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Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower bound on the desired integral to be approximated, e.g. marginal likelihood. The lower bound is then optimised with respect to its free parameters, the so-called variational parameters. However, this is not always possible as for certain integrals it is very challenging (or tedious) to come up with a suitable lower bound. Here, we propose a simple scheme that overcomes some of the awkward cases where the usual variational treatment becomes difficult. The scheme relies on a rewriting of the lower bound on the model log-likelihood. We demonstrate the proposed scheme on a number of synthetic and real examples, as well as on a real geophysical model for which the standard variational approaches are inapplicable.
Large, compressional earthquakes cause surface uplift aswell as widespread mass wasting. Knowledge of their trade-off is fragmentary. Combining a seismologically consistent model of earthquake-triggered landsliding and an analytical solution of coseismic surface displacement, we assess how the mass balance of single earthquakes and earthquake sequences depends on fault size and other geophysical parameters. We find that intermediate size earthquakes (M-w 6-7.3) may cause more erosion than uplift, controlled primarily by seismic source depth and landscape steepness, and less so by fault dip and rake. Such earthquakes can limit topographic growth, but our model indicates that both smaller and larger earthquakes (M-w < 6, M-w > 7.3) systematically cause mountain building. Earthquake sequences with a Gutenberg-Richter distribution have a greater tendency to lead to predominant erosion, than repeating earthquakes of the same magnitude, unless a fault can produce earthquakes with M-w > 8 or more.
Zircon (ZrSiO4), hafnon (HfSiO4) and five intermediate compositions were synthesized from a Pb silicate melt. The resulting crystals were 20-300 mu m in size and displayed sector and growth zoning. Raman spectra were acquired at locations in the sample for which preceding electron microprobe (EMP) analyses revealed sufficient compositional homogeneity. The dataset documents shifts of Raman bands with changing composition. In this study, bands that have previously not been reported were found for the intermediate compositions and for pure hafnon, in particular at wavenumbers less than 200 cm(-1). For these external modes, the dataset provides new insight into the compositional dependence of their frequencies. Density-functional theory calculations support the observations and are used for a detailed interpretation of the spectra. The pitfalls of the EMP analysis along the zircon-hafnon join are highlighted.
Solute concentration variability is of fundamental importance for the chemical and ecological state of streams. It is often closely related to discharge variability and can be characterized in terms of a solute export regime. Previous studies, especially in lowland catchments, report that nitrate is often exported with an accretion pattern of increasing concentrations with increasing discharge. Several modeling approaches exist to predict the export regime of solutes from the spatial relationship of discharge generating zones with solute availability in the catchment. For a small agriculturally managed lowland catchment in central Germany, we show that this relationship is controlled by the depth to groundwater table and its temporal dynamics. Principal component analysis of groundwater level time series from wells distributed throughout the catchment allowed derivation of a representative groundwater level time series that explained most of the discharge variability. Groundwater sampling revealed consistently decreasing nitrate concentrations with an increasing thickness of the unsaturated zone. The relationships of depth to groundwater table to discharge and to nitrate concentration were parameterized and integrated to successfully model catchment discharge and nitrate export on the basis of groundwater level variations alone. This study shows that intensive and uniform agricultural land use likely results in a clear and consistent concentration-depth relationship of nitrate, which can be utilized in simple approaches to predict stream nitrate export dynamics at the catchment scale. (C) 2016 Elsevier Ltd. All rights reserved.
We present a new, seismologically consistent expression for the total area and volume of populations of earthquake-triggered landslides. This model builds on a set of scaling relationships between key parameters, such as landslide spatial density, seismic ground acceleration, fault length, earthquake source depth, and seismic moment. To assess the model we have assembled and normalized a catalog of landslide inventories for 40 shallow, continental earthquakes. Low landscape steepness causes systematic overprediction of the total area and volume of landslides. When this effect is accounted for, the model predicts the total landslide volume of 63% of 40 cases to within a factor 2 of the volume estimated from observations (R-2 = 0.76). The prediction of total landslide area is also sensitive to the landscape steepness, but less so than the total volume, and it appears to be sensitive to controls on the landslide size-frequency distribution, and possibly the shaking duration. Some outliers are likely associated with exceptionally strong rock mass in the epicentral area, while others may be related to seismic source complexities ignored by the model. However, the close match between prediction and estimate for about two thirds of cases in our database suggests that rock mass strength is similar in many cases and that our simple seismic model is often adequate, despite the variety of lithologies and tectonic settings covered. This makes our expression suitable for integration into landscape evolution models and application to the anticipation or rapid assessment of secondary hazards associated with earthquakes.
