عنوان مقاله [English]
The Mean Dynamic Topography (MDT) of the seas is a quantity which comes from subtracting the Geoid Height (GH) from the Mean Sea Surface (MSS) at every point on the sea. The direction of geostrophic currents is obtained through the calculation of the MDT slope relative to the Geoid. In this research, a series of GOCE geopotential coefficients resulted from the 4 year collection of GOCE observations was used to estimate the reference geoid height in the Persian Gulf, the Oman Sea and the Indian Ocean, i.e., in the area of interest. Two MDT models data were available at the time of performing this research: Denmark Technical University’s model, named ‘Mean Dynamic Topography of Denmark Technical University 2010’ (MDT_DTU_2010) which has been available on a geographical grid of 2 arc minutes spacing (Knudsen & Andersen, 2010). This model is based on the mean sea surface topography model MSS_DTU_2010 and the 2 month of GOCE geopotential data for the Geoid as the reference surface. The second model is the Mean Dynamic Topography Centre National d'Etudes Spatiales collecte localisation satellites 2009 (MDT_CNES_CLS09) with 15 minutes resolution (Rio et al, 2011). This model contains the east-west and north-south geostrophic current components with itself as well. It is based on MSS_CLS01 (Hernandez and Schaeffer, 2001) and 4.5 years of GRACE geopotential data used for the reference geoid.
Materials and Methods
In this research a new Mean Dynamic Topography (MDT) model with the name of MDT_IAU_TN_2014 is presented. Also, the surface permanent current vectors in a grid with 2 minutes resolutions is computed in the Persian Gulf, the Oman Sea and the north of Indian Ocean. This MDT is formed by a Mean Sea Surface (MSS) model computed from 6 altimetry satellites data (Topex/Poseidon, Jason 1 and 2, ERS 1 and 2 and Geosat Follow-On) and GOCE satellite data with 21 and 4 years ranges in 1992-2013 are calculated. The first step for the Mean Sea Surface (MSS) computation is to calculate the mean of Sea Surface Heights (SSH) along the repeated (in time) sub-tracks of altimetry satellites over the years available in the area of interest. The mean value of SSHs over time in a same track is then called Mean Height (MH). The Basic Radar Altimetry Toolbox (BRAT) version 3.1.0 was used for the MH computation. The correction term includes the tidal periodic variations, physical earth corrections such as troposphere, ionosphere, and sea state biases. All of these corrections are considered from the satellite handbooks T/P (AVISO/ALTIMETRY, 1996), J1 (AVISO and PODAAC USER HANDBOOK, 2012), J2 (OSTM/Jason-2 Products Handbook, 2001), ERS (RA/ATSR products - User Manual, 2001), GFO (GEOSAT Follow-On GDR User's Handbook, 2002). Among altimetry satellites, T/P (J1 and J2) has the highest orbit and longest data sets so it has been selected as a reference for corrections.
Results & Discussion
To homogenize the spectral of MSS and the Geoid, a truncated Gaussian filter with 1.386 degree radius has been used. MDT results have been compared with two global model and have 0.033 and 0.051 RMS of differences in order. Among altimetry satellites used in this research, J2 and GFO satellites have the ability to measure shallow waters. Hence, the data provided by these satellites in shallow waters, i.e. Persian Gulf are valuable. MHS differences between E1 and T/P are larger than the MHS of other satellites, because there are differences between the two missions, i.e., there are 8 km distances between E1 sub-tracks at equator but long repeatability period of 35 days of data acquisition time and T/P sub-tracks spacing are 315 km at equator and short repeatability period of 9.9 days. Also, the orbit elevations are different: T/P at altitude of 1336 km and E1 at altitude of 785 km. Inclusion of E1 data in the MSS_IAU_TN_2014 solution would globally decrease the RMS difference of the solution relative to the MSS_CNES_CLS_2011 model from 0.4 m (without E1 data) to 0.1 m. This improvement by the E1 data is probably due to the higher resolution of the data in the region of interest.
Changing the filtering radius of 1.386 degree down to lower degrees until 1 degree would increase the MDT_IAU_TN_2014 differences (relative to the MDT_DTU_2010) and MDT_CNES_CLS09 from 0.033m and 0.051m RMS up to larger values. At the 1.386 degree, the differences are minimum. For filtering radiuses of more than 1.386 degree the MDT surface would become unreasonably much smoother and the RMS difference would increase. Geostrophic and Ekman velocity currents using 22 years data of surface wind has been calculated. Total currents of the released model in this research have been compared with OSCAR in-situ data and have 0.047 and 0.031 meter RMS of differences in North-South and East-West current components. The total currents from MDT_IAU_TN-2014 model vary between 0 to 0.61 m/s in the north Indian ocean region. The comparison shows that all three models show almost the same range of variations in the region of interest. SLA an In-Situ data could be used to make the MDT_IAU_TN_2014 independent from any other models. The lack of In-Situ data in the region of interest forced MDT_IAU_TN_2014 to use MDT_DTU_2010 to cover filtered parts. Also using other gravity models with higher Spherical harmonic coefficients degree and orders such as EIGEN-6c and EGM08, would make filtering not needed in the dynamic modeling.