# reshape_daily

`reshape_daily` reshapes daily time series from 1D to 3D or from 3D to 1D. 3D time series coordinates correspond to DAYSxMONTHSxYEARS and will always be 31x12xNUMBEROFYEARS. Missing data values and non-real days (e.g. April 31) are replaced by `NaN` when reshaping to 3D.

## Contents

## Syntax

[s,t] = reshape_daily(s,t) [s,t,year,month,day] = reshape_daily(s,t)

## Description

`[s,t] = reshape_daily(s,t)` returns reshaped time series arrays corresponding to time `t` and the signal `s`. If input arrays are Nx1 or 1xN, 3D arrays `s` and `t` are returned. If input arrays are 3D, Nx1 arrays are returned. Time array `t` must be in `datenum` format.

`[s,t,year,month,day] = reshape_daily(s,t)` also returns year, month, and day arrays corresponding to `t`.

## Example 1: Daily time series of temperature data.

Consider the following data collected daily, with a few days of missing data.

t = (datenum(1937,3,5):datenum(1941,6,9))'; % daily time vector t(105) = []; % missing measurements, perhaps t(210:215) = []; % more missing data temp = -12*cos(2*pi*t/365.25)+t*5e-4-280+rand(size(t)); % daily temperature data figure plot(t,temp,'b-') datetick xlabel('time') ylabel('measured temprature ({\circ}F)')

Above we see our measurements. There seems to be a strong seasonal cycle, with a slight positive trend over the measurement period. Before we start analyzing this data, let's start by exploring the structure of the 3D output of `reshape_daily`. First, let's only look at days of the month.

[~,~,~,~,days] = reshape_daily(temp,t);

Each month has up to 31 days, there are 12 months in the year, and our data set contains data from five years, so our `days` matrix is 3D of dimensions `31x12x5`. Each `31x12` matrix along dimension 3 is identical, so we will only look at days of the month from the first year:

days(:,:,1)

ans = 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 16 16 17 17 17 17 17 17 17 17 17 17 17 17 18 18 18 18 18 18 18 18 18 18 18 18 19 19 19 19 19 19 19 19 19 19 19 19 20 20 20 20 20 20 20 20 20 20 20 20 21 21 21 21 21 21 21 21 21 21 21 21 22 22 22 22 22 22 22 22 22 22 22 22 23 23 23 23 23 23 23 23 23 23 23 23 24 24 24 24 24 24 24 24 24 24 24 24 25 25 25 25 25 25 25 25 25 25 25 25 26 26 26 26 26 26 26 26 26 26 26 26 27 27 27 27 27 27 27 27 27 27 27 27 28 28 28 28 28 28 28 28 28 28 28 28 29 NaN 29 29 29 29 29 29 29 29 29 29 30 NaN 30 30 30 30 30 30 30 30 30 30 31 NaN 31 NaN 31 NaN 31 31 NaN 31 NaN 31

With this structure in mind, it's easy to start asking questions about our data. Perhaps you'd like to know, what was the temperature on May 10th, 1939? Start by reshaping the data:

[temp3D,t3D] = reshape_daily(temp,t);

Now we have a 3D matrix containing to the temperature data, and another 3D matrix with corresponding dates. Missing data and non-real dates have been filled with `NaN`. 1939 is the third year of our data set, so the coordinates of May 10, 1939 will be DAY,MONTH,YEAR, or `10,5,3`. See:

datestr(t3D(10,5,3))

ans = 10-May-1939

So, the temperature on May 10, 1939 is in the 3D temperature matrix here:

temp3D(10,5,3)

ans = 79.7808

It was about 80 degrees that day. Sounds delightful. Is May 10th always this nice?

mean(temp3D(10,5,:))

ans = 79.7532

std(temp3D(10,5,:))

ans = 0.3797

Well, five years of data may not be enough for proper statistical analysis, but yes, it seems that May 10th tends to be real nice.

Daily values are often subject to high variability, so you may wish to look at the entire month of May. How did May temperatures look from 1937 to 1941?

MayTemps = squeeze(mean(temp3D(:,5,:))) figure plot(1937:1941,MayTemps,'-s') xlabel('year') ylabel('May monthly average temp')

MayTemps = 80.2884 80.4223 80.5307 80.7292 80.9565

Perhaps you would like to look at *all* monthly averages. For this we'll use the `nanmean` function which is in the Statistics Toolbox. You can also find a similar version of `nanmean` here: http://www.mathworks.com/matlabcentral/fileexchange/6837

monthlyAvg = squeeze(nanmean(temp3D)) figure plot(1937:1941,monthlyAvg,'-o') legend('jan','feb','mar','apr','may','jun','july','aug','sept','oct','nov','dec') xlabel('year') ylabel('monthly average temperatures')

monthlyAvg = NaN 62.5993 62.7255 62.9494 63.0591 NaN 64.1665 64.3837 64.4945 64.7655 68.6635 68.4097 68.5203 68.9098 69.0135 74.2630 74.4626 74.4896 74.9030 75.0827 80.2884 80.4223 80.5307 80.7292 80.9565 84.5445 84.7833 84.9414 85.1760 84.1798 86.0997 86.4182 86.6034 86.6924 NaN 84.5552 84.7987 84.8963 85.1269 NaN 80.2348 80.3245 80.6865 80.7135 NaN 73.6814 74.4581 74.6800 74.7186 NaN 68.3297 68.5399 68.7864 68.9123 NaN 63.9710 64.3024 64.3980 64.5967 NaN

Note that the first couple of months in 1937 have missing data, and the last several months in 1941 also have missing data. That's because we never had data for those months in the fist place. Also note that March of the first year shows a monthly average despite not have a full monthsworth of data. Same goes for June of 1941.

## Example 2: From 3D to 1D.

To return back to columns of dates and data, simply feed those 3D matrices back into the `reshape_daily` function:

[temp1D,t1D] = reshape_daily(temp3D,t3D);

Now `temp1D` and `t1D` should be identical to the `t` and `temp` vectors we started with.

## Author Info

This script was written by Chad A. Greene of the University of Texas Institute for Geophysics, May 2014. This function includes code from Jos van der Geest's insertrows v2, which can be found here: http://www.mathworks.com/matlabcentral/fileexchange/9984