Doubly stochastic Poisson pulse model for fine-scale rainfall

Stochastic rainfall models are widely used in hydrological studies because they provide a framework not only for deriving information about the characteristics of rainfall but also for generating precipitation inputs to simulation models whenever data are not available. A stochastic point process model based on a class of doubly stochastic Poisson processes is proposed to analyse fine-scale point rainfall time series. In this model, rain cells arrive according to a doubly stochastic Poisson process whose arrival rate is determined by a finite-state Markov chain. Each rain cell has a random lifetime. During the lifetime of each rain cell, instantaneous random depths of rainfall bursts (pulses) occur according to a Poisson process. The covariance structure of the point process of pulse occurrences is studied. Moment properties of the time series of accumulated rainfall in discrete time intervals are derived to model 5-min rainfall data, over a period of 69 years, from Germany. Second-moment as well as third-moment properties of the rainfall are considered. The results show that the proposed model is capable of reproducing rainfall properties well at various sub-hourly resolutions. Incorporation of third-order moment properties in estimation showed a clear improvement in fitting. A good fit to the extremes is found at larger resolutions, both at 12-h and 24-h levels, despite underestimation at 5-min aggregation. The proportion of dry intervals is studied by comparing the proportion of time intervals, from the observed and simulated data, with rainfall depth below small thresholds. A good agreement was found at 5-min aggregation and for larger aggregation levels a closer fit was obtained when the threshold was increased. A simulation study is presented to assess the performance of the estimation method.     

A stochastic model for the analysis of the temporal change of dry spells

In the present paper a stochastic approach which considers the arrival of rainfall events as a Poisson process is proposed to analyse the sequences of no rainy days. Particularly, among the different Poisson models, a non-homogeneous Poisson model was selected and then applied to the daily rainfall series registered at the Cosenza rain gauge (Calabria, southern Italy), as test series. The aim was to evaluate the different behaviour of the dry spells observed in two different 30-year periods, i.e. 1951–1980 and 1981–2010. The analyses performed through Monte Carlo simulations assessed the statistical significance of the variation of the mean expected values of dry spells observed at annual scale in the second period with respect to those observed in the first. The model has then been verified by comparing the results of the test series with the ones obtained from other three rain gauges of the same region. Moreover, greater occurrence probabilities for long dry spells in 1981–2010 than in 1951–1980 were detected for the test series. Analogously, the return periods evaluated for fixed long dry spells through the synthetic data of the period 1981–2010 resulted less than half of the corresponding ones evaluated with the data generated for the previous 30-year period.     

Rainfall stochastic modeling for runoff forecasting

Rainfall fields estimation over a catchment area is an important stage in many hydrological applications. In this context, weather radars have several advantages because a single-site can scan a vast area with very high temporal and spatial resolution. The construction of weather radar systems with dual polarization capability allowed progress on radar rainfall estimation and its hydro-meteorological applications. For these applications of radar data it is necessary to remove the ground clutter contamination with an algorithm based on the backscattering signal variance of the differential reflectivity. The calibration of the GDSTM model (Gaussian Displacements Spatial-Temporal Model), a cluster stochastic generation model in continuous space and time, is herewith presented. In this model, storms arrive in a Poisson process in time with cells occurring in each storm that cluster in space and time. The model is calibrated, using data collected by the weather radar Polar 55C located in Rome, inside a square area of 132 × 132 km², with the radar at the centre. The GDSTM is fitted to sequences of radar images with a time interval between the PPIs scans of 5 min. A generalized method of moment procedure is used for parameter estimation. For the validation of the ability of the model to reproduce internal structure of rain event, a geo-morphological rainfall-runoff model, based on width function (WFIUH), was calibrated using simulated and observed data. Several rainfall fields are generated with the stochastic model and later they are used as input of the WFIUH model so that the forecast discharges can be compared to the observed ones.     

