Fluvial inverse modeling for inferring the timing of Quaternary uplift in the Simbruini range (Central Apennines, Italy)

The timing of Quaternary uplift evolution of the Simbruini range (Central Apennines, Italy) is poorly known due to the lack of reliable chronological constraints of the post‐orogenic continental clastic units, deposited after the upper Messinian thrust‐top facies, and tectonic events. In this regard, we identified the main geomorphic markers, including several levels of continental units, whose plano‐altimetric projection along the river longitudinal profile has been correlated with the main non‐lithological knickpoints. Furthermore, we inferred the uplift history of the range by applying the inverse modeling of the river longitudinal profiles. Assuming a block uplift model, the drainage network cutting the Simbruini range recorded 2.4 ± 0.5 Ma of tectonic history, characterized by variable base‐level fall rates (corresponding to variable uplift rates).

The study area is located in the Simbruini-Ernici range along the axial part of the Central Apennines.
The Central Apennines developed since the Late Oligocene to present, as a consequence of the convergence and the following collision between the Africa and Eurasia plates (e.g., Carminati, Lustrino, Cuffaro, & Doglioni, 2010;Doglioni, Moretti, & Roure, 1991;Malinverno & Ryan, 1986). The long-term evolution of post-orogenic extensional tectonics in the Central Apennines is demonstrated by the presence of faultbounded intermontane sedimentary basins (e.g., Fucino, Sulmona, L'Aquila, Rieti) that host thick stacks of continental deposits (e.g., Giaccio et al., 2015Giaccio et al., , 2019. These deposits have been dated using biostratigraphy and magnetostratigraphy, allowing for partial reconstruction of the onset and subsequent history of extensional tectonics in these sectors of the Apennines (e.g., Cosentino et al., 2017). The topographic growth was slow during the phase of major crustal shortening that occurred during the Miocene-Pliocene, but strongly accelerated in the Quaternary, when the shortening slowed down and the whole area was affected by strong uplift and extensional faulting striking mainly NW-SE (D'Agostino, Jackson, Dramis, & Funiciello, 2001;Molin & Fubelli, 2005).
The Simbruini-Ernici range represents one of the most important tectonic structures of the chain and its topographic relief, with deeply incised valleys, testifies to a significant local uplift. However, the timing and relevance of Quaternary tectonics in the range is far from being fully understood, despite the clear structural and geological evidence of normal faulting (e.g., Fabbi, 2018), which clearly dissects the Late Miocene to Early Pliocene compressional structures. In fact, in contrast with other sectors of the Central Apennines, this part of the chain lacks well-defined intermontane basins, except for the northern termination of the Simbruini ridge, the Oricola-Carsoli basin, which has recently been described in detail (D'Orefice et al., 2014). The post-orogenic tectono-sedimentary history is only recorded by several sedimentary cycles of alluvial and slope deposits, cropping out along the mountain slopes and on top of the relief, where they represent the relicts of paleosurfaces (e.g., Fabbi, 2018).
Nevertheless, the study of these coarse-grained alluvial deposits is strongly hampered by the absence of fossils and other reliable stratigraphic and chronological data, and most of them have not been studied and mapped in detail, leaving the post-orogenic evolution of this sector of the chain substantially unknown (Bosi & Messina, 1990;Damiani, Catenacci, Molinari, Panseri, & Tilia, 1998;Devoto, 1967aDevoto, , 1967bDevoto, , 1970. Moreover, a river profile inverse model has not been applied to drainage in the region yet.
In this article, we present a geological and morphometric study of the area corresponding to the axial culmination of the antiformal central Simbruini range, where the history of post-orogenic extension has been characterized by the deposition of continental clastic deposits, whose remnants crop out at different heights above the present base level, as a consequence of strong uplift and river incision. The general purpose of this work is therefore to shed light on the final stages of the post-orogenic deformation in the central Simbruini range. To achieve this objective, it has been necessary to: 1. study, classify, and map the alluvial and slope deposits through detailed geological and geomorphological surveys; 2. project the relict basal surfaces of the different levels of the continental sequence along the main river longitudinal profiles, in order to identify the most important phases of the regional morpho-evolution; and 3. reconstruct the uplift history of the range through the fluvial inverse modeling. | 2457 DELCHIARO Et AL.
The orogenic phases caused uplift and emersion of this sector of the Central Apennines, and were followed by SW-directed extensional tectonics, with NW-SE trending, SW dipping, normal faults, dissecting the fold-andthrust structures and producing the progressive down-throwing of the stratigraphic succession in the western sector of the Simbruini range.
The study area is located at the core of the antiformal structure of the Simbruini Mts. and is characterized by a complex structural architecture and by a high local topographic relief. The outcropping geology of the area is synthesized in Figure 1b and consists of a Mesozoic bedrock unconformably covered, in its eastern side, by Upper Miocene carbonate clastics ("Brecce della Renga" Fm.), hemipelagic and foredeep siliciclastic units, and, with another angular unconformity, polygenic psephitic-psammitic deposits ("Puddinghe Poligeniche"), which represent the last marine units in the area. The outcropping deposits are arranged in two main tectonic units separated by a regional low-angle fault. The lower tectonic unit is formed by a homocline dipping to NE, made of Triassic-Jurassic units. The upper tectonic unit is mostly formed by Cretaceous carbonates, generally dipping to the NE. The nature of the "Vallepietra-Filettino" fault, characterized by younger-on-older geometry, has largely been debated in the scientific literature and has been interpreted as: (1) a thrust fault which involved an already deformed structure (Parotto, 1971); (2) a thrust fault which was reactivated as a normal fault (Cosentino et al., 2010); or (3) a low-angle extensional detachment fault (Calamita, Di Domenica, Viandante, & Tavarnelli, 2008). The tectonic structure of the area is further complicated by the presence of high-angle normal faults, dipping to the SW, which dissect the homocline in a sequence of fault-bounded tilted blocks which progressively lowered the entire structure to the SW, where the upper portion of the stratigraphy is preserved.
In this framework, due to a lack of intermontane basins, the last recorded sedimentary event is represented by several cycles of continental clastic deposits, resulting from the intense fluvial erosion of the carbonate deposits.
The landscape evolution in subaerial conditions started diachronically and is testified by the remnants of clastic deposits at different heights above the present-day base level of the drainage network.
A precise evaluation of regional uplift rates in the Middle-Late Pleistocene is hampered by the relative scarcity of remnant shoreline deposits and uncertainties in their ages, especially on the Adriatic coast. Nevertheless, approximate long-term uplift rates have been estimated by Bigi et al. (1995) in the order of 0.3-0.5 mm a −1 in the last 1 Ma, based on the present maximum elevation (480-500 m) of the Lower Pleistocene shorelines and associated deposits. Similar values (0.1-0.26 mm a −1 ) can be estimated for the long-term uplift on the Tyrrhenian side based on the elevation (∼200-400 m) of the Early Pleistocene shoreline (∼1.8-2.6 Ma). These rates are likely to be higher along the axis of the Apennines itself (D'Agostino et al., 2001;Molin & Fubelli, 2005), as reported also by Girotti and Piccardi (1994), suggesting 0.5-0.7 mm a −1 .

