**Author details**

*τ<sup>u</sup>* = *t*

**Table 3.** Comparison between GPS and GLONASS.

136 Multifunctional Operation and Application of GPS

*τ<sup>g</sup>* = *t*

combining GPS/GLONASS data processing.

**12. Advantages of combined GPS and GLONASS**

positioning solution.

*UTC* − *t*

**GLONASS GPS**

Constellation Number of satellite 24 32

Signal characteristics Multiplexing FDMA CDMA Carrier frequencies 1602 + k × 0.5625 MHz

Coordinates system PZ-90.02 WGS-84 Time system GLONASS time GPS time

Code frequencies C/A code: 0.511

Number of orbits 3 6 Orbital inclination 64.8° 55°

Orbital radius 25,510 km 26,560 km Orbital altitude 19,130 km 20,200 km Orbit period 11 h 15.8 min 11 h 58 min

1246 + k × 0.4375 MHz

Broadcast ephemerides Position, velocity, acceleration Keplerian elements

P code: 5.11

*GPS* − *t*

In combined GPS/GLONASS data processing, the differences between these time scales must be accounted for. Otherwise, systematic errors are introduced that will affect the combined

**Table 3** summarizes vital parameters of GPS and GLONASS that must be considered when

In many cases, such as navigating in urban or mountainous areas, during aircraft highdynamic scenario, or under the effect of interference, satellite visibility becomes an issue. In such situations, incorporating both GPS and GLONASS constellations in the navigation system may significantly improve the accuracy of the navigational solution. Merging both

systems in one navigation solution provides the next significant advantages:

*UTC*(*SU*) (9)

1575.42 MHz 1227.60 MHz

C/A code: 1.023 P code: 10.23

*UTC* (10)

Mohamed Tamazin<sup>1</sup> , Malek Karaim<sup>2</sup> \* and Aboelmagd Noureldin2,3

\*Address all correspondence to: malek.karaim@queensu.ca

1 Electronics and Communications Engineering Department, Arab Academy for Science, Technology and Maritime Transport (AASTMT), Egypt

2 Electrical and Computer Engineering Department, Queen's University, Canada

3 Electrical and Computer Engineering Department, Royal Military College of Canada, Canada

## **References**

[1] Bradford P, James S. Global Positioning System: Theory and Applications, Volume I. The American Institute of Aeronautics and Astronautics, Inc: Washington; 1996

[2] Pratap M, Per E. Global Positioning System: Signals, Measurements and Performance. 2nd ed. Massachusetts: Ganga-Jamuna Press; 2006

[19] Braasch MS and Van Dierendonck AJ. GPS Receiver Architectures and Measurements.

GNSSs, Signals, and Receivers

139

http://dx.doi.org/10.5772/intechopen.74677

[20] Ralph E, Arthur W. Dual down Conversion GPS Receiver with Single Local Oscillator.

[21] Lachapelle G. GPS Theory and Applications. ENGO 625 Course Lecture Notes. Department

[22] GLONASS ICD [Internet]. 2008. Available from: http://www.GLONASS-ianc.rsa.ru

[23] Yuri U, Valeriy S, Grigory S, Vyacheslav D, Alexander P, Sergey K. GLONASS develop-

[24] Keong J. Determining Heading and Pitch Using a Single Difference GPS/GLONASS Approach. UCGE Reports No. 20134. Department of Geomatics Engineering, University

[25] GPS ICD [Internet]. 2010. Available from: http://www.gps.gov/technical/icwg [Accessed:

[26] Abbasiannik S. Multichannel Dual Frequency GLONASS Software Receiver in Combination with GPS L1 C/A. UCGE Reports No. 20215. Department of Geomatics Engineering,

[27] Cai C. Precise Point Positioning Using Dual-Frequency GPS and GLONASS Measurements. UCGE Reports No. 20291. Department of Geomatics Engineering, University of Calgary,

ing strategies for the future. In: GPS World Magazine. April 2011. p. 42-49

In: Proceedings of the IEEE; January 1999. p. 48-64

of Geomatics Engineering, University of Calgary, 2009

Google Patents (US5108334 A), 1992

[Accessed: 2011-20-04]

of Calgary, 1999

University of Calgary, 2009

2011-09-04]

2009


[19] Braasch MS and Van Dierendonck AJ. GPS Receiver Architectures and Measurements. In: Proceedings of the IEEE; January 1999. p. 48-64

[2] Pratap M, Per E. Global Positioning System: Signals, Measurements and Performance.

