Modelling the geomorphic history of the Tribeč Mts. and the Pohronský Inovec Mts. (Western Carpathians) with the CHILD model

1 Introduction

Methods of investigation of the land surface are changing with the rapid development of computer technology. Nowadays, modelling of geomorphic processes is increasingly preferred, including simulations of landscape evolution. Earth processes are expressed by numerical equations in physically based landscape evolution models. Under the assumption that the models are relevant they are suitable tools for supporting of hypotheses about landscape evolution in the past or future. On the other hand, the models are able to represent only a simplification of the real landscape and it is not possible to include all processes in one modelling tool. Models are specialized mainly according to dominant processes (e.g. karst, glaciation, fluvial). Several landscape evolution models have been developed with numerical expressions of main geomorphic processes in humid, temperate climate zones – hillslope diffusion (processes controlled by local slopes) and fluvial incision into bedrock [1–6]. Many of these landscape evolution models provide appropriate computational frameworks to create simulations of long-term landscape evolution of small- or moderatesized drainage basins (several square kilometres). With some limitations they can be used to model the evolution of terrain on the scale of a mountain belt [7–11]. Here we test the ability of the Channel-Hill slope Integrated Landscape Development (CHILD) model [6] to solve problems of reconstruction of geomorphic history, because CHILD overcomes many of the limitations of the previous generation of models (e.g. climate variability, meandering, etc.) and it allows flexible simulation through optional use of model components (as described below). We attempt to model the landscape evolution of the Tribeč Mts. and the Pohronský Inovec Mts. (Figure 1), uplands on the SW boundary of the Western Carpathians, to support or reject some different working hypotheses about neotectonic development of the area. These hypotheses were created on the basis of geological, tectonic and geomorphic data.

Figure 1

Position and subdivision of modelled area.

Comparison of forms of hypsometric curves and abundance of remnants of planation surfaces in simulations and the real surface is a basic criterion for the evaluation of the validity of particular simulations. CHILD is introduced as a tool for appraisal of various concepts of planation at local scales. It is in line with a demand of Calvet et al. [12] and the generally renewed interest in complex development of planation surfaces [e.g. 13, 14].

2 Regional settings and geomorphic history

The Western Carpathians are generally assumed to be a dome-like morphostructure [15] with concentrically arranged neotectonic subregions [16, 17]. They differ in geomorphometric characteristics (altitude, slope, dissection) but also in the altitude and preservation of planation surfaces. Remnants of these surfaces are considered as indicators of tectonics and denudation chronology; they were mapped throughout almost all the Western Carpathians (for overview see e.g. [18, 19]). For a long time, simultaneous formation of a large initial planation surface in the Miocene followed by synchronous tectonic differentiation during the Late Miocene and Pliocene was assumed. The uplift rate was considered greatest in the centre of the dome [15,20–22]. Figure 2 sketches the simplest traditional scheme of the planation surfaces.

Figure 2

Scheme of simultaneous creation of the planation surfaces in the Western Carpathians ([18, 20, 21], adapted).

At the turn of the century, an alternative concept of planation surfaces evolution was suggested. Simultaneous development of planation surfaces was questioned on the basis of indicators which implied different ages for some segments formerly assumed to be integral parts of one initial planation surface. This idea was termed ‘non-simultaneous evolution of the Western Carpathians’ [23–25] and the Tribeč and Pohronský Inovec Mts. were proposed as a region of probable non-simultaneous evolution [25].

Both modelled mountain ranges belong to the West Marginal Region that presents a low periphery (up to 900 m.a.s.l.) of the fragmented western part of the Western Carpathians [17]. Although they are very similar in terms of generalmorphometry (altitude, slope, dissection) they differ significantly in detailed landform composition and distribution (Figure 3) as well as geological structure ([26, 27], Figure 4).

Figure 3

Topography of the Tribeč Mts. and the Pohronský Inovec Mts. Cross-sections along red lines on map.

Figure 4

Simplifed geological map of the Tribeč Mts. and Pohronský Inovec Mts. (After [26, 27], modifed).

