In the current era of accelerated sea-level rise, accurate measurements of relative sea-level change are critical to predict the conditions that coastal areas will face in the coming decades and beyond. Such measurements traditionally come from tide gauges, which provide the longest available instrumental records of relative sea-level rise (RSLR). Some of the oldest tide gauges have records spanning 150–200 or more years (e.g., Key West, USA, Maul and Martin, 1993; Brest, France; Świnoujście, Poland; New York, USA; and San Francisco, USA, Woodworth et al., 2011; and Boston, USA, Talke et al., 2018). Tide-gauge data have played a central role in calculations of global sea-level rise (e.g., Gornitz et al., 1982) and they continue to do so today (e.g., Church and White, 2011; Church et al., 2013; Hay et al., 2015).

Tide-gauge data are also heavily relied upon to evaluate the vulnerability of low-elevation coastal zones (LECZs) (e.g., Syvitski et al., 2009; Nicholls and Cazenave, 2010; Kopp et al., 2014; Pfeffer and Allemand, 2016). LECZs include large deltas and coastal plains that have often accumulated thick packages (tens of meters or more) of highly compressible Holocene strata and are home to some of the world's largest population centers (e.g., Tokyo, Shanghai, Bangkok, Manila) that are increasingly at risk due to RSLR. At the regional level, tide-gauge data have been used to study a variety of spatially variable processes. For example, in coastal Louisiana, the largest LECZ in the United States, tide-gauge data have been used to measure land subsidence (Swanson and Thurlow, 1973), the acceleration of RSLR (Nummedal, 1983), multi-decadal rates of subsidence and RSLR (Penland and Ramsey, 1990), and the impact of fluid extraction on RSLR (Kolker et al., 2011).

The Permanent Service for Mean Sea Level (PSMSL; http://www.psmsl.org, last access: 3 January 2019; Holgate et al., 2013) maintains records for nearly 2000 tide gauges globally, including 5 in coastal Louisiana: Eugene Island (data from 1939–1974), Grand Isle (1947–present), South Pass (1980–1999), Shell Beach (2008–present), and New Canal Station (2006–present). In many parts of the world, however, tide gauges with long, continuous records are few and far between. As a result, many studies of RSLR rely on tide-gauge records that are too short (longer than 50 years is preferable but at least 30 years is necessary to filter out natural variability due to phenomena such as storms, El Niño–Southern Oscillation cycles, changes in the orbital declination of the moon, shifts in ocean currents, and atmospheric pressure variability; Pugh, 1987; Douglas, 1991; Shennan and Woodworth, 1992), from inappropriate locations (e.g., outside of the area being studied), or both. For example, of the 32 tide gauges used by Syvitski et al. (2009), 21 were located outside the delta of interest, 11 had records of < 30 years, and 8 had both shortcomings. Furthermore, subsidence rates are highly spatially variable, often increasing or decreasing 2- to 4-fold within short distances (a few kilometers or less) as a result of subsurface fluid withdrawal and differential compaction, among other factors (e.g., Teatini et al., 2005; Törnqvist et al., 2008; Minderhoud et al., 2017; Koster et al., 2018; also see the review by Higgins, 2016). As a result, tide gauges provide limited information on subsidence rates beyond the instrument's immediate surroundings. Even if a tide gauge has a sufficiently long record and is appropriately located, it is critical to determine what processes the tide gauge is measuring and what it is not measuring. In LECZs, this is commonly not straightforward.

Tide gauges measure RSLR with respect to a nearby set of benchmarks. Leveling campaigns are conducted regularly (for example, at least once every 6 months for National Oceanic and Atmospheric Administration, NOAA, tide gauges; NOAA, 2013) to account for any changes in the elevation of the tide gauge with respect to these reference points. Tide gauges are typically leveled using a benchmark designated as the primary benchmark; secondary benchmarks are used to assess the stability of the primary benchmark (NOAA, 2013).

