Nonstationary Changes Research Articles

Meta-Reinforcement Learning in Nonstationary and Nonparametric Environments.

Recent state-of-the-art artificial agents lack the ability to adapt rapidly to new tasks, as they are trained exclusively for specific objectives and require massive amounts of interaction to learn new skills. Meta-reinforcement learning (meta-RL) addresses this challenge by leveraging knowledge learned from training tasks to perform well in previously unseen tasks. However, current meta-RL approaches limit themselves to narrow parametric and stationary task distributions, ignoring qualitative differences and nonstationary changes between tasks that occur in the real world. In this article, we introduce a Task-Inference-based meta-RL algorithm using explicitly parameterized Gaussian variational autoencoders (VAEs) and gated Recurrent units (TIGR), designed for nonparametric and nonstationary environments. We employ a generative model involving a VAE to capture the multimodality of the tasks. We decouple the policy training from the task-inference learning and efficiently train the inference mechanism on the basis of an unsupervised reconstruction objective. We establish a zero-shot adaptation procedure to enable the agent to adapt to nonstationary task changes. We provide a benchmark with qualitatively distinct tasks based on the half-cheetah environment and demonstrate the superior performance of TIGR compared with state-of-the-art meta-RL approaches in terms of sample efficiency (three to ten times faster), asymptotic performance, and applicability in nonparametric and nonstationary environments with zero-shot adaptation. Videos can be viewed at https://videoviewsite.wixsite.com/tigr.

Monitoring and warning for ammonia nitrogen pollution of urban river based on neural network algorithms.

Ammonia nitrogen (AN) pollution frequently occurs in urban rivers with the continuous acceleration of industrialization. Monitoring AN pollution levels and tracing its complex sources often require large-scale testing, which are time-consuming and costly. Due to the lack of reliable data samples, there were few studies investigating the feasibility of water quality prediction of AN concentration with a high fluctuation and non-stationary change through data-driven models. In this study, four deep-learning models based on neural network algorithms including artificial neural network (ANN), recurrent neural network (RNN), long short-term memory (LSTM), and gated recurrent unit (GRU) were employed to predict AN concentration through some easily monitored indicators such as pH, dissolved oxygen, and conductivity, in a real AN-polluted river. The results showed that the GRU model achieved optimal prediction performance with a mean absolute error (MAE) of 0.349 and coefficient of determination (R2) of 0.792. Furthermore, it was found that data preprocessing by the VMD technique improved the prediction accuracy of the GRU model, resulting in an R2 value of 0.822. The prediction model effectively detected and warned against abnormal AN pollution (> 2mg/L), with a Recall rate of 93.6% and Precision rate of 72.4%. This data-driven method enables reliable monitoring of AN concentration with high-frequency fluctuations and has potential applications for urban river pollution management.

Hydroformer: Frequency Domain Enhanced Multi‐Attention Transformer for Monthly Lake Level Reconstruction With Low Data Input Requirements

AbstractLake level changes are critical indicators of hydrological balance and climate change, yet long‐term monthly lake level reconstruction is challenging with incomplete or short‐term data. Data‐driven models, while promising, struggle with nonstationary lake level changes and complex dependencies on meteorological factors, limiting their applicability. Here, we introduce the Hydroformer, a frequency domain enhanced multi‐attention Transformer model designed for monthly lake level reconstruction, utilizing reanalysis data. This model features two innovative mechanisms: (a) Frequency‐Enhanced Attention (FEA) for capturing long‐term temporal dependence, and (b) Causality‐based Cross‐dimensional Attention (CCA) to elucidate how specific meteorological factors influence lake level. Seasonal and trend patterns of catchment meteorological factors and lake level are initially identified by a time series decomposition block, then independently learned and refined within the model. Tested across 50 lakes globally, the Hydroformer excelled in reconstruction periods ranging from half to three times the training‐test length. The model exhibited good performance even when training data missing rates were below 50%, particularly in lakes with significant seasonal fluctuations. The Hydroformer demonstrated robust generalization across lakes of varying sizes, from 10.11 to 18,135 km2, with median values for R2, MAE, MSE, and RMSE at 0.813, 0.313, 0.215, and 0.4, respectively. Furthermore, the Hydroformer outperformed data‐driven models, improving MSE by 29.2% and MAE by 24.4% compared to the next best model, the FEDformer. Our method proposes a novel approach for reconstructing long‐term water level changes and managing lake resources under climate change.

