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In physical oceanography, observations are mainly acquired by space-bornesensors that cannot measure the interior ocean state. As a result, most avail-able data are limited to the sea surface, with gaps arising from satellite tra-jectories and sensor coverage. To fill in these gaps, data inversion is usuallyperformed using reduced-order models. These models are based on assumptionswhich simplify the flow dynamics. One such framework is the 1.5-layer quasi-geostrophic model which resolves only the upper layer flow by considering thatthe underlying layer remains at rest. However, it is actually a truncation ofthe quasi-geostrophic (QG) framework which describes the dynamics of a three-dimensional flow. Although motivated by the lack of sublayer data, reducingthe dynamics solely to its surface component remains a strong assumption.We wish to mitigate the systematic error introduced by this truncation toimprove surface flow reconstruction. We also aim at keeping a sparse expressionfor the correction as it allows the problem to remain well-constrained by theobservations. Using the QG equations, we introduce a truncation-correctingterm bridging the gap between the 1.5-layer model and its multilayer counter-part. This correction is prescribed through the transport of the sublayer streamfunction by the upper layer flow. Since the dynamics of the correction is re-fined by the surface flow, it can be parameterized with a reasonable number ofparameters.Using simulations of different complexity, we evaluate the performance of theproposed method. As it identifies the correction term to a physical quantity, wemake use of the potential vorticity conservation in the sublayer to constrain ourparameterization. Correction is finally estimated using a variational method.Results show a significant improvement over a state-of-the-art error modelingstrategy. The additional constraint helps reconstructing a much smoother fieldfor the surface flow. Our method also allows the correction term to compensatefor an incorrect deformation radius. This approach then mitigates the pas-sive sublayer assumption while improving the reconstruction capabilities of themodel.