Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov Chain Monte Carlo sampling

In the last few decades hydrologists have made tremendous progress in using dynamic simulation models for the analysis and understanding of hydrologic systems. However, predictions with these models are often deterministic and as such they focus on the most probable forecast, without an explicit estimate of the associated uncertainty. This uncertainty arises from incomplete process representation, uncertainty in initial conditions, input, output and parameter error. The generalized likelihood uncertainty estimation (GLUE) framework was one of the first attempts to represent prediction uncertainty within the context of Monte Carlo (MC) analysis coupled with Bayesian estimation and propagation of uncertainty. Because of its flexibility, ease of implementation and its suitability for parallel implementation on distributed computer systems, the GLUE method has been used in a wide variety of applications. However, the MC based sampling strategy of the prior parameter space typically utilized in GLUE is not particularly efficient in finding behavioral simulations. This becomes especially problematic for high-dimensional parameter estimation problems, and in the case of complex simulation models that require significant computational time to run and produce the desired output. In this paper we improve the computational efficiency of GLUE by sampling the prior parameter space using an adaptive Markov Chain Monte Carlo scheme (the Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm). Moreover, we propose an alternative strategy to determine the value of the cutoff threshold based on the appropriate coverage of the resulting uncertainty bounds. We demonstrate the superiority of this revised GLUE method with three different conceptual watershed models of increasing complexity, using both synthetic and real-world streamflow data from two catchments with different hydrologic regimes.     

Modelling distribution of marine benthos from hydroacoustics and underwater video

Broad-scale mapping of marine benthos is required for marine resource management and conservation. This study combines textural derivatives based on bathymetry from multibeam hydroacoustics with underwater video observations to model and map sessile biota between 10- and 60-m water depth over 35 km² in Point Addis Marine National Park (MNP), Vic., Australia. Classification tree models and maps were developed for macroalgae (all types, mixed red algae, Ecklonia, and rhodoliths) and sessile invertebrates (all types, sponges, and ascidians). Model accuracy was tested on 25% of the video observation dataset reserved from modelling. Models fit well for most macroalgae categories (correct classification rates of 67–84%), but are not as good for sessile invertebrate classes (correct classification rates of 57–62%). The poor fit of the sessile invertebrate models may be the combined result of grouping organisms with different environmental requirements and the effect of false absences recorded during video interpretation due to poor image quality. Probability maps, binary single-class maps, and multi-class maps supply spatially explicit, detailed information on the distribution of sessile benthic biota within the MNP and provide information at a landscape-scale for ecological investigations and marine management.     

Response to comment by Keith Beven on “Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in hydrologic modeling?”

In recent years, a strong debate has emerged in the hydrologic literature regarding what constitutes an appropriate framework for uncertainty estimation. Particularly, there is strong disagreement whether an uncertainty framework should have its roots within a proper statistical (Bayesian) context, or whether such a framework should be based on a different philosophy and implement informal measures and weaker inference to summarize parameter and predictive distributions. In this paper, we compare a formal Bayesian approach using Markov Chain Monte Carlo (MCMC) with generalized likelihood uncertainty estimation (GLUE) for assessing uncertainty in conceptual watershed modeling. Our formal Bayesian approach is implemented using the recently developed differential evolution adaptive metropolis (DREAM) MCMC scheme with a likelihood function that explicitly considers model structural, input and parameter uncertainty. Our results demonstrate that DREAM and GLUE can generate very similar estimates of total streamflow uncertainty. This suggests that formal and informal Bayesian approaches have more common ground than the hydrologic literature and ongoing debate might suggest. The main advantage of formal approaches is, however, that they attempt to disentangle the effect of forcing, parameter and model structural error on total predictive uncertainty. This is key to improving hydrologic theory and to better understand and predict the flow of water through catchments.     

Melting of enriched mantle beneath Pitcairn seamounts: Unusual U–Th–Ra systematics provide insights into melt extraction processes

U-series systematics as well as Sr isotopes were measured on young seamount lavas from the Pitcairn hotspot collected during the Polynaut cruise. The combined U-series and Sr isotope data reveal typical mixing relationships between two endmembers. One typical ‘plume’ endmember with radiogenic ⁸⁷Sr/⁸⁶Sr and relatively low ²³⁰Th/²³⁸U and a ‘lithosphere’ endmember with less radiogenic ⁸⁷Sr/⁸⁶Sr and relatively larger ²³⁰Th/²³⁸U. Remarkably, all the lavas, except for a few arguably older samples, are characterized by ²²⁶Ra deficits relative to ²³⁰Th. On the basis of water content and trace element systematics, we argue that this is due to melting in the presence of phlogopite, which is only stable at lithosphere temperatures. A melting model including the diffusive exchange of elements among phlogopite, garnet and melt is used to constrain melting conditions of the lithosphere. These unusual ²²⁶Ra–²³⁰Th signatures can be explained by relatively slow melting rates at low matrix porosity. Our model also demonstrates that the effective partitioning behavior is dependent on the melting rate. A simple thermal model for lithosphere heating and melting is in good agreement with predicted melting rates.     

Wave train model for knickpoint migration

Rivers respond to a drop in their base level by incising the topography. The upstream propagation of an incision, as usually depicted by a knickpoint migration, is thought to depend on several parameters such as the drainage area, lithology, and the amplitude of the base level drop. We first investigate the case of the Messinian Salinity Crisis that was characterized by the extreme base level fall (1500 m) of the Mediterranean Sea at the end of the Miocene. The response of drainage areas of three orders of magnitude (10³ to 10⁶ km²) highlights the dominant role of the drainage area (with a square root relationship) in controlling the knickpoint migration after a base level fall. A compilation of mean rates of knickpoint propagation for time durations ranging from 10² to 10⁷ years displays a similar relationship indicating that successive wave trains of knickpoint can migrate in a river: first, wave trains linked to the release of the alluvial cover and then, wave trains related to the bedrock incision, which correspond to the real time response of rivers. Wave trains with very low retreat rates (long lived knickpoints > 1 My) rather correspond to the response time of regional landscape.     

Identifying causes of ground-penetrating radar reflections using time-domain reflectometry and sedimentological analyses

Ground-penetrating radar (GPR) is a geophysical technique widely used to study the shallow subsurface and identify various sediment features that reflect electromagnetic waves. However, little is known about the exact cause of GPR reflections because few studies have coupled wave theory to petrophysical data. In this study, a 100- and 200-MHz GPR survey was conducted on aeolian deposits in a quarry. Time-domain reflectometry (TDR) was used to obtain detailed information on the product of relative permittivity (ɛ_r) and relative magnetic permeability (μ_r), which mainly controls the GPR contrast parameter in the subsurface. Combining TDR data and lacquer peels from the quarry wall allowed the identification of various relationships between sediment characteristics and ɛ_rμ_r. Synthetic radar traces, constructed using the TDR logs and sedimentological data from the lacquer peels, were compared with the actual GPR sections. Numerous peaks in ɛ_rμ_r, which are superimposed on a baseline value of 4 for dry sand, are caused by potential GPR reflectors. These increases in ɛ_rμ_r coincide with the presence of either organic material, having a higher water content and relative permittivity than the surrounding sediment, or iron oxide bands, enhancing relative magnetic permeability and causing water to stagnate on top of them. Sedimentary structures, as reflected in textural change, only result in possible GPR reflections when the volumetric water content exceeds 0·055. The synthetic radar traces provide an improved insight into the behaviour of radar waves and show that GPR results may be ambiguous because of multiples and interference.