Stochastic overland flows

A theoretical solution framework to the nonlinear stochastic partial differential equations (SPDE) of the kinematic wave and diffusion wave models of overland flows under stochastic inflows/outflows, stochastic surface roughness field and stochastic state of flows was obtained. This development was realized by means of an eigenfunction representation of the time-space overland flow depths, and by transforming the problem into the phase space. By using Van Kampen's lemma and the cumulant expansion theory of Kubo-Van Kampen-Fox, the deterministic partial differential equation (PDE) for the evolutionary probability density function (pdf) of overland flow depths was finally obtained. Once this deterministic PDE is solved for the time-varying pdf of overland flow depths, then the time-space varying pdf of overland flow depths can be obtained by a transformation given in the text. In this solution framework it is possible to incorporate the stochastic dynamic behavior of the parameters and of the forcing functions of the overland flow process. For example, not only the individual rainfall duration and fluctuating rain intensity characteristics but also the sequential behavior of rainfall patterns is incorporated into the evolutionary probability density function of overland flow depths.     

Stochastic overland flows Part 1: Physics-based evolutionary probability distributions

A theoretical solution framework to the nonlinear stochastic partial differential equations (SPDE) of the kinematic wave and diffusion wave models of overland flows under stochastic inflows/outflows, stochastic surface roughness field and stochastic state of flows was obtained. This development was realized by means of an eigenfunction representation of the time-space overland flow depths, and by transforming the problem into the phase space. By using Van Kampen's lemma and the cumulant expansion theory of Kubo-Van Kampen-Fox, the deterministic partial differential equation (PDE) for the evolutionary probability density function (pdf) of overland flow depths was finally obtained. Once this deterministic PDE is solved for the time-varying pdf of overland flow depths, then the time-space varying pdf of overland flow depths can be obtained by a transformation given in the text. In this solution framework it is possible to incorporate the stochastic dynamic behavior of the parameters and of the forcing functions of the overland flow process. For example, not only the individual rainfall duration and fluctuating rain intensity characteristics but also the sequential behavior of rainfall patterns is incorporated into the evolutionary probability density function of overland flow depths.     

Improved understanding of spatio‐temporal controls on regional scale groundwater flooding using hydrograph analysis and impulse response functions

Controls on the spatio‐temporal extent of groundwater flooding are poorly understood, despite the long duration of groundwater flood events and distinct social and economic impacts. We developed a novel approach using statistical analysis of groundwater level hydrographs and impulse response functions (IRFs) and applied it to the 2013/2014 Chalk groundwater flooding in the English Lowlands. We proposed a standardized index of groundwater flooding which we calculated for monthly groundwater levels for 26 boreholes in the Chalk. We grouped these standardized series using k‐means cluster analysis and cross‐correlated the cluster centroids with the Standardized Precipitation Index accumulated over time intervals between 1 and 60 months. This analysis reveals 2 spatially coherent groups of standardized hydrographs that responded to precipitation over different timescales. We estimated IRF models of the groundwater level response to effective precipitation for 3 boreholes in each group. The IRF models corroborate the Standardized Precipitation Index analysis showing different response functions between the groups. We applied identical effective precipitation inputs to each of the IRF models and observed differences between the hydrographs from each group. It is suggested this is due to the hydrogeological properties of the Chalk and of overlying relatively low permeability superficial deposits (recent unconsolidated sediments overlying the bedrock, such as clays and tills), which are extensive over 1 of the groups. The overarching controls on groundwater flood response are concluded to be a complex combination of antecedent conditions, rainfall, and catchment hydrogeological properties. These controls should be taken into consideration when anticipating and managing future groundwater flood events. The approach presented is generic and parsimonious and can be easily applied where sufficient groundwater level and rainfall data are available.     

Conditional simulation of remotely sensed rainfall data using a non-Gaussian v-transformed copula

Quantification of rainfall and its spatial and temporal variability is extremely important for reliable hydrological and meteorological modeling. While rain gauge measurements do not provide reasonable areal representation of rainfall, remotely sensed precipitation estimates offer much higher spatial resolution. However, uncertainties associated with remotely sensed rainfall estimates are not well quantified. This issue is important considering the fact that uncertainties in input rainfall are the main sources of error in hydrologic processes. Using an ensemble of rainfall estimates that resembles multiple realizations of possible true rainfall, one can assess uncertainties associated with remotely sensed rainfall data. In this paper, ensembles are generated by imposing rainfall error fields over remotely sensed rainfall estimates. A non-Gaussian copula-based model is introduced for simulation of rainfall error fields. The v-transformed copula is employed to describe the dependence structure of rainfall error estimates without the influence of the marginal distribution. Simulations using this model can be performed unconditionally or conditioned on ground reference measurements such that rain gauge data are honored at their locations. The presented model is implemented for simulation of rainfall ensembles across the Little Washita watershed, Oklahoma. The results indicate that the model generates rainfall fields with similar spatio-temporal characteristics and stochastic properties to those of observed rainfall data.     

