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.     

How do hydrologic modeling decisions affect the portrayal of climate change impacts?

End users face a range of subjective decisions when evaluating climate change impacts on hydrology, but the importance of these decisions is rarely assessed. In this paper, we evaluate the implications of hydrologic modelling choices on projected changes in the annual water balance, monthly simulated processes, and signature measures (i.e. metrics that quantify characteristics of the hydrologic catchment response) under a future climate scenario. To this end, we compare hydrologic changes computed with four different model structures – whose parameters have been obtained using a common calibration strategy – with hydrologic changes computed with a single model structure and parameter sets from multiple options for different calibration decisions (objective function, local optima, and calibration forcing dataset). Results show that both model structure selection and the parameter estimation strategy affect the direction and magnitude of projected changes in the annual water balance, and that the relative effects of these decisions are basin dependent. The analysis of monthly changes illustrates that parameter estimation strategies can provide similar or larger uncertainties in simulations of some hydrologic processes when compared with uncertainties coming from model choice. We found that the relative effects of modelling decisions on projected changes in catchment behaviour depend on the signature measure analysed. Furthermore, parameter sets with similar performance, but located in different regions of the parameter space, provide very different projections for future catchment behaviour. More generally, the results obtained in this study prompt the need to incorporate parametric uncertainty in multi‐model frameworks to avoid an over‐confident portrayal of climate change impacts. Copyright © 2015 John Wiley & Sons, Ltd.     

Hydrologic drought prediction under climate change: Uncertainty modeling with Dempster–Shafer and Bayesian approaches

Representation and quantification of uncertainty in climate change impact studies are a difficult task. Several sources of uncertainty arise in studies of hydrologic impacts of climate change, such as those due to choice of general circulation models (GCMs), scenarios and downscaling methods. Recently, much work has focused on uncertainty quantification and modeling in regional climate change impacts. In this paper, an uncertainty modeling framework is evaluated, which uses a generalized uncertainty measure to combine GCM, scenario and downscaling uncertainties. The Dempster–Shafer (D–S) evidence theory is used for representing and combining uncertainty from various sources. A significant advantage of the D–S framework over the traditional probabilistic approach is that it allows for the allocation of a probability mass to sets or intervals, and can hence handle both aleatory or stochastic uncertainty, and epistemic or subjective uncertainty. This paper shows how the D–S theory can be used to represent beliefs in some hypotheses such as hydrologic drought or wet conditions, describe uncertainty and ignorance in the system, and give a quantitative measurement of belief and plausibility in results. The D–S approach has been used in this work for information synthesis using various evidence combination rules having different conflict modeling approaches. A case study is presented for hydrologic drought prediction using downscaled streamflow in the Mahanadi River at Hirakud in Orissa, India. Projections of n most likely monsoon streamflow sequences are obtained from a conditional random field (CRF) downscaling model, using an ensemble of three GCMs for three scenarios, which are converted to monsoon standardized streamflow index (SSFI-4) series. This range is used to specify the basic probability assignment (bpa) for a Dempster–Shafer structure, which represents uncertainty associated with each of the SSFI-4 classifications. These uncertainties are then combined across GCMs and scenarios using various evidence combination rules given by the D–S theory. A Bayesian approach is also presented for this case study, which models the uncertainty in projected frequencies of SSFI-4 classifications by deriving a posterior distribution for the frequency of each classification, using an ensemble of GCMs and scenarios. Results from the D–S and Bayesian approaches are compared, and relative merits of each approach are discussed. Both approaches show an increasing probability of extreme, severe and moderate droughts and decreasing probability of normal and wet conditions in Orissa as a result of climate change.     

Distribution of ~(226)Ra in the Arctic Ocean and the Bering Sea and its hydrologic implications

The Arctic Ocean, the northernmost parts of the earth, covers the total surface area of 14.79 million square kilometers and amounts to only about 4% of global ocean surface area. Although its surface area is the smallest in the four major oceans, the Arct…     

How does DEM resolution affect microtopographic characteristics,hydrologic connectivity,and modelling of hydrologic processes?

