Shoreline retreat and beach nourishment are projected to increase in Southern California

Abstract

Sandy beaches in Southern California are experiencing rising coastal erosion due to changes in precipitation patterns and urban growth. As a result, beach nourishment is necessary for mitigation. In our study, we forecast the rates of shoreline retreat and the required volumes of sand nourishment to mitigate it for the coming decades. We employ photogrammetric multi-decadal shoreline positioning and Digital Shoreline Analysis System methods to measure and predict the coastal evolution of the Gulf of Santa Catalina in Southern California. This region is hypothesized to be globally representative of other semi-arid sandy coasts facing similar hydroclimatic and anthropogenic challenges. Our findings indicate that Southern California’s shoreline retreat rates for sandy beaches will increase from the present average value of ~−1.45 to −2.12 meters per year in 2050 and to −3.18 meters per year in 2100. Consequently, the annual volume of sand required for beach nourishment could triple by 2050, increasing from the present-day amount of ~1223 to ~3669 cubic meters per year per kilometer. However, the associated cost for this nourishment will grow five times, exacerbating several coastal communities’ economic and logistical pressures. Similar trends are emerging globally, with semi-arid developing nations already grappling with coastal hazards and may struggle to manage the escalating costs of curbing beach nourishment.

Introduction

Over the 21st century, low-lying semi-arid urban coasts are undergoing rising coastal erosion trends and increasing marine hazards, impacting a growing part of the world’s global population^1,2,3. Sea-level rise (SLR) projections are expected to aggravate these coasts’ vulnerability to flooding and accelerate shoreline retreat along most sandy beaches^4,5. The shorelines of low-lying semi-arid urban areas are particularly interesting, as they are witnessing increased ‘hot spots’ of erosion due to abrupt changes in multiple environmental and climatic drivers^6,7. Today, these coastal areas host some of the world’s fastest-growing populations, with most having poorly defined coastal management strategies to curb the increase in shoreline retreat in response to anthropogenic and hydroclimatic drivers that remain undermined and poorly quantified.

Hence, it is crucial to quantify and forecast the morphodynamical changes in these coastlines, which can trigger substantial degradations in coastal aquifers, wetlands, vegetation coverage, and agricultural productivity, compromising the sustainability of these coastal urban areas under rapid population growth^8,9. Historically, the acceleration of shoreline retreat in sandy beaches on the local and regional scales has been stated as an initial assessment of SLR^10,11,12 for both open and semi-closed seas¹³. However, Leatherman et al.¹⁴ and Zhang et al.¹⁵ suggested that a substantial part of shoreline retreat along sandy beaches is mainly attributed to long-term coastal erosion resulting from sediment imbalance and sea level rise, among other factors.

The semi-arid urban areas of Southern California and Northern African Mediterranean coasts, both known for their year-long temperate climate, are among the key areas where both sea-level rise and shoreline erosion have rapidly evolved over the last few decades² because of significant changes in sedimentation processes¹⁶ caused by extensive inland aridity and change in land use⁹. These changes are also observed in other arid and semi-arid areas¹⁷, which occupy 41% of the Earth’s continental surface and are home to more than a third of the world’s population¹⁸. Of particular interest, sandy beaches in Southern California’s rapidly growing urban coastal areas can undergo additional shoreline retreat rates originating from structural sources, such as subsidence in the coastal substratum due to excessive groundwater pumping¹⁹, faults dynamics, and large urban infrastructures such dikes and extended concrete-covered areas. In Southern California, during the intense El Niño events of 2015 and 2016, the shoreline was observed to retreat by 10 to 80 m in some parts of the coastline due to the energetic waves²⁰. The storminess of the ocean surge is causing severe erosion at the seafront of several urban communities. The extent and spatial distribution of shoreline erosion and the damage to infrastructure in seafront urban areas are rising challenges for sustainable coastal management and the preservation of its ecosystems. The Global Scale Assessment Model (GSAM) provided unique insights into shoreline retreats on a global scale, mainly covering ambient sandy beaches. However, arid and semi-arid ones, such as the coast of The Gulf of Santa Catalina, with more complex sedimentation processes²¹, were not fully treated in GSAM due to the lack of publicly available datasets.

The increase in aridity in the semi-arid areas is forecasted in the short and mid-term, as suggested by several multi-decadal climate modeling efforts^22,23,24. Most of these aridification trends in the last 52 years have been observed in North Africa, East Russia, China, Eurasia, Australia, and South America²³. Moreover, increasing aridity is also observed in several parts of North America, notably in Southern California, and continues to expand geographically under increased drought conditions²⁵. For instance, severe heatwaves and dust storms occur widely in the southwest United States and adjacent Mexico²⁶.

To mitigate coastal erosion, sand nourishment has been widely used for the last few decades along the intensely eroded coastline segments²⁷, such as in the US east and West coasts, Netherlands, Australia, China, and the Mediterranean coasts^{28,29,30,31,32}. Artificial nourishment is established as a soft coastal management adaptation to changing and fluctuating hydroclimatic conditions³³. Nourishment practices synergize economic activities such as tourism by preserving a suitable beach width and agriculture by restoring water quality in coastal aquifers³⁴. Although nourishment is often considered eco-friendly for beach restoration and protection, it also negatively impacts its ecosystem’s sustainability³⁵. Fauna and flora habitats are often altered by dredging operations resulting from changes in marine turbidity and sedimentation^36,37. While the environmental impact assessment studies for nourishments are improving in accuracy, the long-term impacts remain largely debatable due to the lack of publicly available datasets for several nourished areas³⁵.

In developing countries, beach nourishment interventions are limited by the financial burden required to conduct these mitigations and the complexity of extracting and laying sand with the proper grain size, quality, and composition. Moreover, the increased frequency of such nourishments due to intense coastal erosion in previously stable areas adds to non-forecasted budget spending for several communities. While beach nourishment can momentarily control shoreline retreat from erosion and sea level rise, it does not stop either^36,38. Hence, the sustainable solution for stabilizing the retreat in sandy beaches in areas undergoing hydroclimate fluctuations, such as semi-arid ones, requires a proper assessment of the short and mid-term evolution of the local and regional drivers of the coastal erosion and relative sea level rise as performed herein.

As such, the primary objective of this investigation is to forecast future needed sand volumes for beach nourishment on the coast of Santa Catalina in Southern California by 2050 and 2070 under increased shoreline retreat associated with the sediment unbalance resulting from the change in land use as a direct consequence of the population density growth. The above is achieved using a photogrammetric multi-decadal shoreline positioning and Digital Shoreline Analysis System methods (see section Materials and methods) to measure and predict the coastal erosion along the 150 km coastline. Using the above, we calculate and cost the sand volume nourishment required to stabilize the beach. Our study area is hypothesized to be globally representative of other semi-arid sandy coasts undergoing similar hydroclimatic fluctuations and rapid changes in urban growth and land use, as discussed further in the materials and methods section.

Results and discussion

Our study uses publicly available datasets and established methods that can be globally replicated in other semi-arid study areas. In particular, our approach allows us to explore the link between coastal urban growth and beach erosion as a result of alteration in sediment transport required for natural beach nourishment. The study area of the Gulf of Santa Catalina and the two validation sites are representatives of the aridity condition of several global semi-arid areas witnessing increasing droughts, flash floods, and high interannual and seasonal precipitation patterns ranging from 250 to 400 mm (e.g., North Africa, Arabian Peninsula, Australia, and Southern Europe). Moreover, the validation sites are two urban areas witnessing high population densities, which represents the global trend in increased urbanism in several of the above-listed areas.