Bedrock landslides, by excavating deep below saprolite-rock interfaces, create conditions for weathering in which all mineral phases in a lithology are initially unweathered within landslide deposits. As a result, the most labile phases dominate the weathering immediately after mobilisation and during a transient period of depletion. This mode of dissolution can strongly alter the overall output of solutes from catchments and their contribution to global chemical cycles if landslide-derived material is retained in catchments for extended periods after mass wasting.
The South American Andes are frequently exposed to intense rainfall events with varying moisture sources and precipitation-forming processes. In this study, we assess the spatiotemporal characteristics and geographical origins of rainfall over the South American continent. Using high-spatiotemporal resolution satellite data (TRMM 3B42 V7), we define four different types of rainfall events based on their (1) high magnitude, (2) long temporal extent, (3) large spatial extent, and (4) high magnitude, long temporal and large spatial extent combined. In a first step, we analyze the spatiotemporal characteristics of these events over the entire South American continent and integrate their impact for the main Andean hydrologic catchments. Our results indicate that events of type 1 make the overall highest contributions to total seasonal rainfall (up to 50%). However, each consecutive episode of the infrequent events of type 4 still accounts for up to 20% of total seasonal rainfall in the subtropical Argentinean plains. In a second step, we employ complex network theory to unravel possibly non-linear and long-ranged climatic linkages for these four event types on the high-elevation Altiplano-Puna Plateau as well as in the main river catchments along the foothills of the Andes. Our results suggest that one to two particularly large squall lines per season, originating from northern Brazil, indirectly trigger large, long-lasting thunderstorms on the Altiplano Plateau. In general, we observe that extreme rainfall in the catchments north of approximately 20 degrees S typically originates from the Amazon Basin, while extreme rainfall at the eastern Andean foothills south of 20 degrees S and the Puna Plateau originates from southeastern South America.
Non-linear time series analysis of precipitation events using regional climate networks for Germany
(2016)
Synchronous occurrences of heavy rainfall events and the study of their relation in time and space are of large socio-economical relevance, for instance for the agricultural and insurance sectors, but also for the general well-being of the population. In this study, the spatial synchronization structure is analyzed as a regional climate network constructed from precipitation event series. The similarity between event series is determined by the number of synchronous occurrences. We propose a novel standardization of this number that results in synchronization scores which are not biased by the number of events in the respective time series. Additionally, we introduce a new version of the network measure directionality that measures the spatial directionality of weighted links by also taking account of the effects of the spatial embedding of the network. This measure provides an estimate of heavy precipitation isochrones by pointing out directions along which rainfall events synchronize. We propose a climatological interpretation of this measure in terms of propagating fronts or event traces and confirm it for Germany by comparing our results to known atmospheric circulation patterns.
The analytical evaluation of diurnal temperature variation in riverbed sediments provides detailed information on exchange fluxes between rivers and groundwater. The underlying assumption of the stationary, one-dimensional vertical flow field is frequently violated in natural systems where subsurface water flow often has a significant horizontal component. In this paper, we present a new methodology for identifying the geometry of the subsurface flow field using vertical temperature profiles. The statistical analyses are based on model optimisation and selection and are used to evaluate the shape of vertical amplitude ratio profiles. The method was applied to multiple profiles measured around in-stream geomorphological structures in a losing reach of a gravel bed river. The predominant subsurface flow field was systematically categorised in purely vertical and horizontal (hyporheic, parafluvial) components. The results highlight that river groundwater exchange flux at the head, crest and tail of geomorphological structures significantly deviated from the one-dimensional vertical flow, due to a significant horizontal component. The geometry of the subsurface water flow depended on the position around the geomorphological structures and on the river level. The methodology presented in this paper features great potential for characterising the spatial patterns and temporal dynamics of complex subsurface flow geometries by using measured temperature time series in vertical profiles. (C) 2016 Elsevier B.V. All rights reserved.
