Differential Interferometric Synthetic Aperture Radar is applied to the coast of the Yellow River delta (YRD) in China. Like many deltas, the coastline of the YRD is dominated by aquaculture. Advanced Land Observation Satellite Phased Array L-Band Synthetic Aperture Radar (SAR) and Envisat Advanced SAR data acquired between 2007 and 2011 show that subsidence rates are as high as 250 mm/y at aquaculture facilities, likely due to groundwater pumping. These rates exceed local and global average sea level rise by nearly 2 orders of magnitude and suggest that subsidence and associated relative sea level rise may present a significant hazard for Asian megadeltas.
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 Coastal subsidence can heighten storm surges, salinate groundwater, intensify river flooding, destabilize infrastructure, and accelerate shoreline retreat. Highly compressible soils make deltas particularly vulnerable to subsidence, which may affect more than 300 million people worldwide [Ericson et al., 2006; Saito et al., 2007; Syvitski et al., 2009]. Despite this risk, direct measurements of delta subsidence are scarce. Global Positioning System or tide gauges are installed on well-studied deltas such as the Mississippi [e.g., Dixon et al., 2006; Ivins et al., 2007; Morton and Bernier, 2010], but these instruments are rare on other deltas and provide only point measurements, whereas spatial coverage is needed to fully characterize subsidence patterns.
 Differential Interferometric Synthetic Aperture Radar (D-InSAR) is a satellite-based technique offering high-resolution spatial coverage of ground deformation. The technique is not commonly applied to deltas because it requires permanent reflectors such as paved roads that may not exist in less-developed areas. Even Persistent Scatterer InSAR [Hooper et al., 2007], which requires fewer reflectors than D-InSAR, has been mainly applied to major delta cities such as New Orleans in the Mississippi River delta [Dixon et al., 2006], Vancouver in the Fraser delta [Mazzotti et al., 2009], or Suzhou in the Yangtze River delta [Shi et al., 2012]. Subsidence rates in nonurban, near-shore areas are virtually unknown.
 Here we apply D-InSAR to the coast of the Yellow River delta (YRD) in China, which is dominated by aquaculture facilities (Figure 1) and has experienced severe coastal erosion in the last 2 decades. We extract deformation patterns from dry land adjacent to aquaculture facilities along the coast, allowing the first remote measurements of subsidence at a nonurban delta shoreline.
2 The Yellow River Delta
 The modern YRD has a land area of 5500 km2. Deltaic deposits of silty clay are 15–20 m thick near the shoreline, underlain by marine clays interrupted by thin peat layers [Shi et al., 2007]. The active delta is less than 160 years old; it began to form in 1855, when the mouth of the Yellow River shifted north from the Yellow Sea to the Bohai Sea.
 In the twentieth century, distributary channels on the delta were artificially shifted to new locations in order to grow land for oil production in the Bohai Sea. Natural compaction of the abandoned lobes then proceeded without sediment accretion by floods. Beginning in the 1960s, dams were built upstream on the Yellow River, reducing water flux from 43 km to 4.9 km3/y [Fan and Huang, 2008]. Sediment discharge to the river mouth decreased simultaneously, from more than 1 Gt/y in the 1960s to 0.15 Gt/y in the 21st century [Wang et al., 2010]. Fish farms and salt works were built along the entire coastline between 1970 and 2000. By 2001, groundwater extraction in the delta had reached 1 billion m3/y [Fan et al., 2006]. Groundwater is brackish in the YRD; the salinity of some groundwater is higher than that of present-day seawater, but some water is useable for irrigation. Oil production in the delta also continued throughout the twentieth century; reservoir rocks are situated at 3 to 5.5 km depth [Guo et al., 2010].
 These pressures have left their mark on the delta. Between 1976 and 2000, the northern shoreline retreated 7 km [Chu et al., 2006]. Seawalls were built in the late 1980s; without such protective measures, the entire delta shoreline would now be eroding [Wang et al., 2006], including the previously prograding river mouth [Cui and Li, 2011]. Though many studies have examined the YRD, no consensus has been reached as to the primary cause of coastal erosion.
3 Data and Methods
3.1 SAR Data and Software
 D-InSAR processing was performed with the open source software package ROI_PAC (Repeat Orbit Interferometry Package) [Rosen et al., 2004]. We use 19 Envisat Advanced SAR (ASAR) (λ=5.6 cm) descending-track images acquired between February 2007 and May 2010 (track 132) and produce 28 interferograms over the northern site (Figure 2). Temporal baselines (the temporal separation of the acquisitions) range from 35 to 140 days, and perpendicular baselines (a measure of orbital drift) range from 2 to 866 m. Over the southern site, we produce four interferograms using eight Advanced Land Observation Satellite (ALOS) Phased Array L-Band SAR (PALSAR) (λ=23.6 cm) ascending-track images spanning January 2007 to March 2011 (path 444, row 73). The temporal baseline for all ALOS PALSAR interferograms is 369 days (Figure 2), and perpendicular baselines range from to 2014 to 3755 m.
