Erosion Assessment at Earthen Archeological Sites by Morphometric Analysis of Digital Surface Models: The Case of Huaca Fortaleza (Pampa Grande, Peru, 600–750 AD)

Abstract

Earthen archeological sites may be damaged by rain-induced erosion processes. Huaca Fortaleza (HF; 600–750 AD) is an originally four-level truncated pyramid in the semi-arid Lambayeque region of northern Peru, an area affected by seasonal intense rain due to El Niño Southern Oscillation (ENSO). We use data from a UAV-based photogrammetric survey and generate a Digital Surface Model from which we extract selected geomorphometric parameters and apply a hillslope diffusion model. The obtained data show that HF steep flanks exhibit a marked erosion expressed by a drainage network of parallel rills and gullies with architectural structures controlling pathways for concentrated flow. The southwestern flank is affected by gravity instability. Localized pits at the top of HF cause infiltration of rainwater. The erosion by ENSO rainfall is responsible for extensive architectural loss, with the HF lower platforms now entirely obliterated. We calculate vertical erosion rates of 0.28–0.38 m/century, a range of values comparable with that estimated for river incision. Erosion due to diffusion processes is estimated in the order of ~0.015 m/century. Our approach represents a transferable methodology applicable to other earthen archeological sites affected by erosion worldwide.

1. Introduction

Rainfall-induced erosion is a critical environmental driver capable of compromising transportation networks, agricultural and industrial settlements, urban centers, and cultural heritage [1,2,3]. Because erosion rates are tied directly to rainfall intensity [4,5], the intensifying rainfall associated with climate change poses a severe risk to historical sites [6,7]. In this framework, effective preservation strategies begin with understanding the link between erosional mechanisms and physical degradation, i.e., damage [6,7,8,9,10,11]. Earthen archeological sites constitute about 10% of World Heritage [12]. These sites are globally distributed across the Americas, Europe, Africa, Asia, and Oceania [13] and built with materials characterized by a low preservation potential such as sand–clay mixtures [14]. In the Lambayeque region of northern Peru, these structures often take the form of huacas (from the Quechua term “wak’a”, meaning sacred place or temple). These ceremonial platforms, which have the shape of truncated pyramids, were built using adobe bricks, a blend of clay, sand, and straw. Spanning from the 2nd millennium BC to the 16th century AD, these structures reached their peak between the 6th century and the Inca annexation in the 16th century [15,16]. The architectural and structural integrity of these pre-Hispanic settlements is frequently endangered by intense rainfall from El Niño Southern Oscillation (ENSO) events [17,18,19]. Historical records and archeological evidence confirm destructive ENSO activity dating back millennia [20,21,22]. Indeed, the decline of the Moche culture in northern Peru is believed to be related to ENSO events between 100 AD and 700 AD, and the more recent ENSO events in 1925, 1982, 1997, and 2023 have devastated local infrastructures and urban/agricultural settlements [23,24,25]. While climate change is expected to increase the frequency of these events, predicting the exact intensity of future ENSO cycles remains a major challenge [26,27]. Consequently, standard probabilistic or scenario-based hazard assessments [28] are often unrealistic for coastal Peru due to a lack of well-constrained forecast models. To bypass these limitations, we propose an alternative analysis focusing on Huaca Fortaleza (HF; about 600–750 AD), also known as Huaca Grande (Pampa Grande Archeological Complex), the tallest, multilevel platform of Peru (Figure 1a–c). HF, which was recognized to be partly dismantled by natural processes [29], is in an area with a semi-arid climate affected by north-directed winds related to the Humboldt Current between May and January, and by east-directed winds and intense rain due to ENSO events between February and April. Our study utilizes a high-resolution (cm-scale) Digital Surface Model (DSM) of HF derived from a photogrammetric survey. DSM has been combined with direct field observations to collect information about the spatial correspondence between geomorphic features shown in the DSM and the location of the main incisions, ridges, and closed depressions. We use morphometric parameters extracted from DSM to (a) quantitatively determine the current preservation state of the site, (b) identify the morphological features related to specific erosion mechanisms, and (c) evaluate the long-term exposure of the HF structure to diffusion processes such as rain splash, surface runoff, and soil creep [30,31]. Unlike previous research relying solely on hydraulic modeling, laboratory decay measurements, or monitoring data [32,33,34,35], our method integrates archeological and morphometric data to analyze the effects of exogenous, climate-driven geomorphological processes on HF.

