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Erwan Koch

Publications and source records attributed to Erwan Koch.

At least 19 recordsLinked to original sources

Stress-Testing Dynamical and Generative Downscaling Using Subseasonal Extreme Precipitation Forecasts

Coarse spatial resolution limits the ability of subseasonal prediction models to resolve extreme precipitation. Downscaling with either dynamical or deep generative models can overcome this issue, but the comparative performance of these models for extremes across different atmospheric regimes remains poorly understood. In this work, we evaluate the Weather Research and Forecasting (WRF) model against a diffusion-based generative model by downscaling two physically distinct, extreme precipitation events up to lead times of 3 weeks. For a fair comparison with WRF, which can downscale boundary conditions from different driving models without model-specific training, the diffusion model is trained in an unpaired fashion. Both approaches improve upon the raw European Centre for Medium-Range Weather Forecasts forecasts, in comparison to fused rain gauge-radar observations in Switzerland (CombiPrecip), but exhibit regime-dependent strengths. WRF achieves the highest probabilistic skill for a multicell, non-stationary event. Conversely, the diffusion model is more consistent across different performance metrics for the two events, outperforming WRF in a more stationary supercell event. These results demonstrate that explicit dynamical modeling can add value for specific precipitation events for subseasonal lead times, and that generative downscaling adds value more broadly in different situations.

physics.comp-ph

SwAIther-Precip: Lead-Time-Aware Bias Correction Enables Kilometer-Scale Downscaling of Global AI Precipitation Forecasts over Switzerland

Skillful medium-range precipitation forecasting at kilometer scale remains challenging over complex terrain because precipitation arises from multiscale nonlinear processes that global models cannot explicitly resolve at affordable cost. Global AI weather models can produce skillful medium-range forecasts, but their native 0.25 degrees resolution limits direct use for local hazard applications. Statistical downscaling can help bridge this gap, yet existing approaches often struggle with state-dependent, and especially lead-time-dependent, biases in global forecasts. We introduce SwAIther-Precip, a lead-time-aware downscaling framework that converts coarse-resolution AIFS forecasts into probabilistic km-scale precipitation fields over Switzerland. First, a U-Net conditioned on lead time via feature-wise linear modulation deterministically corrects systematic biases at coarse resolution. This targeted correction enables a cheaper super-resolution stage conditioned only on corrected precipitation, allowing direct training on observations rather than on the full atmospheric state. A diffusion-based model then generates fine-scale spatial variability independently of lead time. Using AIFS forecasts and CombiPrecip radar-gauge observations, SwAIther-Precip reduces CRPS by 48% relative to raw AIFS. The generated fields reproduce observed spatial variability with spectral fidelity above 0.85 at large scales and 0.88 at small scales, corresponding to an effective resolution of approximately 4 km on a 1 km grid for lead times up to 5 days. Training across lead times further improves long-range performance, yielding a 13% CRPS reduction at 6 days relative to lead-time-specific models. These results show that explicitly correcting lead-time-dependent biases before generative super-resolution is key to efficient km-scale probabilistic downscaling of global AI precipitation forecasts.

physics.ao-ph

Spatiotemporally Consistent Multivariate Bias Correction for Climate Projections via Nested Vine Copulas

Climate models are essential for understanding large-scale climate dynamics and long-term climate change, yet they exhibit systematic biases when compared with historical observations. Existing multivariate bias correction (MBC) approaches do not explicitly handle spatiotemporal dependence. However, preserving both spatiotemporal and inter-variable consistency is essential for realistic climate dynamics and reliable regional impact assessments. To address this gap, we propose a novel MBC method called GN-VBC that uses generalized additive models (GAMs) to disentangle spatiotemporal deterministic effects from stochastic residuals. To model joint distributions and dependencies across variables and locations, we introduce nested vine copulas (NVCs), a hierarchical vine merging strategy. NVC in the context of MBC combines two dependence levels: (i) spatial dependence across locations, modeled separately for each variable, and (ii) inter-variable dependence modeled at a selected reference location, which links the spatial models into a coherent multivariate and spatial structure. An application to Switzerland shows improvements in preserving inter-variable, spatial and temporal dependence across a wide range of evaluation metrics.

stat.ME

Investigating the Robustness of Extreme Precipitation Super-Resolution Across Climates

