Profile extrema for visualizing and quantifying uncertainties on excursion regions. Application to coastal flooding

We consider the problem of describing excursion sets of a real-valued function $f$, i.e. the set of inputs where $f$ is above a fixed threshold. Such regions are hard to visualize if the input space dimension, $d$, is higher than 2. For a given projection matrix from the input space to a lower dimensional (usually $1,2$) subspace, we introduce profile sup (inf) functions that associate to each point in the projection's image the sup (inf) of the function constrained over the pre-image of this point by the considered projection. Plots of profile extrema functions convey a simple, although intrinsically partial, visualization of the set. We consider expensive to evaluate functions where only a very limited number of evaluations, $n$, is available, e.g. $n<100d$, and we surrogate $f$ with a posterior quantity of a Gaussian process (GP) model. We first compute profile extrema functions for the posterior mean given $n$ evaluations of $f$. We quantify the uncertainty on such estimates by studying the distribution of GP profile extrema with posterior quasi-realizations obtained from an approximating process. We control such approximation with a bound inherited from the Borell-TIS inequality. The technique is applied to analytical functions ($d=2,3$) and to a $5$-dimensional coastal flooding test case for a site located on the Atlantic French coast. Here $f$ is a numerical model returning the area of flooded surface in the coastal region given some offshore conditions. Profile extrema functions allowed us to better understand which offshore conditions impact large flooding events

Addressing ambiguity in probabilistic assessments of future marine flooding using possibility distributions

International audienceToday, decision making in the area of coastal adaptation is facing a major challenge due to the deep uncertainties of sea level projections. These deep uncertainties (aka ambiguity or epistemic uncertainties), reflect the intrinsically imprecise nature of global sea level rise (GSLR) due to the lack of knowledge regarding the melting of ice, particularly in Antarctica. Possibility distributions are one of the mathematical tools enabling to overcome the ambiguity in the selection a unique probability laws by bounding all the plausible ones. By adopting this new mathematical tool, we aim at evaluating how GSLR uncertainties accumulate with other sources of uncertainties, namely: the choice in Representative Concentration Pathway (RCP) scenario, the ranking of high-end scenarios, the regional bias, the contributions of extremes and wave effects. The case study corresponds to a local low-lying coastal urban area exposed to storm surge and waves in the north-western Mediterranean coast. We focus on the probability of future flooding by 2100 defined as the probability of exceeding a critical threshold corresponding to the height of coastal defences. The joint sensitivity analysis of the probabilistic, possibilistic and scenario-like sources of uncertainty enables to highlight the key role of deep uncertainties of GSLR, of the statistical uncertainty related to extremes and to a lesser extent of the choice in the RCP scenario. These results heavily depend on the decision maker’s attitude to risk (neutral, averse), which suggests the importance of entering into a loop of interactions with users, in order to collect their requirements and feedbacks, and involves research at the interface between behavioural and decision analytics, climate and coastal science as well as applied statistics

Self-organized kilometer-scale shoreline sand wave generation: sensitivity to model and physical parameters

The instability mechanisms for self-organized kilometer-scale shoreline sand waves have been extensively explored by modeling. However, while the assumed bathymetric perturbation associated with the sand wave controls the feedback between morphology and waves, its effect on the instability onset has not been explored. In addition, no systematic investigation of the effect of the physical parameters has been done yet. Using a linear stability model, we investigate the effect of wave conditions, cross-shore profile, closure depth, and two perturbation shapes (P1: cross-shore bathymetric profile shift, and P2: bed level perturbation linearly decreasing offshore). For a P1 perturbation, no instability occurs below an absolute critical angle ¿c0˜ 40-50°. For a P2 perturbation, there is no absolute critical angle: sand waves can develop also for low-angle waves. In fact, the bathymetric perturbation shape plays a key role in low-angle wave instability: such instability only develops if the curvature of the depth contours offshore the breaking zone is larger than the shoreline one. This can occur for the P2 perturbation but not for P1. The analysis of bathymetric data suggests that both curvature configurations could exist in nature. For both perturbation types, large wave angle, small wave period, and large closure depth strongly favor instability. The cross-shore profile has almost no effect with a P1 perturbation, whereas large surf zone slope and gently sloping shoreface strongly enhance instability under low-angle waves for a P2 perturbation. Finally, predictive statistical models are set up to identify sites prone to exhibit either a critical angle close to ¿c0 or low-angle wave instability.Postprint (author's final draft

Quantizing rare random maps: application to flooding visualization

Visualization is an essential operation when assessing the risk of rare events such as coastal or river floodings. The goal is to display a few prototype events that best represent the probability law of the observed phenomenon, a task known as quantization. It becomes a challenge when data is expensive to generate and critical events are scarce, like extreme natural hazard. In the case of floodings, each event relies on an expensive-to-evaluate hydraulic simulator which takes as inputs offshore meteo-oceanic conditions and dyke breach parameters to compute the water level map. In this article, Lloyd's algorithm, which classically serves to quantize data, is adapted to the context of rare and costly-to-observe events. Low probability is treated through importance sampling, while Functional Principal Component Analysis combined with a Gaussian process deal with the costly hydraulic simulations. The calculated prototype maps represent the probability distribution of the flooding events in a minimal expected distance sense, and each is associated to a probability mass. The method is first validated using a 2D analytical model and then applied to a real coastal flooding scenario. The two sources of error, the metamodel and the importance sampling, are evaluated to quantify the precision of the method.Comment: 40 pages, 11 Figures, submitted to Journal of Computational and Graphical Statisti

