# Correcting the Sea Surface Temperature by Data Assimilation Over the Persian Gulf

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## Abstract

In this paper, the impact of sea surface temperature (SST) data assimilation on the results of a finite volume community ocean model has been examined by using the nudging scheme. In this regard, the advanced very high-resolution radiometer satellite SST data were selected as the observational data for assimilation. The numerical modeling was performed over the Persian Gulf from 1998 to 2003 in two different modes: with and without SST data assimilation. The performance of data assimilation with the nudging scheme was evaluated by comparing the simulated SST with the in situ SST measurements and optimum interpolation SST data. Both the spatial and temporal comparisons show the efficiency of assimilation in correcting the model results. The spatial root mean square error in the assimilated run depicts meaningful improvements in the whole of the domain. Also, the temporal comparisons of the results show the capability of assimilation in lowering the model output errors. The simulated SST obtained by applying the data assimilation in the shallow parts of the Persian Gulf matched exactly with the measured ones, especially near the Hormuz Strait. Finally, the results show significant improvements in the SST simulated by using the nudging schemes.

## Keywords

Data assimilation SST Nudging FVCOM Persian Gulf## 1 Introduction

Sea surface temperature (SST) is one of the most important variables for studying the ocean and the atmosphere and their interactions. Because of its importance and simple methods for measuring, there is a considerable amount of in situ measurements. In marine science, SST has a key role in research of climate change. Due to the importance of the ocean's upper level in studying the processes which occur at the interface of water and the atmosphere, the satellite SST data can be accessed by the users less than 3 h after measurements. The accuracy of SST can definitely facilitate a better understanding of these processes. Although in situ measurements are the most exact method, due to scarcity of these data, using satellite observational data is the most appropriate option to compensate for this lack. Fortunately, the collection of SST maps has been accomplished by satellite sensors for more than three decades.

Nowadays, use of the SST product from satellite sensors due to its wide coverage (> 1000 km^{2}) and suitable spatial (~ 1 km at nadir) and temporal (two times per day) resolutions has been habitual (Kilpatrick et al. 2015).

Although the recent and improved ocean models can simulate many of the characteristic parameters of the ocean systems, the model outputs have some errors due to uncertainty in factors such as initial and boundary conditions and the intrinsic numerical and input data errors.

Inaccurate numerical simulation of wind-induced phenomena like wind waves and wave-induced currents in the Persian Gulf is a result of the lack of offshore wind stations and heat flux data; this is a considerable source of error for this simulation.

Therefore, to reduce the simulation errors, nowadays, remotely observed data are combined with ocean models by using data assimilation methods.

The first attempt in employing data assimilation in ocean research was the assimilation of SST and vertical profile measurements in a global circulation model by Derber and Rosati (1989). Carton and Hackert (1990) did the same work by adding a correction technique into the Tropical Atlantic model. Clancy et al. (1990, 1992) combined synoptic ship, bathythermograph, buoy and satellite data with the prediction of a mixed-layer model by using an optimal interpolation (OI) scheme. Behringer (1994) applied an objective interpolation scheme for assimilating SST and expendable bathythermograph (XBT) observations to improve the SST maps.

The most common techniques in data assimilation are nudging, 3D and 4D variational methods, optimal interpolation and the Kalman filter (KF). Manda et al. (2005) recognized the skill and feasibility of the nudging method as compared to sophisticated assimilation methods such as the ensemble Kalman filter (EnKF) for estimating the upper mixed layer of the ocean.

Also, many previous studies have been carried out to recognize the SST pattern and variations in the Persian Gulf. Shirvani et al. (2015) denoted increasing Persian Gulf SST over approximately the last 20 years. Johns et al. (2003) studied the heat and freshwater budgets of the Persian Gulf and showed an annual heat loss of about −7 ±4 W/m^{2} in this domain. Nazemosadat (1998) showed a relationship between the Persian Gulf SST and drought diagnostics in the southern parts of Iran. Nazemosadat et al. (2008) depicted the effect of El Niño–Southern Oscillation (ENSO) on the Persian Gulf SST. Glibert et al. (2002) showed that the SST is the governing item controlling fin-fish dynamics and is related to summertime fish kills in Kuwait Bay. Sheppard and Rayner (2002) associated coral bleaching in the southern part of the Persian Gulf to high seawater temperatures.

In this study, the nudging scheme was used to assess the ability of this assimilation scheme to improve the structure of the temperature field in a high-resolution setup of a finite volume community ocean model (FVCOM; Chen et al. 2006). After the SST assimilation process, the modeled oceanic state variables were compared with the observed data to evaluate the improvement yielded by the assimilation procedure.

The structure of this paper is as follows: first, the FVCOM is briefly described and then the observational data, statistical methods and nudging assimilation scheme are illustrated. Next, the results of the effects of the SST assimilation on the SST and subsurface temperature profiles are presented. Finally, a summary and discussion are offered.

