scholarly journals Spatial interpolation of rain-field dynamic time-space evolution based on radar rainfall data

2020 ◽  
Vol 51 (3) ◽  
pp. 521-540
Author(s):  
Peng Liu ◽  
Yeou-Koung Tung
Keyword(s):  
Temporal Distribution ◽  
Radar Data ◽  
Indicator Kriging ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Radar Rainfall ◽  
Time Space ◽  
Geostatistical Approach ◽  
Wide Range ◽  
Dynamic Time

Abstract Accurate and reliable measurement and prediction of the spatial and temporal distribution of rain field over a wide range of scales are important topics in hydrologic investigations. In this study, a geostatistical approach was adopted. To estimate the rainfall intensity over a study domain with the sample values and the spatial structure from the radar data, the cumulative distribution functions (CDFs) at all unsampled locations were estimated. Indicator kriging (IK) was used to estimate the exceedance probabilities for different preselected threshold levels, and a procedure was implemented for interpolating CDF values between the thresholds that were derived from the IK. Different probability distribution functions of the CDF were tested and their influences on the performance were also investigated. The performance measures and visual comparison between the observed rain field and the IK-based estimation suggested that the proposed method can provide good results of the estimation of indicator variables and is capable of producing a realistic image.

scholarly journals Quantile mechanics II: changes of variables in Monte Carlo methods and GPU-optimised normal quantiles

2014 ◽  
Vol 25 (2) ◽  
pp. 177-212 ◽  
Author(s):  
WILLIAM T. SHAW ◽  
THOMAS LUU ◽  
NICK BRICKMAN
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Processing Unit ◽  
Model Risk ◽  
Change Of Variables ◽  
Special Cases ◽  
Wide Range ◽  
Branch Divergence

With financial modelling requiring a better understanding of model risk, it is helpful to be able to vary assumptions about underlying probability distributions in an efficient manner, preferably without the noise induced by resampling distributions managed by Monte Carlo methods. This paper presents differential equations and solution methods for the functions of the form Q(x) = F−1(G(x)), where F and G are cumulative distribution functions. Such functions allow the direct recycling of Monte Carlo samples from one distribution into samples from another. The method may be developed analytically for certain special cases, and illuminate the idea that it is a more precise form of the traditional Cornish–Fisher expansion. In this manner the model risk of distributional risk may be assessed free of the Monte Carlo noise associated with resampling. The method may also be regarded as providing both analytical and numerical bases for doing more precise Cornish–Fisher transformations. Examples are given of equations for converting normal samples to Student t, and converting exponential to normal. In the case of the normal distribution, the change of variables employed allows the sampling to take place to good accuracy based on a single rational approximation over a very wide range of sample space. The avoidance of branching statements is of use in optimal graphics processing unit (GPU) computations as it avoids the effect of branch divergence. We give a branch-free normal quantile that offers performance improvements in a GPU environment while retaining the best precision characteristics of well-known methods. We also offer models with low probability branch divergence. Comparisons of new and existing forms are made on Nvidia GeForce GTX Titan and Tesla C2050 GPUs. We argue that in both single- and double-precisions, the change-of-variables approach offers the most GPU-optimal Gaussian quantile yet, working faster than the Cuda 5.5 built-in function.

scholarly journals Characterization of dynamic evolution of the spatio-temporal variation of rain-field in Hong Kong

2015 ◽  
Vol 47 (2) ◽  
pp. 468-482 ◽  
Author(s):  
Peng Liu ◽  
Yeou-Koung Tung
Keyword(s):  
Hong Kong ◽  
Spatial Structure ◽  
Temporal Structure ◽  
Radar Data ◽  
Small Scale ◽  
Large Set ◽  
Time Space ◽  
Main Challenge ◽  
Geostatistical Approach ◽  
Spatio Temporal

A significant part of Hong Kong has hilly terrain with relatively short flow concentration time and, hence, is susceptible to the threat of flash floods and landslides during intense convective thunderstorms and tropical cyclones. For places like Hong Kong, a rainfall model that could adequately capture small-scale temporal and spatial variations would be highly desirable. The main challenge in rain-field modeling is to capture and describe the dynamic time-space evolution of the rainfall during rainstorm events. In this study, radar data with a high spatial (1 km2) and temporal (6 min) resolution of four rainstorm events in Hong Kong are analyzed. A geostatistical approach based on indicator variograms of rain-fields is used. The spatial structure of a rain-field is found to be highly anisotropic and should be adequately considered in the model. Variability of the spatial structure of a rain-field was described well by the main features of the variograms. Moreover, it is possible to identify whether multiple rainstorm centers exist by comparing the mean length and range. In order to establish reliable statistics on the spatial and temporal structure of rain-fields in Hong Kong, this approach could be applied to a large set of rainstorm events in this same region in the future.

