Research papersManifold methods for assimilating geophysical and meteorological data in Earth system models and their components

- A novel manifold method of reconstructing spatiotemporal data is presented.
- Method outperformed several standard methods often used for reconstructing data.
- The cross-validation method can lead to misleading conclusions.

A novel manifold method of reconstructing dynamically evolving spatial fields is presented for assimilating data from sensor networks in integrated land surface - subsurface, oceanic/lake models. The method was developed based on the assumption that data can be mapped onto an underlying differential manifold. In this study, the proposed method was used to reconstruct meteorological forcing over Lake Michigan, the bathymetry of an inland lake (Gull Lake), and precipitation over the Grand River watershed in Michigan. In the first case study, hourly meteorological forcing data were reconstructed and used to run a three-dimensional hydrodynamic model of Lake Michigan and to quantify the improvement that results from the use of the new method. In the second example, the bathymetry of Gull Lake was reconstructed from measured scatter point data using the manifold technique. A hydrodynamic model of Gull Lake was developed and refined using the improved bathymetry. In the last case study, improved daily participation data for a six-year period over the Grand River watershed were used as input to an integrated, distributed hydrologic model. All three examples illustrate the superior performance of the manifold method over standard methods in terms of accuracy and computational efficiency. Our results also indicate that using the cross-validation technique to evaluate the performance of data reconstruction methods can lead to misleading conclusions about their relative performance.

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