scholarly journals Third-Order Polynomial Normal Transform Applied to Multivariate Hydrologic Extremes

Water ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 490 ◽  
Author(s):  
Yeou-Koung Tung ◽  
Lingwan You ◽  
Chulsang Yoo
Keyword(s):  
Flood Control ◽  
Random Variables ◽  
Rainfall Data ◽  
Normal Space ◽  
Modeling Framework ◽  
Third Order ◽  
Maximum Rainfall ◽  
Normal Distributions ◽  
Order Polynomial ◽  
Hydrologic Extremes

Hydro-infrastructural systems (e.g., flood control dams, stormwater detention basins, and seawalls) are designed to protect the public against the adverse impacts of various hydrologic extremes (e.g., floods, droughts, and storm surges). In their design and safety evaluation, the characteristics of concerned hydrologic extremes affecting the hydrosystem performance often are described by several interrelated random variables—not just one—that need to be considered simultaneously. These multiple random variables, in practical problems, have a mixture of non-normal distributions of which the joint distribution function is difficult to establish. To tackle problems involving multivariate non-normal variables, one frequently adopted approach is to transform non-normal variables from their original domain to multivariate normal space under which a large wealth of established theories can be utilized. This study presents a framework for practical normal transform based on the third-order polynomial in the context of a multivariate setting. Especially, the study focuses on multivariate third-order polynomial normal transform (TPNT) with explicit consideration of sampling errors in sample L-moments and correlation coefficients. For illustration, the modeling framework is applied to establish an at-site rainfall intensity–duration-frequency (IDF) relationship. Annual maximum rainfall data analyzed contain seven durations (1–72 h) with 27 years of useable records. Numerical application shows that the proposed modeling framework can produce reasonable rainfall IDF relationships by simultaneously treating several correlated rainfall data series and is a viable tool in dealing with multivariate data with a mixture of non-normal distributions.

Point process models of rainfall: developments for fine-scale structure

2007 ◽  
Vol 463 (2086) ◽  
pp. 2569-2587 ◽  
Author(s):  
Paul Cowpertwait ◽  
Valerie Isham ◽  
Christian Onof
Keyword(s):  
Poisson Process ◽  
Time Scales ◽  
Rain Gauge ◽  
Historical Record ◽  
Rainfall Data ◽  
Process Models ◽  
Third Order ◽  
Time Intervals ◽  
Historical Series ◽  
Derived Properties

A conceptual stochastic model of rainfall is proposed in which storm origins occur in a Poisson process, where each storm has a random lifetime during which rain cell origins occur in a secondary Poisson process. In addition, each cell has a random lifetime during which instantaneous random depths (or ‘pulses’) of rain occur in a further Poisson process. A key motivation behind the model formulation is to account for the variability in rainfall data over small (e.g. 5 min) and larger time intervals. Time-series properties are derived to enable the model to be fitted to aggregated rain gauge data. These properties include moments up to third order, the probability that an interval is dry, and the autocovariance function. To allow for distinct storm types (e.g. convective and stratiform), several processes may be superposed. Using the derived properties, a model consisting of two storm types is fitted to 60 years of 5 min rainfall data taken from a site near Wellington, New Zealand, using sample estimates taken at 5 min, 1 hour, 6 hours and daily levels of aggregation. The model is found to fit moments of the depth distribution up to third order very well at these time scales. Using the fitted model, 5 min series are simulated, and annual maxima are extracted and compared with equivalent values taken from the historical record. A good fit in the extremes is found at both 1 and 24 hour levels of aggregation, although at the 5 min level there is some underestimation of the historical values. Proportions of time intervals with depths below various low thresholds are extracted from the simulated and historical series and compared. A tendency for underestimation of the historical values is evident at some time scales, with a close fit being obtained as the threshold is increased.

