Gullies can be incised into coastal cliffs and bluffs in a variety of geologic settings around the world, owing their formation to a complex interaction of hydrologic, lithospheric, tectonic and atmospheric processes. While much research has focused on gully formation and evolution in non-coastal settings in response to changes, such as land cover and use, natural hazards and/or changes in precipitation, relatively little work has focused on gully geomorphology and morphodynamics in coastal cliffs and bluffs. The most commonly accepted mechanism for coastal gully formation is through concentrated overland flow and knick point migration (Ye et al., 2013; Leyland and Darby, 2008, 2009; Mackey et al., 2014; Limber and Barnard, 2018). Changes in land cover and use due to agriculture, logging, forest fires and other factors can decrease surface roughness and increase concentrated overland flow, which, given sufficient energy and/or time, can erode a narrow section of coastal cliff and form a knick point. Depending on the resistive forces (e.g. geology and uplift) relative to the erosive force of the overland flow, this knick point will migrate inland over time, incising a gully into the cliff or bluff. Recent work has focused on modelling coastal gully formation and evolution as knick point migration (Limber and Barnard, 2018).

Coastal cliff stability and gully incision can be affected by processes of concentrated overland flow, quarrying by waves at the base of the cliff and groundwater discharge (Limber and Barnard, 2018; Kline et al., 2014), although it is unclear when and where each of these factors is important (Collins and Sitar, 2009, 2011). While overland flow is a common formation mechanism, it is possible to have coastal gullies form where the cliff is affronted by a beach, which limits the basal quarrying or notching by waves, and where there is no outward sign of overland flow. Relatively little attention has been paid to the potentially important role of groundwater as a driver of coastal gully formation and evolution, despite the potential for groundwater to affect the geotechnical properties of coastal cliffs (Collins and Sitar, 2009, 2011).

Groundwater has been implicated as an important geomorphic agent in channel network development, both on Earth and on Mars (Kochel and Piper, 1986; Higgins, 1984; Dunne, 1990; Malin and Carr, 1999; Harrison and Grimm, 2005; Salese et al., 2019; Abotalib et al., 2016). The classic model entails a channel headwall that lowers the local hydraulic head and focuses groundwater flow to a seepage face. This leads to upstream erosion by undercutting, the rate of which is limited by the capacity of seepage water to transport sediment from the seepage face (Dunne, 1990; Howard and McLane, 1988; Abrams et al., 2009). Groundwater seepage has been shown to unambiguously lead to channel formation in unconsolidated sand- to gravel-sized sediments (Lapotre and Lamb, 2018; Dunne, 1990), e.g. gravel-braided river deposits in Alaska (Sunderlin et al., 2014) and the Canterbury Plains (Schumm and Phillips, 1986), conglomerates in the Kalahari (Nash et al., 1994), outwash and alluvial sands in Florida (Schumm et al., 1995), Martha's Vineyard (Uchupi and Oldale, 1994) and Vocorocas (Coelho Netto et al., 1988), dune sand and tephra in South Taranaki (Pillans, 1985), and granodiorite regolith in the Obara area of Japan (Onda, 1994). In sediments finer than sands, erosion is typically limited by detachment of the grains at the seepage face. In silts and clays, the permeability is so low that the groundwater discharge is often less than that required to overcome the cohesive forces of the grains (Dunne, 1990). The role of groundwater seepage and channel formation in bedrock, on the other hand, remains controversial (Lamb et al., 2006; Pelletier and Baker, 2011).

Our understanding of channel evolution by groundwater seepage is predominantly derived from theoretical, experimental and numerical models (Howard, 1995; Lobkovsky et al., 2004; Chu-Agor et al., 2008; Wilson et al., 2007; Petroff et al., 2011; Pelletier and Baker, 2011; Higgins, 1982). Such studies suggest that the velocity at which channel heads advance is a function of the groundwater flux and the capacity of seepage water to transport sediment from the seepage face (Fox et al., 2006; Howard and McLane, 1988; Abrams et al., 2009; Howard, 1988), and that channel head erosion occurs by episodic headwall slumping (Kochel et al., 1985; Howard, 1990). Channels incised by groundwater seepage have been shown to branch at a characteristic angle of 72∘ at stream tips, which increases to 120∘ near stream junctions (Devauchelle et al., 2012; Yi et al., 2017), whereas growing indentations competing for draining groundwater results in periodically spaced channels (Dunne, 1990; Schorghofer et al., 2004). Channel network geometry appears to be determined by the external groundwater flow field rather than flow within the channels themselves (Devauchelle et al., 2012).

