Inversion of the Full-Depth Temperature Profile Based on Few Depth-Fixed Temperatures

Round 1

Reviewer 1 Report

This paper investigated Inversion method of the full-depth temperature profile based on few depth-fixed temperatures.

 It shows that the temperatures at the depths which are the three extreme  points of the first two empirical orthogonal function (EOF) modes, contain the largest amount of  information. Based on the back propagation (BP) neural network, a model for reconstructing the  full-depth temperature profile using few temperatures at fixed depth is established. The method seems sound, but to obtain the temperatures at fixed depth still need on-site observations. The author should add discussion on the  practical use of this method. I recommend to Reconsider after major revision.

Author Response

Response to Reviewer 1 Comments

Point 1: This paper investigated Inversion method of the full-depth temperature profile based on few depth-fixed temperatures. It shows that the temperatures at the depths which are the three extreme points of the first two empirical orthogonal function (EOF) modes, contain the largest amount of information. Based on the back propagation (BP) neural network, a model for reconstructing the full-depth temperature profile using few temperatures at fixed depth is established. The method seems sound, but to obtain the temperatures at fixed depth still need on-site observations. The author should add discussion on the practical use of this method. I recommend to Reconsider after major revision.

Response 1: As the reviewer said, the nonlinearity and uncertainties of the marine vehicle model, and environmental disturbances exert challenges on the depth tracking design in the practical application. However, with the development of marine mobile platforms, AUVs and other underwater vehicles can obtain depth-fixed temperatures in real-time through depth control. It is shown that the AUVs can achieve depth tracking with steady-state error in decimeters or even centimeters. And the temperature profile variation within the error range can be ignored. So, the temperatures at fixed depth are simulated by the temperatures of the thermistor chain at this depth.

   Therefore, this paper investigated inversion method of the full-depth temperature profile based on few depth-fixed temperatures. Relevant papers are as follows,

   In the article “A hierarchical disturbance rejection depth tracking control of underactuated AUV with experimental verification”, Liu et al. proposed a hierarchical disturbance rejection depth tracking control scheme for the underactuated AUVs, which transforms the depth control problem into the pitch tracking in the kinematics layer. The effectiveness and remarkable performance of the proposed control scheme under different experimental cases are verified using a small underactuated AUV prototype named ARMs-AUV 1.0. Experimental results show that the accuracy of depth control can reach the centimeter level, as shown in Fig.1.

Fig.1 Comparative control performances in different experimental cases

In the article “Depth control for an over-actuated, hover-capable autonomous underwater vehicle with experimental verification”, Kantapon et al. implement the hover-style operation of AUVs by continuously operating the two vertical thrusters to counter a net positive buoyancy. Even when a change in the net buoyancy suddenly occurs, the AUV depth tracking performance can recover within 20s and eventually converges to the desired depth with steady-state error in centimeters, as shown in Fig.2.

Fig.2 Results show control performance when the system is subjected to a variation in the net buoyancy

Reference:

[1] Liu, C.; Xiang, X. B.; Yang, L. C; Li, J. J; Yang, S. L. A hierarchical disturbance rejection depth tracking control of underactuated AUV with experimental verification. Ocean Engineering. 2022, 264, 112458. doi:10.1016/j.oceaneng.2022.112458.

[2] Tanakitkorn, K.; Wilson, P. A.; Turnock, S.R.; Phillips, A. B. Depth control for an over-actuated, hover-capable autonomous underwater vehicle with experimental verification. Mechatronics. 2017, 41, 67-81. doi: 10.1016/j.mechatronics.2016.11.006.

Author Response File: Author Response.docx

Reviewer 2 Report

In 'Inversion of the full-depth temperature profile based on few depth-fixed temperatures', the authors propose a new idea of reconstructing the temperature field using limited depth-fixed temperatures in the South China Sea. By analyzing the physical meaning of the first two EOF modes and intrinsic statistical relationship of the EOF coefficients, the authors explain the reason about the choice of measurement depths. This paper also uses the BP neural network to establish a model for reconstructing the full-depth temperature profile only using the temperatures at three chosen depths. The method proposed in this paper can make the inversion of temperature field with high precision by limited measurements. The method is new, and I think it’s publishable in this journal. For this paper, I have some comments listing below.