The Tribeč Mts. are composed of igneous rocks in the SW and metamorphic rocks in the NE. The Palaeozoic and Mesozoic sedimentary cover is built mainly of various sandstones and shales in the centre of the NE (Rázdiel) part and limestones, dolomites and quartzites on the periphery (mainly Jelenec and Zobor parts). Bedrock of the boundary of the Tribeč Mts. and their small erosive basins is formed by sedimentary rocks (relatively cohesive Eocene conglomerates overlain by layers of softer Neogene and Quaternary sediments). The Pohronský Inovec Mts. are built mostly of Miocene andesite lava flows and conglomerates, with ignimbrites in the N part ([26, 27], Figure 4).

Remnants of a nearly fat Miocene initial planation surface (the intramontane level) in both centres, and Late Pliocene – Early Pleistocene pediment (river-side level) on the periphery (Figure 2) were mapped in both mountains. Both levels of planation surfaces continuously merge from one range to another at a similar altitude ([28, 29], Figure 5).

Figure 5

Planation surfaces mapped by Lukniš [28] and Minár [29].

The older and higher-elevated initial planation surface is equivalent to the intramontane (mid-mountain) level described in the whole Western Carpathians [22, 30]. Dating of the intramontane level is relatively clear – its initiation is estimated from the age of neovolcanic andesites (∼ 12 Ma) which are truncated by this surface in the Pohronský Inovec Mts. [28]. The Late Miocene age of the intramontane level is also confirmed by the character of sedimentary infill of adjacent part of Pannonian Basin – refning of sediments during Pannonian and coarsening or hiatus in the sedimentary record on the Miocene/Pliocene boundary [31–33]. The assumed topography of this initial surface was nearly fat (Figure 6). The Tribeč Mts. probably represented only separate hills up to 250 m.a.s.l. which were not a barrier for river flows (this assumption is confirmed by Miocene sediments accumulated equally both in Rišňovce (north) and Komjatice (south) Depressions of the Pannonian Basin, (Figure 4, [33, 34]).

Figure 6

Hypothetical topography of study area after creation of intramontane level (Late Miocene).

However, the character of recent topography of these mountains raises some questions. The Pohronský Inovec Mts. are a massive horst dissected by deep V-shaped valleys with well-preserved remnants of the intramontane level [35, 36]. By contrast, the intramontane level is nearly missing in the western and central parts of the Tribeč Mts., which form an old passive morphostructure with wide erosion basins (elongated depressions developed on softer rocks), cuestas, wider and shallower valleys, and only limited numbers of less distinctive fault slopes ([25, 28], see also Figure 3). This geomorphic contrast was the main reason for questioning simultaneity of neotectonic evolution in both mountains, including formation of the intramontane level: ’If both mountains were likewise planated in Miocene how it is possible that the Pohronský Inovec Mts. retained the character of a young active morphostructure and the Tribeč Mts. developed to passive morphostructure by simultaneous neotectonic development?’ [25].

A suggested answer to this question was that the differences could result from burial of a mature topography below Neogene sediments and latter exhumation during neotectonic uplift in the Tribeč Mts. [36]. Therefore, the intramontane level is nearly missing in the SW part of the Tribeč Mts., but not completely (Figure 5), because the intramontane level was produced as an erosion-accumulation surface in the Tribeč Mts. During the subsidence of the adjacent Pannonian Basin depocentres (Rišňovce and Komjatice Depression), the periphery of the Tribeč Mts. near depressions (Zobor, Jelenec and periphery of Veľký Tribeč part) probably subsided below the base level and accumulation of sediments resulted in a fat initial surface above the buried mature palaeorelief. The Rázdiel part of the Tribeč Mts. and the Pohronský Inovec Mts. were exposed to denudation and here a predominantly erosive initial planation surface was formed. Remnants of this initial surface are best preserved in the Pohronský Inovec Mts. due to relatively more resistant andesite lava flows [35, 36].

The burial of the Tribeč Mts. is supported by the presence of residual boulders at the base of the Neogene sedimentary sequence in the SW and central part of the mountains, up to 450 m.a.s.l. [28]. Well preserved Pannonian (∼ 8 Ma) freshwater limestone bodies (Hlavina Member, [33, 37]) of medium resistance lie likewise at altitudes ca 400 m.a.s.l. and were apparently accumulated near to the contemporary base level of erosion (otherwise they would have been more denuded). Moreover, the burial of the Tribeč Mts. is presumed also in a broader regional context. E.g. Dunkl & Frisch [38] suppose a high magnitude of post-Middle Miocene sediment removal along the belt marginal to the Eastern Alps and the Western Carpathians on the basis of fission track data and the high organic maturation of the Neogene sediments. They quantified sediment removal in the range of 1–1.5 km.