Integrating remotely sensed imagery in a forest gap model to study North American boreal forests in a changing world

Abstract Boreal forests of Alaska and Western Canada are experiencing rapid climate change characterized by higher temperatures, more extreme droughts, and changing disturbance regimes, resulting in forest mortality and composition changes. Mechanistic models are increasingly important for predicting future forest trends as the region experiences novel environmental change. Previously, many process-based models have generated starting conditions by ‘spinning up’ to equilibrium. However, setting appropriate initial conditions remains a persistent challenge in using mechanistic forest models, where stochastic events and latent parameters governing tree establishment have long-lasting impacts on simulation outcomes. Recent advances in remote sensing analysis provide information that can help address this issue. We updated an individual-based gap model, the University of Virginia Forest Model Enhanced (UVAFME), to include initial conditions derived from aerial and satellite imagery at two locations. Following these updates, material legacies (e.g., trees, seed banks, soil organic layer) allowed new forest types to persist in UVAFME simulations, landscape-level forest heterogeneity increased, and forest-wide biomass estimates increased. At both study sites, initialization from remotely sensed data had a strong impact on forest cover and volume. Climate change impacts were simulated decades earlier than when the model was ‘spun up'. In Alaska’s Tanana Valley State Forest, warmer climate scenarios drove deciduous expansion, increased drought stress, and resulted in a 28% decrease in overall biomass by 2100 between historical and high emissions climate scenarios. At a lowland site in Northern British Columbia, lodgepole pine (Pinus contorta) remained dominant and became more productive with exogenous climate forcing as temperature, nutrient, and flooding limitations decreased. These case studies demonstrate a new framework for forest modeling and emphasize the advantages of integrating remotely sensed data with mechanistic models, thereby laying groundwork for future research that explores near-term impacts of non-stationary ecological change.

Fundamental Frequency Extraction by Utilizing Accumulated Power Spectrum based Weighted Autocorrelation Function in Noisy Speech

This research suggests an efficient idea that is better suited for speech processing applications for retrieving the accurate pitch from speech signal in noisy conditions. For this objective, we present a fundamental frequency extraction algorithm and that is tolerant to the non-stationary changes of the amplitude and frequency of the input signal. Moreover, we use an accumulated power spectrum instead of power spectrum, which uses the shorter sub-frames of the input signal to reduce the noise characteristics of the speech signals. To increase the accuracy of the fundamental frequency extraction we have concentrated on maintaining the speech harmonics in their original state and suppressing the noise elements involved in the noisy speech signal. The two stages that make up the suggested fundamental frequency extraction approach are producing the accumulated power spectrum of the speech signal and weighting it with the average magnitude difference function. As per the experiment results, the proposed technique appears to be better in noisy situations than other existing state-of-the-art methods such as Weighted Autocorrelation Function (WAF), PEFAC, and BaNa.

Evaluation of the sensitivity of meteorological drought in the Mediterranean region to different data record lengths.