1. The second EOF mode in Figure 4 has four extreme points, but the authors only select two. Why?

2. How do the authors obtain the background field coefficient and background field mode mentioned in Equation (9)? Please describe this clearly in the paper.

3. The unit of the horizontal axis in Figure 6b is unmarked.

4. The temperature profiles selected in the training set are relatively stable. Please explain why the temperature profiles with drastic fluctuations in the test set can be accurately predicted.

5. In Figure 10, the authors invert the full-depth temperature profile with the temperature at 10 m. What is the reason for choosing the measurement temperature at 10 m?

6. Figure 12 shows that even if the temperature data at the depth of the first two EOF extreme points are input, the temperature prediction error is still a little large at the depth of 30-50 m. Please explain the reason.

Author Response

Response to Reviewer 2 Comments

Point 1: The second EOF mode in Figure 4 has four extreme points, but the authors only select two. Why?

Response 1: The second EOF mode has four extreme points. According to the physical meaning of the first two EOFs, it is considered that the two extreme points near z₁ represent the upper and lower bounds of the thermocline, and their corresponding depths are z₂=50m and z₃=63m.

Point 2: How do the authors obtain the background field coefficient and background field mode mentioned in Equation (9)? Please describe this clearly in the paper.

Response 2: An orthogonal representation of the temperature profile considering the background field variation is proposed in this paper. Different from the traditional EOF method, this method directly performs SVD on the temperature matrix, so the component with the most significant contribution represents the background field. The component decomposes to be the background field coefficient and background field mode.

Point 3: The unit of the horizontal axis in Figure 6b is unmarked.

Response 3: The unit of temperature gradient in Figure 6 (b) is °C/m, and the horizontal axis in Figure 6(b) has been marked in the paper.

Point 4: The temperature profiles selected in the training set are relatively stable. Please explain why the temperature profiles with drastic fluctuations in the test set can be accurately predicted.

Response 4: The completeness of the training set is directly related to the training model’s performance. Therefore, two types of experimental data are selected for the training set. The first type of data are relatively stable temperature profiles observed at 11:00-16:00 on September 13, which can reflect the general trend of seawater temperature changes in the experimental area. The others are the temperature profiles with drastic fluctuation observed at 19:30-24:00 on September 13, which can reflect transient characteristics of temperature profiles. The training set with good completeness can generate the training model with specific generalization abilities, so the temperature profiles with drastic fluctuations in the test set can be accurately predicted.

Point 5: In Figure 10, the authors invert the full-depth temperature profile with the temperature at 10 m. What is the reason for choosing the measurement temperature at 10 m?

Response 5: The temperature at 10m is taken because it is the shallowest depth of the thermistor chain. And this temperature can be considered as the sea surface temperature, which could be easily obtained by a surface velocimeter. The surface velocimeter is usually fixedly installed on autonomous navigation platforms such as ships and submarines to obtain sea surface data. If the measured data of the surface velocimeter is available, the surface temperature is replaced by the actual measured value. Since the sea surface temperature is the most easily obtained depth-fixed temperature data, the temperature profile of the test set was firstly reconstructed using only the sea surface temperature.

Point 6: Figure 12 shows that even if the temperature data at the depth of the first two EOF extreme points are input, the temperature prediction error is still a little large at the depth of 30-50 m. Please explain the reason.

Response 6: The introduction mentions that the temperature field can be expressed as a random process consisting of the large-scale background and small-scale dynamic changes. The large-scale background changes mainly depend on the seasonal background temperature field. And the small-scale dynamic changes usually refer to a spatially localized contribution from linear and non-linear internal waves. The background field has strong seasonal regularity, so its characteristics are easily captured. However, the small-scale dynamic processes, such as internal waves, change dramatically in the thermocline, especially the solitary internal wave has a certain randomness, so it is difficult to predict. Therefore, even if the temperature data at the depth of the first two EOF extreme points are input as a limiting condition, it can only reduce the sea temperature prediction error in the thermocline, but it cannot eliminate this error. Therefore, the temperature prediction error is still a little significant at a depth of 30-50 m.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report