The coarse spatial resolution of gridded climate models, such as general circulation models, limits their direct use in projecting socially relevant variables like extreme precipitation. Most downscaling methods estimate the conditional distributions of extremes by generating large ensembles, complicating the assessment of robustness under distributional transformations, such as those induced by climate change. To better understand and potentially improve robustness, we propose super-resolving the parameters of the target variable's probability distribution directly using analytically tractable mappings. Within a perfect-model framework over Switzerland, we demonstrate that vector generalized linear and additive models can super-resolve the generalized extreme value distribution of summer hourly precipitation extremes from coarse precipitation fields and topography. We introduce the notion of a "robustness gap", defined as the difference in predictive error between present-trained and future-trained models, and use it to diagnose how model structure affects the generalization of each quantile to a pseudo-global warming scenario. By evaluating multiple model configurations, we also identify an upper limit on the super-resolution factor based on the spatial auto- and cross-correlation of precipitation and elevation, beyond which coarse precipitation loses predictive value. Our framework is broadly applicable to variables governed by parametric distributions and offers a model-agnostic diagnostic for understanding when and why empirical downscaling generalizes to climate change and extremes.

physics.ao-ph

Improving Predictions of Convective Storm Wind Gusts through Statistical Post-Processing of Neural Weather Models

Issuing timely severe weather warnings helps mitigate potentially disastrous consequences. Recent advancements in Neural Weather Models (NWMs) offer a computationally inexpensive and fast approach for forecasting atmospheric environments on a 0.25{\deg} global grid. For thunderstorms, these environments can be empirically post-processed to predict wind gust distributions at specific locations. With the Pangu-Weather NWM, we apply a hierarchy of statistical and deep learning post-processing methods to forecast hourly wind gusts up to three days ahead. To ensure statistical robustness, we constrain our probabilistic forecasts using generalised extreme-value distributions across five regions in Switzerland. Using a convolutional neural network to post-process the predicted atmospheric environment's spatial patterns yields the best results, outperforming direct forecasting approaches across lead times and wind gust speeds. Our results confirm the added value of NWMs for extreme wind forecasting, especially for designing more responsive early-warning systems.

physics.ao-ph

Forecasting with Markovian max-stable fields in space and time: An application to wind gust speeds

Hourly maxima of 3-second wind gust speeds are prominent indicators of the severity of wind storms, and accurately forecasting them is thus essential for populations, civil authorities and insurance companies. Space-time max-stable models appear as natural candidates for this, but those explored so far are not suited for forecasting and, more generally, the forecasting literature for max-stable fields is limited. To fill this gap, we consider a specific space-time max-stable model, more precisely a max-autoregressive model with advection, that is well-adapted to model and forecast atmospheric variables. We apply it, as well as our related forecasting strategy, to reanalysis 3-second wind gust data for France in 1999, and show good performance compared to a competitor model. On top of demonstrating the practical relevance of our model, we meticulously study its theoretical properties and show the consistency and asymptotic normality of the space-time pairwise likelihood estimator which is used to calibrate the model.

stat.ME

Next-Generation Earth System Models: Towards Reliable Hybrid Models for Weather and Climate Applications

We review how machine learning has transformed our ability to model the Earth system, and how we expect recent breakthroughs to benefit end-users in Switzerland in the near future. Drawing from our review, we identify three recommendations. Recommendation 1: Develop Hybrid AI-Physical Models: Emphasize the integration of AI and physical modeling for improved reliability, especially for longer prediction horizons, acknowledging the delicate balance between knowledge-based and data-driven components required for optimal performance. Recommendation 2: Emphasize Robustness in AI Downscaling Approaches, favoring techniques that respect physical laws, preserve inter-variable dependencies and spatial structures, and accurately represent extremes at the local scale. Recommendation 3: Promote Inclusive Model Development: Ensure Earth System Model development is open and accessible to diverse stakeholders, enabling forecasters, the public, and AI/statistics experts to use, develop, and engage with the model and its predictions/projections.

physics.ao-ph

Correlation of powers of Hüsler-Reiss vectors and Brown-Resnick fields, and application to insured wind losses

Hüsler-Reiss vectors and Brown-Resnick fields are popular models in multivariate and spatial extreme-value theory, respectively, and are widely used in applications. We provide analytical formulas for the correlation between powers of the components of the bivariate Hüsler-Reiss vector, extend these to the case of the Brown-Resnick field, and thoroughly study the properties of the resulting dependence measure. The use of correlation is justified by spatial risk theory, while power transforms are insightful when taking correlation as dependence measure, and are moreover very suited damage functions for weather events such as wind extremes or floods. This makes our theoretical results worthwhile for, e.g., actuarial applications. We finally perform a case study involving insured losses from extreme wind speeds in Germany, and obtain valuable conclusions for the insurance industry.