Thermal Error Modeling of Precision Positioning Stage

2013 ◽  
Vol 694-697 ◽  
pp. 767-770
Author(s):  
Jing Shu Wang ◽  
Ming Chi Feng
Keyword(s):  
Thermal Deformation ◽  
Thermal Error ◽  
Error Modeling ◽  
Precision Positioning ◽  
Third Order ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Positioning Stage ◽  
Order Polynomial ◽  
The Relationship

As the thermal deformation significantly impacts the accuracy of precision positioning stage, it is necessary to realize the thermal error. The thermal deformation of the positioning stage is simulated by the finite element analysis. The relationship between the temperature variation and thermal error is fitted third-order polynomial function whose parameters are determined by genetic algorithm neural network (GANN). The operators of the GANN are optimized through a parametric study. The results show that the model can describe the relationship between the temperature and thermal deformation well.

scholarly journals Optimal Rainfall Estimation by Considering Elevation in the Han River Basin, South Korea

2013 ◽  
Vol 52 (4) ◽  
pp. 802-818 ◽  
Author(s):  
Seong-Sim Yoon ◽  
Deg-Hyo Bae
Keyword(s):  
South Korea ◽  
River Basin ◽  
Flood Control ◽  
Rainfall Data ◽  
Spatiotemporal Variability ◽  
Radar Rainfall ◽  
Mountainous Regions ◽  
Han River ◽  
Orographic Rainfall ◽  
Han River Basin

AbstractMore than 70% of South Korea has mountainous terrain, which leads to significant spatiotemporal variability of rainfall. The country is exposed to the risk of flash floods owing to orographic rainfall. Rainfall observations are important in mountainous regions because flood control measures depend strongly on rainfall data. In particular, radar rainfall data are useful in these regions because of the limitations of rain gauges. However, radar rainfall data include errors despite the development of improved estimation techniques for their calculation. Further, the radar does not provide accurate data during heavy rainfall in mountainous areas. This study presents a radar rainfall adjustment method that considers the elevation in mountainous regions. Gauge rainfall and radar rainfall field data are modified by using standardized ordinary cokriging considering the elevation, and the conditional merging technique is used for combining the two types of data. For evaluating the proposed technique, the Han River basin was selected; a high correlation between rainfall and elevation can be seen in this basin. Further, the proposed technique was compared with the mean field bias and original conditional merging techniques. Comparison with kriged rainfall showed that the proposed method has a lesser tendency to oversmooth the rainfall distribution when compared with the other methods, and the optimal mean areal rainfall is very similar to the value obtained using gauges. It reveals that the proposed method can be applied to an area with significantly varying elevation, such as the Han River basin, to obtain radar rainfall data of high accuracy.

Calibration of pneumotachographs using a calibrated syringe

2003 ◽  
Vol 95 (2) ◽  
pp. 571-576 ◽  
Author(s):  
Yongquan Tang ◽  
Martin J. Turner ◽  
Johnny S. Yem ◽  
A. Barry Baker
Keyword(s):  
Calibration Method ◽  
Linear Range ◽  
Data Sets ◽  
Constant Flow ◽  
Calibration Constant ◽  
Third Order ◽  
Polynomial Coefficients ◽  
Calibration Curves ◽  
Order Polynomial ◽  
Better Than

Pneumotachograph require frequent calibration. Constant-flow methods allow polynomial calibration curves to be derived but are time consuming. The iterative syringe stroke technique is moderately efficient but results in discontinuous conductance arrays. This study investigated the derivation of first-, second-, and third-order polynomial calibration curves from 6 to 50 strokes of a calibration syringe. We used multiple linear regression to derive first-, second-, and third-order polynomial coefficients from two sets of 6–50 syringe strokes. In part A, peak flows did not exceed the specified linear range of the pneumotachograph, whereas flows in part B peaked at 160% of the maximum linear range. Conductance arrays were derived from the same data sets by using a published algorithm. Volume errors of the calibration strokes and of separate sets of 70 validation strokes ( part A) and 140 validation strokes ( part B) were calculated by using the polynomials and conductance arrays. Second- and third-order polynomials derived from 10 calibration strokes achieved volume variability equal to or better than conductance arrays derived from 50 strokes. We found that evaluation of conductance arrays using the calibration syringe strokes yields falsely low volume variances. We conclude that accurate polynomial curves can be derived from as few as 10 syringe strokes, and the new polynomial calibration method is substantially more time efficient than previously published conductance methods.

