# Improving the Modeling of Sea Surface Currents in the Persian Gulf and the Oman Sea Using Data Assimilation of Satellite Altimetry and Hydrographic Observations

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Description

#### 2.2. Methodology of Calibrating MIKE Model

- Selecting the equation solution as “discretization of equations with high degrees”;
- Considering density as a function of temperature and salinity;
- Variable Coriolis force in place;
- Variable wind force;
- Tidal force by applying TM-IR01 model tidal components;
- Precipitation and evaporation;
- The Smagorinsky formula was used for horizontal eddy viscosity [30], with a constant value of 0.28 for the Smagorinsky coefficient as the suggested number for the MIKE 21 model;
- In the MIKE 21 model, one of the most valuable features is the ability to dynamically adjust the domain of the computations. This enables one to calculate SSCs in areas that sometimes are dry and sometimes are wet, such as tidal zones;
- Manning’s coefficient of 0.03 was applied for the bed resistance

_{f}), initial conditions (e

_{i}), boundary conditions (e

_{b}), in situ measurements (e), and the model (e

_{m}), was defined as follows [33]:

_{f}is the covariance matrix of the force field, I is the estimated initial conditions, i is the initial conditions (including the SLH and SSC components), C

_{i}is the covariance matrix of the initial conditions, B is the estimated boundary conditions, b is the boundary conditions (including SLH data), C

_{b}is the covariance matrix of the boundary conditions, y is the observations for data assimilation (including SLH and SSC components), H is the interpolation operator or observation operator, C

_{y}is the covariance matrix of the data assimilation observations, x

^{a}is the assimilated model, C

_{m}is the covariance matrix of the model, and x

^{m}is the output of the numerical model, including the SLH and SSC components derived from the MIKE model.

_{f}may arise from errors in surface wind forcing. It may also arise from simplifications in equations of motion, such as hydrostatic approximation or parametrization of turbulent mixing. The initial and boundary errors (e

_{i}and e

_{b}) usually arise from errors in observation. Errors in the model occur due to discretization and numerical calculations, which have a solely mathematical nature [33].

_{f}) [33], initial and boundary conditions (C

_{i}and C

_{b}), observations (C

_{y}), and model or background (C

_{m}) were constructed. For the covariance matrix of the force field, including the covariance matrix of the wind (C

_{Wind Force}), the covariance matrix of the tidal force (C

_{Tidal Potential}), and the covariance matrix of the bed resistance (C

_{Bed Resistance}), one could write:

_{Tidal Potential}, we used the standard deviation of the tidal components, which were specified in the TM-IR01 model. The unit weight was considered for C

_{Bed Resistance}. To this end, the covariance matrix of the wind was formed using a spatio-temporal empirical covariance function:

_{sea level}) and the horizontal components of the SSC (C

_{u}and C

_{v}), (the initial conditions (SLH, u, and v) were in the form of a gridded file at the initial time), we used a spatial empirical covariance function (C

_{s}) to determine the covariance of each observation [35]. Thus, one could write:

_{b}in Equation (1)), we set C

_{b}= C

_{TG}, namely it was equal to the covariance matrix of the tide gauge observations. As it was discussed, the SLH observations from tide gauge stations were used as boundary conditions. To this end, for the covariance matrix of the tide gauge observations, the average of the SLH time series (MSL) was first subtracted from the SLH time series (SLA = SLH-MSL, which is a residual time series), and then its standard deviation was considered as the covariance matrix of the boundary conditions (C

_{b}).

_{sea level ALT}), coastal tide gauge observations (C

_{sea level TG}), and in situ current meter observations (C

_{u}and C

_{v}), was considered as follows:

_{sea level ALT,}C

_{sea level TG}, C

_{u}, and C

_{v}could be formed by taking the standard deviation of their residual time series in a similar manner to explained for C

_{b}. As it was seen, the computation of C

_{u}and C

_{v}for C

_{y}was different from the computation of C

_{u}and C

_{v}for C

_{i}.

