equations and, as a consequence, the time of computation. For this reason, physical dispersion in the investigations presented in this paper is replaced by numerical dispersion owing to a special choice of spatial and temporal steps. The numerical scheme for solving the shallow water equations is based on the leapfrog method. The equations are solved in spherical coordinates fixed to the rotating Earth with allowance for dissipative effects in the near-bottom layer with the use of the developed NAMI-DANCE code. For waves of seismic origin, the initial conditions for solving the hydrodynamic equations are taken from the solution of an elasticity theory problem to describe earthquake evolution (the Okada solution). In the case of a meteotsunami, atmospheric factors are taken into account as external forces and included in the right-hand sides of shallow water equations. Finally, generation of tsunami waves by submarine landslides is considered within the framework of a two-layer model with a lower viscous layer modeling the motion of the landslide. Two kinds of boundary conditions are used: free wave passage through open boundaries (in straits, etc.) using linear shallow-water equations and full reflection on the coast or in the near-shore area. Some test problems (benchmarks) on which the computational complex was verified are listed. The difficulties in the representation of tsunami characteristics due to bad data on the bottom bathymetry and topography of the land are mentioned. The possibility of using the developed code for the analysis of tsunami action on coasts and constructions is also discussed.

Sediment distribution and organic carbon burial in a subtropical hydroelectric reservoir

Reservoir sediment is a major player in the terrestrial carbon (C) budget, and the quantification of C burial in sediments is important in assessing the reservoir’s role in the global C budget. However, assessments of C burial in sediments of sub-tropical hydroelectric reservoirs and their potential as C sinks are thus far limited due to a lack of whole reservoir assessments of C burial. In this study, a combined seismic survey with sediment core analysis was conducted in the Xin’anjiang Reservoir, the first large hydroelectric reservoir in China. The total organic carbon (TOC), total nitrogen, isotopic C composition (δ13C), and sediment grain size were analyzed. 210Pb and 137Cs were used to obtain the sediment chronologies. The data suggest that bottom bathymetry of the pre-existing reservoir is an important factor on sediment accumulated within the reservoir. The sediment OC content and trophic state became controlling factors and accelerated the OC burial in the sediment. Based on the interpolated sediment thickness data and total reservoir area, the average TOC burial rate was estimated at 34.0 g C m−2 year−1 (ranging 0–676.7 g C m−2 year−1). This rate is within that estimated by sediment coring (mean 40.4 g C m−2 year−1, ranging 15.8–110.1 g C m−2 year−1) as a result of high heterogeneity of sediment distribution and irregular sedimentation. However, the result was close to the estimates of previous studies, demonstrating that the combined method here can also be an effective way to conduct future estimation of C burial in freshwater reservoirs.

Intrusions and solitons: Propagation and collision dynamics

Triggering and evolution of internal solitary waves (ISWs) generated by intrusive gravity currents (IGCs) propagating into a stratified ambient fluid is analyzed by laboratory experiments. After the release of a fluid of uniform density, intermediate with respect to the upper (lower-density) and lower (higher-density) layers in the channel, the IGC develops and flows downstream, intruding into the pycnocline. Near the IGC leading front, the compression of the upper layer generates ISWs: they gradually separate from the current that propagates slower. Shoaling downstream over a uniform sloping boundary, solitons break and partially reflect. We investigate the dynamics of the interaction between the reflected ISWs and the incoming IGC. During the engage, an increase in the ISW celerity occurs, leading the celerity of the reflected waves to be even larger than the incident wave. Our analysis shows how both ISWs and IGCs can significantly change their features as they experience a change of the density structure in the water column. This is expected to occur, for example, in stratified small-scale basins, where river plumes intrude the seasonal thermocline. The radial ISWs, originated by IGCs, can then be reflected by the adjacent bottom bathymetry, spreading against the intrusive current from which they are generated.

Can simple KdV-type equations be derived for shallow water problem with bottom bathymetry?

In this study, we give a survey of derivations of KdV-type equations with an uneven bottom for several cases when small (perturbation) parameters $\alpha, \beta, \delta$ are of different orders. Six different cases of such ordering are discussed. Surprisingly, for all these cases the Boussinesq equations can be made compatible only for the particular piecewise linear bottom profiles, and the correction function has a universal form. For such bottom relief, several new KdV-type wave equations are derived. These equations generalize the KdV, the extended KdV (KdV2), the fifth-order KdV (KdV5) and the Gardner equations.

