Effects of Earthquakes on Flood Hazards: A Case Study From Christchurch, New Zealand

: Earthquakes can influence flood hazards by altering the flux, volumes, and distributions of surface and/or subsurface waters and causing physical changes to natural and engineered environments (e.g., elevation, topographic relief, permeability) that affect surface and subsurface hydrologic regimes. This paper analyzes how earthquakes increased flood hazards in Christchurch, New Zealand, using empirical observations and seismological data. Between 4 September 2010 and 4 December 2017, this region hosted one moment magnitude (Mw) 7.1 earthquake, 3 earthquakes with Mw ≥ 6, and 31 earthquakes with local magnitude (ML) ≥ 5. Flooding related to liquefaction-induced groundwater pore-water fluid pressure perturbations and groundwater expulsion occurred in at least six earthquakes. Flooding related to shaking-induced ground deformations (e.g., subsidence) occurred in at least four earthquakes. Flooding related to tectonic deformations of the land surface (fault surface rupture and/or folding) occurred in at least two earthquakes. At least eight earthquakes caused damage to surface (e.g., buildings, bridges, roads) and subsurface (e.g., pipelines) infrastructure in areas of liquefaction and/or flooding. Severe liquefaction and associated groundwater-expulsion flooding in vulnerable sediments occurred at peak ground accelerations as low as 0.15 to 0.18 g (proportion of gravity). Expected return times of liquefaction-induced flooding in vulnerable sediments were estimated to be 100 to 500 years using the Christchurch seismic hazard curve, which is consistent with emerging evidence from paleo-liquefaction studies. Liquefaction-induced subsidence of 100 to 250 mm was estimated for 100-year peak ground acceleration return periods in parts of Christchurch.


Introduction
Earthquakes can impart major influences on surface and subsurface hydrologic regimes over a variety of spatial (i.e., 0 km to more than 1000 km from the epicenter, from single sites to total areas exceeding 1000 km 2 ) and temporal scales (i.e, transient to permanent effects generated immediately during the earthquake or accumulated over millions of years, e.g., mountain building, drainage divide migration, aquifer partitioning) [1][2][3][4] (Table 1). These include tsunamis, earthquake-induced water waves, landslides into water bodies, landslide dam outburst floods, river avulsions, liquefaction-associated ground deformations and fluid expulsions, surface subsidence, surface uplift, lateral spreading, changes to cross-sectional and longitudinal stream profiles, redistribution of surface materials (e.g., in coastal and alluvial environments), changes in stream flows and water levels in groundwater and wells (via transient and permanent deformations and permeability changes to surficial and subsurface materials and aquifers), and fracturing and deformation of engineered surface and subsurface infrastructure (e.g., levees, storm drains, pipes). Vice versa, natural and anthropogenically-influenced hydrologic regimes can impart major influences on the timing, locations, rates, and magnitudes of earthquakes [5][6][7][8][9][10] (Table 2). Tables 1 and 2 are not exhaustive lists but provide selected examples of the many ways in which earthquakes can influence the flux, volume, and distribution of surface and subsurface waters (Table  1) and how water influences earthquakes ( Table 2). The processes described in Table 1 can be immediate or delayed and can be generally classified as (i) processes that directly alter the volume and/or flux of surface and/or subsurface waters, or (ii) processes that induce permanent and/or transient physical changes to natural and engineered environments (e.g., elevation, topographic relief, permeability) that subsequently affect surface and subsurface hydrologic regimes. Significant hydrologic effects can include surface flooding during or immediately after the earthquake [11][12][13] and changes to the surface and subsurface that subsequently influence flood hazards, including floods of meteorological origin [14]. Table 2 includes processes that influence pore-fluid pressures and permeability in and proximal to fault zones and/or those that perturb stress states in rock volumes surrounding faults, primarily through mass redistributions.
Within this context, this paper synthesizes observations of liquefaction (also known as soil liquefaction, the process whereby saturated, unconsolidated sediment temporarily loses shear strength and deforms in a fluid-like manner when subjected to seismic loading or other phenomena) and flooding in Christchurch during and after the 2010 to 2012 Canterbury earthquake sequence (CES) [15] and compares them to quantitative measurements of ground surface deformation and seismic data. Many of the phenomena in Table 1 were directly observed during the CES (e.g., landslides that partially diverted rivers, partial river avulsions, liquefaction, anomalous waves in harbors, large localized waves caused by cliff collapses in water bodies, spring temperature and discharge variations, and transient and permanent groundwater table changes) [15]. None of the processes described in Table 2 have been invoked as potential contributors to the CES seismicity to date.
The overarching purpose of this study was to provide specific examples of how individual and collective earthquakes influenced the urban flood hazard in Christchurch using empirical observations and data. We also estimated the expected return times of liquefaction-inducing ground motions that could induce flooding in Christchurch for the next 500 years. The superposition of this hazard with other hazards, such as sea-level rise [16], highlights the importance of implementing engineering and land-use practices aimed at reducing exposure and vulnerability to flood hazards in Canterbury [17] and analogous settings globally. Table 1. Examples of earthquake-induced influences on surface and subsurface hydrology.