| P OS T-OROG ENI C DEP OS ITS
The study of the continental coarse-grained clastic deposits outcropping in the Simbruini range had been strongly hampered by the scarcity of sufficiently detailed and reliable stratigraphic data. The continental nature of these deposits is clearly demonstrated by the pink to reddish color of the matrix, by the carbonatic cement related to meteoric water circulation, and by the sporadic finding of ostracod as only fossil content. Most of these deposits are still to be studied, mapped, and dated in detail, despite their depositional history being crucial for providing chronological constraint on the history of Quaternary tectonics in the Central Apennines (Damiani et al., 1998;Devoto, 1967a). For these reasons, we performed a detailed geological and geomorphological survey in order to sample and genetically classify the continental deposits. In this section we describe the analyzed clastic deposits related to the post-orogenic history of this sector of the Simbruini range ( Figure 2).
The study area, comprised among Trevi nel Lazio, Vallepietra, and Filettino, is characterized by the presence of a huge amount of continental coarse-grained, mainly carbonatic, deposits (Accordi & Carbone, 1986). Here, the combined effects of uplift, normal faulting, and climatic oscillations strongly influenced the landscape evolution (Accordi & Carbone, 1986).
The landscape evolution in subaerial conditions is testified by the remnants of clastic deposits hanging at  (1928,1929), Damiani and Pannuzi (1976, 1980, and Jaurand (1994). Traces of glacial modeling relating to the last glaciation are evident, along the slopes of Viglio, Cotento, and Tarino Mts., where numerous glacial cirques outcrop. Furthermore, Campo Catino ( Figure 2) has been interpreted as of glacial origin, since it is partly occupied by morainic deposits and dotted with erratic boulders (Damiani & Pannuzi, 1976, 1980Jaurand, 1994).
Nevertheless, all the deposits described in the following subsections are referred to fluvial processes.