[3] Elliott K, Christopher H. Understanding GPS: Principles and Applications. 2nd ed.

[4] Aboulmagd N, Tashfeen K, Jacques G. Fundamentals of Inertial Navigation, Satellite-

[5] Kai B, Dennis A, Nicolaj B, Peter Ri, Søren J. A Software-defined GPS and Galileo

[6] Ahmed E. Introduction to GPS: The Global Positioning System. Artech House: Norwood;

[7] ICD G. Navstar GPS Space Segment/Navigation User Interfaces, Interface Specification.

[8] Malek K. The Long Journey of a GPS Signal. Inside Signal Processing Newsletter. [Internet]. 2017. Available from: https://signalprocessingsociety.org/newsletter/2017/10/

[9] Camacho-Lara S. Current and Future GNSS and their Augmentation Systems in

[10] USA Force. Space Segment [Internet]. Available from: http://www.gps.gov/systems/gps/

[11] USA Force. Control Segment [Internet]. Available from: http://www.gps.gov/systems/

[13] Hofmann-Wellenhof B, Herbert L, James C. GPS Theory and Practice. New York:

[15] Malek K. Real-Time Cycle-Slip Detection and Correction for Land Vehicle Navigation

[16] Mohamed T. High Resolution Signal Processing Techniques for Enhancing GPS Receiver

[17] Sheffer DK, Lee TH. A 1.5-V, 1.5-GHz CMOS low noise amplifier. IEEE Journal of Solid-

[18] Jonas T, Per-Ludvig N, Christian S. A High-performance real-time GNSS software receiver and its role in evaluating various commercial front end ASICs. In: Proceedings of the 15th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS 2002); 24 September 2002; Portland: ION;2002. p. 2554-2560

[14] Jay F. Aided Navigation GPS with High Rate Sensors. New York: McGraw-Hill; 2008

Handbook of Satellite Applications. New York: Springer; 2013. pp. 617-654

[12] Dan D. Fundamentals of GPS Receivers: A Hardware Approach. Springer; 2012

Using Inertial Aiding [Thesis]. Kingston: Queen's University; 2013

Performance [Thesis]. Kingston: Queen's University; 2015

State Circuits. 1997;**32**:745-759. DOI: 10.1109/4.568846

Receiver: A Single-Frequency Approach. Birkhauser Boston: Springer; 2007

2nd ed. Massachusetts: Ganga-Jamuna Press; 2006

Based Positioning and their Integration. Springer; 2013

Artech House: Norwood; 2006

138 Multifunctional Operation and Application of GPS

IS-GPS-200E El Segundo, CA, USA2010

space/ [Accessed: 2017-01-12]

Springer; 1993

gps/space/ [Accessed: 2017-01-12]

long-journey-gps-signal [Accessed: 2017-17-12]

2002


**Section 7**

**Navigation System – Principles and Functions**

**Navigation System – Principles and Functions**

**Chapter 7**

**Provisional chapter**

**Applications of GNSS Slant Path Delay Data on**

**Applications of GNSS Slant Path Delay Data on** 

DOI: 10.5772/intechopen.75101

This chapter focuses on applications of Global Navigation Satellite Systems (GNSS) slant path delay data (SPD) to obtain signals from thunderstorms or rainbands. Current operational numerical weather prediction systems (NWPs) use water vapor distributions derived by GNSS technology as vital information for predicting convective rainfall. Mostly, zenith total delay or integrated water vapor data are used at horizontal scales of several tens of kilometers for this purpose. Beyond such operational use, SPD can be used to obtain information on storms (cumulonimbus) at horizontal scales of less than 10 km. For instance, found that SPD represents very small-scale phenomena of less than 10 km and can be used to estimate water vapor distribution around a thunderstorm with a strong tornado, and succeeded in improving the forecast skill of a rainband at 10 km scale. This chapter reviews SPD, which is

