time interpolation of a 3d matrix containing wind speed data

Hello everyone,

I am not an expert user and I would like to ask some information regarding time interpolation. I am running simulations to generate wind waves and as you know, the crucial point is to have wind data with good quality. For my simulations I used ERA5 wind data ( reanalysis) but I was told to compare the wind field with wind data coming from altimeters, for example IFREMER. The objective of the comparison is to correct some possible biases in the wind field.

Now, the problem is that ERA5 collects data every hour while IFREMER provides data every 6 hours. Since I am now focusing on the year 2011, for example, in the first case I have 8760 values while in the second case I have 1460 values.

Basically I have two 3D matrices: u10_ERA5 (81x109x8760) and u10_IFREMER (81x109x1460). The first two dimensions represent wind intensity for defined sets of longitude and latitudes ( the same for both matrices). Since the wind data coming from IFREMER is more accurate, I would like to modify the ERA5 matrix in order to increase the quality of the wind.

Here I attached two drawings I made ( just to give an idea of what I am thinking to do)

Could you provide a code that can help me in this?

Thank you a lot

Answer 1

[Star Strider]

The retime or synchronize would likely be more apporpriate here, however the resample function could work (and interp1 is an option as well). I would downsample the hourly data to the every-six-hour data rather than upsample the every-six-hour data. The reason is that upsampling creates data where none previously existed. You cannot determine what the IFREMER data actually were at the hourly times, so any comparisons of interpolated hourly data to the ERA5 data would likely not be valid.

So I would use retime or synchronize to downsample the ERA5 data to the same times as the IFREMER data and go from there.

[Tiziano Bagnasco]

thank you a lot for your answer! I actually relized that the two 3d matrices are defined on the same longitude and latitude points but for u10_ERA5 latitude goes from 29 to 2 degrees while for u10_IFREMER latitude goes from 2 to 29. Which means that I cannot make comparisons considering the same index, right?

I need to rearrange one of the two matrices but i don't kow how.. Do you know a way to do it? thank you again.

[Star Strider]

My pleasure!

This might be possible using the flip function, however I would need your data to experimant with, since I do not know how to simulate it.

EDIT — (5 Jun 2023 at 14:32)

I just now figured out how to simulate it.

The flip approach seems to work, although the plots are the same because of the way the MATLAB plotting functions (here surf) work.

The matrices themselves are flipped appropriately, as can be seen by examining the first and third dimensions of both ‘A3’ and ‘flipLatA3’ (the second dimension is the same column-wise, so it does not demonstrate any changes) —

Latv = linspace(29,2, 7);
Lonv = linspace(90, 120, 8);
[Lat,Lon] = ndgrid(Latv,Lonv);
WVel = Lat.^2/100 + Lon.^2/100;

A3 = cat(3, Lat,Lon, WVel)

A3 = 
A3(:,:,1) =

   29.0000   29.0000   29.0000   29.0000   29.0000   29.0000   29.0000   29.0000
   24.5000   24.5000   24.5000   24.5000   24.5000   24.5000   24.5000   24.5000
   20.0000   20.0000   20.0000   20.0000   20.0000   20.0000   20.0000   20.0000
   15.5000   15.5000   15.5000   15.5000   15.5000   15.5000   15.5000   15.5000
   11.0000   11.0000   11.0000   11.0000   11.0000   11.0000   11.0000   11.0000
    6.5000    6.5000    6.5000    6.5000    6.5000    6.5000    6.5000    6.5000
    2.0000    2.0000    2.0000    2.0000    2.0000    2.0000    2.0000    2.0000


