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The overall objective of this study is envisaged to provide decision makers with actionable insights and access to multi-risk maps for the most in-danger stave churches (SCs) among the existing 28 churches at high spatial resolution to better understand, reduce and mitigate single- and multi-risk. In addition, the present contribution aims to provide decision makers with some information to face the exacerbation of the risk caused by the expected climate change.

Material and data collection started with the consultation of the available literature related to: (1) SCs' conservation status, (2) available methodologies suitable in multi-hazard approach and (3) vulnerability leading indicators to consider when dealing with the impact of natural hazards specifically on immovable cultural heritage.

The paper contributes to a better understanding of place-based vulnerability with local mapping dimension also considering future threats posed by climate change. The results highlight the danger at which the SCs of Røldal, in case of floods, and of Ringebu, Torpo and Øye, in case of landslide, may face and stress the urgency of increasing awareness and preparedness on these potential hazards.

The contribution for the first time aims to homogeneously collect and report all together existing spread information on architectural features, conservation status and geographical attributes for the whole group of SCs by accompanying this information with as much as possible complete 2D sections collection from existing drawings and novel 3D drawn sketches created for this contribution. Then the paper contributes to a better understanding of place-based vulnerability with local mapping dimension also considering future threats posed by climate change. Then it highlights the danger of floods and landslides at which the 28 SCs are subjected. Finally it reports how these risks will change under the ongoing impact of climate change.

In this paper we talk about complex matrix quaternions (biquaternions) and we deal with some abstract methods in mathematical complex matrix analysis.

We introduce and investigate the complex space HC consisting of all 2 × 2 complex matrices of the form ξ=z1+iw1z2+iw2−z‾2−iw‾2z‾1+iw‾1, (z1,w1,z2,w2)∈C4.

We develop on HC a new matrix holomorphic structure for which we provide the fundamental operational calculus properties.

We give sufficient and necessary conditions in terms of Cauchy–Riemann type quaternionic differential equations for holomorphicity of a function of one complex matrix variable ξ∈HC. In particular, we show that we have a lot of holomorphic functions of one matrix quaternion variable.