Formation of the initial planation surface was interrupted by Pliocene tectonic uplift that significantly changed the land surface. Tectonic blocks were uplifted along normal faults under an extension regime oriented NW - SE [39–41]. Uplift was discontinuous (in pulses) with tectonically quiet periods during which pediments below the intramontane level could be created (up to three levels of pediments are considered in the Western Carpathians generally [19, 42]). Lukniš [28] mapped in the Tribeč Mts. only one pediment, termed in the Western Carpathians as river-side level [20, 22]. Because this lies directly above the oldest Quaternary river terraces it is generally assigned a Late Pliocene – Early Pleistocene age [21, 22]. River-side level pediment formation is probably also connected with resumption of an accumulation regime in the adjacent Danube Basin during the Late Pliocene [33]. However, its negligible height above Middle Pleistocene terraces on the rim of the Pohronský Inovec Mts. points to its Early Pleistocene age here [29, 35]. The river-side level has the character of a pediment created in the mountains by retreat of hillslopes and widening of river valleys. Nevertheless, on the basis of limited extent and/or character similar to the intramontane level in some places, Minár [29] suggested the river-side level has a locally hybrid character. As a consequence of very small Pliocene uplift the original intramontane level here during Early Pleistocene lay near to erosion base level, and was slightly remodelled and integrated into the river-side level (Figure 5 – this situation was mapped only in the Pohronský Inovec Mts.). Since the end of Early Pleistocene the last tectonic pulse started with an extension regime oriented between NE - SW and ENE-WSW [39–41].It caused uplift of the river-side level and (together with climatic oscillations) influenced the creation of river terraces and recent foodplains (Figure 2).

This local geomorphic historyiscompatible with modern tectonic concepts of the Carpathian-Pannonian domain. The Western Carpathians began to rise with the extrusion of microplate ALCAPA from the Eastern Alps domain during the Early Miocene. Subsequent northeastward movement was connected with subduction and later collision in front of the orogen. While compressional tectonics in the accretionary wedge zone was characteristic in the front, the intra-Carpathian domains were subjected to stretching caused by the “slab-pull effect” of the subducting plate [43]. This produced a mosaic of intramountain basins and mountains. Back-arc extension led to initial rifting and development of the Pannonian Basin south of the Western Carpathians [44]. Therefore, subsidence and burial of mountain ridges below Neogene sediments was most notable in the south, including the domain of the Tribeč Mts. Asthenospheric mantle uplift was followed by voluminous acid and calc-alkaline volcanism in the Middle Miocene [45, 46]. The Štiavnický stratovolcano is the biggest resultant volcanic structure and the Pohronský Inovec Mts. is in the SW periphery of it.

The slow subsidence supported planation of the southern part of the Western Carpathians, culminating after termination of subduction in the NE and oblique collision with the Bohemian massif in the NW. The relatively quiet period before tectonic inversion is suggested for completion of the intramontane level as a ’tectoplain’ [47] at least in the Central Western Carpathians. Tectonic inversion of the Pannonian Basin and discontinuous uplift of the Western Carpathians during Pliocene and Quaternary was probably a consequence of renewed pressure from the Adriatic plate, after relative cooling and strengthening of the Pannonian Basin lithosphere and delamination and/or convective removal of thickened lithosphere of the Western Carpathians [17].

A geotectonic reason for regional creation of ’river-side level’ (or other pediments) is not evident until now. However, the systematic presence of its remnants in the river valleys and mountain rims suggests a tectonic conditionality, such as a slow-down of tectonic uplift during the second half of the Pliocene, continuing into the Early Pleistocene. Ending of the collision regime, with gradual gravitational collapse of the orogeny, could be a hypothetical reason. More pediments could be created by punctuated relative tectonic quiescence or by formation of individual levels shaped simultaneously at different altitudes [19].