Simulation of the time-space evolution of an extratropical cyclonic precipitation field over USA

The time-space evolution of an extratropical cyclonic precipitation field over U S A is simulated in a stochastic setting as outlined in Kavvas et al. (1988). The birth of a cyclonic storm is characterized by the simultaneous birth of a cyclone center and births of subsynoptic precipitation areas (SPA) at preferred locations around the cyclone center. The precipitation cores and cells which are used as the fundamental building blocks of the SPAs are approximated by circular precipitation areas (CPA) of different sizes. The time space evolution of the precipitation field after the birth is governed by (1) the movement of the synoptic cyclone described by the cyclone center trajectory, (2) independent nonidentically distributed random velocities of the individual CPAs relative to the cyclone center, (3) the births of new CPAs in time and space relative to the cyclone center, (4) the independent evolution in time of the individual spatially uniform intensities of the existing CPAs, (5) the expansion and shrinkage of the existing CPAs in the course of movement and (6) the dissipation (death) of a random number of existing CPAs within the cyclonic system. The computer simulation, the results of which are presented in this paper, successfully reproduced the general mesoscale and synoptic scale features of the radar detected cyclonic rain fields as observed by Austin and Houze (1972), Houze et al. (1976), Hobbs (1978), Hobbs and Locatelli (1978), Houze (1981), Houze and Hobbs (1982) and others.     

Some factors controlling the concentration of small ions near the ground

Summary During continuous measurements of the concentration of small ions near the ground made over the period of many months, several causes of variation were identified. During rain in large electric fields, ions of sign opposite to that of the potential gradient were produced in sufficiently large numbers to give rise to very high concentrations over short periods. Sometimes, after rain, a considerable increase in the density of small ions was found, suggesting a reduction in the numbers of nuclei and large ions. In moderate electric fields, a reduction was observed in the concentration of ions of sign opposite to that of the potential gradient in a way corresponding to the electrode effect. A simplified theory of the effect predicts results similar to those found in practice.The paper will appear elsewhere.     

Effect of the inter-annual variability of rainfall statistics on stochastically generated rainfall time series: part 1. Impact on peak and extreme rainfall values

A noble approach of stochastic rainfall generation that can account for inter-annual variability of the observed rainfall is proposed. Firstly, we show that the monthly rainfall statistics that is typically used as the basis of the calibration of the parameters of the Poisson cluster rainfall generators has significant inter-annual variability and that lumping them into a single value could be an oversimplification. Then, we propose a noble approach that incorporates the inter-annual variability to the traditional approach of Poisson cluster rainfall modeling by adding the process of simulating rainfall statistics of individual months. Among 132 gage-months used for the model verification, the proportion that the suggested approach successfully reproduces the observed design rainfall values within 20 % error varied between 0.67 and 0.83 while the same value corresponding to the traditional approach varied between 0.21 and 0.60. This result suggests that the performance of the rainfall generation models can be largely improved not only by refining the model structure but also by incorporating more information about the observed rainfall, especially the inter-annual variability of the rainfall statistics.     

Evidence for magma in the Katmai volcanic range

Several independent observations during the summer of 1965 suggest the presence of magma in the volcanic range of Katmai. A high value of 0.3 for Poisson’s ratio and the screening of predominantly the vertical component of the elastic shear waves have been observed. Narrow negative Bouguer anomalies possibly indicate the presence of low density material at shallow depth. The location of magma reservoirs has been attempted, using the calculated wave path and the screening of the mainly vertically polarized shear wave. Of the possible ten chambers thus located, the ones of shallow depth (to 20 km) correspond to the location of active volcanoes. The ones between the 20 km level to the upper mantle seem to spread over a rather wide area and are not clearly related to the geographical position of a particular volcano. Theoretical considerations on the propagation of elastic waves substantiate the observed absence of vertically polarized shear waves.     