The northern Tien Shan of Kyrgyzstan and Kazakhstan has been affected by a series of major earthquakes in the late 19th and early 20th centuries. To assess the significance of such a pulse of strain release in a continental interior, it is important to analyze and quantify strain release over multiple time scales. We have undertaken paleoseismological investigations at two geomorphically distinct sites (Panfilovkoe and Rot Front) near the Kyrgyz capital Bishkek. Although located near the historic epicenters, both sites were not affected by these earthquakes. Trenching was accompanied by dating stratigraphy and offset surfaces using luminescence, radiocarbon, and Be-10 terrestrial cosmogenic nuclide methods. At Rot Front, trenching of a small scarp did not reveal evidence for surface rupture during the last 5000 years. The scarp rather resembles an extensive debris-flow lobe. At Panfilovkoe, we estimate a Late Pleistocene minimum slip rate of 0.2 +/- 0.1 mm/a, averaged over at least two, probably three earthquake cycles. Dip-slip reverse motion along segmented, moderately steep faults resulted in hanging wall collapse scarps during different events. The most recent earthquake occurred around 3.6 +/- 1.3 kyr ago (1 sigma), with dip-slip offsets between 1.2 and 1.4 m. We calculate a probabilistic paleomagnitude to be between 6.7 and 7.2, which is in agreement with regional data from the Kyrgyz range. The morphotectonic signals in the northern Tien Shan are a prime example of deformation in a tectonically active intracontinental mountain belt and as such can help understand the longer-term coevolution of topography and seismogenic processes in similar structural settings worldwide.
Climatic controls on debris-flow activity and sediment aggradation: The Del Medio fan, NW Argentina
(2016)
In the Central Andes, several studies on alluvial terraces and valley fills have linked sediment aggradation to periods of enhanced sediment supply. However, debate continues over whether tectonic or climatic factors are most important in triggering the enhanced supply. The Del Medio catchment in the Humahuaca Basin (Eastern Cordillera, NW Argentina) is located within a transition zone between subhumid and arid climates and hosts the only active debris-flow fan within this intermontane valley. By combining Be-10 analyses of boulder and sediment samples within the Del Medio catchment, with regional morphometric measurements of nearby catchments, we identify the surface processes responsible for aggradation in the Del Medio fan and their likely triggers. We find that the fan surface has been shaped by debris flows and channel avulsions during the last 400 years. Among potential tectonic, climatic, and autogenic factors that might influence deposition, our analyses point to a combination of several favorable factors that drive aggradation. These are in particular the impact of occasional abundant rainfall on steep slopes in rock types prone to failure, located in a region characterized by relatively low rainfall amounts and limited transport capacity. These characteristics are primarily associated with the climatic transition zone between the humid foreland and the arid orogen interior, which creates an imbalance between sediment supply and sediment transfer. The conditions and processes that drive aggradation in the Del Medio catchment today may provide a modern analog for the conditions and processes that drove aggradation in other nearby tributaries in the past.
Fluvial fill terraces preserve sedimentary archives of landscape responses to climate change, typically over millennial timescales. In the Humahuaca Basin of NW Argentina (Eastern Cordillera, southern Central Andes), our 29 new optically stimulated luminescence ages of late Pleistocene fill terrace sediments demonstrate that the timing of past river aggradation occurred over different intervals on the western and eastern sides of the valley, despite their similar bedrock lithology, mean slopes, and precipitation. In the west, aggradation coincided with periods of increasing precipitation, while in the east, aggradation coincided with decreasing precipitation or more variable conditions. Erosion rates and grain size dependencies in our cosmogenic Be-10 analyses of modern and fill terrace sediments reveal an increased importance of landsliding compared to today on the west side during aggradation, but of similar importance during aggradation on the east side. Differences in the timing of aggradation and the Be-10 data likely result from differences in valley geometry, which causes sediment to be temporarily stored in perched basins on the east side. It appears as if periods of increasing precipitation triggered landslides throughout the region, which induced aggradation in the west, but blockage of the narrow bedrock gorges downstream from the perched basins in the east. As such, basin geometry and fluvial connectivity appear to strongly influence the timing of sediment movement through the system. For larger basins that integrate subbasins with differing geometries or degrees of connectivity (like Humahuaca), sedimentary responses to climate forcing are likely attenuated.
A link between chemical weathering and physical erosion exists at the catchment scale over a wide range of erosion rates(1,2). However, in mountain environments, where erosion rates are highest, weathering may be kinetically limited(3-5) and therefore decoupled from erosion. In active mountain belts, erosion is driven by bedrock landsliding(6) at rates that depend strongly on the occurrence of extreme rainfall or seismicity(7). Although landslides affect only a small proportion of the landscape, bedrock landsliding can promote the collection and slow percolation of surface runoff in highly fragmented rock debris and create favourable conditions for weathering. Here we show from analysis of surface water chemistry in the Southern Alps of New Zealand that weathering in bedrock landslides controls the variability in solute load of these mountain rivers. We find that systematic patterns in surface water chemistry are strongly associated with landslide occurrence at scales from a single hillslope to an entire mountain belt, and that landslides boost weathering rates and river solute loads over decades. We conclude that landslides couple erosion and weathering in fast-eroding uplands and, thus, mountain weathering is a stochastic process that is sensitive to climatic and tectonic controls on mass wasting processes.