| Faito plateau
The Faito plateau (Figure 2b) covers an area of about 6 km 2 and lies among the deeply incised Simbrivio, Fiumata, and Granara valleys, at an elevation ranging between 1,442 m in the southern area and 1,676 m to the north (near Tarinello Mt.).
The origin of these deposits has been studied by Beneo (1938) and Devoto (1967a), who considered them Quaternary in age because of their continental nature. Damiani (1990Damiani ( , 1998, on the other hand, hypothesized a correlation with the "Brecce della Renga Fm.", which crops out extensively on the eastern slope of the Simbruini range and which has later been recognized as a lower Tortonian-lower Messinian marine clastic unit, resulting from the sedimentation along the margins of the Simbruini structural high, developed as a result of the early Tortonian extensional tectonics (Fabbi & Rossi, 2014).
Based on their texture, geometric relationships, and petrographic observations, the Faito clastic deposits have been subdivided into three sub-units: F1, F2, and F3 (Figures 3a-d). Clast size ranges from centimetric to plurimetric, with angular aspect. The average thickness of the F1 sub-unit is 80 m. The F1 cycle is clearly cut and tilted by a NW-SE oriented normal fault system.
The F2 sub-unit, which represents the main deposit of the Faito plateau, rests with a disconformity on top of the F1 sub-unit and Mesozoic bedrock. The basal disconformity is characterized by a slightly marked red surface, clearly observable at the contact with both the F1 cycle and Mesozoic bedrock. The F2 sub-unit has a thickness of about 250 m. In the lower portion the deposit is generally well cemented, massive, or poorly stratified, and poorly sorted. In the upper part, the F2 sub-unit becomes more organized, with well-defined bedding, 20-40 cm thick, also showing cross-laminations. The F2 sub-unit shows a gentle tilting (20°-40°) to N-NNE ( Figure 3b).
Different from F1, F2 shows an alternation of clasts and matrix-supported layers. The clasts are sub-angular to sub-rounded, with size ranging from millimetric to centimetric (Figure 3f), with a minor content of larger cobbles.
The analysis of the clast composition shows that the F2 sub-unit is mostly made by Cretaceous carbonate rocks.
The F2 sub-unit is also cut and tilted by a NW-SE normal fault system.
At higher elevation, in the northern sectors of the plateau, the younger cycle F3 crops out, representing the development of an alluvial fan system. The F3 cycle is in stratigraphic contact both with F2 and Cretaceous and Jurassic limestone/dolostone ( Figure 3b). The bedding shows local variations, from sub-horizontal to a few degrees of inclination to north and south. The deposit is well cemented, very porous, generally well organized, with crosslaminations and channelization features, and represents the development of an alluvial fan system (Figure 3d). The clast size ranges from millimetric to centimetric, mainly sub-angular, rarely sub-rounded in aspect. Clast content is made up mostly of dolostones with a lower content of limestones, both deriving from the Mesozoic carbonate substratum. The average thickness has been estimated at about 80 m, but is extremely variable and discontinuous.
The Faito deposits lie at the top of isolated mountains, disconnected from their source, like "remnants" of old relict clastic sedimentary bodies. The contact with the bedrock follows the mountainside and describes a complex paleotopography. In general, the Faito plateau deposits fill a N-S oriented wide synclinorium, related to a relict landscape, today obliterated. This hypothesis is also suggested by the findings of a similar deposit on the other side of the Simbrivio valley, at the same height and resting with a disconformity on the Cretaceous limestone (S1 unit, discussed later). These deposits crop out in correspondence with the Campo dell'Osso relict surface, with a setting similar to the one observed in the Faito plateau. These relict surfaces are widely distributed in the area (i.e., "Campo dell'Osso," "Camposecco," "Campo Rotondo"), as shown in Figure 2.

