A structured approach to enhance flood hazard assessment in mountain streams

Abstract

An evidence-based flood hazard analysis in mountain streams requires the identification and the quantitative characterisation of multiple possible processes. These processes result from specific triggering mechanisms on the hillslopes (i.e. landslides, debris flows), in-channel morphodynamic processes associated with sudden bed changes and stochastic processes taking place at critical stream configurations (e.g. occlusion of bridges, failure of levees). From a hazard assessment perspective, such possible processes are related to considerable uncertainties underlying the hydrological cause-effect chains. Overcoming these uncertainties still remains a major challenge in hazard and risk assessment and represents a necessary condition for a reliable spatial representation of process intensities and the associated probabilities. As a result of an accurate analysis of the conceptual flaws present in the procedures currently employed for hazard mapping in South Tyrol (Italy) and Carinthia (Austria), we propose a structured approach as a means to enhance the integration of hillslope, morphodynamic and stochastic processes into conventional flood hazard prediction for mountain basins. To this aim, a functional distinction is introduced between prevailing one-dimensional and two-dimensional process propagation domains, i.e., between confined and semi- to unconfined stream segments. The former domains are mostly responsible for the generation of water, sediment and wood fluxes, and the latter are where flooding of inactive channel areas (i.e. alluvial fans, floodplains) can occur. For the 1D process propagation domain, we discuss how to carry out a process routing along the stream system and how to integrate numerical models output with expert judgement in order to derive consistent event scenarios, thus providing a consistent quantification of the input variables needed for the associated 2D domains. Within these latter domains, two main types of spatial sub-domains can be identified based on the predictability of their dynamics, i.e., stochastic and quasi-deterministic. Advantages and limitations offered by this methodology are finally discussed with respect to hazard and risk assessment in mountain basins.

Annex 1: Formative Scenario Analysis procedure:

• 1. A team of individuals familiar with the problem setting lists v ₁, i = 1, …, N impact variables relevant for the setting, also referred to as system variables, impact factors or case descriptors. The individuals assign every selected impact variable to one of the following categories:

  • Variables describing the inflow characteristics at the homogenous stream segment upstream boundary (US);

  • Variables describing the outflow characteristics at the homogenous stream segment downstream boundary (DS);

  • Variables describing the homogenous stream segment initial conditions (IC);

  • Variables describing the homogenous stream segment adjustment descriptors (AD).

The union of the above listed categories represents the entire set of impact variables $D = US \cup DS \cup IC \cup AD$

• 2. In a next step, the individuals define the impact levels for each individual impact variable. Since the combinatorial number of scenarios is considerably influenced by the number of levels defined for each impact variable, impact variables and their levels should be defined parsimoniously. Each impact variable v _i requires the definition of at least two discrete levels (N _i  ≥ 2) which are denoted by $v_{i}^{1} ,v_{i}^{2} , \ldots ,v_{i}^{{N_{i} }}$.

• 3. Formally, a scenario is a vector $S_{k} = \left( {v_{1}^{{n_{1} }} , \ldots ,v_{i}^{{n_{i} }} , \ldots ,v_{N}^{{n_{N} }} } \right)$ with k = 1, …, k ₀; the number of scenarios is $k_{0} = \prod\nolimits_{i = 1}^{N} {N_{i} }$.

• 4. In this step, the consistency matrix is constructed as $C = \left[ {c\left( {v_{i}^{{n_{i} }} ,v_{j}^{{n_{j} }} } \right)} \right]$ containing the consistency ratings, c(.,.), for all pairs of impact variables at all levels c, $\left( {i,j = 1, \ldots ,N,i \ne j,n_{i} = 1, \ldots ,N_{i} ,n_{j} = 1, \ldots ,N_{j} } \right)$.

• 5. For each scenario a consistency value is calculated respectively as additive measure as $c^{*} \left( {S_{k} } \right) = \sum {c\left( {v_{i}^{{n_{i} }} ,v_{j}^{{n_{j} }} } \right)}$ or as multiplicative measure as $c^{*} \left( {S_{k} } \right) = \prod {c\left( {v_{i}^{{n_{i} }} ,v_{j}^{{n_{j} }} } \right)}$ with $i,j = 1, \ldots ,N,i \ne j,v_{i}^{{n_{i} }} ,v_{j}^{{n_{j} }} \in S_{k}$.

• 6. The scenario selection is based conjointly on the consistency value of the scenarios and the difference between them. The distance measure Δ corresponds to the number of differences between the scenarios $\Updelta \left( {S_{k} ,S_{l} } \right) = \sum\nolimits_{i = 1}^{n} {\left\{ {\begin{array}{*{20}c} 1 & {{\text{if }}v_{i} \left( {S_{k} } \right) \ne v_{i} \left( {S_{l} } \right)} \\ 0 & {\text{otherwise}} \\ \end{array} } \right.}$. The scenarios are ranked in decreasing order according to consistency in an array. The scenario with the highest consistency value S _k is selected from the array and compared with the second scenario S _l . If Δ(S _k , S _l ) is sufficiently large, e.g. Δ(S _k , S _l ) ≥ Δ*, where Δ* was a chosen threshold value, then scenario S _l is also selected and becomes the new comparison reference for scenario three, otherwise the third scenario is compared with the first scenario, etc.

• 7. Scenario interpretation completes the adapted steps of Formative Scenario Analysis