We define the observed shoreline retreat in semi-arid urban coasts as the sum of shoreline retreat due to (1) coastal erosion resulting from sediment imbalance⁹ and (2) coastal erosion resulting from sea-level rise caused by the direct rise of sea level^10,39,40, as described in the material and methods, Section Observed shoreline retreat rate. We describe the results of measuring and calculating the above components of total shoreline retreat and their dependency on land coverage. Finally, we forecast the shoreline retreat up to 2100 and its implications on current beach nourishment costs in the Gulf of Catalina in Southern California.

Observed shoreline retreat

The temporal shoreline evolution, as monitored from diachronic airborne and orbital scenes for our study area and two validation sites, reveals rapidly changing coastlines for the Gulf of Santa Catalina, Corona Del Mar, and HAM, as shown in Fig. 1a–c. The Digital Shoreline Analysis System (DSAS) method allows the detailed assessment of non-linear shoreline change over the medium-term temporal monitoring periods of 1992–2005 and 2018, especially for coastal erosion hot spots, as defined by⁸. We classify observed erosion rates according to the classes of shoreline trends established by Esteves and Finkl⁴¹. In Table 1, we observe an overall pattern of erosion (−0.5 to −1 m yr⁻¹), intense erosion (−1 to −3 m yr⁻¹), severe erosion (−3 to −5 m yr⁻¹), and extreme erosion (>−5 m yr⁻¹) that is prevalent throughout the study area and the two validation sites (Fig. 1a–c).

Fig. 1: Multi-date shoreline evolution analysis using the DSAS model.

a Shoreline evolution analysis from 1992 to 2018 for the beaches of the Gulf of Santa Catalina in Southern California, USA, projected over the 2014 ESRI scene. b Shoreline evolution in the validation site of Corona del Mar State Beach (CA, USA). c Shoreline evolution of the validation site of Hammamet North Beach, Tunisia. The net shoreline movement in both validation sites, from 1992 to 2018, is −35 m for Corona Del Mar and −90 m for Hammamet North Beach.

Table 1 The shoreline evolution analysis for the Gulf of Santa Catalina beaches in Southern California and the two validation sites: Corona Del Mar Beach, USA, and Hammamet North Beach, Tunisia

The shoreline movement analysis in the Gulf of Santa Catalina in Southern California falls under the stable range during the study period 1992–2018 with an EPR rate of 0.04 ± 0.15 m yr⁻¹ (Table 1). However, changes in shoreline retreat rates for the validation sites in Corona del Mar State Beach in Southern California and Hammamet North Beach in Tunisia clearly show the erosion-dominated trend. For areas with the highest erosion rates, sandy beaches show severe retreat, as shown in Fig. 1b, c, with maximum Net Shoreline Movement (NSM) shoreline retreat rates over the last three decades (1992–2018) that exceed −35 m at the Corona del Mar State Beach and −90 m at Hammamet North beach, in urbanized areas.

For the End-Point Rate (EPR) of shoreline change of the Southern Californian beach along the Gulf of Santa Catalina, the medium-term assessment of the shoreline in the modern period (1992–2018) shows a variable small retreat range of −0.36 ± 0.18 m yr⁻¹ from 1992 to 2005. Hence, the average rate of the total observed shoreline movement between 1992 and 2018 for Southern California is ~ −1 m yr⁻¹. These changes are primarily attributed to natural coastal hazards such as the strong El Niño and flooding events. As a result, the Southern California coast shows a maximum EPR of retreat by −0.75 m yr⁻¹ (±0.1) during the modern period from 2005 to 2018 (Table 1).

Our results show that the current average shoreline retreat rates observed in the sandy beaches in these areas range from −0.75 to −1.24 m yr⁻¹ in Southern California and from −0.21 to −4.49 m yr⁻¹ in HAM under similar aridity, land coverage, and precipitation patterns. Our analysis suggests that the average total shoreline retreat rates for semi-arid areas, as deduced from our two validation sites and accounting for both coastal erosion and SLR, is the present value of ~−1.45 m yr⁻¹ (Table 2).

Table 2 Measured and projected End Point Rate (EPR) Shoreline Retreat Rate values between 1992 and 2100 at the validation beaches

Even though the observed maximum EPR rate falls under the erosion rate (−0.5 m yr⁻¹), it is identified as a hot spot of shoreline retreat by the GSAM⁸, where transects suggest erosive change rates greater than −0.5 m yr⁻¹ over the decadal period of 1984–2016 for multi-kilometer-long sandy beaches using the automated analysis of orbital photogrammetric scenes.

Orbital time-series photogrammetric observations confirm alarming shoreline retreat rates along the sandy coast of the northern bay of the Gulf of Hammamet⁹. The validation site is presently eroding at higher rates with maximum NSM losses of −93.48 m (±6.5) and with an EPR rate ranging between −4.49 m yr⁻¹ to −0.21 m yr⁻¹ (±0.18) and within an average of −2.35 m yr⁻¹ over the last few decades (1992–2018) as shown in Table 1 and Fig. 1c.

Naturally, during the short-term period (i.e., inter-annual scale), the swash-aligned beaches move under seasonal storm surge variability along the cross-shore profile. During summer, the seaward sandbank features feed the shoreline via the cross-shore currents. The longshore current from the neighboring sediment cell also drives sediments. The construction of harbors disturbs the longshore drift, resulting in a sediment budget deficit at the beach face. Moreover, urban construction disturbs the coast’s natural accretion/erosion equilibrium state; hence, the erosion trends persist (Table 1, Fig. 1b).

Sandy beaches undergo non-linear evolution that is governed by the coastline’s physical characteristics, such as its hydrodynamic conditions, nearshore bathymetry, nearshore orientations of its currents, and geological settings^6,42. As coastal sediments for both headland coast and embayed beaches are provided by fluvial sedimentation from several local drainage networks (Fig. 2a, b), the build-up of dams since the early to mid-century has considerably reduced natural sediment discharge to the coast, resulting in a sediment budget imbalance that causes the observed shoreline retreat⁴³.

Fig. 2: Contextual maps showing the coastline, the major rivers, streams, dams, lakes, and reservoirs for our study area and validation sites.

a The Gulf of Santa Catalina and the validation site of Corona Del Mar Beach (CA, USA). b Gulf of Hammamet in Tunisia, and the validation site of Hammamet North Beach.

Similarly, erosion problems along the Gulf of Santa Catalina in Southern California beaches are augmented by the damming and flood control measures of many local watersheds and rivers, which cut off the sand supply to the beaches^16,44. Additionally, the construction of dike harbor infrastructure on both Southern California and the Hammamet Gulf shores disturbs longshore drift, leading to a sediment budget deficit at their beaches. Hence, the response of shoreline evolution to such anthropogenic structures is clearly expressed by severe erosion during the modern period (1992–2018)⁹.

The validation site of Corona del Mar’s pocket beach, which is geomorphologically representative of the Southern California coast, spans along the San Pedro beach compartment and Laguna littoral sub-cell, where ~59% of the sediment budget is supplied by anthropogenic beach nourishment⁴⁴. The Santa Ana and San Gabriel Rivers provide the total budget replenishment of natural sand for the coast. Damming in recent decades has obstructed sand transport to the beaches in Southern California by 47% of the entire natural fluvial sand yield, estimated at nearly 1.5 million cubic meters of sand annually⁴⁵. In addition, sea cliff armoring reduces the sand supplied to Southern California’s beaches by another 10% of the natural sand supply, accounting for more than 26,750 cubic meters annually, representing less than 7% of the total sand input⁴⁵.

