Interpolating through time and space with empirical orthogonal functions


Interpolation is necessary when working with many types of real-world data – for example, it is required to overcome limited spatial and temporal resolution and data gaps. Interpolation through both space and time together can be particularly difficult. We present a novel approach using singular value decomposition to decouple the spatial and temporal components, interpolate them independently, and reconstruct the original field on an as-needed basis. The empirical orthogonal functions (EOFs) describe the spatial variability, and their expansion coefficients (ECs) capture the temporal variability. This decomposition simplifies the problem. Since the leading EOF modes capture the majority of the spatial information, the original variable can often be reconstructed using fewer EOFs than original timesteps. Additionally, the interpolants over the EOFs and ECs can be pre-computed, and building the interpolant is often more costly than evaluating it at the desired coordinates. We demonstrate the new method in three example applications using surface current data in Monterey Bay: upsampling the current fields, calculating the path of a surface drifter, and tying in with forecast data generated by a compact ocean model.

ASLO Ocean Sciences Meeting. Honolulu, HI