地震自动定位的综合解决方案

针对已有两类地震自动定位方法各自的优点和限制，提出了综合利用这两类方法以形成一个统一系统的方案，希望以此提高地震自动定位能力。该方案的基本流程是：利用波形相关方法在连续地震波形上检测出地震事件并初定其震源位置和发震时刻；利用初定的震源位置和发震时刻，预测各台站各震相的到时；以预测的各震相到时为参考点，利用单台波形(单道或三分向)在该参考点附近精确测定震相到时；利用修定后的震相到时测定震源位置和发震时刻；根据震中距判定地震类型(地方震、近震、远震)，在预期的波形段自动测定波形最大振幅和相应周期，进而测定相应类型的震级(ML、Ms或mb)。     

Long-range Earthquake Forecasting with Every Earthquake a Precursor According to Scale

Scaling relations previously derived from examples of the precursory scale increase before major earthquakes show that the precursor is a long-term predictor of the time, magnitude, and location of the major earthquake. These relations are here taken as the basis of a stochastic forecasting model in which every earthquake is regarded as a precursor. The problem of identifying those earthquakes that are actually precursory is thus set aside, at the cost of limiting the strength of the resulting forecast. The contribution of an individual earthquake to the future distribution of hazard in time, magnitude and location is on a scale determined, through the scaling relations, by its magnitude. Provision is made for a contribution to be affected by other earthquakes close in time and location, e.g., an aftershock may be given low weight. Using the New Zealand catalogue, the model has been fitted to the forecasting of shallow earthquakes exceeding magnitude 5.75 over the period 1965–2000. It fits the data much better than a baseline Poisson model with a location distribution based on proximity to the epicenters of past earthquakes. Further, the model has been applied, with unchanged parameters, to the California region over the period 1975–2001. There also, it performs much better than the baseline model fitted to the same region over the period 1951–1974; the likelihood ratio is 10¹⁵ in favor of the present model. These results lend credence to the precursory scale increase phenomenon, and show that the scaling relations are pervasive in earthquake catalogues. The forecasting model provides a new baseline model against which future refinements, and other proposed models, can be tested. It may also prove to be useful in practice. Its applicability to other regions has still to be established.     

苏鲁豫皖地区地磁异常场时空近期动态演化特征

以苏鲁豫皖地区2005年至2008年四期地磁矢量场的观测数据为基础,分别建立了该区域的F、D、I三个独立分量四期的地磁异常场模型。通过对郯庐断裂带中段地磁异常场时空动态演化特征分析,发现该区域的F、D、I分量地磁异常场形态在2005年11月九江地震前后出现了较大程度的变化,甚至出现了地磁正负异常场的反转,从2007年春季至2008年春季,该区域地磁异常场分布形态基本保持稳定。     

Simulating time-histories and pseudo-spectral accelerations from the 1992 Cairo earthquake at the proposed El-Fayoum New City Site,Egypt

El-Fayoum New City represents one of the new urban settlements that are recently erected all over Egypt. Because seismic recordings are not available, I used the stochastic method to simulate the largest damaging earthquake from the closest seismic source to the proposed area of the city. To verify the method and its computed results in Egypt, a study termed “method verification” was performed. I found that the October 12, 1992, earthquake (M _b = 5.8) that occurred southwest of Cairo in the vicinity of the Dahshour region, at the coordinates 29.77°N, 31.07°E, is a significant earthquake to the city. The parameters of the path from the hypocenter of the event to the city were taken into consideration. To determine the site parameters, a shallow seismic refraction survey was carried out in the studied area. Accordingly, I simulated time-histories and pseudo-spectral accelerations from the October 12, 1992, earthquake at the location of seismic profiles. Finally, it is demonstrated that the site is characterized by high ground motion amplification factors, producing a high ground motion acceleration value.     

