Elsevier

Computers & Geosciences

Volume 32, Issue 9, November 2006, Pages 1283-1298
Computers & Geosciences

Finding the right pixel size

https://doi.org/10.1016/j.cageo.2005.11.008Get rights and content

Abstract

This paper discusses empirical and analytical rules to select a suitable grid resolution for output maps and based on the inherent properties of the input data. The choice of grid resolution was related with the cartographic and statistical concepts: scale, computer processing power, positional accuracy, size of delineations, inspection density, spatial autocorrelation structure and complexity of terrain. These were further related with the concepts from the general statistics and information theory such as Nyquist frequency concept from signal processing and equations to estimate the probability density function. Selection of grid resolution was demonstrated using four datasets: (1) GPS positioning data—the grid resolution was related to the area of circle described by the error radius, (2) map of agricultural plots—the grid resolution was related to the size of smallest and narrowest plots, (3) point dataset from soil mapping—the grid resolution was related to the inspection density, nugget variation and range of spatial autocorrelation and (4) contour map used for production of digital elevation model—the grid resolution was related with the spacing between the contour lines i.e. complexity of terrain. It was concluded that no ideal grid resolution exists, but rather a range of suitable resolutions. One should at least try to avoid using resolutions that do not comply with the effective scale or inherent properties of the input dataset. Three standard grid resolutions for output maps were finally recommended: (a) the coarsest legible grid resolution—this is the largest resolution that we should use in order to respect the scale of work and properties of a dataset; (b) the finest legible grid resolution—this is the smallest grid resolution that represents 95% of spatial objects or topography; and (c) recommended grid resolution—a compromise between the two. Objective procedures to derive the true optimal grid resolution that maximizes the predictive capabilities or information content of a map are further discussed. This methodology can now be integrated within a GIS package to help inexperienced users select a suitable grid resolution without doing extensive data preprocessing.

Introduction

A grid cell, popularly known as pixel, is the fundamental spatial entity in a raster-based GIS (Gatrell, 1991, DeMers, 2001). Although there is practically no difference between pixel and grid cell, geoinformation scientists like to emphasize that pixel is a technology and grid is a model (De By, 2001). A grid means ideal properties—orthogonal matrix, fixed resolution, which a raster image does not necessarily has to fit. For example, an aerial photo first needs to be ortho-rectified and then resampled to a regular grid to (approximately) fit the grid model (Rossiter and Hengl, 2002).

Grid cell can be also related (but should not be confused) with the support size, which is typically a fixed area or volume of the land that is being sampled. Support size can be increased by using composite samples or by averaging point-sampled values belonging to the same blocks of land. In geostatistics, one can also control the support size of the output models by averaging multiple predictions per regular blocks of land, which is known as “block kriging” (Heuvelink and Pebesma, 1999). This means that we can sample at point locations, then make predictions for blocks of 10×10m. The latter often confuses GIS users because we can produce predictions at regular point locations (point kriging) and then display them using a raster map, but we can also make predictions for blocks of land (block kriging) and display them using the same raster model (Bishop et al., 2001). This distinction is especially important for the validation of the spatial prediction models because it can lead to serious misconceptions—validating a point model (support size of few centimeters) at 1 km support or vice versa can be quite discouraging (Stein et al., 2001).

Although the raster structure has a number of serious disadvantages such as of under- and over-sampling in different parts of the study area and large data storage requirements, it will remain the most popular format for spatial modelling in the coming years (DeMers, 2001). What makes it especially attractive is that most of the technical characteristics are controlled by a single measure: grid resolution, expressed as ground resolution in meters. The enlargement of grid resolution leads to aggregation or upscaling and decrease of grid resolution leads to disaggregation or downscaling. As grid becomes coarser, the overall information content in the map will progressively decrease and vice versa (McBratney, 1998, Kuo et al., 1999, Stein et al., 2001). In cartography, coarser grid resolutions are connected with smaller scales and larger study areas, and finer grid resolutions are connected with larger scales and smaller study areas. The former definition often confuses non-cartographers because bigger pixel means smaller scale, which usually means larger study area (Fig. 1). Note in Fig. 1, that both aggregation and disaggregation can be done before or after geo-computation. If the model is linear, the two routes should yield the same results (Heuvelink and Pebesma, 1999); if not, there can be serious differences. Aggregation is fairly useful procedure to reduce the small scale variation and get better idea about the general pattern (Stein et al., 2001). In contrast, if our objective is to locate extremes (hot spots), then aggregation is something we should avoid.