3 Methods and settings of simulations

The number of parameters in the CHILD model is potentially quite large [6, 48] because the modular structure of the model (Figure 7) allows selection of various process equations and configuration of these with appropriate initial and boundary conditions (threshold values). Use of the CHILD model requires a good theoretical knowledge of the mathematical expression of processes, together with comprehensive terrain data collection.

Figure 7

Components of the CHILD model [6]. Applied modules are highlighted by thick outlines.

3.1 Initial conditions

The most important initial conditions of simulation are initial topography, setting of computational mesh, duration of simulation, climatic variables (rainfall intensity, storm and interstorm intervals), division into tectonic blocks, rate of tectonic uplift and lithology (thickness and spatial distribution of rocks). Most of these were set equal for all simulations; only the last two (tectonic uplift and lithology) were changed according to the three working hypotheses.

The simulations were started at the Miocene – Pliocene boundary (∼ 5, 5 Ma BP) because all indicators suggest the start of dissection of a nearly flat initial surface at the time.

Considering the size of modelled territory (35 × 45 kilometres), the duration of simulation and computational (technical) limitations dictated use of a coarse spatial discretization (150 m grid). CHILD uses an adaptive, triangulated irregular spatial discretization of the modelled area [49] and provides several options for generation and/or reading an initial mesh [48]. We used the option of mesh construction from an input set of (x, y, z, b) points (b is boundary code) and assigned z-coordinates from a proposed initial DEM (Figure 6).

Regarding the goals of the simulation and the availability of data we chose simpler settings of initial climatic and hydrologic conditions. Climate was set as a series of uniform rainfall events (T_r) followed by uniform interstorm intervals (T_b). Because of the very long time of simulation and absence of palaeoclimatic data, it was not possible to simulate real individual storms. The ratio between duration of storm and interstorm interval was set to 1:9, which is considered realistic [6]. This approach is analogous to other long-time simulations [50, 51].

As a very rough estimation, average annual precipitation was set differently for two stages – 850 mm yr^-1 during Pliocene and Early Pleistocene (5,5 Ma – 1 Ma BP) and 650 mm yr^-1 later (1 Ma BP to recent), given the essentially qualitative knowledge of palaeoclimate here. In practice, experiments not presented here showed that increasing or decreasing precipitation by about one hundred mm yr^-1 influenced results only slightly. Estimation of Pliocene – Early Pleistocene precipitation is set close to the recent value: this could average several contrasting oscillations with various rainfall amounts [52]. Despite practically semiarid conditions during the Messinian salinity crisis (at the start of simulations), most of the period is characterized by creation of red soils in more humid condition [53]. Palaeoecological reconstructions point to drier climates during glacial periods of the Middle and Late Pleistocene (chernozem steppe conditions with precipitation up to 400mm yr^-1, [54]). Therefore, we assumed slightly drier conditions for the second period (1 Ma BP – recent) as an average value of glacial and interglacial periods.

Overland runoff caused by separate rainfall events was modelled by the steepest-descend method [6] and for simplicity it was assumed that all rainfall became runoff. This setting is typical in applications of the model for large territory [e.g. 11, 50, 51] where assessment of a uniform value of infiltration across the whole area is difficult. Considering the simplified hydrological conditions, we carefully set the efficiency of erosion by streams (because of higher surface runoff amount the estimation of rock resistance was generally increased – see next chapter).

CHILD provides several options to simulate vertical motion of points (positive or negative), from simply homogeneous uplift to a sophisticated uplift rate pattern [48]. We used the latter, changing the uplift rate (m yr^-1) in both space and time and using an uplift rate map. For any particular period, an individual uplift rate can be defined for every point in the computational TIN. Individual movement of tectonic blocks, different in various stages, can be simulated by this way.

We considered tectonic uplift in two stages (5.5 – 2.3 Ma BP and 1 Ma BP to recent). The quiet period (2.3 – 1 Ma BP) simulated conditions for completing the riverside level. We divided the area into several tectonic blocks with homogeneous altitude of remnants of planation surfaces. Boundaries of the blocks were defined by faults and morpholineaments (Figure 8). Because more precise data are missing, we simply assumed a uniform continuous uplift rate within defined stages.

Figure 8

Delimitation of tectonic blocks on the basis of altitude of planation surfaces (Figure 5), faults (Figure 4) and morpholinea-ments derived from DEMs at two scales.