Category Effects References
Landslide dam Dams and other drainage-impeding landslides may be triggered by earthquakes and alter the distribution, volume, and flux of surface waters in a catchment [13,[18][19][20]. Generally, many small dams are formed, along with one or two larger dams. Breaks may occur rapidly or after several years, and a catastrophic breach may cause widespread flood-related casualties. In 1786, >100,000 people were killed by a dam-break flood following a catastrophic breach of a 50 × 10 6 m 3 earthquake landslide dammed lake [21]. [13,[18][19][20][21][22][23][24][25][26] River avulsion The avulsion of rivers occurs where the channel crosses a geomorphic scarp or channel gradient anomaly, including over a blind fault rupture [27]. The consequences depend on the sense of the scarp [12], flow direction of the river, stream power relative to gradient perturbation [28], and relative relief of the scarp and surrounding landscape [29]. The fault displacement of streams commonly occurs at mountain fronts where the displaced rivers are deeply incised and avulsion does not occur. Avulsion is more commonly reported from paleoseismic studies than contemporary (historic) records. [12,[27][28][29][30][31] Liquefaction Release of artesian groundwater pressure may contribute to recurrent liquefaction above extensive alluvial aquifers [32]. The occurrence of [15,[32][33][34][35][36][37][38][39][40][41][42] liquefaction depends on the magnitude-distance scaling [33]. Liquefaction-induced ground failure and lateral spreading [34] may result in the widespread failure of horizontal infrastructure, such as sewerage pipes. Liquefied gravity flows may contribute to a tsunami in the marine environment [35] or directly result in mass casualties onshore. Large-scale submarine liquefaction may cause coastal areas to slip below sea level (as at Port Royal in 1692) [36] and result in large-scale coastal geomorphic reorganization. Even in recent times and in areas with a relatively small perceived seismic hazard, tailings dams may liquefy, resulting in catastrophic failure [37] Seiche Seiches may be generated at vast distances from the epicenter of an earthquake. Following the 2002 Denali earthquake, seiches on Lake Union in Seattle, Washington, damaged houseboats. The Lisbon earthquake of 1755 caused meter-scale river-level changes across Europe at least and the great Assam earthquake of 1950 generated seiches in Norway and Britain. The 1964 Alaska earthquake generated measurable seiches at >10% of gauging stations across North America and many more beyond that. The distribution of reports was strongly related to the rigidity of near-surface sediments.
[ [43][44][45][46] Tsunami Tsunami-induced flooding may occur as a result of a submarine coseismic landslide and/or an offshore fault rupture. Subductionrelated tsunamogenic earthquakes may occur in the lower plate [47]; plate interface [48,49]; or upper crustal, upper plate faults [50]. Furthermore, low rigidity faults may cause a major tsunami even at relatively low magnitudes [51]. Climate change may have a major impact on the distribution of tsunami potential as ice-unloading redistributes the stresses around ice sheets (see, for example, Mörner [52]).
[ [47][48][49][50][51][52][53][54][55][56][57][58][59] Surface-water changes Sustained changes in river discharge may occur over weeks to months following the earthquake with a range of tens to hundreds of kilometers, especially as a result of gradient changes and groundwater expulsion. [2,32] Groundwater changes Groundwater responses to earthquakes are well documented following many earthquakes in areas including China, the United States, New Zealand, Indonesia, Japan, and Italy, among others. Well levels may respond over thousands of kilometers and temperature and pressure of spring discharge may respond over hundreds of kilometers. The scale of the well response is linked to the earthquake magnitude but responses are common across a range of moderate-to large-magnitude earthquakes.

Category Effects References
Natural changes in groundwater level Groundwater recharge at seasonal to centennial timescales may result in increased seismicity rates or local earthquakes. Groundwater unloading may control the slip distributions during earthquakes. [5,6] Aquifer drawdown Groundwater drawdown and the resulting seasonal changes in groundwater loading may cause significant changes in local stress regimes, resulting in the redistribution of seismicity on seasonal timescales. Examples include seismicity rate variations [6,7,65,66] in California, the Dead Sea region, and the central Appenines of Italy.

Reservoirinduced seismicity
In many cases, large lake-level rises following initial impoundment or dam-raising lead to the development of reservoir-induced seismicity. Although this may decrease initially, the filling of the reservoir may transmit long-term pore pressure changes to seismogenic depths, triggering larger earthquakes. The dam height, reservoir volume, and seasonal variations in dam capacity are key influences. Large seasonal variations in the water depth may result in protracted histories of induced earthquakes, such as Koyna, India; Nurek, Tajikistan; and Aswan, Egypt. The largest earthquake potentially attributed to reservoir seismicity is the Mw 7.9 Wenchuan earthquake, for which the Zipingpu Reservoir may have advanced the earthquake due to the reservoir induced stress changes of several tens of kPa at the focal depth. [8,[67][68][69][70][71][72][73][74][75][76][77] Geological disposal of fluids Fracking has been suggested to dramatically affect earthquake hazards but its importance may be secondary to the disposal of fluids [78], such as oil and gas field brines and wastewater, which may result in pressure diffusion over tens of kilometers from an injection site, as well as swarms of seismicity. The flow rate and volume are critical parameters and magnitude exceedance may scale with volume [79]. Induced seismicity due to fluid removal and reinjection has continued for over a hundred years, although analysis of earthquakes in California and Oklahoma indicates that the mechanisms have varied with industry practices [9,10]. The geological sequestration of CO2, which is a critical component of any climate management strategy, may [80] (or may not [81]) result in significant changes in seismicity rates around storage sites. [9,10,78-85]

