Dear questioners,
> Dear community, > > we are applying kriging to remove clouds from satellite observations of > chlorophyll (phytoplankton). In order to estimate the error we need also to > quantify cloud patchiness. We do this by using the histogram of the number > of available data points as a function of the distance (that I will call just > ''histogram" in the following) as a kind of spectral analysis of the cloud > coverage. The scale of the patches appear very clear in this histogram. My > questions are: > 1. Is there a standard name for the "number of available data points as a > function of the distance"? It is in fact a kind of two-point structure > function. > I do not exactly understand how your "histogram" is exactly defined (one decision would be: cumulative number of points, number of points in a ring, maybe normalized with the perimeter and another decision would be whether or not to condition to presence or absence of data) and likewise I do not really understand the input data (is the available data more an image with holes like with image analysis or more a set of scattered points like with point processes). However in at least 6 of the 3*2*2=12 possibilities the object you describe seams at least closely related to structure functions used in spatial statistics either in indicator kriging, points processes or with random closed sets/mathematical morphology. So if you would be more precise, I could be more precise in the answer. Your function might well be a) the pair correlation of points processes or b) the second product moment of random closed sets or c) the covariance function indicator kriging+p(1-p). All three objects would be roughly compatible with your short description. Obviously in these disciplines the interpretation would not be in terms of "available data/not available data" but in terms of "cloud/non cloud". But the interpretation is not relevant as long as we are discussing characterization only, e.g. as characterization of objects (i.e. clouds) or available data (point processes). > 2. Has anybody before used this histogram for quantifying patchiness? Since > patches in kriging reconstruction are typical, the use of this histogram > should be quite standard, but I could not find anything in the literature. > Obviously such structure function have been applied to characterize structures including things like fractal behavior or sizes of typical objects. As you point out your histogram is a second order structure function. And therefore the question would be, what is in the histogram, what is not in the standard second order structure function used in the situation (e.g. in the indicator variogram or indicator covariance)? Maybe the histogram (in this case an affinely transformed variogram) has a more direct and easy interpretation. And probably you can offer an interpretation in terms of kriging error. I would therefore ask the following questions: 1) Is your "available data" better described by a black and white image (white=available, black=unknown) (making the patch an object of mathematical morphology) or by a list of coordinates of available data (making the patch a cluster of point processes), or is the situation somehow in between kriging with a "nearly" complete grid? 2) I assume the histogram reports number of available points per area in a given distance (with some tolerance defined by the width of the bar) 3) Does "in a given distance" mean: -> distance from a typical location (probably useless) -> distance from a not available location (variogram type) -> distance from an available location (product moment type) 4) What is the relation to kriging? Because for the problems looks like an image reconstruction problem. Applying kriging seams quite tricky here. Best regards, Gerald v.d. Boogaart Am Freitag, 5. Januar 2007 13:21 schrieb L.: > Dear community, > > we are applying kriging to remove clouds from satellite observations of > chlorophyll (phytoplankton). In order to estimate the error we need also to > quantify cloud patchiness. We do this by using the histogram of the number > of available data points as a function of the distance (that I will call just > ''histogram" in the following) as a kind of spectral analysis of the cloud > coverage. The scale of the patches appear very clear in this histogram. My > questions are: > > 1. Is there a standard name for the "number of available data points as a > function of the distance"? It is in fact a kind of two-point structure > function. > > > 2. Has anybody before used this histogram for quantifying patchiness? Since > patches in kriging reconstruction are typical, the use of this histogram > should be quite standard, but I could not find anything in the literature. > > Laurent Dubrocca, Francesco d'Ovidio, Yoav Lehahn > > > > > > __________________________________________________ > Do You Yahoo!? > En finir avec le spam? Yahoo! Mail vous offre la meilleure protection > possible contre les messages non sollicités > http://mail.yahoo.fr Yahoo! Mail > > + > + To post a message to the list, send it to [email protected] > + To unsubscribe, send email to majordomo@ jrc.it with no subject and > "unsubscribe ai-geostats" in the message body. DO NOT SEND > Subscribe/Unsubscribe requests to the list > + As a general service to list users, please remember to post a summary of > any useful responses to your questions. > + Support to the forum can be found at http://www.ai-geostats.org/ > -- ------------------------------------------------- Prof. Dr. K. Gerald v.d. Boogaart Professor als Juniorprofessor fuer Statistik http://www.math-inf.uni-greifswald.de/statistik/ B�ro: Franz-Mehring-Str. 48, 1.Etage rechts e-mail: [EMAIL PROTECTED] phone: 00+49 (0)3834/86-4621 fax: 00+49 (0)3834/86-4615 (Institut) paper-mail: Ernst-Moritz-Arndt-Universitaet Greifswald Institut f�r Mathematik und Informatik Jahnstr. 15a 17487 Greifswald Germany -------------------------------------------------- + + To post a message to the list, send it to [email protected] + To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
