Introduction

Heritage buildings are part of the history of many settlements worldwide, and their conservation is essential for their survival [1] and the people's cultural identity. Nonetheless, cases of aggressive, irreversible deterioration and destruction are becoming more and more frequent, even in landmark buildings made with materials considered to be highly durable. For example, Vettori et al. [2] describe the deterioration of the stone architecture of Hierapolis (Turkey) due to environmental factors; Cantisani et al. [3] study the red stain type discoloration in the Baptistery of St. John (Italy); and Lucejko et al. [4] analyzes the effects of fungal activity on wooden substrates with different degrees of natural degradation in the site of Biskupin (Poland).

In this same context is the Ingapirca Archaeological Complex (IAC) located in Ecuador, province of Cañar, which presents relevant historical and constructive characteristics. This petrological monument was built during the pre-Hispanic [5], integration period (700/800–1500 AD) [6, 7] and is composed of different Cañari and Inca structures located at 3100 m.a.s.l. [8]. Among these structures, the Temple of the Sun (TS) stands out, also known as the Castle or Ellipse, which is the landmark of the tremendous multifunctional center [9]. This construction is comprised of the ceremonial building and an elliptical base wall (EW), which is built with green andesite of volcanic origin, cut and carved in a square and rectangular shape [10] and is the object of study of this research.

Specifically, the EW has undergone numerous physical transformations that sought to adapt it to different needs derived from parallel processes such as the oil bonanza, patronage [9], and the beginning of inbound tourism [11]. On the other hand, factors such as weather and climate conditions have significantly impacted the monument's deterioration. Indeed, many durable materials, such as stone, are prone to weathering [12] depending on climatic conditions and their petrophysical properties worldwide. Temperature, humidity, rain, or solar exposure can set the optimum conditions to emphasize deterioration [13, 14]. This material can present a wide variety of physical, mechanical, anthropic, and chemical pathological processes, which can cause flaking, concentric slumping, delicate exfoliation, or honeycombing [15], in addition to the growth of microorganisms that also deteriorate the surfaces [13, 14].

The impact of weathering on the TS is vital given its geographic location, close to latitude 0°, which makes humidity and solar radiation relevant [16]. According to several studies [17, 18], high levels of water vapor in the atmosphere contribute to condensation on surfaces, which has an impact on the deterioration of elements that do not have a high capacity for drying by solar gain [19], as is the case of several monuments in Cambodia [18]. The influence of these factors on the deterioration of archaeological monuments has been extensively studied in regions of low altitudes [13, 17, 18, 20]; however, there are few analyses in regions at altitudes above 3000 masl as is the case of the TS [21].

Given the importance of the TS and its EW, archaeological vestiges of Ecuador's cultural heritage, and because of its significant deterioration [11], numerous studies have been carried out [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50]. These have addressed its historical characteristics [22,23,24, 29, 51], constructive aspects and deterioration [27, 32, 35, 52], archaeological aspects [30,31,32,33, 37, 53], executed interventions [28, 36, 40,41,42, 44,45,46,47, 50] and other aspects. However, no comprehensive study relates the building dynamics and the existing conditions with the climatic conditions where this monument is located.

Likewise, and although several authors [12, 54,55,56,57] resort to traditional multi-analytical diagnosis (scanning electron microscopy, optical microscopy, Fourier transform infrared micro-spectroscopy or X-ray diffraction), for Patil et al. [16], the analysis and documentation of the forms of deterioration guarantee a better understanding [58] i.e., there are different types of techniques and tools to study and describe the deterioration of heritage buildings. One of the most popular for this purpose is the wall stratigraphic reading. This tool allows to extend the pathological knowledge [59] and to evaluate of the destructive notion of certain interventions carried out [60] from the particularized and interconnected analysis of materials, construction systems, typological diversity [61,62,63], productive cycles, and sociocultural incidences [62, 63]. Examples of these applications are presented by several authors [16, 64, 65]. In addition, it includes a detailed analysis of the historical and constructive reality from practical-analytical relations [66].

In this context, the main objective of this research is to relate the current deterioration conditions with the influence of the monument's condensation and solar gain capacity. This process allows an integrated approach to promoting physical and symbolic recovery [59].

Methodology

The methodology proposed for this research is the Mural Stratigraphy (MS) [67], applied to the EW of the Temple of the Sun located in the IAC (Fig. 1). The MS focuses on describing the different historical constructive and destructive stages [59, 68] according to the current state of conservation. In the final stage of the MS, an analysis of the condensation and solar gain capacity is evidenced from in situ measurements and digital simulations, respectively.

Fig. 1
figure 1

a South view and b Location of the Temple of the Sun in the Ingapirca Archaeological Complex

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A three-dimensional aerial photogrammetric survey of the TS with an area of influence of 2 ha was carried out for the thorough analysis. The equipment used was an unmanned aircraft type DJI, model Mavic 2 PRO, a Sokia CX105 total station of 5 s of precision, and a differential GPS RTK system brand SINO GNSS T300. The survey is performed through vertical and oblique aerial photographs oriented with the differential GPS linked to the Ecuadorian geodetic network (UTM WGS84). It allows for a geopositioning accuracy of less than 3 mm and a dimensional accuracy of 1.63 cm in the total model, making it easy to scale. The survey is accompanied by the base tacheometry, useful for 3d mesh processing, point cloud, and orthophotos executed in Archicad software.

The full-resolution model in Autocad 2021 software was utilized to obtain vectorial elevations. The processing and drawing sought to build a single elevation displayed horizontally to perform a joint evaluation of the entire EW focused on its state of conservation and constructive particularities (Fig. 2).