Total uplift of tectonic blocks (m) was derived from the mean altitude of remnants of the intramontane level, or of ridges where the intramontane level is absent. Division of uplift between Pliocene and Quaternary was different for each of three simulations with increasing degree of detail, based on morphotectonic indicators:

1. Maximum Pliocene and minimum Quaternary uplift throughout was supposed in the first simulation (Figure 9, Simulation 1), in line with the traditional concept of dominant Pliocene uplift of the Western Carpathians [15]. However, the most elevated remnants of river-side level in the Tribeč Mts. mapped by [28] are taken as intramontane level in this case. Spatial differentiation of the Pliocene uplift is in line with recorded extension oriented NW-SE [39].

2. New morphostructural subdivision of the Western Carpathians [17] suggests division of the Tribeč Mts. between two major Western Carpathians subregions: NE part together with the Pohronský Inovec Mts. is part of the West Marginal Region, while the SW part of the Tribeč Mts. (Zobor, eventually Jelenec – see Figure 1) is part of the South–West Foreland (transitional to the Pannonian Basin). Differential Quaternary tectonics between these regions is reflected in the second simulation, with major Quaternary uplift in the east (Figure 9, Simulation 2). Pliocene uplift of particular blocks was estimated here as differences between the elevations of intramontane and river-side levels where preserved. Quaternary uplift was similarly estimated as elevation of the highest parts of river-side level above the recent erosion base.

3. The last simulation (Figure 9 – Simulation 3) uses the same basic principles as the second. However, limitation of the blocks was slightly modified on the basis of results of previous simulations and partition of uplift between Pliocene and Quaternary was modified too. Quaternary uplift was estimated from the height of the lowest part of the river-side level and where remnants of planation surfaces were missing a trend of recorded extension was reflected in uplift en echelon. Therefore, this simulation best reflects the change of tectonic regime from NW-SE oriented extension during Pliocene to NE-SW, respectively, ENE-WSW oriented extension during the Quaternary uplift period [39–41].

Figure 9

Estimate of Pliocene total tectonic uplift (left column) and tectonic uplift since Early Pleistocene (right column) to be input in the CHILD model for the three scenarios.

3.2 Processes modules

Because the simulated area is large and lithologically varied, we could not use many advances and modules of the CHILD model (e.g. generation of runoff by infiltration-excess or saturation-excess mechanisms, size-selective erosion, transport and deposition of sediments, meandering and overbank sedimentation on floodplains, etc.). Therefore, wefocusedonthe appropriate setting of numerical parameters of hillslope and fluvial processes.

Incision of streams into bedrock importantly influences the morphology of modelled landscapes and it is the most significant aspect of landscape evolution theory in unglaciated mountainous regions. The CHILD model uses a generic set of the stream-power family of equations for river incision. ’Stream-power’ means that it is based on the simple assumption that river incision rate depends on the power of streams or the mean bed shear stress. Fluvial incision equal to the excess of river bed shear stress is mostly used in the CHILD model [6, 48]. However, it is possible to model river incision equal to the excess of stream power by assuming that under conditions of steady uniform flow, unit stream power scales with shear stress powered to 3/2 [55]: we used this model and, for simplicity, neglected the effect of the critical shear stress; erosion rate is directly proportional to unit stream power.

The modelled area is built predominantly of cohesive, fine-grained rocks, so we chose a detachment-limited model to express river incision into bedrock given by erosion rate E [e.g. 2, 56–58, etc.]:

E=−Kbr(Kt(Q/W)MbSNb)Pb,(1)

where K_br represent detachment rate coefficient [m yr^-1 Pa^-Pb], (P_b is a coefficient that makes it possible to set river erosion either equal to excess of unit stream power P_b = 3/2, or to bed shear stress P_b = 1), Q is discharge [m³ s^-1], W is channel width [m], S is river gradient [m m^-1], and values of parameters M_b = 0.6 and N_b = 0.7 were set because of use of Manning roughness coefficient (N_m). Shear stress coefficient (K_t) is estimated by the following equation:

Kt=ρgNm3/5,(2)

where ρ is bulk density of water with sediments, g is gravity acceleration and N_m is Manning roughness coefficient.

