Confidence limits of expected monthly rainfall

1950 ◽  
Vol 40 (1-2) ◽  
pp. 169-176 ◽  
Author(s):  
H. L. Manning
Keyword(s):  
Weather Forecasting ◽  
Monthly Rainfall ◽  
Confidence Limits ◽  
Optimum Time ◽  
Frequency Distributions ◽  
Normal Distributions ◽  
Accurate Representation ◽  
Practical Applications ◽  
Climatic Regions ◽  
Special Cases

Precise confidence limits of expected monthly rainfall must be regarded as fundamental to the specification of the climatic regions of an agricultural region. The science of weather forecasting is necessarily based on extensive statistics of past experience. However, unless account is taken of such factors as skewness, the means and standard deviations calculated from such statistics will lack the necessary precision and may often be misleading.This paper shows that frequency distributions of monthly rainfall, which were demonstrably skew, may be suitably transformed so that on the new scale they approximate closely to theoretical normal distributions. As a result precise fiducial or confidence limits—shown in fact to fit the data satisfactorily—may be estimated and afterwards reconverted to the original units.Practical applications of these confidence limits include the more accurate representation of rainfall patterns, valuable guides to the vital question of optimum time of planting, and finally, better estimates of the range of mean monthly rainfall where data are available only from a limited number of years.Application of these limits to some special cases is discussed in some detail.

Collagen and elastin fibers in human pulmonary alveolar walls

1988 ◽  
Vol 64 (4) ◽  
pp. 1659-1675 ◽  
Author(s):  
S. S. Sobin ◽  
Y. C. Fung ◽  
H. M. Tremer
Keyword(s):  
Transpulmonary Pressure ◽  
Collagen Fibers ◽  
Capillary Blood ◽  
Fiber Bundles ◽  
Cube Root ◽  
Inflation Pressure ◽  
Frequency Distributions ◽  
Normal Distributions ◽  
Statistical Frequency ◽  
The Mean

The morphology and morphometric data of collagen and elastin fibers in the pulmonary alveolar walls are presented. Specimens were obtained from postmortem lungs quick-frozen at specified transpulmonary pressures. Collagen was stained by silver, and elastin was stained by orcein. Photomicrographs were composed by computer. Young lungs typically show small collagen fibers that radiate from the "posts," whereas larger fiber bundles traverse the septum irrespective of capillary blood vessels. In older lungs, rings of collagen around the posts appear enlarged. Elastin bundles do not show obvious variation in pattern with age and inflation pressure. Statistical frequency distributions of the fiber width and curvature are both skewed, but the square root of the width and the cube root of the curvature have approximate normal distributions. Typically, for young lungs at transpulmonary pressure of 4 cmH2O, the mean of (width)1/2 (in micron1/2) for collagen fibers is 0.952 +/- 0.242 (SD), that of (curvature)1/3 (in micron-1/3) is 0.349 +/- 0.094. The corresponding values for elastin are 0.986 +/- 0.255 and 0.395 +/- 0.094.

scholarly journals Analyzing the turbulence in the Planetary Boundary Layer by the synergic use of remote sensing systems: Doppler wind lidar and aerosol elastic lidar

2018 ◽  
Author(s):  
Gregori de Arruda Moreira ◽  
Juan Luís Guerrero-Rascado ◽  
Jose Antonio Benavent-Oltra ◽  
Pablo Ortiz-Amezcua ◽  
Roberto Román ◽  
...  
Keyword(s):  
Remote Sensing ◽  
Boundary Layer ◽  
Planetary Boundary Layer ◽  
Weather Forecasting ◽  
Saharan Dust ◽  
Aerosol Layer ◽  
Frequency Distributions ◽  
Sensing Systems ◽  
Turbulent Characteristics ◽  
Remote Sensing Systems

Abstract. The Planetary Boundary Layer (PBL) is the lowermost region of troposphere and endowed with turbulent characteristics, which can have mechanical or thermodynamic origins. Such behavior gives to this layer great importance, mainly in studies about pollutant dispersion and weather forecasting. However, the instruments usually applied in studies about turbulence in the PBL have limitations in spatial resolution (anemometer towers) or temporal resolution (aircrafts). In this study we propose the synergetic use of remote sensing systems (microwave radiometer [MWR], Doppler lidar [DL] and elastic lidar [EL]) to analyze the PBL behavior. Furthermore, we show how some meteorological variables such as air temperature, aerosol number density, vertical wind, relative humidity and net radiation might influence the PBL dynamic. The statistical moments of the high frequency distributions of the vertical velocity, derived from DL and of the backscattered coefficient derived from EL, are corrected by two methodologies, namely first lag and −2/3 correction. The corrected profiles present small differences when compare against the uncorrected profiles, showing low influence of noise and the viability of the proposed methodology. Two case studies were analyzed in detail, one corresponding to a well-defined PBL and another one corresponding to a situation with presence of a Saharan dust lofted aerosol layer and clouds. In both cases the results provided by the different instruments are complementary, thus the synergistic use of the different systems allow us performing a detailed monitoring of the PBL.