Fig. 2
figure 2

Deployed elevation of the TS EW

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Based on the elevation, the principles of Murial Stratigraphy [67] are applied to establish correlations between the different masonry bodies, their interventions, types, and direction of adosections, and the deposited fills [69] that make up the EW To this end, the correlation of the Positive (PMSU) and Negative (NMSU) Mural Stratigraphic Units and the positive (PMSG) and negative (NMSG) Mural Stratigraphic Groups [70, 71] are the leading resources for analyzing homogeneous and heterogeneous strata. The latter frames the deterioration processes on the stone material characterized by analytical techniques according to previous research [15]. Due to many activities, these have been grouped (AG) and coded according to their orientation (S, E, N, W). In each of these AGs, the activities found concerning each EW row have been described [72]. Furthermore, the total of MSUs and MSGs are systematized in a spreadsheet to discriminate the original (FO) and reconstructed (FR) factories as reported in the existing documentary repertoire and to discuss the implications on the state of conservation of the andesite vertically and horizontally [69].

Following the above, an analysis of a) the level of complexity, or the assessment of stratigraphies through time, b) the Level of fragmentation and incompleteness or determination of the essence of the stratification from each preserved part of the non-recoverable MSUs and MSGs, and c) Level of mutability, or the acceptance of transformation by human and natural actions [66], is included. The elements and symbology proposed by Doglioni [73] are included as particular elements of analysis, with a particular interest in (1) uncertain perimeters, (2) waiting joint, (3) negative interface surface visibility limit, (4) negative interface visible surfaces, and, (5) altered visible surfaces.

EW's condensation potential and solar gain are evaluated to complement the stratigraphic analysis. For the former, two in situ measurement campaigns were carried out in two different periods, the first from September 2 to 7, 2021, and the second from April 25 to May 02, 2022. These campaigns were established as per the two seasons that can be evidenced in the analysis region according to its relative humidity levels, outside air temperature, and dew temperature (Fig. 3). According to the data, the first season corresponds to the period from January to June with relative humidity and an average temperature of around 60% and 14 °C. The second season corresponds to the period from July to December with the highest humidity levels of the year and the lowest temperatures, around 82%, and 11 °C, which implies that the dew temperature is closer to the air temperature and, therefore, a higher probability of condensation.

Fig. 3
figure 3

Mean monthly air temperature, dew point temperature, and relative humidity in Cañar, according to the data taken from Cañar meteorological station in 2015 and 2016

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The parameters measured in these two campaigns were air temperature and relative humidity using a Testo 174H datalogger placed in a covered area of the IAC. The measurements of these two climatic factors were taken at 10 min intervals. In addition, the surface temperature of the elliptical wall was measured using the thermographic imgaing technique with the Flir E8-XT camera. This technique has been used in numerous studies to describe the thermal behavior of building surfaces [74, 75].

The infrared images were focused on establishing an average surface temperature of each elevation according to the same configuration used in the stratigraphic analysis (Fig. 2). For this, thermal images were taken from three different points, from the northeast, southeast, and southwest sides, at a distance of approximately 14 m to measure the entire surface of the EW (Fig. 4). These measurements were taken every 3 h during the 24 h of the day. Once the in situ images were obtained, the average surface temperatures of each elevation were acquired using the camera software (FLIR Tools) through the surface tool. The camera emissivity parameter was set to 0.95, corresponding to the average emissivity of the stone [76]. The ambient temperature correction was set based on field measurements using the infrared camera software.

Fig. 4
figure 4

a Point position of infrared camera and datalogger, and b infrared perspectives in each point

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Additionally, the air temperature and relative humidity corresponding to each of the hours in which the infrared images were taken were used to calculate the dew point from the in situ measurements at each of those times. The psychrometer calculator from Engineering Tools [77] was used to obtain this value, considering an altitude of 3100 masl to set the atmospheric pressure.

Lastly, for the solar gain analysis, Ecotect Analysis software was used to simulate the average solar radiation received by the EW surface (Wh/m2) in monthly and annual periods. For the simulation, the detailed point cloud model was simplified. This model comprised 134 planes of 0.60 m by 4.00 m that compose the shape of the ME The EPW file of the city of Cañar, located 7.2 km from the IAC, was used for the simulations. This file considers the direct and diffuse components for the computation of global solar radiation, and measurements and calculations have been obtained according to the file specifications.

Results and discussion

Historical-constructive study

According to the analysis conducted using the MS, nine temporary phases and one additional phase have been determined, which includes the synthesis of the impact of the solar gain and condensation analysis in the definition of possible intervention priorities. Moreover, 38 construction, reconstruction, and maintenance activities have been identified, shown below through the historical and construction sequence, the degradation sequence, and a possible intervention phase based on the solar gain and condensation capacity.

Historical-constructive sequence

The analysis identifies four stages in the EW orientations described below (Fig. 5).

Fig. 5
figure 5

a Simplified reading and b Harris' matrix of the simplified historical-constructive sequence of the EW

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Stage 1_Primary construction

This stage, corresponding to Phase 1 (Phase 1, Fig. 5), identifies that the original construction elements (AG_S/E/N/W_100, AG_ S/E/N/W_101 and AG_ S/E/N/W_102) of the perimeter present a notorious superposition, succession, continuity, and typological identity, i.e., they are contemporary and belong to the Cañari-Inca period. Furthermore, they respond to the authentic construction system of the TS defined by Fresco [28, 37]. Thus, AG_ S/E/N/W_100 is the prolonged foundation of the bedrock, followed by AG_ S/E/N/W_102 as the filler masonry (clay mortar and pebbles), which allows AG_ S/E/N/W_101, a wall of cushioned ashlar and rectangular greenish andesite, to be attached without the need of mortar. In addition, there are original zones in the four orientations (AG_ S/E/N/W_101). In the south segment, the ten courses of its east and west sides (AG_S_101); in the east segment, the eight courses of its west side and the six courses of its east side (AG_E_101) and in the north segment, the ten courses of its southwest and southeast sides. In the case of the west segment, the wall and the existing courses are recorded as original (AG_W_101) since they have not suffered constructive or typological alterations, which is corroborated in other studies [78, 79].