^{48}and x

^{24}are, respectively, the 48 h and 24 h predictions of the model at a certain time; the upper bar indicates averaging over time or space; x

_{true}is the correct value of the model (without error and bias); and ${\epsilon}^{48}$ and ${\epsilon}^{24}$ are the respective random errors. We also assumed that there was no bias or that the bias was constant over time (b

^{48}= b

^{24}). As a result, the forecast difference could be expressed as follows [37]:

## 3. Results

#### 3.1. Numerical Ocean Model and Data Assimilation

#### 3.2. Validation and Control of Calibrated Model

_{k}is the amplitude of the tidal components, F

_{K}is the frequency of the tidal components, ${\phi}_{k}$ is the phase of the tidal components, and m is the number of tidal frequencies. As an example, Figure 14 shows the SLH observation at Khark station and the reconstruction of the time series using the TM-IR01 and assimilated models. Table 6 shows the RMSE results between the tide gauge stations and TM-IR01 model, as well as the assimilated model.

#### 3.3. Analyzing the Results of the SSC and Its Application in Producing Renewable Energy

^{3})—1000 (kg/m

^{3})).

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Sea level height before data assimilation (calibration); (

**b**) east–west component (u) of the SSC before data assimilation; (

**c**) north–south component (v) of the SSC before data assimilation.

**Figure 2.**(

**a**) Sea level height after data assimilation (calibration); (

**b**) east–west component (u) of the SSC after data assimilation; (

**c**) north–south component (v) of the SSC after data assimilation.

**Figure 3.**(

**a**) The performance of each optimization method at tide gauge stations with and without considering covariance matrices. (

**b**) The performance of each optimization method at current meter stations with and without considering covariance matrices.

**Figure 5.**Correlations between the observations of the SLH at the Rajaei tide gauge station and the model output in three cases: (

**a**) before data assimilation, (

**b**) after data assimilation without considering the variance–covariance matrices, and (

**c**) considering the variance–covariance matrices.

**Figure 6.**The correlations between the east–west component (u) of the SSC at Taheri current meter station and the model in three cases: (

**a**) before data assimilation (calibration), (

**b**) after data assimilation without considering the variance–covariance matrices, and (

**c**) after considering the variance–covariance matrices. The correlations between the observations of the north–south component (v) of the SSC at the Taheri current meter station and the model in three cases: (

**d**) before data assimilation, (

**e**) after data assimilation without considering variance–covariance matrixes, and (

**f**) considering variance–covariance matrixes.

**Figure 8.**Two missions of satellite altimetry passes, coastal tide gauges, and current meter stations used in the study area.

**Figure 9.**SLH and SSC observations at Rajaei and Nayband control stations obtained from the model before and after data assimilation. (

**a**) SLH observations at Rajaei control station (blue), the model before data assimilation (green), and the model after data assimilation (red). (

**b**) East–west components of SSC at Nayband control station (blue), the model before data assimilation (green), and the model after data assimilation (red). (

**c**) North–south components of SSC at Nayband control station (blue), the model before data assimilation (green), and the model after data assimilation (red).

**Figure 10.**(

**a**) Performances of Manning coefficients (MCs) of 0.015, 0.021, and 0.023 at Rajaei control station and their effects on SLH; (

**b**) separated portion of (

**a**) to show more details.

**Figure 12.**(

**a**) Performances of Smagorinsky coefficients (SCs) of 0.13, 0.15, and 0.17 at Rajaei control station and their effects on SLH; (

**b**) separated portion of (a) to illustrate more details.

**Figure 14.**As a typical example, (

**a**) SLH observations at Khark station (blue) and reconstructions of SLH time series with the TM-IR01 model (green) and the assimilated (calibrated) model (red); (

**b**) separated portion of part (

**a**) to show more details.

**Figure 15.**SSCs in the Persian Gulf and Oman Sea regions after the data assimilation of observations at 3:00 a.m. on 1 January 2008: (

**a**) the whole area, (

**b**) Persian Gulf, (

**c**) Strait of Hormuz, (

**d**) Oman Sea, (

**e**) North Indian Ocean adjacent to Oman, (

**f**) North Indian Ocean adjacent to India, (

**g**) Oman Sea adjacent to Pakistan, and (

**h**) Oman Sea and North Indian Ocean.

Station | Country | Latitude [°] | Longitude [°] | Time Period | Data Source | Performance |
---|---|---|---|---|---|---|