Sediments flowing from the two principal drainages of the Santa Ana and the San Gabriel Rivers, which cross the mesa in the southwestern part of the Newport Bay estuary area (Fig. 2a), formed the beaches, sandbars, and mudflats of the coastline of the Gulf of Santa Catalina. These lowlands and salt marsh areas were altered during the last century to deepen maritime navigation routes and form habitable urban artificial islands⁴⁶.

The aridity trend is assessed from the decrease in precipitations and occurrence of extended drought periods, as illustrated in Supplementary Fig. 1 in the two validation sites. Indeed, during the last decades, from 1980 to 2010 and 2010 to 2018, the precipitation annual average in SC and HAM sites was reduced by ~25% and ~56%, respectively. Therefore, the capacity to transport sediment by the river to the coastal areas is reduced by the decline in sediment discharge yield driven by a lack of precipitations.

Another factor that can affect the observed shoreline retreat is the ground subsidence as induced by tectonic and hydrological activities. The coastal area forming the Gulf of Santa Catalina is fully urbanized, as shown in Supplementary Fig. 2. Hence, there are no coastal agricultural developments to generate significant subsidence on the coastline. However, the Southern California substratum exposes several seismically active faults with significant late Quaternary deformation (Supplementary Fig. 3). As such, Southern California undergoes an annual subsidence of ~3 mm yr⁻¹⁴⁷ compared to the ~5.7 mm yr⁻¹ observed in Tunisian coastal ridges³⁹. Several areas of Newport Beach are also vulnerable to liquefaction and related ground failures caused by seismically induced settlement. Such areas along the Southern California coastline include the Balboa Peninsula and the surroundings of both the Newport and Upper Newport Bays, all in the lower discharging parts of major streams in Newport Beach and the floodplain of the Santa Ana River¹⁹. Stream erosion has strongly shaped the coastal upland at the southern margin of the Los Angeles Basin, resulting in moderate to steep cliffs along Upper Newport Bay. More geophysical investigations are needed to validate the potential correlation between the shoreline retreat rate and local subsidence.

Decadal-scale coastal cliff erosion observed along the California-Mexico beaches from 1930 to 2010 suggests that unconsolidated cliffs of friable materials fronted by sandy beaches retreated and eroded ~49% more than those without beaches²⁰. Naturally, sandy beaches would protect cliffs against wave-driven erosion. Still, as the beaches continuously thinned, the sea waves directly hit the cliff base during storms and daily tide fluctuations, triggering erosion from the base. Changes in precipitation and periods of drought in semi-arid regions also structurally destabilize the coarse-grained substratum of cliffs with friable materials⁴⁷. Shoreline retreat has subsequently threatened the substratum’s geotechnical stability and increased the occurrence of landslides. For example, the Corona del Mar area is located on the recent (1998 to 2009–2010) hot spot for cliff retreat, with a net cliff face retreat of −0.042 m yr⁻¹ (mean range) and cliff top retreat rates with a mean of −0.12 m yr^{−1 20}. Our study from 1992 to 2005 shows an erosion rate for the sandy beach with an average NSM rate of −4.84 m (±2.3) (Table 1, Fig. 1b). This is validated by comparing the coastline position from aerial and orbital photogrammetric images with a temporal baseline of a few decades, as shown in Supplementary Fig. 2.

The observed widespread erosion over South California beaches is associated with energetic wave storms such as El Niño events⁴⁸. Historically, the natural morphodynamic processes of the low sandy barrier and inlets extending into the San Pedro cell show a seasonal migration southward of the source yield (i.e., the river mouth)³⁹. At the Oceanside cell, the sandy pocket beaches backed by low cliffs depend on the forcing between wave energy levels and sediment supply from source to sink.

Shoreline Retreat from sea level rise

We use the common Bruun rule¹⁰ to calculate the Shoreline Retreat Rate (SRR) associated with the coastal retreat from sea-level rise (SLR) from 1906 and 1925 to 2018 for our two validation sites based on the nearshore morphology and physical parameters as described in section Materials and methods. The calculated values are listed in Table 3. As expected, the SRR induced by SLR calculated from the Bruun formula is inferior to the observed ones, as they do not account for the contribution of coastal erosion processes to the observed SRR. The SRR in Corona del Mar was calculated at −0.67 m yr⁻¹ in 2018 from the Bruun approach, whereas the observed SRR from DSAS is about −0.83 m yr⁻¹ (Fig. 3a). For the North African coast of HAM, the Bruun rule indicates an SRR of −1.4 m yr⁻¹ caused by SLR, while the observed SRR is at −2.45 m yr⁻¹ using the DSAS approach (Table 3, Fig. 3a). The observed shoreline rate (DSAS), which considers the sand supply imbalance and the beach face topography, is higher than the Bruun calculation by 12% to 19% in Southern California (SC) and by 75% to 43% in HAM in Tunisia, respectively, from 1992 to 2018. This suggests that coastal erosion is rapidly growing along urban semi-arid areas as the sediment imbalance becomes more prominent due to the abrupt change in land coverage and increased aridification.

Table 3 Calculated Shoreline Retreat Rate (SRR) parameters between 1992 and 2018 according to the Bruun rule and the measured approach (EPR-DSAS) in the two validation sites

Fig. 3: Comparative analysis of the evolution of shoreline retreat rates induced by DSAS, SLR and GSWE models from 1990 to 2018 for the investigated sites.

a Shoreline Retreat Rate due to the Sea Level Rise as calculated from the Bruum formula and the measured Digital Shoreline Analysis System (EPR in m yr⁻¹) in the validation sites of Corona del Mar (CA, USA) and the Hammamet-North (Tunisia) coasts. Error bars for the measured shoreline retreat, as deduced from DSAS, correspond to the error in assessing the EPR values, as detailed in Table 4. Bruun model errors are calculated from the standard SLR rate, which errors are associated with the regional tide gauges ranging from ±0.17 mm and ±1 mm in San Diego and Hammamet stations^39,60. The water occurrence errors of the GSWE model correspond to the margin of ~6%⁸⁶. b Net Shoreline Movement rates calculated from DSAS, Bruun, and GSWE Models.

The Bruun rule notably assumes decadal chronic recession of low-lying sandy beaches under sea level rise when local wave climate characteristics are quasi-constant. We, therefore, apply the Bruun model in SC and HAM sandy beaches to calculate the contribution of SLR to the shoreline retreat. The coastline in low-lying sandy beaches responds rapidly to sea level rise, such that the beach profile attains a dynamic equilibrium with future sea levels in the long or short term. This assumption by the Bruun rule does not consider other possible causes for retreat, such as the long-term variability of the wave climate or sand availability from other sources or sinks¹¹. The Bruun rule is an established approach that has been globally adopted and validated in several sandy beaches and nearshores within common morphological, sedimentological, and hydrodynamic characteristics⁴⁹. For instance, the results of Le Cozannet et al.⁵⁰ illustrate that the Bruun rule is valid when the beach slope is gentle with a slight longshore drift gradient, is sheltered from storm surges, and undergoes minimal human impact⁵⁰. Similarly, several studies validated the Bruun Rule along the eastern coasts of the US¹⁴, along the Mediterranean coast of Egypt⁵¹, and along Pacific US beaches⁵².

