Geodesy
Seyyed Reza Ghaffari-Razin; Navid Hooshangi
Abstract
Extended Abstract
Introduction
In geodesy, three levels are considered: the physical surface of the earth on which mapping measurements are made, the ellipsoidal reference surface (geometric datum) which is the basis of mathematical calculations, the geoid physical surface (physical datum) which is ...
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Extended Abstract
Introduction
In geodesy, three levels are considered: the physical surface of the earth on which mapping measurements are made, the ellipsoidal reference surface (geometric datum) which is the basis of mathematical calculations, the geoid physical surface (physical datum) which is the basis for measuring heights. Satellite positioning systems measure the height of points relative to the ellipsoid surface. The geoid is one of the equipotential surfaces of the earth's gravity field, which approximates the mean sea level (MSL) by least squares. Geoid is very important in geodesy as a representative of the physical space or the space of observations made on the earth and also as the base level of elevations. The separation between the geoid and the geocentric reference ellipse is called geoid height (N). Although there is only one equipotential surface called geoid, various methods are used to determine it. These methods include: geometric method, geoid determination by satellite method, Gravimetric methods and geoid determination using GPS/leveling.
Materials and Methods
In this paper, the aim is to estimate the height of the local geoid using machine learning models. To do this, artificial neural network (ANN), adaptive neuro-fuzzy inference model (ANFIS), support vector regression (SVR) and general regression neural network (GRNN) models are used. The geodetic coordinates of 26 GPS stations in the north-west of Iran along with their orthometric height (H0) and normal height (h) were obtained from the national cartographic center of Iran. In all stations, the difference of orthometric height and normal height is considered as geoid height (N). Therefore, the geodetic longitude and latitude of the GPS stations are considered as the input of the machine learning models, and the corresponding geoid height was considered as the output. In order to test the results of machine learning models, two modes of 4 and 7 test stations are considered. Also, the output of the models is compared with the local geoid model IRG2016 presented by Saadat et al. for the Iranian region and also the global geoid model EGM2008.
Results and Discussion
Due to the availability of a complete set of observations of GPS stations along with orthometric height obtained from leveling in the north-west region of Iran, the study and evaluation of the models proposed in the paper has been carried out in this region. Observations of 26 GPS stations of North-west of Iran were prepared from the national cartographic center (https://www.ncc.gov.ir/). Two modes are considered for training and testing of ANN, ANFIS, SVR and GRNN models. In the first case, the number of training stations is 22 and the number of test stations is 4. But in the second case, by increasing the number of test stations to 7 stations, the error evaluation of the models has been done. It should be noted that the distribution of training and test stations is completely random.
After the training step of machine learning models and choosing the optimal structure, the test step is performed in two different modes (4 and 7 stations). At this step, the value of the geoid height in the test stations is estimated and compared with the value obtained from the difference of orthometric height and normal height as a basis. Two statistical indices of relative error in percentage and RMSE in centimeters were calculated for all models and presented in Table (1) for the first case.
Table 1. Relative error (%) of ANN, ANFIS, SVR, GRNN and IRG2016 models in the test stations considered for the first case
According to the results of Table (1) and comparing the relative error values of all models in the test stations, it shows that the ANFIS model was more accurate than other models. After ANFIS model, IRG2016 model has higher accuracy than ANN, SVR and GRNN models. It should be noted that the IRG2016 local model uses the observations of all Iranian plateau stations to model the local geoid, and therefore it is expected that this model will be more accurate in the study area than other models.
Conclusion
The evaluations show that in the case of 22 training stations and 4 test stations, the RMSE of ANN, ANFIS, SVR, GRNN and IRG2016 models in the test step are 37.32, 19.83, 49.34, 53.82 and 29.65 cm, respectively. However, in the case of 19 training stations and 7 test stations, the error values of the models are 36.63, 58.31, 39.64, 41.29 and 24.68 cm, respectively. Comparison of RMSE shows that ANN model with less number of training stations provides higher accuracy than ANFIS, SVR and GRNN models. The results of this paper show that by using ANN and ANFIS models, geoid height can be estimated and used with high accuracy locally in civil and surveying applications.