| Granara, Fiumata, and Simbrivio valleys
Along the sides of the Granara, Fiumata, and Simbrivio valleys, at lower elevation with respect to the Faito plateau, different slope and alluvial fan clastic deposits crop out, distributed on both sides of the valleys, with a thickness ranging from 50 m up to at least 150 m (Figures 3g,h).
The stratigraphy and age of the continental deposits of the Granara valley are still unclear and several interpretations have been proposed in the past (Beneo, 1938;Damiani, 1990;. The newly collected data allowed us to discriminate different sedimentary cycles, which show different clast lithology and relationships with the present-day topography. To the north of Filettino village, the FIU1 unit crops out ( In the context of Simbrivio valley, two deposits have been detected: (1) a terraced one which crops out north of Vallepietra (S2); and (2) a minor one cropping out on top of the valley, near the Campo dell'Osso relict surface, at the same height but on the other side of the valley from the Faito plateau (S1, Figure 2b).
To the north of the "Campo dell'Osso" relict surface, at 1,443 m a.s.l., the S1 deposit crops out, hanging on the Simbrivio valley bottom. The clastic deposit is very porous, sub-horizontal, and poorly stratified. Despite the extremely weathered aspect of the deposit, a matrix-supported level was detected, which is characterized by a pink calcarenitic matrix, such as the Faito plateau deposits. The total thickness of the deposit does not exceed 15 m.
The clasts are mostly angular and derive from the local Mesozoic succession. Due to the strong weathering of the deposit, it is not possible to make many considerations, but the elevation and nearness to Faito units suggests a possible age correlation with these deposits, and hints that the Faito units could be part of a more extensive landscape unit, eroded during the formation of the Simbrivio gorge.
S2 crops out between 899 and 970 m a.s.l. The contact with the underlying Triassic dolostones is sharp. It has been interpreted as a slope breccia, since it is very heterometric and chaotic, well cemented and mostly clastsupported, in beds with a thickness comprised between 20 and 80 cm. Layers with a matrix-supported texture are rarely observed and could be associated with debris flow events fed by the same slope deposits. Clasts vary from millimetric to metric, from angular to rounded in aspect. The macroscopic observation revealed only the presence of clasts belonging to the Mesozoic carbonate platform.

| PROJEC TI ON S OF THE G EOMORPHI C MARK ER S
The best geomorphic markers preserved in the study area are represented by the continental clastic deposits identified during the field survey, including the Faito (F1-F3), Simbrivio (S1, S2), Granara (G1, G2), and Fiumata (FIU1, FIU2) suites. In detail, we refer to the relict basal surfaces of the deposits as markers of the morphoevolutive erosive phases.
We investigated the plano-altimetric distribution of the main geomorphic markers represented by the continental deposits identified during the field survey, as well as the main non-lithological knickpoints along the river longitudinal profiles of the valleys cutting the Simbruini range, included in the upper Aniene river drainage basin.
The drainage network was extracted from the 10 m-resolution TINITALY digital elevation model (DEM) (Tarquini & Nannipieri, 2017) and analyzed using TopoToolbox, a set of Matlab functions for topographic analysis (Schwanghart & Scherler, 2014)  Specifically, the TAK function "ProjectOntoSwath" was used to project points (from basal surfaces of geomorphic markers) on the river longitudinal profiles. The knickpoints were detected using the TopoToolbox function "knickpointfinder," with a tolerance value of 30 m. This value reflects uncertainties associated with longitudinal river profile data, as it is higher than the maximum expected error between the measured and the true river profile.

| Results
A plano-altimetric analysis of the major knickpoints distinguished based on their elevation drop, as well as the geomorphic markers identified during the field survey, was conducted ( Figure 4). The knickpoint histogram in Figure 4b shows quite well a cluster correlating with the highest clastic deposits (between 1,550 and 1,300 m a.s.l.) that are associated with the presence of a large anomalous patch of low-relief/slope landscape. The lowrelief areas are especially visible in the Vallepietra, Granara, and Campocatino networks, elevated by at least 700 m above the Aniene trunk channel, and have low-slope hanging reaches with increasing vertical drop toward downstream segments (Figure 4). The histogram also shows two other minor knickpoint clusters at elevations of 1,000-800 and 600-400 m a.s.l., respectively, in the Granara, where the G1 and G2 breccias crop out, and along the lower reach of the upper Aniene river valley.
Specifically, it is possible to observe that the Faito suite encompasses the morphology of the plateau with a decreasing slope from F1 to F3. The F1 deposits appear tilted with dip angles from 60 to 30°, while the F2 deposits are characterized by 47-5° and F3 by 35-5°. Since the deposit basal surface is erosive, it is possible to assume that the low-relief morphology was formed during the F3 emplacement, and the erosive wave associated with the knickpoint cluster between 1,550 and 1,300 m a.s.l. has started subsequently. Moreover, S1 fits very well, respectively, with the F2 projection and the S2 deposits with the two minor clusters of the knickpoint. While along the Granara valley network, the projections marked the second phase of the erosive wave passage. It is important to note that the deposit dip angles range from 40 to 5° and appear undeformed. In detail, the FIU1 deposits lie above a quite steep slope, indicating that they are probably associated with debris flow/debris cone emplacement in the hillslope domain. The G1 deposits are at higher elevations, while the last recorded impulse of the erosive wave was followed by the deposition of FIU2 and G2 suites that are correlated with the minor knickpoints between 1,100 and 800 m a.s.l.

