4DVar Tutorial Introduction

4-Dimensional Variational (4D-Var) Data Assimilation Tutorial

This tutorial shows several examples of ROMS 4D-Var data assimilation algorithms in the California Current System (CCS).

Model Set-up

The WC13 model domain is shown in Fig. 1 and has open boundaries along the northern, western, and southern edges of the model domain.

Fig. 1: Model Bathymetry with 37°N Transect

In the examples, you will perform a 4D-Var data assimilation cycle that spans the period 3-6 January, 2004. The 4D-Var control vector δz is comprised of increments to the initial conditions, δx(t₀), surface forcing, δf(t), and open boundary conditions, δb(t). The prior initial conditions, x_b(t₀), are taken from the sequence of 4D-Var experiments described by Moore et al. (2010b) in which data were assimilated every 7 days during the period July 2002- December 2004. The prior surface forcing, f_b(t), takes the form of surface wind stress, heat flux, and a freshwater flux computed using the ROMS bulk flux formulation, and using near surface air data from COAMPS (Doyle et al., 2009). Clamped open boundary conditions are imposed on (u,v) and tracers, and the prior boundary conditions, b_b(t), are taken from the global ECCO product (Wunsch and Heimbach, 2007). The free-surface height and vertically integrated velocity components are subject to the usual Chapman and Flather radiation conditions at the open boundaries. The prior surface forcing and open boundary conditions are provided daily and linearly interpolated in time. Similarly, the increments δf(t) and δb(t) are also computed daily and linearly interpolated in time.

The observations assimilated into the model are satellite SST, satellite SSH in the form of a gridded product from Aviso, and hydrographic observations of temperature and salinity collected from Argo floats and during the GLOBEC/LTOP and CalCOFI cruises off the coast of Oregon and southern California, respectively. The observation locations are illustrated in Fig. 2.

a) In Situ Temperature	b) In Situ Salinity
c) Aviso SSH	d) Blended SST

Download the code

All of the additional scripts necessary to run the 4D-Var tests are available from the ROMS Subversion (SVN) repository. The 4D-Var test cases are for the California Current System, 1/3 degree resolution, (WC13).

> svn checkout --username joe_roms https://www.myroms.org/svn/src/test my_test

Download Lectures and Exercises

Links to the upcoming 2010 ROMS 4D-Var workshop lectures are provided below. We are planning to record the audio for these lectures to combine with the slides for future reference. These lectures are meant to supplement this 4D-Var tutorial.

• Lecture 1:   PDF   Primal 4D-Var
• Lecture 2:   PDF   The Mechanics of 4D-Var
• Lecture 3:   PDF   Dual 4D-Var
• Lecture 4:   PDF   4D-Var Diagnostics
• Lecture 5:   PDF   Observation Impact and Observation Sensitivity

Below are the exercises pertinent to the upcoming 2010 ROMS 4D-Var workshop:

• Exercise 1:   PDF   Incremental, Strong Constraint 4D-Var
• Exercise 2:   PDF   I4D-Var with Multiple Outer-loops
• Exercise 3:   PDF   Dual Formulation 4D-Var: R4D-Var and 4D-PSAS
• Exercise 4:   PDF   Weak Constraint Dual Formulation 4D-Var
• Exercise 5:   PDF   Array Modes
• Exercise 6:   PDF   Observation Impacts

Directory Structure

When the checkout is complete, you will have the following directory structure under your my_test directory.

 /WC13                      Main California Current System 4D-Var applications
      /ARRAY_MODES          Stabilized representer matrix array modes and clipping
      /Data                 Input data directory
      /Functionals          Analytical expression header file
      /I4DVAR               Primal form of incremental, strong constraint 4D-Var, I4D-Var
      /I4DVAR_impact        I4D-Var observation impact
      /Normalization        4D-Var error covariance normalization coefficients
      /plotting             4D-Var plotting scripts (Matlab and ROMS plotting package)
      /PSAS                 Dual form of 4D-Var, Physical-space Statistical Analysis System, 4D-PSAS
      /PSAS_impact          4D-PSAS observation impact
      /PSAS_sensitivity     4D-PSAS observation sensitivity (adjoint of 4D-PSAS)
      /R4DVAR               Dual form of 4D-Var, indirect representer method, R4D-Var
      /R4DVAR_impact        R4D-Var observation impact
      /R4DVAR_sensitivity   R4D-Var observation sensitivity (adjoint of R4D-Var)