Global Mapping Function Research Articles

Retrieval of tropospheric delays from multi-GNSS observations in the polar region: effect factors and performance

Precise point positioning (PPP) technique is practical in estimating the zenith tropospheric delay (ZTD). To comprehensively study the factors affecting its accuracy in the polar region, different elevation cutoff angles for each single system and multi-system combination, different tropospheric mapping functions, tropospheric gradients and also seasonal variations are assessed. Meanwhile, European Centre for Medium-Range Weather Forecasts (ECMWF) products are adopted to validate the accuracy of PPP-derived ZTD. The results show that the root mean square (RMS) value of the estimated ZTD and ECMWF products is around 4 mm when the elevation cutoff angle is set to 10 degrees or less. From the view of system combination, it improves the ZTD accuracy in comparison with each individual system. The dual-system combination has 21.8%, 19.0% and 19.1% improvements in its ZTD accuracy compared with the Global navigation satellite system (GLONASS), Beidou navigation satellite system (BDS) and Galileo satellite navigation (GAL) systems. The four-system combination can reach 7.7% further improvement in ZTD estimation than that of the dual-system. For mapping functions, Vienna mapping function 3 (VMF3) function has the best accuracy among the four mapping functions of Niell mapping function (NMF), global mapping function, VMF1 and VMF3, while NMF does not perform as well as others. Considering the tropospheric gradients could get higher accuracy in ZTD estimation than ignoring them. The tropospheric delay estimated in winter is more accurate than that in summer and specifically the RMS value in winter is about 0.9 mm lower than that in summer. Overall, from investigation the estimation of ZTD in the polar region can be optimally handled with a multi-system and VMF3 mapping function at an elevation cutoff angle of 7°, considering the tropospheric gradients.

Refinement of global gridded ray-traced Zenith tropospheric delay over Nigeria based on local GNSS network observations

• Application of deep structured supervised neural network modelling technique. • Data derived from the local GNSS observation within the study area. • A refinement model is developed to predict ZTD parameters at user-defined points. • Improvement in the accuracy of the local refine VMF1-ZTD estimates. Recent studies on the application of Zenith Tropospheric Delay (ZTD) in meteorology and geodesy have shown improved accuracy with the use of locally estimated ZTD compared to Global ZTD. This paper focuses on the refinement of global gridded ray-traced Vienna Mapping Functions 1 (VMF1) ZTD over Nigeria, using ZTD estimates derived from local GNSS Continuously Operating Reference Stations (CORS) observations. Three (3) years of GNSS observations collected at 13 CORS located within the study area were post-processed using GNSS Analysis and Processing Software (GAPS) to derive the local GNSS-ZTD estimates. The global VMF1-ZTD were interpolated at the locations of the local GNSS-CORS. An optimal deep structured supervised Neural Network (NN) was derived by training feedforward networks using the Levenberg-Marquardt backpropagation algorithm, with spatiotemporal variables and VMF1-ZTD as inputs and the GNSS-ZTD as the target. The outputs from the NN model were assessed using internal and external data. Results from internal data evaluations indicated a robust and accurate model output with optimum network performances indicating MSE of ∼7.22 × 10 −6 m and ∼4.56 × 10 −4 m for hydrostatic and wet ZTD networks respectively. The external data evaluations performed using the International GNSS Services (IGS) Zenith Path Delay (ZPD), indicated an RMSE range of ∼0.041 m to 0.095 m for global-VMF1 and ∼0.030 m to 0.037 m for the Local Refine (LR)-VMF1. The results suggest that the application of ZTD estimates derived from local GNSS observations in the refinement of global gridded VMF1-ZTD yields an improved accuracy over Nigeria. Consequently, the LR-VMF1 ZTD estimates are recommended for improved accuracy, required for geodetic and meteorological applications in and around Nigeria :