3.2 D-InSAR Methods and Uncertainty
 D-InSAR uses phase changes between two acquisitions of a Synthetic Aperture Radar (SAR) to measure path-length changes between the radar and the ground [Bamler and Hart, 1998]. In a SAR image, the phase at a single pixel is the coherent sum of all reflectors within that pixel. The total phase change Δφ between repeat passes of the SAR is the sum of phase changes due to ground deformation, atmospheric delays, local topography, pixel decorrelation, thermal noise, and satellite orbital drift:
where Δφ is the quantity that is directly measured. The phase change due to ground deformation (Δφg) is the signal of interest; to isolate Δφg, the other terms are calculated and removed and their uncertainty quantified as follows.
 Δφa and Δφn: Atmospheric water vapor beam delays were minimized by restricting the study to days in which the Moderate Resolution Imaging Spectroradiometer (MODIS) Level 2 Water Vapor Product showed < 2 cm of precipitable water over the delta within 2 hours of the SAR acquisition. The combined atmospheric delay (Δφa) and thermal noise (Δφn) were measured by Sandwell et al. ; root-mean-square errors (RMSE) are 0.47 radians (rads) (2.1 mm) for ASAR and 0.18 rads (3.3 mm) for PALSAR at the look angles of this study.
 Δφt: Topographic contributions to phase occur when topography is viewed from different angles due to changes in the satellite's position between acquisitions. Topographic contributions were removed by subtracting a synthetic interferogram [Rosen et al., 2004] generated by ROI_PAC from orbit metadata and the 90 m Shuttle Radar Topography Mission (SRTM) Digital Elevation Model (DEM). Uncertainty then comes from the uncertainty in the DEM itself and varies for each interferogram due to their variable perpendicular baselines (the shortest distance between the two orbital tracks perpendicular to the look direction). The relative height RMSE of SRTM in the world's flat-lying areas is between 1.1 and 1.6 m [Schumann et al., 2008], which corresponds to a topographic RMSE of 4 mm for the longest ASAR perpendicular baseline and 9 mm for the longest PALSAR perpendicular baseline in this study.
 Δφd: Pixel decorrelation occurs due to changing ground reflectors as well as satellite drift that introduces geometric decorrelation across the image. Decorrelated pixels are incoherent; their phases at the two acquisitions are no longer related to one another in a meaningful way [Zebker and Villasenor, 1992]. The phase change due to decorrelation takes a random value between 0 and 2π. Geometric decorrelation scales linearly with perpendicular baseline, and total geometric decorrelation occurs at the critical baseline: 6.5 km for PALSAR dual-polarization mode, 13.1 km for PALSAR single-polarization mode, and 1.1 km for ASAR [Sandwell et al., 2008]. Baselines in this study reach one half of the critical baseline over the southern site, resulting in noisy images. Four interferograms over the northern site reach three fourths of the critical baseline; the other 24 interferograms have baselines less than half of the critical value. The wet, muddy coast of the delta also shows extensive decorrelation due to inundation on the ground. To reduce noise from geometric and physical decorrelation, each interferogram was multilooked (spatially averaged) 4 times in the range direction and 20 times in the azimuth direction. The extent of decorrelation after multilooking was then estimated with a complex correlation coefficient calculated from the phase variance of each multilooked interferogram [Rosen et al., 2004]. The correlation coefficient ranges from 0 to 1, and the proportion p of pixels with a correlation coefficient < 0.7 was used as the probability that any given pixel had decorrelated. A uniform noise probability density function between 0 and 2π with a variance of π2/3 radians was used in conjunction with the proportion p of decorrelated pixels to establish uncertainty for each interferogram due to pixel decorrelation.
 Δφo: Satellite drift can introduce long-wavelength phase ramps across interferograms. A fifth-order polynomial phase ramp is fitted and removed from each interferogram before cropping areas of interest [Rosen et al., 2004]. Residual phase ramps have a wavelength much larger than the width of the entire SAR image (~100 km) and are assumed to contribute an effectively constant phase offset at the km-scale sites in this study. This offset is assumed to be equal to the mean phase of the interferogram far from deformation features. Its variance is not included in the uncertainty calculations because its value (~0.2 mm) is more than an order of magnitude lower than the variances of other terms in equation (1).
 After contributions from topography and orbital drifting are removed, phase change Δφg must be unwrapped with (Δφg=Δφ+g±2π). Phase change Δφg can then be converted to vertical deformation Δh by
where λ is the radar wavelength and θ is the angle of incidence. In the deformation plots, 2-σ uncertainty is derived from the uncertainties of the thermal noise, atmospheric, topographic, and decorrelation terms added in quadrature and doubled.
