Refinement of higher-order logic programs

A refinement calculus provides a method for transforming specifications to executable code, maintaining the correctness of the code with respect to its specification. In this paper we extend the refinement calculus for logic programs to include higher-order programming capabilities in specifications and programs, such as procedures as terms and lambda abstraction. We use a higher-order type and term system to describe programs, and provide a semantics for the higher-order language and refinement. The calculus is illustrated by refinement examples

Natural hazards in Australia : sea level and coastal extremes

The Australian coastal zone encompasses tropical, sub- and extra-tropical climates and accommodates about 80 % of Australia’s population. Sea level extremes and their physical impacts in the coastal zone arise from a complex set of atmospheric, oceanic and terrestrial processes that interact on a range of spatial and temporal scales and will be modified by a changing climate, including sea level rise. This review details significant progress over recent years in understanding the causes of past and projections of future changes in sea level and coastal extremes, yet a number of research questions, knowledge gaps and challenges remain. These include efforts to improve knowledge on past sea level extremes, integrate a wider range of processes in projections of future changes to sea level extremes, and focus efforts on understanding long-term coastline response from the combination of contributing factors

Global-scale changes to extreme ocean wave events due to anthropogenic warming

Extreme surface ocean waves are often primary drivers of coastal flooding and erosion over various time scales. Hence, understanding future changes in extreme wave events owing to global warming is of socio-economic and environmental significance. However, our current knowledge of potential changes in high-frequency (defined here as having return periods of less than 1 year) extreme wave events are largely unknown, despite being strongly linked to coastal hazards across time scales relevant to coastal management. Here, we present global climate-modeling evidence, based on the most comprehensive multi-method, multi-model wave ensemble, of projected changes in a core set of extreme wave indices describing high-frequency, extra-tropical storm-driven waves. We find changes in high-frequency extreme wave events of up to ∼50%-100% under RCP8.5 high-emission scenario; which is nearly double the expected changes for RCP4.5 scenario, when globally integrated. The projected changes exhibit strong inter-hemispheric asymmetry, with strong increases in extreme wave activity across the tropics and high latitudes of the Southern Hemisphere region, and a widespread decrease across most of the Northern Hemisphere. We find that the patterns of projected increase across these extreme wave events over the Southern Hemisphere region resemble their historical response to the positive anomaly of the Southern Annular Mode. Our findings highlight that many countries with low-adaptive capacity are likely to face increasing exposure to much more frequent extreme wave events in the future

A global ensemble of ocean wave climate statistics from contemporary wave reanalysis and hindcasts

There are numerous global ocean wave reanalysis and hindcast products currently being distributed and used across different scientific fields. However, there is not a consistent dataset that can sample across all existing products based on a standardized framework. Here, we present and describe the first coordinated multi-product ensemble of present-day global wave fields available to date. This dataset, produced through the Coordinated Ocean Wave Climate Project (COWCLIP) phase 2, includes general and extreme statistics of significant wave height (Hs), mean wave period (Tm) and mean wave direction (θm) computed across 1980–2014, at different frequency resolutions (monthly, seasonally, and annually). This coordinated global ensemble has been derived from fourteen state-of-the-science global wave products obtained from different atmospheric reanalysis forcing and downscaling methods. This data set has been processed, under a specific framework for consistency and quality, following standard Data Reference Syntax, Directory Structures and Metadata specifications. This new comprehensive dataset provides support to future broad-scale analysis of historical wave climatology and variability as well as coastal risk and vulnerability assessments across offshore and coastal engineering applications

Uncertainty and Bias in Global to Regional Scale Assessments of Current and Future Coastal Flood Risk

This study provides a literature-based comparative assessment of uncertainties and biases in global to world-regional scale assessments of current and future coastal flood risks, considering mean and extreme sea-level hazards, the propagation of these into the floodplain, people and coastal assets exposed, and their vulnerability. Globally, by far the largest bias is introduced by not considering human adaptation, which can lead to an overestimation of coastal flood risk in 2100 by up to factor 1300. But even when considering adaptation, uncertainties in how coastal societies will adapt to sea-level rise dominate with a factor of up to 27 all other uncertainties. Other large uncertainties that have been quantified globally are associated with socio-economic development (factors 2.3–5.8), digital elevation data (factors 1.2–3.8), ice sheet models (factor 1.6–3.8) and greenhouse gas emissions (factors 1.6–2.1). Local uncertainties that stand out but have not been quantified globally, relate to depth-damage functions, defense failure mechanisms, surge and wave heights in areas affected by tropical cyclones (in particular for large return periods), as well as nearshore interactions between mean sea-levels, storm surges, tides and waves. Advancing the state-of-the-art requires analyzing and reporting more comprehensively on underlying uncertainties, including those in data, methods and adaptation scenarios. Epistemic uncertainties in digital elevation, coastal protection levels and depth-damage functions would be best reduced through open community-based efforts, in which many scholars work together in collecting and validating these data

Global ocean wave fields show consistent regional trends between 1980 and 2014 in a multi-product ensemble

Historical trends in the direction and magnitude of ocean surface wave height, period, or direction are debated due to diverse data, time-periods, or methodologies. Using a consistent community-driven ensemble of global wave products, we quantify and establish regions with robust trends in global multivariate wave fields between 1980 and 2014. We find that about 30-40% of the global ocean experienced robust seasonal trends in mean and extreme wave height, period, and direction. Most of the Southern Hemisphere exhibited strong upward-trending wave heights (1-2 cm per year) and periods during winter and summer. Ocean basins with robust positive trends are far larger than those with negative trends. Historical trends calculated over shorter periods generally agree with satellite records but vary from product to product, with some showing a consistently negative bias. Variability in trends across products and time-periods highlights the importance of considering multiple sources when seeking robust change analyses

Global ocean wave fields show consistent regional trends between 1980 and 2014 in a multi-product ensemble

Historical trends in the direction and magnitude of ocean surface wave height, period, or direction are debated due to diverse data, time-periods, or methodologies. Using a consistent community-driven ensemble of global wave products, we quantify and establish regions with robust trends in global multivariate wave fields between 1980 and 2014. We find that about 30–40% of the global ocean experienced robust seasonal trends in mean and extreme wave height, period, and direction. Most of the Southern Hemisphere exhibited strong upward-trending wave heights (1–2 cm per year) and periods during winter and summer. Ocean basins with robust positive trends are far larger than those with negative trends. Historical trends calculated over shorter periods generally agree with satellite records but vary from product to product, with some showing a consistently negative bias. Variability in trends across products and time-periods highlights the importance of considering multiple sources when seeking robust change analyses.publishedVersio