Tone Mapping Method Based on the Least Squares Method

Tone mapping is used to compress the dynamic range of image data without distortion. To compress the dynamic range of HDR images and prevent halo artifacts, a tone mapping method is proposed based on the least squares method. Our method first uses weights for the estimation of the illumination, and the image detail layer is obtained by the Retinex model. Then, a global tone mapping function with the parameter is used to compress the dynamic range, and the parameter is obtained by fitting the function to the histogram equalization. Finally, the detail layer and the illumination layer are fused to obtain the LDR image. The experimental results show that the proposed method can efficiently restore real-world scene information while preventing halo artifacts. Therefore, tone mapping quality index and mean Weber contrast of the tone-mapped image are 8% and 12% higher than the closest competition tone mapping method.

Parallel voice conversion with limited training data using stochastic variational deep kernel learning

There are two types of voice conversion methods: statistical and deep learning-based. Although statistical methods can train with limited data, they face challenges, including spectral oversmoothing and time-domain discontinuity. On the other hand, extensively researched deep learning-based methods rely primarily on massive amounts of data, which limits their practical applicability. Given that voice conversion is an engineering problem with limited training data, it is crucial to develop techniques that can produce satisfactory results in terms of quality and similarity in the absence of a large amount of data.This paper proposes a voice conversion model based on stochastic variational deep kernel learning (SVDKL), which works with limited training data. The model allows the use of both the deep neural network’s expressive capability and the high flexibility of the Gaussian process, which is a Bayesian and non-parametric method. The model utilizes a cascade of a deep neural network and a conventional kernel as the covariance function, which enables it to estimate non-smooth and more complex functions. Furthermore, the model’s sparse variational Gaussian process solves the scalability problem of exact inference and enables the learning of a global mapping function for the entire acoustic space. One of the most important aspects of the proposed scheme is that the model parameters are trained using marginal likelihood optimization, which takes into account both data fitting and model complexity. Considering model complexity reduces the training data by increasing the robustness to overfitting. To evaluate the proposed scheme, we examined the model’s performance with as little as approximately 80 s of training data. The results indicated that our method obtains a higher mean opinion score, smaller spectral distortion, and better preference tests than the state-of-the-art limited data methods.

Inversion correction method based on the mapping function approach for correcting troposphere refraction error

Atmospheric refraction error is an important factor affecting the positioning accuracy of satellite navigation and radar. In this research, we focused on an inversion correction method based on the mapping function approach to improve the correction accuracy of atmospheric refraction error. First, we analyze the sensitivity of different coefficients on the correction accuracy in the continued fraction function of global mapping function model and conclude that coefficient a in the function is the main factor. Then, the mapping function method is reduced to an inversion correction model with undetermined parameters including coefficient a in the continued fraction function and zenith delay τ , in which the undetermined parameters involve inversion according to observation data by particle swarm optimization so as to improve the correction accuracy of atmospheric refraction error. Finally, application of the inversion method and an example indicate that the inversion correction method can correct the atmospheric refraction error at an impending moment and by using the refraction error under a partial elevation angle.

Real-Time Deep Image Retouching Based on Learnt Semantics Dependent Global Transforms.

Although artists' actions in photo retouching appear to be highly nonlinear in nature and very difficult to characterize analytically, we find that the net effects of interactively editing a mundane image to a desired appearance can be modeled, in most cases, by a parametric monotonically non-decreasing global tone mapping function in the luminance axis and by a global affine transform in the chrominance plane that are weighted by saliency. This allows us to simplify the machine learning problem of mimicking artists in photo retouching to constructing a deep artful image transform (DAIT) using convolutional neural networks (CNN). The CNN design of DAIT aims to learn the image-dependent parameters of the luminance tone mapping function and the affine chrominance transform, rather than learning the end-to-end pixel level mapping as in the mainstream methods of image restoration and enhancement. The proposed DAIT approach reduces the computation complexity of the neural network by two orders of magnitude, which also, as a side benefit, improves the robustness and generalization capability at the inference stage. The high throughput and robustness of DAIT lend itself readily to real-time video enhancement as well after a simple temporal processing. Experiments and a Turing-type test are conducted to evaluate the proposed method and its competitors.