4 Deformation Measurements
 In the northern part of the delta, Envisat ASAR interferograms reveal rapid subsidence centered over a fish hatchery, which is surrounded by fish ponds that are dry in the winter (Figure 3). Consistent deformation of >20 mm per month occurred in January–April 2007 and in Winter 2007–2008. Rates of >10 mm per month occurred consistently through Winter 2008–2009, with slight rebound occurring in Spring 2009. Deformation of 6 mm per month occurred in Winter 2009–2010 but is only within uncertainty in the longest (140 day) interferogram. The subsiding area has a minimum diameter of 2.2 km, crosses seawalls, and affects tidal flats beyond the seawalls. Summer interferograms were not coherent at this site, likely due to monsoon rainfall and the filling of the surrounding fish ponds at the end of winter. Although the edge of the Chengdong oil field lies 2 km from the hatchery, we suggest that deformation is associated with the hatchery rather than the oil field, for four reasons: (1) oil extraction from depths of 3 to 5.5 km would produce a heavily dampened signal at the surface [Geertsma, 1973], (2) the shape of the signal suggests a point source rather than a broad reservoir accessed by hundreds of pumps, (3) deformation is centered over the hatchery, not the oil field, and (4) rates are consistent with compaction due to a water table drop of tens of centimeters, given YRD silty clay porosities of 41% to 55% [Shi et al., 2007]. The entire ASAR time series is presented in Supporting Information. Deformation rates are highly variable at this site, and no deformation occurs during Spring 2008 or 2009, possibly due to the cessation of pumping during these periods.
 In the southern part of the delta, the longer wavelength of ALOS PALSAR allowed 1 year interferograms to be generated over a large aquaculture and salt production facility (Figure 4). At least 70 km2 were observed to subside > 50 mm/y over the entire 4 year study period. Within the subsiding area, numerous overlapping features thought to be associated with single pumps are sinking at rates of 100–250 mm/y at their centers. These features range from 0.5 to 6 km in diameter; some cross seawalls and affect what remains of the wetlands and tidal flats in this area. One of the largest and most consistently coherent features is highlighted in Figure 4b; it subsides >450 mm at its center between 2008 and 2009. No uplift or rebound is evident in any PALSAR interferograms, which have nearly continuous coverage over the 4 year study period. The complete PALSAR interferograms at this facility are presented in the Supporting Information.
 Long-wavelength regional signals cannot be resolved with D-InSAR, which measures only relative deformation between pixels that lie within the SAR scenes. The groundwater extraction signals presented in this study may ride on top of additional regional subsidence caused by basin movement or isostatic adjustment due to sediment loading [e.g., Ivins et al., 2007].
5 Implications for Other Deltas
 Groundwater extraction is well known to cause land subsidence in many types of settings, e.g. up to 300 mm/y of subsidence in Mexico City measured with InSAR [Osmanoglu et al., 2010]. River deltas are highly compressible landforms, and groundwater extraction has been shown to produce rapid subsidence in delta cities: 150 mm/y in Suzhou (Yangtze River delta) [Shi et al., 2012] and 220 mm/y in six Indonesian delta cities [Chaussard et al., 2013]. Here we have shown that groundwater extraction at an aquaculture-dominated coastline can induce the same subsidence as extraction in a city: more than 250 mm/y. D-InSAR can measure these signals on short time scales even in wet, muddy areas directly at the coast.
 The subsidence rates reported in this study have serious implications for the stability of aquaculture-dominated coastlines. Because farmed fish is a vital protein source for millions of people, world aquaculture is experiencing explosive growth. The number of fish farmers in the world has quadrupled in the last 2 decades, and global annual production of farmed fish reached 60 million tons in 2010 [FAO, 2012]. Asia produces 89% of the world's farmed fish, and much of this production occurs in river deltas. Fish and shrimp ponds have become the boundary between land and sea in deltas such as the Yellow, the Pearl, and the Mekong. In the year 2000, for example, more than 250,000 hectares in the Mekong delta were converted from rice paddies to shrimp ponds [Tho et al., 2008]. The delta is built from interbedded silt and clay layers comparable to YRD deposits, and freshening shrimp ponds with groundwater is common.
 Much consideration has been given to the impacts of global sea level rise on aquaculture, but no mention is given to relative sea level rise produced by the industry itself [FAO, 2012]. We have shown that large deltaic aquaculture facilities can induce land subsidence of 1 m every 4 years, more than global average sea level rise is expected to produce in a century [Bindoff et al., 2007]. Consequently, the largest threat to coastal stability in deltas may not be global sea level rise but effective sea level rise due to land subsidence from groundwater extraction.
 This work was supported by NASA grant 10-LCLUC10-2-0038: Global-scale assessment of threatened river delta systems. SH was supported by NSF grant DGE 0707432. IO was supported by NSF-EAR Award 1123880. We thank ESA for ENVISAT ASAR data and support. METI and JAXA retain ownership of the original ALOS PALSAR data, which were distributed by ERSDAC. We thank E. Fielding for software and methodological support.
 The Editor thanks two anonymous reviewers for assistance evaluating this manuscript.