Assessing local and spatial uncertainty with HER method

2021 ◽  
Author(s):  
Stephanie Thiesen ◽  
Uwe Ehret
Keyword(s):  
Uncertainty Analysis ◽  
Spatial Configuration ◽  
Order Relation ◽  
Uncertainty Estimation ◽  
Indicator Kriging ◽  
Distribution Functions ◽  
Spatial Uncertainty ◽  
Cumulative Distribution ◽  
Trade Offs ◽  
Entropy Reduction

<p>Uncertainty analysis is a critical subject for many environmental studies. We have previously combined statistical learning and Information Theory in a geostatistical framework for overcoming parameterization with functions and uncertainty trade-offs present in many traditional interpolators (Thiesen et al. 2020). The so-called Histogram via entropy reduction (HER) relaxes normality assumptions, avoiding the risk of adding information not available in the data. The authors showed that, by construction, the method provides a proper framework for uncertainty estimation which accounts for both spatial configuration and data values, while allowing one to introduce or infer properties of the field through the aggregation method. In this study, we explore HER method in the light of uncertainty analysis. In general, uncertainty at any particular unsampled location (local uncertainty) is frequently assessed by nonlinear interpolators such as indicator and multi-gaussian kriging. HER has shown to be a unique approach for dealing with uncertainty estimation in a fine resolution without the need of modeling multiple indicator semivariograms, order-relation violations, interpolation/extrapolation of conditional cumulative distribution functions, or stronger hypotheses of data distribution. In this work, this nonparametric geostatistical framework is adapted to address local and spatial uncertainty in the context of risk mapping. We investigate HER for handling estimations of threshold-exceeding probabilities to map the risk of soil contamination by lead in the well-known dataset of the region of Swiss Jura. Finally, HER method is extended to assess spatial uncertainty (uncertainty when several locations are considered together) through sequential simulation. Its results are compared to indicator kriging and benchmark models available in the literature generated for this particular dataset.</p><p>Thiesen S, Vieira DM, Mälicke M, Loritz R, Wellmann JF, Ehret U (2020) Histogram via entropy reduction (HER): an information-theoretic alternative for geostatistics. Hydrol Earth Syst Sci 24:4523–4540. https://doi.org/https://doi.org/10.5194/hess-24-4523-2020</p>

scholarly journals Hygroscopicity distribution concept for measurement data analysis and modeling of aerosol particle mixing state with regard to hygroscopic growth and CCN activation

2010 ◽  
Vol 10 (15) ◽  
pp. 7489-7503 ◽  
Author(s):  
H. Su ◽  
D. Rose ◽  
Y. F. Cheng ◽  
S. S. Gunthe ◽  
A. Massling ◽  
...  
Keyword(s):  
Chemical Composition ◽  
Measurement Data ◽  
Particle Diameter ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Cloud Condensation Nucleus ◽  
Mathematical Framework ◽  
Hygroscopic Growth ◽  
Mixing State ◽  
Wide Range

Abstract. This paper presents a general concept and mathematical framework of particle hygroscopicity distribution for the analysis and modeling of aerosol hygroscopic growth and cloud condensation nucleus (CCN) activity. The cumulative distribution function of particle hygroscopicity, H(κ, Dd) is defined as the number fraction of particles with a given dry diameter, Dd, and with an effective hygroscopicity parameter smaller than the parameter κ. From hygroscopicity tandem differential mobility analyzer (HTDMA) and size-resolved CCN measurement data, H(κ, Dd) can be derived by solving the κ-Köhler model equation. Alternatively, H(κ, Dd) can be predicted from measurement or model data resolving the chemical composition of single particles. A range of model scenarios are used to explain and illustrate the concept, and exemplary practical applications are shown with HTDMA and CCN measurement data from polluted megacity and pristine rainforest air. Lognormal distribution functions are found to be suitable for approximately describing the hygroscopicity distributions of the investigated atmospheric aerosol samples. For detailed characterization of aerosol hygroscopicity distributions, including externally mixed particles of low hygroscopicity such as freshly emitted soot, we suggest that size-resolved CCN measurements with a wide range and high resolution of water vapor supersaturation and dry particle diameter should be combined with comprehensive HTDMA measurements and size-resolved or single-particle measurements of aerosol chemical composition, including refractory components. In field and laboratory experiments, hygroscopicity distribution data from HTDMA and CCN measurements can complement mixing state information from optical, chemical and volatility-based techniques. Moreover, we propose and intend to use hygroscopicity distribution functions in model studies investigating the influence of aerosol mixing state on the formation of cloud droplets.