Muscat | Oman | 23.633 | 58.567 | 2008–2009 | UHSLC ^{1} | modeling (CB ^{2}) |

Masirah | Oman | 20.683 | 58.867 | 2008–2009 | UHSLC | modeling (CB) |

Salalah | Oman | 16.933 | 54.007 | 2008–2009 | UHSLC | data assimilation |

Karachi | Pakistan | 24.85 | 67.067 | 2008–2009 | UHSLC | modeling (CB) |

Khark | Iran | 29.31 | 50.33 | 2008–2009 | NCC ^{3} | validation |

Jask | Iran | 25.66 | 57.77 | 2008–2009 | NCC | data assimilation |

Chabahar | Iran | 25.296 | 60.603 | 2008–2009 | UHSLC | modeling (CB) |

Rajaei | Iran | 27.1 | 56.04 | 2008–2009 | NCC | validation |

Lengeh | Iran | 26.55 | 54.88 | 2008–2009 | NCC | modeling (CB) |

Khomeini | Iran | 30.43 | 49.083 | 2008–2009 | NCC | data assimilation |

Bushehr | Iran | 28.98 | 50.83 | 2008–2009 | NCC | data assimilation |

Bahman | Iran | 26.95 | 56.28 | 2008–2009 | NCC | modeling (CB) |

Point_1 | NIO ^{4} | 15 | 55.231 | 2008–2009 | TM-IR01 | data assimilation |

Point_2 | NIO | 15 | 60.45 | 2008–2009 | TM-IR01 | modeling (OB ^{5}) |

Point_3 | NIO | 15 | 65.45 | 2008–2009 | TM-IR01 | modeling (OB) |

^{1}University of Hawaii Sea Level Center (Uhslc.soest.hawaii.edu).

^{2}Closed boundary.

^{3}National Cartography Center of Iran.

^{4}North Indian Ocean.

^{5}Open boundary.

Station | Instrument | Position | Period of Data | Source of Data | Performance |
---|---|---|---|---|---|

Taheri | ADCP | 27.63 52.36 | 2008–2009 | PMO ^{6} | Data assimilation |

Nayband-Gulf | ADCP | 27.42 52.65 | 2008–2009 | PMO | validation |

Nakhl-Taghi | ADCP | 27.49 52.57 | 2008–2009 | PMO | Data assimilation |

Kangan | ADCP | 27.83 52.04 | 2008–2009 | PMO | Data assimilation |

^{6}Ports and Maritime Organization of Iran.

Mission | Period | Source | Performance |
---|---|---|---|

Jason 1 | 2008–2009 | NASA, AVISO | Creation of point-wise time series for data assimilation and validation |

ENVISAT | 2008–2009 | ESA | Creation of point-wise time series for data assimilation and validation |

Data | Description |
---|---|

Bathymetry | GEBCO, see: https://www.gebco.net/data_and_products/gridded_bathymetry_data/ (accessed on 1 January 2022). |

Domain | GSHHG, see: https://www.ngdc.noaa.gov/mgg/shorelines/ (accessed on 1 January 2022). |

Wind | ERA5 hourly data, see: https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-pressure-levels?tab=form (accessed on 1 January 2022). |

Evaporation | Copernicus data center, see: https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-land?tab=overview (accessed on 1 January 2022); these data were used for climatology condition |

Precipitation | Copernicus data center, see: https://cds.climate.copernicus.eu/cdsapp#!/dataset/satellite-precipitation?tab=overview (accessed on 1 January 2022); these data were used for climatology condition |

Tidal potential | TM-IR01 from NCC [26]; these data were used for tidal force consideration |

SLA ^{7} | Copernicus data center, see https://cds.climate.copernicus.eu/cdsapp#!/dataset/satellite-sea-level-global?tab=overview (accessed on 1 January 2022); these data were used for initial condition of modeling |

SSC components | Copernicus data center, see:https://cds.climate.copernicus.eu/cdsapp#!/dataset/satellite-sea-level-global?tab=overview (accessed on 1 January 2022); these data were used for initial condition of modeling |

^{7}Sea level anomaly.

**Table 5.**RMSE values between the assimilated (calibrated) model and tide gauge observations at Rajaei and Khark control stations and current meter observation at Nayband control station.