The Earth's atmosphere, including the ionosphere, affects navigation signals transmitted by Global Navigation Satellite Systems (GNSS), which causes positioning errors. It is able to eliminate the ionospheric effect using a pair of GNSS carrier waves, and then GNSS analysis estimates the signal delay by the atmosphere as an unknown parameter [1–4]. The atmospheric delay is obtained by integrating the refractivity along the ray path, which is calculated with the variables of temperature, pressure, and water vapor pressure in the atmosphere. In the 1980s, several studies showed the feasibility of sensing the atmosphere using GNSS signal delay. For instance, Askne and Nordius [5] found a relationship between signal delay in the

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

**Meteorology at Storm Scales**

**Meteorology at Storm Scales**

Takuya Kawabata and Yoshinori Shoji

Takuya Kawabata and Yoshinori Shoji

http://dx.doi.org/10.5772/intechopen.75101

**Abstract**

**1. Introduction**

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

invaluable for predicting thunderstorms and/or rainbands. **Keywords:** slant path delay, storm scale, data assimilation

**Chapter 7 Provisional chapter**

#### **Applications of GNSS Slant Path Delay Data on Meteorology at Storm Scales Applications of GNSS Slant Path Delay Data on Meteorology at Storm Scales**

DOI: 10.5772/intechopen.75101

Takuya Kawabata and Yoshinori Shoji Takuya Kawabata and Yoshinori Shoji

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.75101

#### **Abstract**

This chapter focuses on applications of Global Navigation Satellite Systems (GNSS) slant path delay data (SPD) to obtain signals from thunderstorms or rainbands. Current operational numerical weather prediction systems (NWPs) use water vapor distributions derived by GNSS technology as vital information for predicting convective rainfall. Mostly, zenith total delay or integrated water vapor data are used at horizontal scales of several tens of kilometers for this purpose. Beyond such operational use, SPD can be used to obtain information on storms (cumulonimbus) at horizontal scales of less than 10 km. For instance, found that SPD represents very small-scale phenomena of less than 10 km and can be used to estimate water vapor distribution around a thunderstorm with a strong tornado, and succeeded in improving the forecast skill of a rainband at 10 km scale. This chapter reviews SPD, which is invaluable for predicting thunderstorms and/or rainbands.

**Keywords:** slant path delay, storm scale, data assimilation

#### **1. Introduction**

The Earth's atmosphere, including the ionosphere, affects navigation signals transmitted by Global Navigation Satellite Systems (GNSS), which causes positioning errors. It is able to eliminate the ionospheric effect using a pair of GNSS carrier waves, and then GNSS analysis estimates the signal delay by the atmosphere as an unknown parameter [1–4]. The atmospheric delay is obtained by integrating the refractivity along the ray path, which is calculated with the variables of temperature, pressure, and water vapor pressure in the atmosphere. In the 1980s, several studies showed the feasibility of sensing the atmosphere using GNSS signal delay. For instance, Askne and Nordius [5] found a relationship between signal delay in the

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

zenith direction (zenith total delay; ZTD) and the precipitable water vapor (PWV; vertically integrated water vapor) in a formulation. Studies such as these led to the establishment of a new interdisciplinary research field (Bevis et al. [6], Businger et al. [7]). The Global Positioning System (GPS) maintained by the United States is the world's first operational GNSS, and has contributed significantly to the progress of the meteorological applications of GNSS. One of the most important contributions of GPS/GNSS meteorology is an innovative application of GNSS observations as a water vapor sensor.