FunQuant: A R package to perform quantization in the context of rare events and time-consuming simulations

Quantization summarizes continuous distributions by calculating a discrete approximation. Among the widely adopted methods for data quantization is Lloyd's algorithm, which partitions the space into Vorono\"i cells, that can be seen as clusters, and constructs a discrete distribution based on their centroids and probabilistic masses. Lloyd's algorithm estimates the optimal centroids in a minimal expected distance sense, but this approach poses significant challenges in scenarios where data evaluation is costly, and relates to rare events. Then, the single cluster associated to no event takes the majority of the probability mass. In this context, a metamodel is required and adapted sampling methods are necessary to increase the precision of the computations on the rare clusters.Comment: 7 pages, 4 figures. Submitted to Journal Of Open Source Softwar

Deep uncertainties in shoreline change projections: an extra-probabilistic approach applied to sandy beaches

ABSTRACT:Global mean sea level rise and its acceleration are projected to aggravate coastal erosion over the 21st century, which constitutes a major challenge for coastal adaptation. Projections of shoreline retreat are highly uncertain, however, namely due to deeply uncertain mean sea level projections and the absence of consensus on a coastal impact model. An improved understanding and a better quantification of these sources of deep uncertainty are hence required to improve coastal risk management and inform adaptation decisions. In this work we present and apply a new extraprobabilistic framework to develop shoreline change projections of sandy coasts that allows consideration of intrinsic (or aleatory) and knowledge-based (or epistemic) uncertainties exhaustively and transparently. This framework builds upon an empirical shoreline change model to which we ascribe possibility functions to represent deeply uncertain variables. The model is applied to two local sites in Aquitaine (France) and Castellón (Spain). First, we validate the framework against historical shoreline observations and then develop shoreline change projections that account for possible (although unlikely) low-end and high-end mean sea level scenarios. Our high-end projections show for instance that shoreline retreats of up to 200m in Aquitaine and 130m in Castellón are plausible by 2100, while low-end projections revealed that 58 and 37m modest shoreline retreats, respectively, are also plausible. Such extended intervals of possible future shoreline changes reflect an ambiguity in the probabilistic description of shoreline change projections, which could be substantially reduced by better constraining sea level rise (SLR) projections and improving coastal impact models. We found for instance that if mean sea level by 2100 does not exceed 1m, the ambiguity can be reduced by more than 50%. This could be achieved through an ambitious climate mitigation policy and improved knowledge on ice sheets.This research has been supported by the BRGM, IHCantabria and the ERA4CS-ECLISEA project (grant no. 690462)

Management of uncertainties on parameters elicited by experts – Applications to sea-level rise and to CO 2 storage operations risk assessment

International audienceIn a context of high degree of uncertainty, when very few data are available, experts are commonly requested to provide their opinions on input parameters of risk assessment models. Not only might each expert express a certain degree of uncertainty on his/her own statements, but the set of information collected from the pool of experts introduces an additional level of uncertainty. It is indeed very unlikely that all experts agree on exactly the same data, especially regarding parameters needed for natural risk assessments. In some cases, their opinions may differ only slightly (e.g. the most plausible value for a parameter is similar for different experts, and they only disagree on the level of uncertainties that taint the said value) while on other cases they may express incompatible opinions for a same parameter. Dealing with these different kinds of uncertainties remains a challenge for assessing geological hazards or/and risks. Extra-probabilistic approaches (such as the Dempster-Shafer theory or the possibility theory) have shown to offer promising solutions for representing parameters on which the knowledge is limited. It is the case for instance when the available information prevents an expert from identifying a unique probability law to picture the total uncertainty. Moreover, such approaches are known to be particularly flexible when it comes to aggregating several and potentially conflicting opinions. We therefore propose to discuss the opportunity of applying these new theories for managing the uncertainties on parameters elicited by experts, by a comparison with the application of more classical probability approaches. The discussion is based on two different examples. The first example deals with the estimation of the injected CO 2 plume extent in a reservoir in the context of CO 2 geological storage. This estimation requires information on the effective porosity of the reservoir, which has been estimated by 14 different experts. The Dempster-Shafer theory has been used to represent and aggregate these pieces of information. The results of different aggregation rules as well as those of a classical probabilistic approach are compared with the purpose of highlighting the elements each of them could provide to the decision-maker (Manceau et al., 2016). The second example focuses on projections of future sea-level rise. Based on IPCC's constraints on the projection quantiles, and on the scientific community consensus level on the physical limits to future sea-level rise, a possibility distribution of the projections by 2100 under the RCP 8.5 scenario has been established. This possibility distribution has been confronted with a set of previously published probabilistic sea-level projections, with a focus on their ability to explore high ranges of sea-level rise (Le Cozannet et al., 2016). These two examples are complementary in the sense that they allow to address various aspects of the problem (e.g. representation of different types of information, conflict among experts, sources dependence). Moreover, we believe that the issues faced during these two experiences can be generalized to many risks/hazards assessment situations. References Manceau, JC., Loschetter, A., Rohmer, J., de Lary, L., Le Guénan, T., Hnottavange-Telleen, K. (2016). Dealing with uncertainty on parameters elicited from a pool of experts for CCS risk assessment. Congrès λµ 20 (St-Malo, France). Le Cozannet G., Manceau JC., Rohmer, J. (2016). Bounding probabilistic sea-level rise projections within the framework of the possibility theory. Accepted in Environmental Research Letters

