Climate and weather variables such as rainfall, temperature, and pressure are indicators for hazards such as tropical cyclones, floods, and fires. The impact of these events can be due to a single variable being in an extreme state, but more often it is the result of a combination of variables not all of which are necessarily extreme. Here, the combination of variables or events that lead to an extreme impact is referred to as a compound event. Any given compound event will depend upon the nature and number of physical variables, the range of spatial and temporal scales, the strength of dependence between processes, and the perspective of the stakeholder who defines the impact. Modeling compound events is a large, complex, and interdisciplinary undertaking. To facilitate this task we propose the use of influence diagrams for defining, mapping, analyzing, modeling, and communicating the risk of the compound event. Ultimately, a greater appreciation of compound events will lead to further insight and a changed perspective on how impact risks are associated with climate-related hazards. WIREs Clim Change 2014, 5:113–128. doi: 10.1002/wcc.252

Conflict of interest: The authors have declared no conflicts of interest for this article.

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A compound event framework for understanding extreme impacts

The use of copulas in hydrology is quite recent, and many important results still are to be discovered and/or derived. In this work we present some recent advances in hydrological modeling that exploit copulas. These include: (1) the calculation of conditional probabilities and their use in bivariate simulation; (2) the calculation of the level curves of joint distributions; (3) the calculation of the return periods of bivariate events, both in the conditional and unconditional cases; (4) the definition and calculation of the secondary return period; (5) a trivariate model for the temporal structure of the sequence of storms; (6) the statistical calculation of the storm depth; and (7) the calculation of the convolution variance. Several applications to hydrological data are shown. The models presented here may have important implications in many areas of water resources and hydrologic systems.

On the Use of Copulas in Hydrology: Theory and Practice

[1] The hydrological literature on flood frequency analysis in the past has placed undue emphasis on solving the estimation problem. In this paper we argue that much better use should be made of the wealth of hydrological knowledge gained in the past century and that it is essential to expand the information beyond the flood sample at the site of interest. We suggest that the expansion of information can be grouped into three types: temporal, spatial, and causal. We present a number of examples from Austria to illustrate the rich diversity of flood processes that are often site specific and difficult to capture by formal methods. On the basis of these examples, and the expansion of information, we illustrate that hydrological reasoning can provide diagnostic findings that give guidance on how to adjust quantitative estimates from formal methods to more fully capture the subtleties of the flood characteristics at the site of interest. We believe that this approach gives a more complete representation of flood processes at a given site than the existing formal methods alone and propose the term “flood frequency hydrology,” as opposed to flood frequency statistics, to reflect the focus on hydrological processes and hydrological reasoning.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2007WR006744

Flood frequency hydrology: 1. Temporal, spatial, and causal expansion of information

https://ewater.org.au/archive/crcch/archive/pubs/pdfs/technical200104.pdf

Monte Carlo simulation of flood frequency curves from rainfall

Derived flood frequency models can be used to study climate and land use change effects on the flood frequency curve. Intra-annual (i.e., within year) climate variability strongly impacts upon the flood frequency characteristics in two ways: in a direct way through the seasonal variability of storm characteristics and indirectly through the seasonality of rainfall and evapotranspiration which then affect the antecedent catchment conditions for individual storm events. In this paper we propose a quasi-analytical derived flood frequency model that is able to account for both types of seasonalities. The model treats individual events separately. It consists of a rainfall model with seasonally varying parameters. Increased flood peaks, as compared to block rainfall, due to random within-storm rainfall time patterns are represented by a factor that is a function of the ratio of storm duration and catchment response time. Event runoff coefficients are allowed to vary seasonally and include a random component. Their statistical characteristics are derived from long-term water balance simulations. The components of the derived flood frequency model are integrated in probability space to derive monthly flood frequency curves. These are then combined into annual flood frequency curves. Comparisons with Monte Carlo simulations using parameters that are typical of Austrian catchments indicate that the approximations used here are appropriate. We perform sensitivity analyses to explore the effects of the interaction of rainfall and antecedent soil moisture seasonalities on the flood frequency curve. When the two seasonalities are in phase, there is resonance, which increases the flood frequency curve dramatically. We are also able to isolate the contributions of individual months to the annual flood frequency curve. Monthly flood frequency curves cross over for the parameters chosen here, as extreme floods tend to mainly occur in summer while less extreme floods may occur throughout the year.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2004WR003439

Linking flood frequency to long‐term water balance: Incorporating effects of seasonality

This paper summarises the results of a 3-year research project by the CRC for Catchment Hydrology (CRCCH) on the joint probability approach (Monte Carlo simulation technique) to design flood estimation and the subsequent research activities to further the CRCCH method towards industrial applications. It identifies significant shortcomings in the current design event approach to rainfall-based design flood estimation, and argues that substantial improvements in the accuracy and reliability of flood estimates can be obtained from a more rigorous treatment of probability aspects in the generation of design floods. Applications of the proposed Monte Carlo simulation approach to test catchments in Victoria and Queensland have produced promising results, and demonstrated the feasibility and in-principle advantages of the approach. More recently, the Monte Carlo simulation approach has been integrated with the industry-based flood estimation model URBS thus significantly broadening its range of application. The paper discusses how far the recent research on the joint probability approach has advanced towards resolving the main research issues, and outlines desirable future development work to allow the new method to be routinely applied as a design tool.

Tam Minh Thi Hoang

Papers

Monte Carlo simulation of flood frequency curves from rainfall

Monte Carlo simulation of flood frequency curves from rainfall : the way ahead

A New Modelling Framework for Design Flood Estimation