Intersite Dependence Research Articles

A Hidden Climate Indices Modeling Framework for Multivariable Space‐Time Data

AbstractRisk assessment for climate‐sensitive systems often relies on the analysis of several variables measured at many sites. In probabilistic terms, the task is to model the joint distribution of several spatially distributed variables, and how it varies in time. This paper describes a Bayesian hierarchical framework for this purpose. Each variable follows a distribution with parameters varying in both space and time. Temporal variability is modeled by means of hidden climate indices (HCIs) that are extracted from observed variables. This is to be contrasted with the usual approach using predefined standard climate indices (SCIs) for this purpose. In the second level of the model, the HCIs and their effects are assumed to follow temporal and spatial Gaussian processes, respectively. Both intervariable and intersite dependencies are induced by the strong effect of common HCIs. The flexibility of the framework is illustrated with a case study in Southeast Australia aimed at modeling “hot‐and‐dry” summer conditions. It involves three physical variables (streamflow, precipitation, and temperature) measured on three distinct station networks, with varying data availability and representing hundreds of sites in total. The HCI model delivers reliable and sharp time‐varying distributions for individual variables and sites. In addition, it adequately reproduces intervariable and intersite dependencies, whereas a corresponding SCI model (where hidden climate indices are replaced with standard ones) strongly underestimates them. It is finally suggested that HCI models may be used as downscaling tools to estimate the joint distribution of several variables at many stations from climate models or reanalyzes.

Adjusting spatial dependence of climate model outputs with cycle-consistent adversarial networks

Climate model outputs are commonly corrected using statistical univariate bias correction methods. Most of the time, those 1d-corrections do not modify the ranks of the time series to be corrected. This implies that biases in the spatial or inter-variable dependences of the simulated variables are not adjusted. Hence, over the last few years, some multivariate bias correction (MBC) methods have been developed to account for inter-variable structures, inter-site ones, or both. As proof-of-concept, we propose to adapt a computer vision technique used for Image-to-Image translation tasks (CycleGAN) for the adjustment of spatial dependence structures of climate model projections. The proposed algorithm, named MBC-CycleGAN, aims to transfer simulated maps (seen as images) with inappropriate spatial dependence structure from climate model outputs to more realistic images with spatial properties similar to the observed ones. For evaluation purposes, the method is applied to adjust maps of temperature and precipitation from climate simulations through two cross-validation approaches. The first one is designed to assess two different post-processing schemes (Perfect Prognosis and Model Output Statistics). The second one assesses the influence of nonstationary properties of climate simulations on the performance of MBC-CycleGAN to adjust spatial dependences. Results are compared against a popular univariate bias correction method, a “quantile-mapping” method, which ignores inter-site dependencies in the correction procedure, and two state-of-the-art multivariate bias correction algorithms aiming to adjust spatial correlation structure. In comparison with these alternatives, the MBC-CycleGAN algorithm reasonably corrects spatial correlations of climate simulations for both temperature and precipitation, encouraging further research on the improvement of this approach for multivariate bias correction of climate model projections.

Modelling Extreme Rainfall Using Adjusted Sandwich Estimator

The Generalized Extreme Value (GEV) distribution is often used to describe the frequency of occurrence of extreme rainfall. Modelling the extreme event using the independent Generalized Extreme Value to spatial data fails to account the behaviour of dependency data. However, the wrong statistical assumption by this marginal approach can be adjusted using sandwich estimator. In this paper, we used the conventional method of the marginal fitting of generalized extreme value distribution to the extreme rainfall then corrected the standard error to account for inter-site dependence. We also applied the penalized maximum likelihood to improve the generalized parameter estimations. A case study of annual maximum rainfall from several stations at western Sabah is studied, and the results suggest that the variances were found to be greater than the standard error in the marginal estimation as the inter-site dependence being considered. Key words: Generalized Extreme Value theory, sandwich estimator, penalized maximum likelihood, annual maximum rainfall

Space-time simulation of precipitation based on weather pattern sub-sampling and meta-Gaussian model

