Modelling the risk of natural hazards for society, ecosystems, and the economy is subject to strong uncertainties, even more so in the context of a changing climate, evolving societies, growing economies, and declining ecosystems. Here, we present a new feature of the climate-risk modelling platform CLIMADA (CLIMate ADAptation), which allows us to carry out global uncertainty and sensitivity analysis. CLIMADA underpins the Economics of Climate Adaptation (ECA) methodology which provides decision-makers with a fact base to understand the impact of weather and climate on their economies, communities, and ecosystems, including the appraisal of bespoke adaptation options today and in future. We apply the new feature to an ECA analysis of risk from tropical cyclone storm surge to people in Vietnam to showcase the comprehensive treatment of uncertainty and sensitivity of the model outputs, such as the spatial distribution of risk exceedance probabilities or the benefits of different adaptation options. We argue that broader application of uncertainty and sensitivity analysis will enhance transparency and intercomparison of studies among climate-risk modellers and help focus future research. For decision-makers and other users of climate-risk modelling, uncertainty and sensitivity analysis has the potential to lead to better-informed decisions on climate adaptation. Beyond provision of uncertainty quantification, the presented approach does contextualize risk assessment and options appraisal, and might be used to inform the development of storylines and climate adaptation narratives.

Societal impacts from natural disasters have steadily increased over the last decades

“Impacts generally refer to effects on lives; livelihoods; health and well-being; ecosystems and species; economic, social and cultural assets; services (including ecosystem services); and infrastructure. Impacts may be referred to as consequences or outcomes, and can be adverse or beneficial.”

The specific setup of climate-risk models depends on the hazard under consideration, the location of interest, and the goal of the study. However, such models often share a similar structure given by three sub-models, usually referred to as

In practice, the quantification of risk with climate-risk models is particularly challenging as it involves dealing with the absence of robust verification data

Uncertainty and sensitivity analyses are among the established methods proposed by the scientific literature to quantitatively treat uncertainties in model simulation

In order to fill this gap and facilitate the widespread adoption and application of uncertainty and sensitivity analyses in climate-risk models, this paper introduces and showcases a new feature of the probabilistic climate-risk assessment and modelling platform CLIMADA (CLIMate ADAptation)

The paper is structured as follows: Sect.

To our knowledge, CLIMADA is the first global platform for probabilistic multi-hazard risk modelling and options appraisal to seamlessly include uncertainty and sensitivity analyses in its workflow, as described in this section. CLIMADA is written in

The hazard is modelled as a probabilistic set of events, each one a map of intensity at geographical locations, and with an associated probability of occurrence. For example, the intensity can be expressed in terms of flood depth in metres, maximum wind speed in metres per second, or heat wave duration in days, and the probability as a frequency per year. The exposure is modelled as values distributed on a geographical grid. For instance, the number of animal species, the value of assets in dollars, or the number of people living in a given area. The vulnerability is modelled for each exposure type by an impact function, which is a function of hazard intensity (for details, see

The risk of a single event is defined as its impact multiplied by its probability of occurrence. The impact is obtained by multiplying the value of the impact function at a given hazard intensity with the exposure value at a given location. The total risk over time is obtained from the impact matrix, which entails the impact of each hazard event at each exposure location, and the hazard frequency vector. The benefits of adaptation measures are obtained as the change in total risk. Both the total risk and the benefits can thus be computed for today and in the future, following climate-change scenarios and socio-economic development pathways

With CLIMADA, risk is assessed in a globally consistent fashion, from city to continental scale, for historical data or future projections, considering various adaptation options, including future projections for the climate, socio-economic growth, or vulnerability changes.

The general workflow of the new uncertainty and sensitivity quantification module unsequa, illustrated in Fig.

We remark that the third and fourth steps typically constitute the core elements of the uncertainty analysis, and the fifth and sixth steps the core elements of the sensitivity analysis. In Sect.

The workflow for uncertainty and sensitivity analyses with the unsequa module in CLIMADA consists of six steps (from left to right). (1) Define the input variables (hazard, exposure, impact function, adaptation measure) and their uncertainty input parameters (e.g. hazard intensity, total exposure value, impact function intensity, measures cost). (2) Generate the input parameter samples. (3) Compute the model output metrics of interest for risk assessment and appraisal of adaptation options for each sample using the CLIMADA engine. (4) Analyse the obtained uncertainty distributions with statistical tools and provide a set of visualizations. (5) Compute the sensitivity indices for each input parameter and each output metric. (6) Analyse the sensitivity indices by means of statistical methods and provide different visualizations.

The CLIMADA engine integrates the input variables exposure (

In literature, the terminology “input factor” instead of “input parameter” is also used. Here we shall exclusively use the terminology “input parameter” for numerical random variables, and “input variable” for the inputs to the CLIMADA model.