scholarly journals A brief history of the development of wind-profiling or MST radars

2000 ◽  
Vol 18 (7) ◽  
pp. 740-749 ◽  
Author(s):  
T. E. Van Zandt
Keyword(s):  
Gravity Waves ◽  
Weather Forecasting ◽  
Acoustic Sounding ◽  
Practical Applications ◽  
Radio Science ◽  
Meteorology And Atmospheric Dynamics ◽  
Mst Radar ◽  
History Of ◽  
Instruments And Techniques ◽  
Atmospheric Phenomena

Abstract. The history of the development of the wind-profiling or MST radar technique is reviewed from its inception in the late 1960s to the present. Extensions of the technique by the development of boundary-layer radars and the radio-acoustic sounding system (RASS) technique to measure temperature are documented. Applications are described briefly, particularly practical applications to weather forecasting, with data from networks of radars, and scientific applications to the study of rapidly varying atmospheric phenomena such as gravity waves and turbulence.Key words: Meteorology and atmospheric dynamics (instruments and techniques) · Radio science (remote sensing; instruments and techniques)

Explicit asymptotic results for open times in ion channel models

1997 ◽  
Vol 29 (04) ◽  
pp. 947-964
Author(s):  
Valeri T. Stefanov ◽  
Geoffrey F. Yeo
Keyword(s):  
Single Channel ◽  
Exponential Families ◽  
Markov Renewal Process ◽  
Actual Process ◽  
Asymptotic Results ◽  
Normal Distributions ◽  
Special Cases ◽  
The Difference ◽  
Asymptotic Normal ◽  
Receptor Channel

The dynamical aspects of single channel gating can be modelled by a Markov renewal process, with states aggregated into two classes corresponding to the receptor channel being open or closed, and with brief sojourns in either class not detected. This paper is concerned with the relation between the amount of time, for a given record, in which the channel appears to be open compared to the amount in which it is actually open and the difference in their proportions; this may be used to obtain information on the unobserved actual process from the observed one. Results, with extensions, on exponential families have been applied to obtain relevant generating functions and asymptotic normal distributions, including explicit forms for the parameters. Numerical results are given as illustration in special cases.

scholarly journals A Reanalysis System for the Generation of Mesoscale Climatographies

2010 ◽  
Vol 49 (5) ◽  
pp. 954-972 ◽  
Author(s):  
Andrea N. Hahmann ◽  
Dorita Rostkier-Edelstein ◽  
Thomas T. Warner ◽  
Francois Vandenberghe ◽  
Yubao Liu ◽  
...  
Keyword(s):  
Dynamical Downscaling ◽  
Mesoscale Model ◽  
Eastern Mediterranean ◽  
Daily Rainfall ◽  
Horizontal Resolution ◽  
Monthly Rainfall ◽  
Method Performance ◽  
Diurnal Variability ◽  
Frequency Distributions ◽  
Downscaling Method

Abstract The use of a mesoscale model–based four-dimensional data assimilation (FDDA) system for generating mesoscale climatographies is demonstrated. This dynamical downscaling method utilizes the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5), wherein Newtonian relaxation terms in the prognostic equations continually nudge the model solution toward surface and upper-air observations. When applied to a mesoscale climatography, the system is called Climate-FDDA (CFDDA). Here, the CFDDA system is used for downscaling eastern Mediterranean climatographies for January and July. The downscaling method performance is verified by using independent observations of monthly rainfall, Quick Scatterometer (QuikSCAT) ocean-surface winds, gauge rainfall, and hourly winds from near-coastal towers. The focus is on the CFDDA system’s ability to represent the frequency distributions of atmospheric states in addition to time means. The verification of the monthly rainfall climatography shows that CFDDA captures most of the observed spatial and interannual variability, although the model tends to underestimate rainfall amounts over the sea. The frequency distributions of daily rainfall are also accurately diagnosed for various regions of the Levant, except that very light rainfall days and heavy precipitation amounts are overestimated over Lebanon. The verification of the CFDDA against QuikSCAT ocean winds illustrates an excellent general correspondence between observed and modeled winds, although the CFDDA speeds are slightly lower than those observed. Over land, CFDDA- and the ECMWF-derived wind climatographies when compared with mast observations show similar errors related to their inability to properly represent the local orography and coastline. However, the diurnal variability of the winds is better estimated by CFDDA because of its higher horizontal resolution.