Simulation methods for design flood estimations in dam safety studies require fine scale precipitation data to provide quality input for hydrological models, especially for extrapolation to extreme events. This leads to use statistical models such as stochastic weather generators. The aim here is to develop a stochastic model adaptable on mountainous catchments in France and accounting for spatial and temporal dependencies in daily precipitation fields. To achieve this goal, the framework of spatial random processes is adopted here.The novelty of the model developed in this study resides in the combination of an autoregressive meta-Gaussian process accounting for the spatio-temporal dependencies and weather pattern sub-sampling discriminating the different rainfall intensity classes. The model is tested from rain gauges in the Ardèche catchment located in South of France. The model estimation is performed in four steps, dealing respectively with: (i) the at-site marginal distribution, (ii) the mapping of the marginal distribution parameters at the target resolution, (iii) the at-site temporal correlation and (iv) the spatial covariance function.The model simulations are evaluated in terms of marginal distribution, inter-site dependence and areal rainfall properties and compared to the observations at calibration stations and also on a set of independent validation stations. Regarding all these aspects, the model shows good abilities to reproduce the observed statistics and presents really small discrepancies compared to the stations data. The sub-sampling is particularly efficient to reproduce the seasonal variations and the marginal mapping procedure induces very small differences in terms of daily rain amounts and daily occurrence probabilities.

Multisite Daily Streamflow Simulation With Time Irreversibility

AbstractSynthetic daily streamflow generation requires a critical understanding of the underlying dynamics resulting from the inherent temporal asymmetry (time irreversibility) in the rising and falling limbs of the hydrograph. Most models considering the time irreversibility deal with single‐site streamflow simulation. Addressing intersite dependencies is, however, crucial for interconnected stream networks. This study presents a time irreversibility dynamics‐based multisite streamflow generating framework to simulate concurrent streamflow sequences at multiple sites in a basin. This framework explicitly takes into account the spatial correlation and time irreversible dynamics of streamflow. To demonstrate the utility and applicability, a few selected streamflow gauging stations in the Godavari River Basin, located in southern India, are considered. The proposed framework shows the ability to adequately generate multisite simulations capturing at‐site statistics as well as intersite correlations for the case study. Furthermore, the approach ensures that the simulated flow values are not merely resampled from the historical data, uses the physical features of the hydrograph, and shows variability beyond that observed in the historical sequence. Such a rich variety of streamflow sequences can help water managers to investigate how existing water resources systems on interconnected stream networks will operate in scenarios which have not been observed in the historical record.

GEMME: A Simple and Fast Global Epistatic Model Predicting Mutational Effects.

The systematic and accurate description of protein mutational landscapes is a question of utmost importance in biology, bioengineering, and medicine. Recent progress has been achieved by leveraging on the increasing wealth of genomic data and by modeling intersite dependencies within biological sequences. However, state-of-the-art methods remain time consuming. Here, we present Global Epistatic Model for predicting Mutational Effects (GEMME) (www.lcqb.upmc.fr/GEMME), an original and fast method that predicts mutational outcomes by explicitly modeling the evolutionary history of natural sequences. This allows accounting for all positions in a sequence when estimating the effect of a given mutation. GEMME uses only a few biologically meaningful and interpretable parameters. Assessed against 50 high- and low-throughput mutational experiments, it overall performs similarly or better than existing methods. It accurately predicts the mutational landscapes of a wide range of protein families, including viral ones and, more generally, of much conserved families. Given an input alignment, it generates the full mutational landscape of a protein in a matter of minutes. It is freely available as a package and a webserver at www.lcqb.upmc.fr/GEMME/.

Multivariate bias adjustment of high-dimensional climate simulations: the Rank Resampling for Distributions and Dependences (R<sup>2</sup>D<sup>2</sup>) bias correction

