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%nakedsoftware.org opensource license, copyright 2010 stephane.poirier@oifii.org % %developed by Stephane Poirier, M.Sc. Optical Physics, Remote Sensing Application Software Developer (1991-2010) % %this function is part of oifii.org's ar\sp\ Microwave- derived 30-year Canada-Alaska Daily Temperature and Snowcover Databases library % %this function is part of oifii.org's ar\sp\'this folder' application (lauched with ar\sp\'this file'.m) %oifii.org's ar\sp\affiche_carte application is part of the oifii.org's ar\sp set of applications which %may also contain similar variant versions of this function with identical filename. % %A geophysical research paper about this work has been submitted in June 2009 for publication in JGR-Atmosphere %Royer, A. and Poirier S., Surface temperature spatial and temporal variations in North America from homogenized %satellite SMMR-SSM/I microwave measurements and reanalysis for 1979-2008, Journal of Geophysical Research - Atmosphere, %Submitted June 2009, http://www.oifii.org/tsatdb/Royer- Poirier_Microwave-derived-daily-surface- temperature_JGR2009JD012760_R2.pdf % %This study's database can be downloaded from the author web site at: %http://www.oifii.org/tsatdb/Royer-Poirier_Microwave-derived- daily-surface-temperature-db_1979-2008.zip % %this function is used to display the raw microwave raster data (NSIDC's SMMR and SSMI satellite, ref. nsidc.org) % %usage: % 20yymmmdd % %version 0.0, 20yymmmdd, spi, initial function draft % %nakedsoftware.org opensource license, copyright 2010 stephane.poirier@oifii.org

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function [a,delta_a,b,delta_b] = trend(x,y,ordre,t,relative) % INPUT % ordre : degre du polynome % t : coef de student % relative % = 0 absolue % = 1 donne coef. directeur et intervalle de confiance % en % [p,s]=polyfit(x,y,ordre) ; % coef des polynome if length(p)==2 n = length(x) ; % degre de liberte dl = length(x)-2 ; % y = ax + b a = p(1,1) ; b = p(1,2) ; % coefficient de correlation r = corrcoef(x,y) ; r = r(1,2) ; % ecart type residuel syx = sum(y.*y) - (sum(y)*sum(y)/n) ; syx = syx - a*a*(sum(x.*x)-(sum(x)*sum(x)/n)) ; syx = sqrt(syx/dl) ; % ecart type de y sy=syx/sqrt(1-r*r) ; % estimateur de ecart type % de la pente Sa = a * sqrt((1-r*r)/(r*r*(dl))) ; % ou encore : Sa = syx / sqrt(sum((x - mean(x)).^2) ) % de l'ordonnee a origine s = 0 ; e = sum(x.* x) / n ; Sb = Sa * sqrt(e) ; clear e ; delta_a = t * abs(Sa / sqrt(dl)) ; delta_b = t * abs(Sb / sqrt(dl)) ; % Variation relative % x1 = x(1) ; % x2 = x(length(x)) ; % aabsolu = a * (x2-x1) ; % arel = (a * (x2-x1)) / mean(y) ; % amax = a + abs(delta_a) ; % amax = (amax * (x2-x1)) / mean(y); % amin = a -abs(delta_a) ; % amin= (amin * (x2-x1)) / mean(y); end %---------------------% % SORTIE % %---------------------% if relative == 1 a=arel ; %abs(arel-amin) %abs(arel-amax) delta_a=mean([abs(arel-amin),abs(arel-amax)]); end

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