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.
Hamid Bayat Barooni; Mojtaba Ezam; Abbasali Aliakbri Bidokhti; Masoud Torabi Azad
Abstract
Extended AbstractIntroductionThe Caspian Seaclassed as the world’s largest lake, lies between Europe and South Western Asia (between 45.43°to 54.20°longitude east and 36.33°to 47.07°latitude north). The Caspian Sea level has changed widely over time. These changes have occurred ...
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Extended AbstractIntroductionThe Caspian Seaclassed as the world’s largest lake, lies between Europe and South Western Asia (between 45.43°to 54.20°longitude east and 36.33°to 47.07°latitude north). The Caspian Sea level has changed widely over time. These changes have occurred gradually and incrementally leading to landward and seaward migration of the coastline. Therefore, it is very important to study and predict futurechanges of the Caspian Seacoastline. Today, experts in atmospheric and marine physics from all around the world consider the Caspian Sea as a natural dynamic model of oscillatory processes in watersurface.High annual rate of water level changeshas made oscillatory processes of this lake different from those of oceans. With the advent of satellite altimetry in 1973, highly accuratemonitoring of sea level has been made possible. The present study seeks to investigate the trend of dynamic topography changes in the Caspian Sea and determine the effects of changes in thesea level on the southern coastline. MethodologyVarious sets of satellite data have been used in the present study. Long-term average ofglobal sea level data was obtained from MSS_CNES.CLS15. Covering a period of 20 years (1993 to 2012),these datasets are produced based on information received from different satellitealtimeters. Mean sea level is calculated foreach point of the network created atthe Caspian Sea (with a distance of 0.25°). The correlation between altimetry data and sea level changes is calculated using gravity changes. Investigating these changes leads us to equipotentialgeomagnetic surfaces called geoid. Geoid is an equilibrium surface of the Earth’s gravitational field showingapproximately the average leveloffree water. Mean sea level does not coincide with geoid and theirdifference at any given point is called absolute dynamic topography. In this study, GOCE model was used to calculate geoid value at every point of the network created at 1′distance from the Caspian Sea. Aviso Altimetry dataset was used to obtain sea level anomaly data. Mean sea level was obtained by adding dynamic topography mean to geoid height.In order to obtain average dynamic sea topography,MDT values were calculated for all the points created in the Caspian Sea. Afterwards, sea level anomaly was added to the mean dynamic sea topography to obtain absolute dynamic topography. Daily SLA data of the Caspian Sea were extracted with a resolution of 0.25° from AVISO and CNES.CLS15 SLA ultrasound satellites and interpolated at the specific location created on the Caspian Seanetwork with a resolutionof 1′.Aabsolute dynamic topography were calculated on a daily basis. These calculations were repeated for a 20 year period (7305 days) from 1993 to 2012 using MATLAB and in this way, a complete database including the Caspian Sea surface topographic datawas obtained for this period. ResultFollowing the calculation of the mean ADT data obtained fromall over the Caspian Sea, time series of daily Sea Level Fluctuations were extracted. These time series indicated that despite the positive trend of the Caspian Sea water level changes in both 1993-1995 and 2000-2005 periods, the overall trend of water level changes over the 20-year period is negative. Moreover, examining sea level changes over this 20-year period shows thatthe highest altitude (-25.914m) has occurred on June 1st, 1995, while the lowest altitude (-27.20) has occurred on November 26th, 2012. In addition, March 20th, 2002 and June 29th, 2005 have experienced two abrupt changes of -26.843m and -26.26m in the time series. In this time series, an upward trend is observed until June 1st, 1995, while a decreasing trend of 93 cmis observed from March 20th, 2002 over a period of approximately 7 years. Between March 20th, 2002 to June 29th, 2005 (a period of approximately 3 years), we observe a decreasing trend of 61 cm. Over a 7-year period (until late 2012), we also observe a 97cm decreasing trend. Altimetry data received from three stations located in the Caspian Sea are used to verify the results obtained from the above mentioned method. Examination of these values and comparing them with the values obtained from the method used in the study confirms the resulting trend. In orderto investigate the shoreline changes caused by changesin the Caspian Sea water level,the southern shoreline of the Sea is mapped based on the obtained trend.Days with the highest and lowest sea level over the 20-year study period were extracted from satellite images. Mapping and overlayingthe coastlines based on the information related to these two time series, changes have been observedthroughthe Caspian coastlines. However, these changes are more significant in the South Eastern Gorgan Bay (Miankale) due to the smaller slope of the South Eastern Caspian Sea compared to other areas of the Sea. ConclusionInvestigating changes of the Caspian Sea level shows anegativetrend of changes, with a -1.287 m difference between thehighest and lowest altitudes. Of course, the trend has not always been negative over these years. For an instance, a positive trend was observed from 1993 to1995 and from 2000 to 2005. Results indicate that the Caspian Sea dynamics of water level fluctuations changes rapidly and long-term prediction of the Caspian Sea water level cannot be very accurate. However, it can be concluded that the Caspian water level changes will continue its decreasing trend in the future. This negative trend of sea level changes has resulted in the seaward migration of the Caspian coastline, which has began in 1995 and still is present today. This has resulted in drying up of more than 12850 hectares of the GorganGulf.
