Keywords

1 Introduction

Starting as a revolutionary theoretical possibility (Bevis et al. 1992), ground based Global Navigation Satellite System (GNSS) has turned into a contributor to weather forecast through assimilation of zenith total delays (ZTD) into numerical weather prediction (NWP) models of meteorological services [e.g., The UK Met Office (Bennitt and Jupp 2012), and others (Mascitelli et al. 2021)]. The collection of GNSS observations dates to the mid-90s with a growing number of stations distributed in permanent global and local networks being established since then. As a reference, we can take the year 1994, the start of IGS as an operational entity (Johnston et al. 2017), as the initial epoch of the continuous data collection. As time series grow longer so does the potential contribution of ground GNSS to climate. Such potential was one of the topics of an important COST Action (European Cooperation in Science and Technology) project (Bock et al. 2018). Essential questions follow: Are we, as a geodetic community, ready to contribute to climate? Are time series of GNSS-generated tropospheric parameters, ZTD, zenith wet delay (ZWD) and gradients good representation of long-terms for climate studies? Are there defined models and procedures for a dedicated estimation of such parameters? Are there established mechanisms for quality control? A reminder that VLBI (Very Long Baseline Interferometry) technique, even though not continuous, started earlier than GNSS.

This paper discusses the methodology and data sets used in the study currently going on within IAG JWG C.2: Quality control methods for climate applications of geodetic tropospheric parameters, as well as presents an early result based on station ALBH. In it, we define the concept of climate normals and the importance of long-term series, we revisit the growing importance of GNSS for meteorology and climate and present the overall strategy used in the research. Results are then presented and discussed, and lessons learned conclude the paper.

2 Climate Normals and the Importance of Long Terms

Climate scientists consider an average in weather taken over a 30 year-period, known as climate normals, as enough to evaluate climatological variables including temperature and precipitation, for a particular site. Under a stationarity assumption, the climate normal is long enough to smooth out year-to-year interannual fluctuations and short enough to represent climatic trends (WMO 2007).

Fig. 1
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IWV trend variations (kg/m2/a) at Wettzell, Germany from ERA5 data

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The integrated water vapour (IWV), defined as the total mass of water vapor along a cross-section of 1 m2 from the station till the topmost layer of the atmosphere, is an important meteorological quantity because it is related to changes in the temperature and the formation of clouds. This and the integrated precipitable water vapor (IPWV), or just precipitable water (PW) can be derived from GNSS estimates of ZWD.

Figure 1 illustrates the importance of long terms. Trends in IWV were computed based on ERA5 (ECMWF 2019) data (1979.0–2019.0). Given the time series, we vary the first and last epoch when estimating the trend together with some seasonal harmonics (the minimum duration set to 10 years) with a step of 1 month. The colour bar indicates the variation in trend values. Two red empty circles connected by a red line indicate where the climate normal falls within the 30-year period, varying from the ‘1979–2009 climate normal’ to the ‘1989–2019 climate normal’ trends. The figure indicates that if we compute the normals using a shorter time span, such as 10 years, the trends values would be different. It is worthy of note that IWV trend variations as a function of the data span are more prominent should the seasonal component be ignored in the estimation process, especially if the data span deviates significantly from an integer factor if the dominant period inherent in the signal (typically the annual cycle).

The World Meteorological Organization (WMO) recommends 30-year normals and decadal updates, making it usual to find intermediary values (WMO 2007). For example, NOAA (National Oceanic and Atmospheric Administration) provides annual/seasonal normals, monthly normals, daily normals and even hourly normals. Climate normals can be computed in different ways (WMO 2011) but the data needs to go through stringent quality control and be made “self-homogeneous.” To be sure (from a statistical viewpoint) that a small trend is valid, one might need even more than 30 years (Alshawaf et al. 2018).

Figure 2 shows a climograph. A climograph is a graphical representation of climatic parameters, such as monthly average temperature and precipitation, at a certain location. It is used for a quick view of the climate of a location. This climograph for station Addison, in Alabama, US, shows monthly normal values of precipitation, and temperature (minimum, medium and maximum).

Fig. 2
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Climograph from Station Addison, AL, USA, 1991–2020 (Courtesy, NOAA)

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Considering that the IGS started in 1994, in 2024 it will be 30 years. Are we ready?

