# Symmetrical and Asymmetrical Rectifications Employed for Deeper Ocean Extrapolations of In Situ CTD Data and Subsequent Sound Speed Profiles

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The Proposed Extrapolation Methodology

- The Chen and Millero Equation (1977) [16];

#### 2.2. Sound Speed Profile (SSP) Computations

#### 2.2.1. SSP Computations Using the Chen and Millero Equation (1977)

#### 2.2.2. SSP Computations Using the UNESCO Algorithm

#### 2.2.3. SSP Computations Using the Del Grosso Equation (1974)

^{2}. The range of validity for temperature is 0 to 30$\mathbb{C}$, whereas that for salinity is 30 to 40 parts per thousand, and that for pressure is 0 to 1000 kg/cm

^{2}, where 100 kPa = 1.019716 kg/cm

^{2}.

## 3. Results

#### 3.1. Extrapolations and Their Subsequent Rectifications for 4000 m Floats

#### 3.2. Extrapolations and Their Subsequent Rectifications for 6000 m Floats

#### 3.3. Experimentation in the Pacific Ocean for Spatiotemporal Coverage and Asymmetric Rectification

#### 3.3.1. Spatiotemporal Coverage through Extrapolations

#### 3.3.2. Symmetric and Asymmetric SSP Rectifications

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The in situ measured and extrapolated salinities and temperature both by first-order and by improved second-order extrapolation (

**a**,

**b**) for the salinities where a difference of ~0.2 psu was reduced to a negligible level after improved second-order rectification and, similarly, (

**c**,

**d**) for temperatures where a difference of ~1.5 $\mathbb{C}$ due to basic first-order extrapolation was reduced to an infinitesimal amount by second-order extrapolation.

**Figure 2.**The in situ measured and extrapolated salinities and temperature both by first-order and by improved second-order extrapolation (

**a**,

**b**) for the salinities, where a difference of ~0.3 psu due to basic first order was reduced to a negligible amount after improved second-order rectification and, similarly, (

**c**,

**d**) for temperatures, where a difference of ~1.3 $\mathbb{C}$ due to basic first-order extrapolation was reduced to an infinitesimal amount by second-order extrapolation.

**Figure 3.**The in situ measured and extrapolated salinities and temperature both by first-order and by improved second-order extrapolation (

**a**,

**b**) for the salinities, where a difference of ~0.3 psu due to basic first order was reduced to a negligible amount by improved second-order rectification and, similarly, (

**c**,

**d**) for temperatures, where a difference of ~1.3 $\mathbb{C}$ due to basic first-order extrapolation was reduced to an infinitesimal amount by second-order extrapolation.

**Figure 4.**The sound speed profiles (SSPs) from the various equations computed via first-order extrapolation are illustrated (

**a**–

**c**). Similarly, the improved second-order extrapolation using the Del Grosso equation is exhibited (

**d**), where the difference was reduced from ~7.5 m/s to almost negligible.

**Figure 5.**The SSPs from the various equations computed via first-order extrapolation are illustrated (

**a**–

**c**). Similarly, the improved second order-extrapolation using the Del Grosso equation is exhibited (

**d**), where a difference of ~8.5 m/s was reduced to be almost negligible.

**Figure 6.**The SSPs from the various equations computed via first-order extrapolation are illustrated (

**a**–

**c**). Similarly, the improved second-order extrapolation using the Del Grosso equation is exhibited (

**d**), where the improved extrapolation is almost identical to the real in situ measured value, unlike the basic first-order extrapolation.

**Figure 7.**The in situ measured and extrapolated salinities and temperature both by first-order and by improved second-order extrapolation (

**a**,

**b**) for the salinities, where a difference of ~0.1 psu due to basic first-order extrapolation was reduced to a negligible amount after improved second-order rectification and, similarly, (

**c**,

**d**) for temperatures, where a difference of ~4 $\mathbb{C}$ due to basic first-order extrapolation was reduced to an infinitesimal amount by second-order extrapolation at 6000 m depth. However, a deviation was observed at 3000–5000 m depth with a maximum of ~2 °C.

**Figure 8.**The in situ measured and extrapolated salinities and temperature both by first-order and by improved second-order extrapolation (

**a**,

**b**) for the salinities, where a difference of ~0.6 psu due to basic first-order extrapolation was comparatively improved to ~0.15 psu at 6000 m depth, though apparent deviations persist for 2000–5200 m with a max deviation of ~0.22 psu. Similarly, (

**c**,

**d**) for temperatures, a difference of ~1 $\mathbb{C}$ due to basic first-order extrapolation was reduced to be negligible all along the depth just below 2000 m from where the extrapolation initiated.