Mehdi Najafi Alamdari; Masoud Torabi Azad; Ali Hakimi
Abstract
Extended Abstract
Introduction
The Mean Dynamic Topography (MDT) of the seas is a quantity which comes from subtracting the Geoid Height (GH) from the Mean Sea Surface (MSS) at every point on the sea. The direction of geostrophic currents is obtained through the calculation of the MDT slope relative ...
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Extended Abstract
Introduction
The Mean Dynamic Topography (MDT) of the seas is a quantity which comes from subtracting the Geoid Height (GH) from the Mean Sea Surface (MSS) at every point on the sea. The direction of geostrophic currents is obtained through the calculation of the MDT slope relative to the Geoid. In this research, a series of GOCE geopotential coefficients resulted from the 4 year collection of GOCE observations was used to estimate the reference geoid height in the Persian Gulf, the Oman Sea and the Indian Ocean, i.e., in the area of interest. Two MDT models data were available at the time of performing this research: Denmark Technical University’s model, named ‘Mean Dynamic Topography of Denmark Technical University 2010’ (MDT_DTU_2010) which has been available on a geographical grid of 2 arc minutes spacing (Knudsen & Andersen, 2010). This model is based on the mean sea surface topography model MSS_DTU_2010 and the 2 month of GOCE geopotential data for the Geoid as the reference surface. The second model is the Mean Dynamic Topography Centre National d'Etudes Spatiales collecte localisation satellites 2009 (MDT_CNES_CLS09) with 15 minutes resolution (Rio et al, 2011). This model contains the east-west and north-south geostrophic current components with itself as well. It is based on MSS_CLS01 (Hernandez and Schaeffer, 2001) and 4.5 years of GRACE geopotential data used for the reference geoid.
Materials and Methods
In this research a new Mean Dynamic Topography (MDT) model with the name of MDT_IAU_TN_2014 is presented. Also, the surface permanent current vectors in a grid with 2 minutes resolutions is computed in the Persian Gulf, the Oman Sea and the north of Indian Ocean. This MDT is formed by a Mean Sea Surface (MSS) model computed from 6 altimetry satellites data (Topex/Poseidon, Jason 1 and 2, ERS 1 and 2 and Geosat Follow-On) and GOCE satellite data with 21 and 4 years ranges in 1992-2013 are calculated. The first step for the Mean Sea Surface (MSS) computation is to calculate the mean of Sea Surface Heights (SSH) along the repeated (in time) sub-tracks of altimetry satellites over the years available in the area of interest. The mean value of SSHs over time in a same track is then called Mean Height (MH). The Basic Radar Altimetry Toolbox (BRAT) version 3.1.0 was used for the MH computation. The correction term includes the tidal periodic variations, physical earth corrections such as troposphere, ionosphere, and sea state biases. All of these corrections are considered from the satellite handbooks T/P (AVISO/ALTIMETRY, 1996), J1 (AVISO and PODAAC USER HANDBOOK, 2012), J2 (OSTM/Jason-2 Products Handbook, 2001), ERS (RA/ATSR products - User Manual, 2001), GFO (GEOSAT Follow-On GDR User's Handbook, 2002). Among altimetry satellites, T/P (J1 and J2) has the highest orbit and longest data sets so it has been selected as a reference for corrections.
Results & Discussion
To homogenize the spectral of MSS and the Geoid, a truncated Gaussian filter with 1.386 degree radius has been used. MDT results have been compared with two global model and have 0.033 and 0.051 RMS of differences in order. Among altimetry satellites used in this research, J2 and GFO satellites have the ability to measure shallow waters. Hence, the data provided by these satellites in shallow waters, i.e. Persian Gulf are valuable. MHS differences between E1 and T/P are larger than the MHS of other satellites, because there are differences between the two missions, i.e., there are 8 km distances between E1 sub-tracks at equator but long repeatability period of 35 days of data acquisition time and T/P sub-tracks spacing are 315 km at equator and short repeatability period of 9.9 days. Also, the orbit elevations are different: T/P at altitude of 1336 km and E1 at altitude of 785 km. Inclusion of E1 data in the MSS_IAU_TN_2014 solution would globally decrease the RMS difference of the solution relative to the MSS_CNES_CLS_2011 model from 0.4 m (without E1 data) to 0.1 m. This improvement by the E1 data is probably due to the higher resolution of the data in the region of interest.
Conclusion
Changing the filtering radius of 1.386 degree down to lower degrees until 1 degree would increase the MDT_IAU_TN_2014 differences (relative to the MDT_DTU_2010) and MDT_CNES_CLS09 from 0.033m and 0.051m RMS up to larger values. At the 1.386 degree, the differences are minimum. For filtering radiuses of more than 1.386 degree the MDT surface would become unreasonably much smoother and the RMS difference would increase. Geostrophic and Ekman velocity currents using 22 years data of surface wind has been calculated. Total currents of the released model in this research have been compared with OSCAR in-situ data and have 0.047 and 0.031 meter RMS of differences in North-South and East-West current components. The total currents from MDT_IAU_TN-2014 model vary between 0 to 0.61 m/s in the north Indian ocean region. The comparison shows that all three models show almost the same range of variations in the region of interest. SLA an In-Situ data could be used to make the MDT_IAU_TN_2014 independent from any other models. The lack of In-Situ data in the region of interest forced MDT_IAU_TN_2014 to use MDT_DTU_2010 to cover filtered parts. Also using other gravity models with higher Spherical harmonic coefficients degree and orders such as EIGEN-6c and EGM08, would make filtering not needed in the dynamic modeling.