More generally, the approach we propose represents a framework to quantify the degree of damage of earthen sites providing the data necessary for future protection strategies. Our analysis is also aimed at identifying the processes responsible for the HF dismantling. This represents the first step for the actions designed at preserving and managing earthen archeological sites [36,37,38].

2. Archeological Setting of Pampa Grande Site and Huaca Fortaleza

Pampa Grande is an archeological site located in the Lambayeque Valley, in northern Peru, situated on the south shore of the Chancay–Lambayeque River, approximately 54 km inland from the Pacific Ocean (Figure 1a,b). The site occupies a strategically critical position at the neck of the river valley, a location that, as suggested by [39], enabled agricultural activities. The Moche civilization grew along the northern coast and valleys of Peru between approximately 100 AD and 800 AD. Although the climate of the Lambayeque Valley is characterized by an arid coastal desert, the proximity of the Pacific Ocean and the influence of Andean river systems mitigate it in the area of Chancay–Lambayeque River. During the Moche occupation, the Pampa Grande area maintained a moderate climate. During the winter months, the El Niño Southern Oscillation (ENSO) current occurs, bringing torrential rains and winds. These severe events are recognized as a major driver of both the Pampa Grande site’s foundation and its ultimate abandonment [40,41]. The earliest occupational evidence at Pampa Grande dates to approximately 600 BC. The site subsequently underwent a dramatic transformation during the late first millennium. Pampa Grande, the largest and most powerful city of the Moche culture on the north coast of Peru, was built, inhabited, and abandoned during the period 550–750 AD, making it one of the few pre-Hispanic cities in South America for which sufficient available data exist [39,41]. The rapid collapse of the Moche culture proposed in earlier studies [39,42,43,44] is no longer considered fully sustainable. More recent studies reporting new radiocarbon ages and stratigraphic data suggest a more gradual process of decline between eighth and ninth century AD [45,46]. During its maximum expansion between 600 and 750 AD, Pampa Grande functioned as the capital of a state that controlled the Lambayeque, La Leche, and Zaña drainages, covering approximately six square kilometers with an estimated population of about 15,000 inhabitants [39]. The major monumental structure of Pampa Grande is Huaca Fortaleza (HF; Figure 1c–e), also known as Huaca Grande. Huaca Fortaleza ritual platform had an estimated original height of 55 m and an accessible 56 m long ramp. The reconstruction provided by [47,48] indicates that original HF covered an area of 0.022 km² and the perimeter was 600 m. The sides of the rectangular base measured 150 m (length axis) and 135 m (width axis). HF is the tallest earthen structure in South America, and it is constructed entirely of adobe bricks. The HF architectural structure consists of truncated prismatic volumes with terraces and platforms disposed on at least four levels [47,48]. Following the abandonment of Pampa Grande, ref. [39] suggests a roughly four-century hiatus before the rise in the major Chimú urban center at Chan Chan, thus contrasting earlier models that suggested a more direct cultural continuity [21]. The role of the highland Wari state in triggering or accelerating the decline remains debated, though most scholars now treat external Wari intervention as a contextual factor rather than a primary cause [45,46].

3. Methods

We conducted a survey of HF and surrounding area by combining traditional field observation with remote sensing techniques. The aim is the detection of geomorphological features indicative of dismantling processes affecting the HF architectural structure.