The resolution of a digital elevation model (DEM) is a crucial factor in watershed hydrologic and environmental modelling. DEM resolution can cause significant variability in the representation of surface topography, which further affects quantification of hydrologic connectivity and simulation of hydrologic processes. The objective of this study is to examine the effects of DEM resolution on (1) surface microtopographic characteristics, (2) hydrologic connectivity, and (3) the spatial and temporal variations of hydrologic processes. A puddle‐to‐puddle modelling system was utilized for surface delineation and modelling of the puddle‐to‐puddle overland flow dynamics, surface runoff, infiltration, and unsaturated flow for nine DEM resolution scenarios of a field plot surface. Comparisons of the nine modelling scenarios demonstrated that coarser DEM resolutions tended to eliminate topographic features, reduce surface depression storage, and strengthen hydrologic connectivity and surface runoff. We found that reduction in maximum depression storage and maximum ponding area was as high as 97.56% and 76.36%, respectively, as the DEM grid size increased from 2 to 80 cm. The paired t‐test and fractal analysis demonstrated the existence of a threshold DEM resolution (10 cm for the field plot), within which the DEM‐based hydrologic modelling was effective and acceptable. The effects of DEM resolution were further evaluated for a larger surface in the Prairie Pothole Region subjected to observed rainfall events. It was found that simulations based on coarser resolution DEMs (>10 m) tended to overestimate ponded areas and underestimate runoff discharge peaks. The simulated peak discharge from the Prairie Pothole Region surface reduced by approximately 50% as the DEM resolution changed from 2 to 90 m. Fractal analysis results elucidated scale dependency of hydrologic and topographic processes. In particular, scale analysis highlighted a unique constant–threshold–power relationship between DEM scale and topographic and hydrologic parameters/variables. Not only does this finding allow one to identify threshold DEM but also further develop functional relationships for scaling to achieve valid topographic characterization as well as effective and efficient hydrologic modelling. Copyright © 2016 John Wiley & Sons, Ltd.     

Geochemical tracing and modeling of surface and deep water–rock interactions in elementary granitic watersheds(Strengbach and Ringelbach CZOs,France)

From the study of the Strengbach and Ringelbach watersheds we propose to illustrate the interest of combining the geochemical tracing and geochemical modeling approaches on surface and deep borehole waters,to decipher the diversity of the water flow and the associated water–rock interactions in such elementary mountainous catchments. The results point to a clear geochemical typology of waters depending on the water circulations(deep vs. hypodermic) within the substratum.     

Variations in solar radiation in the solar activity cycle: Response of Earth’s atmospheric parameters (numerical modeling and analysis of observational data)

The results of a three-dimensional numerical simulation of changes in the temperature and wind within a height range of up to 100 km caused by changes in fluxes in the solar ultraviolet (UV) radiation in the 23rd solar activity cycle (which was characterized by unusually low values of UV-radiation fluxes) and also of global changes in the ozone content are presented. The simulation results showed that the response of the temperature to variations in the UV radiation are substantially of a nonzonal character, which is caused by the presence in the model of sources of quasi-stationary waves corresponding to the observational data.     

Empirical approaches in prediction of reservoir sediment distribution——An experience of 57 reservoirs in the USA and India

An accurate prediction of sediment distribution may minimize economic losses through proper and timely planning of the functional activities of a reservoir.This study assesses different temporal and spatial factors that affect for sediment deposition in a reservoir and its distribution.This study also focuses on evaluation of two popular distribution prediction methodologies,Area Increment and Empirical Area Reduction,based on experience with sediment distribution in 57 reservoirs in the USA and India.A non-iterative processed empirical distribution model(NPEDM) and a linear regression trend model(LRTM) are proposed to predict sediment distribution.Silt contributing area and inflow entering a reservoir are found to be the most significant factors affecting in reservoir sediment deposition.Compared to the Empirical Area Reduction method,the Area Increment method provided better prediction.The reservoir classification approach and empirical design distribution type curves given by Borland and Miller(1960) are found to be rational.Shape factor values for different periods indicate that reservoir shape(type) changes with time.Thus,long term prediction is not desirable in Type-Ⅱ Ⅲ reservoirs using the Empirical Area Reduction method.Newly developed the NPEDM shows reasonably good prediction of sediment distribution.The NPEDM is very easy to apply and can be used in any reservoir of any size.Extrapolation of the trend of sediment distribution obtained from the LRTM indicates an accurate short term prediction in a few reservoirs as causes of temporal and spatial variations of sediment distribution including the factors of uncertainties of sediment deposition are implicit within the methodology.     

Fault-block structure and the stress state of the upper crust of lake Baikal’s eastern coast (field observations and modeling)

The fault-block structure and stress state of the upper crust at one of the sites of the Baikal rift (Ust-Barguzin fault node) is studied on the basis of a complex of geomorphological, geological-structural, and tectonophysical methods. A map reflecting specific features of the fault-block structure of the upper crust in the region under investigation is compiled. In situ data are collected, and the stress state is reconstructed from residual deformations in local rock volumes. Systematization of the reconstructed stress fields with respect to ruptures of various ranks made it possible to reveal specific features of the stress state of the upper crust of the region associated with its fault-block structure. Optical modeling of the stress state was performed both for the area of the Ust-Barguzin fault node as a whole (regional structure) and for the vicinity of conjugation zones of lower-rank ruptures (local structures) composing zones of regional faults. It is shown that stress changes in the areas of fault conjugation nodes, both in value and in the strike of the principal axes, can be caused by the cooperative behavior of ruptures during the activation in the zone of influence of a larger fault or a fault node.     

