This paper proposes a method for the representation of functions describing a measured geophysical property (via sparsely scattered ordensely defined point data) by tensor and triple product interval B-splines (IBS). The spline representation facilitates archiving, data storage reduction, visualization and more general high-level interrogation. Interval methods allow for the representation of the function values together with their uncertainty. The uncertainty is introduced, for example, because the measurement (or dependent variable) or the location of the sensor (the independent variable(s)) is known only to a finite precision. In this paper, we present algorithms for the creation of IBS geometries based on minimization with linear constraints and we illustrate the method using geophysical ocean data and their interrogation.