Spatiotemporal assimilation-interpolation of discharge records through inverse streamflow routing

Poorly monitored river flows in many regions of the world have been hindering our ability to accurately estimate global water budgets as well as the variability of the global water cycle. In situ gauging sites, as well as a number of satellite-based systems, make observations of river discharge throughout the globe; however, these observations are often sparse due to, for example, the sampling frequencies of sensors or a lack of reporting. Recently, efforts have been made to develop methods to integrate these discrete observations to gain a better understanding of the underlying processes. This paper presents an application of a fixed interval Kalman smoother-based model, called inverse streamflow routing (ISR), to generate spatially and temporally continuous river discharge fields from discrete observations. The method propagates the observed information across all reachable parts of the river network (up/downstream from gauging point) and all reachable times (before/after observation time) using a two-sweep procedure that first propagates information backward in time to the furthest upstream locations (inverse routing) and then propagates it forward in time to the furthest downstream locations (forward routing). The ISR methodology advances prediction of streamflow in ungauged basins by accounting for a physical representation of the river system that is not generally handled explicitly in more-commonly applied statistically based models. The key advantages of this approach are that it (1) maintains all the physical consistencies embodied by a diffusive wave routing model (flow confluence relationships on the river network and the resulting mass balance, wave velocity, and diffusivity), (2) updates the lateral influx (runoff) at the pixel level (furthest upstream) to guarantee exhaustive propagation of observed information, and (3) works both with a first guess of initial river discharge conditions from a routing model (assimilation) and without a first guess (pure interpolation of observations). Two sets of experiments are carried out under idealized conditions and under real-world conditions provided by United States Geological Survey (USGS) observations. Results show that the method can effectively reproduce the spatial and temporal dynamics of river discharge in each of the experiments presented. The performance is driven by the density of the gauge network as well as the quality of the data being assimilated. We find that when assimilating the actual USGS observations, the performance decreases relative to our idealized scenario; however, we are still able to produce an improved discharge product at each validation site. With further testing, as well as global application, ISR may prove to be a useful method for extending our current network of global river discharge observations.