3 Ground-Based GNSS for Meteorology: From Zero to Hero

Ground-based GNSS for meteorology has come a long way. In the beginning of the GNSS era, the meteorological community saw it with caution, sometimes with disbelief. In the early 1990s, an unmentioned meteorologist even stated, “There is no information of any quality that GPS can provide to weather analysis or forecast.”

Nearly 30 years later, the consideration given to GNSS is very different. For example, during the December 2017 EGVAP Expert Meeting, Owen Lewis, from the UK Met Office, referred to ground based GNSS as the one providing the “second best observation impact among the various types of observations.”

The GNSS-derived information that has found major use by the meteorological services for weather forecast is ZTD. The reason is simple to understand. As we are aware, from ZWD we can derive IWV and PW. However, the computation from ZWD to IWV requires water vapour-weighted mean temperature of the air column above the GNSS station, which depends on the vertical profile of temperature and humidity, at times not easily available.

In terms of climate, atmospheric water vapour is of great significance, as it is the major greenhouse gas. Therefore, the importance of its accurate, long-term monitoring and evaluation of trends and variability, potentially serving as independent benchmarks to climatological models. Climate scientists would love to have longer trends derived from GNSS, but also shorter trends, which could be used for assimilation and validation of climate models.

In the study that follows, we deal only with ZTD.

4 Research Questions

There are four underlying research questions we would like to tackle.

“Anyone can generate ZTD trends. How reliable are they?” One may think that it is, or that it tends to be as computational advances, easy to compute a long time series and derive trends from that. Let us work under this hypothesis. If so, anyone could feed GNSS trends to the climate community. But it is not just a question of estimating trends, but estimating trends that contain the proper information. This fosters another question.

“Can we define metrics to ascertain the quality of long-term trends provided to the climate community?” The word metrics here is used meaning standards of evaluation. That could involve from the treatment of input data, processing models and proper ways to determine trends, in such a way that they are meaningful to the climate community.

As far as processing modes are concerned, precise point positioning (PPP) seems to be a very attractive way to deal with the problem at hand. For example, the IGS tropospheric products are generated via a dedicated PPP processing. At the same time, the IGS Analysis Centers are in a continuous processing effort, and each one of them provide solutions that can be either used independently or cross-evaluated as a tool of quality control. We could, or probably, should, use the ZTD resulting from the IGS Analysis Centers, even considering that not all provide that, but a good number of them do that anyway, or per request as in the case of the REPRO3. This fact brings the fourth questions. “Are there advantages of combining ZTD estimates over not combining them? Is there any ‘loss of information’ if they are combined?”

Fig. 3
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Selectedstations

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Table 1 List of selected stations ordered by duration of operation (discounted gaps)
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Therefore, just looking from the ZTD time series derived by the IGS, either its tropospheric product or solutions generated by individual Analysis Centers, it is possible to estimate trends from each one of them. “Would there be difference in trends derived from them?” If so, that may have implication for feeding information to the climate community, either for validation or assimilation of models.

This WG wants to investigate that.

5 Methodology

A summary of the overall methodology is presented first, followed by a discussion on the only station dealt with so far, ALBH.

We take advantage of estimated ZTD resulting from the REPRO3 effort. The inclusion of ZTD estimates in REPRO3 followed from a request from the IGS to the Analysis Centers and represents a great opportunity for this study. A few problems arise though, namely, not all Analysis Centers provide ZTD, they do not use the same processing strategies and their output follow a different rate. At the end, six ZTD solutions were made available. In the sequel, each Analysis Center is represented by its three-letter code, followed by their own output rate: COD, 1 h; ESA, 1 h; GFZ, 1 h; GRG, 2 h; JPL, 100 s; TUG 5 m.

Dependency on the availability of REPRO3 was a delaying factor for the practical start of the work of this WG, but the wait was worthwhile.

The choice of using ZTD solutions resulting from REPRO3 brings a few challenges. The first one is that not all Analysis Centers provided ZTD, which narrowed down the number of ZTD time series to six. Another issue is that the Analysis Centers apply different strategies to their data processing. And, finally, their ZTD output rate is also different.

Besides REPRO3 ZTD estimates, we also used ERA-5 extracted ZTD, serving as a trustful independent reference. We plan to include the IGS ZTD product into the analysis as well, but it is not part of this paper.

We have selected a total of thirty-nine stations with long-term GNSS time series. They are distributed around the world to cover different climatic regimes. Some stations are relatively close to provide some extra level of comparison. Figure 3 present the location of the chosen stations. Table 1 lists the stations, ordered with the ones with longer operation period appearing first. The time shown discounts eventual interruptions or gaps during the period.

