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.     

Single explosions at Stromboli in 2002: Use of clast microtextures to map physical diversity across a fragmentation zone

A combination of fortuitous eruptive and wind conditions at Stromboli volcano in September 2002 enabled the collection of samples of multiple lapilli from individual observed explosions. These ejecta present the first opportunity to analyze the vesicularity of material ejected in a single Strombolian explosion. Samples of between 40 and 92 lapilli were collected from each of six sequential explosions on 30 September 2002, and 28 lapilli were obtained from a single explosion  24 h later (1 October). Density measurements and microtextural observations show that considerable heterogeneity existed within each of the seven samples. Centimeter to millimeter size bubble-rich and bubble-poor zones are present and are, in places, mingled together. These data confirm that the shallow conduit at Stromboli is a texturally diverse environment at the instant of a single explosion, and that a similar range of heterogeneity can persist through closely-spaced sequences of explosions on a timescale of hours and, probably, days, despite the dynamic processes of ascent of melt and decoupled gas phases.     

The thermospheric semiannual density response to solar EUV heating

The goal of this study was to characterize the thermospheric semiannual density response to solar heating during the last 35 years. Historical radar observational data have been processed with special orbit perturbations on 28 satellites with perigee heights ranging from 200 to 1100 km. Approximately 225,000 very accurate average daily density values at perigee have been obtained for all satellites using orbit energy dissipation rates. The semiannual variation has been found to be extremely variable from year to year. The magnitude of the maximum yearly difference, from the July minimum to the October maximum, is used to characterize the yearly semiannual variability. It has been found that this maximum difference can vary by as much as 100% from one year to the next. A high correlation has been found between this maximum difference and solar EUV data. The semiannual variation for each year has been characterized based on analyses of annual and semiannual cycles, using Fourier analysis, and equations have been developed to characterize this yearly variability. The use of new solar indices in the EUV and FUV wavelengths is shown to very accurately describe the semiannual July minimum phase shifting and the variations in the observed yearly semiannual amplitude.     

A 2000 year varve-based climate record from the central Brooks Range,Alaska

Varved minerogenic sediments from glacial-fed Blue Lake, northern Alaska, are used to investigate late Holocene climate variability. Varve-thickness measurements track summer temperature recorded at Atigun Pass, located 41 km east at a similar elevation (r ² = 0.31, P = 0.08). Results indicate that climate in the Brooks Range from 10 to 730 AD (varve year) was warm with precipitation inferred to be higher than during the twentieth century. The varve-temperature relationship for this period was likely compromised and not used in our temperature reconstruction because the glacier was greatly reduced, or absent, exposing sub-glacial sediments to erosion from enhanced precipitation. Varve-inferred summer temperatures and precipitation decreased after 730 AD, averaging 0.4°C above the last millennial average (LMA = 4.2°C) from 730 to 850 AD, and 0.1°C above the LMA from 850 to 980 AD. Cooling culminated between 980 and 1030 AD with temperatures 0.7°C below the LMA. Varve-inferred summer temperatures increased between 1030 and 1620 AD to the LMA, though the period between 1260 and 1350 AD was 0.2°C below the LMA. Although there is no equivalent to the European Medieval Warm Period in the Blue Lake record, two warm intervals occurred from 1350 to 1450 AD and 1500 to 1620 AD (0.4 and 0.3°C above the LMA, respectively). During the Little Ice Age (LIA; 1620 to 1880 AD), inferred summer temperature averaged 0.2°C below the LMA. After 1880 AD, inferred summer temperature increased to 0.8°C above the LMA, glaciers retreated, but aridity persisted based on a number of regional paleoclimate records. Despite warming and glacial retreat, varve thicknesses have not achieved pre-730 AD levels. This reflects limited sediment availability and transport due to a less extensive retreat compared to the first millennium, and continued relative aridity. Overall, the Blue Lake record is similar to varve records from the eastern Canadian Arctic that document a cool LIA and twentieth century warming. However, the occurrence and timing of events, such as the LIA and Medieval Warm Period, varies considerably among records, suggesting heterogeneous climatic patterns across the North American Arctic.

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.     