Uncertainty estimation of a complex water quality model: The influence of Box–Cox transformation on Bayesian approaches and comparison with a non-Bayesian method

In urban drainage modelling, uncertainty analysis is of undoubted necessity. However, uncertainty analysis in urban water-quality modelling is still in its infancy and only few studies have been carried out. Therefore, several methodological aspects still need to be experienced and clarified especially regarding water quality modelling. The use of the Bayesian approach for uncertainty analysis has been stimulated by its rigorous theoretical framework and by the possibility of evaluating the impact of new knowledge on the modelling predictions. Nevertheless, the Bayesian approach relies on some restrictive hypotheses that are not present in less formal methods like the Generalised Likelihood Uncertainty Estimation (GLUE). One crucial point in the application of Bayesian method is the formulation of a likelihood function that is conditioned by the hypotheses made regarding model residuals. Statistical transformations, such as the use of Box–Cox equation, are generally used to ensure the homoscedasticity of residuals. However, this practice may affect the reliability of the analysis leading to a wrong uncertainty estimation. The present paper aims to explore the influence of the Box–Cox equation for environmental water quality models. To this end, five cases were considered one of which was the “real” residuals distributions (i.e. drawn from available data). The analysis was applied to the Nocella experimental catchment (Italy) which is an agricultural and semi-urbanised basin where two sewer systems, two wastewater treatment plants and a river reach were monitored during both dry and wet weather periods. The results show that the uncertainty estimation is greatly affected by residual transformation and a wrong assumption may also affect the evaluation of model uncertainty. The use of less formal methods always provide an overestimation of modelling uncertainty with respect to Bayesian method but such effect is reduced if a wrong assumption is made regarding the residuals distribution. If residuals are not normally distributed, the uncertainty is over-estimated if Box–Cox transformation is not applied or non-calibrated parameter is used.     

Geological analysis and physical modeling of structural pumping in high effective formation of Kela 2 gas field

In a 3-D closed geological body, in case “structural expanding” inside is induced by stress, it can produce the pressure difference between the expanding cell and surrounding rock, then generate a pumping force directed toward the cell and accelerate the directional flow of fluid in the strata. The structural style and conditions of gas reservoir-formation in the Kuqa depression are favorable to the structural pumping. According to similarity principle, a physical modeling of structure formation and gas filling process of the Kela 2 gas field has justified the occurrence of structural pumping and its important role in gas-reservoir formation with high efficiency under the compressive and well-sealed circumstance. Therefore, authors propose that structural pumping is an important mechanism of gas reservoir-formation with high efficiency in the Kuqa depression.     

Stability of arsenopyrite and As(III) in low-temperature acidic solutions

Arsenopyrite is one of the most important pri-mary arsenic mineral. In the Eh-pH diagram of the As-O2-S-H2O system, if the total arsenic concentration (TAs) is taken to be 0.75 mg/L, the total sulfur con-centration, 32 mg/L, the temperature, 25℃and the pressure, one atmosphere pressure for the discrimina-tion of arsenic species, it may be found that under hy-pergene conditions, arsenopyrite is a moderately stable mineral. Only in the strongly alkaline and reducing environment can arsenopy…     

Robust data assimilation in hydrological modeling – A comparison of Kalman and H-infinity filters

Hydrological model and observation errors are often non-Gaussian and/or biased, and the statistical properties of the errors are often unknown or not fully known. Thus, determining the true error covariance matrices is a challenge for data assimilation approaches such as the most widely used Kalman filter (KF) and its extensions, which assume Gaussian error nature and need fully known error statistics. This paper introduces H-infinite filter (HF) to hydrological modeling and compares HF with KF under various model and observation error conditions. HF is basically a robust version of KF. When model performance is not well known, or changes unpredictably, HF may be preferred over KF. HF is especially suitable for the cases where the estimation performance in the worst error case needs to be guaranteed. Through the application of HF to a hypothetical hydrologic model, this paper shows that HF is less sensitive to the uncertainty in the initial condition, corrects system bias more effectively, and converges to true state faster after interruptions than KF. In particular, HF performs better in dealing with instant human inputs (irrigation is used as an example), which are characterized by non-stationary, non-Gaussian and not fully known errors. However HF design can be more difficult than KF design due to the sensitivity of HF performance to design parameters (weights for model and observation error terms). Through sensitivity analysis, this paper shows the existence of a certain range of those parameters, in which the “best” value of the parameters is located. The tuning of HF design parameters, which can be based on users’ prior knowledge on the nature of model and observation errors, is critical for the implementation of HF.     

