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In situ observation is one of the most direct and efficient ways to understand the ocean, but it is usually limited in terms of spatial and temporal coverage. The determination of optimal sampling strategies that effectively utilize available resources to maximize the information content of the collected ocean data is becoming an open problem. The historical sea surface temperature (SST) dataset contains the spatial variability information of SST, and this prior knowledge can be used to optimize the configuration of sampling points. Here, a configuration method of sampling points based on the variability of SST is studied. Firstly, in order to get the spatial variability of SST in the ocean field to be sampled, the historical SST data of the field is analyzed. Then,

SST is a key input to atmospheric and oceanic forecasting and prediction systems [

The common sampling strategy is the

Recent advances in the field of compressive sensing (CS) [

Due to the large impact of wind and ocean current, the distribution of SST varies spatially. For example, the East China Sea is the main area of the Kuroshio in the midlatitudes and it has obvious hydrological characteristics. As the areas with high spatial variability always contain the maximum information of the sampled field, intensive observations or multiple-samplings are necessary in these areas. How to configure the sampling points is the key question in in situ observation with resource constrains. Here, we propose an optimal configuration method of sampling points based on variability of SST. This paper is organized as follows. Section

Our goal is to design a sampling method to take more measurements in areas with high SST spatial variability while taking less measurements in areas with low SST spatial variability. How to choose the most suitable sampling points to gather maximum information is the fundamental task in SST sampling. The historical SST data of the sampled field contains rich prior knowledge which can then be used to optimize the configuration of sampling points. Sampling rate calculation criteria based on the results analyzed are designed. In order to make the configuration of sampling points more accurate, the

Optimal configuration method of sampling points.

The ocean is an extremely complex dynamical system with strong spatial-temporal variability. Geostatistics is a great tool for analyzing the spatial-temporal variability of natural phenomenon. The semivariogram function is used to quantitatively assess the spatial variability of a physical variable in geostatistics. Here, the physical variable is SST value. Assuming that the SST value at a specific location

Figure

The monthly mean SST field in February 2009 in the East China Sea.

Monthly mean SST field

Sub-SST field

The spatial variability of the SST is analyzed using geostatistics in each subsampled field. As shown in Figure

Four directions’ semivariogram functions of Figure

Semivariogram function (N-S)

Semivariogram function (NE-WS)

Semivariogram function (E-W)

Semivariogram function (NW-SE)

One assumes that the average sampling rate is

As shown in Figure

In Section

Even though

Taking the SST data points as the data objects, SST data objects in a subsampled field are divided into

Configuration of sampling points.

The aim of optimal configuration of sampling points is to collect the richest information with limited resources (time or energy). In order to seek the sampling points with the richest information, all clusters in one subsampled field are placed with the same number of sampling points. Then the cluster with larger change in the magnitude of gradient is sampled with higher sampling rate while the cluster with smaller spatial change is sampled with lower sampling rate. So the sampling points number of each cluster in one subsampled field is

As the new sampling method does not require to sample at the specific locations, sampling points are randomly placed in each cluster. Figure

The SST field can be reconstructed based on the sampled data and the reconstruction error can be used to evaluate the sampling performance of the sampling method. CS is a new sampling theory which is often used to construct a data field. In CS, a

The reconstruction of SST field is a blind sparse reconstruction question. There are many algorithms which can reconstruct the signal without the prior knowledge of sparse, such as BP, SP, SAMP, ASMP, and StOMP. ASMP not only inherits the backtracking refinement that attaches to CoSaMP/SP but also does not require the sparse as an input parameter. Therefore, ASMP algorithm [

Here, we take one subsampled field as a reconstructing unit. One assumes that the vector of SST data measured is

In order to test the performance of the new sampling strategy, the eastern part of the East China Sea (22°N

Experimental area.

Experimental area

Experimental area division

Reconstruction error is used to evaluate the sampling performance of the new sampling method. For comparison, we also conducted a traditional random sampling method. The number of sampling points for both the new sampling method and random sampling method is 928. And the average sampling rate is about 22%. The reason to take this sampling rate is that reconstruction error in most of the months with sampling rate 22% has reduced significantly. The measured SST data of the two methods are reconstructed by ASMP algorithm with an input threshold of 1.3.

For the random sampling method (RS), all subsampled fields use the same sampling rate (22%). The sampling points are randomly placed in each subsampled field. For the optimal configuration method of sampling points (OS). First, the sampling rate of each subsampled field and the number of sampling points are obtained by the distribution characteristic analysis. Then each subsampled field is divided into 3 clusters. And the number of sampling points in each cluster is the same and sampling points are placed randomly in each cluster. The sampling points placement of the two methods is shown in Figure

The distribution of sampling points.

RS sampling points

OS sampling points

Table

The sampling number distribution of OS and RS.

Field number | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14) | (15) | (16) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

RS | 58 | 58 | 58 | 58 | 58 | 58 | 58 | 58 | 58 | 58 | 58 | 58 | 58 | 58 | 58 | 58 |

OS | 44 | 55 | 52 | 43 | 56 | 58 | 55 | 50 | 64 | 78 | 55 | 57 | 81 | 55 | 70 | 55 |

It can be seen from Table

Figure

Reconstruction error in the sampled field from February 2008 to January 2009.

Figure

Difference of the reconstruction error in the sampled field from February 2008 to January 2009.

February 2008

March 2008

April 2008

May 2008

June 2008

July 2008

August 2008

September 2008

October 2008

November 2008

December 2008

January 2009

Figure

OS and RS reconstructed SST field in February, May, and August.

RC_HS (February 2008)

RC_RS (February 2008)

RC_OS (February 2008)

RC_HS (May 2008)

RC_RS (May 2008)

RC_OS (May 2008)

RC_HS (August 2008)

RC_RS (August 2008)

RC_OS (August 2008)

RC_HS (November 2008)

RC_RS (November 2008)

RC_OS (November 2008)

How to choose the most suitable sampling points to gather maximum information is the main task in ocean in situ observation. A new optimal configuration method of sampling points based on the variability of SST is proposed in this paper. The variability of SST is examined by geostatistics and the

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was funded by the National Natural Science Foundation of China (no. 41676088), the National Key Research and Development Project of China (2017YFC1404100, 2017YFC1404102), the Fundamental Research Funds for the Central Universities (HEUCF041705), the Foundation of Key Laboratory of Marine Environmental Information Technology, and the Natural Science Foundation of Heilongjiang Province (no. QC2017067).