• Courant, R., and D. Hilbert, 1962: Methods of Mathematical Physics. Vol. II. Interscience, 830 pp.

  • Xu, Q., 1996a: Generalized adjoint for physical processes with parameterized discontinuities. Part I: Basic issues and heuristic examples. J. Atmos. Sci.,53, 1123–1142.

  • ——, 1996b: Generalized adjoint for physical processes with parameterized discontinuities. Part II: Vector formulations and matching conditions. J. Atmos. Sci.,53, 1143–1155.

  • ——, 1997a: Generalized adjoint for physical processes with parameterized discontinuities. Part III: Mutiple threshold conditions. J. Atmos. Sci.,54, 2713–2721.

  • ——, 1997b: Generalized adjoint for physical processes with parameterized discontinuities. Part IV: Problems in time discretization. J. Atmos. Sci.,54, 2722–2728.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 14 14 4
PDF Downloads 5 5 1

Generalized Adjoint for Physical Processes with Parameterized Discontinuities. Part V: Coarse-Grain Adjoint and Problems in Gradient Check

View More View Less
  • 1 Naval Research Laboratory, Monterey, California
  • | 2 CAPS, University of Oklahoma, Norman, Oklahoma
  • | 3 Department of Atmospheric Sciences, Nanjing University, Nanjing, China, and CIMMS, University of Oklahoma, Norman, Oklahoma
© Get Permissions
Restricted access

Abstract

When on/off switches are triggered at discrete time levels by a threshold condition in a traditionally discretized model, the model solution is not continuously dependent on the initial state and this causes problems in tangent linearization and adjoint computations. It is shown in this paper that the problems can be avoided by introducing coarse-grain tangent linearization and adjoint without modifying the traditional discretization, although the coarse-grain gradient check can be performed only for finite perturbations.

Corresponding author address: Dr. Qin Xu, Naval Research Laboratory, 7 Grace Hopper Drive, Monterey, CA 93943-5502.

Email: xuq@helium.nrlmry.navy.mil

Abstract

When on/off switches are triggered at discrete time levels by a threshold condition in a traditionally discretized model, the model solution is not continuously dependent on the initial state and this causes problems in tangent linearization and adjoint computations. It is shown in this paper that the problems can be avoided by introducing coarse-grain tangent linearization and adjoint without modifying the traditional discretization, although the coarse-grain gradient check can be performed only for finite perturbations.

Corresponding author address: Dr. Qin Xu, Naval Research Laboratory, 7 Grace Hopper Drive, Monterey, CA 93943-5502.

Email: xuq@helium.nrlmry.navy.mil

Save