| FLU VIAL INVER S E MODELING
To infer the uplift history of the Simbruini range, we applied the stream power law (SPL) equation system (Howard & Kerby, 1983). In detachment-limited conditions, typical of tectonically active regions, the evolution of the river profile is described as the change in elevation z of a channel point x through time t (Howard & Kerby, 1983), which relates to the competition between erosion (E) and uplift (U): where the fluvial erosion E is computed as: The powers m and n are positive constants controlling the erosion mechanism. Specifically, m depends on the climatic conditions and hydraulic properties of the discharge, and n is a function of other erosional thresholds (Di Biase & Whipple, 2011;Whipple & Tucker, 1999). The erodibility, K, accounts for the lithology, the climatic conditions, and the channel geometry. In the general case, K can vary in space and time, but in the treatment presented here, it is taken as a constant, as it is representative of the long-term evolution of climatic and lithologic conditions (e.g., Lague, 2014). Indeed, since there are no independent constraints on this parameter in the study area, it is not possible to define its variation over time. According to the steady-state conditions, the surface elevation is the The longitudinal profiles of all the stream networks (including Simbrivio, Granara, and Campocatino sub-catchments) of the upper Aniene river basin along which the knickpoints and the erosive base outcrops of the identified continental clastic sequences are projected. Moreover, dips related to the projected clastic deposits are shown. (b) The knickpoint elevation histogram is reported resulting equilibrium between the erosion rate and the relative uplift rate, U(x, t) = E(x, t). A power-law relationship between the local channel slope (S) and the upstream drainage area (A) reveals the steady-state river profile: where k sn = (E(t, x)/K) 1/n is known as the steepness index and the mn ratio, or θ, is defined as the concavity index. When n = 1, the steepness index takes the form (Kirby & Whipple, 2012): If U and K are space-invariant, we can perform the integration of (U/K) 1/n from a base level x b to an arbitrary upstream point x of the channel to predict the elevation of a river profile (Perron & Royden, 2013): where A 0 is an arbitrary scaling area and χ is an integration of river horizontal coordinates defined by the equation The erosional wave celerity C(x) = KA(x) m S(x) n−1 controls the speed at which perturbations travel along the channel (Whipple & Tucker, 1999). The response time τ(x) for perturbations to propagate from the river outlet, at x = 0, to a point x along the channel is expressed as (Whipple & Tucker, 1999): where x′ is an integer variable. The response time τ(x) increases constantly with x, from the base level to the high channel reaches. The τ-plot is the starting point for the linear inverse scheme to study the rock-uplift/base-level fall history recorded in the fluvial topography (Di Biase & Whipple, 2011;Whipple & Tucker, 1999). The mathematical expression of the current river elevation can be reported as : where The parameters t* and χ are in units of length, and U* is a dimensionless rate of rock uplift. Along the channel profile on the χ-z plot, the slope of different channel segments represents the corresponding channel steepness In this regard, spatially constant K and U were assumed as in a block uplift scenario employing the inverse approach stream power model solution proposed by Goren et al. (2014) and Gallen (2018). Moreover, a linear dependency between the local slope S and the erosion rate E in the stream power erosion model was assumed according to Equation (3) (i.e., the slope exponent n = 1 and the drainage area of the fluvial channels was kept fixed during the history, represented by the long profiles of the rivers).

