Formalism for Comparing Rain Estimation Designs

North, Gerald R.; Nakamoto, S.

doi:10.1175/1520-0426(1989)006<0985:ffcred>2.0.co;2

Cited by 110 publications

(86 citation statements)

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“…There are differences in treating the attenuation and scattering in the signal, separating rainfall response from surface variability, accounting for rainfall inhomogeneity in the radiometer field-of-view, and distinguishing between warm rain events and non-precipitating cloud liquid water (Wilheit et al 1994). The nonlinear relationship between measured radiances and rain rates, when coupled with rain rate variability within the instantaneous instrument field-of-view, contributes to a retrieval underestimation commonly referred to as the beam filling error (Ferriday and Kummerow 1992;North and Nakamoto 1989). Variations in surface properties and cloud structure contribute additional challenges to estimation algorithms when applied to the global environment (Kummerow et al 1989;Grody 1991).…”

Section: Rainfall Monitoring Techniquesmentioning

confidence: 99%

“…Instantaneous estimates are often averaged in space and time to produce monthly totals at 1-5 degrees resolution. Although random errors in instantaneous estimates tend to cancel out when averaged together over longer time and space scales, the extreme variability of rainfall results in spatial and temporal sampling errors (Atlas et al 1990;North and Nakamoto 1989).…”

Section: Algorithm Implementationmentioning

confidence: 99%

“…The significance of the temporal and spatial sampling errors depend on the scales at which the rainfall is reported. Instantaneous rain rate errors are usually reported to be about a factor of two, whereas sampling errors are usually reported to be between 25% 50% for global monthly oceanic totals (Chang et al 1993; North and Nakamoto 1989). The diurnal cycle of rainfall, more pronounced over land due to the convection initiated by the daytime warming of the surface, is not adequately sampled by a sun-synchronous orbit.…”

Section: Algorithm Implementationmentioning

confidence: 99%

“…This means that a global mean monthly rainfall estimate may be very accurate even though individual grid points may have substantial sampling errors. North and Nakamoto (1989) proposed that the diurnal component of the sampling error can be separated from the random sampling error, and proposed a formulation for the random component.…”

Section: Errors In Monthly Estimatesmentioning

confidence: 99%

“…As a first step in estimating the theoretical temporal sampling error for monthly and annual rainfall totals, the formulation presented by North and Nakamoto (1989) is used to calculate expected random sampling errors for SSM/I F8 monthly global rainfall totals at one degree resolution. The mean square random sampling error is derived from the characteristic temporal autocorrelation, the time between samples, the integration period, and the coefficient of variance.…”

Section: Errors In Monthly Estimatesmentioning

confidence: 99%

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Satellite remote sensing of global rainfall using passive microwave radiometry

Ferriday¹

1994

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Section: Rainfall Monitoring Techniquesmentioning

confidence: 99%

Section: Algorithm Implementationmentioning

confidence: 99%

Section: Algorithm Implementationmentioning

confidence: 99%

Section: Errors In Monthly Estimatesmentioning

confidence: 99%

Section: Errors In Monthly Estimatesmentioning

confidence: 99%

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Satellite remote sensing of global rainfall using passive microwave radiometry

Ferriday¹

1994

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Statistical intercomparison of idealized rainfall measurements using a stochastic fractional dynamics model

2014

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A statistical method is developed for comparing precipitation data from measurements performed by (hypothetical) perfect instruments using a recently developed stochastic model of rainfall. The stochastic dynamical equation that describes the underlying random process naturally leads to a consistent spectrum and incorporates the subtle interdependence of the length and time scales governing the statistical fluctuations of the rain rate field. The main attraction of such a model is that the complete set of second-moment statistics embodied in the space-time covariance of both the area-averaged instantaneous rain rate (represented by radar or passive microwave data near the ground) and the time-averaged point rain rate (represented by rain gauge data) can be expressed as suitable integrals over the spectrum. With the help of this framework, the model allows one to carry out a faithful intercomparison of precipitation estimates derived from radar or passive microwave remote sensing over an area with direct observations by rain gauges or disdrometers, assuming all the measuring instruments to be ideal. A standard linear regression analysis approach to the intercomparison of radar and gauge rain rate estimates is formulated in terms of the appropriate observed and model-derived quantities. We also estimate the relative sampling error as well as separate absolute sampling errors for radar and gauge measurements of rainfall from the spectral model. Key Points: • Radar and gauge rain estimates are compared using a stochastic rainfall model • The model is based on a stochastic differential equation of fractional order • Estimates of radar-gauge regression parameters are computable from the model Correspondence to: (2014), Statistical intercomparison of idealized rainfall measurements using a stochastic fractional dynamics model,In this paper we apply the stochastic fractional dynamics model formulated in KT13 to a typical precipitation intercomparison scenario that is encountered in the course of ground validation, namely, an intercomparison between radar and gauge estimates of rain. Such an intercomparison involves taking into account two A major caveat in the above argument is the assumption of the retrieval errors being uncorrelated with true rain. An improved treatment would require a more elaborate error model. Fuller [1987] gives examples of such measurement error models. Such an analysis is beyond the scope of our study.

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Regio‐ and Stereoselectivity in the Decatungstate Photocatalyzed Alkylation of Alkenes by Alkylcyclohexanes

Dondi¹,

Ravelli

Fagnoni

et al. 2009

Chemistry A European J

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Tetrabutylammonium decatungstate (WO) photocatalyzes radical alkylation reactions starting directly from alkanes. When using tert-butylcyclohexane and methylcyclohexane as the radical precursors, the addition to electrophilic alkenes (beta,beta-dialkylmethylenemalononitriles, acrylonitrile, methyl acrylate, methyl vinyl ketone) is regioselective and exclusively gives 3- and 4-substituted cyclohexyl adducts, with no significant functionalization of the other positions. Furthermore, when a beta,beta-disubstituted alkene is used, the reaction is stereoselective (cis stereochemistry for the 1,3-cyclohexane derivatives and trans for the 1,4 isomers). Some of the reactions have also been carried out by using benzophenone as the photocatalyst, giving the same product distribution. However, the decatungstate anion is a superior catalyst from a preparative point of view, because it is efficient at low concentrations (0.002 m, 2 mol %) and allows for a simple work up. From a mechanistic point of view, the role of both the alkyl radicals and the radical adducts has been assessed by trapping experiments in the presence of suitable additives (alpha-phenyl-N-tert-butylnitrone, PBN, and 2-methyl-2-nitrosopropane, MNP) and by EPR spectroscopic detection of the resulting nitroxides in solution. Furthermore, trapping by the nitroxide TEMPO (TEMPO = 2,2,6,6-tetramethylpiperidine N-oxide) gives O-(tert-butylcyclohexyl)hydroxylamines, again as only the 3- and the 4-substituted isomers. We conclude that the observed regioselective activation originates from the initial hydrogen abstraction step (the statistically corrected ratio for positions 3 and 4 ranges from 1.1 to 1.35 for all of the trapping products). The selectivity is mainly due to steric hinderence.

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Formalism for Comparing Rain Estimation Designs

Cited by 110 publications

References 0 publications

Satellite remote sensing of global rainfall using passive microwave radiometry

Satellite remote sensing of global rainfall using passive microwave radiometry

Statistical intercomparison of idealized rainfall measurements using a stochastic fractional dynamics model

Regio‐ and Stereoselectivity in the Decatungstate Photocatalyzed Alkylation of Alkenes by Alkylcyclohexanes

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