scholarly journals Normal Distribution on the Rotation Group So(3)

1997 ◽  
Vol 29 (3-4) ◽  
pp. 201-233 ◽  
Author(s):  
Dmitry I. Nikolayev ◽  
Tatjana I. Savyolov
Keyword(s):  
Normal Distribution ◽  
Orientation Distribution ◽  
Rotation Group ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
Normal Distributions ◽  
The Central Limit Theorem ◽  
Special Cases ◽  
Wrapped Normal ◽  
Circular Normal Distribution

We study the normal distribution on the rotation group SO(3). If we take as the normal distribution on the rotation group the distribution defined by the central limit theorem in Parthasarathy (1964) rather than the distribution with density analogous to the normal distribution in Eucledian space, then its density will be different from the usual (1/2πσ) exp⁡(−(x−m)2/2σ2) one. Nevertheless, many properties of this distribution will be analogous to the normal distribution in the Eucledian space. It is possible to obtain explicit expressions for density of normal distribution only for special cases. One of these cases is the circular normal distribution.The connection of the circular normal distribution SO(3) group with the fundamental solution of the corresponding diffusion equation is shown. It is proved that convolution of two circular normal distributions is again a distribution of the same type. Some projections of the normal distribution are obtained. These projections coincide with a wrapped normal distribution on the unit circle and with the Perrin distribution on the two-dimensional sphere. In the general case, the normal distribution on SO(3) can be found numerically. Some algorithms for numerical computations are given. These investigations were motivated by the orientation distribution function reproduction problem described in the Appendix.

scholarly journals Genetic Algorithm for Mixed Integer Nonlinear Bilevel Programming and Applications in Product Family Design

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Chenlu Miao ◽  
Gang Du ◽  
Yi Xia ◽  
Danping Wang
Keyword(s):  
Bilevel Programming ◽  
Product Family ◽  
Mixed Integer ◽  
Product Family Design ◽  
Practical Applications ◽  
Special Cases ◽  
Product Family Optimization ◽  
Np Hard Problem ◽  
Family Case ◽  
Continuous And Discrete Variables

Many leader-follower relationships exist in product family design engineering problems. We use bilevel programming (BLP) to reflect the leader-follower relationship and describe such problems. Product family design problems have unique characteristics; thus, mixed integer nonlinear BLP (MINLBLP), which has both continuous and discrete variables and multiple independent lower-level problems, is widely used in product family optimization. However, BLP is difficult in theory and is an NP-hard problem. Consequently, using traditional methods to solve such problems is difficult. Genetic algorithms (GAs) have great value in solving BLP problems, and many studies have designed GAs to solve BLP problems; however, such GAs are typically designed for special cases that do not involve MINLBLP with one or multiple followers. Therefore, we propose a bilevel GA to solve these particular MINLBLP problems, which are widely used in product family problems. We give numerical examples to demonstrate the effectiveness of the proposed algorithm. In addition, a reducer family case study is examined to demonstrate practical applications of the proposed BLGA.

scholarly journals Statistical inference of prehistoric demography from frequency distributions of radiocarbon dates: a review and a guide for the perplexed

2021 ◽  
Author(s):  
Enrico R. Crema
Keyword(s):  
Frequency Data ◽  
Statistical Nature ◽  
Radiocarbon Dates ◽  
Frequency Distributions ◽  
Practical Applications ◽  
Time Frequency ◽  
Comparative Demography ◽  
Frequency Changes ◽  
Past Population

The last decade saw a rapid increase in the number of applications where time-frequency changes of radiocarbon dates have been used as a proxy for inferring past population dynamics. Although its simple and universal premise is appealing and undoubtedly offers some unique opportunities for research on long-term comparative demography, practical applications are far from trivial and riddled by challenges. Here I review: 1) the most common criticisms concerning the nature of radiocarbon time-frequency data as a demographic proxy; 2) the statistical nature of the problem; and 3) three classes of inferential approaches proposed so far in the literature.

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