Real Time Flow Estimation in Channel Networks using Lagrangian Data
- Author(s): Wu, Qingfang;
- Advisor(s): Bayen, Alexandre M.;
- et al.
The Sacramento-San Joaquin River Delta in California becomes inadequate in fresh water resources, while the water demand in California keeps increasing. Large-scale numerical flow models, for example Delta Simulation Model II (DSM2) and River, Estuary, And Land Model (REALM), used as crucial water resources management tools, are capable of providing critical information about tidal forcing and salinity transport in the bays and channels of the Delta. Reliable flow estimation and prediction of these models, however, largely depend on an accurate representation of open boundary conditions and initial conditions, which are usually calibrated against historical data sets acquired from Eulerian measurements near the boundaries.
In large watershed, unfortunately, these measurements have demonstrated many intrinsic limitations, for example small spatial coverage and sparse temporal sampling. Also, existing Eulerian sensors have many recorded failures, such as broken gauges, sensor drifts, process leaks, improper measuring devices, and many other random sources. More importantly, if the hydraulic system is radically altered, as in the case of extensive levee failures, the historical data sets can be of limited usage.
In this dissertation, a sensing-modeling system featuring rapidly deployed Lagrangian drifters is developed. The system is capable of predicting regional flows and transport in the Delta in a real-time mode, without dependence on historical data.
Lagrangian data is obtained when floating drifters move along with the flow and report their locations. The data provides instant information about the flow, including flow advections and eddy dispersions, and is further assimilated into underlying shallow water equation (SWE) models to characterize the flow state.
Different approaches to facilitate the flow estimation have been investigated in this dissertation. First, a variational assimilation method (Quadratic Programming) is applied to a 1D SWE model (Linearized Saint-Venant equations). The assimilation method poses the problem of estimating the flow state in a channel network as a quadratic programming by minimizing a quadratic cost function -- the norm of the difference between the drifter observations and the model velocity predictions -- and expressing the constraints in terms of linearized equalities and inequalities. The problem is then efficiently solved using a fast and robust algorithm. The approach is easy to implement and low in computation costs.
Later, a sequential assimilation method (Ensemble Kalman Filtering) is implemented to a 2D SWE model (depth-integrated Navier-Stokes equations). The assimilation method involves a series of state analysis and updates, where the observed Lagrangian data is incorporated into the state one step at a time to incrementally correct the model prediction. The implementation of this method demands powerful computation ability, and is achieved on high-performance computing clusters at NERSC.
To assess the performance of the proposed data assimilation methods, we investigated a distributed network of channels, subject to quasi-periodic tidal forcing, in the Sacramento-San Joaquin River Delta. Field operational experiments were carried out with a fleet of over 70 floating drifters, deployed within approximately 0.55 km2 of the river network. During the experiments, more than 325,000 GPS readings were taken from the floating drifters and collected, in real time, onto a central server. It is the first experiment of this kind conducted at such scale, where high-density Lagrangian data have been collected in a real river environment and successfully assimilated over a full tidal cycle.
It is demonstrated that both of the proposed assimilation methods (i.e., QP in 1D SWE model and EnKF in 2D SWE model) can handle the Lagrangian data with sufficiently accurate estimations. In many practical cases, the 1D flow estimation is adequate for water resource management to retrieve critical flow characteristics in a prompt and efficient manner. In the case of complex channel geometry, however, the 2D flow estimation is vital to describe the hydraulic system.