| Parameter setting
The drainage network was extracted from the 10 m-resolution TINITALY DEM (Tarquini & Nannipieri, 2017) with a flow accumulation threshold for the fluvial domain at 10 6 m 2 . Then, the following assumptions were made.
1. A linear dependency between the local slope S and the erosion rate E in the stream power erosion model was assumed, considering n = 1. It means that an advection equation predicting the parallel retreat of knickpoints at a celerity depending on erodibility and drainage area as in Equation (7) is considered suitable for the purpose of this study. However, when n ≠ 1, the celerity becomes dependent on slope and the knickpoint geometry is altered as it propagates (Finnegan, Sklar, & Fuller, 2007;Lague, 2014;Tucker & Whipple, 2002). If n > 1, the steeper part of the knickpoint propagates faster and a knickpoint will become a concave-up knickzone with a steep upstream boundary mimicking a slope-break knickpoint. If n < 1, the opposite occurs and a knickpoint will progressively become a convex-up knickzone migrating upstream with a sharp downstream boundary (Lague, 2014). In this regard, to obtain the best mn ratio that in a linear context is equal to m, we applied the linear regression of the χ-z plot. In detail, the χ-z plot for every value of m from 0.1 to 1 and the coefficient of determination, or R 2 , were computed, indicating −0.45 as the best solution ( Figure 5).
to a mountain range or when the source of uplift/base-level fall is localized at the outlet of the drainage basin, and U is unlikely to vary spatially across the region.

| Results
From the slope map of Figure 7, it is possible to note that the clastic deposits are associated with different levels of flat surfaces outcropping at several elevations, among which the most evident are the Campo dell'Osso, Camposecco, and Faito plateaus. Associated with the escarpments of the plateaus, the highest values of the k sn index characterized the stream networks, while along the flat surfaces, they have low values. The knickpoints separated the upstream low-relief landscapes from the downstream steep valleys. In Figure 8, the stream network elevation was converted in τ space for the different values of K by applying Equation (7). Regarding the linear river inversion curves under the block uplift assumption, the tectonic histories that we generically interpret F I G U R E 5 The "Linearize χ-z relationship" for identifying the mn ratio, or θ. The procedure varies the mn ratio until it finds a value that maximizes the linear correlation coefficient between the χ-transformed profile and a straight line.

| Misfit analysis
To apply the inversion scheme, we reconstructed the rate of uplift (or base-level fall) from the river network during discrete time intervals using Equation (8). The data are organized such that there are N data points of z and τ along the fluvial network that share a common uplift history and are ordered according to elevation. A time step of constant length, ΔT (0.010 Ma), is chosen that will determine the number of discrete time intervals q.
Using the discretization described above, Equation (8) can be written for each data point and the equations can be organized in matrix form: The slope-area plot of all the stream networks (including Simbrivio, Granara, and Campocatino sub-catchments) of the upper Aniene river basin. The mn ratio, or θ, is set fixed at −0.45 by the linear regression shown in Figure 4b. The confidence prediction bounds were set to 95%. The goodness-of-fit is expressed in SSE (sum of squared errors), R 2 , adjusted R 2 , and RMSE (root mean square error). The resulting k sn range is used to calibrate the erodibility parameter where A is an N × q matrix, and z is elevation. This is an overdetermined inverse problem, as there are more known data points than unknown parameters. As such, a least-squares estimate for U is used (Tarantola, 1987): where is a prior guess at the uplift rate, Γ is a dampening coefficient that determines the smoothness imposed on the solution, and I is the q × q identity matrix. Since there are no independent constraints on the uplift rate before the start of the tectonic history recorded by the stream network, we have chosen to use the U pri values obtained through Slope map with k sn values associated with the stream networks of the upper Aniene river basin (including Simbrivio, Granara, and Campocatino sub-catchments). The k sn values were computed following Equation (3), keeping fixed the mn ratio, or θ, at −0.45, resulting from the linear regression shown in Figure 5.
The coordinate system is WGS84-33N, EPSG: 32633. Both the slope map and the k sn values are derived from the 10 m-resolution TINITALY DEM (Tarquini & Nannipieri, 2017) Equation (12), as described in Goren et al. (2014) and Gallen (2018). The computed values are 0.62, 0.5, and 0.4 mm a −1 for K max , K mean , and K min , respectively.
We calculated the normalized misfit between the elevation of the pixels in the upper Aniene river basin, z i , and the predicted elevations with the inferred uplift history, z i : Colored lines = empirical τ plots for the entire upper Aniene river basin. Black line = mean bestfit τ plots resulting from inverse modeling, where m = 0.45 and K = K min . (b) As (a), but for K = K mean . (c) As (a), but for K = K max . (d) The linear river inversion curves describing the uplift rate histories, obtained for K max , K mean , and K min . The parameters chosen in the modeling are described in the text and summarized in the panel where N is the number of pixels of fluvial network data and M = q is the number of discrete time intervals. Figure 9 shows the normalized misfit as a function of 1/Γ computed for three erodibility values K max , K mean , and K min . The optimal solution is chosen at the corner of the normalized misfit versus 1/Γ relationship, or "L-curve" (Parker, 1994), highlighted by the points in Figure 8. We obtain values of Γ of 1.21, 1.10, and 0.87 for K max , K mean , and K min , respectively.

