Closed (endorheic) sedimentary basins are key recorders of the climatic, erosional, and tectonic history of their surrounding topography, playing an active role in its evolution by changing the local geomorphological base level. When these basins become exorheic, the accelerated incision along the new fluvial network can excavate excellent stratigraphic outcrops, but this often removes the uppermost infill, and essential information about the late basin history is lost. Here we propose estimating the opening age and past elevation of captured closed basins by combining the flexural isostatic compensation of the eroded volume with available constraints on sediment age. We use this method to constrain the post-tectonic evolution of the Cenozoic Ebro basin in northeast Iberia. The similar results obtained for 4 dated stratigraphic columns show the robustness of the model and date the basin opening as 12.0–7.5 Ma, with a maximum paleoelevation of the basin of 535–750 m. The isostatic rebound associated with basin erosion, as much as 630 m in the center of the basin, may explain the absence of a canyon excavated by the Ebro River during the Mediterranean sea-level fall associated with the Messinian salinity crisis.


Intramountain basins often drain to endorheic lacustrine systems that may reopen by drainage capture, water overspill, or by sediment overfilling, leading to widespread erosion and to exceptional sediment exposures that record tectonic-climatic interactions (e.g., Carroll and Bohacs, 1999; Craddock et al., 2010). However, the mechanisms and the timing that govern this transition are not well understood, even for basins where the latest sedimentary record is relatively well preserved, such as the Colorado Plateau in North America (House et al., 2008; Karlstrom et al., 2014). Modeling studies show that post-tectonic flexural isostatic motions are key in determining the pace of the drainage change (Garcia-Castellanos et al., 2003; Zeilinger and Schlunegger, 2007; Heller et al., 2010; Lazear et al., 2013). Other basins, such as the Cenozoic Ebro basin (Spain; Evans and Arche, 2002; Garcia-Castellanos et al., 2003) or the Sichuan Basin (China; Richardson et al., 2008), lack the youngest part of their sedimentary record due to post-opening erosion, impeding a direct dating of the change in drainage. Both the Ebro basin and the Sichuan Basin underwent a long period of internal drainage (endorheism) during the Cenozoic, and have kilometer-thick sedimentary accumulations often deposited in lacustrine environments well above the geomorphological base level of the ocean. The Ebro foreland basin (northeast Iberia; 110,000 km3 in sediment volume, 40,000 km2 in sediment area, 84,000 km2 in catchment area) has attracted particular interest because the late widespread erosion has uniquely exposed syntectonic strata, allowing the study of tectonic-sedimentary relationships. However, due to the gap in its youngest sedimentary record, the drainage opening is only indirectly dated, with results spanning the middle Miocene to the Pliocene, and several mechanisms have been pointed as responsible, including a drainage capture from a Mediterranean stream (Riba et al., 1983; Coney et al., 1996; Garcia-Castellanos et al., 2003; Babault et al., 2006; Calvet and Gunnell, 2008) or the sediment overfilling and spillover of the basin (Evans and Arche, 2002; Garcia-Castellanos et al., 2003).


This study proposes a simple method to constrain the age of basin opening and the maximum sedimentary infill, provided that: (1) at least one well-dated, sufficiently thick stratigraphic section is preserved in the basin; (2) constraints on the total volume of sediment eroded from the basin (Ve) are available; and (3) the regional equivalent elastic thickness of the lithosphere (Te) is known from independent studies. The method consists of restoring the vertical uplift of the basin in response to erosion, using a flexural isostatic model, and searching for the paleoelevation of the maximum basin infill, zmax, that fits Ve (Fig. 1); zmax is in turn unequivocally linked to the age of opening through the sedimentation rates measured at the stratigraphic section.

Consider a sedimentary basin eroded to its present-day topography zt(x, y) (Fig. 1). The volume eroded (Ve) since the time (tmax) when the basin reached its maximum sediment infill surface (zmax) can be calculated integrating the topographic difference between zmax and zt(x, y) plus the erosional vertical rebound w(x, y) in response to sediment unloading. 
w(x, y) is calculated by flexurally compensating the weight of the sediment missing between zmax and zt, using the thin-plate approach (e.g., Garcia-Castellanos et al., 2003): 
where zmaxzt is limited to positive values only, ρs and ρa are the densities of sediment (bulk) and asthenosphere (2000 and 3300 kg m–3 for the reference model), and the rigidity D is related to the equivalent elastic thickness Te by 

A Young’s modulus of E = 7 × 1010 N/m2 and a Poisson coefficient of ν = 0.25 are adopted.