The division and evaluation of data series used in monitoring drought into different time intervals is a practical approach to detecting the spatial and temporal extent of drought spread. This study aimed to determine meteorological drought's spatial and temporal distribution using overlapping and consecutive periods and cycles of the standardized precipitation index (SPI) time series in the Mediterranean region, Turkey. In the scope of the research, SPI values for the SPI12, SPI6 (1), and SPI6 (2) seasons were calculated for consecutive and overlapping hydrological years (1978-1998/21years, 1978-2008/31years, and 1978-2018/41years) at 28 meteorological stations. Autocorrelation, Mann-Kendall, and Sen slope trend tests were applied at a 5% significance level for each season (SPI12, SPI6 (1), and SPI6 (2)) and different time scales (21, 31, and 41years). For each season and period, maps of the SPI drought class, average formation of drought class, Mann-Kendall (MK) trend, and Sen's slope (SS) trend test statistics for the Mediterranean region were obtained, and the spatial distribution rate of trends was determined by drawing hypsometric curves. Changes in drought occurrence at different time scales were thoroughly evaluated with the changing length of data recording.Consequently, it was determined that the mild wet (MIW) and mild drought (MID) classes dominate the study area in the Mediterranean region. Significant and nonstationary changes detected in extreme wet and drought occurrences (extreme wet, EW; severe wet, SW; extreme drought, ED; severe drought, SD) were found to pose a risk in the study area. It was observed that there were spatially and temporally insignificant decreasing drought trends in the Mediterranean basin, considering that the time scales of these trends slowed down. Despite a nonsignificant trend from the MID drought class to the MIW drought class, it is predicted that the MIW and MID classes will maintain their dominance in the Mediterranean region. The central part of the study area (central Mediterranean basin) is the region with the highest drought risk.

Nonstationary Changes in Annual Rainfall over Indonesia’s Maritime Continent

The investigation into changing rainfall patterns in the Indonesian Maritime Continent (IMC) involved testing for trends, step changes, and variance nonstationarity using the Mann–Kendall, Pettitt, and White tests, respectively. The analysis covered data from 106 meteorological stations over the period from 1981 to 2021, with all tests conducted at annual time scales to understand the evolving precipitation dynamics in the region. According to the findings of this study, the average annual rainfall in IMC is nonstationary. Rainfall has increased dramatically by 12.72 mm with a significant shift point in 1994. However, this characteristic is likely to vary if the analysis period is extended, reduced, or conducted in different time frames. The spatial analysis indicates that 35.8% of meteorological stations observed a notable increase in rainfall, while 28.3% experienced a significant shift, and 16% displayed considerable variation. Consequently, the study only partially identified the nonstationary nature of rainfall in the IMC. Moreover, the research highlights a substantial rise in rainfall in the central to eastern IMC region, whereas the central to western region predominantly shows a decrease. This nonstationary test helps avoid errors in climatic conditions and analytical methods, presenting recommendations for hydrological projects. Consequently, employing this nonstationary test helps prevent inaccuracies in understanding climatic conditions and analytical techniques, thereby offering valuable suggestions for hydrological projects.

Assessing decadal- to centennial-scale nonstationary variability in meteorological drought trends

Abstract. There are indications that the reference climatology underlying meteorological drought has shown nonstationarity at seasonal, decadal, and centennial timescales, impacting the calculation of drought indices and potentially having ecological and economic consequences. Analyzing these trends in meteorological drought climatology beyond 100 years, a time frame which exceeds the available period of observation data, contributes to a better understanding of the nonstationary changes, ultimately determining whether they are within the range of natural variability or outside this range. To accomplish this, our study introduces a novel approach to integrate unevenly scaled tree-ring proxy data from the North American Seasonal Precipitation Atlas (NASPA) with instrumental precipitation datasets by first temporally downscaling the proxy data to produce a regular time series and then modeling climate nonstationarity while simultaneously correcting model-induced bias. This new modeling approach was applied to 14 sites across the continental United States using the 3-month standardized precipitation index (SPI) as a basis. The findings showed that certain locations have experienced recent rapid shifts towards drier or wetter conditions during the instrumental period compared to the past 1000 years, with drying trends generally found in the west and wetting trends in the east. This study also found that seasonal shifts have occurred in some regions recently, with seasonality changes most notable for southern gauges. We expect that our new approach provides a foundation for incorporating various datasets to examine nonstationary variability in long-term precipitation climatology and to confirm the spatial patterns noted here in greater detail.