3.1. Photogrammetric Survey and Digital Surface Model (DSM)

The photogrammetric survey of HF was carried out on 2 May 2025. We follow the acquisition procedure detailed in [49,50], and only the main steps are summarized here. The aerial survey was performed using a UAV quadcopter DJI Inspire 1.0 (DJI, Shenzhen, China) equipped with a DJI Zenmuse X3 camera (CMOS 1/2.3” sensor; 12-megapixel resolution; DJI, Shenzhen, China) and an integrated navigation system comprising a GNSS receiver, gyroscopes, an altimeter, and a magnetic compass. This platform was selected for its suitability to low-altitude, high-resolution photogrammetric surveys over archeological sites, where the combination of maneuverability and payload capacity makes it particularly effective for documenting complex topographic surfaces such as those of earthen monuments [51]. The data acquisition was conducted using a freely flown mission strategy, in which the UAV operator manually guided the aircraft to ensure adequate coverage of all visible surfaces of the huaca, including the irregular flanks and the summit platform. The flight altitude was maintained at 37 ± 2 m above the takeoff point, which was located on top of HF at approximately 224 m above sea level. This flight altitude was deliberately chosen to maximize the spatial resolution of the acquired imagery and to capture fine-scale surface features such as erosional scarps, cracks, and surface crusting on the adobe masonry. A total of 781 images, each with a resolution of 12 megapixels, were acquired during the survey. The images were captured with a forward and lateral overlap of 82–92%, ensuring redundant coverage of all areas and providing a robust dataset for photogrammetric reconstruction. The density was 843 pixel/m². Georeferencing of the survey was achieved through a network of 12 pre-marked ground control points (GCPs), which were distributed across the accessible surfaces of HF prior to the flight. The coordinates of these targets were measured using a Trimble R6 GPS Receiver (Trimble Inc., Westminster, CO, USA) providing high-precision positional data in UTM coordinates (WGS84, zone 17S). The plane (x, y) and elevation (z) accuracies of GCPs are 2 cm and 5 cm, respectively. Communication between the base station and the UAV was maintained via a radio communication system throughout the survey. The Root Mean Square Error (RMSE) of the horizontal coordinates of the control points was 1 cm on both the x and y axes, and 3 cm on the z axis, confirming the high geodetic accuracy of the GCP measurements. The acquired images of HF have an overall ground resolution of 3.44 cm/pixel and a positional accuracy of 4.5 cm, values that reflect both the flight altitude and the quality of the georeferencing network.

The three-dimensional reconstruction of HF was completed using Agisoft Metashape software (v. 1.7.4; https://www.agisoft.com). The workflow followed in Metashape included image alignment, dense point cloud generation, mesh construction, and texture mapping, with the GCPs incorporated at the alignment stage to ensure accurate georeferencing of the final products. The DSM was built by Kriging and visualized using Surfer software (version 20.1.195, Golden Software) (Figure 1c). The DSM of HF has a spatial resolution of 9 cm/pixel, with RMSE values of 5 cm on the x and y axes and 7 cm on the z axis. This value of spatial resolution was selected to maintain a safe margin above the image accuracy to avoid the propagation of errors into the final model. In addition, the 9 cm resolution was considered appropriate to account for potential interpolation errors within the Agisoft Metashape reconstruction processing, particularly in areas characterized by deep shadows cast by cracks along the summit of the huaca, and by major topographic depressions. In these areas, the limited illumination and complex geometry can reduce the density and reliability of the tie-point matches introducing local inaccuracies in the reconstructed surface. The Surfer by Golden Software version 13 was also used to derive and visualize the maps of morphometric parameters defined in the following section.

3.2. Morphometric Parameters

We select some morphometric parameters extracted from the DSM of HF with the aim to (a) characterize the present HF architectural structure and morphology and (b) quantify the impact of dismantling processes. The selected morphometric parameters are Slope, Aspect, Topographic Position Index (TPI), Stream network and watershed basins, Topographic Wetness Index (TWI), Valley depth, L-S factor, Stream Power Index (SPI), and Closed depressions. The last 6 parameters are specific for the analysis of erosional features related to waterflow or stagnation [31,52]. We also apply a diffusion model [53,54] to DSM with the aim to identify the areas potentially affected by erosion or deposition associated with long-term diffusion processes. Here below, we report the analytical expressions and morphological significance of the above listed morphometric parameters.

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Slope is measured in degrees and calculated according to [55]:

Slope = 360/2π arctan √ [(Z_E − Z_W)/2∆x)]² + [(Z_N − Z_S/2∆y)]²

(1)

where Z is the vertical component, x and y the horizontal components, and the subscripts N, S, E, and W the cardinal points.