Detachment-limited systems are simpler and more appropriate (compared to transport-limited models) for long-term simulation of mountain ranges, through their computing efficiency and speed. However, there is one significant limitation: any eroded material is immediately removed from the territory, so we are not able to simulate evolution of depositional landforms (e.g. alluvial cones, colluvium, etc.).

Using the detachment-limited model of river incision we needed to determine suitable values of the detachment rate coefficient K_br. It is the major parameter of the detachment-limited model and significantly influences river incision into bedrock. Values of K_br vary with local climate, rock strength, and settings of parameters P_b and M_b (Eq. 1). They differ from the well-known erosion coefficient K [2, 57]. Determination of K_br values is most often performed by a combination of statistical methods and field measurements. Because of the impossibility of performing the field measurements in such a large territory, and the duration of simulation (with changing local climate - so K_br value too), we estimated values of K_br as follows:

1. We divided the rocks of our territory into groups with similar ’Brazilian tensile strength’ [59]. Experimental work [60] showed a relationship between bedrock erosion rate and the tensile strength of rock to the power -2. On the basis of this relationship and documented erosion rates for medium resistant limestones [51], we estimated K_br values for each of the rock types in our territory (Table 1).

2. Subsequently, we checked the obtained values of K_br (Table 1) by a further set of numerical simulations (not presented here). We controlled whether estimated values K_br create characteristic landforms (peaks, ridges, wide erosion basins, deep valleys, etc.). Because plausible morphological effects were achieved by the control simulations we used them in the main simulations. For cohesive and fine-grained rocks, we assumed very similar values of the K_br coefficient. The whole territory of Neogene and Quaternary sediments was taken as an area of cohesive rocks, because it is problematic to distinguish areas with cohesive and non-cohesive sediments below Quaternary slope deposits, and because calcareous conglomerates, travertines and marlstone dominate in outcrops and boreholes.

Table 1

Estimation of detachment rate coefficient K_br relevant to various rock types.

Detachment rate coefficient (Kbr)	Brazilian tensile strength (σt)	Types of rocks
0.0007 mm yr-1 Pa-3/2	13 – 15 MPa	The most resistant quartzites, limestones and dolomites forming cuestas and homoclinal ridges
0.001 mm yr-1 Pa-3/2	10.5 – 12 MPa	Resistant quartzites, dolomites, limestones, andesite flows and amphibolites
0.0015 mm yr-1 Pa-3/2	10 MPa	Granitoides with lower degree of tectonic fracturing
0.002 mm yr-1 Pa-3/2	7.5 – 9.5 MPa	Mixture of resistant types of cohesive rocks, e.g. granitoides, limestones, dolomites, micaschists, phillites, arkoses, greywackes, mixture of andesites, resistant conglomerates, breccias, ignimbrites, etc
0.004 mm yr-1 Pa-3/2	6 MPa	Cohesive medium resistant rocks, with tectonic grinding or otherwise slightly weakened rocks (limestones, mudstones, shales)
0.008 mm yr-1 Pa-3/2	5 MPa	Tectonically fractured cohesive rocks on faults or otherwise slightly weakened rocks that influenced evolution of river network
0.01 mm yr-1 Pa-3/2	4 MPa	Less resistant cohesive rocks -infill of erosive basins (calcareous conglomerates, siltstones, marlstones, travertines)
0.2 mm yr-1 Pa-3/2	0.5 – 1.5 MPa	Faults in less resistant rocks that influenced evolution of river network in basins or deeply incised rivers in mountains

Although each CHILD node may include a number of layers of variable thickness with different values of the K_br coefficient [48], we used only one layer with spatially different values of the K_br for various types of rocks in Simulations 1 and 2 (Figure 10). For the third simulation we used two layers, with a basal layer the same as the one layer for Simulations 1 and 2. The top layer of less resistant sediments (K_br = 0.5 mm yr^-1 Pa^-3/2) represented hypothetical burial of part of the territory below soft marine, lacustrine or volcanic sediments of various thickness (Figure 11). The thickness of the upper layer was estimated as the difference between the topmost occurrence of Neogene sediments and recent topography (we suppose minimal erosion of the exhumed surface because a mature palaeosurface is well preserved – see Regional settings and geomorphic history).

Figure 10

Estimation of K_br (detachment rate coefficients) derived eroded from above the exhumed palaeosurface.