Many researchers investigated the effects of grid resolution on the accuracy of their models. Applications range from mapping of soil properties (Florinsky and Kuryakova, 2000), modelling of surface runoff (Kuo et al., 1999, Molnr and Julien, 2000), sea currents (Davies et al., 2000) or modelling of meteorological data (McQueen et al., 1995, Noda and Niino, 2003). In the case of terrain data, aggregation of grid resolutions will seriously deteriorate accuracy of terrain parameters (Weihua and Montgomery, 1994, Dietrich et al., 1995, Thompson et al., 2001). Wilson et al. (2000) demonstrated the impact the grid resolution makes on hydrological analysis: as the grid resolution increased from 30 to 200 m the flow-path length and specific catchment area maps changed drastically. The grid resolution can also be crucial for the accuracy of the simulation model such as surface runoff or erosion models (Sánchez Rojas, 2002). Kienzle (2004) gives a systematic overview of effects of various grid resolutions on the reliability of terrain parameters suggesting finer grid resolutions from 5–20 m. Liang et al. (2004), on the other hand, observed impacts of different spatial resolutions on modelling surface runoff and concluded that the resolution needs to be improved only to a critical level after which the model will not necessarily perform better. Weihua and Montgomery (1994) also got a substantial improvement with 10 m grid resolution over 30 and 90 m data, but 2 or 4 m data gave only marginal improvements. Florinsky and Kuryakova (2000) focused specifically on the importance of grid resolution of terrain parameters on the efficiency of spatial prediction of soil variables. They plotted correlation coefficients versus different grid resolutions and looked for the grid size with most powerful prediction efficiency. Bishop et al. (2001) suggested use of the Shannon's information criterion to select the optimal block size for block kriging. All these experiments clearly prove two things: (1) grid resolution plays an important role for the efficiency of the mapping and (2) its selection can be optimized, to a certain level, to satisfy both processing capabilities and representation of spatial variability.

Although much has been published on the effect of grid resolution on the accuracy of spatial modelling, choice of grid resolution is seldom based on the inherent spatial variability of the input data (Vieux and Needham, 1993, Bishop et al., 2001). In fact, in most GIS projects, grid resolution is selected without any scientific justification. In the ESRI's package ArcGIS, for example, the default output cell size is suggested by the system using some trivial rule: in the case the point data is being interpolated in Spatial Analyst, the system will take the shortest side of the study area and divide it by 250 to estimate the cell size (ESRI, 2002). Obviously, such pragmatic rules do not have a sound scientific background.

This motivated me to produce methodological guides to select a suitable grid resolution for output maps based on the inherent properties of the input data. I tried to relate the choice of grid resolution to measurable cartographic and statistical concepts such as: scale, processing power, positional accuracy, inspection density, spatial dependence structure and complexity of terrain. I will first recommend some general rules of thumb to select the grid resolution and then demonstrate how to select a legible grid resolution given the real datasets.

Section snippets

Grid resolution and cartographic concepts

Although we live in a digital era where we do not necessarily work with hard copy maps, spatial resolution and extent are still strongly related with the traditional cartographic concepts (Quattrochi and Goodchild, 1997, Goodchild, 2001). For example, in traditional soil cartography the scale of an existing map is commonly assessed by estimating either the maximum location accuracy (MLA) or average size area (ASA) of the polygons on the ground (Rossiter, 2003). These cartographic definitions

Example 1: GPS positioning

In this example, I will first demonstrate how to select a grid resolution based on the evaluation of the GPS positioning method. In this case, 100 positioning fixes were recorded using the single-fix GPS positioning method (Arnaud and Flori, 1998) at the control point with a known location. The fluctuation of the GPS readings can be seen in Fig. 8a. The errors ranged from 0.7 to 23.9 m, average error was 8.5 m with a standard distribution of 5.2 m. The error vectors seem to follow the log-normal

Discussion and conclusions

There are three important concepts brought out in this paper that need to be further emphasized. First, principles from the general statistics and information theory, such as Nyquist frequency concept from signal processing and equations to estimate the probability density function, can be closely related to selection of the grid resolution. Second, there are three standard grid resolutions that can be derived for each input data:

  • Coarsest legible grid resolution—this is the largest resolution

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    Detailed instructions to derive a suitable grid resolution available at http://spatial-analyst.net/pixel.php

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