首都圈地区的地壳厚度及泊松比

利用2002~2003年中国地震局地质研究所台阵实验室以唐山大震区为中心布设的40个流动宽频带地震台站和首都圈数字台网的107个固定台站的远震数据,采用接收函数叠加搜索方法测定了首都圈地区地壳厚度和平均泊松比.综合利用首都圈数字地震台网的宽频带和短周期台站,以及流动地震台阵的观测数据,使我们的结果具有较前人更好的空间分辨率,为我们研究首都圈地壳的变形及其与地震的关系提供了重要的数据平台.结果表明: (1)首都圈地区地壳厚度和泊松比具有明显的横向分块特征,并与断层切割的地质块体有较好的相关性,地壳厚度变化形成了由涵盖北京—三河—唐山的NE向地壳厚度变化过渡带与张家口—北京—天津的NW向壳幔界面凹陷带构成的交汇构造,后者与所谓的张家口—渤海地震带基本吻合,而且本文给出的深部构造背景与首都圈地区的NE向和NW向地震带的交汇特征相吻合;(2)首都圈地区地壳厚度具有较大的差异,区域内地壳厚度的变化达15 km.其中,台站SZJ下方地壳厚度达到43.8 km,而台站BDH下方地壳厚度仅为28.8 km,总体上研究区西北侧的张家口—怀来地区的地壳厚度较大(~40 km),而唐山以东地区地壳较薄(28~32 km);(3) 研究区地壳的平均泊松比值为0.26左右,其最大值偏离泊松介质（σ=0.25）21%以上,而最小值偏离标准泊松比值9.6%,北京周边地区被高泊松比的介质环绕,而唐山东侧为低泊松比介质,地壳泊松比的分布特征反映了华北克拉通裂解过程中地幔物质的侵入;(4)研究区中强地震大多发生在地壳厚度和泊松比变化的陡变带,且偏于低泊松比的一侧,首都圈地震的成因仅考虑由于板块作用引起的水平应力场是不够的,有必要充分重视由于上地幔变形引起的地壳垂直变形和上地幔物质侵入造成的地壳变形运动与热效应.     

On the computation of area probabilities based on a spatial stochastic model for precipitation cells and precipitation amounts

A main task of weather services is the issuing of warnings for potentially harmful weather events. Automated warning guidances can be derived, e.g., from statistical post-processing of numerical weather prediction using meteorological observations. These statistical methods commonly estimate the probability of an event (e.g. precipitation) occurring at a fixed location (a point probability). However, there are no operationally applicable techniques for estimating the probability of precipitation occurring anywhere in a geographical region (an area probability). We present an approach to the estimation of area probabilities for the occurrence of precipitation exceeding given thresholds. This approach is based on a spatial stochastic model for precipitation cells and precipitation amounts. The basic modeling component is a non-stationary germ-grain model with circular grains for the representation of precipitation cells. Then, we assign a randomly scaled response function to each precipitation cell and sum these functions up to obtain precipitation amounts. We derive formulas for expectations and variances of point precipitation amounts and use these formulas to compute further model characteristics based on available sequences of point probabilities. Area probabilities for arbitrary areas and thresholds can be estimated by repeated Monte Carlo simulation of the fitted precipitation model. Finally, we verify the proposed model by comparing the generated area probabilities with independent rain gauge adjusted radar data. The novelty of the presented approach is that, for the first time, a widely applicable estimation of area probabilities is possible, which is based solely on predicted point probabilities (i.e., neither precipitation observations nor further input of the forecaster are necessary). Therefore, this method can be applied for operational weather predictions.     

Directional and correlation analysis from the geomagnetic monitoring and seismic data on the Boso Peninsula in 2000

The mathematical technique is developed for cluster analysis of the orientation structure of the vector geophysical fields. In order to solve the problem of revealing correlations between quasi-linear processes, the notion of the correlation with the nonrigid metric of distance is introduced for the vectors generated by the flows of discrete events with a high degree of sparseness in time. The method is tested on the data from monitoring the magnetic field in a seismically active region of Japan. It is found that the cluster portrait of the orientation structure of the magnetic field is substantially different during quiet and disturbed days. The influence of seismic vibrations of the ground on the results of magnetic measurements is established.