Thus, from the stratigraphic aspect, the ashlar segments of the EW have a set of actions defining succession and continuity. They are arranged with each other, following the characteristic sequence of the emblematic Inca sedimentary ashlar walls or Inca imperial masonry. According to the rigging, the stone pieces of four-angled, rectangular and/or trapezoidal shapes seated in horizontal rows have joints with perfect joints, polished and without mortar [80]. Derived from this in the EW, AG_S/E/N/W_101 is typically adjoined as a sedimentary type wall made up of carved stones, which have been seated in horizontal rectilinear-wavy courses typical of Inca architecture [81]. According to the studies of Swieciochowski, Espinoza [78] and Jadán [82], its identity and temporality are reaffirmed. In addition, according to Swieciochowski's research [79], it is possible to confirm that the analyzed elements (AG_S/E/N/W_100, AG_ S/E/N/W_101, and AG_ S/E/N/W_102) are in their natural state and conform the same stage.

Stage 2_Destructive beginnings

This stage, which corresponds to phases 2, 3, and 4, includes the possible temporal discontinuities caused by physical destructions or negative actions (AG_S/E/N_101) between the eighteenth and twentieth centuries (Fig. 5). This is conspicuous according to historical documentation [22, 79, 83, 84], but above all, according to the phenomena of temporal discontinuity and the increased importance of hiatuses [72]. The destruction and irreversible loss of the central zone (AG_S_108) of the southern primitive wall, the western zone of the access stairway (AG_S_109), the upper and lower northern zones (AG_E_107) of the eastern primitive wall, and the upper and lower zones (east, west and southwest) of the northern primitive wall (AG_N_111, AG_N_112, and AG_N_113) are confirmed. Stratigraphically, these are physical-temporal losses corroborated by the limits and cut edges produced by the overlapping filling. Reconstruction was carried out in the north, west, and south segments that make up the EW. There is also a coincidence with the photo-historical analysis done by the National Institute of Cultural Heritage (Instituto Nacional de Patrimonio Cultural -INPC-, in Spanish) [84].

It means that, despite not being in physical contact with the stratigraphic elements identified in phase 1, those forming phases 2, 3, and 4 are interfaces possibly belonging to the stone elements of the original constructive succession [72] of the EW (AG_N/W/S_101). For this reason, their location in the constructive sequence is earlier than what exists today.

Stage 3. Reconstructions

This stage has been subdivided into two: the uncertain reconstructions in phase 5, and the maintenance exercises and reconstructions in phases 6, 7, and 8.

  1. a

    Uncertain reconstructions in the original north (N) and east (E) segments.

    This stage is after the previous phases and the present study (phase 5, Fig. 5). The reconstructions are infill actions that evidence cuts and generate recognizable physical discontinuities at the edges of the elements of the upper and lower southwestern zones of the eastern (AG_E_103 and AG_E_104) and northern (AG_N_103 and AG_N_104) segments. These actions are presented as repair exercises of possible destructive hiatuses (AG_E_107 and AG_N_113) identified in the original walls, east (AG_E_101) and north (AG_N_101) of phases 2, 3, and 4.

    To confirm the above, the principles of typological identity and the included fragments indicate that the reconstructions use the same material and constructive rigging of the segments of the original north (AG_N_101) and east (AG_E_101) wall of phase 1. Nevertheless, they are later due to the existing imprecision in the constructive succession of the original ashlars and the deformities and flaws of the joints [79] . It is believed in the application of the concept of reuse of the EW material; however, the origin of the same is not particular, and as such, it is not possible to be sure if it was or was not part of the original wall [78]. The temporal range of the reconstructions in the north and east segments is also uncertain, although they are fully identifiable [79] thanks to photographic records [78, 83, 84].

  2. b

    Maintenance exercises and reconstructions of the south (S) and north (N) segments.

    This stage, corresponding to phases 6, 7, and 8, took place in the 20th century (1967–1999) (Fig. 5) and is documented. According to the application of the principles of superposition, the relationships of crossing or cut, the included fragments, and typological identity, the EW records punctual reconstructions in the south (AG_S_101) and north (AG_N_101) segments of phase 1, which in turn are the repair of the destructive hiatuses of phases 2, 3 and 4. Filling activities and reuse of original material are identified in the central zone of the south wall (AG_S_103) and the lower, upper western, and eastern zones of the north wall (AG_N_105, AG_N_106, and AG_N_107). Reconstruction of the stairs (AG_S_104) in the south segment is also reported.

    From the constructive, historical, and stratigraphic points of view, the activities described are recognized through the limits and physical cut edges produced by the overlapping and filling. All of them correspond to the works of Bedoya [28, 33, 37, 85] and have different scopes. In detail, the use of andesite pieces similar to those of the EW of phase 1, the rigging adjustment, and the imperfect Inca construction technique [78, 79] allow their temporal differentiation. In fact, Swieciochowski and Espinoza [79] mention that the authentic stone pieces recovered in the vicinity of the TS were used; for the reconstruction of the stairs, the stone pieces were taken from original buildings belonging to the IAC such as the "Casa del Inca" (Inca House) or the "Casa del Guardián" (Keeper House) [79]; for the intervention of the platform (base floor of the elliptical wall) (AG_S/E/N/W 100), yellow earth and grass (AG_S/E_105, AG_N_108, and AG_W_103) are used.