An online fuzzy fraud detection framework for credit card transactions

Credit card transaction fraud is one of the challenging security concerns for financial firms globally. The continuously changing environment of fraud characteristics and the class imbalance and complete separation issues in fraud data create difficulties in accurately and efficiently predicting fraudulent transactions and implementing fraud detection systems in real-time. The study aims to develop a new real-time fraud detection framework that can efficiently be implemented online and address the issues caused by non-stationary changes in transaction and fraud characteristics, class imbalance, and complete separation. We propose a new approach to handle the impact of non-stationary changes in fraud transaction patterns. It enables efficiency in model training, given the sheer size of datasets. By implementing a robust fuzzy logistic regression model against class imbalance and separation problems, we address the challenge of having a very low rate of fraudulent transactions in the dataset and having separation issues due to specific characteristics of transactions. The analysis of the performance versus efficiency nexus of the proposed methodology reveals that the proposed framework shows strong performance results with specificity and sensitivity greater than 0.90 and Matthew’s correlation coefficient greater than 0.80 even on small sample sizes and produces highly accurate results in identifying fraudulent and non-fraudulent transactions with an accuracy greater than 0.99. Benchmarking with machine learning and other fraud detection approaches reveals that the proposed framework provides better detection performance while maintaining a higher rate of identifying non-fraudulent transactions than the alternative approaches. Improved classification performance leads to detecting fraudulent transactions with higher precision while avoiding misclassifying legitimate transfers, resulting in lower financial losses and improved customer satisfaction.

LRFD methodology for river embankments against non-stationary flooding under climate change

Riverine floods have become increasingly prevalent on a global scale, posing significant risks to infrastructure systems and communities. The escalating impacts of climate change associated with the increase in rainfall intensities and frequencies necessitate the improvement of the existing design methodologies to account for the non-stationary climate change effects to ensure that the reliability is above the target level and mitigate future flood disasters. This paper presents a novel LRFD approach for river embankments subjected to extreme rainfall under non-stationary climate change effects. This approach introduces an additional partial factor to account for the effects of climate change. Precipitation and temperature projections are collected from various climate models considering several cases of emission scenarios. An integrated hydrological and hydraulic modeling of the analyzed river is carried out to estimate the associated time-variant river discharge and water surface elevation. The non-stationary extreme value associated with the maximum flood level is leveraged using the peak-over-threshold approach. The embankment reliability and the corresponding most probable points are evaluated using limit states associated with overtopping and slope failures. Based on the estimated and target reliability indexes, the design point for each random variable is assessed considering the cases with and without climate change effects. Finally, the partial factors associated with climate change effects are determined. As an illustrative example, the proposed framework is applied to the Ashida River in Fukuyama city of Japan.

Statistical Analysis and Scenario Modeling of Non-Stationary Runoff Change in the Loess Plateau: A Novel Application of the Generalized Additive Model in Location, Scale and Shape

The hydrological series in the Loess Plateau region has exhibited shifts in trend, mean, and/or variance as the environmental conditions have changed, indicating a departure from the assumption of stationarity. As the variations accumulate, the compound effects caused by the driving variables on runoff variations grow complex and interactive, posing a substantial risk to water security and the promotion of high-quality development in regions or river basins. This study focuses on the Tuwei River Basin in the Loess Plateau, which experiences significant changes in vegetation coverage and minimal human disturbance, and examines the cross-driving relationship between the runoff change and its driving variables (including hydrometeorological and environmental variables). A quantitative statistical analysis method based on the GAMLSS is then developed to estimate the interacting effects of changes in the driving variables and their contribution to runoff changes. Finally, various anticipated scenarios are used to simulate the changes in driving variables and runoff disturbances. The findings indicate the following: (1) The developed GU, LO, and NO distribution-based GAMLSSs provide a notable advantage in effectively capturing the variations in groundwater storage variables, actual evapotranspiration, and underlying surface parameters, as well as accurately estimating the impacts of other relevant variables. (2) The precipitation and groundwater storage variables showed predominantly positive contributions to the runoff change, but actual evapotranspiration had an adverse effect. The changes in underlying surface parameters, particularly since 2000, increase actual evapotranspiration, while decreasing groundwater storage, resulting in a progressive decrease in runoff as their contribution grows. (3) The scenario simulation results reveal that alterations to the underlying surface have a substantial influence on the evolution of runoff in the Tuwei River Basin. Additionally, there are cross-effects between the impact of various driving variables on runoff, potentially compounding the complexity of inconsistent changes in runoff sequences.