Abstract. Climate simulations often suffer from statistical biases with respect to observations or reanalyses. It is therefore common to correct (or adjust) those simulations before using them as inputs into impact models. However, most bias correction (BC) methods are univariate and so do not account for the statistical dependences linking the different locations and/or physical variables of interest. In addition, they are often deterministic, and stochasticity is frequently needed to investigate climate uncertainty and to add constrained randomness to climate simulations that do not possess a realistic variability. This study presents a multivariate method of rank resampling for distributions and dependences (R2D2) bias correction allowing one to adjust not only the univariate distributions but also their inter-variable and inter-site dependence structures. Moreover, the proposed R2D2 method provides some stochasticity since it can generate as many multivariate corrected outputs as the number of statistical dimensions (i.e., number of grid cell × number of climate variables) of the simulations to be corrected. It is based on an assumption of stability in time of the dependence structure – making it possible to deal with a high number of statistical dimensions – that lets the climate model drive the temporal properties and their changes in time. R2D2 is applied on temperature and precipitation reanalysis time series with respect to high-resolution reference data over the southeast of France (1506 grid cell). Bivariate, 1506-dimensional and 3012-dimensional versions of R2D2 are tested over a historical period and compared to a univariate BC. How the different BC methods behave in a climate change context is also illustrated with an application to regional climate simulations over the 2071–2100 period. The results indicate that the 1d-BC basically reproduces the climate model multivariate properties, 2d-R2D2 is only satisfying in the inter-variable context, 1506d-R2D2 strongly improves inter-site properties and 3012d-R2D2 is able to account for both. Applications of the proposed R2D2 method to various climate datasets are relevant for many impact studies. The perspectives of improvements are numerous, such as introducing stochasticity in the dependence itself, questioning its stability assumption, and accounting for temporal properties adjustment while including more physics in the adjustment procedures.

A new scheme for multivariate, multisite weather generator with inter-variable, inter-site dependence and inter-annual variability based on empirical copula approach

Weather generators (WGs) are often used to develop an ensemble of plausible climate scenarios across multiple spatial and temporal scales for vulnerability assessment and impact studies. Most of the conventional WGs are single-site models, which neglect the spatial dependence in the simulated meteorological field, are improper for regional impact studies. In recent several decades, efforts have been devoted to develop multivariate, multisite weather generators (MMWGs), which are able to reproduce the inter-variable and inter-site dependencies as well as the temporal structures observed in the historical records. Though several improvements have been achieved, the existed MMWGs are either conceptually complex or computationally expensive, and have difficulty in preserving the entire desired attributes. This study proposes a new two-stage scheme for constructing a MMWG. At the first stage, the meteorological series are simulated from a single-site multivariate weather generator (SMWG), which preserves the marginal distributional attributes for each meteorological variable. For the second stage, the inter-variable and inter-site dependencies as well as the temporal structures are reproduced using the Empirical Copula (EC) approach. An application of the proposed MMWG is presented for the Upper Thames River Catchment, Canada, and the performance is evaluated and compared with another two-stage MMWG based on the Iman shuffle approach. Results show that the proposed MMWG not only preserves the marginal distributional attributes, but also restores the inter-variable and inter-site dependencies, the temporal persistence, and the inter-annual variability almost perfectly. The performance of the proposed MMWG outperforms the one based on the Iman shuffle approach in terms of reconstruction of temporal persistence and inter-annual variability, as well as the reproduction of multivariate dependencies. Being conceptually simple and computationally inexpensive, the proposed scheme based on the EC approach is well suited for developing ensemble-based climate scenarios for vulnerability assessment and impact studies.

Homogeneity testing for skewed and cross-correlated data in regional flood frequency analysis

In regional flood frequency analysis the homogeneity of a group of stations is an essential assumption. A standard procedure in hydrology to evaluate this condition is the homogeneity measure of Hosking and Wallis, which applies L-moments. Disadvantages of it are the lack of power when analysing highly skewed data and the implicit assumption of spatial independence. To face these issues we generalize this procedure in two ways. Copulas are applied to model intersite dependence and trimmed L-moments as a more robust alternative to ordinary L-moments. The results of simulation studies are presented to discuss the influence of different copula models and different trimming parameters. The usage of asymmetrically trimmed L-moments improves the heterogeneity detection in skewed data. Simple copula models are sufficient to incorporate the dependence structure of the data in the procedure. Additionally, a more robust behaviour against extreme events at single stations is achieved with the use of trimmed L-moments. Strong intersite dependence and skewed data reveal the need of a modified procedure in a case study with data from Saxony, Germany.

The sandwich estimator approach counting for inter-site dependence of extreme river flow in Sabah

Regional estimation method is often used for estimating parameters of a distribution when data are available at many sites in a region to capture inter-site dependence. In this paper, we fit generalized extreme value distribution independently to model data of river flows at each sites in Sabah to avoid extreme value complex modeling. Since our approach violated the condition of spatial analysis, we consider the adjusted standard error to correct the wrong assumption of our marginal approach. As a result, we have an appropriate corrected variance of the generalized extreme value parameters.