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Aspect is the azimuth that a terrain surface faces. Aspect is measured in degrees from the north in a clockwise trend following [55]:

Aspect = 270 − 360/2π atan 2 [(Z_N − Z_S)/2∆y, (Z_E − Z_W)/2∆x]

(2)

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Geomorphons. This parameter reflects a land-surface classification method identifying terrain forms by analyzing the spatial pattern of relative elevation differences around each point in a DSM [56]. Geomorphons are computed using a ternary pattern of line-of-sight comparisons between a central cell and a set of surrounding cells distributed along eight cardinal and intercardinal directions. For each direction, the relationship between the central cell and the outer cell is encoded as one of three states (higher, lower, or equal) producing a ternary pattern that is then matched to one of the following fundamental landform types: depression, summit, ridge, spur, slope, hollow, and valley.

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Drainage network and watershed basins. The map of the stream network and watershed basins has been determined with the Deterministic 8 Neighbor algorithm [57,58,59] (https://saga-gis.sourceforge.io/en/index.html, (accessed on 20 March 2026)). The algorithm requires the DSM and the threshold for the Strahler order as data input. The threshold of Strahler is required to initiate the channel network and delimit the basins. We select a Strahler order of 5 and delete the streams with length < 10 m to obtain a sufficiently detailed network of the main streams by avoiding minor incisions.

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Valley depth. This parameter is determined following [59] as specified at https://saga-gis.sourceforge.io/saga_tool_doc/6.1.0/ta_channels_7.html (accessed on 15 January 2026). Valley depth is determined as difference between the altitude and an interpolated ridge level. Ridge level interpolation uses an algorithm performing the following steps: (a) outlining ridges using Strahler order on an inverted DSM, (b) interpolation of the ridge levels, and subtraction of the original elevations from the ridge levels.

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LS factor combines the following two components: the L factor, which represents the effect of slope length (i.e., the horizontal distance from the point of origin of overland flow to the point where either deposition begins or runoff enters a defined channel), and the S factor, which expresses the influence of slope gradient. Together, these two components capture the potential erosive power of water moving downslope. The underlying physical rationale of the LS factor is that longer and steeper slopes generate higher flow velocities and greater shear stress at the soil surface, thereby increasing the transport capacity of overland flow.

The analytical expression of LS factor is [60]:

LS = (As/22.13)^0.4 (sinβ/0.0896)^1.3

(3)

where As is the specific catchment area (upslope contributing area per unit width) and β is the local slope angle in degrees. Beyond soil erosion modeling, LS factor has been widely applied in geomorphological research as an indicator of erosion susceptibility, landscape instability, and sediment connectivity, and has been used in studies of both natural hillslopes and anthropogenic structures, including archeological sites [61,62].

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Topographic Wetness Index (TWI) defines the areas characterized by water flow or stagnation during rain episodes [63]. TWI is a dimensionless parameter defining the balance of catchment water supply and local drainage. TWI calculation requires the following two input parameters [64]: the local upslope area draining through a certain point per unit contour length A, and the local slope S in radians. The analytical expression is:

TWI = ln[(A)/tan(S)]

(4)

TWI allows us to obtain information on the potential runoff generation areas.

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Closed depressions define the zones where the water may stagnate, i.e., the zones surrounded by higher terrains in all directions. We use the algorithm by [57], which has been validated by [65]. The digital map of the depth of then closed depressions is obtained by subtracting the depression-free DSM from the original DSM.

