In a turbulent flow, a miscible contaminant is confined to sheets and strands of the very thin Batchelor conduction cut-off length. This fact has been surmised for some time and has recently been observed directly through high precision measurements. This fine-scaled texture of the contaminant concentration field makes it an extraordinary challenge to achieve (experimentally) adequate continuum scale resolution, particularly in important environmental flows such as the atmospheric boundary layer. In this paper, an extrapolation scheme is proposed whereby the systematic measurement (with known sample volumes) of the lower-order moments of the concentration fluctuations are used to approximate the true, perfectly resolved values, and hence to approximate the true probability density function. Such a scheme relies on empirical data, and so the need for more experiments designed to investigate the effects of spatial resolution cannot be over-emphasized.