We consider zmax varying laterally with a depositional slope S toward a topographic minimum (the last lake system of the closed basin). As a reference, we adopt S = 0.1% (Calvet and Gunnell, 2008), similar to the topographic slope of the Tarim intramountain basin, the largest current analogue to the Miocene Ebro basin.

Now consider a location xd, yd, zd on the present surface of the basin where both the sediment age td and the paleo–sedimentation rate Rd (at t = td) are known (Fig. 1; Table 1). The elevation of that rock at t = tmax was zd– w(xd, yd), and thus tmax can be approached as: 

Note that t is chosen negative in the past and t = 0 corresponds to the present; w > 0 implies uplift. While zmax is unknown, note that it is linked unequivocally with both Ve (through Equations 1 and 2) and tmax (Equation 4), if Te is well constrained. Previous modeling studies of the basement of the Ebro foreland basin found Te = 20 ± 5 km for the northeast Iberian plate (Gaspar-Escribano et al., 2001).


The model is tested for four composite magnetostratigraphic sections of the Ebro basin: San Caprasio (SC, summit of Sierra de Alcubierre; Pérez-Rivarés et al., 2002), Esteban (ES, Castejón Mountains; Pérez-Rivarés et al., 2004), Sancho Abarca (SA, Bardenas; Larrasoaña et al., 2006), and Tarazona (TA, near the Borja plateau; Vázquez-Urbez et al., 2013) (Fig. 2; Table 1).

The volume of the Pliocene–Quaternary part of the Ebro delta has been estimated as 30,000 km3 (Nelson and Maldonado, 1990), and the volume of the earlier Castellon Group amounts to 10,000 km3 (Arche et al., 2010). Part of this sediment comes from the mountain ranges surrounding the Ebro basin, but for the sake of simplicity this is partly neglected in our calculations due to the lack of good constraints on their original spatial distribution, and also because the ranges are much less erodible and more distant from the base level. This contribution to Ve may account for up to 10,000 km3 (Garcia-Castellanos et al., 2003; Babault et al., 2006; Fillon et al., 2013), and would imply older ages of drainage opening than estimated here. Mountain erosion also enhances the rebound of the adjacent basin areas, perhaps explaining why the Tarazona section yields somewhat younger tmax ages. On the other hand, the Ebro delta may underestimate the sediment yield because the finest detrital fraction and the dissolved salts may have been transported beyond the Valencia trough. Accordingly, we consider a wider range between 25,000 km3 and 45,000 km3 for the total volume of sediment reworked from the Ebro basin (Fig. 3) (Garcia-Castellanos et al., 2003; Babault et al., 2006).

We choose the San Caprasio section, combined with a maximum infill elevation of zmax = 700 m, as a reference model. The uplift distribution obtained for this reference model (Fig. 2) yields a maximum of 518 m of uplift near the basin center. The lateral distribution of this uplift is consistent with the tilting of carbonate lacustrine strata preserved in the neighboring Duero basin (Páramo unit, Fig. 2B; Mikeš, 2009), independently validating the elastic thickness reported previously. Nevertheless, the amplitude of that tilting requires a higher zmax (close to 1000 m above present sea level) or a higher average sediment bulk density for the basin (2200 kg m–3) than estimated in this study.

We repeat these calculations for a range of zmax, ρs, and S values (Fig. 3). The tmax obtained for the four data locations is remarkably consistent, in spite of the different age and elevation of each section, showing the robustness of the method. The results are also relatively insensitive to changes in Te, and the results for a lower Te = 15 km delay the opening by <0.5 m.y. The most important parameters influencing the tmax versus Ve relationship are the depositional slope S and the sedimentation rate Rd (the latter subject to significant spatial and temporal variations). We show results for 2 scenarios where the top of the infill had a depositional slope of S = 0.1% (reference model) and S = 0, measured toward the last lake system that drained the region. The scenario with a flatter depositional surface yields the most recent age of drainage opening: tmax = –7.5 m.y. It is important that higher, more realistic S values (Calvet and Gunnell, 2008) lead to older opening ages. The same applies to plausible changes to ρs, for which we use a lower-end value of 2000 kg m–3 that results in a younger tmax (Fig. 3). This allows the method to constrain the youngest possible tmax (the oldest limit is given by the 12.0 Ma uppermost strata in the Tarazona section).