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Hillslope diffusion model. This model estimates the areas of possible deposition and erosion related to diffusion processes. We apply a hillslope evolution model defined by the equation [53,54]:

δh/δt = Dδ²h δx² + δ²hδy²

(5)

where D is the diffusion coefficient, h is height, t is time, x and y are the spatial dimensions. Diffusion processes occur over timescales of seasons (months) to years. The main mechanisms of diffusion include earth and soil expansion/contraction due to exsiccation or humidity, creep, discontinuous surface, and bioturbation. Diffusion processes are responsible for the smoothing of slopes and changes in the geometry of incisions and formation of rills, gullies, and deepening, or filling, of pre-existing incisions [31]. Because of the HF area semi-arid climate and the clay-dominated HF adobes, we select a value of D = 360 10⁻⁴ m²/yr [66] and perform the calculation over a time of 1 century. We selected this value of D because the study by [66] focuses on an area characterized by a semi-arid to hot Mediterranean climate constituted by a high-plasticity clay soil on a 30° slope. These are climatic, geological, and morphological conditions comparable to those of HF. We remark that the selected D value is the only one available in the scientific literature for semi-arid to hot Mediterranean climate terrains. The areas of HF where erosion or deposition may potentially concentrate in the future are computed as difference in altitude between the measured DSM and that calculated by applying Equation (5) to such DSM. In defining the spatial distribution of the values of the above defined morphometric parameters we exclude from the DSM all the areas covered by vegetation based on the analysis of orthophotos and manual vector masking. The morphometric parameters have been determined without filtering of the original DSM and have been calculated using the SAGA software (version 9.11.3) developed by [59] and Surfer (version 13.0) by Golden Software. The histograms of the grids from the above detailed parameters (Slope, Aspect, Valley depth, LS factor, TWI and Depth of closed depressions) in the surveyed area are reported in Figure S1 of the Supplementary Material. The histograms of the grids from the above detailed parameters (Slope, Aspect, Valley depth, LS factor, TWI and Depth of closed depressions) in the HF architectural structure alone are reported in Figure S2. The statistics of grids are reported in Table S1.

4. Results

Results of the geomorphometric analysis of HF DSM are summarized in Figure 1c,d, Figure 2, Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7. The shaded relief DSM and the cross section in Figure 1c,d provide a comprehensive view of the HF structure. DSM indicates that HF has been built on a northwest facing, ~8° sloping surface. This surface is partially interrupted by rectilinear, up to 1 m high orthogonal ridge network with individual ridges striking NW-SE and NE-SW (Figure 1c). This arrangement is also well-delineated in the slope and aspect maps reported in Figure 2. The ridge network probably represents the remnants of walls delimiting enclosures [39]. The HF main structure has the shape of a truncated pyramid constituted by an upper, square-shaped platform at an altitude of 210 to 224 m a.s.l. (above the sea level), and a lower, rectangle-shaped terrace built on the northwestern flank of the main building at an altitude between 184 m and 196 m a.s.l. (Figure 1c). The HF flanks face toward NW, NE, SE, and SW with slopes between 20° and spur (average value 42°) (Figure 2). The NE and SE facing flanks show a width of 31 and 46 m, respectively, while the SW and NW flanks have a width of 28 m and 21 m, respectively. The distribution of geomorphons (Figure 3) reveals that the nearly planar slope on which HF lies mainly consists of slopes with minor spurs and small incisions (valleys) with few ridges delineating the previously mentioned remnants of a wall network (Figure 3).

The top of the HF main structure is constituted by ridges, spurs, and minor incisions, while the flanks consist of ridges, deeper incisions, and slopes (Figure 1c and Figure 3). A small, NE-SW striking rectilinear incision departs from the middle NW facing flank and propagates downward to the right of the enclosure. A larger valley is located at the base of the SE and SW flanks of HF.

Figure 4a summarizes the main architectural elements we extract from the combined analysis of Figure 1c, Figure 2 and Figure 3 and field observations. The main elements we recognize are (Figure 4a): the already mentioned remnants of walls in the plain surrounding HF, the HF lower terrace, the ramp, which is defined by the above reported NE-SW striking rectilinear incision departing from the middle NW facing flank, and the top of HF, which consists of a lower platform, a middle platform, a room delimited by a small, now nearly totally dismantled wall, and an upper enclosure. The comparison of the archeological boundaries based on the local morphology depicted in Figure 4a, and the reconstruction of HF based on archeological data by [47] (Figure 4b) clearly evidences that most of the original architectural elements of HF are now totally or heavily dismantled. In particular, the present-day terrace corresponds to an enclosure located on the second level, while the platforms of levels 1 and 2 are now totally covered by the present-day incisions affecting the flanks of HF. Only parts of the lower and middle platforms, the room, and the upper platform (Figure 4a) correspond to the original enclosures of the third and fourth level.

