I have been carrying out sobol analysis for global sensitivity analysis of a simple analytical model.
My understanding is the total sobol indices should sum to one and represent the contribution of the input parameterâ€™s variance to the total variance of the property of interest.

I have noticed my total sobol indices often sum to more than 1. What could be causing this? Note my input parameters are not correlated at all.

Actually, the total Sobolâ€™ indices will, in general, sum to more than 1. I think you might have mistaken the total Sobolâ€™ indices for the first-order Sobolâ€™ indices (whose sum cannot be larger than 1). The total Sobolâ€™ index of an input parameter is the sum of the first-order Sobolâ€™ index and all the higher-order Sobolâ€™ indices involving that parameter.

So, if you sum the total indices, you would double count many indices. It is only for a special case that the sum of the total indices is 1. That is, if all the higher-order indices are 0; in other words, the sum of the first-order indices is 1. Note that this property is not about whether your inputs are correlated or not, but whether they are interacting with respect to the output.

Regarding this topic, the explanation from the Wikipedia article might be helpful: