Interpretation of the tropospheric gradients estimated with GPS during hurricane Harvey

Interpretation of the Tropospheric Gradients Estimated With GPS During Hurricane Harvey Victoria Graffigna1,2 , Manuel Hernández-Pajares3, Mauricio Gende1,2 , Francisco Azpilicueta1,2 , and Pablo Antico1,2 1Facultad de Ciencias Astronómicas y Geofísicas Department, Universidad Nacional de La Plata, La Plata, Argentina, 2Consejo Nacional de Investigaciones Científicas y Técnicas (Conicet), Argentina, 3Department of Mathematics, Universitat Politècnica de Catalunya (UPC), Barcelona, Spain Abstract During the last decade Global Positioning System (GPS) Continuous Operating Reference Stations networks have become a new important data source for meteorology. This has dramatically improved the ability to remotely sense the atmosphere under the influence of severe mesoscale and synoptic systems. The zenith tropospheric delay (ZTD) is one of the atmospheric variables continuously observed, and its horizontal variations, the horizontal tropospheric gradients, are routinely computed nowadays within the dual-frequency GPS processing, but their interpretation and relationship with the weather is still an open question. The purpose of this paper is to contribute in this direction by studying the effect that Hurricane Harvey had on the spatial and temporal behavior of the ZTDs and gradients, when it reached Texas coast, during 18–31 August 2017. The results show that ZTD time series present a clear and rapid increase larger than 10 cm in a few hours when the hurricane reached the area. Gradients behaviors show that the hurricane also produced significant changes on them, since the magnitude and predominant directions before and after the hurricane arrived are completely different. Noticeably, the gradient vectors before the landing are consistently related to the horizontal winds and pressure fields. In this manuscript we demonstrate that the ZTD gradients can show a consistent signature under severe weather events, strongly suggesting their potential application for short-term weather forecasting. 1. Introduction and Motivation The Global Positioning System (GPS) was initiated in the 1970s, became fully operational in 1994, and rapidly showed its potential as a resource for high-precision (millimeter-level) geodetic measurement, apart from its wide use in navigation. The need to precisely estimate the error sources on the GPS signal to improve the positioning gave place to a new application of GPS, the remote sensing of atmospheric water vapor (Bevis etal.,1992).GPSmeteorologyisabletoprovide atmospheric variableswithhighspatiotemporalresolution at no further cost. Nowadays, this new area is a well-established field in both research and operation (Guerova et al., 2016) for some large regions in the world and has become an important source of climate monitoring. However, as a consequence of the significant improvements in GPS processing algorithms, inconsistencies in long-term time series have been introduced; therefore, there is a need for a homogeneous set of data for GPS meteorology. In this sense, the GPS community has contributed with reprocessed data that are useful for many applications (Dousa et al., 2017; Pacione & Di Tomaso, 2016). The zenith tropospheric delay (ZTD) is indeed one of the parameters estimated in the GPS data processing, and it represents the vertically integrated atmospheric refractivity, which is a function of pressure, temperature, and water vapor content (Davis et al., 1985). The slant (STD) is modeled as the ZTD plus its horizontal gradients, because the ZTD is common to all the lines of sight for a given GPS receiver at a given time and therefore computed for all the satellites as only one unknown. Moreover, studying and understanding the azimuthal distribution of the tropospheric delay increases the ability of sensing the atmosphere with GPS (Elgered et al., 2018). The densification of the GPS networks like Continuous Operating Reference Stations (CORS) in North America, Europe (EUREF Reference Frame Sub-Commission for Europe Permanent Network - EPN; Bruyninx et al., 2012), Japan (GeoNet; Sagiya, 2004) and South America (SIRGAS-CON; Brunini, 2007), have strengthened the application of the tropospheric gradients on the study of mesoscale distribution of RESEARCH ARTICLE 10.1029/2018EA000527 Key Points: • Major hurricane over dense GPS network gives unique opportunity to study ZTD gradients • The ZTD gradients show changes in orientation and magnitude when synoptic front approaches Correspondence to: V. Graffigna, vgr[email protected] Citation: Graffigna, V., Hernández-Pajares, M., Gende, M. A., Azpilicueta, F. J., & Antico, P. L. (2019). Interpretation of the tropospheric gradients estimated with GPS during Hurricane Harvey. Earth and Space Science,6, 1348–1365. https://doi.org/10.1029/2018EA000527 Received 31 DEC 2018 Accepted 2 JUL 2019 Accepted article online 8 JUL 2019 Published online 7 AUG 2019 ©2019. The Authors. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. GRAFFIGNA ET AL. 1348 Earth and Space Science 10.1029/2018EA000527 atmospheric variables, typically not well monitored (Boniface et al., 2009). Several projects have been pursuedto study thissubject,starting as early asin the 1990s (GPS/MET fromUCARin1993) until now [ESSEM COST Action ES1206/GNSS4SWEC or E-GVAP [the EUMETNET EIG Global Navigation Satellite Systems (GNSS) water vapor programme] dealing with the usage of ground-based GPS delay in operational meteorology) . Zhang et al. (2015) have found that thanks to the dense GPS networks, Victorian CORS in this case in Australia, it was possible to follow a synoptic signature of the dynamics of the event and offer precursors to severe weather with tropospheric parameters derived from GPS observations. On a global scale, the tropospheric gradient vector appears pointing toward the equator, and annual and semiannual frequencies are usually detected on long time series (Meindl et al., 2004). However, this behavior can change locally and when strong convection takes place or when the topography appears rugged (Karabati´ c et al., 2011; Shoji, 2013; Shoji et al., 2004). An important question that is still open and that several recent works have tried to answer is to what extent the horizontal tropospheric gradients contain real tropospheric information. Many studies have been developed and showed that horizontal gradients from ECMWF (European Centre for Medium-Range Weather Forecasts) and water vapor radiometers (WVR) do agree with GPS-estimated ones at the level of 0.5 mm for ECMWF and with a correlation of about 50% with WVR. See, for instance, Kaˇ cmaˇ rík et al. (2017), Dousa et al. (2017), Lu et al. (2016), Li et al. (2015), and Bar-Sever et al. (1998). Morel et al. (2015) have studied the behavior of the tropospheric gradients in Corsica island and have found that they can be influenced by both the slope of the relief and land/sea contrast in a mean year behavior. Indeed, more study on the subject is still required to understand their physical meaning. More recently, Elgered et al. (2018) have found that linear horizontal gradients derived from GPS are related to meteorological phenomena and that if any linear trend is detected, then it is likely to be related to monumentation or receiver problems. Implementation of tropospheric gradients can be treated as a piecewise linear function or assumed constant for a significant period of time, as in GAMIT (Herring et al., 2006) from Massachusetts Institute of Technology or Bernese (Dach et al., 2015) from University of Berne. This strategy can provide ngradients per day, which can assure convergence and stability on the processing, where the resulting parameters are somehow averaged over the period. However, high-resolution gradients are needed to contribute to heavy rainfall nowcasting (Shoji, 2013), and they can be estimated with higher frequency, as an epoch-wise dependent parameter, for example, random walk (stochastic process) like in GISPY-OASIS (GNSS-Inferred Positioning System and Orbit Analysis Simulation Software package (Bar-Sever et al., 1998), from here on called GIPSY) from the Jet Propulsory Laboratory. In this work we have pursued the latest method, because we want to be able to capture sudden variations of the gradients, like prominent peaks, not necessarily linear which can be associated with synoptic fronts (Lu et al., 2016). Therefore, we have modified an in-house software to estimate horizontal gradients as an stochastic variable, adding a pair of unknowns per epoch to the system. We will show the corresponding agreement with respect to an external source that has implemented independently the same methodology. Over the last past decade a lot of effort has been put on precise quantification of atmospheric parameters with space and ground techniques aiming to support weather forecasting (see, e.g., De Haan, 2013). The ZTD has played an important role on forecasting the weather, and its assimilation into weather systems is an important issue to assess (Poli et al., 2007). Many analysis centers nowadays are producing and disseminating real-time ZTDs, and the effort has shown to improve monitoring severe storms conditions, like for instance the Geodetic Observatory Pecný (Dousa & Vaclavovic, 2014). Karabati´ c et al. (2011) have shown that introducing ZWD to weather front analysis can forecast heavy rainfall better than only by using ground meteorological data, due to the fact that GPS derived parameters do not present a delay like those from meteorological ground stations and the improvement can be seen specially during the summer. Horizontal tropospheric gradients have become of interest for such applications, and the effective assimilation by the centers of these values into their predictions is yet an open scenario. In this sense, data assimilation algorithmsarebeingdevelopedinorder to assess the improvement on the refractivityfieldbymeansofincorporating horizontal delay gradient in addition to ZTD (Zus et al., 2019). The temporal and spatial resolution of GPS observations as long as epoch-wise parameter estimation set a potential improvement on forecasting events. Hence, precise determination of gradient delays and realistic interpretation of their variability is needed before assimilating them. GRAFFIGNA ET AL. 1349 Earth and Space Science 10.1029/2018EA000527 Figure 1. GPS Network selected for the study and track followed by Hurricane Harvey's eye in red. Annotated as dd.dd are the days of August of 2017 (UTC) of the eye's position. The isolines correspond to the moment of the landfall pressure field, and the units are in hectopascals. Note: arp8 and txpo are sites located at 1-km distance but have been plotted separated for clarity of the map. txpo is on its actual location. In this contribution we are going to assess the possible relationship that the horizontal gradients derived from GPS data processing can have with physical processes. In this case we have selected a hurricane that made landfall around 03:00 UTC on 26 August (DOY [day of year] 238) 2017, Hurricane Harvey, at peak intensity on the southern coast of United States with winds of 215 km/hr and an atmospheric pressure of 937 hPa. The isolines in Figure 1 represent the pressure field at DOY 238 at 00 hr. Harvey originated on 12 August (DOY 224) over the eastern Atlantic Ocean just west from northern Africa and traveled westward becoming a tropical storm on the 17th (DOY 229) of the same month. The system continued its motion entering the Caribbean Sea on the 18th striking land several times on different islands and the Gulf of Mexico later on the 23rd (DOY 235) with a significant low surface pressure. This hurricane became the first major one to make landfall in the United States since Wilma in 2005 and, as it is known, GPS receivers are mostly located on ground and very few ones are found offshore; therefore, monitoring this type of storms with this method is unlikely, due to rapid weakening of its intensity when touching land. CORS network is located and densified in the area where Harvey mostly occasioned disaster, and its permanent receivers have already been used to study this event. Milliner et al. (2018) have been able to use this feature to track how much of the water it brought was absorbed by the ground and how much it drained rapidly to the sea, finding that that a third of Harvey's total stormwater was captured on land, indicating that the rest drained rapidly into the ocean, with the remaining stored water gradually lost over the following 5 weeks. We have selected 11 GPS receivers from CORS network, chosen to capture the behavior of the landfall of the hurricane. Considering the track showed in Figure 1, plotted in red numbers denoting the day of August of the eye's position, we have selected sites on one and other side of the path the storm followed on ground. The 11 sites and their positions are listed in Table 1, together with detailed information about the GPS site. We have selected them rather aligned with the front, and more over the northeast region above the track of the hurricane, where the strongest intensities are to be expected. We have also added two more stations further away from the cyclone to test how they were affected. One of the main motivations of this work is to detect and characterize early stages of a hurricane on the tropospheric gradients in order to assess if anomalous (not typical) patterns on the gradients are related to the state previous to the development of the low pressure center so called cyclone. GRAFFIGNA ET AL. 1350 Earth and Space Science 10.1029/2018EA000527 Table 1 Ellipsoidal Coordinates of the Selected Sites for the Experiments, Detailed Information About the GPS Sites, and Baseline Lengths Between Reference Station txan and Given Site Site Longitude (◦) Latitude (◦) Height (m) City GPS receiver GPS antenna/dome Baseline (km) sam2 −97.83647886 30.23901344 212.801 Oak Hill TRIMBLE NETR9 TRM57971.0/NONE 109,566988 lcsm −97.12548843 30.00845332 74.000 Smithville LEICA GRX1200+GNSS LEIAR10/NONE 151,414801 txan −98.57663350 29.49120649 265.062 San Antonio TRIMBLE NETR9 TRM57971.00/NONE 0 txen −99.85998169 31.21745586 608.351 Eden TRIMBLE NETR9 TRM57971.00/NONE 228,01.690 txab −99.75681092 32.50325278 489.758 Abilene TRIMBLE NETR9 TRM57971.00/NONE 353,221676 txha −96.92180618 29.45108699 63.834 Hallettsville TRIMBLE NETR9 TRM57971.00 /NONE 160,234003 txho −99.13444043 29.34385895 249.876 Hondo TRIMBLE NETR9 TRM57971.00/NONE 56,450824 txct −99.24462706 28.44208356 112.631 Cotulla TRIMBLE NETR9 TRM57971.00 /NONE 133,516290 txkc −97.90430947 28.87388094 111.246 Karnes City TRIMBLE NETR9 TRM57971.00/NONE 94,707800 txpo −97.06990232 27.83945659 −19.432 Port Aransas TRIMBLE NETR9 TRM57971.00/NONE 235,201219 arp8 −97.05922454 27.83836206 −15.081 Aransas Pass TRIMBLE NETR9 TRM41249USCG/SCIT 235948.629 Note. All stations are located in the United States, in the state of Texas. This article is organized as follows. We first detail our methodology for processing the GPS data and introduce the in-house software and its validation. Then we draw a simple method for finding anomalous peaks on the horizontal tropospheric gradients time series. In section 3.1 we show the behavior of the horizontal gradients during the event. The conclusions are described in section 4. 2. GPS Processing and Validation 2.1. TOMION Software The TOmographic Model for precise IOnospheric sounding and GNSS Navigation (TOMION) is fed with global GPS data in order to compute in real time and in postprocessing, among others, geodetic parameters, such as site coordinates, ZTD, global Vertical Total Electron Content maps (Roma-Dollase et al., 2017), carrier phase ambiguity fixing (Hernández-Pajares et al., 2003), etc. The GPS computations in this research have been done based on TOMION geodetic estimation mainly developed by the second author during the last 20 years. Although the first approaches were focused on the tomography of the ionosphere, TOMION indeed acquired further features for estimating geodetic and atmosphere parameters. The background for this software on tropospheric estimations (Hernández-Pajares et al., 2001) indeed sets a potential real-time assessment of precise tropospheric gradients as well. However, back then, the strategy used was Wide Area Real-Time Kinematic (WARTK; see Hernández-Pajares et al., 2002; Hernández Pajares et al., 2010), while for this work we have used absolute positioning mode. In particular, we have applied Precise Point Positioning (PPP) as it is developed by Zumberge et al. (1997) for estimating the tropospheric parameters used for this work, and WARTK to compare and validate the new results, since the latter is extensively known. 2.2. Linear Horizontal Gradients in TOMION The parameter estimation can be summarized as follows. The linearized prefits residuals (“observed minus computed”) for a PPP setup, for the Iono-Free Combination can be expressed as 𝛿PC=xsat −xrec0 𝜌sat rec0 Δx+𝑦sat −𝑦rec0 𝜌sat rec0 Δ𝑦+zsat −zrec0 𝜌sat rec0 Δz+ct r(rec)+Tsat rec and 𝛿LC=xsat −xrec0 𝜌sat rec0 Δx+𝑦sat −𝑦rec0 𝜌sat rec0 Δ𝑦+zsat −zrec0 𝜌sat rec0 Δz+ct r(rec)+Tsat rec +𝜆wsat rec +BC, (1) for the code and the phase observables, PCand LCrespectively. In our experiments, we have taken the final coordinates of a PPP static 2-day run as a priori coordinates, computed for the sites with TOMION for the days previous to the window we are analyzing here, that is, for DOYs 229 to 230. Therefore, xrec0,yrec0, and zrec0are the a priori coordinate for the given site and 𝜌sat rec0denotes the distance between the satellite (sat) and the a priori coordinate for the site (rec0), while xsat,ysat, and zsat are the satellite's coordinates. In equation (1) also cis the speed of light, BCis the Iono-Free ambiguity (integer part plus noninteger components of the GRAFFIGNA ET AL. 1351 Earth and Space Science 10.1029/2018EA000527 Figure 2. TOMION's implementation of tropospheric corrections. In blue are the external parameters needed for feeding the models in red. In yellow are TOMION's tropospheric estimations. ahand aware the hydrostatic and wet mapping functions continued fraction form (mh/w) coefficients, respectively. Psis the surface pressure, esis the water vapor partial pressure at mean sea level, Tmis the weighted mean temperature at height H(orthometric) along the local vertical, and 𝛺is the water vapor decrease factor with height. The constants K2′=K2−K1(Rd∕Rw)and K3are empirically determined first by Thayer (1974). Rdis the specific gas constant for the dry constituents, and Rwfor the wet ones. The gm, which is the gravity acceleration at the mass center of the vertical column of the atmosphere, can be computed as a function of the locations' latitude and Hc, which is the height of the center of mass of the vertical column of air. All the meteorological information required for the models aforementioned, including the coefficients for the mapping functions, have been taken from a model available at GGOS (2017). TOMION = TOmographic Model for precise IOnospheric sounding and GNSS Navigation ZTD = zenith tropospheric delay; ATD = asymmetrical tropospheric delay; DOY = day of year. instrumental delays from receiver and transmitter); 𝜆the wavelength; wis the wind-up and tris the receiver clock error. The terms 𝛥x,𝛥y, and 𝛥zare the corrections to the a priori values to be estimated. The delay induced by the troposphere on GPS signals, Tsat rec in equation (1), herein called T, can be modelled as: T=md(𝜀)ZHD +mw(𝜀)ZWD +mg(𝜀)[GNcos(𝛼)+GEsin(𝛼)].(2) according to Chen and Herring (1997). The first term in equation (2), The zenith hydrostatic delay (ZHD), has been modelled in TOMION following Saastamoinen (1972). The zenith wet delay (ZWD) has been approximately computed according to Askne and Nordius (1987). The mapping function used for this processing has been Vienna Mapping Function (VMF1; Böhm & Schuh, 2004), according to the form in Marini (1972). Detailed description of the tropospheric corrections implemented on TOMION can be seen in Figure 2. For most applications, the first and second term in equation (2) provides enough accuracy for the user. However, for precise geodetic applications or under severe weather conditions, a third term can be considered: the asymmetrical tropospheric delay (ATD). In Figure 3 a simplification has been assumed for the sake of the approach but is valid for any direction. In this case the azimuth (𝛼in equation (2)) is set to 90◦, and Figure 3. Scheme of asymmetric tropospheric delay, where for simplicity of the figure, east-west section is represented. In yellow is what would be accounted for if azimuthal symmetry is assumed. In orange is the correction for asymmetry. 𝛽is the tilting angle of the neutral atmosphere as defined in Meindl et al. (2004), and miso is the isotropic mapping function (VMF1). ZTD = zenith tropospheric delay. GRAFFIGNA ET AL. 1352 Earth and Space Science 10.1029/2018EA000527 Table 2 Processing Specifications for the Four Experiments Carried Out Solution Specific settings Resolution PPP static Coordinates as random variables (constant) 15 min PPP kinematic tight Coordinates as random walk parameters 0.3 mm/√h15 min PPP kinematic loose Coordinates as random walk parameters 3 mm/√h15 min Relative Coordinates as random walk parameters 3 mm/√h30 s Note. PPP = Precise Point Positioning. only the east gradient (GE) is different from 0 and greater than 0. Here, the atmosphere would be “thicker” toward the east of the station and “thinner” over the west. The ATD is also mapped into the zenith by: mg(𝜀)= 1 sin(𝜀)tan(𝜀)+C,(3) proposed on Chen and Herring (1997). Here only the elevation angle is needed for computations and C is an empirical constant taken equal to 0.032, as suggested on the reference. In TOMION what are left as unknowns for constructing the Tterm are the residual ZWD, which means that the model on Askne and Nordius (1987) would take place as an priori value for the estimate, and GNand GEcomponents, for the ATD term. Then for a PPP, using the iono-free combination, for which more than 99 % of the ionospheric induced error is typically eliminated, for static antennas and P1and P2observables, our unknowns are reduced to X=[ΔxΔ𝑦Δzt rZWD GNGE](4) which are computed per epoch of observation, where the information a priori is available, which is 15 min for PPP and 30 s for relative. 2.3. Validation Test In this work we have carried out four experiments. First, we have performed three different PPP processing strategies: static and kinematic, where this last one was set up for two different random walk processes for the site's coordinates, 3 and 0.3 mm∕√happroximately. We are referring to them from now on as loosely and tightly constrained, respectively. These process noise are very small and equivalent to up to 10and 1-cm coordinate displacements over a period of 2 weeks respectively, for events similar to Harvey (see, e.g., Miyazaki et al., 2003). As it is stated in Zumberge et al. (1997), precise final orbits and satellite clocks are needed for these implementations that have been taken from the International GNSS service, with a resolution of 15 min. Thus, the spacing of our estimates will be set to 15 min as well. Relative positioning was only carried out in loosely constrained kinematic mode (only for 3 mm∕√happroximately), because we will use this experiment for assessing the PPP ones. Since the clock is eliminated in the double differences, the interval between two consecutive estimates is 30 s, which corresponds to the sampling rate of the observations for this case. For the baseline configuration, we have chosen txan as the reference station as it is located in the center of the selected network, as can be seen in Figure 1. Pairs for differentiating only with respect to reference station have been included in the computations having baselines ranging from 56 to 353 km. Detailed distances can be seen in Table 1. Both for PPP and relative we have discarded observations below 7◦over the horizon, and the weighting function of the observations has been considered as a negative exponential of the elevation angle of the transmitter. All four experiments depicted in Table 2 have been analyzed in Appendix A; the methodology was validated by studying the repeatability of the sites coordinates, where it is known from previous studies that accounting for the gradients on GPS processing causes a better repeatability (see, e.g., Bar-Sever et al., 1998; MacMillan, 1995). Accordingly, it was observed that for all the receivers in our study, the repeatability improves about 25% when the gradients are estimated. Moreover, we have also tested the repeatability for different processing strategies and modes: absolute and relative positioning in static and in kinematic modes. We have found that the looser the constrains on the coordinates, then the more affected the coordinates are when neglecting the gradients. Moreover, relative positioning showed to be more sensitive to not GRAFFIGNA ET AL. 1353 Earth and Space Science 10.1029/2018EA000527 Figure 4. TOMION and UNR tropospheric east (left) and north (right) gradients for sam2. (top row) Correlation and coefficients in annotations at the bottom right. Linear regression at the top left. (bottom row) Time series from both sources. TOMION = TOmographic Model for precise IOnospheric sounding and GNSS Navigation; UNR = University of Nevada, Reno; DOY = day of year. considering the gradients than absolute positioning. We have also seen that the horizontal gradients differed under 1 mm among all the procedures; hence, any set of gradients was valid for the study of the dynamics of the hurricane. With these statistics we were able to say that we can rely on our in-house software, since we have internally validated it obtaining consistent and comparable results with different modes and strategies. 2.4. Validation Versus UNR Products For validating and comparing TOMION's estimates, UNR (University of Nevada, Reno, USA) products (Blewitt et al., 2018) have been downloaded from its server, which are provided with a 5-min sampling rate. Comparisons were performed for 10 of the 11 sites studied (lcsm was not available), and correlations coefficients of 0.57 and 0.62 were found for the east and north gradients, respectively. The linear regression performed between the TOMION and UNR east gradient time series resulted in 0.46 mm/mm for the slope and 0.22 mm for the independent term, while that for the north component resulted in 0.55 mm/mm and 0.11 mm. These results imply that there are no significant biases between the series. The discrepancies found between the different sources can be explained by the fact that the external source applies flat weighting on the observations, while TOMION makes use of negative exponential of the elevation angle of the transmitter. Another cause of scale differences can be the different mapping functions used for the gradient term: Chen and Herring (1997) in TOMION and Bar-Sever et al. (1998) in GIPSY, and as it is stated in Kaˇ cmaˇ rík et al. (2018), systematic errors effects of up to 0.3 mm were observed in estimatedtroposphericgradientswhenusing differentgradientmapping functionswhichdependon theapplied observation elevation-dependent weighting as well. Furthermore, in TOMION, we use VMF1, whereas UNR adopts GMF (Global Mapping Function; Böhm et al., 2006) for mapping the symmetric term (mdand mwin equation (2)). The temporal evolution of the two series canbe seen in the bottom row in Figure 4, where one can appreciate that they are in in great coherence. Also, there is a slight time delay of TOMION's estimates with respect to the reference, which could be a reasonable explanation for the correlations coefficients estimated. The aspect that we want to remark here is that UNR gradients as long as TOMION's estimates are able to detect anomalies, which will be the focus of our study. For example, such gradients can be appreciated on sam2 north parameter, almost at UTC midnight for DOY 236. GRAFFIGNA ET AL. 1354 Earth and Space Science 10.1029/2018EA000527 Figure 5. Time series of the ZTD for the 11 sites used for this experiment: (top) the sites on the coast and the ones further away; (bottom) the rest. For clarity of the plot, the mean of each series has been subtracted. In this section we have introduced the software we are using for our computations, TOMION, and briefly explained the processing strategy. Then we have validated the estimations with an independent source (UNR) and with an independent strategy within the same software (relative positioning) which has been detailed in Appendix B. Even though there are some differences, the results and the estimated parameters show to be coherent between the different softwares or modes. Now we will proceed to analyze the behavior of the time series. 3. The Hurricane Harvey Test Case 3.1. ZTD The ZTD is the main variable estimated with GPS that contains information of the lower atmosphere, and we have observed clear patterns on it evidencing the advance of the storm toward the area. The evolution of the ZTD over DOYs 231–239 for the 11 sites are plotted in Figure 5, where the relative variation of the ZTD shows an increase of about 10 to 15 cm over the 9-day time window. We have plotted in the top panel the ZTD for four sites, two on the coast and two further inland: arp8,txpo,txen, and txha. The bottom panel corresponds to the other seven sites. Such a distinction has been done because their behavior is slightly different: The sudden increase noticed over midnight of DOYs 235 to 236 is larger for the subset of the bottom panel than that of the top. This increment clearly reflects the effect of the hurricane. This behavior is due to the increase of the partial pressure of water vapor (Seco et al., 2009), which is closely related to the ZWD (Askne & Nordius, 1987). Decreasing surface pressure values, that is, in a cyclone, cause a smaller ZHD (Saastamoinen, 1972); hence, the increase on the ZTD is due to the increase on the water vapor partial pressure. We have analyzed the nature of the ZTD, and we define the Quiet state to a set of data where the atmosphere was relatively calm within the analyzed window. The criterion to split the series was the time for which the detrended ZTD reached an absolute maximum. As it can be seen in Figure 6, this time label was found to be approximately DOY 235.27 for sam2. Therefore, Quiet state is before such time and Stormy is after sam2, within days 232 and 238 inclusive of 2017, that is from 19 to 26 August. In this figure, we have also added the east and north horizontal gradients, which will be studied in detail in the following section. GRAFFIGNA ET AL. 1355 Earth and Space Science 10.1029/2018EA000527 Figure 6. ZTD for sam2 in DOYs of 2017, detrended ZTD (scaled by a factor of 100 to fit with the scale) and east and north gradients. The left yaxis contains the values for  Z(t)and east and north gradients, and the right yaxis for the ZTD. We have considered a detrended ZTD (Hernández-Pajares et al., 2012) as  Z≡ZTD(t)−1 2[ZTD(t+Δt)+ZTD(t−Δt)](5) where 𝛥twas chosen as 24 hr, to mitigate effects of the local time, since we are subtracting from the ZTD value, the mean of the previous day and the following day. Each time tag found for each site, denoted as DOY ZMAX , is depicted in Table 3 together with the maximum of ZTD series and its reference time, as well as the relative increment of the ZTD before and after DOY ZMAX . The increase was found to be between 3.4% and 4.7% for 9 of the 11 sites. The other two, txen and txab, are the receivers located further away from the hurricane, which can be appreciated on the distance of the sites to the track of the hurricane. This increase in the mean of the ZTD, given by an increase on the ZWD, shows the heavy rains the area suffered after the hurricane struck land and weakened. In addition we have added the mean of the ZTD before and after DOY ZMAX . It was also found that the maximum of the entire ZTD series of each station was found between 2 and 4 days after DOY ZMAX , which shows that the water vapor actually accumulated after the hurricane hit Texas. Table 3 Time Tag for the Maximum of the Directional Derivative of the ZTD Site DOY ZMAX ZTDQZTDSDOYZTDMAX MaxZTD % of change Distance to the track arp8 235.948 2.579 2.650 237.760 2.726 4.0 114.501 txpo 235.833 2.580 2.670 237.802 2.743 3.5 115.3 txkc 235.260 2.527 2.645 238.885 2.678 4.7 255.608 txha 235.229 2.552 2.670 238.333 2.713 4.6 271.077 txct 235.302 2.526 2.611 238.729 2.663 3.4 329.044 lcsm 234.927 2.542 2.655 238.917 2.731 4.4 335.772 txan 235.438 2.473 2.571 238.594 2.611 4.0 350.016 txho 235.802 2.484 2.574 237.729 2.660 3.6 376.465 sam2 235.270 2.490 2.597 238.521 2.647 4.3 382.459 txen 233.760 2.375 2.441 238.760 2.485 2.8 576.211 txab 233.896 2.421 2.458 237.781 2.523 1.5 689.042 Note. Mean for the period with storm and without, ZTD's maximum and the relative change during the storm for the ZTD. Note that the table has been ordered with respect to the minimum distance to the track, which is expressed in the last column. Units in DOYs of 2017 and meters, except for distance to track which is in kilometers. ZTD = zenith tropospheric delay; DOY = day of year. GRAFFIGNA ET AL. 1356 Earth and Space Science 10.1029/2018EA000527 Table A1 Relative Bias, SD, and RMS of the Coordinates for the Different Processing Modes for All the Stations Metric 𝛤Metric 𝛬 Period Strategy 𝛤Bias 𝛤SD 𝛤RMS 𝛬Bias 𝛬SD 𝛬RMS 231–239 PPP Static 0.87 0.88 0.87 0.88 0.88 0.88 231–239 PPP Const. 