Dear Mr. Suman,

If you have missing data and still you want to find any kind of Harmonics than sure FFT will not help you. You can use LSP method as it considers the missing value and finds the possible harmonics if present.

Hope this will help you.

Dear Chintan

Thank you very much for your answer. For your kind information, it is not like missing data. I want to use seasonal data that have only June, July, August and September for the purpose. My question is whether for continuous seasonal data the idea as I mentioned is applicable? What do you mean LSP method? Will you please elaborate?

Please reply.

Regards

Suman

Lomb Scargle Periodogram (LSP) will give you harmonics if present in your data set whether it is continuous or discrete.

Dear Chintan

Thank you so much for quick response. Actually I am not so familiar with these topic. Will you please tell me what I will get from the 1st harmonic from jjas data? I mean when I am applying the same for all months data, first harmonic is called annual, 2nd one is semi annual etc. Whether the same interpretation is valid for this case?

Regards

Suman

Suman,

Your question is not at all silly. It's a common problem and requires some thought to answer it well. But you did leave out one important piece of imformation: how will the JJAS data be used after applying a statistical procedure to eliminate higher harmonics? There are several procedures that might be useful, but which is "best" and which is invalid depends on what you plan to do next with the data. Please give me an idea what is your purpose, hypothesis, and subsequent processing plans, and I will get back to you with a suggestion.

Eric

[email protected]

Respected

Eric S Posmentier

Sir

Thank you very much for your concern. Actually I am a Ph.D scholar studying intra-seasonal and inter-annual variability of Indian Summer Monsoon (ISM) based on seasonal (June-July-August-Sepetmber) rainfall. My research involves the impact of different prominent mode of oscillation such as 10-20 days mode, 30-60 days mode in intraseasonal scale and large scale features like ENSO, IOD in inter-annual scale. Therefore I want to analyze the daily/monthly rainfall data to identify those pattern.

It is reported in earlier literatures of similar kind that for the identification of intraseasonal oscillation they eliminate 1st, 2nd and 3rd harmonic from the data. They are using long term (For example 30 years) monthly data having all the months. In that sense, 1st harmonic gives annual, 2nd harmonic half yearly and 3rd harmonic gives 4 monthly signal and hence after elimination all the three from the data, only the seasonal will retain. This idea is used by a no. of past researchers. As I have told, I am using four months data in each year. I have the following queries:

1) Whether the same idea is valid for my data? I mean for a 30 years of continuous monthly data, harmonic 1 implies annual, harmonic 2 implies 6 monthly, 3rd harmonic implies 4 monthly and so on. As my dataset contains only four months data in each year and therefore not continuous whether the same will be applied?

2) What is the meaning of "seasonal pattern" in the climatological data? Is it the annual one? I have seen that people are subtracting the climatological data from the original data to get the anomaly? what is the reason behind that? Is it for the same?

Please reply. For any further queries, write me.

Sincerely

Suman

Why not look at NCEP reanalysis which is available at least four times daily worldwide for decades: https://www.esrl.noaa.gov/psd/data/composites/hour/

As for Fourier analysis, if you know the time variations of the data (decadal, annual, seasonal, etc.), then you can extract the frequency of oscillation from that dataset, reconstruct a separate dataset based on that, and remove it from the original dataset. This will give you a new dataset that removes this part. Additionally you can separate this into a matrix of datasets that have the climate varying (decadal), seasonal, etc. Also if you're missing months of data each year then you won't be able to understand seasonal variation. A seasonal pattern implies variation dictated by seasonal changes that happen over the course of a year and repeat, hence the pattern. They subtract the long-term variation (climate signal) from the dataset to get seasonal and to ensure that the dataset is not skewed by shifts in climate oscillations that might mask or overwhelm the seasonal signal.

Dear

Edward J Strobach

Sir

Thank you so much for the information. I have observation data which is much better than the reanalysis and hence want to use that.

I couldn't understand some of the points of your reply. Let me clarify:

1) For example if I have a 12 months rainfall data for India, then there will be less rainfall in (Jan, Feb, March), relatively higher in (April, May, June), peak in (July, August, September) and again less in (November, December). This pattern forms a cycle repeats in each year.

Whether to call this is a seasonal cycle or an annual cycle?

What will be its periodicity? As I know annual cycle are those whose periodicity is 1 year? please make the explanation.

2) You have correctly mentioned that this can be done by Fourier Analysis. But for your kind information, I couldn't find a correct practical document to to understand the topic that have the Fourier code and alongwith input data and explanation. Do you have? If yes please share. Is there any easier software like cdo, grads etc. to implement these?

3) Practically, I have seasonal (June-July-August and September) rainfall data for 30 years over all India. I want to find various intra-seasonal oscillation pattern like 10-20 days (Active-Break) and 30-60 days (MJO) oscillation from the data. Will you be so kind to help me how to find those?

Please reply.

Regards

Suman

Dear Suman,

I am not sure to understand very well what you want. If you just want to filter out some frequencies, it may be good to use a spectral filter. I would suggest the Lanczos' one: https://journals.ametsoc.org/doi/10.1175/1520-0450%281979%29018%3C1016%3ALFIOAT%3E2.0.CO%3B2

If you definitely need to use your method, I would say that for this you cannot just use up to three harmonics on your data. Actually, since it is a 4-month period, the first harmonic gives a single cycle over the 4 months ( a 4-month periodicity) , the second harmonic 2 cycles (a 2-month periodicity), the third harmonic 3 cycles (1.3 month periodicity)... Thus considering only the first harmonic should eliminate your "seasonal" cycle.

For more documentation, please go through "Time Series Analysis in Meteorology and Climatology: An Introduction" by Duchon and Hale.

As for software, NCL is the easiest to use in my sense. However, other languages including R and Python can do the job.

Kindest regards