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

© Crown copyright Met Office 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

© Crown copyright Met Office NEMOVAR SST Bias correction system

© Crown copyright Met Office NEMOVAR SST Bias correction system Overview 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.

© Crown copyright Met Office SST Bias correction system Algorithm 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 obsBiased obs Matchups Bias field Bias background Relaxation to climatology This algorithm is applied individually to each biased data type.

© Crown copyright Met Office Bias for AVHRR after 3 days Correlation length scale = 7º SST Bias correction system Example field

© Crown copyright Met Office The Diurnal model

© Crown copyright Met Office Diurnal model Overview 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.

© Crown copyright Met Office Diurnal Model Theory Based on the Takaya, 2010 bulk diurnal model. Implemented both as standalone system & within NEMO. T:- ΔSST t :- Time Q:- Thermal energy flux D T :- Layer depth ρ:- Water density c p :- Heat capacity ν:- Structure parameter u w *:- Friction velocity L a :- Langmuir number k:- Von Karmans constant g:- Acceleration due to gravity α w :- Thermal expansion coefficient Bulk thermal heating of a layer Turbulent damping These equations are solved using an implicit scheme

© Crown copyright Met Office Diurnal modelNEMO top level Diurnal Model Peak ΔSST in NEMO for Jan 07

© Crown copyright Met Office The Data Assimilation System

© Crown copyright Met Office Data assimilation system Overview 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.

© Crown copyright Met Office Initial temperature Thermal energy flux at all timesteps Friction velocity at all timesteps Data assimilation system Control vector

© Crown copyright Met Office T, Q & u w * assumed uncorrelated with each other. Temporal correlations modelled as a Gaussian Diagonal, observations assumed uncorrelated y includes observations of T only. NOTE: The model is assumed perfect at night Data assimilation system Cost function (inner loop)

© Crown copyright Met Office The Python Test System

© Crown copyright Met Office Python Test system Overview 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.

© Crown copyright Met Office The Python Test system Example output ForcingΔSST

© Crown copyright Met Office Future Plans – The diurnal analysis system

© Crown copyright Met Office The diurnal analysis system Overview 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 SST skin OSTIA SST found Analysis SST found ΔSST

© Crown copyright Met Office Summary

© Crown copyright Met Office 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.

© Crown copyright Met Office The End