stat.AP

Space-time extremes of severe US thunderstorm environments

Severe thunderstorms cause substantial economic and human losses in the United States. Simultaneous high values of convective available potential energy (CAPE) and storm relative helicity (SRH) are favorable to severe weather, and both they and the composite variable $\mathrm{PROD}=\sqrt{\mathrm{CAPE}} \times \mathrm{SRH}$ can be used as indicators of severe thunderstorm activity. Their extremal spatial dependence exhibits temporal non-stationarity due to seasonality and large-scale atmospheric signals such as El Ni\~no-Southern Oscillation (ENSO). In order to investigate this, we introduce a space-time model based on a max-stable, Brown--Resnick, field whose range depends on ENSO and on time through a tensor product spline. We also propose a max-stability test based on empirical likelihood and the bootstrap. The marginal and dependence parameters must be estimated separately owing to the complexity of the model, and we develop a bootstrap-based model selection criterion that accounts for the marginal uncertainty when choosing the dependence model. In the case study, the out-sample performance of our model is good. We find that extremes of PROD, CAPE and SRH are generally more localized in summer and, in some regions, less localized during El Ni\~no and La Ni\~na events, and give meteorological interpretations of these phenomena.

stat.AP

Stochastic derivative estimation for max-stable random fields

We consider expected performances based on max-stable random fields and we are interested in their derivatives with respect to the spatial dependence parameters of those fields. Max-stable fields, such as the Brown--Resnick and Smith fields, are very popular in spatial extremes. We focus on the two most popular unbiased stochastic derivative estimation approaches: the likelihood ratio method (LRM) and the infinitesimal perturbation analysis (IPA). LRM requires the multivariate density of the max-stable field to be explicit, and IPA necessitates the computation of the derivative with respect to the parameters for each simulated value. We propose convenient and tractable conditions ensuring the validity of LRM and IPA in the cases of the Brown--Resnick and Smith field, respectively. Obtaining such conditions is intricate owing to the very structure of max-stable fields. Then we focus on risk and dependence measures, which constitute one of the several frameworks where our theoretical results can be useful. We perform a simulation study which shows that both LRM and IPA perform well in various configurations, and provide a real case study that is valuable for the insurance industry.

q-fin.RM

Extremal dependence and spatial risk measures for insured losses due to extreme winds

A meticulous assessment of the risk of impacts associated with extreme wind events is of great necessity for populations, civil authorities as well as the insurance industry. Using the concept of spatial risk measure and related set of axioms introduced by Koch (2017, 2019), we quantify the risk of losses due to extreme wind speeds. The insured cost due to wind events is proportional to the wind speed at a power ranging typically between 2 and 12. Hence we first perform a detailed study of the correlation structure of powers of the Brown-Resnick max-stable random fields and look at the influence of the power. Then, using the latter results, we thoroughly investigate spatial risk measures associated with variance and induced by powers of max-stable random fields. In addition, we show that spatial risk measures associated with several classical risk measures and induced by such cost fields satisfy (at least part of) the previously mentioned axioms under conditions which are generally satisfied for the risk of damaging extreme wind speeds. In particular, we specify the rates of spatial diversification in different cases, which is valuable for the insurance industry.

math.PR

Trends in the extremes of environments associated with severe US thunderstorms

Severe thunderstorms can have devastating impacts. Concurrently high values of convective available potential energy (CAPE) and storm relative helicity (SRH) are known to be conducive to severe weather, so high values of PROD=$\sqrt{\mathrm{CAPE}} \times$SRH have been used to indicate high risk of severe thunderstorms. We consider the extreme values of these three variables for a large area of the contiguous US over the period 1979-2015, and use extreme-value theory and a multiple testing procedure to show that there is a significant time trend in the extremes for PROD maxima in April, May and August, for CAPE maxima in April, May and June, and for maxima of SRH in April and May. These observed increases in CAPE are also relevant for rainfall extremes and are expected in a warmer climate, but have not previously been reported. Moreover, we show that the El Niño-Southern Oscillation explains variation in the extremes of PROD and SRH in February. Our results suggest that the risk from severe thunderstorms in April and May is increasing in parts of the US where it was already high, and that the risk from storms in February tends to be higher over the main part of the region during La Niña years. Our results differ from those obtained in earlier studies using extreme-value techniques to analyze a quantity similar to PROD.