To validate water level changes along the transitional environment, we compare SRR induced by SLR and the total measured SRR driven by the global permanent surface water changes between 1985 and 2018 in Southern California and North African coastal lands. Therefore, we generate the annual shoreline movement rate (m yr⁻¹) from the High-resolution Global Surface Water Explorer (GSWE) datasets, as shown in Fig. 3b. According to the generated histograms of the SRR based on the GSWE datasets (section, Materials and Methods), sandy beaches show a retreat trend of −0.76 m yr⁻¹ and −1.92 m yr⁻¹ between 1992 and 2018 in SC and in HAM, respectively. These values are almost equal to the SRR-Bruun approach within a difference ranging from 0.09 and 0.52 m yr⁻¹ for SC and HAM beaches, respectively, if we consider the GSWE processing error (6%) (Fig. 3b). Although SLR has doubled since the early 1990s⁵³, the shoreline retreat prediction remains largely uncertain through 2050 and 2100 when solely relying on the Bruun rule or a modified beach equilibrium assumption⁵⁰. To address this uncertainty owing to the above-mentioned limiting assumptions, we establish the shoreline retreat projection by incorporating forecasted changes in land use, which is one of the primary drivers altering the sediment transport to the coast, as described below.

Decadal changes in land-use occupation

As stated in section Land-use classification of the Materials and Methods, our supervised classification aims to quantify coastal land use components which contain five classes: (1) continental water bodies, (2) bare soils, (3) vegetation, (4) urban spaces and (5) sandy deposits in the studied sites as shown in Fig. 4a, b. Two supervised-scene classifications of orbital images from Landsat 1985 and 2015 provide a land-cover classification for the Gulf of Santa Catalina (Fig. 4a) and for the Gulf of Hammamet (Fig. 4b) and the temporal evolution of land-use and occupation class statistics in both (Fig. 5). We use a confusion matrix in post-classification algorithms in ENVI to corollate physical, environmental, and social variables with the landscape attributes and composition.

Fig. 4: Detection of changes in land use from the supervised classification between 1985 and 2015 from Landsat 5 (1985) and Landsat 8 (2015) scenes.

a In the Gulf of Catalina (CA, USA) and (b) in the Gulf of Hammamet (Tunisia). Land-use maps are used to assess the changes inland and are not used for shoreline delineation.

Fig. 5: Temporal evolution of land-use and occupation classes in Orange County in Southern California and the Gulf of Hammamet between 1985 and 2015.

The error bars of both land-use maps are ~2% to ~4%, respectively, as stated in the section decadal changes in land-use occupation.

Evaluation of classification results for the two orbital scenes sets from the confusion matrices indicate that the Kappa indices are 0.89 to 0.93 for Landsat 5 scenes (acquired in 1985) and 0.94 to 0.95 for Landsat 8 scenes (acquired in 2015) for OC and HAM respectively. The accuracy of both land-use maps is ~98% to ~96%, respectively, suggesting high confidence in our terrain classifications approach.

The vegetation and urban space classes cover more than 95% and 91% of the total areas for the Gulf of Santa Catalina and the Gulf of Hammamet, respectively. At the same time, the continental water, bare soil, and sand deposits classes represent the most diminutive proportions under 5 to 9%, respectively, as shown in Fig. 6a, b.

Fig. 6: Detection of changes in land-use surface occupation from the supervised classification between 1985 and 2015 from Landsat 5 (1985) and Landsat 8 (2015) scenes.

a in the Corona del Mar coasts and (b) in the Hammamet North coasts.

Figure 5 shows that during the period between 1985 and 2015, over the studied areas, urban sprawl increased along with a recession of vegetation coverage and fluctuations in classes of continental water bodies, bare soils, and sandy deposits.

To assess the land use and occupancy patterns for different classes, we compare the Landsat dataset between the 1985 and 2015 scenes expressed herein using statistical diagrams for the two studied areas (Fig. 5). The main changes experienced between 1985 and 2015 over the SC and HAM littoral cells were the decrease in vegetated areas and the significant expansion of the urban ones (Fig. 6a, b). During this period, urban areas doubled in the SC zones, where 61,500 hectares of vegetation were transformed into urban space, with over 20 million inhabitants living within the Southern California coastal watersheds. HAM has exhibited the same alarming changes in the landscape over the last 30 years. During this period, 38,837 hectares of vegetation disappeared and were changed into urban areas. However, we also note that the bare soil class reveals an increase of 10% over the HAM littoral cell (Fig. 5). Our results suggest a dramatic recession of vegetation crops by regression of ~19% to ~18% in the coastal plain in the SC and HAM coastal areas, respectively. It confirms that anthropogenic impacts have been widespread and extensive in scale in semi-arid regions⁵⁴.

The other classes in this case (namely, continental water covering the wetlands and fresh water and sandy deposits) have not undergone significant modification.

Rapid regional urbanization and human infrastructure development have considerably altered the coastal sediment dynamic and reduced terrestrial sand yield of the validation sites, the Corona Del Mar and Hammamet North coastal areas, as shown in Fig. 5a, b. Rainfall records in Southern California and North African areas also reveal temporal variability from 1980 to 2018 (Supplementary Fig. 1). The combined effect of global warming and anthropogenic drivers provoke rainfall fluctuations and the periodic occurrence of high-temperature increases and intensification of extreme hydrological and surge events, such as droughts, heavy rainfall events, El Niño and medicanes⁵⁵.

Due to global warming, Southern California is experiencing severe multiyear droughts unprecedentedly, which have not been witnessed in its recent hydroclimatic records²¹. The above leads to a long-term increase in aridity conditions, increasing the sediment imbalance at the coast.

Hence, the increase in droughts could also increase the coastal vulnerability of the semi-arid regions such as Southern California and North Africa due to precipitation deficits and resulting imbalance in the sediment supplied by the natural river network to the coastline, making those sites a representative regional case of a global response of the arid-high urbanized coastal area to the rapid warming changes. Shoreline retreat resulting from anthropogenic trapping of sediment discharges to the coast is identified as the main factor for high coastal vulnerability in arid and semi-arid areas, surpassing climate change drivers⁵.

Forecasting shoreline retreat and associated beach nourishment cost

Shoreline Retreat Rates from 1992 to 2100 are illustrated in Fig. 7. From 1992 to 2018, the ratio of the SRR to PDR (i.e., SRR/PDR) for the Corona del Mar validation site is ~0.03 and 0.11 for HAM. We can observe that an increase in PDR by 10% triggers a change in land use that consequently increases the sediment imbalance at the coastline, which results in a shoreline retreat rate of 0.40 m yr⁻¹ for the sandy beach of Corona Del Mar. The same PDR will result in a 0.8 m yr⁻¹ retreat for HAM over the same period. The foresight scenarios of the SRR and PDR along the SC and HAM coasts reveal significant shoreline retreat rates by 2100, especially for the urban beaches, i.e., Corona Del Mar, that exceeds an average of −2 m yr¹ (scenario 2) (Fig. 7a & Table 2). The HAM coast reveals an alarming trend with an average SRR projection of −4 m yr⁻¹ (scenario 2), as shown in Fig. 7b.