Note that the choice of the variation and the associated range and distribution can substantially affect the results of uncertainty and sensitivity analysesOverall, the user must define one method for each of the uncertain input variables

As one example, suppose we are modelling the impact of heat waves on people in Switzerland. As exposure layer, we might use gridded population data based on the total population estimate from the UN World population prospect

As another example, we are interested in the risk of floodplain flooding for gridded physical assets in the Congo basin. The flood hazard is generated from a floodplain modelling information system (FMIS) with uncertainty parameters describing the uncertainty in the geospatial data, the temporal data, the model parameters (Mannings), and the hydraulic structure, such as shown in

Defining the appropriate input variable uncertainty and identifying the relevant input parameters for a given case study are not trivial tasks. In general, only a small subset of all possible parameters can be investigated

In general, there are two basic approaches regarding how samples can be drawn. In the local “one-at-a-time” approach, the input parameters are varied one after another, keeping all the others constant

Hence, the basic premise of the unsequa module is to use a global sampling algorithm based on (quasi-) Monte Carlo sequences

CLIMADA imports the (quasi-) Monte Carlo sampling algorithms from the

For each sample of the input parameters, the model output metrics are computed using the CLIMADA engine, e.g. for the risk assessment, the impact matrix

Similarly, for the appraisal adaptation options, each sample is assigned with the corresponding input variables. The CLIMADA engine is then used to compute the impact matrix

We remark that no direct evaluation of the convergence of this quasi-Monte Carlo scheme is provided in the unsequa module, as it is not generally available for all the possible sampling algorithms available through the

In all of the uncertainty and sensitivity analyses, computing the model outputs is usually the most expensive step computationally. For convenience, an estimation of the total computation time for a given run is thus provided in the unsequa module. Experiments showed that the computation time scales approximately linearly with the number of samples

The output metrics values for each sample are characterized and visualized. To this effect, various plotting methods have been implemented as shown in Sect.

The sensitivity index

For typical case studies using CLIMADA, Sobol

The last step consists of analysing and visualizing the obtained sensitivity indices. To this effect, a series of visualization plots are provided, such as bar plots or sensitivity maps for first-order indices, and correlation matrices for second-order indices, as shown in Sect.

In the following discussion, we revisit a case study on tropical cyclone storm surges in Vietnam

We only consider the parts of the climate-risk study by

Below, we showcase uncertainty and sensitivity analyses for the risk of storm surges in terms of affected people under present (2020) climate conditions in Sect.

For simplicity, hereafter

The six steps of the uncertainty and sensitivity analyses (cf. Fig.

We identified four main quantifiable uncertainty parameters which are summarized in the upper row of Table

For the exposure, the total population is assumed to be subject to random sampling errors that are well captured by a normal distribution, and a maximum error of

For the hazard, we apply a bootstrapping technique, i.e. uniform resampling of the event set with replacement to account for the uncertainties of sample estimates. Since the default Sobol

Finally, for the impact function, we consider the uncertainty in the threshold of the original step function that was used to estimate the number of people “affected” (widely defined) by storm surges. In the original case study, the threshold was

Summary of the input parameter distributions. The input parameters

We use the default Sobol

For each of the samples

In the following discussion, we concentrate on the analysis of the full uncertainty distribution of various risk metrics. For convenience, the original case study value, the uncertainty mean value, and standard deviation are also reported. However, as we shall see below, focusing only on these numbers would provide a limited picture.

The full uncertainty distribution for each of the return periods, as well as the exceedance frequency curve are shown in Fig.

Uncertainty distribution for storm surge risk in terms of affected people in Vietnam for present climate conditions (2020).

The bimodal form of the impact uncertainty distribution is interesting, as one could rather expect statistical white or coloured noise (e.g. Gaussian or power-law distributions). As a consistency proof that this is not due to a computational setup error, we verified that the distribution of the total asset value, shown in Fig.

Ideally, we should choose the sensitivity method best suited for the data at hand. In our case, the uncertainty distribution is strongly asymmetric (cf. Fig.

We thus computed the total-order and the second-order Sobol

As shown in Fig.

Total order Sobol

A further analysis of the average annual impact aggregated value in function of the impact function threshold shift

Finally, the largest sensitivity index for the average annual impact at each exposure point is reported on a map in Fig.

We focus on the appraisal of the three adaptation measures, i.e. mangroves, sea dykes, and gabions, to reduce the number of people affected by storm surges assuming the high-emission climate-change scenario RCP

We identified four additional quantifiable uncertainty input parameters for the appraisal of adaptation options compared to the risk-assessment study (cf. Sect.

For the sampling, we use the default Sobol

For each of the samples, we obtained the cumulative output metrics over the whole time period 2020–2050. In particular, we obtained the total risk without adaptation measures, the benefits (averted risk) for each adaptation measure, and the cost of each adaptation measure (for details see

The uncertainty for the cumulative, total average annual risk from storm surges aggregated over all exposure points is shown in Fig.

Uncertainty distribution (histogram bars) for benefits (averted risk) from the adaptation measures:

We use the same method as for the risk assessment to compute the total-order ST and the second-order S2 Sobol

The total risk without adaptation measure is most sensitive to the impact function threshold shift

The uncertainty of the benefits for all adaptation measures are most sensitive to the impact function threshold shift, with

Note that the 95th percentile confidence intervals of the sensitivity indices (indicated with vertical black bars in Fig.

