Fig. 3 shows a detail of the top 300 m at the equator for the same day (Jan 10, 2008) for the simulation and assimilation runs. The assimilation causes a deepening of the mixed layer and the increase of the vertical gradient of temperature in the thermocline region. An unstable profile is produced around 50 m depth between 25 o W and 30 o W, showing that realization of data assimilation in HYCOM still needs further developments. For instance, a rigorous quality control of the input data is necessary. The data assimilation reduced the difference between model and observation along the 10-day integration (Fig. 4). 2.2 MOM4 For the MOM4 experiment, the model was also run for 30 years from rest and Levitus temperature and salinity, and then forced from Jan 1995 until Dec 2000 with monthly mean data from the Common Ocean-ice Reference Experiments (CORE) ( RE.html). The model was configured with a global grid of 1 o resolution, except in between 10 o S – 10 o N in which the resolution was 1/3 o, and between 10 o – 30 o in both hemispheres where the resolution was linearly increasing from 1/3 to 1 o. Fig. 5 shows the annual mean of the potential temperature at the equator. Comparing with Fig. 1, the simulation of MOM4 is able to resolve more accurately the vertical structure of temperature than HYCOM. Fig. 6 shows the model simulation, assimilation and the difference for 5 m depth temperature on January 2, The model is mostly corrected with positive increments of temperature at the surface. Fig. 7 shows the vertical profiles of temperature at two points, one in which there is a mooring and the other in which the average of neighbooring moorings. 2. Numerical Experiments Two different applications of the data assimilation scheme were done. In the first, the Hybrid Ocean Coordinate Model (HYCOM) was used to assimilate PIRATA data, and in the second the Geophysical Fluid Dynamics Laboratory (GFDL/NOAA) Modular Ocean Model v4 (MOM4) MOM4 was used to assimilate TAO/TRITON data. Only vertical profiles of temperature were used and just a few assimilation steps were realized in each experiment. The goals of these experiments are to verify the feasibility of the scheme and to face the model biases and difficulties in the numerical realization process. The present data assimilation scheme may be used as part of a numerical ocean forecast system for the Atlantic Ocean, with emphasis over the region along the Brazilian Coast that is today under construction by the Oceanographic Modeling and Observation Research Network (REMO). This effort is supported by Petrobras and the Brazilian Agency for Petroleum, Natural Gas and Biofuels. 2.1 HYCOM HYCOM was configured for the Atlantic Basin using a 1/3 o spatial grid and 22 vertical hybrid layers with the top layer at its minimum thickness of 3m. In coastal waters, there are up to 12 sigma levels and the coastline is at 10m isobath. North and south boundaries for temperature, salinity and pressure are linearly relaxed toward the Levitus seasonal climatological data (Levitus and Boyer, 1994). Initially, the model was run for a 30-year period forced with COADS climatological atmospheric fields in order to produce a climatological ocean state. The fields used to force HYCOM were the surface air temperature, surface air specific humidity, precipitation rate, net shortwave radiation, net radiation and wind stress. Fig. 1 compares the temperature annual mean at the equator for the last year of the climatological run versus Levitus data. It shows that this HYCOM run was not able to produce a well-defined thermocline region despite the temperature at sea surface and well below the thermocline being close to climatology. After the 30-year run, the 6-hour 2007 NCEP reanalysis atmospheric forcing fields were used to produce more realistic oceanic conditions for actual time. The model was run sequentially for 4 years with the 2007 atmospheric reanalysis data to force the model towards the 2007 ocean state. For the realization of the assimilation scheme, the covariance matrix of observational data γ ij was prescribed as a function of the area averaged temperature and the distance between each pair of observations. Constant C presented in the poster by Belyaev and Tanajura was estimated as the difference between the spatial average among the available observations and the model at each grid point. All assimilation was performed in each model vertical layer independently. The PIRATA daily data used in the assimilation were converted into potential temperature and vertically interpolated to each model hybrid layer depth. Before this procedure, data was passed quality control tests to