Seismologic Characteristics
The evolution of the 2010-2011 Canterbury earthquake sequence (CES) and associated ground motion and environmental effects are described by Bannister and Gledhill [86], Bradley et al. [87], and Quigley et al. [15], respectively. The CES initiated with the complex multi-fault Mw 7.1 Darfield earthquake with an epicenter ≈38 km west of the Christchurch central business district (epicentral location from https://quakesearch.geonet.org.nz/) (Figure 1a). This earthquake ruptured at least seven geometrically-distinct faults [88] and generated an approximately 30 km surface rupture [89] spanning three source faults (Figure 1a). Early aftershocks (i.e., within 1 month of the Darfield earthquake) included 11 ML ≥ 5 earthquakes and spanned a 70 km (E-W) by 40 km (N-S) area encompassing the city of Christchurch (Figure 1a). The aftershock rate decreased following the Darfield earthquake in accordance with Omori's Law [90] (Figures 1-3). The 22 February Mw 6.2 also involved a complex rupture, including two to three distinct source faults [88]. The overall spatiotemporal evolution of the CES following the Darfield earthquake involved a general eastward migration of seismicity to beneath the city and offshore, although persistent activity continues in some areas throughout the region (e.g., SW of Christchurch) (Figure 1d). The CES earthquake frequency-magnitude distributions fit Gutenberg-Richter scaling well with b ≈ 1 ( Figure  2). Earthquake shaking throughout the CES was instrumentally recorded by more than 30 strong ground motion instruments in the Canterbury region. Summaries of CES ground motions are provided by Bradley and others [87,[91][92][93][94]. More than 50 earthquakes generated peak horizontal ground accelerations (PGA) ≥ 20 cm s −2 in central Christchurch during the CES [95]. Terrestrial areas with PGA ≥ 0.1 g ranged from hundreds to >9000 km 2 from individual earthquakes [15]. The spatiotemporal nature of the recurrent seismicity generated multiple episodes of liquefaction [33], subsidence [14], and flooding [15,96], as described below. At least eight distinct earthquakes caused damage to surface (e.g., buildings, bridges, roads) and subsurface (e.g., pipelines) infrastructure in areas of liquefaction and flooding ( Figure 3). The wealth of geospatial data acquired prior to and throughout the CES allowed for high-precision measurements of topographic changes due to specific earthquakes to be determined throughout the region, with a particularly high density of geospatial data available for Christchurch. Information on the relationships between liquefaction-associated phenomena, land damage, and damage to the engineered environment is available from peerreviewed academic literature [14,15,34,[97][98][99][100][101][102], Geotechnical Extreme Events Reconnaissance (GEER) reports [96,103,104], and other consultancy reports [105][106][107].

Ground Deformation
Major CES earthquakes caused (permanent) horizontal and vertical displacements of the land surface that were measured using a variety of techniques, including airborne and terrestrial light detecting and ranging (LiDAR) datasets, interferometric synthetic aperture radar (InSAR) and other satellite-based data (e.g., optical data), continuous and campaign GPS data, total station and real-time kinematic GPS surveys (including cadastral surveys of faulting-affected properties and cross-channel profile surveys of urban streams), and sonar echo sounding beneath water bodies [12,14,88,89,105,108,109]. Faulting-induced surface deformations were caused by ground surface fault ruptures associated with discrete fault scarps, and more distributed ground deformation above faults that did not rupture the surface [12,88,89]. Faulting-induced deformation caused relative vertical surface displacements of several centimeters to greater than 1 meter across low relief rural and urban landscapes. Surface displacements changed stream gradients, floodplain slopes, elevations of the land surface relative to water tables, and surface and subsurface hydrology, causing partial stream avulsion and influencing flood hazards. Seismically-triggered mass movements (e.g., liquefaction, lateral spreading, subsidence, landsliding, rockfalls) also caused significant surface topography changes [14]. Liquefaction processes, including lateral spreading and subsidence, caused the shallowing of stream bottoms, narrowing of stream areas, changes in stream profile gradients, changes in floodplain slopes and elevations, and caused major-to-severe damage to land and infrastructure and increased the flood hazard in Christchurch [14].  [89]. The locations of liquefaction (liq) with and without flood-inducing earthquakes (see also Figure 3) are shown with stars. The areas of flooding associated with the expulsion of groundwaters (most commonly associated with liquefaction) are shown in light blue (a,b areas were simplified from Townsend et al. [102] and including the present authors' reconnaissance field observations; c,d were from reconnaissance field observations by the present authors). Areas of flooding due to partial stream avulsion were associated with fault surface rupture in the Darfield earthquake from Duffy et al. [12].

