Enlola, the first thing that comes to mind is that climate variables are time series. So all the rules that apply to climate series apply to these anomalies.

As I understand your approach, you standardize the variables by assuming a normal distribution and calculating z-scores.

I did this for rainfall in Cambodia during the wettest month and the PDO index because I wanted to determine whether or not floods were related to global or regional factors.

I do believe that standardizing is useful so long as you have a hypothesis to test. My hypothesis is that continental climates are driven by oceanic oscillations.

Eniola, here are some approaches to help answer your question: anomalies show us how strong a deviation is for that specific climate measure. The choice of approach very much depends on what specific property of the climate signal you are interested in. I’d recommend you evaluate them based on as much understanding of the physical phenomenon that causes them. Here are three types of signal analysis evaluation approaches you can apply to analyse climate anomalies:

A. Dynamic process evaluation: For example, the Southern Oscillation Index, a pressure difference standardized anomaly, tells us about tropical ENSO wave dynamics and the chaotic process that is the Pacific ENSO phenomenon. You can evaluate the Eigen modes of this process using Dominant Frequency State Analysis (see Bruun et al., 2017).

B. Extreme value processes: If your question is about the occurrence and potential impact of extremely rare events, evaluate your climate time series using Extreme Value distributions (see Bruun and Tawn, 1998, for a coastal flooding evaluation method of this type).

C. Individual events: where the interest is on 'locally specific in time' events, such as the impact caused by a volcanic eruption, I’d recommend to evaluate the anomalies using transfer function models that include an ARMA intervention function.

It might be useful for readers if you could add some detail to your "climate anomalies". Which datasets are you interested in?

If you are interested in paleoclimatology, NOAA has an online dataset for a 1,100 year reconstruction of El Nino.

https://www.ncdc.noaa.gov/paleo-search/study/11194

I recall someone posing the hypothesis that a Poisson distribution fits the data but I cannot find the reference. The idea was that extreme El Ninos are described by a Poisson distribution.

I can see first standardizing the data using a normal distribution and then running a series of tests using 3 sigma and progressively smaller values to define "extreme" El Nino events. I would expect to see a progression of confirmation of the tests as follows, Poisson, Binomial, Gaussian (normal).

This might be a way to proceed beyond standardization of anomalies. You might find some subsets of the data in which extreme values persist for long periods either on the positive or negative side of the mean. Alternatively, you might find that neither the mean nor the anomalies are stable over time.

Reference:

Li, J., S.-P. Xie, E.R. Cook, G. Huang, R. D'Arrigo, F. Liu, J. Ma, and X.-T. Zheng. 2011. Interdecadal modulation of El Niño amplitude during the past millennium. Nature Climate Change, Vol. 1, Issue 2, pp. 114-118, May 2011 doi:10.1038/nclimate1086

Eniola,

anomalies are a tool to try and answer at best a question. What question are you trying to answer with your anomalies analysis? As you said, there are many ways to compute anomalies. Which on is the best depends on the question you ask.

Remi's suggestion is excellent. Why not share with us at least some details of the variable(s) you intend to analyse?

The question I am trying to answer is to identify wet and dry years, hotter and cooler years from rainfall and temperature records (40 years), respectively in a drainage basin. I want to relate this to groundwater recharge in the drainage basin, because rainfall amount has been argued to be the most significant climate variables that determine the amount of direct recharge in the drainage basin.

would you like to show me the formula of your

so_called "standardized anomalies index; perhaps, i could share some new methods with you! at least, can do a little discussion with you...

thank you

So I would recommend to start simple. Identify the months during which rainfall matters to the recharging process. If in Nigeria, I assume something during April-October for instance. Compute seasonal averages or totals so that you'll get 1 value per year and remove the all years mean of that.

Since you are looking at groundwater recharge at the scale of a basin and at yearly time scale, I would think that high frequency characteristics of rainfall would not matter too much and therefore seasonal average or total would be a good proxy. I am saying this because at smaller time and spatial scale, when soils are saturated with water, there could be runoff instead of recharge, but on bigger scales, the rainfall water will have to end up in the ground at some point.

For temperature, my proposed anomalies might not be too great because wherever your basin is, you probably have a significant trend associated with global warming. So with my anomalies, to caricature a bit, you may have the first 20 years negative anomalies and the last 20 years positive anomalies. If so, you can simply remove the linear trend of those yearly anomalies and that should be good enough.

In any case, unless you have inside knowledge from the beginning, it is always better to start simple, or naively. Then if you don't find the correlations that you would have expected, the naive approach may help you find out why it's too naive, and lead to understand better the processes and refine your analysis. Rather than going straight to very sophisticated analysis that might give you good correlation but that one can't really explain why...

Good luck!

Eniola

Dr Oguntoyinbo collaborated with Derek Hayward in writing the Climatology of West Africa. My copy of their book was published in 1987 a few years before I acquired it. I am not certain if Dr Oguntoyinbo was already at the University of Ibadan when I visited in 1986.

The book has a section on the climatic effects of the Togo Gap, which I understand is related to the question you are raising here. I am certain you have studied the book. At the time the book was written Trewartha was still considered an authority on the causes of climate variations based on atmospheric circulation. We now consider oceanic oscillation such as the ENSOi, the PDO and the AMO to be important drivers of decadal and longer climate variations.

As I mentioned above, I did some work on rainfall for Cambodia last year. The rainfall data I used was from the World Bank website.

URL: http://sdwebx.worldbank.org/climateportal/index.cfm?page=global_map

I was interested in the cost of urban stormwater drainage based on the appropriate design parameters for the (lake) Tonle Sap Region.

But if I were working in Western Nigeria, I would be more interested in drought than flooding, though flooding is probably also a problem in Western Nigeria during the wet season.

For Cambodia, I found 100 years of monthly data on the World Bank web site. I assumed a normal distribution and calculated the mean and standard deviation and z-scores. I found no trend from 1901 to 2001. What I found were extreme events that correlated with the index for the Pacific Decadal Oscillation. I found similar extreme events that corresponded with the ENSO. To find the extreme events, I determined which month had the most rainfall over the entire period and then used that month.

For Western Nigeria I would probably use the driest month for estimating the pattern of extreme drought. So there is a similarity in the statistical approaches.

You might have a look at the WB web site and also at oceanic oscillations that affect the Gulf of Guinea. Unfortunately, some oceanic influences operate on long cycles, too long to be revealed by 40 years of data. Still it is worth a few days effort.

Also, you might find data related to lake levels for lakes outside Nigeria, such as Lake Volta or Lake Kainji that are affected by the same climatic regime you have data for.

However, I am a little puzzled why you are not focusing more on rainfall in the wet season as that would be as much or more related to groundwater resources than the drawdown in the dry season,

There is another factor in your mind map. I wonder if it is the rate of abstraction of the groundwater in comparison with the amount of recharge?

One last point, there are known teleconnections between oceanic oscillations in various ocean basins. Why not test the existence of synchonous patterns by comparing variations in rainfall with ENSO, PDP, and AMO, WASMI, etc. The intensity of the West Aftican Monsoon may be linked to these other indices. Standardization using z-scores would make these comparisons fairly straightforward.

Frederick Colbourne, thank you so much for your contribution. I will greatly appreciate if you can send me a copy of the work you did in Cambodia. Thank you once again.

OK, Eniola. I got your email address from one of your papers and have sent an email.