Identification of conceptual rainfall-runoff models of large drainage basins based on GRACE and in-situ data

Since 2002, estimates of the spatio-temporal variations of Earth’s gravity field derived from the Gravity Recovery and Climate Experiment (GRACE and now GRACE-FO) mission measurements have provided new insights into large scale water redistributions at inter-annual, seasonal and sub-seasonal timescales. It has been shown for example that for many large drainage basins the empirical relationship between aggregated Terrestrial Water Storage (TWS) and discharge at the outlet reveals an underlying dynamic that is approximately linear and time-invariant.

In this contribution, we further analyse this relationship in the case of the Amazon basin and sub-basins by investigating different physically interpretable, lumped-parameter models for the TWS-discharge dynamics. To this end, we first put forward a linear and continuous-time model using a state-space representation. We then enhance the model by introducing a non-linear term accounting for the observed saturation of the discharge. Finally, we reformulate the model by replacing the discharge by the river stage at the outlet and add a prescribed model of the rating curve to obtain the discharge. The suggested models are successively calibrated against TWS anomaly derived from GRACE data and discharge or river stage 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. This quantity is estimated to be on average 1,750 km³ during the period 2004-2009. These models are eventually combined with the equation of water mass balance, in order to obtain a consistent representation of the basin-scale rainfall-runoff dynamics suited to data assimilation.