Discrete wavelet decomposition (wavedec) using less than 365 days per year

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Sara Alonso Vicario 2022-6-25

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https://ww2.mathworks.cn/matlabcentral/answers/1747850-discrete-wavelet-decomposition-wavedec-using-less-than-365-days-per-year

评论： Jonas 2022-6-30

Hi!

I am trying to run a wavelet coherence analysis of daily streamflow from two gage stations. I have for each year daily streamflow from October and November (61 days) over a period of 75 years, that means that I have daily flow only for 61 days a year. This results on 4575 daily flows (75 years x 61 days) in each station.

When I run the wavelet coherence analysis using the 4575 samples I got the following image

However, I do not know how to convert the Normalized Frequency (cycles/sample) to period of years?

I want to understand how coherent were the daily streamflow data for October and November (the fall season) of each year for different periodicities of 1 year, 2years, 4years, and 8years.

How can i understand this normalized frequency?

Thank you for the help!

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Sara Alonso Vicario 2022-6-27

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Hi Jonas,

I am doing the following and please correct me if i am wrong:

I have 61 samples per year, then to estimate the frequency I did the following:

61 (samples / year) * (1 year / 365 days) * (1 day / 24 hours) * (1 hour / 3600 seconds) = 1.9343 E-6 (samples / seconds) or what it is the same 1.9343 E-6 Hz

Then, I calculate the wcoherence function as:

wcoherence(upstream,downstream,0.0000019343)

where I put the two signals (upstream and downstream) and at the end the frequency in Hz as they do here in the Effect of Sampling Frequency on Wavelet Coherence: https://www.mathworks.com/help/wavelet/ref/wcoherence.html

Doing that, I got the following figure:

Then to transform the frequency of the Y axes that it is in nano hertz (nHZ). I did the following knowing that 1 nHz = 1.0E-9 Hz and time = 1 / frequency:

For example to convert 64 nHZ to time in seconds I did:

1 / (64 nHz * 1.0E-9) = 15625000 seconds

and from seconds to years:

15625000 seconds / (1 year * 365 days * 24 hours * 60 minutes * 60 seconds) = 0.495465 years

Therefore, 64 nHz corresponds to approximately half of a year.

I am sure there are simpler ways to do it, but this is how I figure out doing it!

Thank you for your help!

Sara Alonso Vicario 2022-6-29

编辑：Sara Alonso Vicario 2022-6-29

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Hi Jonas!

Thank you for the feedback!

About the first approach to try, do you mean to multiply the nHz of the y axis in the frist Figure by 6, this will mean then 512 nHz * 6 = 3072 nHz?

I have tried to run the wcoherence function using 6 samples/year (365/61) with a frequency equal to:

6 (samples / year) * (1 year / 365 days) * (1 day / 24 hours) * (1 hour / 3600 seconds) = 1.9024E-7

wcoherence(upstream,downstream,0.000000190259)

and this is the resul I got, it is not correct because I got a time period of 700 years in the axis x.

I am not sure why you say "another thing is your sampling frequency, you cut the 365 part here. sampling frequency in the second case is 1/d which equals 1/(24*60*60). you can see also that there must be an error since the x axis range is not correct".

You are right on this affirmation, do you know where the problem may it come? I have 55 years, when I should have 75 years. I checked and I have as input 27394 days of streamflow that are equal to 75 years. I think the sampling frequency is correct that it is 1/(24*60*60) = 0.000015741

I am not into the idea of delete the part where I padded the zero values, I do not think I am going with that option.

I am not sure which approach to take now with these data.

Jonas 2022-6-30

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I have re-run the wavelet coherence function over this new data but with the new frequency:

365 (samples / year) * (1 year / 365 days) * (1 day / 24 hours) * (1 hour / 3600 seconds) = 1.1574E-5

using the following expresion:

wcoherence(upstream,downstream,0.0000157431)

just an error from typing you forgot a 1

num2str(1/(24*60*60),'%.12f')
ans =
    '0.000011574074'

About the first approach to try, do you mean to multiply the nHz of the y axis in the frist Figure by 6, this will mean then 512 nHz * 6 = 3072 nHz?

Yes, the first figure and the yticklabels changed by factor of 6 to compensate for the fact, that the data were taken ober two months only and not over a whole year. in addition, you can also change the yticklabels by your formular from nano Herz to years, to make it better readable

I have tried to run the wcoherence function using 6 samples/year (365/61) with a frequency equal to:

6 (samples / year) * (1 year / 365 days) * (1 day / 24 hours) * (1 hour / 3600 seconds) = 1.9024E-7

i think this does not make sence.

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