Homogeneity testing for spatially correlated data in multivariate regional frequency analysis

AbstractIdentification of homogeneous regions is a key task in regional frequency analysis (RFA) to obtain adequate quantile estimates for an event of interest. Recently, the frequently used univariate Hosking‐Wallis L‐moment homogeneity test was extended to the multivariate case. Multivariate L‐moments are used as a tool to define the test statistic and copula models to describe the statistical behavior of the analyzed dependent variables. To avoid drawbacks in fitting a parametric joint distribution to the data and a rejection threshold which is based on simulations, its nonparametric alternatives were also proposed. Although the simulation studies performed demonstrated the usefulness of both the parametric and nonparametric tests, the powers obtained were valid only for regions without intersite dependence. Examples from practice nevertheless demonstrate that intersite correlation may be expected for some kinds of data. To overcome the problem of cross correlation between stations, the parametric testing procedure is generalized using D‐vine copulas to model intersite dependence when generating synthetic homogeneous regions during the testing procedure. Monte Carlo simulations were performed and illustrate how intersite dependence negatively impacts the multivariate L‐moment homogeneity tests by significantly reducing their powers. The results of simulations also demonstrate the superiority of the proposed modification over both the original parametric and nonparametric procedures inasmuch as it improves the heterogeneity detection and avoids miscategorization of a region. The modified test is also applied in a case study for meteorological data in the Czech Republic.

Combining regional estimation and historical floods: A multivariate semiparametric peaks‐over‐threshold model with censored data

AbstractThe estimation of extreme flood quantiles is challenging due to the relative scarcity of extreme data compared to typical target return periods. Several approaches have been developed over the years to face this challenge, including regional estimation and the use of historical flood data. This paper investigates the combination of both approaches using a multivariate peaks‐over‐threshold model that allows estimating altogether the intersite dependence structure and the marginal distributions at each site. The joint distribution of extremes at several sites is constructed using a semiparametric Dirichlet Mixture model. The existence of partially missing and censored observations (historical data) is accounted for within a data augmentation scheme. This model is applied to a case study involving four catchments in Southern France, for which historical data are available since 1604. The comparison of marginal estimates from four versions of the model (with or without regionalizing the shape parameter; using or ignoring historical floods) highlights significant differences in terms of return level estimates. Moreover, the availability of historical data on several nearby catchments allows investigating the asymptotic dependence properties of extreme floods. Catchments display a significant amount of asymptotic dependence, calling for adapted multivariate statistical models.

Spatio-temporal characteristics of the extreme precipitation by L-moment-based index-flood method in the Yangtze River Delta region, China

The regionalization methods, which “trade space for time” by pooling information from different locations in the frequency analysis, are efficient tools to enhance the reliability of extreme quantile estimates. This paper aims at improving the understanding of the regional frequency of extreme precipitation by using regionalization methods, and providing scientific background and practical assistance in formulating the regional development strategies for water resources management in one of the most developed and flood-prone regions in China, the Yangtze River Delta (YRD) region. To achieve the main goals, L-moment-based index-flood (LMIF) method, one of the most popular regionalization methods, is used in the regional frequency analysis of extreme precipitation with special attention paid to inter-site dependence and its influence on the accuracy of quantile estimates, which has not been considered by most of the studies using LMIF method. Extensive data screening of stationarity, serial dependence, and inter-site dependence was carried out first. The entire YRD region was then categorized into four homogeneous regions through cluster analysis and homogenous analysis. Based on goodness-of-fit statistic and L-moment ratio diagrams, generalized extreme-value (GEV) and generalized normal (GNO) distributions were identified as the best fitted distributions for most of the sub-regions, and estimated quantiles for each region were obtained. Monte Carlo simulation was used to evaluate the accuracy of the quantile estimates taking inter-site dependence into consideration. The results showed that the root-mean-square errors (RMSEs) were bigger and the 90 % error bounds were wider with inter-site dependence than those without inter-site dependence for both the regional growth curve and quantile curve. The spatial patterns of extreme precipitation with a return period of 100 years were finally obtained which indicated that there are two regions with highest precipitation extremes and a large region with low precipitation extremes. However, the regions with low precipitation extremes are the most developed and densely populated regions of the country, and floods will cause great loss of human life and property damage due to the high vulnerability. The study methods and procedure demonstrated in this paper will provide useful reference for frequency analysis of precipitation extremes in large regions, and the findings of the paper will be beneficial in flood control and management in the study area.