Stage 4_Maintenance activities

This stage corresponds to phase 9; it is framed in the twenty-first century (from 2000 onwards) and corresponds to the maintenance and conservation activities conducted by the INPC [46] in the original segments and the reconstructions of phases 5, 6, 7, and 8 (Stage 3). In addition, cleaning the stone surface (AG_S_106, AG_N_109, AG_W_104) and pest control (AG_S_107, AG_E_106, AG_N_110, and AG_W_105) are carried out in this stage to reduce the deterioration of the monument.

Degradation sequence

The study allows evidence of nine temporal phases of degradation based on the physical-constructive evidence of the 4 stages and 9 phases determined in the historical-constructive sequence (Fig. 6).

Fig. 6
figure 6

Harris' Matrix of the simplified EW Degradation Sequence related to the Historical-Constructive Sequence

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Stage 1_ Original construction: natural deterioration

It comprises phase 1, which is the deterioration of the original EW (NMSG_S/E/N/W_012) due to natural wear and tear of the stone (phase 1, Fig. 6).

Stage 2_ Destructive beginnings

It covers phases 2, 3, and 4, comprising the first stage of degradation and progressive deterioration of the original EW (NMSG._ S/E/N/W _13, NMSG_W_014, and NMSG_E/W_15), as well as the major destruction of the south, east, and north wall segments (MSG_S/E/N_014 and MSG_S/N_015) (phase 2, 3 and 4, Fig. 6). When analyzing the photo-historical documentation [78, 83,84,85], similar incidences of conditions such as deposits and biological growths (lichens and mosses) caused by the synergy of climatic agents, the passage of time and neglect were observed [85]. There is also evidence of cuts or hiatuses identified in phases 2, 3, and 4 of the historical-constructive sequence produced by the collapse and detachment of ashlars in the original wall's south, east and north segments. Indeed, several studies [28, 33, 34] mention that such destructions result from the instability of the foundations of the EW due to heavy rains that generated landslides.

It is concluded that phases 2, 3, and 4 provide continuity to the deterioration recorded in phase 1. Similarly, it is believed that the progressive deterioration of the original EW (NMSG._ S/E/N/W_13, NMSG_W_014, and NMSG_E/W_15) remained active until the historical-constructive phase 5. Based on the historical basis, Hadden [85] carried out cleaning activities on the hard rocks that possibly stabilized the affections until 1967, phase 6 of the historical-constructive sequence. Despite this, and due to the passage of time (more than six decades), the deterioration was reactivated and potentiated until the subsequent phases, making the significant destruction of the southern, eastern, and northern original wall segments (MSG_S/E/N_014 and MSG_S/N_015) passive. This is feasible since, in the historical-constructive phases 5, 6, 7, and 8, reconstruction activities are carried out [33, 37, 85, 86].

Stage 3_ Reconstructions: beginning and destructive continuity

This stage includes phases 5, 6, 7, and 8, subdivided into three activities within the EW:

  1. a

    Phase 5 Uncertain destructive beginnings in the reconstructions of the east (E) and north (N) wall segments (NMSG_E/N_017) (phase 5, Fig. 6). In this phase, it has not been possible to define or approximate possible affectations and their temporality. Despite this, when analyzing the historiographic sources linked to the intervention of the EW [28, 85]. It is believed that deterioration was generated due to the temporal distance with its later phases (6, 7, 8, and 9), the nature of the stone itself, and the incidence of various anthropic, physical and environmental factors. Such processes were also believed to be active until the historical-constructive phase 6. According to the state of conservation documented by Hadden [85], the stones of the TS were in constant degradation, demanding cleaning exercises. Notwithstanding, phase 5, being an uncertain period and presenting a temporal amplitude (more than 40 years approximately) until the later phases, probably a reactivation of the deterioration took place.

  2. b

    Phases 06 and 07 Beginning of the destructive affections in the reconstructions of the south (S) and north (N) segment (GEMN_S/N_018 and NMSG_S/N_019) on account of the intrinsic conditions of the andesite and the repercussion of anthropic, physical and environmental agents (phases 6 and 7, Fig. 6). According to Bedoya [28, 33, 85], it is ratified that the EW presented gradual deterioration and affections in the ashlars. Based on this, it is estimated that the destructive activity remains active, and there are no stabilization actions.

  3. c

    Phase 08 It is the second stage of degradation and progressive deterioration of the original EW and the destructive continuity of the reconstructions (phase 8, Fig. 6). Physical and physical–chemical damages have been identified. Cataphyllous exfoliation (NMSG_S/E/N/W_011), which has generated flaking and concentric-curved separation; fine lamellar exfoliation (NMSG._ S/E/N/W_007) from the separation of thin layers in banded form; sliding by detachment (NMSG._ S/E/N/W/W_003), which causes lifting and separation of plates on the surface; detachment by fragments (NMSG._ S/E/N/W_010); and alveolar erosion (NMSG._ S/E/N/W_002), causing the formation of cavities and granular disintegration on the stone surface [42, 87, 88]. It is believed that its origin is due to the interaction of anthropic and environmental incidences [89]. That is to say; the intervention works in the construction system of the backfill and drainage slab carried out by Alcina Franch [33, 34] and Tomansz et al. [90] affect the accumulation and embedding of rainwater and, therefore, the sliding of incompatible materials towards the stone, originating physical–chemical processes related to gelifraction, crystallization and internal ruptures in the stone matrix [89].

    It is also considered that the recorded conditions (NMSG._ S/E/N/W_011, NMSG._ S/E/N/W_011, NMSG._ S/E/N/W_003, NMSG._ S/E/N/W_010 and NMSG._ S/E/N/W_002) are active and progressive. Although Coello [46] conducted cleaning and fumigation works at the beginning of the historical-constructive phase 9, this did not stabilize the physical-chemical conditions, probably the biological conditions, according to the report of [42]. It is worth mentioning that these conditions were —evidently— passive until the beginning of phase 9, which is extensive (approximately 22 years) and reaches the present, so it is considered that the possible biological deterioration was reactivated and potentiated.