avoid assimilation of spurious data. Despite using temperature data only, salinity was directly affected by the assimilation procedure. After having the temperature ammendment, salinity was re-calculated through the state equation maintaining the model density unchanged. To perform the data assimilation scheme more rigorously the analysis increment was added to the model background in smaller parts. In the present realization, two steps were taken. First, the model error with respect to observations was calculated. Then, this error was divided by two and the assimilation increment was calculated twice in a row. This procedure can be realized for any number of intervals until a maximum restricted by the model time step. The results presented here deal with the daily assimilation of PIRATA data from January 1 until January 10, HYCOM was initialized with the last output produced by the 2007 run, and it was forced with 6hr NCEP reanalysis data. Fig. 2 shows the potential temperature at 30 m produced by the model simulation (without assimilation), the assimilation run, and the difference assimilation minus simulation on January 10, The assimation run imposes corrrections in the PIRATA region, with a warming of about 2 o C between 20 o N and 30 o N and cooling between the equator and 20 o S. A sequential data assimilation method based on the properties of a diffusion-type process and its applications with the ocean models MOM4 and HYCOM Clemente A. S. Tanajura 1,2 and Konstantin Belyaev 1,3 1 Centro de Pesquisa em Geofísica e Geologia (CPGG/UFBA) 2 Dept. de Física da Terra e do Meio Ambiente, Instituto de Física (IF/UFBA) Universidade Federal da Bahia, Salvador, Brazil (UFBA) 3 Shirshov Institute of Oceanology, Russian Academy of Sciences (Shirshov) References Kalnay, E Atmospheric Modeling, Predictability and Data Assimilation. Springer. Tanajura, C.A.S. and K. Belyaev. A sequential data assimilation method based on the properties of a diffusion-type process. Applied Mathematical Modelling (in press) (2008) Fig 2. January 10, 2008 temperature for (a) the HYCOM simulation; (b) assimilation; and (c) the difference assimilation minus simulation. Unit is o C. 3. Conclusions The results presented here show the data assimilation scheme was successfully applied in different models and it works properly. However, the correct procedure to assimilate vertical profiles of temperature in HYCOM is still not completely dominated, mainly because of the difficulties in interpolating the in situ temperature in the corresponding model isopicnal layers. Acknowledgements. This work was financially supported by PETROBRAS and Agência Nacional do Petróleo, Gás Natural e Biocombustíveis (ANP), Brazil, via the Oceanographic Modelling and Observation Research Network (REMO). Fig. 7. Temperature vertical profiles by the model simulation (thin line), assimilation (thick line) and observation (dashed line) at the points (0°N, 180°E) and (2°N, 190°E) on January 2, Unit is o C. UFBA. Fig. 6. MOM4 simulation on Jan 2, 2001 of 5 m depth temperature in contour lines and mooring locations marked by shaded circles (top); assimilation; difference assimilation minus simulation (bottom)( o C). 1. Introduction Data assimilation methods are important tools for numerical weather and climate forecasts, for diagnostic studies and to complement monitoring offered by observational systems in the oceans and the atmosphere (e.g. Kalnay 2003). In the present study, a new formulation for sequential data assimilation schemes is proposed based on the mathematical properties of a diffusion-type process. The detailed mathematical formulation of the method and the conditions for the convergence of the finite dimensional distributions of random process into the distribution of a stochastic process are given in Tanajura and Belyaev (2008) and in the poster presented by Belyaev and Tanajura in the present workshop. The method may be reduced to the well-known optimal interpolation scheme the model is unbiased and all covariances are known a priori. Also, this scheme may be reduced to the linear Kalman-Bucy filter when observational data have Gaussian noise. Fig. 1. Vertical structure of the annual mean of temperature at the equator for the last year of the 30- year climatological run and Levitus climatology. ( o C) Fig. 3. Vertical structure of temperature at the equator for Jan 4, 2008 from simulation and assimilation runs. Fig. 5. Vertical structure of temperature at the equator for the last year of MOM4 climatological run. ( o C) Fig. 4. Temperature RMSE time evolution ( o C) from Jan 1 until Jan before (solid line) and after assimilation (dashed line).