Since the development of the GPS/GNSS meteorology, the applications of slant path delays (SPDs; delays along paths from GNSS satellites to GNSS receivers) have been studied for water vapor variation in local and its role in the development of hazardous thunderstorms. One such approach is the tomographic method, which estimates structures of water vapor in 3D. For this purpose, several GPS/GNSS observational campaigns with dense networks have been conducted, and obtained successful results [11–13]. However, it is difficult for operational GNSS networks to retrieve 3D structures of water vapor using only GNSS SPDs, due to the low density of the network, small number of SPDs, and slow movement of GNSS satellites.

Applications of GNSS Slant Path Delay Data on Meteorology at Storm Scales

http://dx.doi.org/10.5772/intechopen.75101

145

Another application is assimilation of GNSS-derived water vapor information for improving the initial fields of numerical weather prediction (NWP) models. The impact of this information on mesoscale NWP systems has been thoroughly investigated (Nakamura et al. [14], Koizumi and Sato [15], Seko et al. [16]). These studies mainly used PWV data retrieved by GNSS analysis using IGS's precise final ephemerides. Shoji [17] developed a near real time (NRT) PWV analysis system. This system provides the PWV data by the time when the Japan Meteorological Agency (JMA) assimilates the data in the operational mesoscale data assimilation (DA) system. Using PWV by the NRT system, Shoji et al. [18] succeeded to predict heavy rainfalls, which JMA's mesoscale NWP model failed operationally. Further, an impact assessment of the local-scale atmospheric phenomena on GNSS positioning was also carried out using mesoscale NWP outputs (Seko et al. [13], Shimada et al. [19], Ishikawa et al. [20]).

Other studies have investigated the assimilation of SPD data. The advantage of SPD for PWV and ZTD is that it includes information about several atmospheric parameters (pressure, temperature, and humidity) in several directions from each receiver. Therefore, the assimilation of SPD data is expected to improve the water vapor field with the thermodynamics field of the

Ha et al. [21] assimilated virtual GNSS slant water vapor observations, which are accumulated water vapor along slant paths (SW data), as an Observation System Simulation Experiment (OSSE). The SW data is advantageous to PWV observations in its various directions from each receiver. They succeeded to simulate a realistic squall line after assimilation of the SW data with a fifth-generation mesoscale model (MM5)-4D-Var system (Zou and Kuo, [22]) at a 27-km grid spacing. Järvinen et al. [23] assimilated SPD data with a High Resolution Local Area Modeling-3D-Var system (HIRLAM; Gustafsson et al. [24]) at a 9-km grid spacing, and showed that the analysis increments of the SPD assimilation were larger that of the ZTD assimilation, and that the horizontal distribution of the SPD analysis increments was different from that of ZTD assimilations. Bauer et al. [25] tried to assimilate SPD data with the MM5-4D-Var system and succeeded to improve quantitative precipitation forecasting skills. Though they demonstrated the superior QPF scores by assimilating SPD data over a month, their horizontal grid spacing was 18 km; this is not enough to represent thunderstorms directly in the model. In the past few years, the German Weather Service (DWD) has developed an assimilation method for SPD data with their operational data assimilation system (Kilometer-Scale Ensemble Kalman Filter; KENDA) and obtained a 20% improvement

on prediction of a convective rainfall system (Potthast 2017; personal communication).

The SPD data represent both vertical and horizontal atmospheric conditions, whereas the ZTD and PWV observations contain only vertical information. Thus, it is advantageous to assimilate

model above and around the observation points.

Water vapor in the atmosphere plays an important role in convective rainfall systems. Particularly in the summer in Japan, convective clouds form frequently during the evening and develop into thunderstorms. Weather radar has been used in several observational studies to investigate the evolution of such convection. However, since weather radar only detects the distribution and movement of raindrops, it is still difficult to predict the precise position and time of the initiation of heavy precipitation. GNSS tropospheric delays are sensitive to water vapor, and can be used with radar to monitor the early stages of the convergence of water vapor before severe precipitation. Since the mid-1990s, procedures for retrieving precipitable water vapor (PWV) using the GNSS have advanced significantly.

