River channel networks are an integral part of land surface models and play an import role in both land-atmosphere and surface-subsurface interactions[1]. To provide a comprehensive prediction of flood wave and backwater behavior for a channel network, the full dynamic Saint-Venant equations must be solved faster than real time -- a challenge for regional to continental-scale river networks. Due to high computational costs and limited data availability, many land surface models use simplified diffusive or kinematic solutions that misrepresent key flood physical processes.

In this talk, we present SPRINT: the Simulation Program for River Networks. SPRINT is the product of an on-going cross-disciplinary effort between hydroscience at the University of Texas and computer science at IBM. By taking advantage of the latest progress in computer science, in particular the fast simulation techniques in Very Large Scale Integration (VLSI) computer chip designs, we have created a dynamic Saint-Venant model that is capable of simulating the channel network of a regional river basin over 100-times faster than real-time on a desktop computer. SPRINT provides three key advances: 1) state-of-the-art nonlinear differential equation solution techniques from VLSI simulation and numerical linear algebra to speed up the simulation; 2) an innovative technique to treat the river channel cross-sections, providing efficient solutions for complex natural channels defined from bathymetric surveys; 3) a clean interface between the simulation engine and data modeling. The combination of these factors makes SPRINT a fast fully-dynamic model that can be easily integrated into other water cycle models.

Each time step in a Saint-Venant model requires solution of a large-scale distributed nonlinear problem. If not programmed efficiently, such solutions are computationally expensive and previously were a barrier to using the Saint-Venant equations with natural river bathymetric cross-sections. Progress in both computer hardware and numerical linear algebra should have made this task less formidable, but the latest advances are not used in legacy models. Solving a matrix of the from tens to hundreds of thousands of elements is readily achievable with only modest computer hardware[2] and hundreds of millions of elements have been solved in microprocessor design using only a desktop workstation[3], so there are significant new possibilities for improving river network modeling. One of the techniques that has proven effective in SPRINT is adaptively adjusting the matrix factorization frequency during the nonlinear solution[4]. Another innovative technique is splining the channel cross-sections to provide smooth Jacobians of the solution matrix[5]. This idea is particularly important for natural river cross sections that have discontinuous derivatives in geometric properties. Spline smoothing of discontinuities does not significantly degrade model accuracy, whereas it does prevent slow convergence and nonlinear solution failure that have historically been a problem for Saint-Venant solutions.

For many applications, a dynamic river channel model is needed as a part of a larger modeling environment, which could include atmospheric, land surface and ground water models. In SPRINT, we provide a clear separation between the data model and the simulation engine itself. A river network is described as a river "netlist" following an intuitive syntax that is patterned after the methods used for microprocessor circuitry. The netlist files can reside locally on a hard drive and can be remotely accessed via a HTTP front-end to execute the model. The core computational components of SPRINT are programmed as a library so that a top-level simulation environment can construct, simulate and retrieve results of a channel network via a Application Programming Interface (API), without writing the netlist files. We believe this flexible-use approach is important for large-scale integration and simulation on a large computer cluster with thousands of cores.

To demonstrate the computational feasibility of SPRINT, we have simulated a major river channel network in Central Texas comprising the Guadalupe and San Antonio River basins. The network has over 3,000 reaches and is modeled by over 200,000 nodes. We are able to simulate a 10-day event on a desktop computer at the runtime of slightly over an hour.

References: [1]Wood, E. F. et al., "Hyperresolution global land surface modeling: Meeting a grand challenge for monitoring Earth's terrestrial water." Water Resources Research 47, W05301, 10 pgs., 2011. [2]Davis, T.A., "A column pre-ordering strategy for the unsymmetric-pattern multifrontal method", ACM Transactions on Mathematical Software, 30:2:165-195, 2004. [3]Rewieński, M. A., "Perspective on Fast-SPICE Simulation Technology," in Simulation and Verification of Electronic and Biological Systems. P. Li, L. M. Silveira and P. Feldmann (eds). New York, Springer: pp. 22-42, 2011. [4]Acar, E., F. Dartu, and L.T. Pileggi, "TETA:transistor-level waveform evaluation for timing analysis", IEEE Transactions on Computer-Aided Design, 21:5:605-616, 2002. [5]de Boor, C. A Practical Guide to Splines", Springer, 346 pgs., 1994