0.74 0.76 0.75 0.72 0.69 0.72 231–239 PPP Loose 0.71 0.72 0.72 0.73 0.71 0.73 231–239 Relative 0.65 0.74 0.68 0.70 0.70 0.70 51–59 PPP Static 0.88 0.89 0.89 0.89 0.94 0.90 51–59 PPP Const. 0.75 0.65 0.73 0.75 0.69 0.73 51–59 PPP Loose 0.84 0.88 0.84 0.84 0.88 0.85 51–59 Relative 0.66 0.81 0.68 0.73 0.81 0.74 Note. First four rows correspond to the Hurricane Harvey DOYS, and the four last rows to a quiet period during the winter of the same year 2017. SD = standard deviation; RMS = root-mean-square; PPP = Precise Point Positioning. We have chosen simple statistical measures to evaluate how each processing mode is affected by the estimations of gradients. In the first place, we have considered the mean of the ratios Rof the biases of the coordinates with and without gradients with respect to an priori coordinate, computed with and without gradients, respectively. This metric is represented by the definition at 𝛬, while 𝛤is given by the ratio of the means of the biases (b) for each methodology, that is, considering and not considering the gradients: Λ= 1 N N ∑ i Riand Γ= 1 N N ∑ i bgrad i 1 N N ∑ i bnograd i ,(A1) where Nis the number of sites, 11 in this case. For the RMS and the SD (standard deviation), the analogous procedure has been performed. These metrics have been computed for all of the sites and are depicted in the first four rows of Table A1. For both metrics, and for all processing modes, the position accuracy will be degraded by from 12% to 35% if horizontal symmetry of the atmosphere is assumed, in the presence of a weather front, for the period of the hurricane and from 6% to 34% for the winter period, considering their bias, SD, or RMS with respect to an a priori coordinate. We can also appreciate in the last four rows of the same table that, for the analysis during the winter, the implications of not considering the gradients is slightly less important than when strong meteorological forcing occurs. The differences between gradients computed for the different processing modes are under the statistical error of the estimations. This means that the different setups chosen for the coordinates do not have a significant impact on the horizontal gradients. We have chosen the gradients computed on the loosely constrained mode for the coordinates to analyze if they represent the behavior of the atmosphere during the hurricane. Hence, we have been able to reproduce established results regarding the stability of the site's coordinates, for most of the cases in all the setups proposed. The WARTK methodology, widely validated, presents results analogous to that of PPP; therefore, we can conclude that our results are consistent. Also, we have shown that neglecting the gradients has more impact the looser the kinematic processing is, and slightly even more for relative mode. The reason why differentiating the observables can show to have more impact on the stability of the processing can be the baselines aligned with the front accumulating more asymmetric delay than those orienting perpendicular to it (Ichikawa et al., 1995). Appendix B: TOMION's Horizontal Gradient Intra-Software Validation Figure B1 shows the coherence between TOMION horizontal gradients for absolute and relative processing mode, both for kinematic in its loosely constrained setup. For each epoch where the estimation of the north and east tropospheric gradients were available for both processing modes, which is every 15 min, the horizontal absolute value of the gradients was computed, as the square root of the addition of the squared components, and a correlation of 62% was obtained for the time series. GRAFFIGNA ET AL. 1363 Earth and Space Science 10.1029/2018EA000527 Figure B1. Correlation between magnitude of TOMION horizontal gradients in relative and in absolute mode for kinematic processing, with process noise equal to 3 mm∕√h. Correlation coefficient annotated at the bottom right, denoted as Rrel. TOMION = TOmographic Model for precise IOnospheric sounding and GNSS Navigation; PPP = Precise Point Positioning. 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