In Japan, the Geospatial Information Authority of Japan (GSI) operates a nationwide permanent ground-based GNSS observation network called the Earth Observation Network (GEONET), which covers the entire Japanese archipelago with an average spacing of 17 km. It is regarded as one of the densest GNSS networks in the world. On July 13, 2012, the GSI began to provide data from the Russian GLONASS (Globalnaya Navigatsionnaya Sputnikovaya Sistema) and Japan's QZSS (Quasi Zenith Satellite System) along with GPS data. Also, from March 2016, the GSI started providing GALILEO data.

Several studies have been shown GNSS PWV as a useful tool for monitoring heavy rainfall. Kanda et al. [8] found that periods of maximum PWV tended to be a precursor of the initiation of heavy rain, and that larger hourly increases in PWV led to higher frequency of precipitation.

Niimura et al. [9] statistically investigated the relationship between precipitation, PWV, and temperature, and found the correlation between the observed PWV and surface temperature. They also found a threshold of PWV depending on the temperature; for instance, when PWV exceeds the threshold, frequency of precipitation rapidly increases. After their statistical study, it was concluded that this threshold is connected with the humidity averaged vertically above the observation point, and that the saturation level of the entire atmosphere can be estimated with PWV. Inoue and Inoue [10] also statistically studied the two-dimensional PWV field derived by GNSS in connection with thunderstorms in summer. They found that cloud-to-ground (CG) strokes were observed 1 hour after large amounts of PWV and its 30-min increments.

These studies have illustrated that observing PWV and its variation are useful for monitoring heavy rainfall. However, monitoring PWV alone is not always enough to capture information on the precursor of a severe storm. For instance, Niimura et al. [9] illustrated a good agreement between the level of saturation of the entire atmosphere given by PWV and stratiform rain, but the relationship was unclear in localized heavy rain cases. Inoue and Inoue [10] statistically showed that the maximum CG stroke only in 40% of the observed thunderstorms was observed 15–30 min after the maximum PWV. Therefore, it is necessary to find other method for the remaining 60%.

Since the development of the GPS/GNSS meteorology, the applications of slant path delays (SPDs; delays along paths from GNSS satellites to GNSS receivers) have been studied for water vapor variation in local and its role in the development of hazardous thunderstorms. One such approach is the tomographic method, which estimates structures of water vapor in 3D. For this purpose, several GPS/GNSS observational campaigns with dense networks have been conducted, and obtained successful results [11–13]. However, it is difficult for operational GNSS networks to retrieve 3D structures of water vapor using only GNSS SPDs, due to the low density of the network, small number of SPDs, and slow movement of GNSS satellites.

zenith direction (zenith total delay; ZTD) and the precipitable water vapor (PWV; vertically integrated water vapor) in a formulation. Studies such as these led to the establishment of a new interdisciplinary research field (Bevis et al. [6], Businger et al. [7]). The Global Positioning System (GPS) maintained by the United States is the world's first operational GNSS, and has contributed significantly to the progress of the meteorological applications of GNSS. One of the most important contributions of GPS/GNSS meteorology is an innovative application of GNSS

Water vapor in the atmosphere plays an important role in convective rainfall systems. Particularly in the summer in Japan, convective clouds form frequently during the evening and develop into thunderstorms. Weather radar has been used in several observational studies to investigate the evolution of such convection. However, since weather radar only detects the distribution and movement of raindrops, it is still difficult to predict the precise position and time of the initiation of heavy precipitation. GNSS tropospheric delays are sensitive to water vapor, and can be used with radar to monitor the early stages of the convergence of water vapor before severe precipitation. Since the mid-1990s, procedures for retrieving pre-