Fig. 7: Shoreline Retreat Rates (SRR) and the associated Population Density growth Rates (PDR) projections to 2100 under three scenarios of Minimum, average, and maximum as derived from Pimienta⁹⁶ & Paskoff and Sanlaville¹³ in semi-arid low-lying coastal regions.

a in the Corona del Mar beach (CA, USA) (b) in the Hammamet-North beach (Tunisia). The measured part of the shoreline retreat rates is derived from the photogrammetric change detections in orbital scenes from 1992 to 2018. Error bars for the measured and projected shoreline retreat rates correspond to the errors of the EPR values detailed in Table 3.

The associated NSM from the above is twice the projected value of −29.5 m suggested by the GSAM for the sandy ambient beaches for the northwestern Pacific coastline under RCP4.5 and RCP8.5 by the year 2100. It is important to note that the GSAM⁸ only considered ambient sandy beaches and did not cover the arid or semi-arid ones addressed in the present study. Our results suggest that semi-arid beaches will be eroding at higher rates than ambient ones.

In Southern California, population and economic growth are the primary drivers of the rapid change in land use⁵⁶. The rise in high-income population increases the demand for coastal housing, including new multi-unit residential developments and large resorts. The above will result in changing the land use and the associated sediment transport mechanism, resulting in a sediment imbalance at the coastline, hence requiring more costly beach nourishment, rising local property taxes, and resort fees to maintain beach stability. The increased vulnerability to coastal hazards, triggered by the forecasted shoreline retreat, will result in a considerable economic loss to beach cities such as the ones in Southern California⁵⁷.

As described in section Observed shoreline retreat, our observed SRR analysis suggests that the average total retreat rates for semi-arid areas, as deduced from our study area and two validation sites and accounting for both coastal erosion and SLR, will increase from the present value of ~−1.45 m yr⁻¹ to reach −2.12 m yr⁻¹ in 2050 and −3.18 m yr⁻¹ in 2100 (Table 2). These figures should be considered as the lower limit for future shoreline retreats. Projected hydroclimatic extremes, such as storms and increased droughts, in semi-arid areas can significantly increase these figures, which have to be quantified in separate upcoming investigations.

To address the severe sediment deficits along Southern California coasts, federal, state, and local authorities have spent over a billion dollars on beach nourishment programs over the past 20 years⁵⁸. For instance, Newport Beach received over 7.64 M m³ of sand between 1934 and 1936, and Santa Monica and Venice Beaches in Los Angeles received 21 M m³ of sand between 1947 and 1948 and another 7.64 M m³ of sand in the early 1960s. By contrast, Huntington Beach in Orange County received ~1B m³ in 1990⁵⁹. The cumulative cost of beach nourishment since 1964 for the Surfside-Sunset Nourishment Program in Orange County is $3.85 M⁶⁰. Although the costs vary from county to county and state to state, an approximate 10-year average is $3.75 M km⁻¹ (approximately $4 m⁻³ as expressed in 1996 dollars) for Western/Pacific coastal states⁶¹.

From 1945 to 2002, more than 19 M m³ of sands were placed on the San Pedro littoral cell as part of a nourishment program. It justifies the positive sediment budget of the shoreline changes (Fig. 1a, Table 1). This nourishment added an average rate of ~305,822 m³ yr⁻¹ to the sand budget of the extensive 24 km of San Pedro public beaches (~3262 m³ yr⁻¹ km⁻¹)^62,63,64.

The present study highlights the increasing rate of shoreline retreat along the Gulf of Santa Catalina along the San Pedro and Oceanside cells. In particular, we observe sites with changing state of the sediment budget, like the Corona del Mar pocket beach, selected here as a validation site for the beach nourishment quantification, which changed from stable (<−0.5 m yr⁻¹) to erosive (>−0.5 m yr⁻¹) over the decadal period of 1984–2016. The overall natural nourishment of the Gulf of Santa Catalina beaches is significantly reduced by river damming, the armoring of sea cliffs, and jetties construction. This pocket headland beach’s nourishment contribution will not be enough to establish shoreface equilibrium⁶.

To assess the cost of beach nourishment, we consider three SRR scenarios (Table 4) over the next 32 years up to 2050 as it reduces the uncertainties associated with long-term forecasting for the SRR, nourishment costs, and inflation rates. It is also the average period for most mortgage payments in Southern Californian properties. The costs for 2075 are included in Table 4 for illustrative purposes. Still, they are more likely to suffer from errors due to the linear assumptions on the socioeconomic drivers of the calculations. All forecasted costs in 2050 and 2075 are in 2018 US dollar values.

Table 4 Estimate of the annual nourishment sand volume and associated cost in Southern California (Corona del Mar, CA) considering the current unit sand price of $20 per m^{3 64} and its forecasted inflation rate of 3% (www.calculator.net/inflation) under three erosion rates scenarios

Scenario 2 provides the best estimate for a realistic average of the SRR for the SC beaches by 2050 and 2075, with an erosion rate of −1.09 and −1.47 m yr⁻¹ over one kilometer of the Corona del Mar State Beach. These rates are four times greater than the presently observed values. This coastline retreat currently requires 1223 m³ yr⁻¹ km⁻¹ of sand beach nourishment to keep the beach at equilibrium⁶⁴. Considering that the current cost for one cubic meter of sand is averaged at $20⁶⁴ and that the sand cost is continuously rising at a rate of ~3% yr⁻¹ (deduced from 2010 to 2022 statistics in Garside⁶⁵, it could reach ~$45 m⁻³ in 2050. The Corona del Mar State Beach will need to be artificially nourished with ~2446 m³ yr⁻¹ km⁻¹ according to our projected erosion rate of scenario 2 in 2050. The associated cost for the 2050 beach nourishment price will rise from the current value of ~ $24,460 to $125,973.05 m³ yr⁻¹ km⁻¹ (Table 4).

For the entire San Pedro littoral cell, the current annual sand volume needed for nourishing the sandy beaches averages 305,822 m³ yr⁻¹⁶¹, considering an average SRR of −0.5 m yr⁻¹. As the cost associated with sand nourishment is expected to increase five times by 2050 (Table 4), the total cost for curbing erosion of sandy beaches and bringing them to equilibrium along the San Pedro coastline would be~ $16 M yr⁻¹. It should be noted that such value is considered at the lower end of the estimate as it does not account for any logistical requirements for other needed structural management to contain the nourished sand. Furthermore, the linear increase in sand price by 3% does not account for punctual increases that arise from surging demands from other industries that can reach a 78% rise in some cases⁶⁶. In this regard, our cost estimates should be considered at the low end of the scale.

It should be noted that the cost of nourishment in California is already higher than it is on the East Coast, with an average sand cost of less than $10 per cubic meter. However, due to the increasing erosion rate, intensive beach nourishment is frequently applied throughout the year to stabilize several areas of the beachfront⁶⁷.

Conclusion

Monitoring of the diachronic shoreline position of the coasts of Southern California, using change detection in the orbital photogrammetric scenes and the DSAS model from 1992–2018, reveals considerable retreat rates of sandy beaches ranging from −0.75 to −1.24 m yr⁻¹ (−1 m yr⁻¹ on average). This trend is also observed in other semi-arid areas, such as the validation site of the Gulf of Hammamet, where shoreline retreat is from −0.21 to −4.49 m yr⁻¹ (−2.35 m yr⁻¹ on average). The current average of both sites representing the end members of global semi-arid coastlines is ~−1.45 m yr⁻¹. Such a rate, when compared to the standard of −0.07 m yr⁻¹ suggested for sandy beach evolution by the Global Scale Assessment Model (GSAM)⁸, indicates the alarming and rapid degradation of these coastlines representing the predominant coastal landscape of Southern California, North Africa, Arabian Peninsula, Australia, and other semi-arid urbanized coastlines.