Data from Figure 5 show that the drainage network is strongly controlled by the architectural elements with the plain surrounding HF characterized by a subparallel to diverging network, the latter related to incisions departing from the HF terrace (Figure 4a). The divergence angle based on the stream network within the main basins in the northwest plain of HF is between 14° and 45°. The incisions affecting the flanks of the HF truncated pyramid show a subparallel arrangement with exception of those located at the edges. The valley depth values (Figure 5b) in the plain around HF are generally less than 3 m, whereas the HF structure shows values up to 8 m in the northwestern edge and terrace of HF, and 14 m in the SW facing flank. However, field observations evidence that this flank of HF is also affected by gravity instability phenomena.

The spatial distribution of the LS factor values shows that the plain surrounding HF is characterized by values less than five, whereas the HF platform and its flanks have an average value of 12 with peaks of 45 in the main incisions. Only the southwestern sector of the HF top shows values less than five. This sector corresponds to the room at the third level recognized by morphological and archeological reconstruction (Figure 4a,b). Higher values of the LS factor imply higher shear stress of the overland water flow on the HF flanks. Therefore, if the shear stress exerted by the water exceeds the shear strength of the adobe, the areas with the higher values of LS factor, as those recorded on the major HF incisions, are expected to be affected by potentially relevant remobilizations of material and erosion.

The distribution of the TWI values (Figure 6a) shows that while the plain around HF is characterized by positive values consistent with rainwater-concentrated flows or stagnation, the HF top and the flanks have prevailing negative values suggesting prevailing washout processes.

A more detailed analysis reveals that such negative values occur on the morphological ridges separating the main incisions on the flanks. The few areas with positive TWI values on HF concentrate on the western sector and its upper platform. These areas overlap zones characterized by closed depressions with depth up to 3.5 m (Figure 6b) where the rainwater could potentially stagnate and/or penetrate downward in the main HF structure. In the surveyed area around HF, evidence of relevant closed depression is lacking. The results of the hillslope diffusion model depicted in Figure 7 reveal that the plain around HF is expected to be not significantly affected by relevant erosion or deposition processes.

In this area, minor erosion processes concentrate on the rectilinear ridges representing the remnants of walls. On the contrary, the HF truncated pyramid is predicted to be impacted by relevant erosion processes mainly concentrated on the present-day ridges separating the incisions affecting the top and flanks of the building. Deposition processes are expected to occur in present-day incisions. The net balance between the amount of erosion and deposition is nearly zero; the distribution of the areas potentially subjected to these two processes is almost symmetric around zero (Figure 7).

5. Discussion

The geomorphometric parameters extracted from the analysis of the HF DSM indicate that erosion is the dominant active process affecting the HF structure. The LS factor values (Figure 5c), a proxy for erosion potential, are markedly elevated across the pyramid’s flanks and platform and contrast sharply with the surrounding plain, where LS factor remains low, highlighting the pronounced erosive susceptibility of the HF structure relative to its natural neighbor plain. This pattern is consistent with the Topographic Wetness Index (TWI) results (Figure 6a), which show prevailing negative values across the top and flanks of HF, indicative of dominantly dispersive, wash-dominated regimes where overland flow accelerates across steep surfaces rather than concentrating into ponded or flow conditions. The ridges separating the main incisions on the flanks are particularly exposed to washout, as the TWI analysis identifies these as zones of divergent flow. A well-developed drainage network, strongly guided by the architectural fabric of HF, is characterized by incisions affecting the flanks of the truncated pyramid displaying a subparallel arrangement, consistent with parallel rills possibly driven by uniform overland flow descending the steep flanks (average slope 42°, locally up to 80°; Figure 2 and Figure 5a). These are not superficial features: valley depth values reach up to 8 m along the northwestern edge and terrace, and up to 14 m on the SW-facing flank (Figure 5b), indicating that incision has penetrated deeply into the adobe structure. The development of a notable NE-SW striking rectilinear incision departing from the middle of the NW-facing flank, interpreted as the remnant of a ramp (Figure 4a), suggests that pre-existing architectural discontinuities, e.g., wall boundaries and access routes, act as preferential pathways for concentrated flow and therefore focus erosion and incision processes. At HF, this interplay between architectural geometry and erosional channeling is a key mechanism accelerating structural degradation. The SW-facing flank exhibits valley depth values up to 14 m, the largest recorded across the monument (Figure 5b). Field observations confirm that this sector is additionally affected by gravity-driven instability phenomena, suggesting that mass movements, in the form of slumping and toppling of weakened adobe blocks, superimposes on the rainwater incision signal. This combination of incision undercutting the flanks and gravitational failure represents the most critical geomorphic threat currently operating on HF and likely accounts for the exceptional valley depth values recorded in this sector.