Flooding and Liquefaction
Flooding was observed in rural properties adjacent to the Greendale Fault ( Figure 4a) and other rural areas (Figure 4b) immediately following the Darfield earthquake. Flooding was also observed in areas of liquefaction following major earthquakes ( Figure 5) and in subsequent large storms (Figure 5e,f). Recurrent liquefaction ( Figure 6) lowered ground surface elevations in liquefactionaffected areas by >30 cm to >1 m; the effect of flood plain lowering was observed most profoundly proximal to urban streams, where high tides locally inundated former floodplains (Figure 6d). These observations are discussed in more detail below. Earthquake-induced damage to stormwater pipelines and the consequent impacts on the connectivity and capacity levels of the pipeline stormwater network contributed to an increased flood hazard in Christchurch [110]. Taylor et al. [17] describe general processes that increased the flood vulnerability in Christchurch, including changes in overland flow paths and a reduction of surface hydraulic gradients, narrowing and shallowing of urban streams and a reduction in flood plain elevations, and land settlement that allowed tidal incursions to exert stronger influence on flood hazards.

Darfield Earthquake
Of the seven fault segments that ruptured during the Mw 7.1 Darfield earthquake, surface rupture was identified on the Greendale Fault West (GFW), Greendale Fault (GF), and Greendale Fault East (GFE) (Figure 7). The traces of these surface-rupturing faults typically consisted of a combination of discrete surface fracturing, and surface folding at broad wavelengths of 10 1 -10 2 m. Topographic bulges (pop-ups) formed at regular intervals, with surface areal extents from less than 10 to more than 1000 m 2 and amplitudes that locally exceeded 1 m; these formed within a strike-slip (lateral displacement) zone that distributed much of the surface deformation 30-300 m into the walls of the fault. Much broader, kilometer-scale areas of uplift and subsidence were revealed using InSAR and GPS data [88] (Figure 7).
The vertical deformation associated with the fault segments depended on their orientation, subsurface geometry, and sense of movement [12,88,[111][112][113][114][115]. The NE side of the GFW subsided by >0.8 m, and the SW side was lifted by as much as 0.4 m [12]. The ≈19 km trace of the GF exhibited mainly right lateral displacement with a small component of south-side-up displacement [89]. The central and western segments linked up through a complex zone of deformation that included the second-largest restraining (compressional) stepover (large area, low amplitude pop-up) on the surface trace [12]. The vertical deformation on the GFE was primarily north-side-up compared with the south-side-up vertical displacement elsewhere on the fault.
Much of the vertical deformation was not associated with a discrete surface rupture. Satellite and GPS data, along with field observations, revealed surface folding across tens of square kilometers on the upthrown side of the surface projections of the Charing Cross fault (CCF) and Hororata anticline fault (HAF) (Figure 7) [88]. The HAF thrusted southwards, such that the uplift of the HAF was steep fronted to the southeast of its axis, gently dipping to the northwest of the axis, and terminated northward against the GFW. The CCF thrusted northwestward and terminated at a triplejunction (point connecting three faults at the surface) with the GF and GFW. These three faults bound a pronounced, approximately 1-m deep area of subsidence (Figure 7) on the north side of the surface rupture. A similar, but minor area of ≈0.3 m subsidence south of the GFE was attributed to a release of right-lateral slip on the GF and GFE. Collectively, these observations highlight how different types of faults with different orientations and geometries may create large variations in relative surface elevation changes that, in the vicinity of surface water bodies, can exert strong and variable influences on the steepness and trajectory of water flow paths.    [33]. The timing of the photographs with respect to each earthquake is shown. (h) Cumulative land subsidence of ≈45 cm induced by recurrent liquefaction relative to a vertically-fixed artesian water pipe fixed into sediment below the liquefiable layer; the white stain and rust-coated pipe segment were below the ground surface prior to the 2010 Mw 7.1 Darfield earthquake.

Christchurch Earthquakes
The series of earthquakes that affected the Christchurch area resulted in a cumulative vertical displacement signature dominated by the approximately 0.45 m of uplift of the Avon-Heathcote Estuary in the hanging wall of a system of blind dextral-reverse oblique faults (Figure 7c). Although liquefaction-related subsidence was locally extreme (see Section 4), tectonic subsidence was limited to less than 0.2 m. Most of the differential displacement was concentrated along a more than 5 km long zone of broad uplift west of the estuary. The hanging wall uplift of the estuary reduced the volume of the tidal prism, namely the body of water that leaves the estuary as the tide ebbs, by approximately 14.6% [116].

Cumulative Tectonic Vertical Displacements During Major CES Earthquakes
The cumulative vertical tectonic displacements caused by the CES earthquakes were small relative to the total displacements induced by tectonic displacements plus liquefaction effects ( Figure  8). Approximately 0.13 ± 0.03 km 3 of onshore rock was uplifted, predominantly in the hanging walls of blind thrusts and on the south side of the GF. About 0.05 ± 0.02 km 3 of rock subsided, primarily in extensional quadrants of the strike-slip fault system (releasing bends), but also in the footwall of the Christchurch earthquake fault, and on the north side of the central segment of the GF.