A number of fundamental questions related to the evolution of channels by groundwater seepage in unconsolidated sediments remain unanswered. First, the temporal scale at which channels form is poorly quantified due to the paucity of process-based observations and detailed instrumental analysis. Field observations of groundwater processes are rare (e.g. Onda, 1994), primarily due to the difficulty with accessing the headwalls of active channels, the potentially long timescales involved and the complexity of the erosive process (Dunne, 1990; Chu-Agor et al., 2008). Quantitative assessments of channel evolution have relied on experimental and numerical analyses, but these tend to be based on simplistic assumptions about flow processes and hydraulic characteristics. Experimental approaches are based on a range of different methods, limiting comparison of their outcomes (Nash, 1996). Published erosion rates vary between 2–5 cm per century (Schumm et al., 1995; Abrams et al., 2009) and 450–1600 m3 per year (Coelho Netto et al., 1988). Second, the influence of geologic heterogeneities on channel evolution is also poorly understood. Lithological strength and permeability contrasts are rarely simulated by experimental and numerical analyses. Third, there are only a few places where the mechanisms by which seepage erosion occurs have been clearly defined (e.g. Abrams et al., 2009). Basic observations and measurements of channel erosion rates and substrate geologic heterogeneities are needed to test and quantify models for channel formation and improve our ability to reconstruct and predict landscape evolution by groundwater-related processes.

In this study, we revisited the Canterbury Plains study site (Schumm and Phillips, 1986) and carried out field observations, geochronological analyses, repeated remote sensing surveys, near-surface geophysical surveying and slope stability modelling of coastal gullies to (i) identify the processes by which groundwater erodes gullies along the coast, (ii) assess the influence of geological/permeability heterogeneity on the gully formation process and (iii) quantify the timing of gully erosion and its key controls.

We have mapped 315 gullies (locally also known as dongas) along 70 km of the Canterbury coastline (mean of 4.5 gullies per square kilometre of coastline). The spatial distribution of the gullies is clustered (nearest-neighbour ratio of 0.33, with a z score of -22.67 and a p value of 0); the majority of the gullies are located between the Rakaia and Rangitata rivers (Fig. 1a), particularly in the vicinity of the Ashburton River. The heads of many gullies connect to shallow, relict meandering channels (Fig. 2a). Some of these channels are visible in aerial photographs, in spite of the terrain having been worked by farmers (Fig. 2b).

In plan view, the gullies are predominantly linear to slightly sinuous (sinuosity of 1–1.3) and characterised by a concave head. In profile, the gullies have linear, gently sloping (2–10∘) axes, with a concave break of slope separating the axis from a steep (up to 70∘) head. In cross section, the gullies are U-shaped, with walls of up to 70∘ in slope gradient. The gullies are between 5 and 1134 m long (mean of 116 m) and between 3 and 637 m wide (mean of 56 m). Gullies generally exhibit a constant width with a distance upslope. They have a length-to-width ratio that varies between 1 and 7.9, with a mean of 2 (standard deviation of 0.89; Fig. 2c).

In May 2017, our study area hosted 33 gullies that vary between 15 and 600 m in length (Figs. 1b, 3a). During the site visits, we did not encounter evidence of surface flow. However, the middle to lower sections of the gully walls and cliffs were consistently wet. These sections were also characterised by failure scars and alcoves, particularly above the sandy lenses. Alcoves were also encountered at the base of gully heads, where they were wet and up to 1 m deep (Fig. 3e). Some sandy layers outcropping across the cliff face hosted tunnels (Fig. 3c–d). Above these tunnels, theatre-shaped scars with a shallow and narrow gully at their base were observed (Fig. 3c). At the base of the scars, the gully heads and some gully mouths, we encountered mass movement debris that was occasionally intact and that predominantly consisted of gravel, sandy gravel and loess (Fig. 3c, h). Gullies have gravel-covered irregular floors. Whereas the smaller gullies have a U-shaped cross section, the three longest gullies have gently sloping V-shaped cross sections, with loess draping their walls (Fig. 3f). Sandy and clean gravel layers outcropping within the gullies were wet; the former appeared weathered, whereas the latter were coated by Fe and Mn (Fig. 3g). Fences were locally seen suspended across a number of gullies (Fig. 3b).

