River levels from multi mission altimetry, a statistical approach

Satellite altimetry is a key technique to measure water level change in continental water bodies. Altimetry-based water level time series of rivers are typically constructed at locations where the satellite ground tracks intersect the rivers, the so-called virtual stations. The relatively low sampling frequency (10-27 days) of the repeat missions may result in an under-sampling of the hydrological regime in rivers with sub-monthly to weekly events. We are currently in a unique position with more than a handful satellite altimetry missions simultaneously mapping the surface elevation of the Earth. In combination, these missions contain an unexploited potential to obtain a more detailed picture of the hydrological regime of many of the Earth's rivers. The task of combining water levels measured at different locations and/or by satellites with different orbits is however, challenging due to e.g. topography, intermission biases, variation in river morphology, and other unidentified causes. In this work, we present a new method to combine multi-mission altimetry-based water levels from a river reach. This will also enable the use of geodetic missions like CryoSat-2 and SARAL/AltiKa (after June 2016) in water level time series. To combine the data we set up a state-space model where the process part is a first-order autoregressive process. The observations as a function of time and distance along the reach are described as a sum of the water level at a given time scaled by a distance-dependent factor, the mean water level at the given distance, and an error term. The scale factor and the mean water level are modeled with spline functions. We employ the model for the six rivers Lena, Solimo similar to es, Mississippi, Danube, Po, and Red, which range in width from 3 km to a few hundred meters. For each river, we consider a reach of 200-300 km and apply water levels from the satellite altimetry missions CryoSat-2, Sentinel-3A/3B, and SARAL/AltiKa. The selected reach must have a continuous elevation profile and preferable no major tributaries, which might alter the hydrological regime considerably. The length of the reach is a compromise of ensuring enough data but not violating the aforementioned criteria. When validated against in situ data we find a root mean square error ranging from 0.34 m (Solimo similar to es River) to 2.53 m (Lena River) and a correlation ranging from 0.83 (Danube River) to 0.99 (Solimo similar to es River). These summary statistics are based on approximately 2000-3000 pairs of in situ and modeled water levels. We find the largest increase in detail for the reconstructed water levels for the Danube, Po, and Red Rivers, where the water level variations are under-sampled at the virtual stations. For the Po River, we can detect sub-weekly events with the model and for the Lena River, the spring flood related to ice and snowmelt is better captured when combining the data. An additional advantage of the approach is that the water level time series can be reconstructed at all locations along the considered reach.