Modelling Catchment Rainfall Using Sum of Correlated Gamma Variables

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Zakaria, R. ◽  
Howlett, P. G. ◽  
Piantadosi, J. ◽  
Boland, J. W. ◽  
Moslim, N. H.
Keyword(s):  
Spatial Analysis ◽  
Random Variables ◽  
Monthly Rainfall ◽  
Rainfall Data ◽  
Weighted Sum ◽  
Statistical Parameters ◽  
Dependent Random Variables ◽  
Rainfall Model

One of the major difficulties in simulating rainfall is the need to accurately represent rainfall accumulations. An accurate simulation of monthly rainfall should also provide an accurate simulation of yearly rainfall by summing the monthly totals. A major problem in this regard is that rainfall distributions for successive months may not be independent. Thus the rainfall accumulation problem must be represented as the summation of dependent random variables. This study is aimed to show if the statistical parameters for several stations within a particular catchment is known, then a weighted sum is used to determine a rainfall model for the entire local catchment. A spatial analysis for the sum of rainfall volumes from four selected meteorological stations within the same region using the monthly rainfall data is conducted. The sum of n correlated gamma variables is used to model the sum of monthly rainfall totals from four stations when there is significant correlation between the stations.

scholarly journals Forecasting of Rainfall in Central Java using Hybrid GSTAR-NN-PSO Model

2019 ◽  
Vol 125 ◽  
pp. 23015
Author(s):  
Hasbi Yasin ◽  
Budi Warsito ◽  
Rukun Santoso ◽  
Arief Rachman Hakim
Keyword(s):  
Neural Network ◽  
Flood Control ◽  
Forecast Accuracy ◽  
Space Time ◽  
Rainfall Data ◽  
Time Data ◽  
Feed Forward Neural Network ◽  
Time Model ◽  
Central Java ◽  
Space Time Model

Forecasting of rainfall trends is essential for several fields, such as airline and ship management, flood control and agriculture. The rainfall data were recorded several time simultaneously at a number of locations and called the space-time data. Generalized Space Time Autoregressive (GSTAR) model is one of space-time models used to modeling and forecasting the rainfall. The aim of this research is to propose the nonlinear space-time model based on hybrid of GSTAR, Feed Forward Neural Network (FFNN) and Particle Swarm Optimization (PSO) and it called GSTAR-NN-PSO. In this model, input variable of the FFNN was obtained from the GSTAR model. Then use PSO to initialize the weight parameter in the FFNN model. This model is applied for forecasting monthly rainfall data in Jepara, Kudus, Pati and Grobogan, Central Java, Indonesia. The results show that the proposed model gives more accurate forecast than the linear space-time model, i.e. GSTAR and GSTAR-PSO. Moreover, further research about space-time models based on GSTAR and Neural Network is needed to improving the forecast accuracy especially the weight matrix in the GSTAR model.

Design and calibration of unicapillary pneumotachographs

1998 ◽  
Vol 84 (1) ◽  
pp. 335-343 ◽  
Author(s):  
A. Giannella-Neto ◽  
C. Bellido ◽  
R. B. Barbosa ◽  
M. F. Vidal Melo
Keyword(s):  
Respiratory Mechanics ◽  
Ambient Pressure ◽  
Animal Experiments ◽  
Small Animal ◽  
Positive Pressure ◽  
Linear Calibration ◽  
Third Order ◽  
Order Polynomial ◽  
Internal Radius ◽  
Volume Measurements

Giannella-Neto, A., C. Bellido, R. B. Barbosa, and M. F. Vidal Melo. Design and calibration of unicapillary pneumotachographs. J. Appl. Physiol.84(1): 335–343, 1998.—This study presents a method for design and calibration of unicapillary pneumotachographs for small-animal experiments. The design, based on Poiseuille’s law, defines a set of internal radius and length values that allows for laminar flow, measurable pressure differences, and minimal interference with animal’s respiratory mechanics and gas exchange. A third-order polynomial calibration (Pol) of the pressure-flow relationship was employed and compared with linear calibration (Lin). Tests were done for conditions of ambient pressure (Pam) and positive pressure (Ppos) ventilation at different flow ranges. A physical model designed to match normal and low compliance in rats was used. At normal compliance, Pol provided lower errors than Lin for mixed (1–12 ml/s), mean (4–10 ml/s), and high (8–12 ml/s) flow rate calibrations for both Pam and Ppos inspiratory tests (P < 0.001 for all conditions) and expiratory tests ( P < 0.001 for all conditions). At low compliance, they differed significantly with 8.6 ± 4.1% underestimation when Lin at Pam was used in Ppos tests. Ppos calibration, preferably in combination with Pol, should be used in this case to minimize errors (Pol = 0.8 ± 0.5%, Lin = 6.5 ± 4.0%, P < 0.0005). Nonlinear calibration may be useful for improvement of flow and volume measurements in small animals during both Pam and Ppos ventilation.

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