Each ZTD time series is then subjected to a process of homogenization (Klos et al. 2022; Van Malderen et al. 2020), using ERA-5 as reference. Homogenization is an important step to derive trends.

Following the homogenization, daily mean values are produced. The reduction to daily mean values is an attempt to accommodate the differences in strategies that each Analysis Center use. The daily mean values are computed using a simple weighted average using the ZTD standard deviation in the process. When available, the IGS final ZTD product in REPRO3 will go through the same process.

The next step in the methodology is to perform the combination among the six daily-averaged homogenized ZTD time series. We envision this process being done in two different ways, as a weighted mean of by computing the least median of squares (Rousseeuw 1984). The combination becomes both a separate time series for analysis and a testbed for quality control of each one of the Analysis Centers. A clarification may be needed here. We are using the term combination even though, among the geodetic community, this term mostly refers to an operation at the level of normal equations, which is not the case.

Now, the trends can be computed. For that purpose, three methods will be used: weighted least squares, robust estimation, and non-parametric estimation. The result shown in Sect. 5, only weighted least squares was used.

At this stage, there will be trends originated from each one of the six Analysis Centers, one derived from the combination, one derived from the IGS final product and one derived from ERA-5.

The final analysis of the trends will involve testing their statistical significance. Analysis in frequency domain will also be performed to understand, for a given site, how their frequency bands differ, what the largest discrepancies between trends are and how do they differ with those from the combined solution and ERA-5, here taken as a reference.

Fig. 4
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Homogenized GFZ ZTD times series of station ALBH, original rate (black dots) and their corresponding daily mean values (red dots)

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Fig. 5
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Homogenized daily mean ZTD times series of all six Analysis Centers and their combination. Colours: combination (black continuous line), COD (navy blue dot), ESA (sky blue dot), GFZ (green dot), GRC (pink dot), JPL (yellow dot) and TUG (red dot)

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6 Results: Station ALBH

As stated before, the results shown in this paper are for station ALBH.

Figure 4 portrays the homogenized ZTD times series of station ALBH, originally provided by GFZ. Black dots indicate homogenized ZTD in their original sampling rate, whereas red dots represent their corresponding daily mean values. Figure 5 displays the homogenized daily mean ZTD time series of all six Analysis Centers and their combination. Colours are indicated in the label.

A careful look at Fig. 5 indicates that there are data gaps in the original time series, which are reflected in the final homogenized daily means. The importance of this fact will be made clear in the sequence.

Table 2 summarizes trends as derived from the homogenized daily mean ZTD time series from each of the six Analysis Centers, and that of the combination. The table shows the trends (mm/decade), the annual amplitudes (mm), the annual phases (degrees), as well as the number of points involved in each solution. The last column indicates that the number of points are different, as the data collected at this particular station ended up being used differently by each Analysis Center. This difference may be the explanation of the large variation seen among the solutions based on different Analysis Centers. The inter-Analysis Center scatter is 1.25 mm/decade for the trends, 0.73 mm for the annual amplitudes and 1.99° for the annual phase.

Table 3 is like Table 2 with a major difference. The trends were computed only using the common epochs between all Analysis Centers, which caused the ZTD time series from ESA and JPL to be disregarded. The inter-Analysis Center scatter decreased to 0.47 mm/decade for the trends, to 0.11 mm for the annual amplitudes, and to 0.29° for the annual phase.

Table 2 Trend, amplitude, and phase of original ZTD time series
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Table 3 Trend, amplitude, and phase of the synchronized ZTD time series
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A simple look at the statistics shows us that the trend using TUG is slightly away from the mean at 1-sigma, whereas amplitude and phase from GRG are negligibly above the mean at 1-sigma. The reason for that was not established, perhaps some kind of jump that was not detected during the homogenization or such a difference could indicate that those parameters should not be used. Such an analysis lies within the discussion on establishing metrics to determine if a trend can be trusted or not. Further analysis will include the testing of the significance level of the parameters.

7 Lessons Learned

A few statements summarize the lessons learned in this study. The quality of the combination depends on processed data. Combination seems to bring benefits and is a tool for quality control particularly if gappy data are involved in the combination. It would be interesting to understand why some Analysis Centers did not process all data available, if similar happens for other stations too. The process is painstaking, but the effort is being continued and expanded. The overall goal is to have a final report presented during the XXVIII General Assembly of the International Union of Geodesy and Geophysics.