GÖÇ VE YAŞAM

Uluslararası Bakalorya Programı, A1 dersi Türk Dili ve Edebiyatı alanında ele alınan bu tezde, Orhan Kemal'in Gurbet Kuşları adlı yapıtında göç olgusu nedenleri ve sonuçlarıyla beraber incelenmiştir. Göç olgusuyla değişen toplumsal yapı, ekonomik ve kültürel farklılıklar çerçevesinde değerlendirilmiştir. Bu tezin amacı, göç olgusunun toplumsal yapıda alt sınıf ve üst sınıflardaki bireyler üzerindeki etkilerini ortaya koymaktır. Üç ana bölümden oluşan tezin ilk bölümünde yapıta adını veren Gurbet Kuşları kavramı üzerinde durulmuştur. Köylülerin aidiyetsizliği ve uyum sorunu bu bölümde aktarılmıştır. Tezin ikinci bölümünde ise köylülerin köyden kente göç sürecinde yaşadıkları kadın ve erkek figürler üzerinden neden ve sonuçlarıyla işlenmiştir. Tezin üçüncü bölümünde şehirliler başlığı altından genel olarak şehirde – İstanbul – yaşayan insanların göç sürecinde köylülerle yaşadıkları uyumsuzluk ve çatışmalara yer verilmektedir. Çalışmada göç sürecinde şehre yerleşen figürlerin şehirlilerle aralarındaki ekonomik ve kültürel farklılıkların sınıflar arasında geçişe olanak tanımadığı sonucuna varılmıştır

Sea-level rise induced change in exposure of low-lying coastal land: implications for coastal conservation strategies

Coastal erosion and flooding are projected to increase during the 21st century due to sea-level rise (SLR). To prevent adverse impacts of unmanaged coastal development, national organizations can apply a land protection policy, which consists of acquiring coastal land to avoid further development. Yet, these reserved areas remain exposed to flooding and erosion enhanced by SLR. Here, we quantify the exposure of the coastal land heritage portfolio of the French Conservatoire du littoral (Cdl). We find that 30% (~40%) of the Cdl lands owned (projected to be owned) are located below the contemporary highest tide level. Nearly 10% additional surface exposure is projected by 2100 under the high greenhouse gas emissions scenario (SSP5-8.5) and 2150 for the moderate scenario (SSP2-4.5). The increase in exposure is largest along the West Mediterranean coast of France. We also find that Cdl land exposure increases more rapidly for SLR in the range of 0–1 m than for SLR in the range 2–4 m. Thus, near-future uncertainty on SLR has the largest impact on Cdl land exposure evolution and related land acquisition planning. Concerning erosion, we find that nearly 1% of Cdl land could be lost in 2100 if observed historical trends continue. Adding the SLR effect could lead to more than 3% land loss. Our study confirms previous findings that Cdl needs to consider land losses due to SLR in its land acquisition strategy and start acquiring land farther from the coast

Coastal Flooding in the Maldives Induced by Mean Sea-Level Rise and Wind-Waves: From Global to Local Coastal Modelling

The Maldives, with one of the lowest average land elevations above present-day mean sea level, is among the world regions that will be the most impacted by mean sea-level rise and marine extreme events induced by climate change. Yet, the lack of regional and local information on marine drivers is a major drawback that coastal decision-makers face to anticipate the impacts of climate change along the Maldivian coastlines. In this study we focus on wind-waves, the main driver of extremes causing coastal flooding in the region. We dynamically downscale large-scale fields from global wave models, providing a valuable source of climate information along the coastlines with spatial resolution down to 500 m. This dataset serves to characterise the wave climate around the Maldives, with applications in regional development and land reclamation, and is also an essential input for local flood hazard modelling. We illustrate this with a case study of HA Hoarafushi, an atoll island where local topo-bathymetry is available. This island is exposed to the highest incoming waves in the archipelago and recently saw development of an airport island on its reef via land reclamation. Regional waves are propagated toward the shoreline using a phase-resolving model and coastal inundation is simulated under different mean sea-level rise conditions of up to 1 m above present-day mean sea level. The results are represented as risk maps with different hazard levels gathering inundation depth and speed, providing a clear evidence of the impacts of the sea level rise combined with extreme wave events