Total-order Sobol

The original case study intended to serve as a blueprint for future analyses of other world regions with limited data availability, and thus focused on the application of established research tools to provide insights into natural hazard risks and potential benefits of adaptation options

In this paper, we described the unsequa module for uncertainty and sensitivity analyses recently added to the climate-risk model CLIMADA. We highlighted its ease of use with an application to a previous case study assessing risks from tropical storm surges to people in Vietnam and appraising local adaptation options. We showed that only providing percentile information without the full distributions can be misleading, and that uncertainty analysis without sensitivity analysis does not provide a thorough picture of uncertainty

The illustrative case study in this paper was run on a computing cluster. However, many potential users will not have access to such computational resources. Nonetheless, meaningful uncertainty and sensitivity analyses can be conducted only on a single computer, for instance by reducing resolution, sample size, or the number of uncertainty input parameters. For example, the illustrative case study in the paper could be run reasonably on a typical laptop by reducing the resolution to

While we showed that quantitative uncertainty and sensitivity are significant steps to improve the information value of climate-risk models, we stress that not all uncertainties can be described with the shown method (see e.g. Appendix

If a climate-risk modeller conducts uncertainty and sensitivity analyses, either by using the CLIMADA module published here, or by implementing a similar analysis in another modelling framework, the next question is: what should be done with the results? We suggest two main areas that could benefit from such analyses. First, within the field, the more that uncertainty and sensitivity analyses become standard practice, the more these analyses will enhance transparency of studies among climate-risk modellers. This can help to focus related research on areas that can provide better understanding of the parameters, or on modelling choices that are most influential on model outputs. Second, for decision-makers and other users of climate-risk modelling, uncertainty and sensitivity analyses have the potential to lead to better-informed decisions on climate adaptation. Several methods exist for inclusion into quantitative decision-making analysis

In future iterations, uncertainty analysis in CLIMADA could for instance be extended with the addition of surrogate models to reduce the computational costs and allow for the testing of a larger number of input parameter with a larger number of samples for models at higher resolution. Overall, we hope that the simplicity of use of the presented unsequa module will motivate modellers to include uncertainty and sensitivity analyses as natural parts of climate-risk modelling. Finally, we caution that numbers even with elaborate error bars and distributions can give a false sense of accuracy

CLIMADA imports the quasi-Monte Carlo sampling algorithms from the

In the unsequa module, a number of helper methods exist to parameterize a few common uncertainty parameter distributions for the main input variables: exposure, impact functions, hazard, and measures, as summarized in Table

For risk assessment, the impact at an exposure location

For the appraisal of adaptation options, the measures are represented as a modification of the exposure, impact functions, or hazard, at a given cost. Thus, all the helper methods for the exposure, impact functions, and hazard defined in Table

Summary of available helper methods to define uncertainty parameter distributions for the main input variables of CLIMADA for risk assessment. For all distributions, the parameters can be set by the user (e.g. the mean and variance of a Gaussian distribution are free parameters).

Summary of available helper methods to define uncertainty parameter distributions for the additional input variables of CLIMADA required for appraisal of adaptation options. For all distributions, the parameters can be set by the user (e.g. the bounds of the uniform distributions are free parameters).

In the Vietnam case study

The spatial distribution of population was obtained from the LitPop module in CLIMADA at a resolution of 1 km and using the population census data only, i.e.

As stated in Sect.

Note that in general, global uncertainty and sensitivity analyses as discussed in this paper apply only to deterministic computer codes, i.e. models for which a specific set of input values always results in the same output

Population distribution obtained by combining population density layer and nightlight satellite imagery

Impact function uncertainty, with a threshold shift of the flood depth above which all people are affected varying between

Samples for the uncertainty analysis of the risk assessment in Sect.

Samples for the uncertainty analysis of the adaptation options appraisal in Sect.

Second-order Sobol

Uncertainty distribution (histogram bars) for the ratio of cost to benefit of the three adaptation options

Histogram of the number of storm surge events in the probabilistic set by their impact (in thousands (K) of affected people) in Vietnam for present climate conditions (2020) for

CLIMADA is openly available at GitHub

All data have been generated using CLIMADA (the LitPop exposures, the impact function, the storm surge hazard, the adaptation measures, all impact and cost–benefit values, the uncertainty distributions, and the sensitivity indices). Detailed tutorials are available at

Conceptualization was by CMK, AC, SM, DNB, ES, LO, and JWM; writing of the original draft was by CMK and AC; writing – review and editing – was by CMK, AC, SM, DNB, ES, LO, JWM, and AR; data curation was by CMK and AR; formal analysis was by CMK; software was the responsibility of CMK and ES; resources were managed by DNB; visualization was by CMK and AC; project administration was by CMK.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors are grateful to Moustapha Maliki and Evelyn Mühlhofer for valuable discussion at the start of this project.

This research has been supported by Horizon 2020 (CASCADES (grant no. 821010) and RECEIPT (grant no. 820712)).

This paper was edited by Christian Folberth and reviewed by Francesca Pianosi and Nadia Bloemendaal.