Four sets of infrared stimulated luminescence ages are presented in Table 2. The pIRIR290 ages are higher than the ages obtained by applying the pIRIR225 protocol. The cause of this difference is not yet fully understood, although it can partially be attributed to the results of the dose recovery test and the poor bleachability of the pIRIR290 signals compared to pIRIR225 signals (Buylaert et al., 2011). Considering that no anomalous behaviour of the investigated signals was observed (see the Supplement), we are unable to explain the overestimation of the K-feldspar ages compared to the polymineralic fine-grain ages in the case of NZ13A, especially since the opposite behaviour is observed in the case of sample NZ14A. However, considering a 95 % confidence level, infrared-stimulated luminescence ages obtained using different methods broadly overlap, with the only exception being the pIRIR225 ages obtained on K-feldspars on sample NZ14A, which we regard as an outlier.

The location of the G-TEM transects is shown in Fig. 1b. An attempt was made to invert the G-TEM slingram-mode responses with 30 m TX–RX offset, using a 1D Occam inversion. A representative inversion result is shown in Fig. 7. The resistivity model is presented in Fig. 7b, whereas the corresponding model response with the actual data points is shown in Fig. 7a. The best-calculated smooth depth profile clearly does not fit well with the measured signal, and there is excessive structure in the ∼ 10–20 m depth range, including the very low resistivity layer (∼ 10-4 Ωm) at depths in excess of ∼ 12–15 m. The resistivity values between 40 and 100 m depth are lower than sea water resistivity (0.3 Ωm), which is not reasonable. The inability to fit a 1D model to the slingram responses suggests that the geoelectrical subsurface structure is strongly heterogeneous within the footprint of the G-TEM transmitter. As a result, we cannot trust 1D inversions of the slingram-mode data in such a 3D geological environment. We did not try to use the 1D inversion software to further analyse and interpret the G-TEM data. However, even though the individual slingram-mode responses cannot be fitted reliably by a 1D model, we can still analyse the lateral changes in the observed response curves along the slingram profiles to reveal information about subsurface heterogeneity; this is elaborated on below.

Instead of performing 1D inversions, we present time gate plots for all three transects. A time gate plot is defined as a graph of the observed G-TEM voltage response, evaluated at a particular time gate, as a function of a position along a profile. Time gate plots are a useful alternative for exploring the lateral variability in the G-TEM response along a profile in the event that the sounding curves at individual stations cannot be fitted with 1D models. It is presumed that the variability in a time gate plot is correlated with lateral heterogeneity in the subsurface geoelectrical structure, since a 1D Earth structure would yield no spatial variability in a time gate plot. In general, due to lengthy signal-averaging times, ambient electromagnetic noise from the environment adds a very small contribution to TDEM responses, such that any along-profile variations are likely caused by geological heterogeneity. However, there is not a straightforward relationship between the magnitude of the TDEM voltage at any given time gate and the resistivity within a particular subsurface volume. The situation becomes more complicated since the true Earth is characterised by multiscale heterogeneity, such that spatial variations in the geology at all length scales superimpose their individual responses on one another to produce the final overall TDEM response that is measured. Thus, any analysis of the spatial variability in a time gate plot, while informative, is largely qualitative and indicates only a first-order spatial distribution of causative subsurface structures.