Stage 4_Maintenance activities and current destructive actions

This stage covers phase 9. It establishes the original EW's current and progressive destructive affections and reconstructions (phase 09, Fig. 6). In this phase, physical, physical–chemical, and biological [89] lesions of deposit type (NMSG._ S/E/N/W_006) were evidenced; chromatic alteration, where the stones have lost their luminosity and chromatic purity (NMSG_S/E/N/W/W_004, NMSG_S/E/N/W/W_005, and NMSG._ S/E/N/W_008); and bio-patina by the growth of moss, lichens, and algae (NMSG._ S/E/N/W_001 and NMSG_S/E/N/W/W_009) [21, 89]. Everything arises from the synergism of environmental factors (rain, wind, humidity, and temperature), but in the case of the EW, they also occur due to incompatibilities in the interventions carried out on the backfill and drainage slab the biological conditions and deposits are associated with the accumulation of water, humidity, and drainage of the existing backfill slab [21]; the chromatic alteration is caused by the intrinsic weathering products of the stone [89].

It can be deduced from the above that the biological (NMSG_S/E/N/W_001 and NMSG_S/E/N/W_009), as well as physical (NMSG_S/E/N/W_006) conditions, were passive until the beginning of this phase thanks to the surface treatments performed by Coello [46], but are now reactivated. As for the physical–chemical conditions (NMSG_S/E/N/W/W_004, NMSG_S/E/N/W/W_005, and NMSG_S/E/N/W_008), these are active, destructive actions, i.e., the deterioration recorded is operative and in need of treatment.

Condensation analysis

According to the in situ measurements, the average surface temperatures of the four EW elevations (Ts_S, Ts_E, Ts_N, Ts_W), air temperature (Ta), relative humidity (RH), and calculated dew point temperature (Tdw) of the two campaigns are shown in Fig. 7.

Fig. 7
figure 7

Measured air temperature (Ta.), relative humidity (RH), and EW surface temperature of each orientation (Ts_S, Ts_E, Ts_N, Ts_W), calculated dew temperature (Tdw) in a September 2021 and b April/May 2022

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In the September measurements, four days with high solar radiation (02–05/09) and one day with low solar radiation (06/09) were recorded (Fig. 7a). On the one hand, in the daytime period, it is shown that on days with higher solar radiation, the maximum air temperature is 17 °C around 13h00 and the relative humidity at that time is 55%, whereas on the day with less radiation, these values are 13 °C and 75%, respectively. Regarding the Ts of the EW, on the day with the highest solar radiation (04/09), the east elevation is the one that reaches the highest values (28 °C) around 11h00, followed by the Ts_N with 25 °C. In comparison, the elevation that reaches the lowest Ts values is the south (15 °C), as in the rest of the days with high solar radiation. It is due to the slight northern orientation of the solar paths on these dates, which means that the southern surface receives less radiation than the northern and eastern surfaces (Fig. 8a). On the day with the lowest solar radiation, the Ts of all orientations do not exceed the air temperature and are less than 11 °C throughout the day. This reflects the minimal solar radiation received by the EW on this day, and the high thermal mass of the andesite stone does not increase its Ts above the air temperature.

Fig. 8
figure 8

Solar stereographic at the geographic location of the IAC at the starting date of the two campaigns: a September 02 and b April 25 obtained from [91]

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On the other hand, during the night period, on days with higher solar radiation, the minimum air temperature is around 11 °C around 06h00, and RH of 66% at that time. On the day with less solar radiation, these values are 9 °C and 82%, respectively. As for the EW Ts, the surfaces of all orientations in the night period reduce their temperature below AT on days with higher and lower solar radiation. However, the south and west orientations on the days with the highest radiation are the only ones that reach a temperature 0.7 °C below Tdw around 06h00. This is due to the lower solar radiation they receive in the daytime. Additionally, on days with lower radiation when humidity reaches the highest values, the Ts of all orientations drop their temperature up to 4 °C below Tdw from 18h00 to 06h00, indicating that these surfaces condense throughout the night period on days with lower solar radiation. On these days, even when solar radiation is low, the Ts of the south orientation shows a lower temperature than the other orientations due to the lower solar gain.

Regarding the measurements made in the second period (April/May), all days had low solar radiation, with air temperature and relative humidity averaging 11.5 °C and 72% (Fig. 7b). On the one hand, in the daytime period, the Ts in all orientations reached values similar to Ta, except for April 27 when the east and north orientations reached a Ts around 24 °C. Moreover, even when solar radiation in this period is low, the Ts of the south orientation show the lowest temperatures of all orientations. This behavior responds to the northern inclination of the solar path on these dates (Fig. 8b), as in the September measurements. Conversely, almost all four orientations reach the dew point during the night on almost all measurement days, especially between 00h00 and 06h00. As in the September measurements, the southern orientation has the lowest Ts with values up to 2.8 °C below Tdw.

Solar capture analysis

From the condensation results, the different solar gain in the four orientations of the EW impacts the surface temperature of these surfaces in the daytime and nighttime periods in the two measurement campaigns. Hence, although the surfaces tend to condense due to the high humidity in the night period and the low surface temperatures, the southern orientation has lower Ts values and, consequently, the highest gain frequency among the EW elevations. These results correlate with the monthly, quarterly, and annual solar gain analysis performed (Fig. 9). Firstly, according to the monthly solar uptake simulation (Fig. 9a); in September, the monthly average solar radiation at the south elevation is 1640 Wh/m2 and at the north, east and west elevations, is 2000 Wh/m2, 2700 Wh/m2 and 2600 Wh/m2, respectively. Similarly, in April, the solar radiation received at the south elevation is 1000 Wh/m2, while at the north elevation, it is 1800 Wh/m2. These results show that the south elevation receives between 18 and 37% less radiation in these months than the other orientations.

