Integrating full-process high resolution hydrodynamic simulations within early warning system (EWS) for marine flooding is hindered by the large computation time cost of such numerical models. This problem can be alleviated through the statistical analysis of pre-calculated simulation results to build a fast (low computation time cost) statistical predictive model (named metamodel). Despite the success of this approach, a direct application of such techniques for EWS is not straightforward in all settings, more particularly in environments where the stochastic character of waves has a significant effect on the induced flood, i.e., where overtopping is on a duration smaller than 500 times the offshore wave period. In such environments, the numerical simulator is not deterministic and provides statistical quantities of the flooding indicators. By focusing on the estimates of quantiles, the objective of the present study is to explore the applicability of random forest (RF) models for marine flooding prediction by providing two levels of information: (1) the quantile of interest via a quantile random forest regression model (qRF); (2) the flooding probability via a classification random forest (cRF). We use the macrotidal site of Gâvres (French Atlantic coast) as an application case for which ~ 2000 numerical simulations were performed (i.e. stochastic simulations given 100 different extreme-but-realistic offshore meteo-oceanic input conditions were repeated 20 times) to compute local and global flooding indicators (respectively the maximum water depth at the coast and the total volume of water entering the territory). Through an extensive repeated cross-validation procedure, we tune the qRF parameters leading to high coefficient of determination of ~ 90% for the quantiles at 25–50–75%, and we show that the qRF models outperform the commonly used Tobit regression model. The comparison with the numerical results on historical events shows very satisfactory prediction for events both leading to major flooding and to absence of impact. For low quantile level and minor-to-moderate flooding events, the second level provided by the cRF-derived flooding probability shows its added value by enabling the EWS user to nuance the qRF prediction and to tag some situations where the prediction remains unsure.

A nuanced quantile random forest approach for fast prediction of a stochastic marine flooding simulator applied to a macrotidal coastal site

Consider the situation when we have training data containing many time series having known group membership and testing data with unknown group membership. The goals are to find timescale features (using training data) that can best separate the groups, and to use these highly discriminant features to classify test data. We propose a method for classification using a bias-corrected nondecimated wavelet transform. Wavelets are ideal for identifying highly discriminant local time and scale features. The observed signals will be treated as realizations of locally stationary wavelet processes, under which we define and rigorously estimate the evolutionary wavelet spectrum (timescale decomposition of variance). The evolutionary wavelet spectrum, which contains the second-moment information on the signals, is used as the classification signature. For each test time series, we compute the empirical wavelet spectrum and its divergence from the wavelet spectrum of each group. The test time series is then assigned to the group to which it is the least dissimilar. Under the locally stationary wavelet framework, we rigorously demonstrate that the classification procedure is consistent (i.e., misclassification probability goes to zero at the rate that is inversely proportional to divergence between the evolutionary wavelet spectra). The method is illustrated using seismic signals (earthquake vs. explosion events) and is demonstrated to work very well in simulation studies.

Consistent classification of non-stationary time series using stochastic wavelet representations

The objective of this article is to propose and statistically validate a more general additive non-Gaussian noise distribution, which we term McLeish distribution, whose random nature can model different impulsive noise environments commonly encountered in practice and provides a robust alternative to Gaussian noise distribution. In particular, for the first time in the literature, we establish the laws of McLeish distribution and therefrom derive the laws of the sum of McLeish distributions by obtaining closed-form expressions for their PDF, CDF, complementary CDF (C$^2$DF), MGF and higher-order moments. Further, for certain problems related to the envelope of complex random signals, we extend McLeish distribution to complex McLeish distribution and thereby propose circularly/elliptically symmetric (CS/ES) complex McLeish distributions with closed-form PDF, CDF, MGF and higher-order moments. For generalization of one-dimensional distribution to multi-dimensional distribution, we develop and propose both multivariate McLeish distribution and multivariate complex CS/ES (CCS/CES) McLeish distribution with analytically tractable and closed-form PDF, CDF, C$^2$DF and MGF. In addition to the proposed McLeish distribution framework and for its practical illustration, we theoretically investigate and prove the existence of McLeish distribution as additive noise in communication systems. Accordingly, we introduce additive white McLeish noise (AWMN) channels. For coherent/non-coherent signaling over AWMN channels, we propose novel expressions for MAP and ML symbol decisions and thereby obtain closed-form expressions for both BER of binary modulation schemes and SER of various M-ary modulation schemes. Further, we verify the validity and accuracy of our novel BER/SER expressions with some selected numerical examples and some computer-based simulations.

