I am not sure whether I understood the question, but, have you tried the Feature Selective Validation method? It seems to me that FSV might be a useful technique for your comparison proposes.

I got an spectra made from data found in literature and do have several ones recorded in the field. I need to compare them.

FSV is a compararon technique used mainly for pairs of datasets of data in the frequency domain. I suggest you to use it.

I suppose you can estimate the centroid, skewness, flatness and any other timbral descriptor. You can find algorithms to compute such measurements in MIRToolbox for Matlab.

I'm not sure whether understood right. If you have spectra already, you should get cross-spectrum of two signals out from your spectra http://en.wikipedia.org/wiki/Coherence_%28signal_processing%29

You also speak temporal signals, mulptiplying two signals in time domain and integrating the result is a way to check whether signals correlate (~are coherent).

One could calculate the correlation coefficient between both spectra by simply performing a Spearman rank order correlation test in a statistic software.

Use a cross-coorelation program, and derive Pearson's coefficient if a single number for a set is needed.

That actually what I did

I'm with Kari. there are a few cyclo models on the matlab file central page that allow you to calculate S and C with just the signal processing toolbox. there are some demos in the comms toolbox but not everyone has it. I have often found the cyclic spectrum (Cxy/Syy) to be useful when you are trying to isolate signal coherence with two different noise backgrounds or too much noise for basic SNR techniques.