**Figure 9.**The SSPs from the various equations computed via first-order extrapolation are illustrated (

**a**–

**c**). Similarly, the improved second-order extrapolation using the Del Grosso equation is exhibited (

**d**), where a difference of ~16 m/s was reduced to be almost negligible at 6000 m depth while exhibiting fewer deviations at depths of 3300–5500 m.

**Figure 10.**The SSPs from the various equations computed via first-order extrapolation are illustrated (

**a**–

**c**). Similarly, the improved second-order extrapolation using the Del Grosso equation is exhibited (

**d**), where a difference of ~6 m/s was reduced to an almost negligible amount.

**Figure 11.**The temperatures and SSPs for varying cycles of WMO5905738 are illustrated (

**a**,

**c**), along with (

**e**) in situ, basic first-order extrapolated, and improved second-order extrapolated temperatures, with discrepancies of ~6 $\mathbb{C}$ rectified to ~2 $\mathbb{C}$ values. Similarly, the SSPs improved from ~9 m/s max to ~3 m/s, as illustrated in (

**b**,

**d**, and

**f**).

**Figure 12.**The SSPs from symmetric extrapolations were rectified by asymmetric extrapolation, resulting in an improvement of ~2 m/s to become almost identical (

**a**,

**b**). Similarly, an improvement was observed from ~7 m/s to negligible difference (

**c**,

**d**). Finally, a difference of ~5 m/s was improved to ~1 m/s, as illustrated in (

**e**,

**f**), respectively.

**Figure 13.**For the transmission loss computation, accordingly, (

**a**) illustrates the measured, basic first-order extrapolated, and improved second-order extrapolated SSPs. Similarly, the transmission loss based on in situ measured values is exhibited in (

**b**). The transmission loss after employing the first-order extrapolation is presented in (

**c**). Finally, the transmission loss with improved second-order extrapolation is illustrated in (

**d**).

Float Identity | Cycle Number | Date | Lat, Long. | Location |
---|---|---|---|---|

WMO2902510 | 24 | 2 March 2014 | 30.447 N, 146.004 E | Pacific Ocean |

WMO2902971 | 08 | 12 May 2016 | 29.566 N, 146.364 E | Pacific Ocean |

WMO1902074 | 08 | 11 April 2016 | 28.998 S, 52.16 E | Indian Ocean |

Float Identity | Cycle Number | Date | Lat, Long. | Location |
---|---|---|---|---|

WMO4902322 | 15 | 17 June 2017 | 24.8972 N, 58.4255 E | Atlantic Ocean |

WMO5902521 | 71 | 5 Jane 2019 | 38.7563 S, 128.6227 E | Indian Ocean |

Float Identity | Cycle | Lat, Long. | Date | Time |
---|---|---|---|---|

WMO5905738 | 10 | 22.9324 N, 158.5839 W | 31 May 2018 | 05:43:00 |

WMO5905738 | 11 | 22.9638 N, 158.705 W | 5 June 2018 | 02:14:00 |

WMO5905738 | 18 | 22.9121 N, 158.715 W | 9 July 2018 | 14:39:00 |

Float Identity | Cycle | Lat, Long. | Date | Time |
---|---|---|---|---|

WMO5905738 | 20 | 22.6443 N, 158.6656 W | 19 July 2018 | 11:52:11 |

WMO5905739 | 20 | 22.8836 N, 158.7888 W | 3 July 2018 | 04:03:52 |

WMO5902521 | 20 | 12.0588 N, 154.0620 W | 19 September 2018 | 07:54:23 |

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**MDPI and ACS Style**

Iqbal, K.; Zhang, M.; Piao, S.
Symmetrical and Asymmetrical Rectifications Employed for Deeper Ocean Extrapolations of In Situ CTD Data and Subsequent Sound Speed Profiles. *Symmetry* **2020**, *12*, 1455.
https://doi.org/10.3390/sym12091455

**AMA Style**

Iqbal K, Zhang M, Piao S.
Symmetrical and Asymmetrical Rectifications Employed for Deeper Ocean Extrapolations of In Situ CTD Data and Subsequent Sound Speed Profiles. *Symmetry*. 2020; 12(9):1455.
https://doi.org/10.3390/sym12091455

**Chicago/Turabian Style**

Iqbal, Kashif, Minghui Zhang, and Shengchun Piao.
2020. "Symmetrical and Asymmetrical Rectifications Employed for Deeper Ocean Extrapolations of In Situ CTD Data and Subsequent Sound Speed Profiles" *Symmetry* 12, no. 9: 1455.
https://doi.org/10.3390/sym12091455