Incorporating spatial dependence in regional frequency analysis.

The efficiency of regional frequency analysis (RFA) is undermined by intersite dependence, which is usually ignored in parameter estimation. We propose a spatial index flood model where marginal generalized extreme value distributions are joined by an extreme-value copula characterized by a max-stable process for the spatial dependence. The parameters are estimated with a pairwise likelihood constructed from bivariate marginal generalized extreme value distributions. The estimators of model parameters and return levels can be more efficient than those from the traditional index flood model when the max-stable process fits the intersite dependence well. Through simulation, we compared the pairwise likelihood method with an L-moment method and an independence likelihood method under various spatial dependence models and dependence levels. The pairwise likelihood method was found to be the most efficient in mean squared error if the dependence model was correctly specified. When the dependence model was misspecified within the max-stable models, the pairwise likelihood method was still competitive relative to the other two methods. When the dependence model was not a max-stable model, the pairwise likelihood method led to serious bias in estimating the shape parameter and return levels, especially when the dependence was strong. In an illustration with annual maximum precipitation data from Switzerland, the pairwise likelihood method yielded remarkable reduction in the standard errors of return level estimates in comparison to the L-moment method.

Modeling intersite dependence for regional frequency analysis of extreme marine events

AbstractThe duration of observation at a site of interest is generally too low to reliably estimate marine extremes. Regional frequency analysis (RFA), by exploiting the similarity between sites, can help to reduce uncertainties inherent to local analyses. Extreme observations in a homogeneous region are especially assumed to follow a common regional distribution, up to a local index. The regional pooling method, by gathering observations from different sites into a regional sample, can be employed to estimate the regional distribution. However, such a procedure may be highly affected by intersite dependence in the regional sample. This paper derives a theoretical model of intersite dependence, dedicated to the regional pooling method in a “peaks over threshold” framework. This model expresses the tendency of sites to display a similar behavior during a storm generating extreme observations, by describing both the storm propagation in the region and the storm intensity. The proposed model allows the assessment of (i) the regional effective duration of the regional sample and (ii) different regional hazards, e.g., return periods of storms. An application to the estimation of extreme significant wave heights from the numerical sea‐state database ANEMOC‐2 is provided, where different patterns of regional dependence are highlighted.

Diagnostics for tail dependence in time-lagged random fields of precipitation

Weather extremes often occur along fronts passing different sites with some time lag. Here, we show how such temporal patterns can be taken into account when exploring inter-site dependence of extr ...

Spatial regression models for extreme precipitation in Belgium

Quantification of precipitation extremes is important for flood planning purposes, and a common measure of extreme events is the T year return level. Extreme precipitation depths in Belgium are analyzed for accumulation durations ranging from 10 min to 30 days. Spatial generalized extreme value (GEV) models are presented by considering multisite data and relating GEV parameters to geographical/climatological covariates through a common regression relationship. Methods of combining data from several sites are in common use, and in such cases, there is likely to be nonnegligible intersite dependence. However, parameter estimation in GEV models is generally done with the maximum likelihood estimation method (MLE) that assumes independence. Estimates of uncertainty are adjusted for spatial dependence using methodologies proposed earlier. Consistency of GEV distributions for various durations is obtained by fitting a smooth function to the preliminary estimations of the shape parameter. Model quality has been assessed by various statistical tests and indicates the relevance of our approach. In addition, a methodology is applied to account for the fact that measurements have been made in fixed intervals (usually 09:00 UTC–09:00 UTC). The distribution of the annual sliding 24 h maxima was specified through extremal indices of a more than 110 year time series of 24 h aggregated 10 min rainfall and daily rainfall. Finally, the selected models are used for producing maps of precipitation return levels.