Specifically, the amplitude of the G-TEM slingram response (in units of 10-10 V m-2) at the first time gate is plotted as a function of the station number along a profile. Figure 8a displays a 1D model (I) that contains a conductive layer of 200 Ωm between a 10 and 20 m depth in a homogeneous 1000 Ωm background. The 1D model (i) is motivated by the inversion results of deep-penetrating 40 × 40 m TX loop TDEM soundings carried out on top of the cliffs several tens of metres inland (Weymer et al., 2020), which revealed such a conductive zone at these depths. Unlike the slingram profiles, the deeper-penetrating, larger-loop sounding curves are readily fitted by a 1D model. This model generates a G-TEM slingram response that has a substantially larger ramp-off voltage amplitude at all time gates than the model does (ii) without the conductive layer, as shown in Fig. 8a. Thus, we regard an enhancement in the response at the first time gate as indicative of a conductive zone at depth beneath the slingram station. The spatial analysis of the time gate plots is not a conventional approach in time domain electromagnetics, but it is somewhat analogous to the spatial analysis of the apparent resistivity profiles in frequency domain electromagnetics using terrain conductivity meters (e.g. Weymer et al., 2016). This is based on the idea that the G-TEM response at a fixed time gate carries information similar to that of a terrain conductivity meter response at a fixed frequency.

The first time gate profile of transect May15-1 is located upslope of small but recently eroded gullies (Fig. 8b). In this figure, the first time gate profile is a plot as a function of the distance along the transect of the G-TEM ramp-off voltage at time gate number 1, which is the first sampled point of the transient response immediately after the TX current has been switched off. Near the middle of this transect, there is a distinctive peak that is much higher than the background. The peak is ∼ 20–30 m wide, and it appears in a similar fashion on each of the gates 1 through 7 (not shown here), although it cannot be clearly observed after gate 7. Transect May15-2 is located upslope of recently eroded gullies in the southwest and relatively less active gullies in the northeast of the investigated area (Fig. 8c). Lateral variations are evident along the 192 m length of the profile. The high-amplitude response at the start of the profile (going from the southwest to the northeast) is followed by a drop in amplitude near the midpoint of the profile, after which there is continuous fluctuation at a lower amplitude until the end of the profile. The time gate plots for gates 2 to 7 remain similar in shape to that of the time gate 1 plot and, hence, are not shown. After time gate 7, the time gate plots start to lose coherence due to the low signal-to-noise ratio of the decaying RX voltage at late times after TX ramp off. The G-TEM slingram profile May17-2 was acquired upslope of the tributary of a large gully covered by mature vegetation (Fig. 8d). As shown in Sect. 4.4, the size and location of this gully have been persistent over recent years, in contrast to the neighbouring, smaller gullies that are under active development. Transect May17-2 shows a lower amplitude response in comparison to the previous two transects (Fig. 8).

Based on all three profiles, a general observation that can be made is that the first time gate amplitude of the slingram response is higher upslope of the more recently active gullies.

The Canterbury gullies initiate and evolve via two types of groundwater-related processes. The first process is the seepage erosion of sand, which leads to the formation of alcoves and tunnels. This inference is based on the exclusive occurrence of tunnels in sandy layers at the study site (Fig. 3c–e). Seepage erosion lowers the overall factor of safety of the slope, as demonstrated by slope stability model results for the slope with sand lens scenario, and is a precursor to the second process, which is slope failure (Fig. 3c). Site observations (Fig. 3h), the UAV data (Fig. 4) and satellite imagery (Fig. 5) show that gullies primarily evolve by retrogressive slope failure, which results in the elongation of the gullies and, to a lesser extent, widening and branching along the gully walls. According to the slope stability model in Fig. 9a, up to 4.4 m3 of seepage water is required to erode 1650 m3 of sediments, which contrasts with the inference by Howard (1988) that 100–1000 times more water than volume of eroded sediment must be discharged in order to create a sapping valley. We infer that wave erosion is responsible for the removal of the failed material at the gully mouths and the base of the cliff. Isotropic scaling of length with width (Fig. 2c) suggests that gully planform shape is generally geometrically similar at consecutive stages of evolution.

