Simple mixing of organic manures with water increases bicarbonate value.
Maybe this will help.
http://www.bing.com/search?q=ph+and+alkalinity+relationship&src=IE-SearchBox&FORM=IESR02&conversationid=CBA01AA3D66B451CAD166D99A3A847D9
Adding the organics may be altering pH or concentration of alkalinity chemicals
The measurement of alkalinity by the Gran method is an acid titration. All coniugate bases are titrated including coniugates of organic acids. Important noncarbonate contributors include organic ligands (especially acetate and propionate) and ions of hydroxide, phosphate, ammonium, silicate, sulfide, borate, and arsenate
(Hem, 1985). In the cases of waters strongly impacted by human or biological acitivities (e.g. highly eutrophic waters), the organic acid contribution can be significant. How to avoid it? You can measure directly bicarbonate by Ion Chromatography. See attached paper and link
Article Determination of total dissolved inorganic carbon in freshwa...
As mentioned alkalinity is determined by acid titration. The version of alkalinity known as carbonate alkalinity is defined by that the endpoint of the titration is there pH is equal to pKa of bicarbonate.
The pKa of bicarbonate is above the pKa of carboxylic acids so the titration should not measure organic acids in general. Thus organic acids isn't likely to interfere with the bicarbonate alkalinity.
Organic manure typically contain a high concentration of ammonia which is measured in the bicarbonate alkalinity titration as it is protonated to ammonium. This could explain the increase in bicarbonate alkalinity with the manure addition to water.
You can measure inorganic carbon with another method than titration if that is the purpose of your analysis but alkalinity is defined by the titration procedure so if the reason for an increase is the addition of ammonia the bicarbonate alkalinity is truly increased.
What Henrik said is correct, but if you use the Gran method, which is an extrapolation method which use a strong acid to titrate well beyond the equivalence point. But the problem does not change. We have to find out alternative method.
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