It is a usual practice of calculating CV for rainfall/precipitation data after detrending the time series as suggested by many authors like (Giorgi et al. 2004; Blazquez et al. 2013). "Say, I have total winter rainfall data in a single time series. I calculated the detrended time series by subtracting the linear trend (or the fitted values of the linear regression) from the actual data. I got both positive and negative values in the detrended time series (Residual). If I calculate the CV (SD/mean) of this time series, the values are infinite as the mean of the time series is nearly zero".
Please kindly guide me. I want to know, where am I doing wrong?
CV use in comparing of two samples or more from different populations and is equal to: CV = [(Standard Deviation of Sample)/(Average of Sample)]*100
Dear Genidy Sir,
That is the definition of CV. But, my query is different. I want to know, if you detrend a time series say X i.e. X - Fittedvalues(x) , the mean is Zero and CV is infinite.
Dear Sergei Sir,
You are correct. If somehow we can remove the slope of the time series than the resulting time series is the detrended time series. I have shown a MatLab plot in this comment please have a look. I think that's what I was actually needed. Now I get a good CV value for the detrended time series. In the figure, we can see the trend line of actual data and the detrended data differ significantly.
Thank you for your short but striking comment.
Dear Arash Sir,
I don't get your point actually. If we have aggregated rainfall data for the winter months (Dec rainfall +Jan rainfall +Feb rainfall), we don't have any zero rainfall there. Still, we could calculate the CV after detrending. So, I don't think there is any concern of removing Zero rainfall.
In case of daily rainfall data, removing zero rainfall events produce erroneous CV values of the "dry day frequency". We just can't ignore the zero rainfall events in such cases.
Yes Sergei Sir,
You pointed out a very crucial point of the curve. As per my understanding, I have a possible answer for this. Please suggest me with your point of view.
To understand this point of intersection we have to think about both ‘climate change’ and the ‘climate variability’. Is there a difference between them? Yes, the answer is the ‘Time’. We all know about the Atlantic Multi Decadal Oscillation (AMO). AMO is nothing but the linearly detrended North Atlantic SST (NASST) anomalies. Again we know that, like ENSO, AMO is an internally generated variability of the global climate system. According to IPCC the internal variability is the variation in the mean state of the climate over a long period of time. As detrending is done to remove the influence of greenhouse gas (GHG) induced global warming from the analysis. So, detrended data can be used to access the internal variability.
I have a short example to first explain your question
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In the first figure (See attachment) of NAO vs NASST against time, we can see the trend line of both NAO and NASST crosses around the time ~1945. If we will have a clear look on that figure we can see that, after 1945, the NASST line lies above the NAO. Before 1945 the scenario is different i.e. the NASST was below the NAO. A possible significance of this point ~1945 is during this time there was a global deeming as seen in the second graph (see attachment). A long term climate of global warming during ~ (1915-1945) changed to global deeming for the period ~ (1945-1975).
So, my answer about the point of intersection is, this is the point where we can see a possible shift in the long term climate. So, we have to find possible reasons for the shift, which may vary from region to region. Getting this intersection point will help in determining point after which there is a significant impact of anthropogenic forcing (or external variability) on the climate change signal.
I'm not sure if it will be useful to you but let me remark that detrending might be misleading if along the time series the statistical proprieties are changing. For that, it can be useful to apply a segmentation method to the time series to identify the intervals where you actually have constant statistical proprieties. The paper http://arxiv.org/pdf/1105.0411v2.pdf provide a possible approach.
Dear Eduardo,
You are right. In a non-stationary time series, we can separate different intervals based on their similar statistical characteristics. As my aim of work is different than doing segmentation, so I have to detrend the data. Thank you for your suggestion.
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