Geodesy
Seyyed Reza Ghaffari-Razin; Navid Hooshangi; Behzad Voosoghi
Abstract
Extended AbstractIntroduction The ionosphere extends from an altitude of 80 to more than 1000 km above the earth. Due to its electrical properties, this layer of the atmosphere has very important and fundamental effects on the electromagnetic waves passing through it. A parameter that can be used to ...
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Extended AbstractIntroduction The ionosphere extends from an altitude of 80 to more than 1000 km above the earth. Due to its electrical properties, this layer of the atmosphere has very important and fundamental effects on the electromagnetic waves passing through it. A parameter that can be used to study the ionosphere is the total electron content (TEC). This parameter is the sum of free electrons in a cylinder with a cross section of one square meter between the satellite and the receiver on the ground. The unit of TEC is electron per square meter (ele/m2). The TEC in the vertical direction is called VTEC. Usually, TEC is expressed in terms of TECU, which is equal to 1016 ele/m2.Different methods have been developed to model the TEC. The simplest and most practical method is to use observations of two-frequency receivers. If there is a proper station distribution, it is possible to obtain accurate TEC and model the ionosphere. The main innovation of this paper is in the long-term prediction of TEC in the period of severe solar activity, as well as the modeling of the ionosphere time series with the long-short term memory (LSTM) neural network model in the Iranian region. This model is used for the first time in Iran to model and predict the time series of the ionosphere. To check the capability of the new model in prediction of TEC in the conditions of severe solar activity, observations from 2007 to 2016 are used for training and the TEC in 2017 is predicted. All the observations are related to the Tehran GPS station, which is one of the stations of the IGS network. To evaluate the accuracy of the model presented in this paper, statistical indicators of relative error, correlation coefficient and root mean square error (RMSE) are used. Materials and MethodsLong-short term memory modelLong short-term memory (LSTM) neural network is a special type of recurrent neural network (RNN). RNN is a type of neural network that has internal memory; in other words, this network is a normal neural network that has a loop in its structure through which the output of the previous step, along with the new input, is entered into the network at each step. This loop helps the network to have the previous information along with the new information and can calculate the desired output based on this information’s. One of the problems of RNNs is the vanishing of the gradient when learning from long-term sequences, which reduces the ability to learn in the algorithm. LSTM networks are actually a type of RNNs that have had a change in their block (RNN Unit). This change makes LSTM recurrent neural networks able to manage long-term memory and not have the problem of gradient vanishing. Results and DiscussionAfter the training step, using the trained models, the VTEC value for 2017 has been estimated and compared with the VTEC values obtained from GPS as a reference observation, GIM and NeQuick models. For the test step, the parameters of correlation coefficient, RMSE and relative error were calculated and presented in table (1). It should be noted that the average of all days of 2017 is showed in this table. Also, VTEC values obtained from GPS are considered as reference observations in this table.Table 1. Statistical values of correlation coefficient, RMSE and relative error in the test step of 2017 for GRNN, LSTM, GIM and NeQuick models.The correlation coefficient value of LSTM model is higher than other models. Also, the values of RMSE and relative error of LSTM model are lower than other models. This model has the ability to show the ionosphere time series variations with an accuracy of about 87%. ConclusionAnalysis of the results of the correlation coefficient in 2017 for LSTM, GRNN, NeQuick and GIM models compared to the GPS-TEC was obtained as 0.84, 0.72, 0.77 and 0.71, respectively. The average annual relative error for these four models was calculated as 16.98%, 25.69%, 29.89% and 51.05% respectively. The results of the analysis showed that in the conditions of severe and quiet solar and geomagnetic activities, the accuracy and precision of the LSTM model is higher than the other models evaluated in this paper. The analysis of the coordinate components of Tehran station with PPP method showed that by using the model proposed in this paper, an improvement of about 5.19 to 56.23 mm can be seen in the coordinates of the station compared to other models.
Seyyed Reza Ghaffari-Razin; Navid Hooshangi
Abstract
Extended AbstractIntroductionThe Earth's atmosphere (atmosphere) is divided into concentric layers with different chemical and physical properties. To study wave propagation, two layers called the troposphere and ionosphere are considered. The troposphere is the lowest part of the Earth's atmosphere ...
