Mathematical Modeling

Variational data assimilation with latest numerical models in California delta area

A floating sensor data assimilation framework is implemented providing the real time estimation and prediction of hydrodynamic systems in Delta area of California. The system currently assimilates Lagrangian data collected by floating drifters from UC Berkeley and the Eulerian data from Department of Water Resources and U.S. Geological Survey.


In this system two flow models, named legacy models, and respectively written in C++ and FORTRAN, are used to perform data assimilation using drifter (a floating sensor in water) velocity measurements:

1. REALM (2D shallow water model):River, Estuary, and Land Model -- the latest model and decision support system funded by the California Department of Water Resources to develop for managing short-term operations in the Sacramento-San Joaquin Delta and its tributaries, and for planning long-term structural changes. Two key techniques are emphasized in order to achieve flexibility and accuracy over a diverse range: adaptive computation and embedded boundaries (Figure 1). Adaptive mesh refinement (AMR) technique allows the model to concentrate computational detail in regions that are difficult or of interest. Embedded boundaries technique evolve accurately in response to tides or floods.

2. DSM2 (1D model): The Delta Simulation Model II (DSM2) is a one-dimensional mathematical model for dynamic simulation of one-dimensional hydrodynamics, water quality and particle tracking in a network of river line or estuarine channels(Figure 2). DSM2 can calculate stages, flows, velocities, mass transport processes for conservative and non-conservative constituents, including salts, water temperature, dissolved oxygen, and trihalomethane formation potential, and transport of individual particles. (

Figure 1. total water depth for San Francisco Bay, San Pablo Bay, Suisun Bay, and Franks Tract. Three levels of adaptive mesh refinement are applied. The largest boxes have a resolution of 750m. The finest level covers channelized areas in the Delta on the east side of the map.

Figure 2. The Schematic Grid of DSM2, covers whole Delta area of California.

Data Assimilation Framework

The basic idea in the framework is that multiple flow model instances are running on a cluster of computers in real time and they communicate to the central server that performs the data assimilation using Ensemble Kalman Filter (EnKF) algorithm (see Figure 3). Since EnKF is a Monte Carlo type algorithm, the result of the algorithm is an ensemble of states. These states are evolved independently (of each other) in the flow models on the client computers during the data assimilation. The ensemble is collected and updated by the EnKF server with the drifter measurements , and hence one data assimilation cycle is accomplished.

Figure 3. Overall data flow.