In this paper, the standard deviation of the spheroid up to degree and order 20 in Iran, when using various satellite-derived geopotential models, has been studied. For the comparison, the standard deviations of potential coefficients in various geopotential models are examined. According to the results, the ElGEM-GL04C geopotential model up to degree and order 20 showed small standard deviation over the territory of Iran.

Introduction Components of verticaldeflection, i. e., North-South component and East-West component, are used for accurate determination of geoid or quasigeoid. Moreover, vertical deflection components area useful source for determination of variations in subsurface density and geophysical interpretations. Generally, there are two definitions for verticaldeflection. According to Helmert definition, vertical deflection at any given pointis the angle between the actualgravity vector (actual plumb line) and a line that is normal to the reference ellipsoid(a straight line perpendicular to the surface of reference ellipsoid). Another definition of vertical deflection is proposed by Molodensky. According this definition, vertical deflection at any given point is the angle between actualgravity vector and normal gravity vector (normal plumb line). Some relations have been introduced to convert Molodensky vertical deflection to Helmert vertical deflection. Helmert vertical deflection is estimated using astrogeodetic observations (combination of astronomical and geodetic observations). Presently, global geopotential models (GGMs) have been expanded to the degree of2190, which is equivalenttoabout 5-min spatial resolution. Vertical deflectionat any point on the Earth can be calculated using the GGM. The resulting vertical deflection is consistent with Molodensky definition. Unfortunately, accuracy of GGMs is not sufficient for estimation of verticaldeflection. In other words, since GGMs are expanded up to a limited degree due to their resolution, omission error(or truncation error) occurs in computation of the earth’ s various gravity field functionals, such as the geoidal height and verticaldeflection. Combining GGM with a digital terrain model (DTM) is a method used to reduce omission error. It should be noted that DTM has a higher spatial resolution as compared to GGM. In this method, the omitted signals of GGM can be modeled using residual terrain model (RTM) derived from subtracting high resolution DTM from a reference smooth surface. The reference smooth surface is obtained from eitherapplying average operator to DTM or expanding global topography into spherical harmonics. Fortunately, DTMs with spatial resolution of 3seconds or more, and reference smooth surface based on 2190 degree spherical harmonics are publicly available. The present study seeks to assess vertical deflectionderived from a combination of GGM and DTM in Iran. Previously, Jekeli(1999) has studied EGM96 geopotential model with the aim of computingvertical deflection in the USA. Hirt(2010) and Hirt et al. (2010a) have assessed vertical deflection in Europe and the Alps using a combination of EGM2008 and RTM models. In Iran, GO_CONS_GCF_2_TIM_R4, a GOCE-only model, and EGM2008 geopotential model have been used toobtain vertical deflection and the results have been evaluated byKiamehr and Chavoshi-Nezhad(2014). Materials & Methods To implement the present study, a EGM2008 model with a spatial resolution of about 5-min is selected asGGM and a SRTM model with 3-sec spatial resolution is considered as DTM. To obtain RTM, DTM2006 model based on2190 degree spherical harmonicsis selected as the reference smooth surface. To compute the residual topography effect, prism method was used in an ellipsoidalmulti-cylindrical equal-area map projection system. First, we compute vertical deflectionusing EGM2008 model. It is also calculated using a combination of EGM2008 model and RTM(EGM2008/RTM method). In the next step, vertical deflection derived from the first method (EGM2008 model) and the second one (combination of EGM2008 model and RTM) are compared with vertical deflectionderived from astrogeodetic observations in 10 available Laplace stations in Iran. Results & Discussion Results indicate that there is a 1. 2sec difference between North-South component of vertical deflection (i. e. ) obtained from EGM2008 model and astrogeodetic observations. With RTM, this will reach 1 sec, which shows a 15% improvement. Moreover, there is a5. 7secdifference between East-West component of vertical deflection () obtained from EGM2008 model and astrogeodetic observations, while this value will reach 5. 6sec using RTM. Improvement in East-West component () is1. 4%, which is smaller than the improvement of North-South component (). Based on the computations, we found that values of and in the Laplace stations canreach 17sec (RMS=7sec) and 15sec (RMS=8sec), respectively. Therefore, it is concluded that the relative error ofNorth-South component ()computation using EGM2008/RTM method is about 6% and the relative error ofEast-West component ()computation is about 37%. Conclusion The present research has studied the RTM effect on the improvement of GGM used for the determination of vertical deflectionin Iran. To performthe study, EGM2008 model with around 5-min spatial resolution was selected as GGM. RTM is also derived from subtracting the DTM2006 model (based on2190 degree spherical harmonics)from the 3-sec spatial resolutionSRTM model. Numerical findings indicate that a combination of RTM and GGM can improve the results of vertical deflectioncomputation, as compared to the results obtained from GGM-only approach. The improvement in North-South component of vertical deflection () is about15%and East-West component of the vertical deflection () undergoes about 1. 4% improvement. In general, EGM2008 model and its combination with RTM have been more successful in the computation of component as compared to computationin the geographical region of Iran. There is no clear explanation for this difference, but it can be due to errors in theastronomical or geodetic observations oflongitude in Laplace stations.

