1 Spatial Modelling of the Terrestrial Environment - Georeferencial

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38 Spatial Modelling of the Terrestrial Environment a. b . c Figure 3.1 Maps of three different snow depth measurement networks: (a) represents the number of stations in the WMO GTS network on 2 February 2001 (maximum snow extent); (b) represents the total COOP station network; (c) represents the FSU network active cooperative station network (COOP) for the contiguous states in the USA. These data are available from the National Oceanic and Atmospheric Administration and have a maximum and mean density of 1 site per 0.26 km 2 and 1 site per 1600 km 2 , respectively. Figure 3.1c shows the station locations of snow depth observations from the former Soviet Union (FSU) for 10 February, 1989. The FSU data are available from the National Snow and Ice Data Center and have a maximum and mean density of 1 site per 0.4 km 2 and 1 site per 14 000 km 2 , respectively. Using the average spatial densities (rather than the maxima), these area densities translate to scale lengths of 1 station per 40 × 40 km, 118 × 118 km and 400 × 400 km for the USA, FSU and WMO datasets, respectively. Therefore, based on McKay and Gray’s specification, potentially the datasets are the most representative at local to regional scales. (It is tempting to consider that the COOP data provide a good opportunity
Snow Depth and Snow Water Equivalent Monitoring 39 to investigate highly local-scale or even micro-scale spatial variability. However, the actual number of stations regularly reporting snow depth or SWE is rather less than this average figure suggests.) To further investigate the spatial variability of snow depth or SWE, the analysis of snow depth variograms was undertaken. Intuitively, there is an inherent spatial dependence of snow depth or SWE in a snow field because locations closer together tend to be more similar than those further apart (see Tobler’s first Law of Geography). This concept can be used to encapsulate the micro-scale of SWE or snow depth variation. ‘Spatial similarity’ of snow depth also can be present over greater distances on account of local or regional controls on snow accumulation (in mountainous terrain or along the track of a snow storm). In other words, spatial autocorrelation of snow depth is probably present at different scales from micro-scales through to broad regional scales. Quantification of the spatial dependence of a variable may be expressed by the semi-variogram. In statistics, observations of a selected property are often modelled by a random variable and the spatial set of random variables covering the region of interest is known as a random function (Isaaks and Srivastava, 1989). In geostatistics, a sample of a spatially varying property is commonly represented as a regionalized variable, that is, as a realization of a random function. The semi-variance (γ ) may be defined as half the expected squared difference between the random functions Z(x) and Z(x + h) at a particular lag h. The variogram, defined as a parameter of the random function model, is then the function that relates semi-variance to lag: γ (h) = 1 2 E[{Z(x) − Z(x + h)}2 ] (1) The sample variogram γ (h) can be estimated for p(h) pairs of observations or realizations, {z (x l + h) , l = 1, 2,...,p (h)} by: ˆγ (h) = 1 p(h) 2 p(h) ∑ {z(x l ) − z(x l + h)} 2 . (2) l=1 As Oliver (2001) states: “[the variogram] provides an unbiased description of the scale and pattern of spatial variation”. It is a useful tool, therefore, for analysing the scale(s) of variation characterized by datasets of measurements of snow depth or snow water equivalent. Variograms were calculated for measured point snow depth data (cm) for three different datasets to investigate spatial dependencies present at different sampling scales. The three dataset frameworks described in Figure 3.1 (the WMO, COOP and FSU snow depth datasets) were used to explore the characteristics of snow depth spatial variability in each dataset. Ideally, datasets containing consistent measurements of SWE should be used, but globally, they are not available routinely so snow depth records are used. Daily samples of snow depth from each dataset were selected for northern hemisphere mid-winters (early February) from the respective archives. Although the same time periods are not represented in each case, the data provide some sense of spatial variability characterized at each scale of measurement. The point snow depth data were projected to the Equal Area Scaleable Earth Grid (EASEgrid) (Armstrong and Brodzik, 1995) and the variograms computed for 2 February, 2001 (WMO), 10 February, 1990 (FSU), 12 February, 1989 (COOP) and 12 February, 1994 (COOP). The WMO data cover the entire northern hemispehere while the FSU data cover
Page 2 and 3: Spatial Modelling of the Terrestria
Page 4 and 5: Copyright C○ 2004 John Wiley & So
Page 6 and 7: Contents List of Contributors Prefa
Page 8 and 9: Contributors Jonathan L. Bamber Sch
Page 10 and 11: List of Contributors xi George Perr
Page 12 and 13: xiv Preface in theory and applicati
Page 14 and 15: 2 Spatial Modelling of the Terrestr
Page 20 and 21: Editorial: Spatial Modelling in Hyd
Page 22 and 23: Editorial: Spatial Modelling in Hyd
Page 24 and 25: 2 Modelling Ice Sheet Dynamics with
Page 26 and 27: Modelling Ice Sheet Dynamics by Sat
Page 46 and 47: 36 Spatial Modelling of the Terrest
Page 68 and 69: 4 Using Coupled Land Surface and Mi
Page 70 and 71: Coupled Land Surface and Microwave
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90 Spatial Modelling of the Terrest
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100 Spatial Modelling of the Terres
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Editorial: Terrestrial Sediment and
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Editorial: Terrestrial Sediment and
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6 Remotely Sensed Topographic Data
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Remotely Sensed Topographic Data fo
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7 Modelling Wind Erosion and Dust E
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Modelling Wind Erosion and Dust Emi
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8 Near Real-Time Modelling of Regio
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Near Real-Time Modelling of Regiona
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High Low TSM Concentration Figure 8
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9 Estimation of Energy Emissions, F
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Fireline Intensity and Biomass Cons
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Figure 9.4 The upper row shows EOS
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PART III SPATIAL MODELLING OF URBAN
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11 Modelling the Impact of Traffic
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Modelling the Impact of Traffic Emi
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PART IV CURRENT CHALLENGES AND FUTU
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268 Index Bi-spectral InfraRed Dete
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270 Index floodplain maps, UK 92 fl
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272 Index Long-Term Ecological Rese
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274 Index snow depth measurement ne
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276 Index urban land use in remotel
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1 Spatial Modelling of the Terrestrial Environment - Georeferencial

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