Two factors control the location of gullies. The first factor is the occurrence of sand lenses across a sandy gravel cliff face. This geological framework is conducive to alcove formation, tunnelling and slope failure (Fig. 3c–e). The higher permeability of the sand and clean gravel lenses, in comparison to the surrounding sandy gravel (Table 1), facilitates faster water transfer to the cliff face; this is also corroborated by the weathering in the sandy layers and Fe and Mn deposits in the clean gravel layers (Fig. 3g). Alcoves and tunnels only form in the sand lenses; however, the latter develop higher pore pressures, and sand is easier to entrain and remove in comparison to clean gravel in view of its lower shear strength (Table 1). Slope failure only occurs in sandy gravel slopes with sand lenses (Figs. 9–10). The higher pore pressure developed in the sand lenses is transferred to the sandy gravel slopes, resulting in a larger decrease in the shear strength and higher water table in comparison to the sandy gravel slope with gravel lens.

The second factor is a hydraulically conductive zone upslope of the gully. This inference is supported by the following observations: (i) braided river channel infills, which tend to comprise highly permeable, coarse-grained materials (Moreton et al., 2002), lead into the gullies' heads (Fig. 2a–b); (ii) clustered distribution of gullies between the two braided rivers with the highest flow rates (Rakaia and Rangitata rivers; Environment Canterbury, 2019; Fig. 1a); (iii) geophysical observations (Fig. 8). With regards to the G-TEM slingram time gate plots (Fig. 8), we interpret the higher-amplitude responses on the time gate 1 plots that are preferentially located upslope of recently active gullies as being zones of relatively high electrical conductivity in the subsurface at depths of ∼ 10 m. These zones are suggestive of buried groundwater conduits made up of gravel and/or sandy units (Weymer et al., 2020) or tunnels formed by subsurface groundwater flow in sand units. Further analysis of the G-TEM data, including 2D modelling and inversion, is required to ascertain the subsurface hydraulic geometry responsible for the along-profile amplitude variations. This is elaborated on in the Supplement. The above observations confirm the importance of spatial variations in hydrogeological properties as a factor controlling the location of a gully. This had initially been suggested by Dunne (1990) and has been documented for gullies in bedrock environments (Laity and Malin, 1985; Newell, 1970). Development of gullies downslope of permeable conduits may also explain why most of the erosion entails the elongation of existing gullies rather than formation of new ones (Figs. 4, 6). It also agrees with the results of the experimental modelling by Berhanu et al. (2012), which suggest that channels grow preferentially at their tip when the groundwater flow is driven by an upstream flow. If seaward-directed groundwater conduits are responsible for the location of gullies, the G-TEM results predict that, along the Canterbury coast, we should generally observe active gully development downslope of peaks in slingram time gate plots. If this is the case, G-TEM could be used to identify the locations of incipient and even future gully development.

Morphological changes derived from the time series of UAV data (Figs. 4–5) and satellite imagery (Fig. 6), and the observations of suspended fences across gullies (Fig. 3b), suggest that gully formation is rapid (on daily timescales) and recent (< 3 years ago). It is an episodic process that occurs after a threshold is exceeded. This threshold entails a rainfall intensity of > 40 mm d-1, which occurs once every 227 d on average. The threshold value is based on UAV and satellite imagery observations, which show that gullies form after rainfall events, with an intensity higher than 40 mm d-1 (Figs. 5, 6), and the plot of the factor of safety with rainfall intensity from the slope stability model for the first scenario ((I-D)3 for the slope with sand lens (Fig. 9). The erosion rate documented in our study area is up to 30 m d-1 (Fig. 4e-f), which is the highest rate documented for gullies formed by groundwater so far.

The majority of the gullies in our study area have shown evidence of erosion in the past 11 years (Figs. 4, 6). The luminescence-dating results (Table 2), however, suggest that the two largest gullies have largely been inactive during at least the last 2 ka; recent erosion is only documented in small gullies located in the central section of their mouths (Figs. 4, 6). This contrasts with the inference by Schumm and Phillips (1986) that they were formed by the spillage of water from swamps behind the cliffs in the 19th century. We therefore propose that the short gullies (< 200 m in length) are recently active features, whereas the largest gullies are relict features that formed as a result of higher groundwater flow, and possibly surface erosion, in the past. The age of sample NZ13A suggests that this may have occurred during the Last Glacial Maximum. Such a difference in age, and possibly formation process, between gullies of different lengths may explain the different cross sectional shape and higher scatter in the plot of length vs. width for the longer gullies (Fig. 2c).