In Japan, the Geospatial Information Authority of Japan (GSI) operates a nationwide permanent ground-based GNSS observation network called the Earth Observation Network (GEONET), which covers the entire Japanese archipelago with an average spacing of 17 km. It is regarded as one of the densest GNSS networks in the world. On July 13, 2012, the GSI began to provide data from the Russian GLONASS (Globalnaya Navigatsionnaya Sputnikovaya Sistema) and Japan's QZSS (Quasi Zenith Satellite System) along with GPS data. Also, from

Several studies have been shown GNSS PWV as a useful tool for monitoring heavy rainfall. Kanda et al. [8] found that periods of maximum PWV tended to be a precursor of the initiation of heavy rain, and that larger hourly increases in PWV led to higher frequency of precipitation. Niimura et al. [9] statistically investigated the relationship between precipitation, PWV, and temperature, and found the correlation between the observed PWV and surface temperature. They also found a threshold of PWV depending on the temperature; for instance, when PWV exceeds the threshold, frequency of precipitation rapidly increases. After their statistical study, it was concluded that this threshold is connected with the humidity averaged vertically above the observation point, and that the saturation level of the entire atmosphere can be estimated with PWV. Inoue and Inoue [10] also statistically studied the two-dimensional PWV field derived by GNSS in connection with thunderstorms in summer. They found that cloud-to-ground (CG)

strokes were observed 1 hour after large amounts of PWV and its 30-min increments.

These studies have illustrated that observing PWV and its variation are useful for monitoring heavy rainfall. However, monitoring PWV alone is not always enough to capture information on the precursor of a severe storm. For instance, Niimura et al. [9] illustrated a good agreement between the level of saturation of the entire atmosphere given by PWV and stratiform rain, but the relationship was unclear in localized heavy rain cases. Inoue and Inoue [10] statistically showed that the maximum CG stroke only in 40% of the observed thunderstorms was observed 15–30 min after the maximum PWV. Therefore, it is necessary to find other method for the remaining 60%.

cipitable water vapor (PWV) using the GNSS have advanced significantly.

March 2016, the GSI started providing GALILEO data.

observations as a water vapor sensor.

144 Multifunctional Operation and Application of GPS

Another application is assimilation of GNSS-derived water vapor information for improving the initial fields of numerical weather prediction (NWP) models. The impact of this information on mesoscale NWP systems has been thoroughly investigated (Nakamura et al. [14], Koizumi and Sato [15], Seko et al. [16]). These studies mainly used PWV data retrieved by GNSS analysis using IGS's precise final ephemerides. Shoji [17] developed a near real time (NRT) PWV analysis system. This system provides the PWV data by the time when the Japan Meteorological Agency (JMA) assimilates the data in the operational mesoscale data assimilation (DA) system. Using PWV by the NRT system, Shoji et al. [18] succeeded to predict heavy rainfalls, which JMA's mesoscale NWP model failed operationally. Further, an impact assessment of the local-scale atmospheric phenomena on GNSS positioning was also carried out using mesoscale NWP outputs (Seko et al. [13], Shimada et al. [19], Ishikawa et al. [20]).

Other studies have investigated the assimilation of SPD data. The advantage of SPD for PWV and ZTD is that it includes information about several atmospheric parameters (pressure, temperature, and humidity) in several directions from each receiver. Therefore, the assimilation of SPD data is expected to improve the water vapor field with the thermodynamics field of the model above and around the observation points.

Ha et al. [21] assimilated virtual GNSS slant water vapor observations, which are accumulated water vapor along slant paths (SW data), as an Observation System Simulation Experiment (OSSE). The SW data is advantageous to PWV observations in its various directions from each receiver. They succeeded to simulate a realistic squall line after assimilation of the SW data with a fifth-generation mesoscale model (MM5)-4D-Var system (Zou and Kuo, [22]) at a 27-km grid spacing. Järvinen et al. [23] assimilated SPD data with a High Resolution Local Area Modeling-3D-Var system (HIRLAM; Gustafsson et al. [24]) at a 9-km grid spacing, and showed that the analysis increments of the SPD assimilation were larger that of the ZTD assimilation, and that the horizontal distribution of the SPD analysis increments was different from that of ZTD assimilations. Bauer et al. [25] tried to assimilate SPD data with the MM5-4D-Var system and succeeded to improve quantitative precipitation forecasting skills. Though they demonstrated the superior QPF scores by assimilating SPD data over a month, their horizontal grid spacing was 18 km; this is not enough to represent thunderstorms directly in the model. In the past few years, the German Weather Service (DWD) has developed an assimilation method for SPD data with their operational data assimilation system (Kilometer-Scale Ensemble Kalman Filter; KENDA) and obtained a 20% improvement on prediction of a convective rainfall system (Potthast 2017; personal communication).