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Extended AbstractIntroductionThe Earth's atmosphere (atmosphere) is divided into concentric layers with different chemical and physical properties. To study wave propagation, two layers called the troposphere and ionosphere are considered. The troposphere is the lowest part of the Earth's atmosphere and extends from the Earth's surface to about 40 kilometers above it. In this layer, wave propagation is mainly dependent on water vapor and temperature. Unlike the ionosphere, the troposphere is not a dispersive medium for GPS signals (seeber, 2003). As a result, the propagation of waves in this layer of the atmosphere does not depend on the frequency of the signals. The delay caused by the troposphere can be divided into two parts of hydrostatic delay and wet delay. The hydrostatic component of the tropospheric delay is due to the dry gases in this layer. In contrast, the wet component of tropospheric refraction is caused by water vapor (WV) in the troposphere. The study of atmospheric water vapor is important in two ways: First, short-term climate change is highly dependent on the amount of atmospheric water vapor. Water vapor has temporal and spatial variations that affect the climate of different regions. Second, long-term climate variation is reflected in the amount of water vapor. Obtaining water vapor using direct measurements and water vapor measuring devices is a difficult task. Radiosonde and radiometers are used to directly measure atmospheric water vapor, but the use of these devices will have problems and limitations, for example, the maintenance cost of these devices is expensive and also these devices do not have a suitable station cover. The best way to get information about water vapor changes indirectly is to use GPS measurements. GPS meteorological technology can provide continuous and almost instantaneous observations of the amount of water vapor around a GPS station.Estimation of precipitable water vapor (PWV) and water vapor density using voxel-based tomography method has disadvantages. The coefficient matrix of tomography method has a rank deficiency. Initial value of water vapor must be available to eliminate it. Also, the amount of WV inside each voxel is considered constant, if this parameter has many spatial and temporal variations. In this method, the number of unknowns is very high and it is computationally difficult to estimate (Haji Aghajany et al., 2020). To overcome these limitations, this paper presents the idea of using learning-based models. To do this, in this paper, 3 models of artificial neural networks (ANNs), adaptive neuro-fuzzy inference system (ANFIS) and support vector regression model (SVR) have been used. Materials and MethodsDue to the availability of a complete set of observations of GPS stations, radiosonde and meteorological stations in the north-west of Iran, the study and evaluation of the proposed models of the paper is done in this area. Observations of 23 GPS stations were prepared in 2011 for days of year 300 to 305 by the national cartographic center (NCC) of Iran. Out of 23 stations, observations of 21 stations are used to training of models and observations of the KLBR and GGSH stations are used to test the results of the models. In the first step, the observations of 21 GPS stations that are for training are processed in Bernese GPS software (Dach et al., 2007) and the total delay of the troposphere in the zenith direction (ZTD) is calculated. It should be noted that for every 15 minutes, a value for ZTD is calculated using the observations of each station. In the second step, the zenith hydrostatic delay (ZHD) is calculated. By subtracting ZHD from ZTD, zenith wet delay (ZWD) are obtained. ZWD values are converted to PWV values. The obtained PWV values are considered as the optimal output of all three models ANN, ANFIS and SVR. Also, the input observations of all three models will be the latitude and longitude values of each GPS station, day of the year and time. Results and DiscussionAfter the training and achievement of the minimum cost function value for all three models, the PWV value is estimated by the trained models and compared at the location of the radiosonde station as well as the test stations. The mean correlation coefficient for the three models ANN, ANFIS and SVR in 6 days was 0.85, 0.88 and 0.89, respectively. Also, the average RMSE of the three models in these 6 days was to 2.17, 1.90 and 1.77 mm, respectively. The results of comparing the statistical indices of correlation coefficient and RMSE of the three models at the location of the radiosonde station show that the SVR model has a higher accuracy than the other two models. The average relative error of ANN, ANFIS and SVR models in KLBR test station was 14.52%, 11.67% and 10.24%, respectively. Also, the average relative error of all three models in the GGSH test station was calculated to be 13.91%, 12.48% and 10.96%, respectively. The results obtained from the two test stations show that the relative error of the SVR model is less than the other two models in both test stations. ConclusionThe results of this paper showed that learning-based models have a very high capability and accuracy in estimating temporal and spatial variations in the amount of precipitable water vapor. Also, the analyzes showed that the SVR model is more accurate than the two models ANN and ANFIS. By estimating the exact amount of PWV, the amount of surface precipitation can be predicted. The results of this paper can be used to generate an instantaneous surface precipitation warning system if the GPS station data is available online.
