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Despite progresses in representing different processes, hydrological models remain uncertain. Their uncertainty stems from input and calibration data, model structure, and parameters. In characterizing these sources, their causes, interactions and different uncertainty analysis (UA) methods are reviewed. The commonly used UA methods are categorized into six broad classes: (i) Monte Carlo analysis, (ii) Bayesian statistics, (iii) multi-objective analysis, (iv) least-squares-based inverse modeling, (v) response-surface-based techniques, and (vi) multi-modeling analysis. For each source of uncertainty, the status-quo and applications of these methods are critiqued in gauged catchments where UA is common and in ungauged catchments where both UA and its review are lacking. Compared to parameter uncertainty, UA application for structural uncertainty is limited while input and calibration data uncertainties are mostly unaccounted. Further research is needed to improve the computational efficiency of UA, disentangle and propagate the different sources of uncertainty, improve UA applications to environmental changes and coupled human–natural-hydrologic systems, and ease UA’s applications for practitioners.

An Emergent Constraint (EC) is a physically-explainable relationship between model simulations of a past climate variable (predictor) and projections of a future climate variable (predictand). If a significant correlation exists between the predictand and the predictor, observations of the latter can be used to constrain model projections of the former and to narrow their uncertainties. In the present study, the EC technique has been applied to the analysis of precipitation, one of the variables most affected by model uncertainties and still insufficiently analysed in the context of ECs, particularly for the recent CMIP6 model ensemble. The main challenge in determining an EC is establishing if the relationship found is physically meaningful and robust to the composition of the model ensemble. Four precipitation ECs already documented in the literature and so far tested only with CMIP3/CMIP5, three of them involving the analysis of extreme precipitation, have been reconsidered in this paper. Their existence and robustness are evaluated using different subsets of CMIP5 and CMIP6 models, verifying if the EC is still present in the most recent ensemble and assessing its sensitivity to the detailed ensemble composition. Most ECs considered do not pass this test: we found one EC not to be robust in both CMIP5 and CMIP6, other two exist and are robust in CMIP5 but not in CMIP6, and only one is verified and is robust in both model ensembles.

Everyday we face decisions that carry an element of risk and uncertainty. The ability to analyze, predict, and prepare for the level of risk entailed by these decisions is, therefore, one of the most constant and vital skills needed for analysts, scientists and managers. Risk analysis can be defined as a systematic use of information to identify hazards, threats and opportunities, as well as their causes and consequences, and then express risk. In order to successfully develop such a systematic use of information, those analyzing the risk need to understand the fundamental concepts of risk analysis and be proficient in a variety of methods and techniques. Risk Analysis adopts a practical, predictive approach and guides the reader through a number of applications. Risk Analysis: Provides an accessible and concise guide to performing risk analysis in a wide variety of fields, with minimal prior knowledge required. Adopts a broad perspective on risk, with focus on predictions and highlighting uncertainties beyond expected values and probabilities, allowing a more flexible approach than traditional statistical analysis. Acknowledges that expected values and probabilities could produce poor predictions - surprises may occur. Emphasizes the planning and use of risk analyses, rather than just the risk analysis methods and techniques, including the statistical analysis tools. Features many real-life case studies from a variety of applications and practical industry problems, including areas such as security, business and economy, transport, oil & gas and ICT (Information and Communication Technology). Forms an ideal companion volume to Aven's previous Wiley text Foundations of Risk Analysis. Professor Aven's previous book Foundations of Risk Analysis presented and discussed several risk analysis approaches and recommended a predictive approach. This new text expands upon this predictive approach, exploring further the risk analysis principles, concepts, methods and models in an applied format. This book provides a useful and practical guide to decision-making, aimed at professionals within the risk analysis and risk management field.

Accurate estimates of groundwater modeling in arid regions have a crucial role in reaching a sustainable management of groundwater sources. However, groundwater modeling has been faced with different uncertainty sources; besides our imperfect knowledge, it is difficult to derive a proper prediction that can lead to reliable planning. This study aimed to improve the groundwater numerical simulations using different Model Averaging Techniques (MATs). For this, three numerical models, such as Finite Difference (FD), Finite Element (FE), and Meshfree (Mfree), were developed and their performance was verified in a real-world case study. Then various MATs including Simple Model Average (SMA), Weighted Average Method (WAM), Multi Model Super Ensemble (MMSE), Modified MMSE (M3SE) and Bayesian Model Averaging (BMA) were employed to improve the simulated groundwater level Fluctuations (outputs of three numerical models). The findings of this study demonstrated that the numerical model uncertainty is considerable and should not be neglected in the uncertainty analysis of groundwater modeling. In terms of RMSE, the lowest value of 0.148 m was obtained by Mfree while higher values of 1.355 m and 0.287 m are calculated for FD and FE respectively. In addition, the performance assessment of MATs showed a capacity to generate a skillful simulation compared to numerical predictions. Although the MMSE and M3SE (with RMSE values of 0.088 and 0.103 m) generated a desirable prediction in the majority of piezometers, they suffer from a main deficiency, such as the multicollinearity issue. From this perspective, it was concluded that the BMA produced a more reliable and reasonable prediction than other MATs.

