|Paper title||Identification of lumped rainfall-runoff models of large drainage basins for satellite data assimilation|
|Form of presentation||Poster|
Estimates of the spatio-temporal variations of Earth’s gravity field based on the Gravity Recovery and Climate Experiment (GRACE) mission observations have shed a new light into large scale water redistribution at inter-annual, seasonal and sub-seasonal timescales. As an example, it has been shown that for many large drainage basins the empirical relationship between aggregated Terrestrial Water Storage (TWS) and discharge at the outlet reveals an underlying dynamics that is approximately linear and time-invariant (see attached figure for the Amazon basin).
We built on this observation to first put forward lumped-parameter models of the TWS-discharge dynamics using a continuous-time linear state-space representation. The suggested models are calibrated against TWS anomaly derived from GRACE data and discharge records using the prediction-error-method. It is noteworthy that one of the estimated parameters can be interpreted as the total amount of drainable water stored across the basin, a quantity that cannot be observed by GRACE alone. Combined with the equation of water mass balance, these models form a consistent linear representation of the basin-scale rainfall-runoff dynamics. In particular, they allow to derive analytically a basin-scale instantaneous unit hydrograph. We illustrate and discuss in more detail the results in the case of the Amazon basin and sub-basins, which present relatively simple TWS-discharge dynamics well approximated by first-order ordinary differential equations. Finally, we briefly discuss how to refine the linear models by introducing non-linear terms to better capture delays and saturations.
With such linear and non-linear models at hands, it is possible to use classical Bayesian algorithms to filter, smooth or reconstruct the basin aggregated TWS and/or discharge in a consistent manner. As such, we claim that these lumped models can be an alternative to more complex and spatially distributed hydrological models in particular for TWS and discharge time series reconstruction. We also briefly examine the conditions under which the linear models can be used to do hydrology backwards, that is, estimating simultaneously the TWS and the unknown input precipitation minus evapotranspiration from discharge records.