Over an Area, I have few random tracks which are spaced unequally. Along the tracks, the observations are taken at an interval of 1.5 km. The minimum and maximum distance between the two nearby tracks are 100 km and 250 km, respectively. (Please refer the attached fig).
Now I have to convert these XYZ data (lat, long and observations) into a grid format for preparing contour/color map. So I want to know is there any rule to choose grid interval/size or what interval should I choose to grid the XYZ data.
Please suggest me an appropriate way.
You did not say whether the observations were elevations, gamma readings, soil moisture, etc., However, it depends on the data features within the grid. If the maximum distance between tracks encompasses relatively flat data or evenly distributed data, then you can try a smaller interval present in your grid. Your grid size should never be smaller than your shortest X or Y track data distance because it can incorrectly extrapolate existing features. However, you also do not want your XY settings too large because it can then overlook smaller features. Usually you have to experiment with the data in order to balance file size with desired output.
The cell size cannot be bigger than half the size of the minimum object of interest ( Nyquist sampling theory) and also should not be much smaller than the mean LiDAR pulse spacing.
Optimal grid size depends not only on available measurements, but also on the studied process. To estimate relevant scale we either use spatial correlation function or scale parameter from the theory. For example, ocean batimetry can be very detailed, but for the study of propagation of tsunami waves (they are long, with periods of several minutes) the details of less than 1 or few km in non-coastal area are of less importance. This is crucial for simulations, because for very detailed grid it will take too much computing time.
The comments of James and Anahita are also correct.
Given the circumstances i.e., 1.5 km inter-point space and 100-250 km inter-track space it is practically impossible to create a correct raster surface. However, if you assume that the surface in between will be flat then you can interpolate a few data points in between and check manually the raster grid size. Generally it should not be less than data spacing interval unless you interpolate data in between.
Though you can still generate contours but I think that will be wrong practices for a wider area (with larger variability between spacing of x and y, in your case it is around 100x). My suggestion will be you try linear track based assessment of surface by generating even/uneven/cross profiles of the area.
Definitely look at the paper:
Smith and Wessel (1990) Gridding with continuous curvature splines in tension. Geophysics vol. 55, no. 3, p. 293-305.
The steps described in this article are easily implemented using GMT (http://gmt.soest.hawaii.edu). Specifically, check out the surface and blockmean commands.
I believe that what you mean is that you want to interpolate/extrapolate the data onto a grid. A first question is why do you want to do this, i.e. what will you use the results for? Most interpolation methods/software assume that the data locations have Euclidean coordinates however there is free software that will convert lat/long to UTM coordinates (do a search for R packages). Several GIS packages such as ArcGIS (which is commercial) and GRASS (which is open source) include interpolation algorithms. Finally note that what looks like a regular grid in terms of lat/long will not be a regular grid when converted to Euclidean coordinates, e.g. UTM. Is your data "point" data or spatial average data?
Finally note that splines are a special case of Radial Basis functions and in turn interpolation with Radial Basis functions is equivalent to Universal kriging (it looks slightly different and the assumptions appear to be different but the results are the same).
The fact that the tracks are "random" is probably irrelevant and perhaps what you really mean is that they are somewhat erratic.
What do you know about the phenomenon that generated the data?
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