Assessing the performance of Vienna Mapping Functions 3 for GNSS stations in Indonesia using Precise Point Positioning

Abstract. Tropospheric delay is one of the major error sources for space geodetic techniques, such as the Global Navigation Satellite Systems (GNSS). Mapping functions are used to scale the delay from zenith direction to the elevation angle of the signal. Several mapping functions have already been published, including the Global Mapping Functions (GMF) and Vienna Mapping Functions 1 (VMF1). Recently, a refined version of VMF1, VMF3, was released. The tropospheric gradients GRAD were also determined using the same data set as VMF3. This study aims to test the performance of VMF3 on GNSS observations in Indonesia, using observations from 21 stations of the permanent GNSS network in Indonesia, InaCORS. Data processing was carried out using Precise Point Positioning in Bernese GNSS Software, version 5.2 for the year 2014. Station coordinates were estimated daily, while the zenith wet delays were estimated every 30 min and tropospheric gradients were estimated hourly. A similar processing scheme was carried out using GMF and VMF1. Generally, the results from VMF3 agree very well with the results from GMF and VMF1, although small biases can be found, especially for the height component. Based on the repeatability, while there is no significant difference for the latitude and longitude, there are slight improvements for the height, particularly compared to GMF. The estimated gradients tend to fluctuate more compared to gradients from GRAD. The correlation coefficients between the estimated gradients and those from GRAD are small, with the largest being 0.65 at site CUKE.

The Performance of Different Mapping Functions and Gradient Models in the Determination of Slant Tropospheric Delay

Global navigation satellite systems (GNSSs) have become an important tool for remotely sensing water vapor in the atmosphere. In GNSS data processing, mapping functions and gradient models are needed to map the zenith tropospheric delay (ZTD) to the slant total tropospheric delay (STD) along a signal path. Therefore, it is essential to investigate the spatial–temporal performance of various mapping functions and gradient models in the determination of STD. In this study, the STDs at nine elevations were first calculated by applying the ray-tracing method to the atmospheric European Reanalysis-Interim (ERA—Interim) dataset. These STDs were then used as the reference to study the accuracy of the STDs that determined the ZTD together with mapping functions and gradient models. The performance of three mapping functions (i.e., Niell mapping function (NMF), global mapping function (GMF), and Vienna mapping function (VMF1)) and three gradient models (i.e., Chen, MacMillan, and Meindl) in six regions (the temperate zone, Qinghai–Tibet Plateau, Equator, Sahara Desert, Amazon Rainforest, and North Pole) in determining slant tropospheric delay was investigated in this study. The results indicate that the three mapping functions have relatively similar performance above a 15° elevation, but below a 15° elevation, VMF1 clearly performed better than the GMF and NMF. The results also show that, if no gradient model is included, the root-mean-square (RMS) of the STD is smaller than 2 mm above the 30° elevation and smaller than 9 mm above the 15° elevation but shows a significant increase below the 15° elevation. For example, in the temperate zone, the RMS increases from approximately 35 mm at the 10° elevation to approximately 160 mm at the 3° elevation. The inclusion of gradient models can significantly improve the accuracy of STDs by 50%. All three gradient models performed similarly at all elevations and in all regions. The bending effect was also investigated, and the results indicate that the tropospheric delay caused by the bending effect is normally below 13 mm above a 15° elevation, but this delay increases dramatically from approximately 40 mm at a 10° elevation to approximately 200 mm at a 5° elevation, and even reaches 500–700 mm at a 3° elevation in most studied regions.

