DATASETS: Global maps of Earth surface temperature $($in Kelvins$)$ and cloud water path $($in g$/$m$^2)$ for July $2004$ every $3$ hrs GMT $(8$ files$/$day x $31$ days$)=248$ x $2,$ Map covers whole globe at $2\mathrm{.}5$ degree intervals $(=72$ x $144$ array$),$ Values are REAL $($xxx$.$xx$)$ in ASCII

Files are in ascii and each data file is a $2\mathrm{.}5$ degree equal angle map $(72$ X$144)$; there are $8$ files per day for $31$ days.

To read JUST one file in matlab:

mtx$=$load$($filename$)$;

mtx$=$reshape$($mtx$,72,144)$

It can be read directly into Excel as well.

ASSIGNMENT: Histogram the whole temperature dataset at $1,2$ and $4$K intervals $($bin width$)$ and the whole cloud water path dataset at $0\mathrm{.}1,1$ and $10$ g$/$m$^2$ intervals

CALCULATE: $(1)$ first three moments of the distributions FROM THE HISTOGRAMS $($NOT using built$-$in statistical functions$)$ at all three resolutions, $(2)$ reduce total population by using only every $9$th file and repeat calculation of moments at all three resolutions, $(3)$ determine the $5$th$,50$th and $95$th percentile values at all three resolutions.

TURN IN PLOTS, RESULTS OF CALCULATIONS and ANSWER THESE QUESTIONS:

$(1)$ What did you have to do to be able to histogram the whole dataset?

$(2)$ What tests did you do to indicate you were histogramming the data correctly?

$(3)$ Did you notice any anomalous values in the dataset? What do you think the valid range of values is$?$ What did you do about the anomalous values $($if there are any$)$ before calculating the moments?

$(4)$ How else did you $$look$$ at the data and know you read it correctly?

$(5)$ How did you determine the moments and percentile values FROM the histograms $$ give formulae?

$(6)$ What adjustments to the plot did you make to be able to SEE the details in the histograms $$ did you normalize, did you change the layout, did you use bars or points?

$(7)$ In the histograms, do you notice any behavior that seems artificial? Is the behavior the same at all three resolutions? Describe it and speculate on possible causes.

$(8)$ Comment on the quality of the data based on your histograms: is the precision constant over the whole range? Can you estimate the noise in the data? How does the noise compare with the $$real$$ variability? How did you decide? How did changing the size of the data set affect the noise in the data?

$(9)$ Is the distribution shape Gaussian? How do the average and $50$th percentile values compare at all three resolutions? How is the average affected if you remove the values below the $5$th percentile and above the $95$th percentile?

Preliminary work due monday the week before full assignment: make histograms for the first binsizes for surface temperature and water path.