function s = skill(data,model,null_model)
% SKILL - Calculate various skill statistics
% s = skill(data,model,null_model)
%
% Input:
%   data, model, and (optional) null_model must be column vectors of equal
%   length (no NaNs)
% Returns structure s with:
%   s.willmott Eqn. 5 in Warner et al. (2005) JGR 110, C05001
%      based on Willmott, C. J. (1981) On the validation of models. Phys.
%      Geogr. 2:184-194.
%   s.brier Based on CRS notes (see also Sutherland, Peet, Soulsby, 2004)
s.willmott = 1 -  ( sum( (abs( model - data )).^2 ) ./ ...
   sum( ( abs( model-mean(data) )+ abs( data - mean (data ) )).^2 ));
if(exist('null_model')~=1),
    null_model = ones(length(data),1).*mean(data);
end
s.brier = 1 - sum( (data-model) .^2 ) ./ sum( (data-null_model).^2 );