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H-SAF Product Validation Report (PVR) PR-OBS-3

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<strong>Product</strong>s <strong>Validation</strong> <strong>Report</strong>, 30 May 2010 - <strong>PVR</strong>-03 (<strong>Product</strong> <strong>PR</strong>-<strong>OBS</strong>-3) Page 38<br />

Fig. 29 - Meshed structure of the sample H02 product footprint.<br />

Determination of the W(r i,m ) weighting function in Equation 1 is crucial. In open literature, various<br />

approaches are proposed for determining this function. For instance, Thiebaux and Pedder 1987 11<br />

suggested weightings in general as,<br />

2 2<br />

R ri<br />

, m<br />

forri<br />

m<br />

R<br />

2 2<br />

,<br />

W ( r ) R r<br />

(2)<br />

i,<br />

m<br />

0<br />

forr<br />

i,<br />

m<br />

i,<br />

m<br />

R<br />

where R is the radius of influence, r is the distance from centre to the point and is a power parameter<br />

that reflects the curvature of the weighting function. Another form of geometrical weighting function<br />

was proposed by Barnes 1964 12 as,<br />

ri<br />

, m<br />

W ( ri<br />

, m)<br />

exp 4<br />

(3)<br />

R<br />

Unfortunately none of these functions are observation dependent but suggested on the basis of the<br />

logical and geometrical conceptualizations only. They are based only on the configuration, i.e. geometry<br />

of the measurement stations and do not take into consideration the natural variability of the<br />

meteorological phenomenon concerned. In addition, the weighting functions are always the same from<br />

site to site and time to time. However, in reality, it is expected that the weights should reflect to a certain<br />

extent the regional and temporal dependence behaviour of the phenomenon concerned.<br />

For the validation activities, the point cumulative semi-variogram technique proposed by Şen and Habib<br />

1998 13 is used to determine the spatially varying weighting functions. In this approach, the weightings<br />

not only vary from site to site, but also from time to time since the observed data is used. In this way,<br />

the spatial and temporal variability of the parameter is introduced more realistically to the validation<br />

activity.<br />

11 Thiebaux H.J. and M.A. Pedder, 1987: “Spatial objective analysis”. Academic Press, 299 pp.<br />

12 Barnes S.L., 1964: “A technique for maximizing details in numerical weather map analysis”. J. App. Meteor., 3,<br />

pp.396-409.<br />

13 Şen Z. and Z. Habib, 1998: “Point cumulative semivariogram of areal precipitation in mountainous regions”. Journal<br />

of Hydrology 205 (1–2), 81–91.

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