McLeish Distribution: Performance of Digital Communications over Additive White McLeish Noise (AWMN) Channels

Fast and accurate P-wave arrival picking significantly affects the performance of earthquake early warning (EEW) systems. Automated P-wave picking algorithms used in EEW have encountered problems of falsely picking up noise, missing P-waves and inaccurate P-wave arrival estimation. To address these issues, an automatic algorithm based on the convolution neural network (DPick) was developed, and trained with a moderate number of data sets of 17,717 accelerograms. Compared to the widely used approach of the short-term average/long-term average of signal characteristic function (STA/LTA), DPick is 1.6 times less likely to detect noise as a P-wave, and 76 times less likely to miss P-waves. In terms of estimating P-wave arrival time, when the detection task is completed within 1 s, DPick’s detection occurrence is 7.4 times that of STA/LTA in the 0.05 s error band, and 1.6 times when the error band is 0.10 s. This verified that the proposed method has the potential for wide applications in EEW.

Deep learning for P-wave arrival picking in earthquake early warning

The objective of this article is to propose and statistically validate a more general additive non-Gaussian noise distribution, which we term McLeish distribution, whose random nature can model different impulsive noise environments commonly encountered in practice and provides a robust alternative to Gaussian noise distribution. In particular, for the first time in the literature, we establish the laws of McLeish distribution and therefrom derive the laws of the sum of McLeish distributions by obtaining closed-form expressions for their probability density function (PDF), cumulative distribution function (CDF), complementary CDF (C2DF), moment-generating function (MGF) and higher-order moments. Further, for certain problems related to the envelope of complex random signals, we extend McLeish distribution to complex McLeish distribution and thereby propose circularly/elliptically symmetric (CS/ES) complex McLeish distributions with closed-form PDF, CDF, MGF and higher-order moments. For generalization of one-dimensional distribution to multi-dimensional distribution, we develop and propose both multivariate McLeish distribution and multivariate complex CS/ES (CCS/CES) McLeish distribution with analytically tractable and closed-form PDF, CDF, C2DF and MGF. In addition to the proposed McLeish distribution framework and for its practical illustration, we theoretically investigate and prove the existence of McLeish distribution as additive noise in communication systems. Accordingly, we introduce additive white McLeish noise (AWMN) channels. For coherent/non-coherent signaling over AWMN channels, we propose novel expressions for maximum a priori (MAP) and maximum likelihood (ML) symbol decisions and thereby obtain closed-form expressions for both bit error rate (BER) of binary modulation schemes and symbol error rate (SER) of various M-ary modulation schemes. Further, we verify the validity and accuracy of our novel BER/SER expressions with some selected numerical examples and some computer-based simulations.

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McLeish Distribution: Performance of Digital Communications Over Additive White McLeish Noise (AWMN) Channels

Principal component analysis in the wavelet domain

Dynamic principal component analysis (DPCA), also known as frequency domain principal component analysis, has been developed by Brillinger [Time Series: Data Analysis and Theory, Vol. 36, SIAM, 198...

Dynamic principal component analysis with missing values

This paper considers the problem of spatio-temporal extreme value prediction of precipitation data. This work presents some methods that predict monthly extremes over the next 20 years corresponding to 0.998 quantile at several stations over a certain region. The proposed methods are based on a novel combination of quantile regression forests and circular transformation. As the core of the methodology, quantile regression forests by combining many decorrelated bootstrapping trees may improve prediction performance, and circular transformation is used for building circular transformed predictors of months, which are put into the quantile regression forests model for prediction. The empirical performance of the proposed methods are evaluated through real data analysis, which demonstrates promising results of the proposed approaches.

Prediction of extremal precipitation by quantile regression forests: from SNU Multiscale Team

A New P‐Wave Detector via Moving Empirical Cumulative Distribution Function

Concerning the national health, it is important to develop an accurate prediction method of atmospheric particulate matter (PM) because being exposed to such ne dust can trigger not only respiratory diseases as well as dermatoses, ophthalmopathies and cardiovascular diseases. The National Institute of Environmental Research (NIER) employs a decision tree to predict bad weather days with a high PM concentration. However, the decision tree method (even with the inherent unstableness) cannot be a suitable model to predict bad weather days which represent only 4% of the entire data. In this paper, while presenting the inaccuracy and inappropriateness of the method used by the NIER, we present the utility of a new prediction model which adopts boosting with quantile loss functions. We evaluate the performance of the new method over various -value’s and justify the proposed method through comparison.

Junhyeon Kwon

Papers

Principal component analysis in the wavelet domain

Dynamic principal component analysis with missing values

Prediction of extremal precipitation by quantile regression forests: from SNU Multiscale Team

A New P‐Wave Detector via Moving Empirical Cumulative Distribution Function

Particulate Matter Prediction using Quantile Boosting