A Wind Wave Co-Cumulative Spectral Model

1970 ◽  
Vol 14 (04) ◽  
pp. 277-295
Author(s):  
Carl F. Kottler

A systematic investigation was made of the parameters chosen to define the Pierson-Moskowitz wind sea spectral model. The model was generalized and the form was extended to give a better fit of the data. Using the same sets of data as those selected by Pierson and Moskowitz for building their model, a least-squares fit of each set of the co-cumulative data gave a corresponding optimum set of parameters. These unique optimum sets of parameters yielded an eightfold decrease in the standard deviation. From this family of parameter sets, a co-cumulative spectral model was. developed to fix some of the parameters and relate the others to surface wind velocity. This modification and extension show that at least a twofold improvement in accuracy over the associated Pierson-Moskowitz co-cumulative model can be achieved.

1984 ◽  
Vol 62 (3) ◽  
pp. 247-253 ◽  
Author(s):  
M. Morillon-Chapey ◽  
G. Guelachvili ◽  
Per Jensen

The infrared spectrum of methyl chloride CH3Cl between 1280 and 1650 cm−1 has been recorded at high resolution (0.005 cm−1). The Coriolis interactions between ν2(A1) and ν5(E) and between 2ν3(A1) and ν5 have been investigated through a least squares fit to the transitions observed for CH335Cl. Ten parameters for the three upper vibrational states and three interaction constants have been determined, reproducing the 1200 observed wavenumbers with a standard deviation of 0.002 cm−1. An accidental resonance of the type l(ΔK = 2, Δl = −1) between ν2 and ν5 was found to be present in the spectrum.


2005 ◽  
Author(s):  
David Wang ◽  
Robert Tamburo ◽  
George Stetten

We have previously developed an algorithm for locating boundaries in an image with sub-pixel resolution, as well as estimating boundary width and image intensity within the adjoining objects. The algorithm operates by finding the parameters of a cumulative Gaussian curve that best approximates an intensity profile taken across a boundary. If intensity is sampled along the image gradient across a boundary, it is reasonable to assume the profile approximates a finite portion of a cumulative Gaussian. Given that assumption, the first derivative of the profile should be the corresponding portion of a Gaussian, completely described by its mean, standard deviation, and amplitude. We present here a simple and rapid method to find those parameters, given that we only have a potentially skewed sample of the Gaussian. The parameters are approximated first for the finite sample, and then both ends of the Gaussian are extrapolated using the resulting parameters. New parameters are then calculated and the procedure is repeated. The optimization rapidly converges, yielding boundary location (mean) with sub-pixel accuracy as well boundary width (standard deviation). Integration then reproduces the cumulative Gaussian, and a least-squares fit is applied to estimate the constant of integration, from which intensity of the adjoining regions can be estimated.


1972 ◽  
Vol 28 (03) ◽  
pp. 447-456 ◽  
Author(s):  
E. A Murphy ◽  
M. E Francis ◽  
J. F Mustard

SummaryThe characteristics of experimental error in measurement of platelet radioactivity have been explored by blind replicate determinations on specimens taken on several days on each of three Walker hounds.Analysis suggests that it is not unreasonable to suppose that error for each sample is normally distributed ; and while there is evidence that the variance is heterogeneous, no systematic relationship has been discovered between the mean and the standard deviation of the determinations on individual samples. Thus, since it would be impracticable for investigators to do replicate determinations as a routine, no improvement over simple unweighted least squares estimation on untransformed data suggests itself.


2015 ◽  
Vol 8 (2) ◽  
pp. 941-963 ◽  
Author(s):  
T. Vlemmix ◽  
F. Hendrick ◽  
G. Pinardi ◽  
I. De Smedt ◽  
C. Fayt ◽  
...  

Abstract. A 4-year data set of MAX-DOAS observations in the Beijing area (2008–2012) is analysed with a focus on NO2, HCHO and aerosols. Two very different retrieval methods are applied. Method A describes the tropospheric profile with 13 layers and makes use of the optimal estimation method. Method B uses 2–4 parameters to describe the tropospheric profile and an inversion based on a least-squares fit. For each constituent (NO2, HCHO and aerosols) the retrieval outcomes are compared in terms of tropospheric column densities, surface concentrations and "characteristic profile heights" (i.e. the height below which 75% of the vertically integrated tropospheric column density resides). We find best agreement between the two methods for tropospheric NO2 column densities, with a standard deviation of relative differences below 10%, a correlation of 0.99 and a linear regression with a slope of 1.03. For tropospheric HCHO column densities we find a similar slope, but also a systematic bias of almost 10% which is likely related to differences in profile height. Aerosol optical depths (AODs) retrieved with method B are 20% high compared to method A. They are more in agreement with AERONET measurements, which are on average only 5% lower, however with considerable relative differences (standard deviation ~ 25%). With respect to near-surface volume mixing ratios and aerosol extinction we find considerably larger relative differences: 10 ± 30, −23 ± 28 and −8 ± 33% for aerosols, HCHO and NO2 respectively. The frequency distributions of these near-surface concentrations show however a quite good agreement, and this indicates that near-surface concentrations derived from MAX-DOAS are certainly useful in a climatological sense. A major difference between the two methods is the dynamic range of retrieved characteristic profile heights which is larger for method B than for method A. This effect is most pronounced for HCHO, where retrieved profile shapes with method A are very close to the a priori, and moderate for NO2 and aerosol extinction which on average show quite good agreement for characteristic profile heights below 1.5 km. One of the main advantages of method A is the stability, even under suboptimal conditions (e.g. in the presence of clouds). Method B is generally more unstable and this explains probably a substantial part of the quite large relative differences between the two methods. However, despite a relatively low precision for individual profile retrievals it appears as if seasonally averaged profile heights retrieved with method B are less biased towards a priori assumptions than those retrieved with method A. This gives confidence in the result obtained with method B, namely that aerosol extinction profiles tend on average to be higher than NO2 profiles in spring and summer, whereas they seem on average to be of the same height in winter, a result which is especially relevant in relation to the validation of satellite retrievals.


1970 ◽  
Vol 13 (2) ◽  
pp. 121-122 ◽  
Author(s):  
H. Späth

Author(s):  
R. Atlas ◽  
R. N. Hoffman ◽  
S. C. Bloom ◽  
J. C. Jusem ◽  
J. Ardizzone

Sign in / Sign up

Export Citation Format

Share Document