Observed trends in timing and severity of streamflow droughts across global tropics

Drought is a recurrent climatic hazard impacting natural and built environmental systems, including human lives. Although several studies have assessed streamflow droughts and their multivariate characterization, very few studies have focused on understanding spatiotemporal changes in drought attributes, such as drought seasonality, severity and duration across global tropics. Further, the nonlinear response between onset time and severity of streamflow droughts at a large scale are unknown. Leveraging ground-based streamflow observations, this study for the first time investigate changes in streamflow drought characteristics across global tropics using two 30 year climate normal periods: 1961–1990 and 1991–2020. Our analyses of changes in probability distributions of onset time and severity (deficit volume) of streamflow droughts over the two time windows show significant shifts towards higher values for Northeast and South American Monsoon region, Western Africa, eastern South Africa, north and eastern Australia. Around 55% of the sites show an increase in drought frequency in recent times. We found that in the recent times, only 27% of sites depict an increase in deficit volume accompanied by delayed onset. Further, we identify a few regional hotspots, such as Northeast and South American monsoon region, and eastern coast of Australia show an increased frequency of droughts with an upward trend in deficit volume in recent years. As expected, the individual changes in drought attributes have translated into changes in joint occurrences of their interdependent attributes, assuming the correlation between onset time and deficit volume. Our analyses show robust dependence strengths between onset time and deficit volume, which strengthen further in the recent time window over 50% of catchments. The nonstationary changes identified here in individual drought attributes and their joint dependence can alter the hazard potential of extreme droughts, which has consequences in risk management, climate adaptation and water resources planning.

ОБНАРУЖЕНИЕ РАЗЛАДОК В НЕСТАЦИОНАРНЫХ РЯДАХ НАБЛЮДЕНИЙ: ОБЗОР ТЕХНОЛОГИЙ И КРИТИЧЕСКИЙ АНАЛИЗ

A critical analysis of modern mathematical technologies used to solve the problem of nonstationary time series change point, taking into account the chaotic nature of the observed processes, is considered. The known methods of the quickest change point detection in nonstationary time series described by traditional models of random processes are considered as initial assumptions. The discrepancy between the known time series observation models and the real processes occurring in unstable immersion environments described by the concept of stochastic chaos is shown. Time series segmentation technologies based on a posteriori analysis of changes in the properties of observation sites of chaotic processes are presented. Options for building online algorithms for the quickest change point detection based on methods of multiregressive data analysis and metric machine learning technologies are considered.

Changing processes flooding a salt marsh in a microtidal estuary with a drying climate

Estuarine salt marshes globally face numerous threats, not least of which include changing hydrological conditions from human alteration and climate change impact to river flows, sea levels and coastal processes. While changing inundation is evident in many systems, often, the detail of which estuarine processes are changing and to what extent they contribute to flooding and habitat distribution remains unknown. Water levels in the microtidal Swan River Estuary (Derbarl Yerrigan), Western Australia, which has experienced significant climate drying since the 1970's, were disaggregated to assess contributions from tides, mean sea level, barometric effects, river flows and river-tide interactions. These contributions were mapped to the habitat of a salt marsh community. The effect of declining river flows on tides were further assessed by wavelet and harmonic analyses. We found that tides and barometric effects presently dominate flooding events of relevance to the salt marsh community. Declining winter runoff resulted in an increase in the tidal amplitude in the upper estuary. There was also a positive winter mean sea level pressure trend, associated with the winter rainfall decline. Altogether, there was zero net change to flooding of a salt marsh in the estuary from these processes. Therefore, steady sea level rise masked changes in the relative contribution of flooding mechanisms in the estuary which have implications for the stability of the marsh ecosystem. Disaggregating process contributions to salt marsh water levels offers a means to better assess the hydrodynamic processes presently sustaining salt marsh communities and to inform how they might change in the future. These results show that numerous hydrological processes can interact to mask non-stationary changes to estuarine hydrology supporting salt marsh habitat.