| D ISCUSS I ON
The Plio-Quaternary continental succession which crops out along the Simbruini-Ernici range was substantially unknown, being interpreted based on scattered and undetailed investigations as Miocene marine sediments, similar to the "Brecce della Renga" or, alternatively, Quaternary continental deposits (Beneo, 1938;Cavinato et al., 2012;Damiani, 1990;. Although it is widely accepted that fluvial landscapes record temporal and spatial variations in rock uplift rates (Delchiaro et al., 2019;Fox et al., 2014;Gallen & Fernández-Blanco, 2021;Goren et al., 2014;Ma et al., 2020;Pritchard et al., 2009;Roberts & White, 2010;Rudge et al., 2015), a river-profile inverse model has not been applied to drainage in the region yet. Moreover, a precise evaluation of regional uplift rates in the Middle-Late Pleistocene is hampered by the relative scarcity of remnant shoreline deposits and uncertainties in their ages, especially on the Adriatic coast. Previous studies are only of limited use as long-term averages (Bigi et al., 1995;D'Agostino et al., 2001;Girotti & Piccardi, 1994;Molin & Fubelli, 2005).
Based on a new field survey of the continental deposits, on their plano-altimetric distribution and correlations and on the inverse modeling of the river longitudinal profiles, we were able to analyze both the erosional and the depositional phases which occurred in this sector of the central Apennines, from Pliocene to recent, and to better define the chronology of the continental deposits outcropping in the Simbruini Mts. (Figure 10).
The analysis focused on a complete drainage basin, the upper Aniene river basin, which shows no evidence of river captures. All the identified markers are associated with such a basin, so it can be assumed that the base-level changes, responsible for the origin of the deposits, influenced all the streams upstream of its outlet. Hence, the amount of error in the plano-altimetric correlations of geomorphic markers, associated with paleo-surfaces, is minimal, as well as the implication for the recovered uplift rates by which the interpretations are inferred.
F I G U R E 9 Normalized misfit [Equation (13)] as a function of 1/Γ, where Γ is the dampening coefficient, computed for K max , K mean , and K min . The points show the optimal inverse models for each erodibility parameter (Parker, 1994) In the Simbrivio basin we identified the Faito suite (F1-F3) and the Simbrivio suite (S1, S2). The Simbrivio basin deposits are composed exclusively by carbonate clasts belonging to the Mesozoic Latium-Abruzzi platform, whereas they do not contain clasts belonging to Miocene carbonate units, siliciclastic foredeep deposits, which outcrop in the Roveto valley, Messinian "Puddinghe Poligeniche." The clasts which made up the Simbrivio deposits derive mostly from Cretaceous and, rarely, from Jurassic carbonate. The clast composition of the Faito units seems to reflect a progressive erosion and dismantling of the Simbruini stratigraphy. In fact, in the lower/older deposits (F1, F2, and S1 sub-units) we observe mostly Upper Cretaceous clasts and only in the upper/younger deposits do we observe a prevalence of dolostones, probably deriving from the Jurassic-Lower Cretaceous stratigraphy (F3).
Moreover, from spatial distribution and geometrical relationships (vertical stacking of slope and conoidal facies) we determined that Faito clastic deposits were fed from the dismantling of reliefs located both to the north and south of the Faito plateau, and deposited onto a complex paleotopography, articulated in steep slopes and valleys.
The F1-F3 sequence suggests the retrogradation of the depositional system, by the stacking of proximal (talus slope) F1 deposits and less proximal (alluvial fan) F2 and F3 facies. Afterwards, all the Faito clastic units were deeply incised and eroded during the erosional phase and a normal fault system dissected the entire structure, lowering the southwestern margin of the Faito plateau and leading to the complete disconnection of the deposits from their source area. From the Faito marker projections and the inverse modeling, we detected that the Faito suite should be deposited before 2.4 ± 0.5 Ma and was shaped by the first erosive phase between 2.4 ± 0.5 and 1.85 ± 0.4 Ma (Early Pleistocene), which fitted well with the survey data. In this time window, the uplift rate increased from 0.5 ± 0.12 to 0.63 ± 0.13 mm a −1 . Then the Faito clastic deposits: (1) deposited onto a relict surface F I G U R E 1 0 Synoptic diagram of the timing of Quaternary uplift in the Simbruini range. The main erosive and depositional phases (with errors) are reported, with which the emplacements of the clastic sequences and the relative base-level fall rates are associated inherited from the last compressional phases (sealing the Vallepietra-Filettino line); (2) do not contain Miocene clasts (which would have been already eroded and re-sedimented in the "Brecce della Renga"); and (3) must have been deposited before the Lower Pleistocene erosive phase. On this basis, we suggest that the Faito units deposited during the Pliocene. The S1 unit is well correlated with the F2 unit, while S2 deposits lay at much lower elevation (but not as much as the Granara suite) and are therefore younger.
In the Granara and Fiumata basins, the morpho-stratigraphic relationships have been defined from geological surveys: in particular, differently from the Faito suite, in this area the older deposits lay scattered on the valley slopes (FIU1 and G1), while the younger deposits (FIU2 and G2) crop out at the bottom of the valleys, embedded in the older ones. From the Granara and Fiumata marker projections and the inverse modeling, we recognized a depositional phase followed by a new erosive phase, between 1.85 ± 0.4 and 0.76 ± 0.2 Ma (Early Pleistocene), and after 0.76 ± 0.2 Ma and still ongoing (Middle Pleistocene-present). In detail, the uplift rate first decreased from 0.63 ± 0.13 to 0.36 ± 0.1 mm a −1 , and then increased from 0.36 ± 0.1 to 0.61 ± 0.15 mm a −1 . Merging field data and geomorphometric analyses, we can suppose that FIU1 and G1 were deposited and eroded during the first phase, while FIU2 and G2 during the more recent phase. Furthermore, field survey data suggest that the G2 alluvial fan deposits are the only (among all those outcropping in the Simbruini sector) that contain clasts from the "Puddinghe Poligeniche," cropping out on the western slope of the Viglio Mt., a sector still connected with the present-day Granara valley morphology. The recent evolution of the Granara valley caused the involvement of the "Puddinghe Poligeniche" in the erosional phase, explaining the presence of "Puddinghe Poligeniche" clasts in G2 alluvial fan deposits.

