# Multivariate Relationship in Big Data Collection of Ocean Observing System
## 1 Introduction  
Observing and modeling the ocean provides us with essential information necessary for preserving marine ecosystems and for the sustainable use of their resources (census UN SDG14). Marine ecosystem health is impacted by human activity; in fact, over the last few decades, the ocean has been increasingly affected by global changes caused by the exponential augmentation of human assets [1]. Observations give us fundamental information for understanding marine ecosystem dynamics, its evolution and the impact of human activities (such as ocean warming [2], sea level-rise [3], ocean deoxygenation [4], and acidification [5]). However, observations are sparse, limited in time and space coverage, and unevenly collected among variables [6]. Historically, the measurements of the marine variable were performed by specific cruises that gathered water samples and subsequently analyzed them in the laboratory. This remains, also today, the most accurate and reliable technique to collect marine data. Nevertheless, there are significant limits: the cost that this marine shipping entails together with the space and temporal under-sampling of these observations [7]. This issue significantly limits our ability to quantitatively describe key processes in the oceanic cycles of carbon, nitrogen, and oxygen as well as overall ecosystem changes. During the last twenty years, new oceanographic instruments have been introduced to gather subsurface measurements as part of the Global Ocean Observing System (GOOS) [8]. Among these new technologies are _floats_[9], namely two-meter-long robotic devices that collect marine variable data by diving in the ocean and varying their depth through buoyancy change. The main strong point of such instruments is that they do not needhuman operation and provide profiles until the batteries are discharged (usually after 4 or 5 years). However, these measurements are less precise than the ones collected by the cruises, also because sensors may decay after some years, making the relative acquired data inaccurate or indeed incorrect. Experience has shown that about 80% of the raw profile data transmitted from the floats respect fixed accuracy standards, and the remaining 20% is usually corrected within quality control procedures [10]. Standard float sensors measure temperature, salinity, and pressure. Additionally, floats can be equipped with _BCG sensors_ (that measure chlorophyll, oxygen, nitrate, pH, and optical variables, such as bbp700), but their cost rises drastically. Thus, even if floats can improve our capacity to observe the ocean, the undersampling problem remains since many sea parameters are measured less frequently. In this work, we present an improved neural network technique for the prediction of relationships between high-frequency sampled variables and low-frequency ones, trained by exploiting a large in situ data collection of marine data from cruise campaigns. The results of the neural network thus allow computing the pseudo-observations of less-sampled variables based on the most commonly sampled variables increasing the effectiveness of the current observing system infrastructures. Specifically, the model predicts nutrient concentrations and carbonate system variables (low-frequency sampled variables) starting from information such as sampling time and geolocation, temperature, salinity, and oxygen (high-frequency sampled variables). The use of large amounts of data provided by sensor instruments to discover knowledge and process information is not limited to oceanography but is also relevant in a wide variety of different fields [11; 12; 13]. The idea of approximating the nutrient concentration and the carbonate system using neural networks was put forward for the first time in [14], where the authors proposed a deterministic network trained on a global ocean data collection. Subsequently, an improvement of this technique, the _canyon-b_, was proposed by [10].