Within the approximations of the model, the sediment volume delivered to the Ebro delta is compatible with the elevation of dated samples in the Ebro basin only for ages of drainage opening ranging between 12.0 and 7.5 m.y. ago (Fig. 3A), the earliest half of this period being more likely. This estimation is consistent with the 9.2 ± 0.5 Ma base-level lowering estimated from thermochronology (Fillon et al., 2013) and with the 13.0–8.5 Ma opening derived from process modeling (Garcia-Castellanos et al., 2003). A hypothetical opening of the basin at 5.5 Ma (acme of the Messinian salinity crisis, MSC) would imply an eroded basin volume larger than 60,000 km3 (Fig. 3), about twice the highest volume estimations for the Pliocene–Quaternary delta (Nelson and Maldonado, 1990; Garcia-Castellanos et al., 2003; Babault et al., 2006). Some have proposed a Messinian or later age for the basin opening (Riba et al., 1983; Coney et al., 1996; Babault et al., 2006), mostly based on the lack of a gorge excavated along the outlet of the basin during the lowering of the Mediterranean sea level associated with the MSC. It has been shown that this canyon is preserved buried offshore the Ebro delta and that important deltaic progradations existed before the MSC (Urgeles et al., 2010), but the question remains as to why this erosion did not propagate hundreds of kilometers upstream as in other Mediterranean rivers like the Rhone or the Nile (Clauzon et al., 1996).

A possible explanation arises from the calculated distribution of isostatic uplift in response to basin excavation. This rebound explains the tilting of lacustrine deposits in the neighboring Duero basin over a distance of nearly 100 km (Fig. 2B). The equivalent isostatic rebound obtained at the Catalan Coastal Range is as much as 400 m in the reference model (Fig. 2A), with plausible values of as much as 520 m. This suggests that a Messinian Ebro canyon may have been subsequently uplifted, exposed, and obliterated by erosion during the emptying of the basin.

The analysis robustly estimates the elevation of the basin at the time of drainage opening: between 535 and 750 m above sea level (the uncertainty being related mainly to the weak constraints on Ve and S, and to the lateral and temporal variability of Rd). This range of paleoelevation is lower than a previous estimation of as much as 1050 m (Garcia-Castellanos et al., 2003) that was severely limited by assumptions on the climatic evolution of the basin. The new results provide a more reliable quantification of the post-tectonic vertical motions and sediment exhumation of the Ebro basin. For example, the highest strata in San Caprasio (today 840 m above sea level; Fig. 1C) were originally deposited at an elevation of 520–550 m (Fig. 1A) and later subsided to 305–470 m above present sea level, buried under 210–488 m of sediment (Figs. 1B and 2B) at the time of maximum basin infill. Unfortunately, available paleoelevation proxies do not provide enough resolution to independently validate these predictions; apatite fission track and (U-Th)/He analyses (Fillon et al., 2013; Rushlow et al., 2013) from the Montsec area (MO in Fig. 2A) suggest that the lower valleys of the region were buried under 0.5–1.6 km of rock at maximum basin infill. The lower end of this burial range is, therefore, compatible with the highest paleoelevation obtained here (750 m above sea level), since the Montsec area would then have undergone an isostatic rebound of as much as 440 m (372 m in the reference model; Fig. 2).

Beyond the Ebro basin scenario, the simplicity of the technique here described is easily reproducible to determine the timing of other basins whose drainage opening cannot be dated because the uppermost strata have been eroded. Examples include several basins in Iberia captured during the Cenozoic, and the Congo Basin in Africa. The results encourage the interpretation of erosion thermochronological data from post-tectonic settings in combination with a flexural isostatic restoration, because this provides quantitative estimations of the absolute past elevation and vertical motions of the basin-orogen system. The consistency of the results obtained for several magnetostratigraphic sections points to a minor role of nonstatic forces (e.g., related to mantle flow) in building dynamic topography in the study region.

We thank Miguel Garcés and Ron Dorn for their thoughtful reviews and Javier Pérez-Rivarés and Charlotte Fillon for field assistance and discussions. The software developed is available at the GitHub public repository as project tisc, under a GNU General Public License. Financial support was provided by the Government of Spain (CGL2011-26670).