Fig. 9
figure 9

Simulations of monthly average solar capture (Wh/m2) in the EW from a southwest perspective

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Given the geographical location of the EW (latitude 2.54S), the sun paths will have a slight north orientation from the March equinox to the September equinox and a slight south orientation from the September equinox to the March equinox, approximately (Fig. 8). Therefore, the north orientation will receive more solar radiation than the south orientation from March 22 to September 21, and the south radiation will capture more radiation than the north orientation from September 22 to March 21 (Fig. 9b). Although the two orientations have similar solar radiation times, the south elevation receives minimal solar radiation in the period from June to September (900 Wh/m2) (Fig. 9b), which coincides with the months of lower temperature and higher humidity (Fig. 3) and consequently higher possibility of condensation. In addition, through an annual calculation (Fig. 9c), it can be identified that the south elevation receives 1640 Wh/m2 and the north elevation receives 1840 Wh/m2 in this period. It is because the IAC is located 2° below the equatorial line, which influences higher radiation in the north orientation than in the south.

In line with the above, the analysis by EW highlights the constant degradation of the wall segments of the EW, with emphasis on the south and north, defined from stage 1 with the natural deterioration of the original construction, and stage 2 of the destructive beginnings of the original EW to stage 3 of the destructive affections of the reconstructions, and stage 4 of the continuity and current destruction throughout the building. These affections reflected in biological deposits and physical lesions respond to the site's climatic conditions, which the analysis of condensation and solar gain has ratified. The former shows that all EW orientations condense at night, especially on days with less solar radiation. However, the north and south orientations receive less solar radiation and, therefore, have a higher frequency of condensation. Under precipitation conditions, the vertical surfaces of the EW have a greater drying capacity than the horizontal surfaces. Nevertheless, the constant surface humidity due to condensation creates optimal conditions for the growth of lichens and mosses [83].

The link between the degradation sequence and the condensation and collection analysis is shown in Fig. 10. These last analyses have been represented in a deployable elevation for the condensation analysis (Fig. 10a), another for the solar capture analysis (Fig. 10b) reflected in phase 10 of the Harris' matrix (Fig. 10c). For these analyses, data acquired on September 05 at 03h00 were used since these were the results within the period with the greatest possibility of condensation and the one with the greatest variation of the four orientations according to the condensation analysis (Fig. 7a).

Fig. 10
figure 10

a Condensation simplified reading, b Solar capture simplified reading, and c Harris' matrix of the simplified EW degradation sequence related to condensation and solar radiation

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The analysis of phase 10 shows differences in these two variables in each of the orientations. Regarding the superficial temperature of the EW, seven different temperatures have been identified in the south orientation, four in the east, four in the north, and three in the west. Concerning solar gain, two levels of solar radiation have been identified for each orientation.

According to these results, the direct relationship between the Ts and the solar radiation captured is again evident. In the four orientations, the segments that reach the highest temperature are those with a high solar gain, in the south orientation with 4.5 °C and 1700 Wh/m2, in the east orientation with 6.3 °C with 2800 Wh/m2, in the north orientation with 6.4 °C and 2010 Wh/m2 and west with 6.6 °C with 2400 Wh/m2. The difference in temperatures found in the four orientations and their wall segments is quite related to the solar radiation captured, except for the south wall segment, probably due to the different surface finish that the EW has according to its variations in deterioration. Although these thermal differences are not so significant, it is essential to emphasize the difference in the north and west orientation, where the differences between the highest and lowest temperatures are 0.90 °C and 0.8 °C, respectively. This more detailed analysis could indicate that these parts, the west side of the north orientation and the west side of the south orientation, could have a higher probability of condensation even though they are part of the north and west orientations. It is because they receive less solar radiation than their other parts in each orientation on the analyzed day (1610 and 2100 Wh/m2) and also on an annual average (1780 and 2200 Wh/m2). Nevertheless, the mentioned segments did not reach a temperature lower than Tdw on the analyzed day, i.e., they do not condense. Although it is evident that there are variations in each of the orientations, the most representative difference is by facades and is more marked with a lower temperature in the south orientation.

Lastly, while the north and south orientations capture similar solar radiation on an annual average, the analysis shows that the south orientation has a greater chance of condensation, even over the north orientation. This is due to the geographical location of the IAC in addition to the drying capacity of this orientation in a day. As condensation processes occur more frequently at night, the southern orientation will take longer to evaporate its humidity because it does not receive direct solar radiation in the morning period, even between December and March, when the solar paths are inclined to the south. Furthermore, the detailed analysis in the Harris matrix shows that two segments can reach a lower temperature than the average of the whole elevation, corresponding to the north and west orientation. In the following section, a quantitative analysis of the conditions of each orientation is carried out to correlate these results.

State of conservation and monumental importance

From the definition of the historical-constructive and degradation sequences [73], in conjunction with the study of condensation and solar analysis, the stratigraphic mentality (conservation capacity and development) [73, 92] of the EW is established, defining the approach to its current state of conservation, and possible future conservation. As a result, from the level of complexity, the EW is established as a building in itself and a complex constructive structure due to the multiple layers, strata and/or constructive-destructive stratigraphic units configured and transformed over time. This, in turn, has made it possible to evidence several activities (A and AG) that establish its historical, constructive, and destructive life (Fig. 11). Such characterization, along with the fragmentation level and incompletion, allows us to understand and value the original architecture with which the EW was conceived and all the constructive and destructive actions.

