The estimation of the shape of an array using a hidden Markov model

A hidden Markov model (HMM) technique for the estimation of the shape of a towed array is presented. It is assumed that there is a far-field source radiating sound containing possibly weak spectral lines. The technique uses either the Fourier coefficients at a given frequency computed from a single time block or the maximal eigenvector of a sample spectral covariance matrix. The technique is illustrated using several simulations. The results of these simulations indicate that the HMM technique yields shape and bearing estimates more accurate than those provided by a maximum-likelihood array shape estimation technique     

Double-diffusive convection with a non-linear equation of state: Part I. The accurate conservation of properties in a two-layer system

If the equation of state is nonlinear, a given flux of heat across a double diffusive interface causes different buoyancy fluxes in the upper and lower layers. This results in different convective activity in the two layers and can lead to preferential entrainment across the interface in one direction (i.e. a migration of the interface). In this paper we derive the conservation equations for properties (e.g. heat and a solute) across a double diffusive interface between two well-mixed layers. A nondimensional measure of the entrainment across an interface and the most suitable choice for the buoyancy flux ratio are presented. Some surprising facts emerge. First, even for a linear equation of state and in the absence of direct entrainment across the interface, the flux of water across a finger interface is shown to be important. Second, for the heat-solute system, the heat balance equations for each well-mixed layer contain terms proportional to the heat of solution of the solute and the partial specific enthalpy of pure water in a seawater solution. Third, the rate of change of gravitational potential energy of the two-layer system is shown to have several extra terms in addition to the two commonly quoted major terms.     

Nutrient attenuation in a shallow,gravel-bed river. II. Spatial and temporal changes in nitrogen dynamics and community metabolism

ABSTRACT

Instream processes alter the concentration and bioavailability of nutrients as they are transported downstream. By relating primary production and periphyton composition to changes in nutrient concentration in a gravel-bed river this study made inferences about recycling and attenuation. Where dissolved inorganic nitrogen (DIN) was abundant, concentrations decreased linearly with distance but by less than required to meet the nitrogen demand of primary production. Where DIN was barely measurable photosynthesis was reduced but only by 50%. We infer that recycling sustained primary production even when DIN concentrations were negligibly small. One implication is that DIN removal underestimates attenuation. Further experimental research on recycling and improved modelling is required to better quantify the length of streams adversely affected by nutrients.     

Effects of detailed soil spatial information on watershed modeling across different model scales

Hydro-ecological modelers often use spatial variation of soil information derived from conventional soil surveys in simulation of hydro-ecological processes over watersheds at mesoscale (10–100 km²). Conventional soil surveys are not designed to provide the same level of spatial detail as terrain and vegetation inputs derived from digital terrain analysis and remote sensing techniques. Soil property layers derived from conventional soil surveys are often incompatible with detailed terrain and remotely sensed data due to their difference in scales. The objective of this research is to examine the effect of scale incompatibility between soil information and the detailed digital terrain data and remotely sensed information by comparing simulations of watershed processes based on the conventional soil map and those simulations based on detailed soil information across different simulation scales. The detailed soil spatial information was derived using a GIS (geographical information system), expert knowledge, and fuzzy logic based predictive mapping approach (Soil Land Inference Model, SoLIM). The Regional Hydro-Ecological Simulation System (RHESSys) is used to simulate two watershed processes: net photosynthesis and stream flow. The difference between simulation based on the conventional soil map and that based on the detailed predictive soil map at a given simulation scale is perceived to be the effect of scale incompatibility between conventional soil data and the rest of the (more detailed) data layers at that scale. Two modeling approaches were taken in this study: the lumped parameter approach and the distributed parameter approach. The results over two small watersheds indicate that the effect does not necessarily always increase or decrease as the simulation scale becomes finer or coarser. For a given watershed there seems to be a fixed scale at which the effect is consistently low for the simulated processes with both the lumped parameter approach and the distributed parameter approach.     

Knickpoint recession rate and catchment area: the case of uplifted rivers in Eastern Scotland

Knickpoint behaviour is a key to understanding both the landscape responses to a base‐level fall and the corresponding sediment fluxes from rejuvenated catchments, and must be accommodated in numerical models of large‐scale landscape evolution. Knickpoint recession in streams draining to glacio‐isostatically uplifted shorelines in eastern Scotland is used to assess whether knickpoint recession is a function of discharge (here represented by its surrogate, catchment area). Knickpoints are identified using DS plots (log slope versus log downstream distance). A statistically significant power relationship is found between distance of headward recession and catchment area. Such knickpoint recession data may be used to determine the values of m and n in the stream power law, E = KA^mSⁿ. The data have too many uncertainties, however, to judge definitively whether they are consistent with m = n = 1 (bedrock erosion is proportional to stream power and KPs should be maintained and propagate headwards) or m = 0·3, n = 0·7 (bedrock incision is proportional to shear stress and KPs do not propagate but degrade in place by rotation or replacement). Nonetheless, the E Scotland m and n values point to the dominance of catchment area (discharge) in determining knickpoint retreat rates and are therefore more consistent with the stream power law formulation in which bedrock erosion is proportional to stream power. Copyright © 2005 John Wiley & Sons, Ltd.     