A Time Series Decomposition and Reinforcement Learning Ensemble Method for Short-Term Passenger Flow Prediction in Urban Rail Transit

Short-term passenger flow prediction (STPFP) helps ease traffic congestion and optimize the allocation of rail transit resources. However, the nonlinear and nonstationary nature of passenger flow time series challenges STPFP. To address this issue, a hybrid model based on time series decomposition and reinforcement learning ensemble strategies is proposed. Firstly, the improved arithmetic optimization algorithm is constructed by adding sine chaotic mapping, a new dynamic boundary strategy, and adaptive T distribution mutations for optimizing variational mode decomposition (VMD) parameters. Then, the original passenger flow data containing nonlinear and nonstationary irregular changes of noise is decomposed into several intrinsic mode functions (IMFs) by using the optimized VMD technology, which reduces the time-varying complexity of passenger flow time series and improves predictability. Meanwhile, the IMFs are divided into different frequency series by fluctuation-based dispersion entropy, and diverse models are utilized to predict different frequency series. Finally, to avoid the cumulative error caused by the direct superposition of each IMF’s prediction result, reinforcement learning is adopted to ensemble the multiple models to acquire the multistep passenger flow prediction result. Experiments on four subway station passenger flow datasets proved that the prediction performance of the proposed method was better than all benchmark models. The excellent prediction effect of the proposed model has important guiding significance for evaluating the operation status of urban rail transit systems and improving the level of passenger service.

Economically optimal hydropower development with uncertain climate change

Climate change affects the planning, construction, operation and management of hydropower plants in various ways. Evaluating hydropower generation with nonstationary climate changes is important for planning electric power infrastructure development. For a new hydropower plant with climate change, specifying too large a reservoir may result in excessive investment if the future becomes drier, while too small a reservoir may cause insufficient utilization of hydropower resources. Whether to build a new hydropower station at once or build it dynamically in stages over time is challenged by uncertainty in future conditions. This study proposes a planning method for developing a flexible hydropower construction schedule to adapt to long-term uncertain hydrology with climate changes. Projected uncertain nonstationary hydrology scenarios were developed first, and Bayes’ theorem is used to update the probability of each scenario based on observed hydrologic conditions over time. A profit maximization model integrates stochastic dynamic programming and linear programming for a cascade hydropower system to evaluate hydropower plant expansion and how to build it dynamically with uncertain nonstationary climate conditions. In this, stochastic dynamic programming evaluates and prescribes inter-stage reservoir upgrades and linear programming prescribes inner-stage hydroelectric power generation. The case study of Jinsha cascade hydropower system in China’s Yunnan province illustrates the method. The intensity and trend of climate change effects on streamflow directly affect the optimized results. If streamflow decreases in the future, the best strategy is to build a small reservoir initially, without future changes. If streamflow increases in the future, it is better to build a small reservoir first, and gradually increase capacity according to observed changes in streamflow and economies of scale in capacity construction. If there is no clear trend in streamflow change, it is also better to build a small reservoir at first, then decide whether to expand the reservoir according to future observed changes in streamflow. This method with uncertain nonstationary climate change and upgrading adaptively with observed hydrology usually produced better results than optimization for a deterministic nonstationary hydrology.

A new transfer entropy approach based on information granulation and clustering for root cause analysis

In complex industrial facilities, a fault may generate in a unit and easily propagate to other units, resulting in degraded performance of process operations and deteriorating the situation. Therefore, it is of great importance to trace the propagation of faults and locate the root causes. The non-parametric causality inference technique known as Transfer Entropy (TE) is successful in identifying cause–effect relations for both nonlinear and linear processes. Even though, TE has two drawbacks limiting its practical use in real industries: (1) It requires the studied process be stationary whereas the presence of faults may lead to nonstationary changes; (2) The computational complexity of TE is high while the real application could be sensitive to the computational cost. Motivated by these issues, this paper proposes a new transfer entropy approach based on the information granulation and clustering to identify the root causes of faults. The contributions of the proposed approach are twofold: (1) the Information Granulation based Transfer Entropy (IGTE) and Information Granulation based Direct Transfer Entropy (IGDTE) are proposed to infer causal and direct causal relations; (2) an Ordering Points To Identify the Clustering Structure (OPTICS) clustering based Probability Density Function (PDF) estimator is designed to estimate joint/conditional probabilities based on the information granule. Two case studies are used to illustrate the effectiveness of the proposed approach.