| CON CLUS IONS
The application of morphometric analyses, together with detailed geological and geomorphological fieldwork, allowed us to shed light on the post-orogenic, Quaternary evolution of the Simbruini range (central Italy). Through the definition of the spatial distribution, clast content, depositional environment, and geometrical relationship of the continental clastic deposits, we were able to define their geometry and relative chronology.
Such data, together with the analyses of the plano-altimetric distribution of geomorphic markers and fluvial inverse modeling technique, offer new chronological insights into the identification of the depositional/erosional phases related to landscape evolution. This is of considerable relevance if we consider that these kind of continental clastic deposits are totally missing in absolute chronostratigraphic constraints.
Our results allow us to define the main phases of river incision and landscape erosion in the Simbruini area and to constrain, for the first time, the chronology of the different generations of continental clastic units, which are the only deposits recording the post-orogenic evolution of this key sector of the Central Apennines. Our findings are the necessary premise for comparing the history of the main Central Apennines reliefs with that of the post-orogenic intermontane sedimentary basins and, ultimately, understanding the long-term morphotectonic and climatic evolution of this sector of the Apennines.

ACK N OWLED G M ENTS
The research was carried out as part of the PhDs of Michele Delchiaro in Earth Sciences at Sapienza University of Rome and Veronica Fioramonti in Earth Sciences at Roma Tre University of Rome, respectively. This study has been funded by Italian MIUR through PRIN_2015 (project 20158A9CBM_002) grant to MM and Department of Science (Roma TRE University, Dipartimento di Eccellenza, Art. 1, com. 314-337, Legge 232/2016) grants. We are also grateful to Simone Fabbi and two anonymous reviewers for their deep and stimulating revision of the manuscript, as well as to the editorial work by the Guest Editor Massimiliano Alvioli and the Editor John Wilson.
Open Access Funding enabled and organized by Universita degli Studi di Roma La Sapienza within the CRUI-CARE Agreement.

CO N FLI C T O F I NTE R E S T
The authors declare no conflict of interest.

DATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are available from the corresponding author upon reasonable request.