# Presentation: 054657

## Improved Analysis of Tropical Upper Ocean Conditions for Seasonal to Interannual Forecasting 

- UMD: *Jim Carton, Gennady Chepurin*
- NCEP: *David Behringer*

## Goal of the research

- Observations have spatially correlated errors while ocean models have slowly varying biases.  Current data assimilation schemes assume zero bias.
- Our goal is to identify the forecast bias in the current ocean assimilation system and explore methods to control its impact on forecasts.

## Forecast Bias

**Causes:**
- Errors in forcing
- Errors in initial conditions
- Errors in physics parameterizations
- Errors in numerics

## NCEP   Global Ocean Data Assimilation System (GODAS)

**Model**: GFDL MOM3
**Grid**: Quasi-global domain extending from 75oS to 65oN; zonal resolution is 1o poleward of 30o increasing to 1/3o within 10o of the equator; 40 vertical levels; 10 meter resolution in the top 200 meters.
**Physics**: KPP mixing; GM isoneutral mixing of tracers; nonlinear horizontal viscosity; explicit free surface; variable thickness bottom cell
**Forcing**: wind stress, heat flux, E-P (NCEP Reanalysis 2 or operational GDAS);  SST relaxed to NCEP SST analysis; SSS relaxed to Levitus climatology
**Method**: 3D Var; background error variance varies geographically and temporally
**Data**: Temperature (XBTs, Argo floats, TAO/Triton moorings),  synthetic salinity profiles
**Period**: 1980 - pres

## Mean temperature bias

## Bias in temperature annual cycle

## Bias in mixed layer depth based on Temperature

## Mixed layer depth based on temperature

## Mixed layer depth based on density

## Forecast bias correction algorithm

-  **First stage –bias correction**

- where:

**Second stage – unbiased analysis**

- where:

## 95m Temperature bias EOF decomposition

## Bias model

- Based on EOF analysis we propose the following bias model:

**where **

**, and *****G*****i**** is i-th EOF.**

## Reduced space bias correction

- where:

- .

- If we assume that the forecast bias can be expressed as a projection
- on a set of N principal components

- where **G **is a matrix of size MxN** **containing the spatial structure of the
- principal components and      is a column vector of length N containing
- time series then cost function to minimize is:

## Test with climatology

- Bias added to Levitus climatology.  Then the climatology is sampled at 5% of grid points and the bias correction algorithm applied.

## Looking at bias in CFS

## Seasonal SST

**CFS**

**OBS**

**CFS-OBS**

- Error is in the SH

## Errors in heat content

**CFS-OBS**

**OBS**

## Summary

- We have developed temperature bias model for GODAS which includes mean and seasonal biases;
- We have developed a two stage bias correction algorithm for 3D-var systems. This algorithm has been coded for implementation into GODAS and intensively tested on a single processor computer;

**                            ****Resources needed**
**We need access to the JCSDA IBM SP computer to **
**Implement our codes into GODAS.**** **

## What’s next ?

- Implement algorithm in GODAS
- Make bias correction multivariate: apply two-stage bias correction algorithm to other assimilating parameters (salinity, sea level,....)
- Continue look at bias in the coupled system