Adaptive Contrast Enhancement for Infrared Images Based on the Neighborhood Conditional Histogram

In this paper, an adaptive contrast enhancement method based on the neighborhood conditional histogram is proposed to improve the visual quality of thermal infrared images. Existing block-based local contrast enhancement methods usually suffer from the over-enhancement of smooth regions or the loss of some details. To address these drawbacks, we first introduce a neighborhood conditional histogram to adaptively enhance the contrast and avoid the over-enhancement caused by the original histogram. Then the clip-redistributed histogram of the contrast-limited adaptive histogram equalization (CLAHE) is replaced by the neighborhood conditional histogram. In addition, the local mapping function of each sub-block is updated based on the global mapping function to further eliminate the block artifacts. Lastly, the optimized local contrast enhancement process, which combines both global and local enhanced results is employed to obtain the desired enhanced result. Experiments are conducted to evaluate the performance of the proposed method and the other five methods are introduced as a comparison. Qualitative and quantitative evaluation results demonstrate that the proposed method outperforms the other block-based methods on local contrast enhancement, visual quality improvement, and noise suppression.

GNSS PPP with different troposphere models during severe weather conditions

Global navigation satellite systems (GNSS)-derived zenith wet delays must be estimated precisely for monitoring weather variations and rain passages in the troposphere. We processed a set of International GNSS Service (IGS) stations within the area affected by the central European Flooding 2013 and assessed the performance of post-processed precise point positioning (PPP) during severe weather by applying different troposphere models: the Vienna Mapping Function (VMF1) together with the European Centre for Medium-Range Weather Forecasts grids, the global mapping function with the Global Pressure and Temperature 2, the Niell mapping function with the University of New Brunswick (UNB), and the VMF1 with the UNB/VMF1 from the National Centers for Environmental Prediction numerical weather model (NWM) data. Wet delay estimates from each PPP session have been verified through the IGS final troposphere products, local surface measurements and double-difference (DD) GNSS solutions performed at the same sites. All the PPP solutions agree well with the IGS. The mean residuals are all below 2.0 mm, and the PPP VMF1 performs better with RMS of 4.0 mm. The PPP solutions applying an NWM offer better agreement with the PPP solutions using real surface measurements to model the troposphere. Both PPP and DD VMF1 solutions agree with RMS of 5.4 mm, which allowed PPP to offer a strong alternative to post-processed DD solutions, even during severe weathers. With respect to the daily ITRF08 coordinate solutions, the gridded VMF1-based PPP height repeatability is better for most stations before and after the observations are corrected for atmospheric non-tidal loading effect.

Monitoring Zenithal Total Delays over the three different climatic zones from IGS GPS final products: A comparison between the use of the VMF1 and GMF mapping functions

The International GNSS Service (IGS) final products (ephemeris and clocks-correction) have made the GNSS an indispensable low-cost tool for scientific research, for example sub-daily atmospheric water vapor monitoring. In this study, we investigate if there is a systematic difference coming from the choice between the Vienna Mapping Function 1 (VMF1) and the Global Mapping Function (GMF) for the modeling of Zenith Total Delay (ZTD) estimates, as well as the Integrated Precipitable Water Vapor (IPWV) estimates that are deduced from them. As ZTD estimates cannot be fully separated from coordinate estimates, we also investigated the coordinate repeatability between subsequent measurements. For this purpose, we monitored twelve GNSS stations on a global scale, for each of the three climatic zones (polar, mid-latitudes and tropical), with four stations on each zone. We used an automated processing based on the Bernese GNSS Software Version 5.2 by applying the Precise Point Positioning (PPP) approach, L3 Ionosphere-free linear combination, 7 ̊ cutoff elevation angle and 2 h sampling. We noticed an excellent agreement with the ZTD estimates and coordinate repeatability for all the stations w.r.t to CODE (the Center for Orbit Determination in Europe) and USNO (US Naval Observatory) products, except for the Antarctic station (Davis) which shows systematic biases for the GMF related results. As a final step, we investigated the effect of using two mapping functions (VMF1 and GMF) to estimate the IPWV, w.r.t the IPWV estimates provided by the Integrated Global Radiosonde Archive (IGRA). The GPS-derived IPWV estimates are very close to the radiosonde-derived IPWV estimates, except for one station in the tropics (Tahiti).