Fig. 11
figure 11

Quantification of the SMU, SMG, A, AG, NSMU, and NSMG identified in the EW

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Thus, the stratigraphic study shows that the EW conserves original and reconstructed areas and the application of surface treatments (Fig. 12), like any long-standing building. The original areas in the masonry are distributed: (a) 92.10% of the south wall segment; (b) 32.86% of the east wall segment; (c) 65% of the north wall segment; and (d) 100% of the west wall segment. The areas of the filled wall identified are original in the totality of the mural segments. At the same time, the areas of reconstruction refer to the masonry wall case: (a) 7.90% in the south wall segment, (b) 67.13% in the east wall segment, and (c) 35% in the north wall segment. Likewise, the treatment areas register their application above 90% in the original and reconstructed areas of the four masonry segments.

Fig. 12
figure 12

Discrimination of areas of original masonry, areas of reconstructions, and areas of surface treatment evidenced in the EW

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Regarding the destructive actions, the areas of deterioration recorded in the original and reconstructed areas that make up the EW are identified (Fig. 13a). Thus, the specific degradation landscape is recognized in the four elevations (S, E, N, and W) through pathological damages identified in their mural segments. Those are associated with physical-destructive stratigraphic characterizations, establishing that:

  1. 1.

    The South elevation (S) represents 41.81% of destructive actions (Fig. 13b), which determines that it is the wall segment with the most significant evidence of deterioration. It is because it accentuates: (1) 47.33% of negative interface surface visibility limits; (2) 15.90% of waiting edges; (3) 4.54% of true negative interface edges; (4) 2.27% of negative interface termination edges; (5) 5.55% of visible negative interface terminated surfaces; (6) 36.11% of visible interface degradation surfaces; (7) 36.11% of visible interface weathering surfaces; and (8) 22.22% of visibly altered surfaces (Fig. 13c).

  2. 2.

    The east (E) and north (N) elevations represent 20.11% and 24.83%, respectively (Fig. 13b), showing evidence of deterioration. Nonetheless, their record is lower than the south elevation (S). In detail, the east elevation (E) records; (1) 7.31% of uncertain perimeters, (2) 17.55% of negative interface surface visibility boundaries; (3) 8.50% of waiting edges; (4) 7.15% of true negative interface edges; (5) 6. 33% negative interface terminus edges; (6) 11.22% degradation interface visible surfaces; (7) 10.50% negative interface terminus visible surfaces; (8) 11.22% wear interface visible surfaces; and (9) 8% altered visible surfaces (Fig. 13c).

  3. 3.

    The north elevation (N) evidences; (1) 9.09% uncertain perimeters, (2) 22.14% negative interface surface visibility boundaries; (3) 7.09% Bordo di attesa; (4) 6.04% true negative interface edges; (5) 18.18% degradation interface visible surfaces; (6) 10.54% terminated negative interface visible surfaces; (7) 16.50% weathering interface visible surfaces; and (8) 11.42% altered visible surfaces (Fig. 13c). Likewise, the west elevation (W) manifests 11.76% of destructive actions (Fig. 13b), which, when contrasted with the previous three elevations (south, east, and north), is the mural segment with a low incidence of deterioration. Specifically, it presents; (1) 10.14% negative interface surface visibility limits; (2) 5.43% Bordo di attesa; (3) 11.55% degradation interface visible surfaces; (4) 11.23% weathering interface visible surfaces; and (5) 9.47% altered visible surfaces (Fig. 13c).

Fig. 13
figure 13

a Evidence discrimination of deterioration identified in the EW, b General statistics of the deterioration traces in the EW, and c Statistical breakdown of the deterioration traces in the four elevations of the EW

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According to the above, and from a general overview, the EW and its four elevations show continuous and progressive deterioration when considering:

  • Uncertain perimeters of the negative interface surfaces in the mural zones of the E and N segments because the causes of deterioration-destruction and temporality have not been clearly identified.

  • Visibility limits of negative interface surfaces clearly demarcate surfaces of alteration, degradation, and weathering in the stone; they are found throughout the EW.

  • Bordo di attesa throughout the EW has recurrent perimeters of altered, degraded, and/or worn-out areas tending to constructive recovery.

  • True negative interface edges are those perimeters configured by stratigraphic boundaries of directed cuts, which have been caused by reconstructions in the elevations' wall segments, except elevation W.

  • Negative interface termination edges represent the simple demolition or removal of the original stairs located on the S elevation.

  • Visible degradation interface surfaces define the surfaces affected at the four elevations by specific pathological lesions such as erosion, exfoliation, collapse, and dislocation.

  • Visible wear interface surfaces evidence the surfaces impacted by physical–chemical injuries. The latter has been recognized in the visible degradation interface surfaces, which have caused the continuous loss of stone material throughout the EW.

  • Visible surfaces of finished negative interface or traces of reconstructions forming a refined architectural surface and/or resembling the original construction of the EW This activity is associated with the reconstruction exercises of the S, E, and N elevations

  • Visible altered surfaces modify the appearance of the petrological material generated by chromatic alteration, deposition, and biological growths. They are found throughout the EW.

Based on the material evidence, fragmentation and incompletion establish that the original areas are fragments tending to be preserved [92]; the reconstructed areas represent the lost, non-recoverable unit and allow understanding of the building. In turn, along with the surface treatment areas, they make possible the EW's physical conservation and architectural, typological, constructive, and stratigraphic legibility. The destructive fragments demonstrate the dynamism of the extrinsic and intrinsic factors to which the EW is subjected throughout the nine defined constructive and destructive phases. It has left the monument vulnerable and made it possible to identify the traces of deterioration as destructive units, that is, the loss of constructive, architectural, and patrimonial capacity.

