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Applying principal components to analyze the distribution of model biases in GNSS tropospheric tomography for a case study in Northwestern Iran

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Abstract

Although GNSS tropospheric tomography is a powerful tool in meteorology, available validation data limit its accuracy and precision analysis. Moreover, it is customary to accept the validation results as a measure of the model performance. This study shows that this is only possible when the sensitivity of the model elements to the input perturbations is the same. We propose the principal component analysis for studying the sensitivity of a tomography model for this purpose. Our model includes 17 GNSS stations in Northwestern Iran. To analyze the contribution of the applied constraints in the sensitivity results, we use the 3D Gaussian, horizontal, numerical weather prediction model and virtual reference stations (VRS) in our analysis. The results show that some parts of our model are more sensitive to perturbations of input parameters, and therefore, they are more prone to regularization bias. This depends not only on time but also on the applied constraints for computing a unique solution. Results show that the response of our model to input perturbations is considerably different when we use the VRS concept for constraining the model. Using the proposed method and the traditional ways of validating a tomography model, one can develop a lower bound limit for the bias in the sensitive parts of the model and an upper bound limit for the bias in the other parts.

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Data availability

All datasets used in this study can be obtained from the corresponding author.

References

  • Adavi Z, Mashhadi-Hossainali M (2014) 4D-tomographic reconstruction of the tropospheric wet refractivity using the concept of virtual reference station, case study: North West of Iran. Meteorol Atmos Phys 125:193–205

    Article  Google Scholar 

  • Aster R, Borchers B, Thurber C (2005) Parameter estimation and inverse problems, 1st edn. Elsevier Academic Press, New York

    Google Scholar 

  • Aster R, Borchers B, Thurber C (2019) Parameter estimation and inverse problems, 3rd edn. Elsevier Academic Press, New York

    Google Scholar 

  • Bender M, Raabe A (2007) Preconditions to ground based GPS water vapour tomography. Ann Geophys 25(8):1727–1734

    Article  Google Scholar 

  • Bender M, Dick G, Ge M, Deng Z, Wickert J, Kahle H-G, Raabe A, Tetzlaff G (2011) Development of a GNSS water vapour tomography system using algebraic reconstruction techniques. Adv Space Res 47:1704–1720

    Article  Google Scholar 

  • Bevis M, Businger S, Herring TA, Rocken C, Anthes RA, Ware RH (1992) GPS meteorology: remote sensing of atmospheric water vapor using the global positioning system. J Geophys Res Atmos 97:15787–15801

    Article  Google Scholar 

  • Böhm J, Niell A, Tregoning P, Schuh H (2006) Global mapping function (GMF): a new empirical mapping function based on numerical weather model data. Geophys Res Lett. https://doi.org/10.1029/2005GL02554

    Article  Google Scholar 

  • Braun J, Rocken C, Meertens C, Ware R (1999) Development of a water vapor tomography system using low cost L1 GPS receivers. In: Ninth ARM science team meeting proceedings, San Antonio

  • Brenot H, Rohm W, Kačmařík M, Möller G, Sá A, Tondaś D, Rapant L, Biondi R, Manning T, Champollion C (2020) Cross-comparison and methodological improvement in GPS tomography. Remote Sens 12:30

    Article  Google Scholar 

  • Chen G, Herring TA (1997) Effects of atmospheric azimuthal asymmetry on the analysis of space geodetic data. Geophys Res 102:20489–20502. https://doi.org/10.1029/97JB01739

    Article  Google Scholar 

  • Chen BY, Liu ZZ, Wong WK, Woo WC (2017) Detecting water vapor variability during heavy precipitation events in Hong Kong using the GPS tomographic technique. J Atmos Ocean Technol 34:1001–1019

    Article  Google Scholar 

  • Dief A (1986) Sensitivity analysis in linear systems. Springer

    Book  Google Scholar 

  • Douša J, Elias M (2014) An improved model for calculating tropospheric wet delay. Geophys Res Lett 41:4389–4397. https://doi.org/10.1002/2014GL060271

    Article  Google Scholar 

  • Elfving T, Nikazad T, Hansen PC (2010) Semi-convergence and relaxation parameters for a class of SIRT algorithms. Electron Trans Numer Anal 37:321–336

    Google Scholar 

  • Flores A (1999) Atmospheric tomography using satellite radio signals. Ph.D. Dissertation, Technical University of Catalonia

  • Guerova G (2003) Application of GPS derived water vapour for numerical weather prediction in Switzerland. Ph.D. Dissertation, University of Bern, Bern

  • Hanna N, Trzcina E, Möller G, Rohm W, Weber R (2019) Assimilation of GNSS tomography products into the weather research and forecasting model using radio occultation data assimilation operator. Atmos Meas Tech 12(9):4829–4848