Depositional history, source rock quality and thermal maturity of Upper Ordovician - Lower Silurian organic-rich sedimentary rocks in the central part of the Baltic Basin (Lithuania)

This study provides a comprehensive geochemical and mineralogical characterisation of the fine-grained, organic matter-rich sedimentary rocks of the Lower Palaeozoic in the central part of the Baltic Basin (Western Lithuania). The primary objective was to deduce environmental conditions for the Lower Palaeozoic succession which is very well preserved in the Baltic Basin, while the secondary goal was to obtain information on maturation and thermal history of the rocks. The sample set covers different stratigraphic units of the Ordovician- Lower Silurian succession and was analysed with a wide range of different methods including elemental analysis, organic petrography, Rock-Eval pyrolysis, molecular geochemical analysis of saturated and aromatic hydrocarbon fractions, inorganic geochemistry, mineralogy (XRF, XRD analysis) and magnetic susceptibility (MS) of rock samples. Their integration allowed a determination of the redox conditions, paleoproductivity and clastic input during sediment deposition. The fine-grained sediments are dominated by clay minerals and quartz and to a lesser extent carbonate, pyrite and feldspar. Microscopic analysis revealed abundant solid bitumen and zooclasts. Biomarker data indicate a marine origin for the precursor organic matter. Maturity parameters revealed the presence of a thermal maturity ‘anomaly’ in the southwestern part of Lithuania, where the late phase of oil generation and possibly beginning of condensate-wet gas generation with corresponding maximum paleotemperatures of 140–180 °C has been reached. Bottom-water conditions varied from oxic to anoxic/euxinic during deposition driven by interaction of climate states, water mass circulation and stratification, water geochemistry and sea bottom bathymetry. Four shaly horizons (at the Upper Ordovician Fjäcka and Mossen Fms., Silurian Dobele Fm., and near Llandovery-Wenlock boundary levels) were recognized as being formed in oxygen-depleted benthic settings as indicated by high TOC and TS contents, sedimentation features, high metal enrichment or degree of piritization. The deposition of highly organic matter-rich Silurian Dobele Fm. might have coincided with oceanic anoxia and Late Aeronian bioevent, accompanied by an upwelling regime with increased paleoproductivity. The interpreted coarsening upward trend at the Early Silurian Adavere Regional Stage terminates with fall in relative sea-level at the Llandovery-Wenlock boundary. The geochemical proxies near Llandovery/Wenlock boundary may reflect the perturbations in oceanic water geochemistry which in turn may have eventually led to Ireviken mass extinction event. • Maturity parameters revealed the presence of a thermal maturity ‘anomaly’. • Bottom-water conditions varied from oxic to anoxic/euxinic during deposition. • Organic matter is of marine algal origin with accompanying bacteria and zooclasts. • Silurian horizons may reflect anoxic events associated with mass extinctions.

Variability of Doppler shift in the ocean bottom reverberation data from the East Sea of Korea

Sea trials measuring the ocean bottom reverberation using an active towed array sensor (ATAS) equipped with triplet receiver array were conducted in the East Sea of Korea during August, 2015. The continuous-wave waveforms with center frequency 3 kHz and pulse lengths of 0.1, 0.3, and 1 s are used as source signals, respectively. Ship velocity was between 4 and 5 knots and the water depth varies from 500 to 1250 m. Also, sound speed profiles were obtained by expendable bathythermographs (XBTs) during the ship maneuvering, where the depths of minimum sound speed appeared between 208 and 306 m. From the measurement results, we observed variability and spreading of reverberation Doppler shifts, which depends on the bottom bathymetry, platform motion, source depth, and receiver array depth. In particular, significant asymmetry of the Doppler spectrum occurred at the depths of the source and receiver below 120 m. The instantaneous frequency Doppler of reverberation signal in each beam direction provides information on the bathymetry and scattering characteristics of the bottom. This frequency shift is traced in time and analyzed.

Validation of a three-dimensional depth-semi-averaged model

The present work completes the validation of the depth-semi-averaged model defined in Antuono et al. [“A depth semi-averaged model for coastal dynamics,” Phys. Fluids 29, 056603 (2017)] providing a numerical implementation in three spatial dimensions. In particular, the model is aimed at describing a wide variety of phenomena typical of the coastal region, as for example nonlinear interaction between waves and the bottom bathymetry (diffraction/refraction phenomena), dispersion effects, and beach inundation. To this purpose, the proposed scheme is tested against benchmark experimental data available in the literature for wave propagation problems in both intermediate and shallow water conditions. A final simulation is carried out by considering a tsunami wave running over a prototype bathymetry resembling a bay-promontory coastline. Different widths of the bay have been considered, describing their influence on the run-up dynamics.

