Cox, DR

Isham, V

Manfreda, S

Porporato, A

Rodriguez-Iturbe, I

English

UCL Discovery

Reply to comment by S. Nadarajah on ‘‘Space-timemodeling of soil moisture: Stochastic rainfall forcingwith heterogeneous vegetation’’S. Manfreda,1 D. R. Cox,2 V. Isham,3 A. Porporato,4 and I. Rodrı ´guez-Iturbe5Received 25 July 2007; accepted 9 August 2007; published 2 October 2007.Citation: Manfreda, S., D. R. Cox, V. Isham, A. Porporato, and I. Rodrı ´guez-Iturbe (2007), Reply to comment by S. Nadarajah on‘‘Space-time modeling of soil moisture: Stochastic rainfall forcing with heterogeneous vegetation,’’ Water Resour. Res., 43, W10602,doi:10.1029/2007WR006378.[1] The comment by Nadarajah [2007] focuses on thespatial correlation function of the rainfall forcing adopted inthe theoretical analysis of the soil water balance addressedby Isham et al. [2005] and Rodrı ´guez-Iturbe et al. [2006]. Inthis expression, we simplified the area of overlap C(u)o ftwo unit discs (representing the rain cells) with centersdistance u apart by adopting a linear approximationCk u ðÞ ¼p   ku 0   u   202   u;8<:ð1Þwhere k is a constant assumed equal to p/2. As shown inFigure 1, this approximation is quite satisfactory. There isonly a slight overestimation in the correlation function ofthe rainfall intensity, as discussed in section 2 of Isham et al.[2005], where the approximated correlation function wascompared with the exact solution of the correlation functionobtained via numerical integration.[2] The great advantage of this hypothesis is that it makesthe model analytically solvable, providing a simple form forthe correlation function of the rainfall field in whichdependence on physically meaningful parameters is clearlydefined. Nevertheless, the use of the solution proposed byNadarajah [2007], based on the Bessel and Struve func-tions, may be useful in further applications of the quotedmodel.ReferencesIsham, V., D. R. Cox, I. Rodrı ´guez-Iturbe, A. Porporato, and S. Manfreda(2005), Representation of space-time variability of soil moisture, Proc.R. Soc., Ser. A, 461(2064), 4035–4055, doi:10.1098/rspa.2005.1568.Nadarajah, S. (2007), Comment on ‘‘Space-time modeling of soil moisture:Stochasticrainfallforcingwithheterogeneousvegetation’’byI.Rodrguez-Iturbe et al., Water Resour. Res., 10, W10601, doi:10.1029/2007WR006257.Rodrı ´guez-Iturbe, I., V. Isham, D. R. Cox, S. Manfreda, and A. Porporato(2006), Space-time modeling of soil moisture: Stochastic rainfall forcingwith heterogeneous vegetation, Water Resour. Res., 42, W06D05,doi:10.1029/2005WR004497.                                                       D. R. Cox, Nuffield College, University of Oxford, Oxford OX1 1NF,UK.V. Isham, Department of Statistical Science, University College London,Gower Street, London WC1E 6BT, UK.S. Manfreda, Dipartimento di Ingegneria e Fisica dell’Ambiente,Universita ` degli Studi della Basilicata, Potenza, I-85100, Italy. (manfreda@unibas.it)A. Porporato, Department of Civil and Environmental Engineering,Duke University, Durham, NC 27708, USA.I. Rodrı ´guez-Iturbe,DepartmentofCivilandEnvironmentalEngineering,Princeton University, Princeton, NJ 08540, USA.Figure 1. Comparison between the area of overlap of twounit discs C(u) and its approximation Ck(u).1Dipartimento di Ingegneria e Fisica dell’Ambiente, Universita ` degliStudi della Basilicata, Potenza, Italy.2Nuffield College, University of Oxford, Oxford, UK.3Department of Statistical Science, University College London, London,UK.4Department of Civil and Environmental Engineering, Duke University,Durham, North Carolina, USA.5Department of Civil and Environmental Engineering, PrincetonUniversity, Princeton, New Jersey, USA.Copyright 2007 by the American Geophysical Union.0043-1397/07/2007WR006378W10602WATER RESOURCES RESEARCH, VOL. 43, W10602, doi:10.1029/2007WR006378, 20071o f1

by the American Geophysical Union.

Comment on ‘‘Space-time modeling of soil moisture:

Representation of space-time variability of soil moisture,

Space-time modeling of soil moisture: Stochastic rainfall forcing with heterogeneous vegetation, Water Resour.

Reply to comment by S. Nadarajah on "Space-time modeling of soil moisture: Stochastic rainfall forcing with heterogeneous vegetation"

Reply to comment by S. Nadarajah on "Space-time modeling of soil moisture: Stochastic rainfall forcing with heterogeneous vegetation"

Abstract

Similar works

Full text

Available Versions

UCL Discovery