Wheat pre-breeders use soil coring and core-break counts to phenotype root architecture traits, with data collected on rooting density for hundreds of genotypes in small increments of depth. The measured densities are both large datasets and highly variable even within the same genotype, hence, any rigorous, comprehensive statistical analysis of such complex field data would be technically challenging. Traditionally, most attributes of the field data are therefore discarded in favor of simple numerical summary descriptors which retain much of the high variability exhibited by the raw data. This poses practical challenges: although plant scientists have established that root traits do drive resource capture in crops, traits that are more randomly (rather than genetically) determined are difficult to breed for. In this paper we develop a Bayesian hierarchical nonlinear modeling approach that utilizes the complete field data for wheat genotypes to fit an idealized relative intensity function for the root distribution over depth. Our approach was used to determine heritability: how much of the variation between field samples was purely random versus being mechanistically driven by the plant genetics? Based on the genotypic intensity functions, the overall heritability estimate was 0.62 (95% Bayesian confidence interval was 0.52 to 0.71). Despite root count profiles that were statistically very noisy, our Bayesian analysis led to denoised profiles which exhibited rigorously discernible phenotypic traits. The profile-specific traits could be representative of a genotype and thus can be used as a quantitative tool to associate phenotypic traits with specific genotypes.