The previous levels conclude at the mutability level, i.e., the EW is the apparent result of stratified architectural appreciation, and how this has allowed the establishment of a building that transforms, even invisibly, from anthropic actions and atmospheric agents. Furthermore, from the stratigraphic mentality and its three levels, the EW demands activities to (1) control and reduce the loss or elimination of original and reconstructed areas and (2) maitenance and reduction of destructive actions.

From a complementary perspective, the authenticity of the EW in terms of conservation allows experiencing the past and offers a sense of identity in the immediate context; it anchors the collective memory and generates tangible links between the past, the present, and the future [93], reflecting and embodying the values of the cultural heritage of a place [94]. It also allows for revealing the true nature of the building, which may be hidden by the various social, economic, and cultural factors that affect long-standing buildings [95]. In this way, the EW reveals three aspects that expose its authenticity [93, 94].

  • Social and spiritual life the EW is associated with active social and spiritual lives; it has experienced birth, growth, aging, rejuvenation, and even death caused by natural and anthropic factors. From the moment of creation-construction and the progressive reconstructions and destructions, it has suffered deterioration over time, probably until the end of its physical and metaphysical existence [93].

  • In detail, the authenticity of the EW from the perspective of social and spiritual life is expressed in; a) the numinous legacy linked to the ancestry and cosmological and cult beliefs characteristic of the Cañari-Inca culture; b) the traditional lifestyle (duties, activities, and human interaction) and, c) as an essential reference in the constitution of collective identities and memories that define its immediate context.

  • Material-technological evidence and transformation are vital elements that inform and expose authenticity [95]. In the case of the EW, the material-technological shreds of evidence are related to a) the use of natural and autochthonous construction materials and b) the imperial Inca-type construction techniques and systems, which are characterized by formal accuracy, morphological-aesthetic singularities, and adaptation to the landscape context and the needs of the place.

    • On the other hand, the material transformations are defined based on the appearance of age and the feelings that this produces through the resulting aging and deterioration and the restoration-reconstruction of the monument. Such particularities have been fully identified in the EW. The aging and deterioration of building materials are established as intrinsic aesthetic traces and marks of beauty and harmony in the substance of it and, in turn, cause a sense of the past [93]. They are considered integral parts of authenticity, as they provide a palpable sense of connection between people and the tangibility of the EW.

    • Concerning the restoration-reconstruction, it evidences the authenticity of the existing intervention exercises in the EW. Those provide meaningful narratives of understanding the monument as a whole. That is, the authenticity of the EW is an example of how it can migrate from its original technological-material characteristics to its reconstructions through connections, meanings, and values, which are forged during the reconstruction process [94]. They also embody and activate networks of links between the EW from its historical-cultural origin with society, place, and contemporaneity.

  • Impact of intangible elements: the EW is a container of intangible characteristics associated with the historical-cultural attachment and defines the architectural authenticity, society, and its immediate context [96]. Consequently, its intangible presence is identified and related through a) artisanal and traditional practices that were part of the Inca period in its location and during the existence of the monument; b) spirituality and transmission of knowledge and wisdom of society; and c) representation and transmission of oral histories, genealogical connections, community activities and events linked to the physical, metaphysical and cultural origin [94, 95]. This evokes links, sociocultural memories, stories, and intangible attachments intimately connected to the fragmented monument [94].

Conclusions

This research has addressed the state of deterioration of the TS EW and its relationship with the climate conditions where it is located. For this, the EW and analysis of condensation and solar gain of the wall have been used. The following specific conclusions were drawn from this analysis.

The monument will continue to be transformed and even eliminate historic strata due to the irreversible deterioration in different sectors and the current difficulties in mitigating it. The climate has acted as a progressive agent of destruction, as have the maintenance and intervention actions. These, at the time, defined iconic actions that, as the EW adapted and became factors of irreversible deterioration, loss of originality, and authenticity. Despite this, their presence in the historiographic record is significant evidence of technical, administrative, and legal lessons learned in the Ecuadorian context.

The historical-constructive sequence and the degradation sequence are relative in nature, despite the articulation of various historiographic sources and previous multidisciplinary studies. However, it has allowed synthesizing a global framework of the historical-constructive context and the pathological process of the EW as key aspects for understanding the architectural reality, the current state, and the possible events of impact on the monument. These particularities operate as a viable basis for conserving and managing the architectural and heritage conditions that the EW represents. Therefore, technically it requires the inclusion of measures and/or actions through structuring processes and technical elements of conservation and effective interventions for its physical recovery.

In this framework, the condensation study is key. All the surfaces of the EW reach the dew point, especially on days with less solar radiation, which simultaneously means a lower temperature and higher relative humidity at night. The surface with the highest frequency of condensation is the south-facing surface because it captures less solar radiation in the two measurement periods and therefore reaches a minimum surface temperature up to 2 °C lower than the other surfaces at night.

Through the analysis of solar radiation, it has been determined that, on an annual average, the southern orientation is the surface that receives the least radiation among all the surfaces of the EW, followed by the northern, eastern, and western orientations. It is due to the geographical location of the EW, which is approximately 2°32' below the equator. In addition, the lower solar gain of this surface is intensified between March and September, when the solar paths have a northern inclination, which will influence more significant condensation since between June and September is when the lowest air temperature values and higher relative humidity values are recorded, thus, a greater possibility of condensation. These results establish a relationship with the high deterioration level of the south wall, evident in all of its NEMG. This study supports that the deterioration processes of the EW are largely influenced by the climatic conditions where it is located, specifically by the condensation capacity and the different solar gain that the four orientations of this wall receive. Based on this, the intervention processes should prioritize the south wall of the monument.

Consequently, and following the above, it is deemed appropriate to propose a strategic framework in the EW focused on a) preventive conservation strategies and b) corrective intervention strategies. In other words, those capable of reducing, eliminating, or blocking the alterations and physical losses of the architectural and constructive language to avoid losing its heritage status.