Darfield Earthquake
Extensive regional liquefaction occurred during the 4 September 2010 Darfield earthquake [15,33,102,104,106]. Liquefaction manifestation at the ground surface included sand blow formation, lateral spreading, surface subsidence, and flooding. Liquefaction-induced land damage affected ≈10,000 residential properties and was generally confined to specific low-elevation (<5 m above sea level) suburbs with shallow (less than 1-2 m depth) groundwater tables [117] and thick (more than 2 m) near-surface layers of loose to medium density silt-to-fine sand sediments. Liquefaction-triggering (threshold) PGAs in areas of significant land damage were >0.15-0.17 g [15]. Surface subsidence ranged from less than 10 cm to more than 30 cm in areas of surface manifestations of liquefaction. Surface subsidence was caused by post-liquefaction volumetric densification, redistribution of liquefaction ejecta, including by anthropogenic removal (Figure 8) [97,118] and lateral spreading [119] ( Figure 9). Liquefaction caused 74% of central and eastern Christchurch to subside; 60% of this area subsided by less than 0.2 m (Figure 8). The most severe land damage occurred proximal to urban rivers, estuaries, and areas underlain by former river channels [120]. These areas were comprised of highly liquefiable sediments that were able to spread laterally due to topographical variations and a lack of lateral confinement (i.e., free faces like unsupported stream banks). Lateral-spreading caused permanent ground displacements that locally exceeded 2-3 m in the areas of severe land damage ( Figure 9). Horizontal ground displacements typically reduced exponentially with increasing distance from the most proximal free face, but in some cases, a block-mode mechanism of failure was exhibited, with large displacements incurring at distances >100 m from adjacent free faces (Figure 9a) [121]. The lateral spreading of sediments toward streams reduced channel widths and caused the shallowing of channel bottoms ( Figure 10). Liquefaction-induced subsidence reduced flood plain elevations. Overland transport of liquefaction ejecta into streams caused increased streambed sedimentation and stream shallowing. These effects were all compounded by further CES events.

Christchurch Mw 6.2 Earthquake
The Mw 6.2 Christchurch earthquake caused the most widespread and severe liquefaction manifestation at the ground surface throughout central, southern, and eastern Christchurch, relative to all the other CES earthquakes, affecting approximately 47,000 residential properties [15]. The most severe manifestations (typically 100 to 300 mm of ejected sand and silt covering areas of more than 10 to 100 m 2 ) were generally observed in the low-elevation suburbs adjacent to the Avon River where the groundwater was close to the ground surface [33,117] and the soils comprised thicker nearsurface layers of loose-to medium-density sandy soils. The ground surface manifestations were less severe (i.e., smaller individual sand blows) in the suburbs farther away from the Avon River, where groundwater was either deeper below the ground surface or the near-surface soil layers comprised medium density to dense sandy soils. Liquefaction caused widespread and severe subsidence throughout eastern and central Christchurch due to lateral spreading, topographic re-levelling, sand and silt ejecta to the ground surface, and post-liquefaction volumetric densification. Generally, the areas where the largest volumes of water, sand, and silt ejecta occurred also experienced the greatest amount of liquefaction-related subsidence (>0.5 m). This earthquake caused 83% of eastern and central Christchurch to subside further; 78% subsided up to 0.3 m, with localized areas exceeding 1 m (Figure 8)

Cumulative Liquefaction-Driven Topographic Effects of CES
Compared to pre-earthquake elevations, 86% of central and eastern Christchurch subsided through the CES; 10% subsided more than 0.5 m, with some localized locations exceeding 1 m. Cumulative liquefaction-induced subsidence was highest in the inner-meander loops of the Avon River and associated abandoned inner meander loops (e.g., area surrounded by Horseshoe Lake Reserve in eastern Christchurch, north of the contemporary Avon River). By removing the tectonic components of uplift or subsidence [14,88], the residual vertical displacements (subsidence) could be attributed to liquefaction-induced effects. Liquefaction-induced subsidence was evident even in areas where the net effect was uplift because the tectonic uplift exceeded liquefaction-induced subsidence (e.g., parts of SE Christchurch near the estuary). The CES cumulative lateral displacements correlated well with the observed surface manifestations of liquefaction, ground cracking, and damage [14,109] (Figure 7b). In areas of severe liquefaction and lateral spreading, upward of 40% of cumulative CES horizontal displacements exceeded 1 m. The 50th percentile displacement for the "No observed ground cracking or ejected liquefiable material" category was between 0.2 and 0.3 m (the smallest displacements that could be identified within the resolution of the optical imaging approach used; see Rathje et al. [109] for details). The majority of areas and properties affected by increased flood vulnerability were already within the 1% annual exceedance probability floodplain; however, many residents were not aware that their property had been in the floodplain before the CES [17]. A comparison of pre-CES and post-13 June 2011 river and floodplain cross-sections, derived from a combination of direct river bed depth measurements and LiDAR data, shows floodplain subsidence and river channel narrowing and shallowing ( Figure 10, inset panels i-v) resulting from lateral spread and sedimentation from liquefaction ejecta entering the waterways [14,17]. Smaller cross-sectional channel areas and lower flood plains collectively reduced channel cross-sectional areas, reduced channel carrying capacity, and thus increased flood hazard.