Topographic masses above the geoid are considered as a major obstacle in geoid determination by using Global Gravitational Models (GGMs). GGMs provide the possibility of the Earth's potential field modeling as the expansion of the external-type series of spherical harmonics. Applying the external expansion to obtain disturbing potential on the geoid within the topographic masses will cause a bias called „ topographic bias‟ . This study deals with calculating geoidal height using Earth Gravitational Model 2008 (EGM08). In order to do so, two methods of Direct Analytical Continuation one and Rapp's Indirect one are utilized. The Analytical Continuation Approach is based on using EGM08 within the topographic masses and applying topographic bias. Alternatively, Rapp‟ s Approach is based on calculating height anomaly and its downward continuation on the geoid. The success of these two methods to geoid simulation on 490 GPS-Levelling stations in mountainous region of Colorado in the USA were evaluated. The results are an indicator of the fact that two methods are compatible with each other with centimetric accuracy compared to GPS-Levelling points. Also, it suggests an improvement in the relative and absolute accuracy of the geoidal height resulting from EGM08 about 60% in both methods. The numerical investigation revealed that taking advantage of height harmonic models instead of point actual height can bring a bias in the matter of a few centimeters on the geoid. Moreover, the absolute accuracy of Rapp's Approach is higher than Analytical Continuation Approach in geoid determination in comparison GPS-Levelling points.

Global geopotential models (GGMs) are mainly used in the remove-compute-restore (RCR) technique applied to gravity field modeling such as geoid determination and height datum unification. The increase in the number and quality of gravity data has led the developers of GGMs to produce models with higher resolution and accuracy. Basically, the long-wavelength coefficients of the gravity field are computed based on satellite data, while the medium- and short-wavelength coefficients are calculated based on terrestrial (land and sea) data. One of the main challenges regarding the evaluation of high-degree GGMs is to compute the associated Legendre functions of the first kind based on the usual recursive formulas. Since most computational softwares use the double-precision format by default, an important question is whether this level of precision is sufficient to numerically evaluate the associated Legendre functions of the first kind? To answer this question, the computation of the associated Legendre functions of the first kind in different degrees and latitudes is studied based on MATLAB software, which uses the double-precision format by default. From the numerical results, we find that the calculation of associated Legendre functions of the first kind up to degree of 2190 (the highest degree of existing GGMs), does not have sufficient accuracy at latitudes between 56°20׳ and 78°33׳, where the most critical state occurs at the latitude 60°. We also find that the accuracy of the calculation of associated Legendre functions at the latitude 60° (the most critical state) significantly decreases for the degrees higher than 2029. These results imply that the usual computational softwares based on the double-precision format are not suitable for calculating the associated Legendre functions in all degrees and latitudes. This is due to the fact that if we consider the associated Legendre functions of the first kind in the form of a matrix with the dimensions corresponding to the degree and order of the functions, as the degree increases, the numbers on the main diagonal approach to the number 10-308 and thus they are considered zero. In the recursive method, the entries below the main diagonal are calculated from the entries on the main diagonal. Since the entries below the main diagonal become very large as they move away from the main diameter, any error in computing the main diagonal entries leads to a large error in computing the entries below the main diagonal. In this paper, we also study the challenges of using the associated Legendre functions of the first kind in the production of gravity field functionals based on a GGM, utilizing MATLAB software. The results show that the gravity potential computation up to degree of 2190 suffers from very large computational errors at latitudes between 57°32׳ and 60°13׳. We observe that the safe degrees for the gravity potential computation in all latitudes are degrees less than 2065. The critical latitudes and degrees for the gravity calculation are somewhat different. The results indicate that the gravity computation up to degree of 2190 leads to very large errors at latitudes between 57°41׳ and 60°13׳. In addition, the maximum degree of expansion that grants sufficient accuracy for the calculation of gravity for all latitudes is estimated to be 2071. Therefore, since the usual computational software based on the double-precision format is not suitable for evaluating the current high-degree GGMs, in this research, a new proposal based on the use of the “long double-precision” format is presented and evaluated. Based on our evaluations, the use of the long double-precision format throughout the computational procedure provides sufficient accuracy to compute the gravity field functionals based on the current high-degree GGMs.