A3(:,:,2) =

   90.0000   94.2857   98.5714  102.8571  107.1429  111.4286  115.7143  120.0000
   90.0000   94.2857   98.5714  102.8571  107.1429  111.4286  115.7143  120.0000
   90.0000   94.2857   98.5714  102.8571  107.1429  111.4286  115.7143  120.0000
   90.0000   94.2857   98.5714  102.8571  107.1429  111.4286  115.7143  120.0000
   90.0000   94.2857   98.5714  102.8571  107.1429  111.4286  115.7143  120.0000
   90.0000   94.2857   98.5714  102.8571  107.1429  111.4286  115.7143  120.0000
   90.0000   94.2857   98.5714  102.8571  107.1429  111.4286  115.7143  120.0000


A3(:,:,3) =

   89.4100   97.3080  105.5733  114.2059  123.2059  132.5733  142.3080  152.4100
   87.0025   94.9005  103.1658  111.7984  120.7984  130.1658  139.9005  150.0025
   85.0000   92.8980  101.1633  109.7959  118.7959  128.1633  137.8980  148.0000
   83.4025   91.3005   99.5658  108.1984  117.1984  126.5658  136.3005  146.4025
   82.2100   90.1080   98.3733  107.0059  116.0059  125.3733  135.1080  145.2100
   81.4225   89.3205   97.5858  106.2184  115.2184  124.5858  134.3205  144.4225
   81.0400   88.9380   97.2033  105.8359  114.8359  124.2033  133.9380  144.0400

figure
surf(A3(:,:,1), A3(:,:,2), A3(:,:,3))
colormap(turbo)
xlabel('Lat')
ylabel('Lon')
zlabel('Wvel')

flipLatA3 = flip(A3,1)

flipLatA3 = 
flipLatA3(:,:,1) =

    2.0000    2.0000    2.0000    2.0000    2.0000    2.0000    2.0000    2.0000
    6.5000    6.5000    6.5000    6.5000    6.5000    6.5000    6.5000    6.5000
   11.0000   11.0000   11.0000   11.0000   11.0000   11.0000   11.0000   11.0000
   15.5000   15.5000   15.5000   15.5000   15.5000   15.5000   15.5000   15.5000
   20.0000   20.0000   20.0000   20.0000   20.0000   20.0000   20.0000   20.0000
   24.5000   24.5000   24.5000   24.5000   24.5000   24.5000   24.5000   24.5000
   29.0000   29.0000   29.0000   29.0000   29.0000   29.0000   29.0000   29.0000


flipLatA3(:,:,2) =

   90.0000   94.2857   98.5714  102.8571  107.1429  111.4286  115.7143  120.0000
   90.0000   94.2857   98.5714  102.8571  107.1429  111.4286  115.7143  120.0000
   90.0000   94.2857   98.5714  102.8571  107.1429  111.4286  115.7143  120.0000
   90.0000   94.2857   98.5714  102.8571  107.1429  111.4286  115.7143  120.0000
   90.0000   94.2857   98.5714  102.8571  107.1429  111.4286  115.7143  120.0000
   90.0000   94.2857   98.5714  102.8571  107.1429  111.4286  115.7143  120.0000
   90.0000   94.2857   98.5714  102.8571  107.1429  111.4286  115.7143  120.0000


flipLatA3(:,:,3) =

   81.0400   88.9380   97.2033  105.8359  114.8359  124.2033  133.9380  144.0400
   81.4225   89.3205   97.5858  106.2184  115.2184  124.5858  134.3205  144.4225
   82.2100   90.1080   98.3733  107.0059  116.0059  125.3733  135.1080  145.2100
   83.4025   91.3005   99.5658  108.1984  117.1984  126.5658  136.3005  146.4025
   85.0000   92.8980  101.1633  109.7959  118.7959  128.1633  137.8980  148.0000
   87.0025   94.9005  103.1658  111.7984  120.7984  130.1658  139.9005  150.0025
   89.4100   97.3080  105.5733  114.2059  123.2059  132.5733  142.3080  152.4100

figure
surf(flipLatA3(:,:,1), flipLatA3(:,:,2), flipLatA3(:,:,3))
colormap(turbo)
xlabel('Lat')
ylabel('Lon')
zlabel('Wvel')

.