Figure 11

Estimation of thickness and type of sedimentary cover from the Figure4and Table1.

Transport by hillslope processes (mainly soil creep) is usually modelled by a linear hillslope diffusion equation [61, 62]:

qc=KdS,(3)

where q_c is volumetric sediment discharge per unit width [m³ yr^-1 m^-1], K_d is transport coefficient [m² yr^-1] and S is gradient [m m^-1]. The hill-slope transport coefficient (K_d) is significantly influenced by climatic conditions and rock resistance (rate of regolith formation). Thus, the K_d value is basically local, it varies from place to place. It is usually estimated on the basis of field measurements (for overview see e.g. [63]): however, the CHILD model allows only one value of K_d across the modelled area. To find an appropriate single value of K_d for territory with varied lithology is very problematic. On the other hand, the CHILD model allows a lithologically varied fluvial erosion coefficient and therefore we substituted modelling of transport by hillslope processes with fluvial erosion on hillslopes (rill erosion) in our case study (Table 2). We were able to model a relevant retreat of hill-slopes during the tectonically quiet period to create river-side level pediments in this way. Moreover, this approach was able provide for preservation of remnants of the intramontane level during simulations. We are conscious of a simplification; however, it did not significantly affect other aspects of the results (setting the most often used values of K_d only slightly influenced the upper parts of hill-slopes in our collateral experiments – not presented here).

Table 2

Values of essential parameters used in all simulations.

Parameter	Value (unit)
GRID spacing	150 m
Storm duration (Tr)	900 yr
interstorm duration (Tb)	8100 yr
Rainfall intensity (P) Infiltration (I)	8.5 and 6.5 m yr-1 0 m yr-1
Detachment rate coeflcient (Kbr)	0.0007 – 0.2
	mm yr-1 Pa-3/2
	(see Table 1)
Mb	0.6
Nb	0.7
Pb	1.5
Manning´s coeflcient	0.03
Diffusion transport coeflcient (Kd)	0 m2 yr-1

3.3 Evaluation of simulations

We present here three simulations of the land surface evolution. Results of the simulations have been evaluated through the main calibration parameters – distribution of remnants of planation surfaces as well as hypsometric curves. The area percentages occupied by planation surfaces mapped in the Tribeč Mts. [28] and in the Pohronský Inovec Mts. [29] were used as baseline values. Remnants of planation surfaces on the modelled surfaces (Figure 12) have been delimited by three criteria: (1) low slope gradient,(2) visual analysis of contour lines with similar character as on real surface, (3) erosion effect during Quaternary and total erosion effect during simulation [m].We have distinguished three types of planation surface on the basis of erosion effect and elevation of planation surface above the Early Pleistocene and recent local erosion base (Table 3).

Figure 12

Remnants of the planation surfaces identifed from results of the modelling (simulations 1, 2, 3), and in the real land surface after [28] and [29].

4 Results and discussion

Results of the simulations are graphically expressed in Figures 12 – 15. The ’intramontane level integrated into riverside level’ is amalgamated to the ’river-side level’ on Figure 13 because it was not previously distinguished in the Tribeč Mts. [28].

Figure 13

Abundance of remnants of the planation surfaces in percentages of area for the terrain (black) and positive or negative deviations of percentages of area of modelled remnants from real planation surfaces: simulation 1 (red), simulation 2 (green) and simulation 3 (blue); Z - Zobor, J - Jelenec, T - Veľký Tribeč, S - Skýcov, R - Rázdiel, PI - Pohronský Inovec, A - average value for the whole territory.

The first tested hypothesis (Simulation 1) represents the old view on landscape evolution (major spatially variable uplift during Pliocene, and minor nearly spatially uniform uplift during Quaternary – Figure 9). In this scenario, denudation of uplifted blocks ran at a similar rate in the whole area; narrow ridges and well incised longer valleys were created. Results of this simulation are satisfying for a part of the Tribeč Mts., but well-preserved intramontane level in the central parts of the Pohronský Inovec Mts. and the Rázdiel part of the Tribeč Mts. are excessively denuded and the remnants of river-side level are too reduced. Figure 13 shows a significantly lower percentage area of intramontane level in the Skýcov and Rázdiel parts of the Tribeč Mts. and in the Pohronský Inovec Mts. in comparison with the real distribution of the intramontane level. Except the Pohronský Inovec Mts. and the Zobor part of Tribeč Mts. this simulation gives the worst fit also with the real distribution of the river-side level remnants, and overall abundance of planation surfaces is also the worst in comparison with the terrain (see ‘All planation surfaces’ in Figure 13). The fit of hypsometric curves (Figure 14) is also generally the worst – Simulation 1 underestimates the hypsometric integral in all parts of the territory except in Jelenec.