Structural-Correlated Self-Examples Based Superresolution of Single Remote Sensing Image

Image superresolution methods are of great importance to image analysis and interpretation and have been intensively studied and widely applied. The main research works on single-image superresolution are how to construct the training image database and how to learn the mapping relationship between low- and high-resolution images. Considering only a single image, a novel super-resolution method for self-examples learning without depending on any external training images is proposed in this paper. The training self-examples are extracted from the gradually degraded versions of the testing image and their corresponding interpolated counterparts to build internal high- and low-resolution training databases. Inspired by the concept of “coarse-to-fine,” the upscaling process is performed gradually as well. The algorithm includes two steps during each upscaling procedure. For each low-resolution patch, the first step is to find structural-correlated patches by sparse representation throughout the training database to learn global linear mapping function between low- and high-resolution image patches without any assumption on the data, and the second step takes the advantage of sparse representation as a local constraint on super-resolution result. At each upscaling procedure, iterative back projection is applied to guarantee the consistency of the estimated image. Moreover, the internal training database will be updated according to the newly generated upscaled image. Experiments show that the proposed algorithm can achieve good performance on peak signal-to-noise ratio and structural similarity index and produce excellent visual effects compared with other super-resolution methods.

Content Aware Image Pre-Compensation.

The goal of image pre-compensation is to process an image such that after being convolved with a known kernel, will appear close to the sharp reference image. In a practical setting, the pre-compensated image has significantly higher dynamic range than the latent image. As a result, some form of tone mapping is needed. In this paper, we show how global tone mapping functions affect contrast and ringing in image pre-compensation. We further enhance contrast and reduce ringing by considering the visual saliency. Specifically, we prioritize contrast preservation in salient regions while tolerating more blurriness elsewhere. For quantitative analysis, we design new metrics to measure the contrast of an image with ringing. Specifically, we set out to find its "equivalent ringing-free" image that matches its intensity histogram and uses its contrast as the measure. We illustrate our approach on projector defocus compensation and visual acuity enhancement. Compared with the state-of-the-art, our approach significantly improves the contrast. We also perform user studies to demonstrate that our method can effectively improve the viewing experience for users with impaired vision.

Assessment of tropospheric delay mapping function models in Egypt: Using PTD database model

For space geodetic measurements, estimates of tropospheric delays are highly correlated with site coordinates and receiver clock biases. Thus, it is important to use the most accurate models for the tropospheric delay to reduce errors in the estimates of the other parameters. Both the zenith delay value and mapping function should be assigned correctly to reduce such errors. Several mapping function models can treat the troposphere slant delay. The recent models were not evaluated for the Egyptian local climate conditions. An assessment of these models is needed to choose the most suitable one.The goal of this paper is to test the quality of global mapping function which provides high consistency with precise troposphere delay (PTD) mapping functions. The PTD model is derived from radiosonde data using ray tracing, which consider in this paper as true value.The PTD mapping functions were compared, with three recent total mapping functions model and another three separate dry and wet mapping function model. The results of the research indicate that models are very close up to zenith angle 80°. Saastamoinen and 1/cos z model are behind accuracy. Niell model is better than VMF model. The model of Black and Eisner is a good model. The results also indicate that the geometric range error has insignificant effect on slant delay and the fluctuation of azimuth anti-symmetric is about 1%.

