On unbiased backtransform of lognormal kriging estimates

Lognormal kriging is an estimation technique that was devised for handling highly skewed data distributions. This technique takes advantage of a logarithmic transformation that reduces the data variance. However, backtransformed lognormal kriging estimates are biased because the nonbias term is totally dependent on a semivariogram model. This paper proposes a new approach for backtransforming lognormal kriging estimates that not only presents none of the problems reported in the literature but also reproduces the sample histogram and, consequently, the sample mean.     

Coping with uncertainties through an automated workflow for 3D reservoir modelling of carbonate reservoirs

Reliable 3D modelling of underground hydrocarbon reservoirs is a challenging task due to the complexity of the underground geological formations and to the availability of different types of data that are typically affected by uncertainties.In the case of geologically complex depositional environments,such as fractured hydrocarbon reservoirs,the uncertainties involved in the modelling process demand accurate analysis and quantification in order to provide a reliable confidence range of volumetric estimations.In the present work,we used a 3D model of a fractured carbonate reservoir and populated it with different lithological and petrophysical properties.The available dataset also included a discrete fracture network(DFN)property that was used to model the fracture distribution.Uncertainties affecting lithological facies,their geometry and absolute positions(related to the fault system),fracture distribution and petrophysical properties were accounted for.We included all different types of uncertainties in an automated approach using tools available in today's modelling software packages and combining all the uncertain input parameters in a series of statistically representative geological realizations.In particular,we defined a specific workflow for the definition of the absolute permeability according to an equivalent,single porosity approach,taking into account the contribution of both the matrix and the fracture system.The results of the analyses were transferred into a 3D numerical fluid-dynamic simulator to evaluate the propagation of the uncertainties associated to the input data down to the final results,and to assess the dynamic response of the reservoir following a selected development plan.The"integrated approach"presented in this paper can be useful for all technicians involved in the construction and validation of 3D numerical models of hydrocarbon-bearing reservoirs and can potentially become part of the educational training for young geo-scientists and engineers,since an integrated and well-constructed workflow is the backbone of any reservoir study.     

Reflexive adaptation for resilient water services: Lessons for theory and practice

‘Adaptive management’ concern attempts to manage complex social-ecological and socio-technical systems in nimble ways to enhance their resilience. In this paper, three forms of adaptive management are identified, ‘scientific’ forms focused on collation of scientific data in response to management experiments, but more recent developments adding processes of collaboration as well as emphasising the need for reflexivity, that is, conscious processes of opening up debates to different perspectives and values. While reflexive adaptive management has been increasingly discussed in theory, there is a lack of examples of what its application means in practice.As a response, this paper examines an ‘Adaptive Planning Process’ (APP), seeking to apply reflexive adaptive management as a means to improve climate resilience in the UK water sector. The APP’s three inter linked workshops – Aspiration, Scenario and Roadmapping – were co-developed and trialled in a water utility. By describing and justifying the choices made in the development of the APP, the paper aims to reveal some of the challenges that arise when trying to design processes that achieve reflexive adaptation.The paper concludes that, if applied to planning for climate change, reflexive adaptation has the potential to explore multiple value positions, highlight different potential futures and acknowledge (and hence, partly address) power differentials, and therefore to offer the possibility of real change. On the basis of the trial, we argue that through tapping the depth and breadth of internal knowledge the APP process created the potential for decision making to be joined up across different parts of the utility, and hence offering new strategies and routes for addressing uncertainties and delivering more resilient water services.     

A tool for the ages: The Probabilistic Cosmogenic Age Analysis Tool (P-CAAT)