Quantifying long-term historical climate is fundamental to understanding recent climate change. Most instrumentally recorded climate data are only available for the past 200 years, so proxy observations from natural archives are often considered. We describe a model-based approach to reconstructing climate defined in terms of raw tree-ring measurement data that simultaneously accounts for nonclimatic and climatic variability. In this approach, we specify a joint model for the tree-ring data and climate variable that we fit using Bayesian inference. We consider a range of prior densities and compare the modeling approach to current methodology using an example case of Scots pine from Torneträsk, Sweden, to reconstruct growing season temperature. We describe how current approaches translate into particular model assumptions. We explore how changes to various components in the model-based approach affect the resulting reconstruction. We show that minor changes in model specification can have little effect on model fit but lead to large changes in the predictions. In particular, the periods of relatively warmer and cooler temperatures are robust between models, but the magnitude of the resulting temperatures is highly model dependent. Such sensitivity may not be apparent with traditional approaches because the underlying statistical model is often hidden or poorly described. Supplementary materials for this article are available online.

This paper assesses the performances of runoff (Ro) and runoff coefficient (α, the ratio of runoff to precipitation) simulations from 23 models during the historical period and then projects their future changes under the two emission scenarios (SSP1‐2.6 and SSP5‐8.5) in the Coupled Model Intercomparison Project. Compared with the UNH/GRDC Ro dataset (0.82 mm day−1), the multi‐model median (MME) Ro of 1995–2014 produces a comparable global mean magnitude (0.80 mm day−1), displays a similar spatial distribution of mean Ro, and also well captures the seasonal cycles at both global and basin scales. The global mean Ro of MME is projected to be increased by 0.01–0.02 mm day−1 (SSP1‐2.6) and 0.02–0.10 mm day−1 (SSP5‐8.5) during the twenty‐first century. Regional hotspots for strong increasing Ro appear across most areas of northern high latitudes, Africa, and southeastern Asia, with high inter‐model consistency. The global mean α is projected to be slightly decreased (−0.17 to −0.63%) except for the long‐term under the SSP5‐8.5 (0.26%). Although signs of changes in Ro vary with the river basins, periods, and scenarios, α in more than half (7 out of 12) river basins are projected to decrease. The uneven distributions of projected Ro changes over global land areas are related to the response of multiple hydroclimatic variables to the global warming. Given regions with inconstancy change signs of the projected precipitation, we speculate that changes in Ro are affected by more complicated hydroclimatic processes that warrant further investigations with physical‐based approaches. Plain Language Summary Evidence has indicated that the terrestrial hydrology would be changed unevenly over global land areas under a warmer climate. Runoff (Ro) is one of the key components of the land water budget and it represents the natural freshwater resource on the earth. This study assesses the historical simulation performances and then projects future changes in Ro and α (the ratio of runoff to precipitation) under two emission scenarios (i.e., SSP1‐2.6 and SSP5‐8.5) based on the simulations from 23 CMIP6 models. The results show that the multi‐model median Ro during the historical period is highly consistent with the reference dataset and captures the seasonal variation in most river basins. During the twenty‐first century, the multi‐model median of global mean Ro is overall projected to increase in the future and the α would slightly decrease except for the long‐term under the SSP5‐8.5. While signs and magnitudes of projection changes depend on regions and basins, those changes are more evident under higher warming levels. The uneven distributions of projected changes of Ro over global land areas are related to the response of other land surface hydrological variables to the global warming induced by anthropogenic emissions in climate models. Key Points The runoff (Ro) and runoff coefficient (α) in CMIP6 are assessed and their future changes are projected under two SSPs in global and basin scales The global mean magnitude, spatial pattern, and seasonal cycles over most river basins are well reproduced by multi‐model median Ro The global mean Ro (α) is projected to increase (decrease), but their projections vary with basins and scenarios

Correlative species distribution models (SDMs) are increasingly being used to predict suitable insect habitats. There is also much criticism of prediction discrepancies among different SDMs for the same species and the lack of effective communication about SDM prediction uncertainty. In this paper, we undertook a factorial study to investigate the effects of various modeling components (species-training-datasets, predictor variables, dimension-reduction methods, and model types) on the accuracy of SDM predictions, with the aim of identifying sources of discrepancy and uncertainty. We found that model type was the major factor causing variation in species-distribution predictions among the various modeling components tested. We also found that different combinations of modeling components could significantly increase or decrease the performance of a model. This result indicated the importance of keeping modeling components constant for comparing a given SDM result. With all modeling components, constant, machine-learning models seem to outperform other model types. We also found that, on average, the Hierarchical Non-Linear Principal Components Analysis dimension-reduction method improved model performance more than other methods tested. We also found that the widely used confusion-matrix-based model-performance indices such as the area under the receiving operating characteristic curve (AUC), sensitivity, and Kappa do not necessarily help select the best model from a set of models if variation in performance is not large. To conclude, model result discrepancies do not necessarily suggest lack of robustness in correlative modeling as they can also occur due to inappropriate selection of modeling components. In addition, more research on model performance evaluation is required for developing robust and sensitive model evaluation methods. Undertaking multi-scenario species-distribution modeling, where possible, is likely to mitigate errors arising from inappropriate modeling components selection, and provide end users with better information on the resulting model prediction uncertainty.