Forecasting decadal shoreline retreat in Corona Del Mar and Hammamet North beaches reveals that the coastal erosion arising from the growth in population density will significantly increase the observed shoreline retreat, aggravating the impacts of sea level rise by 2050 and 2100. Our analysis suggests that the average total shoreline retreat rates for semi-arid areas, accounting for both coastal erosion and SLR, will increase from the present value of ~−1.45 m yr⁻¹ to reach −2.12 m yr⁻¹ in 2050 and −3.18 m yr⁻¹ in 2100. Intensive and costly beach nourishment will be increasingly needed to mitigate the growing shoreline retreat impacting city seafront infrastructures. The environmental and ecological impacts of the needed artificial beach nourishment have yet to be fully assessed and are not addressed herein.

Our estimate of the needed sand volume for beach nourishments to mitigate these intense retreat rates suggests that the yearly artificial nourishment will increase from the present-day amount of 1223 to ~3669 m³ yr⁻¹ km⁻¹ in 2050. Consequently, the associated cost for this nourishment per kilometer will rise on average from the current value of ~$24,460 to $125,973.05, adding additional economic and logistical pressures for several semi-arid urban coastal communities in Southern California. Similar trends are emerging globally, with aggravated impacts expected in semi-arid developing nations that are already struggling with coastal hazards and may not be able to cover the rising costs of curbing beach nourishment.

Materials and methods

Our study site extends over all of the Gulf of Santa Catalina in Southern California, considered herein as a representative location of rapidly growing semi-arid coastal urban areas, as detailed further in Section Study area. Herein, we summarize the physical and morphodynamic processes in the Gulf of Santa Catalina, particularly the extent of the coastal sedimentary cell, river outflows, the extent of their catchments, and the various sediment sources along the coast. This knowledge provides crucial insights to analyze the relationship between the change in land cover and its impact on sedimentary imbalance at the coastline, which derives the shoreline retreat⁶⁸. To validate our assessment of the latter, we identified two validation sites where the relationship between shoreline retreat and changes in land use is established using publicly available datasets detailed in Table 5.

Table 5 Photogrammetric scenes used to assess shoreline retreat in the two studied areas

To quantify the physical drivers governing the shoreline retreats in semi-arid sandy beaches and forecast their magnitudes, we compare the erosion rates in the two validation sites with similar precipitation, sedimentation processes, and geomorphological characteristics to assess the impact of urban growth on the coastline dynamic. The physical characteristics of these sites are described in sections Study area and Validation sites.

The first step is quantifying the total observed shoreline retreat resulting from the sum of both coastal erosion and sea-level rise. We then calculate the shoreline retreat resulting from coastal erosion after deconvolving the effect of the relative SLR, as detailed below in sections Observed shoreline retreat rate, Forecasting shoreline retreat and associated beach nourishment cost, and Shoreline Retreat Rate From SLR.

To weigh the sediment imbalance that causes shoreline erosion, we evaluate the temporal evolution of the sea-land interface and the different land-use classes using multiple time-series analyses of orbital photogrammetric scenes and semi-automated terrain classification. We monitored the shoreline evolution in 1992, 2005, and 2018, corresponding to the era of rapid urban growth in Southern California. Furthermore, these dates’ physical and socioeconomic data are publicly available for the study area and the two validation sites.

The observed evolution in the coastline is integrated into a conceptual model to forecast the Shoreline Retreat Rate (SRR) as a function of the Population Density growth Rate (PDR). We finally quantify how population growth in semi-arid urban areas and its associated change in land use will increasingly impede the sediment transport processes, resulting in additional erosion and higher shoreline retreat rates at the local and regional scales by the years 2050, 2075 and 2100 under three different urban growth rate scenarios. Finally, we quantify the sand nourishment volume needed to mitigate the SRR and calculate its implementation costs under three erosion rate scenarios.

Study area

Our study area is the Gulf of Santa Catalina in Southern California (SC). The Gulf is 150 km long and is formed of extended beaches, from the embayed Corona Del Mar State, in Orange County (OC) to La Jolla beaches (Fig. 2a). Pocket beaches, valleys, lagoons, headland, and cliffs characterize the South California primary beaches. The studied area is on the southern margin of the Los Angeles Basin. The seismicity is characterized by numerous active faults, dominated by the San Andreas Fault System (Supplementary Fig. 3). The San Andreas Fault is a compressive system with northwest-southeast and east/west direction trends between the Pacific Plate in the west and the North American Plate, which lies east of the fault zone⁶⁹.

Our study area along the Los Angeles, Orange, and San Diego counties is characterized by a semi-arid Mediterranean climate with dry summers and sporadically wet winters, with the highest rainfall between November and March and annual average precipitation between 250 and 300 mm⁷⁰.

The dominant littoral drift of the SC beaches comes from northward along the southwest-facing beaches of the San Pedro and Oceanside cells⁷¹. Summer swells drive the cross-shore current, and the southerly direction occurs locally when southerly stormy waves are coming from western Mexico and the southern hemisphere⁷². The mixed tide is predominantly semi-diurnal and microtidal, with a tidal range of 1.65 m⁴⁴. The study area covers two littoral cells. The San Pedro cell extends from the promontory Point Fermin to Dana Point along 70 km, and the Oceanside cell extends 80 km from Dana Point cape to La Jolla submarine canyon (Fig. 2a).

Rivers provide the principal natural source of sand to the Southern California (SC) beaches. Major streams are the Santa Ana River, the San Gabriel River, and the Los Angeles River basin covering 9200 km² of catchment (Fig. 2a). The construction of the east Jetty in the early 1940s diminished the San Gabriel River discharge to the coast. The Santa Ana River sediment supply to the shore is estimated at 20,000 to 40,000 cubic meters per year⁷³. After the flood of 1938, the river was controlled by flood structures and an embankment Prado dam in 1941 (Supplementary Fig. 4a). The Oceanside River basin covers 5500 km² over the Santa Margarita (1900 km²) and San Luis Rey (1450 km²) rivers. The basins provided the most sedimentation supply to the Oceanside littoral cell before the dam construction. In the state of California, the rate of population growth over the last decade, from 1990 to 2018, is 1.3%, with a high urban growth rate of 81%⁷⁴. The 2020 Census reveals that California has the highest urban population density and urbanization share of the total population among all the union states⁷⁵.

Validation sites

The validation sites were chosen as they show significant shoreline and land-use changes with in-situ observations. Both sites have comparable hydroclimatic, geomorphological, and morpho-hydrodynamic characteristics, as shown in Fig. 2a, b. The first validation site is Corona Del Mar beach, located in the north-central part of the Gulf of Santa Catalina (Fig. 2a). The beach is ~500 m long, ~40 m wide, and surrounded by headlands and cliffs.