Atmospheric opacity estimation based on IWV derived from GNSS observations for VLBI applications

Thermal emission of atmospheric water vapor has a great influence on the calibration of radio astronomical observations at millimeter wavelengths. The phenomenon of an atmospheric water vapor emits noise signal and attenuates astronomical emission. At 22 GHz, integrated water vapor (IWV) obtained from global navigation satellite systems (GNSS) is strictly related to atmospheric opacity (tau_{0}), which is a crucial parameter for data calibration. Therefore, providing highly precise and accurate IWV from GNSS measurements may be an alternative for microwave radiometers. Whereas it is not possible to estimate IWV directly from GNSS measurements, its value is strictly correlated with the zenith wet delay (ZWD) that is estimated together with the coordinates during the GNSS positioning. In this study, differential and Precise Point Positioning methods for ZWD estimation are tested using two different tropospheric mapping functions: Vienna mapping function (VMF) and global mapping function (GMF). After positioning, the IWV conversion is performed using meteorological parameters derived from a meteorological station located near a GNSS site. Analyses for a 3-month period from June 1 to August 30, 2016, were conducted. Based on these, we obtained a very high correlation between IWV and tau_{0} as measured by the Torun 32 m radio telescope, which amounts about 0.95, for both PPP and differential solutions. Thus, techniques can be successfully used to estimate IWV and calculate tau_{0}. However, the linear regression coefficients depend on the used positioning method.

Histogram-Based Color Transfer for Image Stitching

Color inconsistency often exists between the images to be stitched and will reduce the visual quality of the stitching results. Color transfer plays an important role in image stitching. This kind of technique can produce corrected images which are color consistent. This paper presents a color transfer approach via histogram specification and global mapping. The proposed algorithm can make images share the same color style and obtain color consistency. There are four main steps in this algorithm. Firstly, overlapping regions between a reference image and a test image are obtained. Secondly, an exact histogram specification is conducted for the overlapping region in the test image using the histogram of the overlapping region in the reference image. Thirdly, a global mapping function is obtained by minimizing color differences with an iterative method. Lastly, the global mapping function is applied to the whole test image for producing a color-corrected image. Both the synthetic dataset and real dataset are tested. The experiments demonstrate that the proposed algorithm outperforms the compared methods both quantitatively and qualitatively.

A Novel Tool for the Determination of Tropopause Heights by Using GNSS Radio Occultation Data

The tropopause is a transitional layer between the troposphere and the stratosphere. The exchange of chemical constituents of the atmosphere (namely masses of air, water vapor, trace gases etc.) and energy between the troposphere and the stratosphere occurs through this layer. We suppose that just exchanges that are taking place at the tropopause heights are strongly influenced by the Global Change forcing. For this reason it is particularly urgent to accumulate temporal data the most accurate possible and with a certain continuity series to understand comprehensively what is happening to our climate. It is well known that Radio Occultation technique applied using Global Navigations Satellite Systems (GNSS-RO) is a powerful tool to detect the tropopause heights. It can be done working on the level 2 data provided by GNSS-RO payload: i.e. atmospheric profiles of pressure and temperature. We propose to measure tropopause using GNSS-RO level 1 data; i.e. the bending angles (BA) of the GNSS signal through the atmosphere. We fit the BA profiles applying in the integral relationship of BA as refractivity profile of background the Hopfield dry model of atmosphere which depends on the fourth degree of the height above the Earth. Through the layers in which tropopause is contained, the residuals between the background model and the observed BA have an anomalous trend. The residuals in this zone form anomalous non-gaussian bumps that we have exploited just to determine the relevant parameters of the tropopause. Such bumps are due to the wrong theoretical assumption made by Hopfield for the re-construction of the dry refractivity that the temperature lapse rate of the atmosphere is constant. But we know that the definition of tropopause according the World Meteorological Organization (WMO) is just the height where a sudden change of the temperature lapse rate usually occurs. Thus in the present work we have determined tropopause heights with new algorithms which exploit the bumps occurring along the BA profiles achieved by GNSS-RO. We have used the huge amount of data provided by several space missions devoted to GNSS-RO (namely COSMIC, METOP, etc.) for tuning the algorithms, performed a validation and provided a robust statistical soundness. The same GNSS-RO observations are helpful also to reconstruct the Mapping Function commonly applied in geodetic applications. Global mapping functions built with GNSS-RO and their evolution in time can be an interesting parameter helpful for climate investigations as well.