Increased Flood Hazard Due to Faulting-Induced Changes in Stream and Flood Plain Gradients
The Hororata River occupies the low-gradient interdistributary zone between the Rakaia Fan to the south and the much smaller Selwyn River Fan to the north. The west segment (GFW) ruptured the surface of the interfluve between the Selwyn and Hororata Rivers, striking approximately parallel with and never more than a few hundred meters away from Hororata River [12,114]. The interfluve here consisted mainly of the surface of the Selwyn River Fan, with southeast-flowing paleochannels of the Selwyn River that merged southward with the Hororata River.
Large rainfall events in the Selwyn and Hororata catchments during August 2010 had preconditioned the landscape by causing ground saturation that contributed to a rapid, nearly 1-m pre-earthquake increase in stage height in the Selwyn River system following a moderate, 3-day rainfall event from ≈28 August onward [122]. The flood stage reached on 1 September 2010, SE of the study area, was the third-highest during the 12 months to 9 December 2010. It was increasing again due to further rainfall on 3 September when the instrument malfunctioned during the earthquake on 4 September. Both the Hororata and Selwyn Rivers would, therefore, have been at a relatively high stage when the earthquake occurred [122].  [14].
Vertical tectonic displacements of 0.8 to 1.8 m along the GFW surface rupture (Figure 7b,d) disrupted the bed of a meander bend in the strongly-flowing Hororata River, uplifting the downstream reach of the meander and forcing the river to avulse and flow along the new fault scarp [12,114]. Water flowing southeast from the avulsion node lapped onto the scarp, proving instrumental in mapping the fault in the absence of LiDAR. Floodwaters reoccupied old channels of the Selwyn River that formed low points in the scarp, eventually rejoining the Hororata River near its confluence with the Selwyn River (Figure 6b). Extensive flooding north of the avulsion node resulted from (i) the backing-up of water at the avulsion node, (ii) the expulsion of groundwater, and (iii) the tectonic damming and avulsion of ephemeral Selwyn River paleochannels that were already flowing because of underflow from the contemporary high-flood stage event in the main Selwyn River channel [15,122].
The net effect of the earthquake for post-seismic flood hazard of the southern reaches of the Hororata River is implicit in the vertical displacements shown in Figure 7. Around 2 km of riverbed was excavated over several weeks to reinstate the river in its pre-earthquake bed; that bed remains located on the footwall of a normal fault, immediately adjacent to and higher than an area of significant new accommodation space. The coseismic avulsion node is expected to be an area of major aggradation as the river (i) flows across the scarp into the bend, excavating the scarp and creating a local knickpoint, and (ii) deposits sediment as it encounters the extremely low gradient imposed by agricultural landscape change since the 1940s [122] and its post-seismic reinstatement. It is reasonable to expect that the river will re-avulse repeatedly at the avulsion node, seeking to occupy the downthrown side of the fault.
Near the village of Hororata, the Hororata River flows NE along the margin of the Rakaia River Fan, before turning to flow SE along the Rakaia-Selwyn inter-fan zone (Figure 7a,b). The angle between the NE-and SE-flowing reaches coincides with the zone of uplift on the hanging wall of the Hororata anticline blind thrust fault, and the SE-flowing reach meanders sub-parallel to the GFW. The net effect on the downstream gradient of the river is shown in Figure 7d. The only drainage reversal occurs at the avulsion node, but the gradient of the Hororata River is perturbed in many small ways that may be significant for flood hazards. For instance, during flooding in August 2017, the Hororata River occupied low lying areas north of the river (Figure 7b). The flooding occurred in a reach with little downstream gradient perturbation. However, it lay between a steepened upstream reach and a reach with a shallowed downstream gradient. Furthermore, the southward slope of the left (north) bank of the river was reduced by subsidence on the downthrown side of the GFW. Each of these changes was relatively small compared to the natural slopes; for example, the GFW subsidence on the north bank of the Hororata River only imposed a northward tilt of 1:4000 on a natural southward slope of 1:200. However, the cumulative effect of upstream steepening, downstream shallowing, and cross-stream tilting may be significant for the behavior of the river in this flood-prone area.
The Selwyn, Waianiwaniwa, and Hawkins Rivers all traverse the zone of subsidence on the hanging wall of the GFW and footwall of the CCF (Figure 7). The bed elevation changes along these rivers steepen their upstream profiles slightly but flatten their downstream profiles by 1/5th (from 0.5% to 0.4% [15]. As previously noted [15], this bed perturbation is likely to favor sedimentation and flooding in the reduced-gradient reaches of the river. The Avon and Heathcote Rivers both traverse a tectonically uplifted zone before reaching the uplifted Avon-Heathcote Estuary (Figure 7c). The uplift reduces the gradient of both rivers (e.g., Figure 7e), increasing the flood hazard in parts of eastern Christchurch. The Flockton Basin, in particular, has effectively become a ponding area for floodwaters of the Avon River and its eastern tributaries, resulting in repeated flooding events since the onset of the CES.