Nonstationary time series change direction forecast method using improved leading indicator

AbstractThis paper presents a method for forecasting the change direction of nonstationary time series using the improved leading indicator. The leading indicator is a method developed by Ehlers that translates a time series mathematically in the future direction with respect to the time axis and calculates the leading value of the time series. However, this method has the problem that the leading value can be calculated only in the low frequency region with a normalized frequency of 0.06 or more (normalized period of 17 or more) at the maximum. In order to solve this problem, by the gentle slope the amplitude characteristics in the low frequency region of the leading indicator, it is possible to calculate the leading value in the frequency domain with a normalized frequency of 0.25 or more (normalized period of four or more) at the maximum. By applying the preceding value to the instantaneous periodic time series by the improved sine wave indicator developed by Ehlers, it is possible to forecast the change direction of the non‐stationary time series in the short term.

Accounting for seasonality in the metastatistical extreme value distribution

The typical approach to account for non-stationarity in the generalized extreme value distribution (GEV) is to model the temporal behavior of the GEV parameters, e.g.,with linear relationships between the parameters and e.g.,the year. When in addition, seasonality, i.e., sub-yearly patterns are of interest, this relationship needs to be more complex. A natural candidate for nonstationary analysis of precipitation extremes is the metastatistical extreme value distribution (MEVD) assuming the ordinary rainfall events being Weibull distributed. It uses all ordinary events of the underlying rainfall distribution and implicitly considers temporal nonstationary changes in the Weibull parameters by a blockwise estimation. However, the MEVD still does not make use of the sub-yearly evolution of the distribution parameters and thus discards a significant part of information. In this paper a modification of the MEVD is proposed. The temporal MEVD (TMEV) relaxes the assumption of constant coefficients of the underlying distribution. The MEVD in each block estimates the Weibull parameters using the number of wet events in that block, regardless whether an individual wet day contributes much or less to the yearly rainfall sum. The newly proposed TMEV weights the single wet days contributions during parameter estimation and is therefore able to explicitly account for seasonal differences of rainfall events. It is shown that the TMEV provides a very similar error characteristic to the simplified MEVD for the estimation of quantiles with different sample lengths. In addition, we demonstrate the ability of the TMEV to identify longterm trends and seasonal variations of extreme precipitation in Austria and discuss possible implications for general trend estimations. We also present a spatio-temporal TMEV model, which is able to reproduce known patterns of a 50-year return level map of daily rainfall in Austria, thereby lending credence to the TMEV approach.

Nonstationary flood and its influencing factors analysis in the Hanjiang River Basin, China

Due to the impact of climate change and human activities, flood disasters have occurred frequently in the Hanjiang River Basin (HRB) in recent years, and the stationary behavior of its flood fluctuation has been disrupted. In this study, we used Generalized Additive Models for Location, Scale, and Shape (GAMLSS) to analyze the nonstationary changes of annual maximum runoff in the HRB and its influencing factors. It has also been complemented with a stationary model for comparative analysis. We found that the annual maximum runoff has a significant decreasing trend. The top four factors influencing this runoff change are the local changes in precipitation and temperature, and the regional climate oscillations as reflected by the North Atlantic Oscillation index (NAO) and the Pacific North American Index (PNA). The nonstationary model had better simulation effect than the stationary model. The stationary model could not reflect the impact of explanatory variables on annual maximum runoff, while the nonstationary model could well analyze the impact of single and dual explanatory variables. The results of this study provide some new insights in support of flood prevention and control in the HRB.