scholarly journals Stochastic simulation experiment to assess radar rainfall retrieval uncertainties associated with attenuation and its correction

2008 ◽  
Vol 12 (2) ◽  
pp. 587-601 ◽  
Author(s):  
R. Uijlenhoet ◽  
A. Berne
Keyword(s):  
Simulation Experiment ◽  
Temporal Distribution ◽  
Single Frequency ◽  
Forward Algorithm ◽  
Radar Rainfall ◽  
Weather Radars ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Raindrop Size ◽  
Rainfall Retrieval

Abstract. As rainfall constitutes the main source of water for the terrestrial hydrological processes, accurate and reliable measurement and prediction of its spatial and temporal distribution over a wide range of scales is an important goal for hydrology. We investigate the potential of ground-based weather radar to provide such measurements through a theoretical analysis of some of the associated observation uncertainties. A stochastic model of range profiles of raindrop size distributions is employed in a Monte Carlo simulation experiment to investigate the rainfall retrieval uncertainties associated with weather radars operating at X-, C-, and S-band. We focus in particular on the errors and uncertainties associated with rain-induced signal attenuation and its correction for incoherent, non-polarimetric, single-frequency, operational weather radars. The performance of two attenuation correction schemes, the (forward) Hitschfeld-Bordan algorithm and the (backward) Marzoug-Amayenc algorithm, is analyzed for both moderate (assuming a 50 km path length) and intense Mediterranean rainfall (for a 30 km path). A comparison shows that the backward correction algorithm is more stable and accurate than the forward algorithm (with a bias in the order of a few percent for the former, compared to tens of percent for the latter), provided reliable estimates of the total path-integrated attenuation are available. Moreover, the bias and root mean square error associated with each algorithm are quantified as a function of path-averaged rain rate and distance from the radar in order to provide a plausible order of magnitude for the uncertainty in radar-retrieved rain rates for hydrological applications.

scholarly journals Hydro-NEXRAD-2: real-time access to customized radar-rainfall for hydrologic applications

2012 ◽  
Vol 15 (2) ◽  
pp. 580-590 ◽  
Author(s):  
Witold F. Krajewski ◽  
Anton Kruger ◽  
Satpreet Singh ◽  
Bong-Chul Seo ◽  
James A. Smith
Keyword(s):  
Data Processing ◽  
Real Time ◽  
Rain Rate ◽  
Time Synchronization ◽  
Handling Time ◽  
Radar Data ◽  
Prototype System ◽  
Radar Rainfall ◽  
Estimation Algorithms ◽  
Wide Range

Hydro-NEXRAD-2 (HNX2) is a prototype system that allows hydrologic users real-time access to NEXRAD radar data in support of a wide range of research. The system processes basic radar data (Level II) and delivers radar-rainfall products based on the user's custom selection of features such as spatial domain, rainfall product space and time resolution, and rainfall estimation algorithms. HNX2 collects real-time, unprocessed data from multiple NEXRAD radars as they become available, processes them through a user-configurable pipeline of data-processing modules, and publishes the processed data-products at regular intervals. Modules in the data-processing pipeline encapsulate algorithms such as non-meteorological echo detection, radar range correction, radar-reflectivity-rain rate (Z-R) conversion, echo advection correction, mosaicking of products from multiple radars, and grid projections and transformations. This paper describes the challenges involved in HNX2's development and implementation, which include real-time error-handling, time-synchronization of data from multiple asynchronous sources, generation of multiple-radar metadata products, and distribution of products to a user base with diverse needs and constraints. HNX2 publishes products through automation and allows multiple users access to published products. Currently, HNX2 is serving near real-time rain-rate maps for Iowa in the USA using data from seven radars covering the state. Hydrologic models operated by The University of Iowa's Iowa Flood Center use these products.

