© Crown copyright Met Office Implementing a diurnal model at the Met Office James While, Matthew Martin

© Crown copyright Met Office

Implementing a diurnal model at the Met OfficeJames While, Matthew Martin


Overview

Table of Contents• The NEMOVAR SST bias correction system

• The diurnal model

• Diurnal data assimilation system

• The Python test system

• Future Plans – The diurnal analysis system


NEMOVAR SST Bias correction system


NEMOVAR SST Bias correction systemOverview

•Before data assimilation we bias correct all SST data to a reference data set – AATSR, In-situ.

•We have recently updated our bias correction system to work within NEMOVAR

•Conceptually the system is similar to an SST analysis system, such as OSTIA, but with longer length scales (7º) and with matchups as observations.

•To perform the bias correction NEMOVAR is run in a 2-D configuration.


SST Bias correction systemAlgorithm

Matchup System•Finds matchups between biased and ‘unbiased‘ reference observations.

•Matchups are found within specified time (1 day) and space (25 km) limits.

•Coded to NEMO standards.

2-D NEMOVAR•Matchups are assimilated as if they are SST observations with long length scales.

NEMO•Bias is subtracted from the observations before they are passed into the observation operator.

Ref obs Biased obs

Matchups

Bias field

Bias background

Relaxation to climatology

This algorithm is applied

individually to each biased data type.


Bias for AVHRR after 3 days

Correlation length scale = 7º

SST Bias correction systemExample field


The Diurnal model


Diurnal modelOverview

•Ultimate aim is to produce a high resolution analysis of diurnal skin SST.

•For this we need a computationally cheap, accurate model that is also amiable to data assimilation.

•We chose to adapt the Takaya et al, 2010 warm layer model for this purpose.

•The model has been coded up in-house and has been adapted to use a 9 band light model (Gentermann et al, 2009)

•We do not fully exploit the wave parameterisation of the Takaya model – The Langmuir number is assumed constant at 0.3.

•To complete the skin SST analysis we are implementing the Artale, 2002 cool skin model.


Diurnal ModelTheory• Based on the Takaya, 2010 bulk diurnal model.

• Implemented both as standalone system & within NEMO.

T:- ΔSSTt :- TimeQ:- Thermal energy fluxDT:- Layer depthρ:- Water densitycp:- Heat capacityν:- Structure parameteruw*:- Friction velocityLa:- Langmuir numberk:- Von Karman’s constantg:- Acceleration due to gravityαw:- Thermal expansion coefficient

Bulk thermalheating of a layer

Turbulentdamping

•These equations are solved using an implicit scheme


Diurnal model NEMO top level

Diurnal ModelPeak ΔSST in NEMO for Jan 07


The Data Assimilation System


Data assimilation systemOverview

•We are designing a Data assimilation system to work with the Takaya model.

•The system will use a 1-D version of a strong constraint 4DVar algorithm.

•It is not sufficient to minimise with respect to the initial temperature, so we also constrain the heat and wind forcing.

•We now have working versions of the Tangent Linear and Adjoint of the Takaya model.

•The cool skin model will not be constrained by the data assimilation.


Initial temperature

Thermal energy flux at all timesteps

Friction velocity at all timesteps

Data assimilation systemControl vector


T, Q & uw* assumed uncorrelated with each

other.Temporal correlations

modelled as a Gaussian

Diagonal,observations assumed

uncorrelated

y includes observations of Tonly.

NOTE: The model is assumed perfect at night

Data assimilation systemCost function (inner loop)


The Python Test System


Python Test systemOverview

•A test system for our data assimilation algorithm has been written in Python using the numpy and scipy repositories.

•The full non-linear, The Tangent Linear, and the Adjoint are all FORTRAN subroutines accessed by the Python system.

•The system has been designed to be similar to NEMOVAR.•Newton conjugate gradient minimiser•Gaussian specification of error covariances

•The user can specify the obs error, model error, correlation scales, and the number of outer loops to perform.


The Python Test systemExample output

Forcing ΔSST


Future Plans – The diurnal analysis system


The diurnal analysis systemOverview

•We plan to create a high resolution (~1/20º) diurnal model based within NEMOVAR.

•This will include our warm layer & cool skin models, which will be coded within NEMO.

•We will use a 1 layer configuration, similar to the SST bias correction, with all ocean physics turned off.

•The model will include horizontal as well as temporal correlations to allow the spreading of observational data.

Diurnal analysis system

SSTskin

OSTIA SSTfound Analysis

SSTfoundΔSST


Summary


Summary

•We have developed a SST bias correction system that uses NEMOVAR in a 2-D configuration.

•We are developing an analysis system for skin SST that uses the Takaya, 2010 and Artale,2002 models.

• Stand alone versions of the full non-linear, Tangent Linear, and Adjoint of the Takaya model have been coded. The non-linear model has been incorporated into NEMO.

•We have developed a 1-D test data assimilation system based upon a 4DVar methodology.

•We plan to develop a high resolution analysis of skin SST using OSTIA, and the Takaya & Artale models incorporated into NEMOVAR.


The End

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© Crown copyright Met Office Implementing a diurnal model at the Met Office James While, Matthew Martin