**1. Introduction**

Information collected from weather station sensors is currently employed in many economy fields, e.g., agriculture, transport [1], and tourism. Based on the received information, it is possible to take rational actions to implement the specific activity in particular areas. This applies particularly to systems classified as critical national infrastructure. Many publications describe and analyse the acquired sensor data and their characteristic properties and estimate missing data in the original meteorological information. Some studies also present research on the quality of information obtained from these sensors. However, no approach takes into account uncertainty estimation of the information quality. When applied to the process of estimating the quality of information obtained from meteorological station sensors, uncertainty modelling allows one to increase the forecasted data reliability.

Analysing the state of knowledge in the field discussed in this article but also delving into the achievements of the scientific community, the following areas can be distinguished:


**Citation:** Stawowy, M.; Olchowik, W.; Rosi ´nski, A.; D ˛abrowski, T. The Analysis and Modelling of the Quality of Information Acquired from Weather Station Sensors. *RemoteSens.* **2021**, *13*, 693. https://doi.org/ 10.3390/rs13040693

Academic Editor: Stefano Mattoccia

Received: 22 January 2021 Accepted: 11 February 2021 Published: 14 February 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

The listed main research areas directly related to the subject of this article are analysed in detail below.

The study described in [5] describes issues related to the adoption of wireless sensor networks to assess air quality. The authors have rightly noticed that, having data from individual sensors on temperature, humidity, carbon monoxide (CO), and carbon dioxide (CO2), it is possible to estimate air quality and decide about the occurrence of an emergency in the warning system. For this purpose, they implemented the classification tree algorithm with regard to entropy and information enhancement. This approach has a practical application, but it does not consider some factors influencing the quality of the information received from individual sensors.

Additionally, in the area of transport (especially in autonomous vehicles and on motorways), the quality of information obtained from meteorological sensors is crucial [6]. Study in this area is presented in monograph [7]. Owing to this, it is possible to detect dangerous weather events and inform drivers about them immediately. Similar studies of stationary weather stations applied in intelligent transport systems (ITS) are presented in [8].

A similar approach in the analysis of the obtained data from meteorological stations was adopted by the authors in the study [9]. They applied decision tree algorithms, analysing precipitation and minimum and maximum temperatures separately. Thanks to the application of algorithms devised by the authors, it is possible to identify flawed sequences contained in meteorological sensors. Similar studies regarding air quality classification using specific algorithms and a decision tree are presented in publication [5]. Inquiry in this area concerns not only land meteorological stations but also marine ones [10].

It is likely to estimate the correctness of meteorological data by comparing them with data from neighbouring meteorological stations. Then, it is possible to determine the consistency of data relating to a given meteorological phenomenon in a specific area [11].

The study described in [12] presents studies aimed at determining the forecast using a hybrid computing network. This approach enables forecasting weather conditions with an insufficient number of meteorological stations.

The next research area, highlighted by the authors of this article, contains publications on the estimation of missing data in meteorological information. Scientifically interesting considerations are presented in the study [13]. It proposes to employ a method consisting in finding time intervals with similar rainfall patterns. Thanks to their analysis, it is possible to interpolate the missing data with better quality compared to the methods used so far.

A study [14] also describes work in this research area. The team of authors proposed models enabling temperature interpolation in a geographical system for agricultural purposes. The conducted analyses resulted in finding that the application of multi-line regression is most beneficial.

Authors adopt various approaches to assess the quality of weather information. One of them is the quality of the data stored in big data. As data from many weather stations equipped with many different sensors are most often (except in sparsely populated areas) available, it is possible to pre-process them in order to eliminate errors. This approach was presented in publication [15]. By pre-processing the data, a weather forecasting system that used data of better quality could be designed.

In order to improve the quality of weather information, a data fusion solution is also employed. In this way, it is possible to combine data from different sensors. This increases the reliability of the weather information. This approach was described in the article [16]. The authors analysed the applied solutions in the area of intelligent transport systems. They considered that, in the fusion of data from sensors, the most important is the application of: fuzzy technique, ranging technique, integrated technique, and clustering technique. Despite considering these techniques and analysing their advantages, these lack the possibility to model uncertainty in estimating information quality. Similar considerations in this area in the field of transport are presented in the study [17]. This is a very important issue in the aspect of current research and design of autonomous vehicles. It

also seems essential to use modelling of the uncertainty of estimating information quality, because it is possible to increase the level of safety of the means of transport.

Methods of variational assimilation of measurement data from various observational systems, including imagery, can also be distinguished among scientific studies in weather information analysis. In publication [18], the authors proposed using a proprietary data assimilation algorithm, which they presented in detail in a mathematical notation. However, they did not take into account the information quality from individual sources.

Some scientific studies propose the use of neural networks for the analysis of weather information [19]. The study in article [20] posits the application of deep neural networks (DNN) with the object of estimating the amount of precipitation on the basis of radar, microwave, and infrared data. The conducted simulations confirm the validity of using DNN to improve the forecast of the amount of precipitation. However, it seems that, by applying uncertainty modelling of estimating information quality, it is possible to increase the accuracy of the forecasted data. Therefore, the authors of this article conducted scientific scrutiny in this direction.

The investigation of the status of the issue allows one to conclude that most of the studies concern the analysis of the correctness of the obtained data from sensors and weather forecasting with the application of various algorithms. To the best of our knowledge, no publications considered the quality of the information received from a meteorological station at the time of conducting the studies. Studies in this area together with the results are presented by the authors in this article.

#### **2. Uncertainty Modelling Applied to Estimate the Quality of Information Obtained from Sensors of a Meteorological Station**

The information quality estimation method uses the calculations of the certainty factor of the hypothesis. The applied CF modelling is based on dependent and independent connections. Such modelling makes it possible to estimate the impact of selected quality dimensions and their factors on the quality of information and to identify reliable measurements from several different data sources (e.g., data from different types of sensors).