Effects of intersite dependence of nested catchment structures on probabilistic regional envelope curves

Abstract. This study analyses the intersite dependence of nested catchment structures by modelling cross-correlations for pairs of nested and unnested catchments separately. Probabilistic regional envelope curves are utilised to derive regional flood quantiles for 89 catchments located in Saxony, in the Southeast of Germany. The study area has a nested structure and the intersite correlation is much stronger for nested pairs of catchments than for unnested ones. Pooling groups of sites (regions) are constructed based on several candidate sets of catchment descriptors using the Region of Influence method. Probabilistic regional envelope curves are derived on the basis of flood flows observed within the pooling groups. Their estimated recurrence intervals are based on the number of effective sample years of data (i.e. equivalent number of uncorrelated data). The evaluation of the effective sample years of data requires the modelling of intersite dependence. We perform this globally, using a cross-correlation function for the whole study area as well as by using two different cross-correlation functions, one for nested pairs and another for unnested pairs. In the majority of the cases, these two modelling approaches yield significantly different estimates for the effective sample years of data, and therefore also for the recurrence intervals. The reduction of the recurrence interval when using two different cross-correlation functions is larger for larger pooling groups and for pooling groups with a higher fraction of nested catchments. A separation into nested and unnested pairs of catchments gives a more realistic representation of the characteristic river network structure and improves the estimation of regional information content. Hence, applying two different cross-correlation functions is recommended.

Monte Carlo 모의를 이용한 지점 간 확률가중모멘트의 교차상관관계

본 연구에서는 지점 간 확률가중모멘트의 교차상관관계를 구하기 위해 Monte Carlo 모의를 이용하여 이를 지점간 표본자료의 교차상관성에 대한 관계식으로 확장하여 근사값을 구하고자 하였다. 모의실험 결과 각각의 확률가중 모멘트간 교차상관계수는 지점 간 표본자료의 교차상관계수와 자료크기가 동일하고 동시간 자료일 경우 기울기 1인 선형관계를 보이며, 자료크기에 따른 동시간 자료의 비율이 작아질수록 선형적인 관계는 점점 약해지게 된다. 따라서 자료크기에 따른 영향을 고려하기 위하여 보정항을 추가한 제곱함수식을 제시하였으며, 이 식에 발생된 자료를 적합시켜 각각의 경우에 따른 매개변수를 추정하였다. 이 결과를 이용하여 지역빈도해석의 지점 간 교차 상관성을 고려한 수문추정량의 분산 추정 등의 연구에 이용될 수 있을 것으로 기대된다. In this study, cross correlations among sample data at each site are calculated to obtain the asymptotic cross correlations among probability weighted moments at each site using Monte Carlo simulation. As a result, the relations between the asymptotic cross correlations among probability weighted moments and the inter-site dependence among sample data at each site are nearly a linear relation with slope 1. The smaller ratio of concurrent data size to entire sample size is, the weaker the relationship grows. Simple power function which the correction term in power function accounts for the differences of the sample size between two sites was fitted to each case to estimate the parameter. It is noted that this result can be used in the various researches which include the estimation of the variance of quantile considering cross correlations.

Analysis of inter-gauge dependence by Kendall’s τK, upper tail dependence coefficient, and 2-copulas with application to rainfall fields

The spatial dependence of rainfall is usually studied considering pairs of rain gauges and analysing the behaviour of Pearson’s correlation coefficient with respect to the distance between the two devices. However, this measure of linear dependence involves the underlying hypothesis that the data follow a bivariate normal distribution. When the data are skewed, as in the case of rainfall, a preliminary transformation is often performed in an attempt to obtain the required bivariate normality. This approach does not always guarantee satisfactory results, resulting in correlation estimator that exhibits bias and high variance. In this work, the inter-gauge dependence is studied by applying the alternative non-parametric Kendall’s rank correlation coefficient and the upper tail dependence coefficient. Exploiting the link between these two indices with copulas allows building an exploratory graphical method useful to drive the definition of a regional 2-copula suitable for the description of the data. Then, this copula is used to generalize the Shimizu’s bivariate mixed model, providing some freedom in the choice of the dependence structure and marginals. The analysis is performed on seven years of rainfall observations with 30-min time resolution collected by 35 gauges located in Central Italy. The effect of zero-measurements and several aggregation time scales are considered as well. Results of this study support some conclusions previously appeared in literature; mainly that only positive contemporaneous pairs of rainfall observations correctly describe the inter-site dependence.