Global Navigation Satellite System (GNSS) is a space-based radio Navigation and Positioning System, which can provide any location, time and speed information on the earth’s surface or near-earth space users with all-weather three-dimensional coordinates. Due to the atmospheric refraction, the tropospheric delay error is generated and is an important error source in GNSS positioning when GNSS signals are propagated in the atmosphere. Water vapor is a major component of the troposphere, but it changes quickly as the time. Water vapor has a uneven spatial distribution and its variation scale is larger than the temperature and the wind. Water vapor plays an important role in the atmospheric movement. The signal transmission of the global satellite navigation system (GNSS) is caused by the water vapor transmission. On the other hand, the estimated ZWD error from GNSS can be converted to precipitable water vapor (PWV), while the conversion process of ZWD-PWV requires a parameter, i.e. the weighted average temperature (Tm). ZWD and Tm are two parameters that are closely related to water vapor. Because of the characteristics of water vapor variability and randomness, studying the global ZWD and Tm are challenging in GNSS research compared to the regional ZWD and Tm. In this paper, ZWD and Tm on the global scale are studied. The main research contents and conclusions are as follows:
(1)Based on some previous research, a ZWD model (NN-ZWD model) is constructed by using the meteorological parameters, coordinate parameters and time parameters at the station. Site with 130 sites around the globe as the modeling of VMF1 troposphere products as modeling data and we use the sounding data of 163 sites as the test data. But the results show that the NN-ZWD are not better than the traditional Saastamoinen model or the Hopfield model.
(2)The ZWD model based on neural network was refined. In order to improve the NN-ZWD model, the author takes into account the water vapor vertical variation characteristics and the introduction of moisture gradient factor (λ) as model variables, will provide the moisture gradient factor GPT2w model (λ-GPT2w) as approximation values. On the basis of this, the ZWD model (NN-ZWD-R model) based on neural network is proposed to discuss the accuracy of nn-zwd-r model worldwide. The results show that nn-zwd-r model is about 16.9% higher than NN-ZWD model. In addition, NN-ZWD-R model has a good applicability: it can maintain good accuracy at different latitudes, different heights and different seasons.
(3)The relationship between Tm and the site meteorological parameters was also studied. Tm is related to the site meteorological parameters Tm is strongly related to the temperature (TS) of the station. Tm is strongly related to the water vapor pressure (eS) of the station, and the atmospheric pressure (PS) of the station is almost irrelevant. The correlation characteristics of Tm-TS and Tm-eS show a certain geographical distribution pattern: their correlation increases roughly with the increase of latitude.
(4)The variation characteristics of Tm time series in time domain were studied. Firstly, the periodic characteristics of spectrum analysis of Tm were studied by using the lomb-scargle periodogram. The annual cycle characteristics of Tm are found in 10 sample sites in different climatic regions around the world, which may be characterized by the semi-annual cycle, and the other cycle characteristics are not obvious. Again, the periodic terms, trend items and random items were used construct the Tm time series model. In tropical regions, the seasonal variation of Tm is often irregular; annul seasonal variation can be a major cyclical feature of Tm. In non-tropical regions, the seasonal variation of Tm shows certain rules: the change of seasons is mainly influenced by the characteristics of the year. In the southern hemisphere, the initial phase of the phase is about January and the annual phase of the northern hemisphere is generally in July. The maximum and minimum values of the Tm time series model are usually in summer and winter respectively. Globally, Tm has a long-term trend of around 0.22 K/decade growth, and the Tm trends are the most visible in high latitudes in the northern hemisphere. The high model error of Tm season model are found in mid-latitude and high latitudes, while the maximum errors of Tm time series model are in the polar region.
(5)Two multi-parameter Tm model based on the neural network were proposed. According to the research content (3) and (4), the author combined of the relationship between Tm and meteorological parameters of the station and Tm time series characteristics, and then the neural network model for the first time as a modeling tool, design for more than two globally applicable parameter Tm model. Thus, Two feedforward neural network (FFNN) models (the NN-1 and the NN-2) were established by a combination of the Tm seasonal variations and its relationship with surface meteorological elements. The NN-1 is used with measurements of both surface temperature TS and surface vapor pressure eS, while the NN-2 is only used with measurements of only TS. Globally, the NN-1 model and NN-2 model have the same accuracy, and their accuracies are higher than that of 5 traditional models, such as GPT2w, BTm, GTm, GTm-I and PTm-I. Under the same conditions, the accuracy of the NN-1 model is about 11.1 % higher than that of the PTm-I model. The accuracy of NN-2 model is about 17.9 % higher than that of GTm-I model. The NN-1 model and the NN-2 model have good applicability: in the long term, different seasons, different heights and different latitudes can maintain high precision.