Coastal fens like the nature reserve "Hutelmoor und Heiligensee" (north-eastern Germany) are important landscape elements along the southern Baltic coast, which exchange fresh water and brackish water with the Baltic Sea. These exchange processes can be understood as experiments with a natural tracer, which may be used to investigate the hydrologic behaviour of these fen systems. With the establishment of coastal protection measures such as dunes and dikes, the installation of surface drainage and, more recently, also nature conservation measures, the hydrologic regime of these coastal wetlands has constantly altered over the last centuries.The rehabilitated wetland "Hutelnnoor und Heiligensee" is suitable for an analysis of hydrologic change as it has been monitored over the time period since nature conservation measures started in the 1990s. Collected data sets included observation of groundwater levels and electrical conductivities, weather data as well as discharge at the outlet of the drainage catchment. In this article, as a second part of the dual publication, processes and quantified process magnitudes have been identified that govern the salt balance of the study area including its variability in space and time. It was detected that - over the period of rehabilitation - salt water entered the catchment with an episodic storm surge by wave overtopping of dunes in 1995. The intruded brackish water was then diluted, which was a slow process extending over decades. It was governed by local groundwater recharge from precipitation and the inflow of relatively fresh groundwater from the hinterland. It is concluded that salt inputs from the Baltic Sea provide a natural tracer of hydrological processes, which can be readily monitored via electrical conductivity measurements.
Landscapes can be viewed as spatially heterogeneous areas encompassing terrestrial and aquatic domains. To date, most landscape carbon (C) fluxes have been estimated by accounting for terrestrial ecosystems, while aquatic ecosystems have been largely neglected. However, a robust assessment of C fluxes on the landscape scale requires the estimation of fluxes within and between both landscape components. Here, we compiled data from the literature on C fluxes across the air–water interface from various landscape components. We simulated C emissions and uptake for five different scenarios which represent a gradient of increasing spatial heterogeneity within a temperate young moraine landscape: (I) a homogeneous landscape with only cropland and large lakes; (II) separation of the terrestrial domain into cropland and forest; (III) further separation into cropland, forest, and grassland; (IV) additional division of the aquatic area into large lakes and peatlands; and (V) further separation of the aquatic area into large lakes, peatlands, running waters, and small water bodies These simulations suggest that C fluxes at the landscape scale might depend on spatial heterogeneity and landscape diversity, among other factors. When we consider spatial heterogeneity and diversity alone, small inland waters appear to play a pivotal and previously underestimated role in landscape greenhouse gas emissions that may be regarded as C hot spots. Approaches focusing on the landscape scale will also enable improved projections of ecosystems’ responses to perturbations, e.g., due to global change and anthropogenic activities, and evaluations of the specific role individual landscape components play in regional C fluxes. WIREs Water 2016, 3:601–617. doi: 10.1002/wat2.1147
Hydrological and climatological controls on radiocarbon concentrations in a tropical stalagmite
(2016)
Precisely-dated stalagmites are increasingly important archives for the reconstruction of terrestrial paleoclimate at very high temporal resolution. In-depth understanding of local conditions at the cave site and of the processes driving stalagmite deposition is of paramount importance for interpreting proxy signals incorporated in stalagmite carbonate. Here we present a sub-decadally resolved dead carbon fraction (DCF) record for a stalagmite from Yok Balum Cave (southern Belize). The record is coupled to parallel stable carbon isotope (delta C-13) and U/Ca measurements, as well as radiocarbon (C-14) measurements from soils overlying the cave system. Using a karst carbon cycle model we disentangle the importance of soil and karst processes on stalagmite DCF incorporation, revealing a dominant host rock dissolution control on total DCF. Covariation between DCF, delta C-13, and U/Ca indicates that karst processes are a common driver of all three parameters, suggesting possible use of delta C-13 and trace element ratios to independently quantify DCF variability. A statistically significant multi-decadal lag of variable length exists between DCF and reconstructed solar activity, suggesting that solar activity influenced regional precipitation in Mesoamerica over the past 1500 years, but that the relationship was non-static. Although the precise nature of the observed lag is unclear, solar-induced changes in North Atlantic oceanic and atmospheric dynamics may play a role. (C) 2016 Elsevier Ltd. All rights reserved.