Increased Flood Hazard Due to Liquefaction-Induced Topographic Changes
In 2013, the Christchurch City Council [123] released revised modified flood extents for projected 1-in-50-year and 1-in-200-year rainfall events using post-earthquake LiDAR-derived digital elevation models. These extents exceeded pre-earthquake extents by area and by severity. Key factors in the increase were the widespread tectonic and liquefaction-induced landscape changes and alteration of the longitudinal and cross-sectional profiles and sediment regimes of urban waterways. The lowering of surface elevations relative to water tables [12,117] is likely to have increased the liquefaction and flood hazard. With groundwater levels (i.e., fully saturated soils) now closer to the ground surface, there is less soil above the water table and therefore less capacity to absorb water during storm events. Leakage of underlying artesian aquifers through breached aquitards may have also influenced local hydrologic conditions [32] and thus impacted surface water infiltration. Another significant contributor to the increased flood hazard was widespread earthquake damage of the urban stormwater network, including open channels and underground pipes that were compromised by breakages, liquefaction blockages, and gradient changes [99,101]. The post-earthquake floodscape may have also been influenced by New Zealand statutory resource management framework changes, instituted in the early 1990s, which were locally translated into a new approach of naturalizing urban waterways and reducing engineered river widening and dredging programs. Pre-1990s development of the urban floodplains that are now experiencing enhanced flood hazards was facilitated by the earlier engineering approach to the urban rivers [124][125][126].
The floodplain areas along the Avon and Heathcote Rivers have an increased flood hazard due to the factors described above, including liquefaction-induced subsidence. An example of how these factors increased the 1-in-100-year storm event (1% annual exceedance probability (AEP)) flood depths (∆F) due to subsidence along the Avon River corridor is shown in Hughes et al. [14]. Christchurch City Council and national insurers (Earthquake Commission) have released a suite of reports on the implications of increased flooding vulnerability in response to the CES (e.g., https://www.eqc.govt.nz/canterbury-earthquakes/land-claims/complex-land-claims/increased-riskof-flooding).
To estimate the potential for future earthquake-induced liquefaction and associated flooding effects, we first plotted the instrumentally-recorded geometric mean PGAs at six selected strong ground motion stations (NNBS-North New Brighton School, NBLC-New Brighton Library, CBGS-Christchurch Botanic Gardens, LINC-Lincoln School, PRPC-Pages Road Pumping Station, SHLC-Shirley Library) for the 11 strongest CES earthquakes with the largest recorded PGAs. The geometric mean PGAs were sourced directly from the values presented in Bradley [92], except for the Mw 5.7 earthquake in 2016, which was computed herein from processed PGAs obtained for these stations from Geonet. The NNBS and NBLC records were merged because of data unavailability for some events; the reported NNBS-NBLC value represents the available value (if only one value was available) or the averaged value (if both records were available). Locations and geotechnical information for stations considered herein are available at (https://www.eqc.govt.nz/sites/public_files/3783-Geotech-characterisation-Chch-strong-motionstations.pdf) and (https://www.geonet.org.nz/data/supplementary/nzsmdb). PGA values were plotted against earthquake Mw and coded by symbols based on whether liquefaction with and without flooding was observed "proximal" (i.e., ≤3 km) to the seismometer sites in the associated earthquakes ( Figure 11a). Estimated "threshold" values for liquefaction and liquefaction plus groundwater expulsion flooding in susceptible sediments were defined by linearly correlating observational data to PGA values. Minor proximal liquefaction was observed at geometric mean PGAs as low as 0.07-0.09 g and liquefaction plus groundwater expulsion surface flooding was observed in earthquakes with a geometric mean PGAs as low as 0.15 g. PGA threshold values decreased with increasing Mw because larger Mw earthquakes had longer shaking durations and thus more potentially effective liquefaction-triggering stress cycles. Using the threshold values from Figure 11a, the expected average return times of geometric mean PGAs (1/annual rate of PGA exceedance) capable of triggering future liquefaction and liquefaction plus associated groundwater expulsion flooding in Christchurch are shown in Figure 11b (using the hazard curve from Bradley [92]). The liquefaction plus groundwater expulsion flooding PGA field (#1) intersects the hazard curve at circa 100-to-475-year return times. Paleoseismic investigations of sites subjected to recurrent liquefaction during the CES revealed evidence for major pre-CES liquefaction event(s) (early historic or pre-historic "paleo-liquefaction") in late Holocene sediments [127,128], providing additional evidence supporting the recurrence over a timescale of hundreds to thousands of years. Figure 11. (a) Geometric mean peak ground acceleration (PGA) vs. Mw for CES earthquakes with the largest recorded PGAs at selected strong ground motion seismometer stations where proximal (i.e., ≤3 km distance) earthquake-induced liquefaction with or without groundwater-expulsion flooding was observed. Threshold boundaries for liquefaction plus flooding (1) and liquefaction only (2) were approximated from observational data points. (b) Christchurch seismic hazard curve from Bradley [92] showing the geometric mean PGA field required for liquefaction plus flooding (expanded to 0.15 to 0.3 g) intersecting the hazard curve at return periods of ≈100 to ≈475 years. NNBS-North New Brighton School, NBLC-New Brighton Library, CBGS-Christchurch Botanic Gardens, LINC-Lincoln School, PRPC-Pages Road Pumping Station, SHLC-Shirley Library.