Incision processes identified on the HF flanks include rills and gullies, two morphologies reflecting the evolution of an incision process that, based on experimental data [67], include the following steps: inter-rill erosion, rill initiation and growth, rill stabilization, ephemeral gully formation, and gully stabilization. During the initial stages, lateral widening of incisions consistently outpaces vertical deepening under low rainfall intensity conditions, whereas the subsequent development of gullies in the later stages is instead dominated by progressive channel incision. High rainfall intensity represents an additional key factor in triggering the transition from rills to gullies. Based on these findings, we interpret the rills documented on HF as erosional features generated by diffusive processes operating under low rainfall intensity conditions, while the gullies could be indicative of a more intense erosional regime possibly driven by the high-intensity precipitation characteristic of ENSO-type events.

A localized but relevant erosion process is identified on the western sector and upper platform of HF, where positive TWI values coincide with closed depressions up to 3.5 m deep (Figure 6a,b). These are pits where rainwater may pond and infiltrate downward into the structural core of the monument, potentially weakening internal cohesion through wetting and dissolution of adobe materials. This dismantling process, while spatially limited compared to the surface erosion affecting the flanks, could have a long-term impact on the structural stability of HF by progressively degrading the interior of the building from within. The Lambayeque region experiences semi-arid climatic conditions, and consequently the erosion processes affecting HF are mainly driven by high-intensity rainfall associated with ENSO episodes occurring between February and May, although limited overland flow and raindrop impact during the June–January period cannot be ruled out. During ENSO events, the prevailing wind direction is oriented from west to east while it is from south to north between June and January [25]. According to these observations, the SW and SE flanks of HF show a reduced width with respect to the NW and NE flanks and are characterized by the highest valley depth (Figure 5b). In this picture, the different exposure to wind-controlled rainfall could explain the asymmetric morphological features of the HF flanks. The mechanisms by which wind-driven rain intensifies lateral erosion on the windward side of a morphological relief as HF are (a) an increase in kinetic energy due to the addition of a horizontal component of velocity to falling raindrops and (b) angle of impact. The wind-driven raindrops strike the windward slope at an oblique angle which, when combined with the high force of impact, maximizes the soil detachment and propels sediment much further downslope by splash-saltation transport.

The cumulative effect of surface washout, parallel rills, deeper incisions, and gravitational instability has resulted in extensive dismantling of the original HF architecture. Comparison between the morphometrically derived present-day map and the historical reconstruction by [47] (Figure 4a,b) reveals that the platforms of levels 1 and 2 are now entirely buried or removed by the incisions affecting the flanks, and only portions of the third and fourth level enclosures remain recognizable in present-day morphology. The lower terrace, now the most prominent surviving architectural element, corresponds to what was originally a second-level enclosure, implying that the entire lower portion of the monument has been substantially reduced. The remnants of the surrounding wall network, preserved as low rectilinear ridges up to 1 m high in the adjacent plain, are themselves subject to minor but ongoing erosion concentrated along their crests, as predicted by the diffusion model (Figure 1c, Figure 4a and Figure 7). While erosion dominates, the hillslope diffusion model, in which the calculated values must be considered as order of magnitude values because strongly dependent on the selection of D, predicts that deposition processes are spatially complementary, occurring within the present-day incisions as material eroded from the intervening ridges is locally redeposited (Figure 7). Importantly, the net volumetric balance between erosion and deposition over a modeled century-scale timeframe is approximately zero, meaning that mass is being redistributed within the structure rather than exported in large quantities to the surrounding plain. This mass redistribution is nonetheless morphologically significant, as it progressively infills incisions while stripping the ridges, a process that over time smooths the surface morphology and obliterates architectural detail. Overall, our geomorphometric analysis paints a picture of a huaca under sustained multi-process deterioration, where steep slopes, architectural discontinuities, and the inherent erodibility of adobe construction materials combine to drive rapid surface lowering, deep incision, and progressive loss of architectural fabric.