stat.AP

Spatial risk measures and rate of spatial diversification

An accurate assessment of the risk of extreme environmental events is of great importance for populations, authorities and the banking/insurance/reinsurance industry. Koch (2017) introduced a notion of spatial risk measure and a corresponding set of axioms which are well suited to analyze the risk due to events having a spatial extent, precisely such as environmental phenomena. The axiom of asymptotic spatial homogeneity is of particular interest since it allows one to quantify the rate of spatial diversification when the region under consideration becomes large. In this paper, we first investigate the general concepts of spatial risk measures and corresponding axioms further and thoroughly explain the usefulness of this theory for both actuarial science and practice. Second, in the case of a general cost field, we give sufficient conditions such that spatial risk measures associated with expectation, variance, Value-at-Risk as well as expected shortfall and induced by this cost field satisfy the axioms of asymptotic spatial homogeneity of order $0$, $-2$, $-1$ and $-1$, respectively. Last but not least, in the case where the cost field is a function of a max-stable random field, we provide conditions on both the function and the max-stable field ensuring the latter properties. Max-stable random fields are relevant when assessing the risk of extreme events since they appear as a natural extension of multivariate extreme-value theory to the level of random fields. Overall, this paper improves our understanding of spatial risk measures as well as of their properties with respect to the space variable and generalizes many results obtained in Koch (2017).

q-fin.RM

A central limit theorem for functions of stationary max-stable random fields on $\mathbb{R}^d$

Max-stable random fields are very appropriate for the statistical modelling of spatial extremes. Hence, integrals of functions of max-stable random fields over a given region can play a key role in the assessment of the risk of natural disasters, meaning that it is relevant to improve our understanding of their probabilistic behaviour. For this purpose, in this paper, we propose a general central limit theorem for functions of stationary max-stable random fields on $\mathbb{R}^d$. Then, we show that appropriate functions of the Brown-Resnick random field with a power variogram and of the Smith random field satisfy the central limit theorem. Another strong motivation for our work lies in the fact that central limit theorems for random fields on $\mathbb{R}^d$ have been barely considered in the literature. As an application, we briefly show the usefulness of our results in a risk assessment context.

math.PR

Geometric ergodicity for some space-time max-stable Markov chains

Max-stable processes are central models for spatial extremes. In this paper, we focus on some space-time max-stable models introduced in Embrechts et al. (2016). The processes considered induce discrete-time Markov chains taking values in the space of continuous functions from the unit sphere of $\mathbb{R}^3$ to $(0, \infty)$. We show that these Markov chains are geometrically ergodic. An interesting feature lies in the fact that the state space is not locally compact, making the classical methodology inapplicable. Instead, we use the fact that the state space is Polish and apply results presented in Hairer (2010).

math.PR

Spatial risk measures and applications to max-stable processes

The risk of extreme environmental events is of great importance for both the authorities and the insurance industry. This paper concerns risk measures in a spatial setting, in order to introduce the spatial features of damages stemming from environmental events into the measure of the risk. We develop a new concept of spatial risk measure, based on the spatially aggregated loss over the region of interest, and propose an adapted set of axioms for these spatial risk measures. These axioms quantify the sensitivity of the risk measure with respect to the space and are especially linked to spatial diversification. The proposed model for the cost underlying our definition of spatial risk measure involves applying a damage function to the environmental variable considered. We build and theoretically study concrete examples of spatial risk measures based on the indicator function of max-stable processes exceeding a given threshold. Some interpretations in terms of insurance are provided.

math.PR

Space-time max-stable models with spectral separability

Natural disasters may have considerable impact on society as well as on (re)insurance industry. Max-stable processes are ideally suited for the modeling of the spatial extent of such extreme events, but it is often assumed that there is no temporal dependence. Only a few papers have introduced spatio-temporal max-stable models, extending the Smith, Schlather and Brown-Resnick spatial processes. These models suffer from two major drawbacks: time plays a similar role as space and the temporal dynamics is not explicit. In order to overcome these defects, we introduce spatio-temporal max-stable models where we partly decouple the influence of time and space in their spectral representations. We introduce both continuous and discrete-time versions. We then consider particular Markovian cases with a max-autoregressive representation and discuss their properties. Finally, we briefly propose an inference methodology which is tested through a simulation study.

math.PR

Diversification and Endogenous Financial Networks

We test the hypothesis that interconnections across financial institutions can be explained by a diversification motive. This idea stems from the empirical evidence of the existence of long-term exposures that cannot be explained by a liquidity motive (maturity or currency mismatch). We model endogenous interconnections of heterogenous financial institutions facing regulatory constraints using a maximization of their expected utility. Both theoretical and simulation-based results are compared to a stylized genuine financial network. The diversification motive appears to plausibly explain interconnections among key players. Using our model, the impact of regulation on interconnections between banks -currently discussed at the Basel Committee on Banking Supervision- is analyzed.

q-fin.RM