ZTD yükseklik düzeltme modellerinin araştırılması: Orta Avrupa örneği

Öz

Yüksek doğruluklu troposfer ürünleri hassas nokta konumlamada kilit bir rol oynamaktadır. Başucu yönündeki troposferik gecikme (Zenith Tropospheric Delay, ZTD), basınç ve sıcaklık gibi parametreler troposfer modelleri yardımıyla elde edilmektedir. Ancak, troposfer modelleri belirli grid veya model yükseklikleri için üretildiğinden, parametrelere yükseklik düzeltmelerinin getirilmesi gerekmektedir. Bu çalışmada Orta Avrupa için üstel, kübik ve hibrit yaklaşım olmak üzere farklı yükseklik düzeltme modelleri incelenmiştir. Bu kapsamda ZTD değerleri 2020-2022 yılları arası ERA5 verileri kullanılarak DNS (Direct Numerical Solutions) yazılımı ile hesaplanmıştır. En yüksek model doğruluğu hibrit yaklaşım ile elde edilmiştir. Ancak, GNSS istasyonlarına dayalı analizlerde üstel ve kübik yaklaşım ile daha yüksek doğruluğa ulaşılmıştır.

Anahtar Kelimeler

• ZTD
• DNS
• GNSS
• Doğruluk

Investigation of the height correction model of ZTD: Case study of Central Europe

Öz

High accuracy tropospheric products play a key role in precise positioning. The parameters, such as Zenith Tropospheric Delay (ZTD), pressure and temperature, are obtained by troposphere models. However, height corrections should be considered for the parameters since troposphere models are produced for specific grid or model heights. In this study, different height correction models, named as exponential, cubic and hybrid, were investigated for Central Europe. In this context, ZTDs were calculated by using the data of ERA5 between 2020 and 2022 with Direct Numerical Solutions (DNS) software. The highest model accuracy was obtained by hybrid approach. However, higher accuracy was achieved in the analysis based on GNSS stations using exponential and cubic approaches.

Anahtar Kelimeler

• ZTD
• DNS
• GNSS
• Accuracy

Kaynakça

1. Askne, J., & Nordius, H. (1987). Estimation of tropospheric delay for microwaves from surface weather data. Radio science, 22(03), 379-386.
2. Böhm, J., Heinkelmann, R., & Schuh, H. (2007). Short note: a global model of pressure and temperature for geodetic applications. Journal of Geodesy, 81(10), 679-683.
3. Davis, J. L., Herring, T. A., Shapiro, I. I., Rogers, A. E. E., & Elgered, G. (1985). Geodesy by radio interferometry: Effects of atmospheric modeling errors on estimates of baseline length. Radio science, 20(6), 1593-1607.
4. Doğan, A. H., Zus, F., Dick, G., Wickert, J., Schuh, H., Durdağ, U. M., & Erdoğan, B. (2024). Improving the wet mapping function by numerical weather models. Advances in Space Research, 73(1), 404-413.
5. Doğan, A. H. (2026). Investigation of the GFS forecast products on RT-PPP solutions. Journal of Atmospheric and Solar-Terrestrial Physics, 280, 106755.
6. Hersbach, H., Bell, B., Berrisford, P., Hirahara, S., Horányi, A., Muñoz‐Sabater, J., ... & Thépaut, J. N. (2020). The ERA5 global reanalysis. Quarterly journal of the royal meteorological society, 146(730), 1999-2049.
7. Hofmann-Wellenhof, B., Lichtenegger, H., & Wasle, E. (2007). GNSS—Global Navigation Satellite Systems: GPS, GLONASS, Galileo, and more. Vienna: Springer Vienna.
8. Huang, L., Zhu, G., Liu, L., Chen, H., & Jiang, W. (2021). A global grid model for the correction of the vertical zenith total delay based on a sliding window algorithm. GPS Solutions, 25(3), 98.

9. Lagler, K., Schindelegger, M., Böhm, J., Krásná, H., & Nilsson, T. (2013). GPT2: Empirical slant delay model for radio space geodetic techniques. Geophysical research letters, 40(6), 1069-1073.
10. Landskron, D., & Böhm, J. (2018). VMF3/GPT3: refined discrete and empirical troposphere mapping functions. Journal of Geodesy, 92(4), 349-360.
11. Lei, X., Xu, X., Tao, J., Yang, T., Zhao, Q., & Guo, J. (2024). High-precision tropospheric correction method for NRTK regions with significant height differences. Measurement Science and Technology, 35(10), 106315.
12. Li, H., Zhu, G., Kang, Q., Huang, L., & Wang, H. (2023). A global zenith tropospheric delay model with ERA5 and GNSS-based ZTD difference correction. GPS Solutions, 27(3), 154.
13. Lin, L. S. (1997). Real-time estimation of ionospheric delay using GPS measurements (Doktora Tezi). The University of New South Wales, School of Geomatic Engineering, Sidney, Avusturalya.
14. Saastamoinen, J. (1972). Atmospheric correction for the troposphere and stratosphere in radio ranging satellites. The use of artificial satellites for geodesy, 15, 247-251.
15. Song, S., Zhu, W., Chen, Q., & Liou, Y. (2011). Establishment of a new tropospheric delay correction model over China area. Science China Physics, Mechanics and Astronomy, 54(12), 2271-2283.
16. Velikou, K., Lazoglou, G., Tolika, K., & Anagnostopoulou, C. (2022). Reliability of the ERA5 in replicating mean and extreme temperatures across Europe. Water, 14(4), 543.
17. Wang, X., Zhu, G., Huang, L., Wang, H., Yang, Y., Li, J., Huang, L., Zhou, L., & Liu, L. (2022). Development of a ZTD vertical profile model considering the spatiotemporal variation of height scale factor with different reanalysis products in China. Atmosphere, 13(9), 1469.
18. Wang, J., Chen, J., & Zhang, Y. (2025). Empirical modeling of tropospheric delays with uncertainty. Geoscientific Model Development, 18(5), 1487-1504.
19. Wessel, P., & Smith, W. H. (1998). New, improved version of Generic Mapping Tools released. Eos, Transactions American Geophysical Union, 79(47), 579-579.
20. Wilgan, K., Hadas, T., Hordyniec, P., & Bosy, J. (2017). Real-time precise point positioning augmented with high-resolution numerical weather prediction model. GPS solutions, 21(3), 1341-1353.
21. Zheng, F., Lou, Y., Gu, S., Gong, X., & Shi, C. (2018). Modeling tropospheric wet delays with national GNSS reference network in China for BeiDou precise point positioning. Journal of Geodesy, 92(5), 545-560.
22. Zus, F., Balidakis, K., Dick, G., Wilgan, K., & Wickert, J. (2021). Impact of tropospheric mismodelling in GNSS precise point positioning: A simulation study utilizing ray-traced tropospheric delays from a high-resolution NWM. Remote Sensing, 13(19), 3944.
23. Zus, F., Balidakis, K., Doğan, A. H., Thundathil, R., Dick, G., & Wickert, J. (2025). DNS (v1. 0): An open source ray-tracing tool for space geodetic techniques. Geoscientific Model Development, 18(15), 4951-4964.