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Implementing a diurnal model at the Met Office. James 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.

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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


  • 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 system


Ref obs

Biased obs

This algorithm is applied individually to each biased data type.

  • 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.


Bias background

  • Matchups are assimilated as if they are SST observations with long length scales.

Bias field

Relaxation to climatology

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

SST Bias correction system

Example field

Bias for AVHRR after 3 days

Correlation length scale = 7º


Diurnal model


  • 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 Model


  • Based on the Takaya, 2010 bulk diurnal model.
  • Implemented both as standalone system & within NEMO.


t :- Time

Q:- Thermal energy flux

DT:- Layer depth

ρ:- Water density

cp:- Heat capacity

ν:- Structure parameter

uw*:- Friction velocity

La:- Langmuir number

k:- Von Karman’s constant

g:- Acceleration due to gravity

αw:- Thermal expansion coefficient



Bulk thermal

heating of a layer

  • These equations are solved using an implicit scheme

Diurnal Model

Peak ΔSST in NEMO for Jan 07

Diurnal model

NEMO top level


Data assimilation system


  • 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.

Data assimilation system

Control vector

Initial temperature

Thermal energy flux at all timesteps

Friction velocity at all timesteps


Data assimilation system

Cost function (inner loop)

T, Q & uw* assumed uncorrelated with each other.

Temporal correlations modelled as a Gaussian


observations assumed


NOTE: The model is assumed perfect at night

y includes observations of T



Python Test system


  • 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 system

Example output




The diurnal analysis system


  • 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

OSTIA SSTfound Analysis






  • 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 & Artalemodels incorporated into NEMOVAR.