Trend variations in large-scale atmospheric systems like subtropical high pressure play a significant role in climate change. In this study, to achieve the objectives, mid-level atmospheric geopotential altitude data were employed based on the European Center Database of Atmospheric Medium-Term Forecasting. The data that have a spatial resolution of 1*1 degree of curveand are collected on a daily average. The statistical period of the research ranges from 1980 to 2018 for Iran and included 155 cells. Mann-Kendall trend test was used to explore the geopotential altitude trend on Iran. The results showed that the atmospheric geopotential altitude on Iran in June, July, and August has an increasing (positive) trend which is at the significant level of 1.96. The decreasing trend of geopotential altitude in the eastern and southeastern regions of Iran is remrkable. Moreover, in all the investigated months, Iranian atmosphere altitude in the central, western and northwestern regions had an upward trend, which is generally influenced by the high-pressure subtropical level. These changes cause abnormalities in climatic patterns of the regions. The study also showed that continuing subtropical pressure stack on top of ever-increasing trend in the region is significant.

In this paper the influence of solid tide on the Earth gravity field is considered. In this consideration the Earth can be regarded as either an elastic or inelastic body. Each one of these elastic and inelastic bodies has two main tidal components, Frequency dependent and trequency independent components. In this article how to compute the effect of these components in the Earth's gravity field is presented. In this investigation, an attempt is made to find out whether the Earth should be regarded as an elastic or inelastic body in practical applications. Computations show equivalent effects on the gravity field due to the elastic and inelastic Earth model. The effect of the Frequency dependent component of solid tide due to the elastic and inelastic Earth is much smaller than the Frequency independent components. It depends on time and tidal constituents and it should be considered in precise applications. Comparisons between the solid tides due to the elastic and inelastic Earth model show that the inelastic Earth is contracted at poles about 3mm and expanded at equator about 2.5mm more than the elastic case.

Iran country because of great spreading with a view to geographical longitude and latitude‚ existence the contortion of unevenness configuration and locating in exposed of air masses attacking has special circumstances in terms of temporal. The overall structure influenced by latitude‚ altitude and air masses. So that with changing each of these factors the temperature will change. In other words the general condition of temperature is a function of latitude and altitude and other factors such as aquatic area and land forms has a role in creating temperature structure that is referred as local factors...

Forecasting temperature as one of the important climatic parameters plays a major role in climate change research. Therefore, in this study, the surface data of the average daily temperature of selected stations in the Caspian Sea (Anzali, Gorgan, Rasht, Babolsar and Ramsar) and the data of Geopotential height of level of 500 hPa whose data were extracted from the website NCEP/DOE under the US National Oceanic and Atmospheric Organization in hours 00: 00, 03: 00, 06: 00, 09: 00, 12: 00, 15: 00, 18: 00, and 21: 00 in the Zulu. During the period from 01/01/1979 to 01/01/2011 AD, four observation days per day were extracted from the NCEP / DOE website for the whole of the northern hemisphere, and then the correlation between the average daily temperature and geopotential data of the 500 hPa equilibrium was calculated throughout the northern hemisphere. The results of the correlation showed that the US with 28, the northern China with 30, Africa with 53 and at last, Japan with 69 pixels have the most pixels. In general, in the northern hemisphere, there are 180 points whose correlation with the temperature of selected station is very high. Also, the forecasting model of stations shows that for each geopotential meter increase, the average daily temperatures of the stations of Anzali, Gorgan, Rasht, Babolsar, and Ramsar increases as 0.1, 1.1, 0.1, 0.1, and 0.1 respectively.