The 2014 April 1, M-w 8.1 Iquique (Chile) earthquake struck in the Northern Chile seismic gap. With a rupture length of less than 200 km, it left unbroken large segments of the former gap. Early studies were able to model the main rupture features but results are ambiguous with respect to the role of aseismic slip and left open questions on the remaining hazard at the Northern Chile gap. A striking observation of the 2014 earthquake has been its extensive preparation phase, with more than 1300 events with magnitude above M-L 3, occurring during the 15 months preceding the main shock. Increasing seismicity rates and observed peak magnitudes accompanied the last three weeks before the main shock. Thanks to the large data sets of regional recordings, we assess the precursor activity, compare foreshocks and aftershocks and model rupture preparation and rupture effects. To tackle inversion challenges for moderate events with an asymmetric network geometry, we use full waveforms techniques to locate events, map the seismicity rate and derive source parameters, obtaining moment tensors for more than 300 events (magnitudes M-w 4.0-8.1) in the period 2013 January 1-2014 April 30. This unique data set of fore- and aftershocks is investigated to distinguish rupture process models and models of strain and stress rotation during an earthquake. Results indicate that the spatial distributions of foreshocks delineated the shallower part of the rupture areas of the main shock and its largest aftershock, well matching the spatial extension of the aftershocks cloud. Most moment tensors correspond to almost pure double couple thrust mechanisms, consistent with the slab orientation. Whereas no significant differences are observed among thrust mechanisms in different areas, nor among thrust foreshocks and aftershocks, the early aftershock sequence is characterized by the presence of normal fault mechanisms, striking parallel to the trench but dipping westward. These events likely occurred in the shallow wedge structure close to the slab interface and are consequence of the increased extensional stress in this region after the largest events. The overall stress inversion result suggests a minor stress rotation after the main shock, but a significant release of the deviatoric stress. The temporal change in the distribution of focal mechanisms can also be explained in terms of the spatial heterogeneity of the stress field: under such interpretation, the potential of a large megathrust earthquake breaking a larger segment offshore Northern Chile remains high.
This manuscript proposes a method to assess hydrological drought in semi-arid environments under high impoundment rate and applies it to the semi-arid Jaguaribe River basin in Brazil. It analyzes droughts (1) in the largest reservoir systems; (2) in the Upper Basin, considering 4744 reservoirs, 800 wells and almost 18,000 cisterns; and (3) in reservoirs of different sizes during multiyear droughts. Results show that the water demand is constrained in the basin; hydrological and meteorological droughts are often out of phase; there is a negative correlation between storage level and drought severity; and the small systems cannot cope with long-term droughts.
Ongoing climate change is known to cause an increase in the frequency and amplitude of local temperature and precipitation extremes in many regions of the Earth. While gradual changes in the climatological conditions have already been shown to strongly influence plant flowering dates, the question arises if and how extremes specifically impact the timing of this important phenological phase. Studying this question calls for the application of statistical methods that are tailored to the specific properties of event time series. Here, we employ event coincidence analysis, a novel statistical tool that allows assessing whether or not two types of events exhibit similar sequences of occurrences in order to systematically quantify simultaneities between meteorological extremes and the timing of the flowering of four shrub species across Germany. Our study confirms previous findings of experimental studies by highlighting the impact of early spring temperatures on the flowering of the investigated plants. However, previous studies solely based on correlation analysis do not allow deriving explicit estimates of the strength of such interdependencies without further assumptions, a gap that is closed by our analysis. In addition to direct impacts of extremely warm and cold spring temperatures, our analysis reveals statistically significant indications of an influence of temperature extremes in the autumn preceding the flowering.
This case study evaluates the suitability of radar-based quantitative precipitation estimates (QPEs) for the simulation of streamflow in the Marikina River Basin (MRB), the Philippines. Hourly radar-based QPEs were produced from reflectivity that had been observed by an S-band radar located about 90 km from the MRB. Radar data processing and precipitation estimation were carried out using the open source library wradlib. To assess the added value of the radar-based QPE, we used spatially interpolated rain gauge observations (gauge-only (GO) product) as a benchmark. Rain gauge observations were also used to quantify rainfall estimation errors at the point scale. At the point scale, the radar-based QPE outperformed the GO product in 2012, while for 2013, the performance was similar. For both periods, estimation errors substantially increased from daily to the hourly accumulation intervals. Despite this fact, both rainfall estimation methods allowed for a good representation of observed streamflow when used to force a hydrological simulation model of the MRB. Furthermore, the results of the hydrological simulation were consistent with rainfall verification at the point scale: the radar-based QPE performed better than the GO product in 2012, and equivalently in 2013. Altogether, we could demonstrate that, in terms of streamflow simulation, the radar-based QPE can perform as good as or even better than the GO product - even for a basin such as the MRB which has a comparatively dense rain gauge network. This suggests good prospects for using radar-based QPE to simulate and forecast streamflow in other parts of the Philippines where rain gauge networks are not as dense.