While revolutionary to the geomorphic community, the application of terrestrial cosmogenic nuclide (TCN) dating is complicated by geological uncertainties, which often lead to skewed or poorly clustered TCN age distributions. Although a range of statistical approaches are typically used to detect and remove outliers, few are optimized for analysis of TCN datasets. Many are mean- or median-based and therefore explicitly assume a single probability distribution (e.g., Mean Squared Weighted Deviates, Chauvenet's Criterion, etc.). Given the ubiquity of pre- and post-depositional modification of rock surfaces, which occur at different rates in different geomorphic settings, these approaches struggle with multimodal distributions which often characterize TCN datasets. In addition, most statistical approaches do not propagate measurement or production rate uncertainties, which become increasingly important as dataset size or clustering increases. Finally, most approaches provide arithmetic single solutions, irrespective of geologic context.To address these limitations, we present the Probabilistic Cosmogenic Age Analysis Tool (P-CAAT), a new approach for outlier detection and landform age analysis. This tool incorporates both sample age and geologic uncertainties and uses Monte Carlo simulations to eliminate dataset skewness by isolating component normal distributions from a cumulative probability density estimate for datasets with three or more samples. This approach allows geologic context to inform post-analysis interpretations, as researchers can assign landform ages based upon statistically distinct subpopulations, informed by the characteristics of geomorphic systems (e.g., exhumation of boulders as moraines degrade through time). To evaluate the effectiveness of P-CAAT, we analyzed a range of synthetic TCN datasets and compared the results to commonly used statistical approaches for outlier detection. Irrespective of dataset size or clustering, P-CAAT outperformed other approaches and returned accurate solutions that improve in precision as sample size increases. To enable more comprehensive utilization of our approach, P-CAAT is packaged with a GUI interface and is available for download at kgs. uky.edu/anorthite/PCAAT.     

大气甲烷浓度变化的源汇因素模拟研究进展

从甲烷大气化学过程、传输模式和反向模拟机理等方面综述了大气甲烷浓度变化及其源汇研究的主要进展及存在的问题。基于数据同化算法的反向模拟能有效降低全球及国家尺度甲烷排放估计的不确定性。但在具体的算法实施中,先验的甲烷排放估计和地面站大气甲烷浓度测定的不确定性量化仍然主要是经验性的,缺乏严格和系统性的量化算法。相对于有限的地面站测定,基于卫星平台的大气甲烷浓度变化监测数据极大地提高了数据的空间覆盖度,进一步促进了反向模拟的应用。当前的反向模拟研究在全球尺度上确认了自然湿地甲烷排放对大气甲烷浓度年际波动的决定性作用;在国家尺度上,反向模拟在国家温室气体清单的"可核查"方面也有广泛的应用前景。     

Stochastic simulations of ocean waves: An uncertainty quantification study

The primary objective of this study is to introduce a stochastic framework based on generalized polynomial chaos (gPC) for uncertainty quantification in numerical ocean wave simulations. The techniques we present can be easily extended to other numerical ocean simulation applications. We perform stochastic simulations using a relatively new numerical method to simulate the HISWA (Hindcasting Shallow Water Waves) laboratory experiment for directional near-shore wave propagation and induced currents in a shallow-water wave basin. We solve the phased-averaged equation with hybrid discretization based on discontinuous Galerkin projections, spectral elements, and Fourier expansions. We first validate the deterministic solver by comparing our simulation results against the HISWA experimental data as well as against the numerical model SWAN (Simulating Waves Nearshore). We then perform sensitivity analysis to assess the effects of the parametrized source terms, current field, and boundary conditions. We employ an efficient sparse-grid stochastic collocation method that can treat many uncertain parameters simultaneously. We find that the depth-induced wave-breaking coefficient is the most important parameter compared to other tunable parameters in the source terms. The current field is modeled as random process with large variation but it does not seem to have a significant effect. Uncertainty in the source terms does not influence significantly the region before the submerged breaker whereas uncertainty in the incoming boundary conditions does. Considering simultaneously the uncertainties from the source terms and boundary conditions, we obtain numerical error bars that contain almost all experimental data, hence identifying the proper range of parameters in the action balance equation.     

STUDY OF INFILTRATION INTO A HETEROGENEOUS SOIL USING MAGNETIC RESONANCE IMAGING

In this paper, the feasibility of using magnetic resonance imaging (MRI) to study water infiltration into a heterogeneous soil is examined, together with its difficulties and limitations. MRI studies of ponded water infiltration into an undisturbed soil core show that the combination of one- and two-dimensional imaging techniques provides a visual and non-destructive means of monitoring the temporal changes of soil water content and the moisture profile, and the movement of the wetting front. Two-dimensional images show air entrapment in repetitive ponded infiltration experiments. During the early stages of infiltration, one-dimensional images of soil moisture profiles clearly indicate preferential flow phenomena. The observed advance of wetting fronts can be described by a linear relationship between the square root of infiltration time (√t) and the distance of the wetting front from the soil surface. Similarly, the cumulative infiltration is also directly proportional to √t. Furthermore, from the MRI infiltration moisture profiles, it is possible to estimate the parameters that feature in infiltration equations. © 1997 by John Wiley & Sons, Ltd.     