## 2 Materials and Methods

### 2.1 FVCOM

The model used for this study is the FVCOM which has been described in its manual (Chen et al. 2006); it uses an unstructured grid, 3D primitive equations and fully coupled current–wave–ice data. This model was originally developed by Chen et al. (2003) and modified and upgraded by a joint effort of the University of Massachusetts-Dartmouth (UMASS-D) and Woods Hole Oceanographic Institution (Chen et al. 2006). The FVCOM is governed by seven primitive equations of momentum, continuity, temperature, salinity and density in the spherical coordinate system, with turbulent mixing parameterized by the general ocean turbulence model (Burchard 2002) in the vertical orientation and the Smagorinsky turbulent closure scheme in the horizontal orientation (Smagorinsky 1963). The flux forms of the governing equations are discretized in the unstructured triangular mesh in the horizontal (Chen et al. 2003) and in the generalized terrain-following coordinate in the vertical (Pietrzak et al. 2002). The FVCOM is integrated with options of various mode splits and semi-implicit schemes in time and the second-order accurate advection schemes in space. The methods using an unstructured grid and finite volume combine the best attributes of the finite difference method for simple discrete computational efficiency and the finite element methods for geometric flexibility. The flux computational approach provides an accurate representation of mass, heat and salt conservation.

^{3}/s and high-flow seasons between March and May. For vertical mixing and horizontal diffusion, we used the Mellor–Yamada level 2.5 turbulence closure (Mellor and Yamada 1982) and Smagorinsky schemes were employed, respectively. The external and internal mode time steps are 6.0 and 60.0 s, respectively.

The study period is from 1998 to 2003 based on the in situ data availability. The surface forcing including daily surface wind, precipitation, evaporation, shortwave and longwave radiation, and latent and sensible heat fluxes were prepared based on European Centre for Medium-Range Weather Forecasts (ECMWF) data with 0.5° spatial and 6-h temporal resolutions available from 1998 to 2003, containing a reanalysis product. To modify and localize the wind data set in the domain, the results of Abbaspour and Rahimi (2011) were used.

### 2.2 SST Data: Assimilation and Comparison

Five years of advanced, very high-resolution radiometer (AVHRR) SST data between 1998 and 2003 were selected for the assimilation. These data were selected due to their low spatial and high temporal resolutions. Ahmadabadi et al. (2009) showed the maximum, minimum and mean of errors for SST in the Persian Gulf as 0.77, −0.09 and ±0.43, respectively, which can be considered acceptable values.

*x*

_{i}and

*y*

_{i}denote the measured and modeled values, respectively. Moreover, \(\bar{x}\) and \(\bar{y}\) are their average values, respectively.

### 2.3 The Nudging Method

The nudging method is one of the easiest and oldest schemes among the data assimilation schemes. However, in spite of the above-mentioned characteristics, it is still widely used for many important applications such as forecast applications and operational assimilation systems. Due to its low computational cost, it is known as a fast and practical method. In this method, the model is slowly nudged (relaxed) towards observations at each time step in the model via a Newtonian relaxation term in the prognostic equation of the variable. The nudging method has been used in ocean data assimilation by Holland and Malanotte-Rizzoli (1989) and Malanotte-Rizzoli and Young (1992).

Manda et al. (2005) studied the SST mixing process and used nudging and EnKF methods. They applied both the nudging and the sophisticated nonlinear EnKF assimilation method and then compared the results. They concluded there is not a significant difference between the sets of results.

The nudging scheme is described as follows (Chen et al. 2006):

*n*is the number of observational points within the search area; \(\gamma_{i}\) is the data quality factor at the

*i*th observational point with a range from 0 to 1; and \(G_{\alpha }\) is a nudging factor that keeps the nudging term scaled by the slowest physical adjustment process. The selection of \(G_{\alpha }\) must satisfy the numerical stability criterion given by

The weight function used here considers the temporal and spatial variation. Likewise, total weight has a value between 0 and 1. *R* is the search radius, \(\bar{r}\) is the distance from the location where the data exists, \(R_{\sigma }\) is the vertical search range, \(T_{w}\) is half of the assimilation time window and \(\Delta \theta\) is the directional difference between the local isobath and the computational point with \(c_{1}\) being a constant ranging from 0.05 to 0.5.

## 3 Results and Discussion

### 3.1 Advantages of Using SST Assimilation

In order to study the influence of SST assimilation on the subsurface temperature, the vertical temperature profile of two runs were compared with the CTD data of ROPME the cruise.

## 4 Conclusions

This study applied the nudging scheme which enables satellite SST observations to be assimilated into the FVCOM in the Persian Gulf. The results show that the assimilation can effectively improve the thermal structure of the domain not only at the surface but also in the subsurface.

This assimilation method can successfully be applied for satellite SST data, such as that collected by NOAA and other satellites. It was demonstrated that over the period of modelling, the agreement of the assimilated SST with the satellite observation was improved by ∼ 11% in comparison with the regular SST without data assimilation. When the satellite-borne SST data were assimilated into the FVCOM through the nudging scheme, the assimilated model state showed improvements compared to those in the non-assimilative model over all the simulation periods for most of the model domain. The regions with the largest errors were found to be the southern coasts and southwestern portion of the Persian Gulf. The northern regions have low SST errors in comparison with OISST.

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