Quantitative Evaluation of Spatial Interpolation Models Based on a Data-Independent Method - Advances in Data, Methods, Models and Their Applications in Geoscience - page 53

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Quantitative Evaluation of Spatial
Interpolation Models Based on a
Data-Independent Method
Xuejun Liu, Jiapei Hu and Jinjuan Ma
Key Laboratory of Virtual Geographic Environment (Nanjing Normal University),
Ministry of Education, Nanjing,
School of Geography Science, Nanjing Normal University, Nanjing,
China
1. Introduction
Spatial interpolation, i.e. the procedure of estimating the value of properties at unsampled
sites within areas covered by existing observations (Algarni & Hassan, 2001), appears
various models using local/global, exact/approximate and deterministic/geostatistical
methods. As being an essential tool for estimating spatial continuous data which plays a
significant role in planning, risk assessment and decision making, interpolation methods
have been applied to various disciplines concerned with the Earth's surface, such as
cartography (Declercq, 1996), geography (Weng, 2002), hydrology (Lin & Chen, 2004),
climatology (Attorre et al, 2007), ecology (Stefanoni & Ponce, 2006), agriculture and
pedology (Wang et al, 2005; Robinson & Metternicht, 2006), landscape architecture (Fencik &
Vajsablova, 2006) and so on.
Since spatial interpolation is based on statistics, there are inevitably a certain assumptions
and optimizations. As a result, errors introduced by spatial interpolation and their
propagation in analysis models will certainly influence the quality of any decision-making
supported by spatial data. This has been one of the hot issues of geographical information
science in recent years (David et al, 2004; Shi, W. Z, et al, 2005; Weng, 2006). There are many
factors affecting the performance of spatial interpolation methods. The errors are mainly
generated from sample data density (Stahl et al., 2006), sample spatial distribution (Collins
and Bolstad, 1996), data variance (Schloeder et al., 2001), grid size or resolution (Hengl,
2007), surface types (Zimmerman et al., 1999) and interpolation algorithms (Weng, 2006).
However, there are no consistent findings about how these factors affect the performance of
the spatial interpolators (Li & Heap, 2011). Therefore, it is difficult to select an appropriate
interpolation method for a given input dataset.
With the increasing applications of spatial interpolation methods, there is a growing concern
about their accuracies and evaluation measures (Hartkamp et al., 1999). The previous
studies have greatly focused on individual evaluation methods of spatial interpolation
(Weber & Englund, 1992 & 1994; Erxleben et al, 2002; Chaplot, 2006; Weng, 2006; Erdogan,
2009; Bater & Coops, 2009). It is necessary to explore comprehensive evaluation methods of
interpolation accuracy. Two fundamental issues related to assessment measures of
interpolation are addressed here as follows.