scholarly journals Uncertainties in rainfall retrievals from ground-based weather radar: overview, case study, and simulation experiment

2006 ◽  
Vol 3 (4) ◽  
pp. 2385-2436
Author(s):  
R. Uijlenhoet ◽  
S. H. van der Wielen ◽  
A. Berne
Keyword(s):  
Simulation Experiment ◽  
Temporal Distribution ◽  
Weather Radar ◽  
Rain Gauge ◽  
Radar Rainfall ◽  
Rain Gauges ◽  
Weather Radars ◽  
Wide Range ◽  
Rainfall Retrieval

Abstract. Because rainfall constitutes the main source of water for the terrestrial hydrological processes, accurate and reliable measurement and prediction of its spatial and temporal distribution over a wide range of scales is an important goal for hydrology. We investigate the potential of ground-based weather radar to provide such measurements through a detailed analysis of the associated observation uncertainties. First, a historical perspective on measuring the space-time distribution of rainfall, from the rain gauge to the radar era, is presented. Subsequently, we provide an overview of the various errors and uncertainties affecting radar rainfall retrievals. As an example, we present a case study of the relation between measurements from an operational C-band weather radar and a network of tipping bucket rain gauges as a function of range. Finally, a recently developed stochastic model of range profiles of rainfall microstructure is employed in a simulation experiment designed to investigate the rainfall retrieval uncertainties associated with weather radars operating in different widely used frequency bands.

Requirements for radar rainfall data in urban catchment modelling and control

1997 ◽  
Vol 36 (8-9) ◽  
pp. 13-18
Author(s):  
Georg Johann ◽  
Hans-Reinhard Verworn
Keyword(s):  
Radar Data ◽  
Rainfall Data ◽  
Rainfall Runoff ◽  
Radar Rainfall ◽  
Urban Catchment ◽  
Space Resolution ◽  
Time Space ◽  
Urban Catchments ◽  
The University ◽  
And Control

The use of radar rainfall data as input for storm runoff models can procure a real benefit if the hydrologic response of the watershed studied is strongly dependent on the spatial and temporal heterogeneity of precipitation over its area. In dynamic management of urban catchments rainfall runoff simulations are sensitive to the resolution of the input data. In this study the influence of varios time/space resolutions of radar rainfall data on the results of rainfall-runoff simulations is inverstigated. Therefore, X-band radar rainfall data with high resolution in space (0.5 × 0.5 km) and time (360° scan every second minute), are compared with radar data with 14 min time and 1 × 1 km space resolution as input for the HYSTEM/EXTRAN hydrodynamic model of a small urban catchment. The presented invstigations are realized within the research project “realtime control of a combined sewer system by radar estimates of precipitataon” carried out by the University of Hannover and the Emschergenossenschaft/Lippeverband.

scholarly journals Do galactic bars depend on environment?: an information theoretic analysis of Galaxy Zoo 2

2020 ◽  
Vol 501 (1) ◽  
pp. 994-1001
Author(s):  
Suman Sarkar ◽  
Biswajit Pandey ◽  
Snehasish Bhattacharjee
Keyword(s):  
Spatial Distribution ◽  
Mutual Information ◽  
Local Density ◽  
Statistical Significance ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Host Galaxy ◽  
Data Sets ◽  
Data Set ◽  
Information Theoretic

ABSTRACT We use an information theoretic framework to analyse data from the Galaxy Zoo 2 project and study if there are any statistically significant correlations between the presence of bars in spiral galaxies and their environment. We measure the mutual information between the barredness of galaxies and their environments in a volume limited sample (Mr ≤ −21) and compare it with the same in data sets where (i) the bar/unbar classifications are randomized and (ii) the spatial distribution of galaxies are shuffled on different length scales. We assess the statistical significance of the differences in the mutual information using a t-test and find that both randomization of morphological classifications and shuffling of spatial distribution do not alter the mutual information in a statistically significant way. The non-zero mutual information between the barredness and environment arises due to the finite and discrete nature of the data set that can be entirely explained by mock Poisson distributions. We also separately compare the cumulative distribution functions of the barred and unbarred galaxies as a function of their local density. Using a Kolmogorov–Smirnov test, we find that the null hypothesis cannot be rejected even at $75{{\ \rm per\ cent}}$ confidence level. Our analysis indicates that environments do not play a significant role in the formation of a bar, which is largely determined by the internal processes of the host galaxy.

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