Yes, CV can exceed 1 (or 100%). This simply means that the standard deviation exceed the mean value.

A caveat about doing these measurements on rainfall. Rainfall follows a positive, continuous (or discrete, depending on the scale of measurement) distribution. And likely, there are many zeroes. So, calculation of standard deviation from these raw data is incorrect, as is taking the mean. Thus, CVs for rainfall data often exceed 1 (or 100%). In fact, most researchers in my field seldom acknowledge this distribution when summarizing such data, and this makes the ability to draw conclusions from their work very difficult.

My recommendation: Model your raw data using a modeling approach that allows specification of the data distribution. You should try a Generalized Linear Modeling approach, probably a Generalized Additive Model with a Poisson or Gamma link with ANPP as a predictor (a nonparametric smoothed term). Try to use the "mgcv" or "gamm4" package in R, as this is very intuitive. The trick of course with Gamma link is to ensure that there are no zeroes in your dataset. So, simply add a very small value to all zeroes in your data (+0.000000000000000000001). This will allow the model to converge. For each predictor level X (a certain value of ANPP) in your output, you will have a mean and standard error/deviation (a normal distribution) that can then be used to calculate CV.

Thanks. Sorry, I wasn't clear enough with the question. I was referring to the CV of ANPP. I used a gamma distribution to model the rainfall, and then calculated ANPP according to the long-term ANPP-rainfall relationship at that site.

For some reason, I read your question too quickly. My apologies. My response did focus on modeling rainfall as the outcome variable, when it should have focused on ANPP. Too many days in front of the computer!

In any case, any NPP data should also be Gamma distributed (as it's a ratio of matter and time), correct? Others can weigh in, but the Gamma should probably be used in this case as well.

Well actually I'm working with annual herbaceous vegetation and just used peak biomass because it is a very good proxy for NPP. Does that change things at all?

Originally I calculated the biomass according to the original linear biomass-rainfall relationship (based on normal distribution), and modeled the error term using the normal distribution with mean=0 and sd= root mean square error (from the original linear equation).

How do you suggest that I calculate the biomass values now? I tried substituting an error term based on the gamma distribution with the shape and scale parameters calculated from the original biomass values, but that gave me really strange results (maybe because the original linear relationship is based on the normal distribution?).

Hi Carly,

Apologies for the lethargic response. Just to clarify a bit (apologies for being daft), you're now using biomass as a proxy for NPP, so you now what to use the rainfall-biomass relationship to predict biomass across a range of rainfall data (perhaps for mapping purposes, extrapolating to other sites, etc.)?

So, it seems like x=rainfall and y=biomass. Biomass is most likely the mass per unit area, so this is a positive, continuous distribution. I'm not sure what your absolute biomass values are (since it depends on the area scale), but I would err on the side of caution and use a Gamma error distribution for a model of biomass as a function of rainfall. I have no idea a priori what that relationship would be, so I would think about using modeling biomass as a quadratic or cubic function of rainfall. Better yet, use a Generalized Additive Model and let the data decide for themselves what relationship they have. The only thing I worry about is that rainfall has comparatively very few high values, so your biomass-rainfall regression will be data sparse for higher rainfall values (higher standard errors).

I hope I haven't too off base here.

Carly - 

I see I come late to this discussion, and it isn't exactly my area, but it sounds interesting. From Patrick's note above though, it appears that -as I believe is generally the case - it is important to include the naturally occurring heteroscedasticity in the error structure of the model.  

Also, I think it extremely helpful, regarding insight into your data, for you to make scatterplot graphs of your data. But, as I have seen noted elsewhere, one data set can be a bit of a fluke, so confirmation can be quite important. 

Cheers - Jim 

Thanks for the insightful responses. The linear response of ANPP to rainfall had been previously confirmed, and I was building a model to predict changes in ANPP and its variation under different scenarios of climate change (less and more variable rainfall). I wanted to built a simple model for the simulation. In the end I kept with my original model - gamma distribution for rainfall, and linear response of ANPP to rainfall, and I added in an error term which brought the ANPP values back within the current range. If ANPP responds linearly to rainfall, and rainfall is modeled on a gamma distribution, then by default, ANPP is also being modeled on a gamma distribution, right? In any case, the results of the simulations were logical, and the paper we wrote has been published.

Is your paper on ResearchGate yet?  Where?