Computational NAMI-DANCE complex in the problem of tsunami waves

Mathematical models applicable to the simulation of generation and propagation of tsunamis of different origin - underwater earthquakes, submarine landslides, meteotsunami - are described. The basic model is based on the well-known nonlinear shallow-water theory and its dispersion generalizations in two horizontal dimensions. Long wave dispersion related to the finiteness of water depth increases the order of PDE and leads to serious computational problems. We replace the physical dispersion with the numerical one using specific conditions for spatial and temporal steps. The numerical scheme is based on a Leap-Frog method. The equations are solved in spherical coordinates fixed to the rotating Earth by taking into account dissipative effects in the near-bottom layer with the use of NAMI-DANCE code. For tsunami waves of seismic origin, the initial conditions for hydrodynamic equations are found from the Okada solution of elastic equations describing the development of an earthquake. In the case of meteotsunami, atmospheric factors are modeled by the external forces. The process of generation of tsunami waves of landslide origin is analyzed in the framework of a two-layer model with lower viscous layer modeling the motion of a submarine landslide. There are two kinds of boundary conditions: free wave passage through open boundaries (in straits, etc.) using linear shallow-water equations, and a full reflection on the coast or in near-shore area. The NAMI-DANCE code has been verified with several benchmarks. The difficulties of tsunami modelling associated with the lack of accuracy in the bottom bathymetry and land topography are mentioned. The use of the developed code for the analysis of tsunami action on the coasts and constructions is discussed.

Interfacial long traveling waves in a two‐layer fluid with variable depth

AbstractLong wave propagation in a two‐layer fluid with variable depth is studied for specific bottom configurations, which allow waves to propagate over large distances. Such configurations are found within the linear shallow‐water theory and determined by a family of solutions of the second‐order ordinary differential equation (ODE) with three arbitrary constants. These solutions can be used to approximate the true bottom bathymetry. All such solutions represent smooth bottom profiles between two different singular points. The first singular point corresponds to the point where the two‐layer flow transforms into a uniform one. In the vicinity of this point nonlinear shallow‐water theory is used and the wave breaking criterion, which corresponds to the gradient catastrophe is found. The second bifurcation point corresponds to an infinite increase in water depth, which contradicts the shallow‐water assumption. This point is eliminated by matching the “nonreflecting” bottom profile with a flat bottom. The wave transformation at the matching point is described by the second‐order Fredholm equation and its approximated solution is then obtained. The results extend the theory of internal waves in inhomogeneous stratified fluids actively developed by Prof. Roger Grimshaw, to the new solutions types.

A fine spatial-scale sea surface temperature atlas of the Australian regional seas (SSTAARS): Seasonal variability and trends around Australasia and New Zealand revisited

The AVHRR SST data were sourced from the Integrated Marine Observing System (IMOS: http://www.imos.org.au) - IMOS is a national collaborative research infrastructure, supported by the Australian Government. The version 2 IMOS AVHRR SST products were produced using the National Computational Infrastructure at the Australian National University. SST from Queensland wave rider buoys was made available by the Department of Science, Information Technology and Innovation, Queensland Government, licensed under Creative Commons Attribution sourced on 27 February 2017. Wave-rider SST data off NSW was provided to us by NSW Office of Environment and Heritage, and was collected by the Manly Hydraulics Laboratory. The port sea level gauge and drifting buoy SST records were made available by the Australian Bureau of Meteorology. NOAA_OI_SST_V2 data were provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their Web site at http://www.esrl.noaa.gov/psd. For bottom bathymetry, we used the Terrainbase product from the National Geophysical Data Center and World Data Center-A for Solid Earth Geophysics in Boulder, Colorado. This work was supported by the author's institutions and the Australian Integrated Marine Observing System. These funders had no input to the study design and analysis.

Delta shock waves in shallow water flow

The shallow-water equations for two-dimensional hydrostatic flow over a bottom bathymetry b(x) areht+(uh)x=0,ut+(gh+u2/2+gb)x=0. It is shown that the combination of discontinuous free-surface solutions and bottom step transitions naturally lead to singular solutions featuring Dirac delta distributions. These singular solutions feature a Rankine–Hugoniot deficit, and can readily be understood as generalized weak solutions in the variational context, such as defined in [13,22]. Complex-valued approximations which become real-valued in the distributional limit are shown to extend the range of possible singular solutions. The method of complex-valued weak asymptotics [22,23] is used to provide a firm link between the Rankine–Hugoniot deficit and the singular parts of the weak solutions. The interaction of a surface bore (traveling hydraulic jump) with a bottom step is studied, and admissible solutions are found.

Three-Dimensional Distribution of Turbulent Mixing in the South China Sea

AbstractA three-dimensional distribution of turbulent mixing in the South China Sea (SCS) is obtained for the first time, using the Gregg–Henyey–Polzin parameterization and hydrographic observations from 2005 to 2012. Results indicate that turbulent mixing generally increases with depth in the SCS, reaching the order of 10−2 m2 s−1 at depth. In the horizontal direction, turbulence is more active in the northern SCS than in the south and is more active in the east than the west. Two mixing “hotspots” are identified in the bottom water of the Luzon Strait and Zhongsha Island Chain area, where diapycnal diffusivity values are around 3 × 10−2 m2 s−1. Potential mechanisms responsible for these spatial patterns are discussed, which include internal tide, bottom bathymetry, and near-inertial energy.