Basal sediment evacuation by subglacial meltwater: suspended sediment transport from Haut Glacier d'Arolla,Switzerland

Proglacial suspended sediment transport was monitored at Haut Glacier d'Arolla, Switzerland, during the 1998 melt season to investigate the mechanisms of basal sediment evacuation by subglacial meltwater. Sub‐seasonal changes in relationships between suspended sediment transport and discharge demonstrate that the structure and hydraulics of the subglacial drainage system critically influenced how basal sediment was accessed and entrained. Under hydraulically inefficient subglacial drainage at the start of the melt season, sediment availability was generally high but sediment transport increased relatively slowly with discharge. Later in the melt season, sediment transport increased more rapidly with discharge as subglacial meltwater became confined to a spatially limited network of channels following removal of the seasonal snowpack from the ablation area. Flow capacity is inferred to have increased more rapidly with discharge within subglacial channels because rapid changes in discharge during highly peaked diurnal runoff cycles are likely to have been accommodated largely by changes in flow velocity. Basal sediment availability declined during channelization but increased throughout the remainder of the monitored period, resulting in very efficient basal sediment evacuation over the peak of the melt season. Increased basal sediment availability during the summer appears to have been linked to high diurnal water pressure variation within subglacial channels inferred from the strong increase in flow velocity with discharge. Basal sediment availability therefore appears likely to have been increased by (1) enhanced local ice‐bed separation leading to extra‐channel flow excursions and[sol ]or (2) the deformation of basal sediment towards low‐pressure channels due to a strong diurnally reversing hydraulic gradient between channels and areas of hydraulically less‐efficient drainage. Copyright © 2005 John Wiley & Sons, Ltd.     

Exploring the sensitivity of coastal inundation modelling to DEM vertical error

As sea level is projected to rise throughout the twenty-first century due to climate change, there is a need to ensure that sea level rise (SLR) models accurately and defensibly represent future flood inundation levels to allow for effective coastal zone management. Digital elevation models (DEMs) are integral to SLR modelling, but are subject to error, including in their vertical resolution. Error in DEMs leads to uncertainty in the output of SLR inundation models, which if not considered, may result in poor coastal management decisions. However, DEM error is not usually described in detail by DEM suppliers; commonly only the RMSE is reported. This research explores the impact of stated vertical error in delineating zones of inundation in two locations along the Devon, United Kingdom, coastline (Exe and Otter Estuaries). We explore the consequences of needing to make assumptions about the distribution of error in the absence of detailed error data using a 1 m, publically available composite DEM with a maximum RMSE of 0.15 m, typical of recent LiDAR-derived DEMs. We compare uncertainty using two methods (i) the NOAA inundation uncertainty mapping method which assumes a normal distribution of error and (ii) a hydrologically correct bathtub method where the DEM is uniformly perturbed between the upper and lower bounds of a 95% linear error in 500 Monte Carlo Simulations (HBM+MCS). The NOAA method produced a broader zone of uncertainty (an increase of 134.9% on the HBM+MCS method), which is particularly evident in the flatter topography of the upper estuaries. The HBM+MCS method generates a narrower band of uncertainty for these flatter areas, but very similar extents where shorelines are steeper. The differences in inundation extents produced by the methods relate to a number of underpinning assumptions, and particularly, how the stated RMSE is interpreted and used to represent error in a practical sense. Unlike the NOAA method, the HBM+MCS model is computationally intensive, depending on the areas under consideration and the number of iterations. We therefore used the HBM+ MCS method to derive a regression relationship between elevation and inundation probability for the Exe Estuary. We then apply this to the adjacent Otter Estuary and show that it can defensibly reproduce zones of inundation uncertainty, avoiding the computationally intensive step of the HBM+MCS. The equation-derived zone of uncertainty was 112.1% larger than the HBM+MCS method, compared to the NOAA method which produced an uncertain area 423.9% larger. Each approach has advantages and disadvantages and requires value judgements to be made. Their use underscores the need for transparency in assumptions and communications of outputs. We urge DEM publishers to move beyond provision of a generalised RMSE and provide more detailed estimates of spatial error and complete metadata, including locations of ground control points and associated land cover.