Based on the data of valley depth (Figure 5b) and taking into account that (a) the average values on the HF flanks are of 4–5 m and (b) the age of HF (600–750 AD), we estimate a rough value of the average incision (vertical erosion) rate, which we estimate in the order of 0.28–0.38 m/century. We remark that the above specified average value of the valley depth has been calculated by excluding from the analysis the areas affected by gravity processes. This interval of values is comparable to that calculated for river erosion on time scales 1–100 yr, which is 0.2–0.3 m/century [68]. Considering the results of the diffusion model (Figure 7) and assuming an average erosion of 1.5 m over 1 century, we estimate an average erosion rate by diffusion processes (earth and soil expansion/contraction due to exsiccation or humidity, creep, discontinuous surface, and light rain) of 0.015 m/century, a value one order of magnitude lower than that calculated using the valley depth as finite erosion parameter. We conclude that the erosion related to heavy rain due to ENSO events is significantly more relevant than that due to diffusion processes alone.

In summary, our results highlight that an effective conservation strategy of earthen archeological sites should be developed after a careful analysis integrating archeological data and outcomes from geomorphological and morphometric investigations. The semi-quantitative morphometric framework adopted here to characterize the natural processes driving the deterioration of HF has the potential to be applied beyond this specific case, serving as a transferable methodology for other earthen archeological sites worldwide, particularly those situated in settings prone to damaging climatic phenomena such as ENSO episodes and/or extreme environmental conditions, including arid and tropical climatic regimes.

6. Conclusions

The results of the geomorphometric analysis of DSM extracted from photogrammetric data may be summarized in the following main points:

• Erosion is the dominant geomorphic process affecting HF, with the structure exhibiting significantly higher erosion intensity than the surrounding plain, as indicated by the geomorphological features, elevated LS factor and predominantly negative TWI values across the HF flanks and top.
• The flanks are dissected by a well-developed network of parallel rills and gullies, with incision depths reaching up to 8 m demonstrating that erosion has penetrated deeply into the adobe fabric of truncated pyramid. Rills are attributed to low-intensity diffusive rainfall processes, whereas gullies formed during high-intensity ENSO precipitation events occurring seasonally between February and May. Asymmetric morphological degradation among the HF flanks is partly explained by wind-controlled rainfall directionality associated with ENSO.
• Architectural discontinuities such as wall boundaries and former access ramps act as preferential pathways for concentrated flow, accelerating localized erosion. The SW-facing flank represents the most critical sector of the HF building, where deep incision is compounded by gravitational instability. Localized water ponding within closed depressions on the upper platform poses an additional long-term risk through downward infiltration and internal dissolution of adobe materials. The cumulative effect of erosion processes has caused extensive architectural loss, with the platforms of levels 1 and 2 now entirely obliterated and only portions of the upper levels remaining recognizable.
• Average vertical erosion rates are estimated at 0.28–0.38 m/century, comparable to fluvial incision rates documented in natural river systems over similar timescales. Erosion due to diffusion processes is roughly estimated in 0.015 m/century. The net volumetric balance between erosion and deposition indicates internal mass redistribution rather than net export. Diffusion processes are expected to progressively smooth the surface and remove architectural detail.

The morphometric methodology applied here is proposed as a transferable and effective tool for the assessment and conservation planning of earthen archeological sites globally, particularly those exposed to ENSO or other extreme climatic conditions.