The SPD data represent both vertical and horizontal atmospheric conditions, whereas the ZTD and PWV observations contain only vertical information. Thus, it is advantageous to assimilate the SPD observations at storm scales. For instance, a GNSS signal with a 30° elevation angle at a GNSS receiver travels from the top of the troposphere to the receiver with a horizontal distance of 17 km. Thus, the SPD data cover only two model grid cells, when an assimilation system with 20-km grid spacing is applied. As a result, it is expected that the assimilation effect of SPD data would be similar to the ZTD assimilation. Therefore, it is important for SPD assimilations to use assimilation systems with high grid spacings, hopefully less than 5 km.

orbit, and errors in clocks of both satellite and receiver). Therefore, to estimate HI, it is necessary to remove all errors not related to atmospheric inhomogeneity. Shoji et al. [1] performed a procedure to eliminate multi-path and satellite clock error-induced residuals to reconstruct HI components. The correlation coefficient of each component retrieved at a different GNSS station and sorted by distance demonstrated that the horizontal scale of the ZTD can be con-

This result suggests that ZTD, G, and HI relate to atmospheric motion of the meso- α, meso- β,

Sato et al. [30] compared zenith-scaled SPD using a mapping function and that retrieved from radiosonde observations. They found that the zenith-scaled SPD, in which the path is closest to a radiosonde path, exhibited better agreement than zenith total delay (ZTD) retrieved by standard GNSS analysis (i.e., a representative value of the inverted-cone-shaped space above

Although it requires some careful effort to retrieve, GNSS SPD possesses information on local-scale atmospheric activity. Shoji [31] proposed procedures for retrieving two indices indicating the degree of inhomogeneity of water vapor using the GNSS SPDs. One index (WVC) describes the spatial concentration of water vapor (Eq. 3), whereas the other (WVI) indicates higher order water vapor inhomogeneity (Eq. 4). The horizontal scales of the two

WVC = −∇<sup>2</sup> PWVG, (3)

where <sup>∇</sup> PWVG is the horizontal gradient of PWV estimated from the atmospheric gradient

*n* ∑ *i*=1 *n*

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \_\_1

*i* − ¯ *HIPWV*)

(*HIPWV*

**Figure 1.** Correlation coefficients of (a) ZTD, (b) gradient component, and (c) postfit residuals as a function of distance. Gray-filled circles are from GEONET, and black-filled circles are from the Tsukuba GPS dense net campaign. Each data point is based on 51 days of data from July 14 to September 2, 2001. (Modified from **Figures 9**–**11** of Shoji et al. [1]).

indices are considered to be approximately 60 km and 2–3 km, respectively.

as 62 ± 23 km, and the HI as 2–3 km.

http://dx.doi.org/10.5772/intechopen.75101

147

Applications of GNSS Slant Path Delay Data on Meteorology at Storm Scales

<sup>2</sup>, (4)

sidered as 644 ± 120 km, the gradient parameter Gn, Ge

and meso- γ scales, respectively (**Figure 1**).

*WVI* <sup>=</sup> <sup>√</sup>

the GNSS antenna).

parameter (G).

In this chapter, the use of SPD data for the monitoring of hazardous convection is described in Section 2, and the first assimilation of SPD data with a DA system with 2-km grid spacing (storm scale) is given in Section 3. The chapter is summarized in Section 4.