This paper states that there are exchange rate forecasting gains when combining in-sample data from different models based on economic theory. Data combination is performed using Bayesian model averaging (BMA). Using pooled data by group of countries (developed and emerging economies) generates accuracy gains in an important amount of cases, with respect to forecasts that use country information.Gains are larger for currencies of developed economies, but accuracy decreases as the forecast horizon is extended. BMA models for developed countries tend to be more “sparse” than emerging countries models Este artículo propone la existencia ganancias en la predicción de tipo de cambio cuando se combinan datos in-sample de diferentes modelos basados en la teoría económica. La combinación se realiza mediante Bayesian Model Averaging. Entrenar el modelo con información de otras economías genera ganancias de precisión en una cantidad importante de casos, respecto a pronósticos que utilizan solo información del país. Mayores ganancias de precisión se encuentran para divisas de economías desarrolladas. Los modelos entrenados para países desarrollados tienden a ser más “escasos” que los modelos de países emergentes

In this paper, we derive the optimal boundary for pair trading. This boundary defines the points of entry into or exit from the market for a given stock pair. However, if the assumed model contains uncertainty, the resulting boundary could result in large losses. To avoid this, we develop a more robust strategy by accounting for the model uncertainty. To incorporate the model uncertainty, we use the relative entropy as a penalty function in the expected profit from pair trading.

Storm‐driven waves significantly increase coastal hazards, especially in densely populated and infrastructure‐rich regions like the Mediterranean, which is a major global hub for tourism, cultural heritage, and shipping. Although the basin has a fetch‐limited environment, extra‐tropical cyclones can still produce high waves. With increasing global temperatures altering the climate system, wave climate changes are anticipated, albeit with varying reliability across modeled climate variables. This study investigates projected wave climate changes in the Mediterranean using an extensive ensemble of EURO‐CORDEX GCM‐RCMs wave simulations based on the high‐emission scenario RCP8.5. We assess future shifts in wave climate statistics while incorporating model variability for comprehensive results. Consistent with previous studies, our results indicate an overall reduction in significant wave height Hs$\\left({H}_{s}\\right)$ , with reductions up to 0.45 m in autumn and winter, alongside significant shifts in wave direction. The future extreme wave climate changes were further evaluated by computing 100‐year Hs${H}_{s}$return levels. Extreme event distributions from all simulations were bias‐corrected and aggregated into a single coherent distribution for each period. Our findings reveal for the first time robust evidence of intensification of extreme waves toward the end of the century in several regions of the Mediterranean, with increases of 0.50–2 m in Hs${H}_{s}$ . While focusing solely on a high‐emission scenario limits the scope of these findings for mitigation strategies, this study underscores the need to analyze both full and extreme distributions in wave climate projections. Each may have distinct implications for coastal management policies and maritime operations. Plain Language Summary The impact of storm‐driven wind‐waves on coastal regions presents significant hazards. Although the Mediterranean Sea is not home to the highest waves worldwide, it occasionally experiences strong extra‐tropical storms that generate powerful waves. The Mediterranean's densely populated coasts, along with its major tourism and shipping activity, make it particularly vulnerable to wave‐related hazards. This study investigates the future trajectory of the Mediterranean wave climate, using a comprehensive ensemble of models to simulate historical and future periods in the context of climate change. Specifically, future changes in the wave climate are assessed and considered significant if there is overall agreement among models. Despite variability in model projections, a consensus emerges regarding the alteration of wave climate dynamics. While overall wave intensity is anticipated to decrease, the most extreme wave events are projected to become more frequent and intense by the end of the century. These findings emphasize the nuanced nature of wave climate changes, urging a holistic approach that considers both the average wave climate and the hazards posed by extreme events. Recognizing the dual implications of shifting wave climates can help stakeholders improve coastal management, optimize maritime traffic planning, and mitigate hazards posed by storm‐driven waves in a changing climate. Key Points Robust results from the large ensemble of GCM‐RCM indicate an overall average reduction of the mean and intense Mediterranean wave climate Future shifts in extreme events differ from the rest of the distribution, as robust increases in Hs 100‐year return levels are projected Estimating changes in Hs return levels using multi‐model mean approaches is largely constrained by the limited number of extreme events