The second validation site is located in North Africa on the central-eastern Tunisian coast in the North of the Gulf of Hammamet (Fig. 2b). It is referred to after this as Hammamet-North (HAM). Similarly to the study area of the Gulf of Catalina, the shore of both validation sites consists of embayed sandy beaches intercepted by swash pocket beaches. The eastern-central region of Tunisia is under a temperate Mediterranean climate with rainfall averaging 400 mm yr^{−1 76}, comparable to the one observed in Southern California, as described in section Study area. The precipitation patterns are highly variable, undergoing strong temporal and spatial fluctuations for the last three decades⁹ (Supplementary Fig. 1). The prevailing seafront wind is blowing from the northwest. Therefore, the dominant active wind that governs the longshore drift along the Gulf of Hammamet is generated from the north-to-south direction. The tide is predominantly semi-diurnal and microtidal, with a tidal range of 0.2–0.3 m. The primary active rivers characterizing this validation site are located in the northern Gulf of Hammamet (Fig. 2b). The sedimentary supply available downstream is significantly reduced after two dams construction in 1963 and 1986⁷⁷ (Supplementary Fig. 4b). The population density rate increased considerably over the last decade between 1990 and 2014 by 45%⁷⁸. The HAM validation site extends over 500 m in length. It is selected as it undergoes significant shoreline and land-use changes with available in-situ data. It is considered a representative sample of dynamic pocket beaches observed in both the Gulf of Hammamet and the Gulf of Santa Catalina. It is likewise constituted of a succession of pocket beaches and littoral cells bordered by promontories and cliffs (Fig. 2b).

Similarly to California, the population growth rate in HAM over the last decade is significant at 1.55%, with a high urban development portion of ~73%⁷⁸. The city of Hammamet is the main coastal tourist city in Tunisia, with the highest urban growth⁷⁹ and a population density of ~2700 people/km²⁷⁸.

Observed shoreline retreat rate

To perform long-term shoreline monitoring of the total observed shoreline retreat rate over the period 1992-2005-2018 (SRR _Observed), we use the Digital Shoreline Analysis System (DSAS) method⁸⁰ implemented with more than 100 datasets from Landsat orbital photogrammetric scenes (1992 and 2005) and Sentinel 2B (2018) and aerial scenes (1992, 2005 and 2018) (Table 5, Fig. 8a, b).

Fig. 8: Assessing shoreline evolution using photogrammetric scenes and the Digital Shoreline Analysis System (DSAS) in Southern California.

a Shoreline evolution analysis for the beaches of the Gulf of Santa Catalina, USA. b The validation site at the Corona Del Mar state beach, where we used the DSAS model with cross-shore transects (in white) and baseline (in purple). Transects are generated using 100 datasets of airborne and orbital photogrammetric scenes. The dates corresponding to different shoreline positions are illustrated in yellow, green, and red lines. A total of 1600 cross-shore transects were generated in the study and validation sites.

In this approach, the DSAS algorithm creates cross-shore transects and analyzes different points along these transects to calculate the shoreline change rate at a specific time interval. For each transect, DSAS estimates the shoreline position⁸¹. Cross-shore transects are 135 km long with 50 m spacing over the Gulf of Catalina study area (Fig. 8a). In the two validation sites of Corona Del Mar and North Hammamet, the cross-shore transects are 500 m long with 50 m spacing. First, we establish a baseline offshore, parallel to the general trend of the coastline (Fig. 8b). Then, the statistics of the computed rate-of-change allow us to generate a time series integrated into the Geographic Information System (GIS), showing the temporal evolution of the shoreline’s geometries and positions over the last few decades. A total of 1600 cross-shore transects were generated in the study and validation sites. The statistical model generates two outputs: (1) the Net Shoreline Movement (NSM), which calculate the total distance between the oldest (1992) and current (2018) shoreline positions; (2) the End Point Rate (EPR), which is the annual rate of shoreline retreat for each date 1992–2005 and 2018 and the Linear Regression Rate (LRR), which represent a least-squares regression line to all shoreline points for each transect. Field visits took place in Hammamet in 2018, for Corona Del Mar in November 2022, and for Huntington beaches in October 2022 to establish georeferenced points and validate observational retreat rates.

These two latter parameters and the changes in land classification are then implemented in the empiric numerical model, described in section Forecasting shoreline retreat as a function of the population density rate, to forecast the short and mid-term shoreline retreat rates in m/year for each site under different urban growth scenarios from 1990 to 2100.

Shoreline retreat from coastal erosion

We define the observed shoreline retreat (SRR _Observed) in semi-arid urban coasts as the sum of the shoreline retreat resulting from coastal erosion caused by sediment imbalance⁶⁸ and the one resulting from sea-level rise caused by direct submersion¹⁰ as follows in Eq. (1):

$${{SRR}}_{({Observed},{DSAS})}={{SRR}}_{({coastal\; erosion})}+{{SRR}}_{({SLR},{calculated\; using\; Bruum}[10])}$$

(1)

From the above, we can assess the contribution of coastal erosion to the observed shoreline retreat in percentage as follows in Eq. (2):

$$\% \,{SRR}({coastal\; erosion})=\frac{{{{{{\rm{SRR}}}}}}({{{{{\rm{Observed}}}}}})-{{{{{\rm{SRR}}}}}}({{{{{\rm{SLR}}}}}})}{{{{{{\rm{SRR}}}}}}({{{{{\rm{Observed}}}}}})}\times 100$$

(2)

Equation (2) allows deconvolving the effect of SRR caused directly by the SLR from the SRR driven by the sedimentation imbalance, namely the coastal erosion. Each of the parameters in Eq. (2) is detailed below.

Shoreline retreat rate from SLR

The estimated equilibrium shoreline retreat rate SRR (mm yr⁻¹) for sandy coasts due to SLR (SRR _SLR) is calculated based on the Bruun rule¹⁰ for the years 1992–2005–2018. It is one of the conventional approaches to forecast the short to mid-term shoreline retreat under a linear SLR. The approach is based on measuring the landward and seaward movement of the active cross-shore profile extended from the Mean Water Level to the closure depth under sea level rise⁸². Here, we adopt the two-dimensional-based approach to quantify the shoreline erosion rate caused by the rise in sea level of the sandy coasts during the last twenty-six years under a quasi-constant wave climate characteristic. The accuracy of this approach has been subject to debate⁸³ as it does not consider the sediment transport beyond the borders of the pocket and embayed beaches, the beach profile (slope), and the sea level height. However, it is a reliable method capable of producing an initial assessment of shoreline loss estimates due to SLR at large spatial scales^58,84,85.

The equilibrium shoreline retreat rate SRR can then be assessed from Eq. (3), which is based on the beach morphology associated with the prevailing wave climate:

$${{{{{\rm{SRR}}}}}}=\left(\frac{{{{{{\rm{l}}}}}}}{\tan {{{{{\rm{\beta }}}}}}}\right)\times {{{{{\rm{SLR}}}}}}$$

(3)

Where l is the horizontal length of the shoreface bottom affected by the sea level rise (mm yr⁻¹), tan β is the beach face cross-shore slope (in degree °), and SLR expresses the sea level rise rate (mm yr⁻¹).

The regional SLR values are extracted from the process-based projections scenarios⁶⁰ measured from tide gauges in the neighboring station of the two validation sites: the San Diego and the Mediterranean Sea stations. Standard SLR rate errors are associated with the regional tide gauges ranging from ±0.17 mm and ±1 mm in San Diego and Hammamet stations, respectively^39,60. The tan β index expresses the slope of the dynamic beach cross-shore profile, which has been considered constant in time³⁹. In our study, we use the dataset of the global distribution of nearshore slopes developed by Athanasiou et al.⁵⁸ for the β slopes parameter calculation⁵⁸. The slope parameter β is computed by Eq. 4, which considers the detailed topo-bathymetric data of the beach cross-profiles, the closure depth (d), and the physical parameters of the wave (i.e., significant wave height Hs and period Ts) based on Nicholls et al.⁵⁹ formula:

$$\tan {{{{{\rm{\beta }}}}}}={{{{{\rm{d}}}}}}/{{{{{\rm{L}}}}}}$$

(4)

Where d is the depth of closure, there is no significant change in bottom elevation in meters, and L is the horizontal distance between the d and the shoreline, both in meters.