    Article  Google Scholar 

  • Higham NJ (2002) Accuracy and stability of numerical algorithms. SIAM, Philadelphia

    Book  Google Scholar 

  • Hirahara K (2000) Local GPS tropospheric tomography. Earth Planets Space 52(11):935–939

    Article  Google Scholar 

  • Jain MK, Iyengar SRK, Jain RK (2003) Numerical methods for scientific and engineering computation. New Age International (P) Limited Publishers, Delhi

    Google Scholar 

  • Johnson RA, Wichern DW (2002) Applied multivariate statistical analysis. Prentice Hall, Upper Saddle River

    Google Scholar 

  • Kleijer F (2004) Troposphere modeling and filtering for precise GPS leveling, Delft, The Netherlands

  • Liou YA, Lin YJ, Chiang CC, Huang CY (2003) Reconstructing 3D wet refractivity structures of the lower troposphere from GPS measurements, In: Proceedings of the GPS-MET conference, Tsukuba, Japan

  • Mashhadi-Hossainali M (2006) A comprehensive approach to the analysis of the 3D kinematics of deformation. Ph.D. dissertation, Institute of Physical Geodesy, Darmstadt University of Technology, p 152

  • Nikazad T (2007) The use of Landweber algorithm in image reconstruction. Ph.D. dissertation, Linkopings University, Linkopings

  • Rohm W, Bosy J (2009) Local tomography troposphere model over mountains area. Atmos Res 93(4):777–783

    Article  Google Scholar 

  • Rohm W, Bosy J (2011) The verification of GNSS tropospheric tomography model in a mountainous area. Adv Space Res 47:1721–1730

    Article  Google Scholar 

  • Shafei MJ, Mashhadi-Hossainali M (2020) Application of the GPS reflected signals in tomographic reconstruction of the wet refractivity in Italy. J Atmos Solar Terr Phys. https://doi.org/10.1016/j.jastp.2020.105348

    Article  Google Scholar 

  • Skamarock WC, Klemp JB, Dudhia J, Gill DO, Barker D, Duda MG, Powers JG (2008) A description of the advanced research WRF version 3. NCAR technical note NCAR/TN-475+STR. National Center for Atmospheric Research, Boulder, Colorado, USA. https://doi.org/10.5065/D68S4MVH

  • Yáñez-Morroni G, Gironás L, Caneo M, Delgado R, Garreaud R (2018) Using the weather research and forecasting (WRF) model for precipitation forecasting in an Andean region with complex topography. Atmosphere 9:304. https://doi.org/10.3390/atmos9080304

    Article  Google Scholar 

  • Zhao Q, Liu Y, Ma X, Yao W, Li X (2020) An improved rainfall forecasting model based on GNSS observations. IEEE Trans Geosci Remote Sens. https://doi.org/10.1109/TGRS.2020.2968124

    Article  Google Scholar 

  • Zus F, Dick G, Douša J, Heise S, Wickert J (2014) The rapid and precise computation of GPS slant total delays and mapping factors utilizing a numerical weather model. Radio Sci 49:207–216. https://doi.org/10.1002/2013RS005280

    Article  Google Scholar 

  • Zus F, Dick G, Heise S, Wickert J (2015) A forward operator and its adjoint for GPS slant total delays. Radio Sci 50:393–405. https://doi.org/10.1002/2014RS005584

    Article  Google Scholar 

  • Zus F, Douša J, Kačmařík M, Václavovic P, Balidakis K, Dick G, Wickert J (2019) Improving GNSS zenith wet delay interpolation by utilizing tropospheric gradients: experiments with a dense station network in central Europe in the warm season. Remote Sens 11(6):674

    Article  Google Scholar 

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Acknowledgements

For this study, we would like to thank the National Cartographic Center (NCC) of Iran for providing the GNSS data that were used in this work. We particularly appreciate the meteorological organization of Iran for giving us access to radiosonde profiles at the stations of this research.

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Authors and Affiliations

  1. Faculty of Geodesy and Geomatics Engineering, K. N. Toosi University of Technology, No. 1346, ValiAsr Street, Mirdamad Cross, Tehran, Iran

    Masoud Mashhadi Hossainali & Hanieh Tabatabaei

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  1. Masoud Mashhadi Hossainali
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  2. Hanieh Tabatabaei
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Correspondence to Masoud Mashhadi Hossainali.

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Mashhadi Hossainali, M., Tabatabaei, H. Applying principal components to analyze the distribution of model biases in GNSS tropospheric tomography for a case study in Northwestern Iran. GPS Solut 26, 133 (2022). https://doi.org/10.1007/s10291-022-01315-2

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