Summary
Christchurch experienced several intensive rainstorms in 2014 and 2017 (Figure 2), resulting in widespread flooding of properties in river suburbs that in some instances exceeded historical flooding depths and spatial extents due to floodplain subsidence through the CES. The documentation of large, loss-inducing flood events following the CES has prompted an urgent and intent governmental focus on appropriate infrastructure and urban planning responses; at present, the city's post-quake floodscape is cited as the primary concern of city authorities.
Relative sea-level rises of 0.5 to 1 m occurred in suburbs adjoining the lower Avon River and Avon-Heathcote Estuary, which experienced tectonic downthrow and significant liquefaction/ lateral spread subsidence through the CES. These areas have thus experienced the equivalent of several centuries of projected relative sea-level rise in the absence of land elevation changes at the current global rate of sea-level rise of 3.3 ± 0.4 mm yr −1 [129], and thus provide useful analogs for the potential impacts of sea-level rise in other settings globally. In this instance, gravel stop-banks were constructed along much of the Avon River in 2011 to temporarily mitigate the post-earthquake flood hazard ( Figure 9, inset panels i-v).
Probabilistic approaches that consider future impacts from natural phenomena, including tropical and extra-tropical cyclones [130], earthquakes [131], and liquefaction [33], are important when considering future risks posed by flooding in Christchurch. Investigations addressing the dynamic geomorphic responses of urban rivers and coastal plains to relative sea-level rise, shoreline retreat, groundwater responses, liquefaction, subsidence, and coastal aquifer resources are all urgently required.
The anthropogenic intervention in long-term geologic processes that previously enabled sediment aggradation to rebuild topography in this area means that, without further anthropogenic redistribution of sediment, subsidence will continue to dominate the topographic evolution of Christchurch. It is quite likely that flood events will also deposit outwash sediment onto low-lying flood plains, such as parts of the residential red zone. Strong earthquakes sourced from previously unidentified and/or blind faults and their impacts on flood and relative sea levels add to the myriad of short-to long-term challenges facing coastal environments in New Zealand and throughout the world.
In the case of future earthquake-induced effects on flood hazards in Christchurch, we view the probability of future liquefaction-inducing earthquakes and associated subsidence and increased flood hazards in eastern Christchurch over the 50, 100, 475, and 2500-year time-scale to be high to almost certain. This is consistent with the interpretations from Brackley et al. [106], who combined subsurface geological and geotechnical data with expected PGAs for return times of various timescales derived from seismic hazard models to forecast likely distributions and magnitudes of future liquefaction and subsidence in the Christchurch area. Liquefaction-induced subsidence of 100-250 mm was estimated at 100-year earthquake PGAs for significant areas in eastern and southwestern Christchurch [106].
Without major intervention, including large engineering works and possible additional land rezoning and restrictive planning revisions, the earthquake-induced flood hazard in Christchurch will only increase with time and be compounded by expected rises in sea-level.
With our current state of knowledge of the recurrence of earthquakes on the major faults that ruptured in the CES (6-8 kyr for the Christchurch faults, 20-30 kyr for the Greendale fault) [108,132], the likelihood of future surface deformation and associated flood responses relating to recurrent movement on these faults is interpreted to be very low on timescales less than 2500 years. Future ruptures on other (unknown) local faults that could influence surface topography and thus flood hazard remains unknown; however, there is no evidence at present to suggest faults of comparable size to those that have ruptured in the CES are present beneath eastern Christchurch. In other parts of the region (western Christchurch, eastern Canterbury Plains), it is quite probable that active faults exist and may have the capacity to cause future surface deformations and drainage modifications. Some faults offshore in the Pacific Ocean and more distal sources, such as the Hikurangi subduction zone, present possible tsunami inundation flood hazards that require careful consideration in future flood assessments for Christchurch.

Conclusions
As previously documented [14,17,110], the discrete and cumulative effects of the Canterbury earthquake sequence increased the presence of flood hazards in Christchurch and the surrounding region through modifying surface flow and stream channel gradients, lowering flood plain elevations, reducing channel carrying capacities, and disrupting surface and subsurface drainage and infrastructure. These effects influenced flood hazards across a variety of urban and rural settings, both proximal to and more distant from streams and coastlines. Increased flood vulnerabilities have been modeled across the region [17] and have insurance implications. The high hazard of future earthquake-induced liquefaction, subsidence, and flood events over 100-to 500-year timescales is relevant to engineering design and land-use planning decisions, particularly when viewed from a multi-hazard perspective.