To examine the impact of the coastal (transitional) water surface dynamic induced by the sea level rises, we use the High-resolution Global Surface Water Explorer (GSWE) database covering the dates from 1984 to 2018 over the past 34 years at 30-resolution based on the Landsat 5 Thematic Mapper (TM), the Landsat 7 Enhanced Thematic Mapper-plus (ETM+) and the Landsat 8 Operational Land Imager (OLI) imageries⁸⁶. Long-term and seasonal water surface changes are performed based on the open access computational infrastructure Google Earth™ Engine and treated within the ArcGIS Pro 3.2.1 tools; according to Pekel et al.⁸⁶ the photogrammetric processing and water occurrence errors correspond to the margin of ~6%.

Land-use classification

We adopt automated approaches to produce land-use maps from Landsat Thematic Mapper (TM) (30 × 30 m spatial resolution) acquired in 1985 and Landsat Operational Land Imager (OLI) acquired in 2015 based on image classification methods, as shown in Fig. 9. The selected color composition allows visualization of individual terrain classes and vegetation coverage.

Fig. 9: Flowchart showing the adopted approach in our conceptual model for forecasting shoreline retreats in semi-arid areas.

The technical approach combines high-resolution orbital time-series photogrammetric change-detection, Digital Shoreline Analysis System (DSAS) algorithm, and conceptual numerical model correlating urban growth, SRR, and PDR.

We adopt the land and water interface delineation approach for coastline identification using a water index algorithm⁸⁷. We generate the water index algorithm in the ENVI 4.5 software using the Band Math function by combining the green and mid-infrared bands. The green band (0.525 to 0.600 µm) is sensitive to water turbidity differences. This band is also used to delineate broad classes of vegetation. We also use the Near Infrared band (1.60–1.70 µm) as it provides a solid contrast to distinguish between land and water surface features due to the absorption by the seawater and the reflectance by the vegetation coverage in the photogrammetric scenes.

Thus, the water index algorithm, a combination of the green and near-infrared bands, is ideal for discriminating between land and water at their interface. The Water index was calculated as (Green - NIR)/(Green + NIR)⁸⁷, where Green and NIR are the reflections in the green and near-infrared bands of the Landsat Thematic Mapper (TM5) and Landsat Operational Land Imager (OLI) TM 8 images, respectively. To unambiguously identify the coastline position, all images used in the two study sites were taken in the dry season as the mean water level (MWL) is quantifiable and moderate, as shown in Table 5.

Next, we perform an unsupervised automatic classification ISODATA to calculate class means distributed evenly in the data space and then cluster the remaining pixels iteratively using minimum distance techniques⁸⁸. Suppose the result of this classification fails to identify the terrain classes that are expected from ground validation; a directed supervised classification is carried out according to the“Maximum Likelihood” method⁸⁷. The supervised classification herein delineates the five terrain classes relevant to quantifying the sediment transport to the coast and the temporal evolution of its imbalance. These five classes are (1) continental water bodies, (2) bare soils, (3) vegetation, (4) urban spaces, and (5) sandy deposits. To evaluate the accuracy classification of Landsat 1985 and 2015, we applied confusion matrices, which allowed us to determine whether the reference pixels were classified in a class that represented a different landscape unit.

Two methods are adopted to validate the supervised classification method and land/water classification. For the Southern California areas, the reference data used for accuracy assessment are from the US Geological Survey (USGS), topographic maps for the image of 1985, and high spatial resolution images from the Google Earth™ engine. The above datasets are used as a reference for the scenes of 2015. For the classification of landscape classes and crop types, we use the Newport Beach General Plan⁸⁹, where the land-use map 2006 is used as a reference. For geospatial analysis of the Hammamet North (HAM) site, Global Position System (GPS) in situ surveys are performed to validate land-use classification criteria. Land use statistical analysis covers 350.000 ha and 250.000 ha in Santa Catalina and Hammamet Gulfs.

Forecasting shoreline retreat as a function of the population density rate

Our conceptual model combines the calculated and observed shoreline retreat rates and population density growth to forecast the coastline evolution in 2100. As urban growth is established as the primary source of sediment imbalance leading to shoreline retreat by erosion in arid and semi-arid coastal urban areas^73,90, we perform these forecasts under three different urban growth rate scenarios^8,46 Minimum, Average and Maximum as described in Table 2.

We combine shoreline retreat rates with population growth percentage density to generate scenario-driven coastal degradation projections. To achieve the above, we calculated the shoreline retreat rate from orbital photogrammetric scenes from 1992 to 2018 (Table 2). The baseline for shoreline retreat rate -S0- corresponds to the measured shoreline change on the 2018 date.

Our forecasting method uses simple extrapolation of the linear regression rate (LRR) on each transect. This method has the following advantages: (1) it uses regularly available datasets with a quantified accuracy, (2) it is based on a widely validated statistical concept⁹¹, and (3) it is easy to use and validate using observable shoreline retreat and land coverage.

To evaluate the performance of our linear forecasting model, we typically calculate the index of agreement (ranging from 0 to 1, with values close to zero indicating poor performance and values close to one indicating excellent performance) using the root-mean-square error (RMSE) by taking the mean of the observed quantities⁸⁰. For this study, we have used 26 years of calibration data (1992–2018) to make more accurate predictions for our shoreline model. In total, we used more than 100 photogrammetric scenes (satellite data, Aerial photography, and historical topographic and bathymetric maps) to validate the observed shoreline retreat rate between 1992 and 2018. The index of agreement in our study using the above dataset is 0.9, which shows a high fidelity of our prediction.

For the same period, we consider the density population growth rate the second parameter, as the study areas undergo higher and faster population growth rates and urbanization extended over the hinterland. Starting from the baseline density of population (P0) from the years 1990 and 1994 for, respectively, SC and HAM communes and the demographic data, we project the coastal Population Density growth Rate (PDR) for the next 82 years^8,46. Then, the projected Shoreline Retreat Rate (SRR) position trends in exposure to 82-year density population growth are computed as shown in Eqs. (5) and (6), where S is the shoreline Retreat Rate value, P is the population Density Rate, and Y the number of the projected years. Then, we estimate the future Shoreline Retreat Rate (SRR) and the Population Density Rate (PDR) for the 2100 date, namely S100 and P100, respectively, using a linear regression of the rates observed from 1992 to 2018 as an initial approximation (Table 2).

Finally, we drive three SRR and PDR scenarios over the two validation sites of Corona Del Mar and Hammamet North beaches (Fig. 1b, c). Scenario 1 is driven from the Minimum observed and computed Shoreline Retreats Rate values. Scenario 2 assesses the average of SRR and PDR values, and scenario 3 corresponds to the Maximum estimated rates.

$${S}_{2100}={S}_{0}+({SRR}\times Y)$$

(5)

$${P}_{2100}={P}_{0}+({PDR}\times Y)$$

(6)

The SRR error bars of the measured and projected curves are calculated according to the uncertainty in the co-registration of orbital scenes and the DSAS methods⁸⁰ (Table 5).

To estimate the required nourishment volumes and costs in the erosional study area, we consider three scenarios of the SRR over the 32 years up to 2050 and for 2070 (see Forecasting shoreline retreat and associated beach nourishment cost).