Multistage scenario-based interval-stochastic programming for planning water resources allocation

In this study, a multistage scenario-based interval-stochastic programming (MSISP) method is developed for water-resources allocation under uncertainty. MSISP improves upon the existing multistage optimization methods with advantages in uncertainty reflection, dynamics facilitation, and risk analysis. It can directly handle uncertainties presented as both interval numbers and probability distributions, and can support the assessment of the reliability of satisfying (or the risk of violating) system constraints within a multistage context. It can also reflect the dynamics of system uncertainties and decision processes under a representative set of scenarios. The developed MSISP method is then applied to a case of water resources management planning within a multi-reservoir system associated with joint probabilities. A range of violation levels for capacity and environment constraints are analyzed under uncertainty. Solutions associated different risk levels of constraint violation have been obtained. They can be used for generating decision alternatives and thus help water managers to identify desired policies under various economic, environmental and system-reliability conditions. Besides, sensitivity analyses demonstrate that the violation of the environmental constraint has a significant effect on the system benefit.     

Assessing the impact of land use change on hydrology by ensemble modelling (LUCHEM) II: Ensemble combinations and predictions

This paper reports on a project to compare predictions from a range of catchment models applied to a mesoscale river basin in central Germany and to assess various ensemble predictions of catchment streamflow. The models encompass a large range in inherent complexity and input requirements. In approximate order of decreasing complexity, they are DHSVM, MIKE-SHE, TOPLATS, WASIM-ETH, SWAT, PRMS, SLURP, HBV, LASCAM and IHACRES. The models are calibrated twice using different sets of input data. The two predictions from each model are then combined by simple averaging to produce a single-model ensemble. The 10 resulting single-model ensembles are combined in various ways to produce multi-model ensemble predictions. Both the single-model ensembles and the multi-model ensembles are shown to give predictions that are generally superior to those of their respective constituent models, both during a 7-year calibration period and a 9-year validation period. This occurs despite a considerable disparity in performance of the individual models. Even the weakest of models is shown to contribute useful information to the ensembles they are part of. The best model combination methods are a trimmed mean (constructed using the central four or six predictions each day) and a weighted mean ensemble (with weights calculated from calibration performance) that places relatively large weights on the better performing models. Conditional ensembles, in which separate model weights are used in different system states (e.g. summer and winter, high and low flows) generally yield little improvement over the weighted mean ensemble. However a conditional ensemble that discriminates between rising and receding flows shows moderate improvement. An analysis of ensemble predictions shows that the best ensembles are not necessarily those containing the best individual models. Conversely, it appears that some models that predict well individually do not necessarily combine well with other models in multi-model ensembles. The reasons behind these observations may relate to the effects of the weighting schemes, non-stationarity of the climate series and possible cross-correlations between models.     

Transmissivity and storage coefficient estimation by coupling the Cooper–Jacob method and modified fuzzy least-squares regression

Traditionally the Cooper–Jacob equation is used to determine the transmissivity and the storage coefficient for an aquifer using pump test results. This model, however, is a simplified version of the actual subsurface and does not allow for analysis of the uncertainty that comes from a lack of knowledge about the heterogeneity of the environment under investigation. In this paper, a modified fuzzy least-squares regression (MFLSR) method is developed that uses imprecise pump test data to obtain fuzzy intercept and slope values which are then used in the Cooper–Jacob method. Fuzzy membership functions for the transmissivity and the storage coefficient are then calculated using the extension principle. The supports of the fuzzy membership functions incorporate the transmissivity and storage coefficient values that would be obtained using ordinary least-squares regression and the Cooper–Jacob method. The MFLSR coupled with the Cooper–Jacob method allows the analyst to ascertain the uncertainty that is inherent in the estimated parameters obtained using the simplified Cooper–Jacob method and data that are uncertain due to lack of knowledge regarding the heterogeneity of the aquifer.