Different State of Objective Function | ||||||
---|---|---|---|---|---|---|

Observations | $\begin{array}{l}{\mathrm{C}}_{f}={\mathrm{C}}_{f};\\ {\mathrm{C}}_{i}={\mathrm{C}}_{i};\\ {\mathrm{C}}_{b}={\mathrm{C}}_{b};\\ {\mathrm{C}}_{y}={\mathrm{C}}_{y};\\ {C}_{m}={C}_{m};\end{array}$ | $\begin{array}{l}{\mathrm{C}}_{f}={\mathrm{C}}_{f};\\ {\mathrm{C}}_{i}={\mathrm{C}}_{i};\\ {\mathrm{C}}_{b}={\mathrm{C}}_{b};\\ {\mathrm{C}}_{y}={\mathrm{C}}_{y};\\ {C}_{m}=I;\end{array}$ | $\begin{array}{l}{\mathrm{C}}_{f}={\mathrm{C}}_{f};\\ {\mathrm{C}}_{i}={\mathrm{C}}_{i};\\ {\mathrm{C}}_{b}={\mathrm{C}}_{b};\\ {\mathrm{C}}_{y}=I;\\ {C}_{m}=I;\end{array}$ | $\begin{array}{l}{\mathrm{C}}_{f}={\mathrm{C}}_{f};\\ {\mathrm{C}}_{i}={\mathrm{C}}_{i};\\ {\mathrm{C}}_{b}=I;\\ {\mathrm{C}}_{y}=I;\\ {C}_{m}=I;\end{array}$ | $\begin{array}{l}{\mathrm{C}}_{f}={\mathrm{C}}_{f};\\ {\mathrm{C}}_{i}=I;\\ {\mathrm{C}}_{b}=I;\\ {\mathrm{C}}_{y}=I;\\ {C}_{m}=I;\end{array}$ | $\begin{array}{l}{\mathrm{C}}_{f}=I;\\ {\mathrm{C}}_{i}=I;\\ {\mathrm{C}}_{b}=I;\\ {\mathrm{C}}_{y}=I;\\ {C}_{m}=I;\end{array}$ |

SLH at Rajaei station (meter) | 0.071 | 0.079 | 0.087 | 0.098 | 0.118 | 0.124 |

SLH at Khark station (meter) | 0.086 | 0.091 | 0.097 | 0.109 | 0.127 | 0.132 |

The east–west component of SSC at Nayband station (U) (meters per second) | 0.069 | 0.076 | 0.088 | 0.091 | 0.105 | 0.114 |

The north–south component of SSC at Nayband station (V) (meters per second) | 0.073 | 0.087 | 0.094 | 0.103 | 0.110 | 0.119 |

**Table 6.**RMSE results between SLH of tide gauge stations and TM-IR01 model, as well as assimilated model.

Station | TM-IR01 Model | Assimilated Model |
---|---|---|

Muscat | 0.121 | 0.081 |

Masirah | 0.112 | 0.084 |

Salalah | 0.126 | 0.097 |

Karachi | 0.109 | 0.078 |

Khark | 0.132 | 0.094 |

Jask | 0.113 | 0.081 |

Chabahar | 0.132 | 0.075 |

Rajaei | 0.129 | 0.088 |

Lengeh | 0.115 | 0.079 |

Khomeini | 0.127 | 0.082 |

Bushehr | 0.131 | 0.081 |

Bahman | 0.127 | 0.086 |

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**MDPI and ACS Style**

Pirooznia, M.; Raoofian Naeeni, M.; Atabati, A.; Tourian, M.J.
Improving the Modeling of Sea Surface Currents in the Persian Gulf and the Oman Sea Using Data Assimilation of Satellite Altimetry and Hydrographic Observations. *Remote Sens.* **2022**, *14*, 4901.
https://doi.org/10.3390/rs14194901

**AMA Style**

Pirooznia M, Raoofian Naeeni M, Atabati A, Tourian MJ.
Improving the Modeling of Sea Surface Currents in the Persian Gulf and the Oman Sea Using Data Assimilation of Satellite Altimetry and Hydrographic Observations. *Remote Sensing*. 2022; 14(19):4901.
https://doi.org/10.3390/rs14194901

**Chicago/Turabian Style**

Pirooznia, Mahmoud, Mehdi Raoofian Naeeni, Alireza Atabati, and Mohammad J. Tourian.
2022. "Improving the Modeling of Sea Surface Currents in the Persian Gulf and the Oman Sea Using Data Assimilation of Satellite Altimetry and Hydrographic Observations" *Remote Sensing* 14, no. 19: 4901.
https://doi.org/10.3390/rs14194901