Determination of Zenith Tropospheric Delay and Precipitable Water Vapor using GPS Technology

Abstract In order to be able to be process GPS data, the GPS signal it has to pass the entire terrestrial atmosphere – both neutral atmosphere and ionosphere – which may cause an alteration of the GPS receiver to perform, resulting in large errors in the final position estimate. The dual frequency GPS receivers are affected by the influence of the atmosphere, especially by the troposphere. To estimate the delay caused by the troposphere and to obtain a high degree of accuracy, mapping function has to be used in the estimation process, which opens the door for remote sensing the atmosphere. Because the wet component from the hydrostatic and non-hydrostatic part, is only 10% of the total neutral atmospheric part, its influence is considerate significant in the application of high-precision positioning in which GPS receivers are employed. The article presents the determination of the precipitable water vapor using relative using four permanent GPS stations. The estimation were done by using the Global Mapping Function - GMF and the apriori pressure and temperature from the GPT2 model.

Alignment for comprehensive two-dimensional gas chromatography with dual secondary columns and detectors.

In each sample run, comprehensive two-dimensional gas chromatography with dual secondary columns and detectors (GC × 2GC) provides complementary information in two chromatograms generated by its two detectors. For example, a flame ionization detector (FID) produces data that is especially effective for quantification and a mass spectrometer (MS) produces data that is especially useful for chemical-structure elucidation and compound identification. The greater information capacity of two detectors is most useful for difficult analyses, such as metabolomics, but using the joint information offered by the two complex two-dimensional chromatograms requires data fusion. In the case that the second columns are equivalent but flow conditions vary (e.g., related to the operative pressure of their different detectors), data fusion can be accomplished by aligning the chromatographic data and/or chromatographic features such as peaks and retention-time windows. Chromatographic alignment requires a mapping from the retention times of one chromatogram to the retention times of the other chromatogram. This paper considers general issues and experimental performance for global two-dimensional mapping functions to align pairs of GC × 2GC chromatograms. Experimental results for GC × 2GC with FID and MS for metabolomic analyses of human urine samples suggest that low-degree polynomial mapping functions out-perform affine transformation (as measured by root-mean-square residuals for matched peaks) and achieve performance near a lower-bound benchmark of inherent variability. Third-degree polynomials slightly out-performed second-degree polynomials in these results, but second-degree polynomials performed nearly as well and may be preferred for parametric and computational simplicity as well as robustness.

Evaluation of Symmetric Neutral-Atmosphere Mapping Functions Using Ray-Tracing Through Radiosonde Observations

Abstract The aim of this paper is to compare the validity of six recent symmetric mapping functions. The mapping function models the elevation angle dependence of the tropospheric delay. Niell Mapping Function (NMF), Vienna Mapping Function (VMF1), University of New Brunswick- VMF1 (UNB-VMF1) mapping functions, Global Mapping Function (GMF) and Global Pressure and Temperature (GPT2)/GMF are evaluated by using ray tracing through 25 radiosonde stations covering different climatic regions in one year. The ray-traced measurements are regarded as “ground truth”. The ray-tracing approach is performed for diverse elevation angle starting at 5° to 15°. The results for both hydrostatic and non-hydrostatic components of mapping functions support the efficiency of online-mapping functions. The latitudinal dependence of standard deviation for 5° is also demonstrated. Although all the tested mapping functions can provide satisfactory results when used for elevation angles above 15°, for high precision geodetic measurements, it is highly recommended that the online-mapping functions (UNBs and VMF1) be used.The results suggest that UNB models, like VMF have strengths and weaknesses and do not stand out as being consistently better or worse than the VMF1. The GPT2/GMF provided better accuracy than GMF and NMF. Since all of them do not require site specific data; therefore GPT2/GMF can be useful as regards its ease of use.