Figure 1 shows a schematic of tide gauges and associated benchmarks in three contrasting environments. Along rocky coastlines, benchmarks are typically anchored directly onto bedrock that is exposed at the surface (Fig. 1a). A tide gauge in such a setting therefore measures RSLR with respect to the land surface. In contrast, benchmarks in LECZs are typically anchored at depth. In thin LECZs, which are defined herein as those with unconsolidated sediment packages < 20 m thick, benchmark foundations typically penetrate the surficial layer of unconsolidated (usually Holocene) sediment and are anchored in the underlying consolidated (usually Pleistocene) strata (Fig. 1b). In thick LECZs, defined as possessing unconsolidated sediment packages that are > 20 m thick, benchmark foundations are generally not sufficiently deep to reach the consolidated strata and are anchored within the unconsolidated sediment (Fig. 1c).

Regardless of the environment, all tide gauges measure changes in water surface elevation with respect to the foundation depth of their associated benchmarks. As a result, tide gauges with benchmarks anchored at depth do not account for processes occurring in the shallow subsurface above the benchmark foundation (Cahoon, 2015). For the purposes of this study, we define the subsidence that occurs above a benchmark's foundation as “shallow subsidence” (sensu Cahoon et al., 1995). Subsidence below a benchmark's foundation is termed “deep subsidence”. In coastal Louisiana, at least 60 % of subsidence occurs in the shallowest 5–1 m (Jankowski et al., 2017). Tide gauges with benchmarks anchored at depth do not record this key component of RSLR (Cahoon, 2015). This issue was also recognized by Jankowski et al. (2017) and Nienhuis et al. (2017), but neither study elaborated on this problem. Here, we present a detailed assessment of benchmark information associated with tide gauges, followed by a discussion of its implications as well as methods to remedy this issue.

In order to better understand the contribution of vertical ground motion to RSLR, tide-gauge data are often used in conjunction with global navigation satellite system (GNSS) data (e.g., Mazzotti et al., 2009; Wöppelmann et al., 2009; Wöppelmann and Marcos, 2016; see also the Intergovernmental Oceanographic Commission manuals on sea-level measurement and interpretation, available at http://www.psmsl.org/train_and_info/training/manuals/, last access: 3 January 2019). In LECZs, GNSS stations are typically mounted on existing buildings or attached to rods that are driven to refusal (i.e., the depth at which friction prevents deeper penetration; see International GNSS Service station information at http://www.igs.org/network, last access: 3 January 2019, and National Geodetic Survey station information at https://www.ngs.noaa.gov/CORS/, last access: 25 October 2018) and record the deep subsidence that occurs beneath their foundations. Similar to tide gauges, GNSS stations are nearly always anchored at depth and thus face many of the same concerns: they do not record shallow subsidence that occurs in the strata above the depth of their foundations.

Accurate measurements of RSLR are vital to predict the sustainability of world deltas and for communities in LECZs to adapt to their changing coastlines. In this study, we investigate the nature of tide-gauge benchmarks and GNSS station foundations in coastal Louisiana and assess the implications for measurements of RSLR and subsidence in LECZs worldwide. Reanalysis of time series from tide gauges and GNSS stations is not the purpose of our study. Instead, we present an alternative approach to measuring RSLR in LECZs through which shallow subsidence is determined using the rod surface-elevation table–marker horizon method (RSET-MH; see Webb et al., 2013, and Cahoon, 2015, for detailed descriptions of this method) and deep subsidence is determined using GNSS data. Using the Mississippi Delta (a thick LECZ) and the Chenier Plain (a thin LECZ) in coastal Louisiana as the primary study areas, we determine benchmark foundation depths and the type of strata in which the foundations are anchored. This allows us to determine which subsidence processes are measured by tide gauges and GNSS stations and to evaluate their usefulness as recorders of RSLR. We then place our findings in the context of LECZs worldwide. Our results suggest that tide gauges (and existing analyses of tide-gauge data) in these environments may underestimate rates of RSLR as observed at the land surface, and as a result, many LECZs may be at higher risk of submergence than previously recognized.