Characteristics of Wave-induced Currents using the SWASH Model in Haeundae Beach

본 연구에서는 SWASH 모형을 이용하여 ê³„ì ˆë³„ 이상파랑에 의한 해운대 해수욕장에서 불규칙파의 파랑 변형 및 해빈류 특성을 분석하였다. 개경계에서 불규칙파는 JONSWAP 스펙트럼을 ì ìš©í•˜ì˜€ë‹¤. ìž ì‚¬íŒŒ 조건은 국립해양조사원에서 ì œê³µí•˜ëŠ” 2014ë „ 파랑관측자료를 바탕으로 ê³„ì ˆë³„ 대표파를 ì„ ì •í•˜ì˜€ë‹¤. SWASH에 의한 ê³„ì ˆë³„ 해빈류 계산결과는 현장조사 결과와 ë¹„êµÂ·ê²€í† í•˜ì˜€ë‹¤. 하계의 경우 S 계열의 파랑이 ì§€ë°°ì ì´ë©° 동백섬측에서 미포측으로 연안류가 ì§€ë°°ì ìœ¼ë¡œ ë°œìƒí•˜ì˜€ê³ í•´ìš´ëŒ€ 해수욕장 중앙부근에서는 이안류가 발생하였다. 동계의 경우 ESE 계열의 파랑이 ì§€ë°°ì ì´ë©° 해운대 해수욕장 중앙부근에서 각각 동백섬측과 미포측으로 향하는 연안류가 발생하였다. 핵심용어: 해빈류, 연안류, 이안류, 쇄파, 불규칙파

Effects of discontinuous submerged breakwater on water surface elevation

Submerged breakwaters are used to prevent shore line erosion and sediment transportation. One of their advantages is low visual impact. In this paper, the effects of discontinuous submerged breakwaters over water surface elevation was numerically studied considering the extended Boussinesq equations as governing equations using MIKE21 software. The result of discontinuous breakwater was compared with a beach without breakwater. The results showed that the gap dramatically effects on surface elevation from shore line to offshore. It is also evident from results that with approaching the center of the gap, fluctuation of surface elevation is generated. It is because of passing longshore currents towards offshore through the gap which leads to an increase in sediment transportation rate. Nevertheless, transferring water mass from breakwater gap results in powerful rip currents leading to high changes on longshore wave profile. As waves propagate towards shore line the transformation phenomena occurs related to sea bottom bathymetry changes. The length and the height of waves moving from deep water to shallow water change and as the wave slope goes over the critical limit and waves reach the breaking line they break and most of the wave energy releases. When high waves approaching the shoreline, water fluctuations occurs leading to beach erosion and sediment transportation. Therefore, preventing land erosion by wave attacks and decreasing the impact of inducing waves on shore structures are important subjects in coastal engineering. Breakwater is a structure which is mainly used to protect the area in its lee from wave attack. In reality, the purpose of building breakwaters is providing a sheltered area for loading and offloading of the ships; as well as to manipulate the littoral transport conditions by trapping the moving sand particles. There are different types of breakwaters like detached breakwater that is completely isolated from shore and attached breakwater that is connected to the shoreline. Both of these types of breakwaters can be floating, emerged and submerged structures. Today the use of detached low-crested or submerged breakwaters in conjunction with beach nourishment is advised for stabilization of beaches. This is mainly related to their small

Characterization of linear and oscillatory behaviours of radiation-induced natural convection boundary layer in response to constant and time-varying thermal forcing

This paper considers linear and oscillatory behaviours of the natural convection boundary layer induced by the absorption of incoming radiation in response to constant and time-varying (ramp) thermal forcing. The considered configuration is relevant to the flow in littoral regions of lakes and reservoirs in response to the daytime thermal forcing due to solar radiation. The absorption of the incoming solar radiation is depth-dependent, following Beer’s law, whilst the residual radiation at the bottom bathymetry is absorbed and released back to the water body as a boundary flux. Therefore, a potentially unstable thermal boundary layer forms adjacent to the bottom bathymetry and the associated thermoconvective instability induces vertical mixing in the form of rising plumes (i.e. intermittent convection). The linear theory is applied to investigate the incipient evolution of the instability, and direct comparisons of linear and direct stability analyses are performed. The fastest growing mode and the corresponding temporal growth rate obtained via a quasi-static linear stability analysis are shown to be in excellent agreement with the results of the direct stability analysis based on numerical simulations of the flow. Further, the time and frequency scales of the unstable bottom thermal boundary layer are derived via a local Rayleigh number analysis. It is then demonstrated that the boundary layer response to the time-varying thermal forcing is in equilibrium with the forcing intensity at each instant of time.