Comparison of Pb(Ⅱ) and Cd(Ⅱ) micro-interfacial adsorption on ?ne sediment in the Pearl River Basin,China

The complex micro-interfacial interaction theories of heavy metal ions such as Pb(II) and Cd(II)adsorption on fine sediment in aqueous solution were not systematically investigated. The aim of this work was to reflect the micro-interfacial adsorption characteristics. Sediment samples were collected from an estuary. The Isothermal and kinetics adsorption experiment were done to acquire the data.Isothermal, kinetics, film diffusion and intraparticle diffusion models were adopted to fit the adsorption experimental data. The results indicated that the Langmuir, Freundlich and Temkin models were suitable for analyzing the isothermal experimental data. The maximum adsorption capacities of Pb(II) and Cd(II)on the sediment were 1.1377 and 0.9821 mg·g_(-1), respectively. The q_m and K_L of the Langmuir model, K_f and n_F of the Freundlich model, and b and A of the Temkin model all exhibited a power function relationship with the initial adsorbate concentration. The pseudo-second-order model provided a better fit for the experimental kinetics data compared with the fit of the pseudo-first-order and Elovich models.The pseudo-second-order parameters k_2 and q_e of Pb(II) and q_e of Cd(II) both had a power function relationship with adsorption time, additionally, the k_2 of Cd(II) had an exponential function relationship with adsorption time. The liquid-film diffusion parameters k_(fd) of Pb(II) and Cd(II) were 0.0569 and 0.1806 min_(-1), respectively. The intraparticle diffusion parameter k_(id) values of Pb(II) and Cd(II) were0.0055 mg·g_(-1)·min_(1/2) and 0.0049 mg·g_(-1)min_(1/2), respectively. The physical significance of the model parameters showed that Pb(II) adsorption on sediment was stronger than Cd(II). The results of this study provided a theoretical reference for the micro-interfacial mechanism of heavy metal ion adsorption on sediment.     

Contrasting responses of oligochaetes (Annelida) and chironomids (Diptera) to the abatement of eutrophication in Lake Neuchâtel

: Lake Neuchâtel (Switzerland) has been recovering from human-induced eutrophication since 1982. Oligochaetes and chironomid larvae were used to monitor the recovery of sediment at a depth of 40 m. In oligochaete communities, the mean proportion of individuals belonging to species indicative of oligotrophic conditions (mostly Spirosperma velutinus and Stylodrilus heringianus) increased from 16 % in 1984 to 33 % in 1992, but decreased to 11 % in 1997. Based on oligochaetes, benthic conditions deteriorated in 1997 whereas, based on the increase of oligotrophic chironomids (mostly Micropsectra), they improved. This difference was attributed to the impact of large planktonic algae whose sedimentation had altered oxygen concentrations at the water-sediment interface. Oligochaetes were more affected than chironomids because they are less mobile and they depend more on the inner sediment for their food and reproduction than the latter. However, based on the combined response of oligochaetes and chironomids, benthic recovery was stalled in 1997 but was not reversed.     

Annual variation in neustonic micro- and meso-plastic particles and zooplankton in the Bay of Calvi (Mediterranean–Corsica)

The annual variation in neustonic plastic particles and zooplankton was studied in the Bay of Calvi (Corsica) between 30 August 2011 and 7 August 2012. Plastic particles were classified into three size classes, small microplastics (0.2–2 mm), large microplastics (2–5 mm) and mesoplastics (5–10 mm).74% of the 38 samples contained plastic particles of varying composition: e.g. filaments, polystyrene, thin plastic films. An average concentration of 6.2 particles/100 m² was observed. The highest abundance values (69 particles/100 m²) observed occurred during periods of low offshore wind conditions. These values rose in the same order of magnitude as in previous studies in the North Western Mediterranean.The relationships between the abundance values of the size classes between zooplankton and plastic particles were then examined. The ratio for the intermediate size class (2–5 mm) reached 2.73. This would suggest a potential confusion for predators regarding planktonic prey of this size class.     

Seasonal and Long-Term Changes in the Intensity of O2(b1Σ) and OH(X2Π) Airglow in the Mesopause Region

Geomagnetism and Aeronomy - Spectral observations of the mesopause airglow at the Zvenigorod Scientific Station have been used to obtain the midnight emission intensities of molecular oxygen...