ARRAYS !!!

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ARRAYS allow us to store large amounts of data.

Often in Meteorology and Climate Science we need to:

Read in large amounts of data Perform calculations, statistical analyses etc.

using that data. Save the results (often large numbers of

results)

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Also we often need to:

Perform calculations relative to a grid of imaginary points superimposed on a region:

http://en.wikipedia.org/wiki/Numerical_Weather_Prediction

http://lightning.met.sjsu.edu/%7Eclifford/www/wrf/wrf.html

ARRAYS allow us to store and work with this gridded information

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Finally – many problems have spatial dimensions!Examples…

Information about elevation as we move west to east (1-D problem)

Information about surface pressure as we move west to east AND south to north (2-D problem)

Information about ozone concentration as we move west to east, south to north AND in the vertical (3-D problem)

ARRAYS allow us to store and work with this information

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Three types of arrays are used extensively in MCS:

1. 1-dimensional arrays2. 2-dimensional arrays3. 3-dimensional arrays

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1. 1-dimensional arrays

Same as vectors in your math classes!

Example: We might compute and store values of the Coriolis

parameter ( f = 2 sin(latitude)) at every one degree of latitude in a1-D array (180 values!)

Faster than re-computing the value every time we need it

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2. 2-dimensional arrays

Same as matrices in your math classes!

Example: We might store and forecast values of surface

pressure at every one degree of latitude and every one degree of longitude across the planet in 2-D array (180 values north-south, 360 values west-east)

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3. 3-dimensional arrays

Example: We might store and forecast values of

temperature at every one degree of latitude and every one degree of longitude across the planet and every 1 km in elevation from the surface to 100 km in a 3-D array (180 values north-south, 360 values west-east, 100 values in the vertical)

The atmosphere is 3-dimensional!!

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4. 4-dimensional arrays?

With the 4th dimension being time?

CAN be defined

BUT very space-consuming

NOT preferred in our science

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1. 1-dimensional arrays

A 1-D array is just a string of numbers.Example…values of Coriolis parameter

At the start of code using arrays, we must set aside or declare 2 things:

Names for the arrays Space (memory) for the arrays

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We do this via the DIMENSION

statement.

Example: REAL, DIMENSION(180) :: CORIOLISSays:1. I am declaring “CORIOLIS” to be the name of

a 1-D array 2. The array is real and has 180 elements.

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Another example:

INTEGER, DIMENSION(360) :: LAT

Says:1. I am declaring “LAT” to be the name of a 1-D

array 2. The array is integer and has 360 elements.

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How to access individual array elements…

Suppose we have declared:

REAL, DIMENSION (10) :: ATEST

Then: ATEST(1) refers to the 1st element of array ATEST ATEST(2) refers to the 2nd element of array ATEST ATEST(10) refers to the 10th element of array ATEST ATEST(11) does not exist error message!!

Generally: ATEST(n) refers to the nth element of array ATEST

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Appearance inside code ??? Given: REAL, DIMENSION (100) :: TIME

We might have:

OPEN (18, FILE=‘TIMES.DAT’, STATUS=‘OLD’) DO K = 1, 100 READ (18, 80) TIME(K) ! Reads in 100 values of TIME ENDDO ! Assigns each to an array location80 FORMAT (1X, F10.4)PRINT*, TIME(1), TIME(100) ! Print start and end times

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Another example:

SUM = 0.AVG = 0. DO J = 1, 100 SUM = SUM + TIME(J) ! Adds together values from

the ENDDO ! Array TIME inside the DO loop AVG = SUM / (100.)PRINT*, SUM, AVG

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So a 1-D array is a subscripted variable.

In Fortran77, we always needed to type the subscript form.

e.g., TEMP(I) Could never write just “TEMP” inside the

code In Fortran90, we can either use the subscript

form - TEMP(I) Or just writing TEMP alone is OK!

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Suppose we wish to add two arrays, each with temperatures measurements recorded every minute: TEMP_AUG01 and TEMP_AUG02.

Fortran90

REAL, DIMENSION(1440) :: TEMP_AUG01, TEMP_AUG02REAL, DIMENSION(1440) :: SUMSUM = TEMP_AUG01 + TEMP_AUG02

This statement is legal as long as each array is of dimension (1440)

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Fortran77 version…

REAL TEMP_AUG01 (1440), TEMP_AUG02(1440) REAL SUM(1440) DO 10 JJ=1,1440 SUM(JJ) = TEMP_AUG01(JJ) + TEMP_AUG02(JJ) 10 CONTINUE

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Other things…

I) With:

REAL, DIMENSION(180) :: CORIOLIS

1. READ (20,10) CORIOLIS1. reads in all 180 values…no need to put in a DO loop 2. from UNIT # 20 3. via FORMAT statement # 10

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II) For an array with unchanging values (such as Coriolis values), we can set values as follows:

Example: latitudes every 30 degrees from pole-to-pole

INTEGER, DIMENSION(7) :: LAT

LAT = (/ -90, -60, -30, 0, 30, 60, 90 /) note format using ‘/’or:LAT(1) = -90DO JJ = 2, 7LAT(JJ) = LAT(JJ-1) + 30END DO

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III) We can access a subset of an array as follows:

REAL, DIMENSION(100) :: ARRTSTREAL, DIMENSION(11) :: BSUB

BSUB = ARRTST(50:60:1)

Takes values from ARRTEST elements # 50 – 60 (11 in all) And puts them into array “BSUB”.

BSUB = ARRTST(50:60) is enough to do this!

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