地球内核粘滞度的动力学估计

最新的地震学研究指出,地球的内核正在对地球的其余部分作相对旋转。根据数值模拟,这一情形可能是由在液态外核中正在作对流运动的流体所保持。另一方面,由于地幔中质量分布的不均匀,巨大的引力将足以便内核与地幔相匹配。内核的不同旋转会通过在旋转时对自身形状的调整民这些强大的引力保持一致,进面可得出在地球最内部区域内有效粘滞度的一个估计。由推测的旋转率得到的内核粘滞度为小于１０＾１６Ｐａ或大于１０＾２０Ｐａ。     

Holocene lake sediment records of Arctic hydrology

Although paleoclimatic research in the Arctic has most often focused on variations in temperature, the Arctic has also experienced changes in hydrologic balance. Changes in Arctic precipitation and evaporation rates affects soils, permafrost, lakes, wetlands, rivers, ice and vegetation. Changes in Arctic soils, permafrost, runoff, and vegetation can influence global climate by changing atmospheric methane and carbon dioxide concentrations, thermohaline circulation, and high latitude albedo. Documenting past variations in Arctic hydrological conditions is important for understanding Arctic climate and the potential response and role of the Arctic in regards to future climate change. Methods for reconstructing past changes in Arctic hydrology from the stratigraphic, isotopic, geochemical and fossil records of lake sediments are being developed, refined and applied in a number of regions. These records suggest that hydrological variations in the Arctic have been regionally asynchronous, reflecting the impacts of different forcing factors including orbitally controlled insolation changes, changes in geography related to coastal emergence, ocean currents, sea ice extent, and atmospheric circulation. Despite considerable progress, much work remains to be done on the development of paleohydrological proxies and their application to the Arctic.     

Late quaternary paleoclimatic reconstructions for interior Alaska based on paleolake-level data and hydrologic models

Hydrologic models are developed for two lakes in interior Alaska to determine quantitative estimates of precipitation over the past 12,500 yrs. Lake levels were reconstructed from core transects for these basins, which probably formed prior to the late Wisconsin. Lake sediment cores indicate that these lakes were shallow prior to 12,500 yr B.P. and increased in level with some fluctuation until they reached their modern levels 4,000-8,000 yr B.P. Evaporation (E), evapotranspiration (ET), and precipitation (P) were adjusted in a water-balance model to determine solutions that would maintain the lakes at reconstructed levels at key times in the past (12,500, 9,000 and 6,000 yr B.P.). Similar paleoclimatic solutions can be obtained for both basins for these times. Results indicate that P was 35-75% less than modern at 12,500 yr B.P., 25-45% less than modern at 9,000 yr B.P. and 10-20% less than modern at 6,000 yr B.P. Estimates for E and ET in the past were based on modern studies of vegetation types indicated by fossil pollen assemblages. Although interior Alaska is predominantly forested at the present, pollen analyses indicate tundra vegetation prior to about 12,000 yr B.P. The lakes show differing sensitivities to changing hydrologic parameters; sensitivity depends on the ratio of lake area (AL) to drainage basin (DA) size. This ratio also changed over time as lake level and lake area increased. Smaller AL to DA ratios make a lake more sensitive to ET, if all other factors are constant.     

Fluid-mobile trace element constraints on the role of slab melting and implications for Archaean crustal growth models

We use published and new trace element data to identify element ratios which discriminate between arc magmas from the supra-subduction zone mantle wedge and those formed by direct melting of subducted crust (i.e. adakites). The clearest distinction is obtained with those element ratios which are strongly fractionated during refertilisation of the depleted mantle wedge, ultimately reflecting slab dehydration. Hence, adakites have significantly lower Pb/Nd and B/Be but higher Nb/Ta than typical arc magmas and continental crust as a whole. Although Li and Be are also overenriched in continental crust, behaviour of Li/Yb and Be/Nd is more complex and these ratios do not provide unique signatures of slab melting. Archaean tonalite-trondhjemite-granodiorites (TTGs) strongly resemble ordinary mantle wedge-derived arc magmas in terms of fluid-mobile trace element content, implying that they did not form by slab melting but that they originated from mantle which was hydrated and enriched in elements lost from slabs during prograde dehydration. We suggest that Archaean TTGs formed by extensive fractional crystallisation from a mafic precursor. It is widely claimed that the time between the creation and subduction of oceanic lithosphere was significantly shorter in the Archaean (i.e. 20 Ma) than it is today. This difference was seen as an attractive explanation for the presumed preponderance of adakitic magmas during the first half of Earth's history. However, when we consider the effects of a higher potential mantle temperature on the thickness of oceanic crust, it follows that the mean age of oceanic lithosphere has remained virtually constant. Formation of adakites has therefore always depended on local plate geometry and not on potential mantle temperature.