Figure 14

Hypsometric curves of particular regions: terrain (black), simulation 1 (red), simulation 2 (green) and simulation 3 (blue).

The second and third simulations assume a difference in tectonic tendencies between western and eastern parts of the territory. A differentiated, major uplift during Pliocene and smaller, nearly spatially uniform uplift during Quaternary was applied to the majority of the Tribeč Mts. The most uplifted central part of the Tribeč Mts. was surrounded with less uplifted marginal blocks: this corresponds to the gravitational collapse during the Neogene extensional tectonic regime [39]. A smaller central part of the Pohronský Inovec Mts. was uplifted similarly during the Pliocene. But (on the basis of the altitudinal difference of river-side level) the majority of tectonic blocks of the Pohronský Inovec Mts., as well as large flat blocks of the Rázdiel part of the Tribeč Mts. were uplifted en bloc less during the Pliocene, but uplifted more and differentially during the Quaternary. This caused slow stream erosion; the river valleys were shorter and a larger area of intramontane level has been preserved in the Pohronský Inovec Mts. and eastern part of the Tribeč Mts. in comparison with the first simulation (Figure 13).

The second simulation overestimated the extent of the intramontane level mainly in the Pohronský Inovec Mts. On the other hand, the extent of river-side level was underestimated not only in the Pohronský Inovec Mts., but also in a major part of the Tribeč Mts. Overall preservation of planation surfaces was very low in the Jelenec and Rázdiel part of the Tribeč Mts. The second simulation also underestimated the hypsometric integral in the Tribeč Mts. (excepting Jelenec) – in the Rázdiel part yet more than first simulation – and significantly overestimated the hypsometric integral in the Pohronský Inovec Mts. (Figures 13, 14).

In the third simulation we tried to improve the model by a refinement of tectonic conditions and by including exhumation of the Neogene palaeosurface mainly in the western and central parts of the Tribeč Mts. (Figure 11). Considering the percentage of planation surfaces in the particular regions (Figure 13), this simulation was similarly successful as the second one. However, the hypsometric curves for this simulation are closest to reality for all six subdivisions (Figure 14). This indicates that Simulation 3, containing the most details of recent understanding of the landscape evolution in the study area (inclusive of exhumation of palaeosurface), is probably closest to the real development of the territory (Figure 15).

Figure 15

Results of Simulation 3, showing fluvial incision during uplift and retreat of slopes and spread of the valleys during quiet period. A. after Pliocene tectonic uplift (∼ 2, 3 Ma), B. after Early Pleistocene quiet period (∼ 1 Ma), C. after Quaternary uplift (recent), D. real topography of the simulated area.

The modelling led to very realistic shapes of hypsometric curves in the eastern part of the territory. Correspondence to the real topography declines southwestwards. It suggests a missing conceptual element of simulations for the south-west part of the Tribeč Mts. The south-westernmost part (Zobor) is the most problematic. Any Pliocene uplift leads not only to a deficit of mass in its upper part (Figure 14), but also to the development of a dense river network that is out of accord with the reality. It suggests a new hypothesis - very young (Quaternary) uplift of the westernmost part of the Tribeč Mts. That could solve not only the problems of Zobor but also some inconsistency in the Jelenec. A shift of main uplift of Zobor and Jelenec to the Quaternary along with slight reduction of K_br value of the most resistant rocks (Table 1) could lead to the better fitting of hypsometric curves as well as planation surfaces here. Finally, results of apatite fission track (AFT) dating from the NW of the Považský Inovec Mts. suggest a similar situation. The south-westernmost part of these mountains shows markedly older AFT ages (∼ 40 Ma) in comparison with the rest of the mountains (∼ 15 – 20 Ma), implying a later neotectonic uplift of the south-westernmost part [64].

Results of all simulations are influenced by the common settings of climatic, tectonic and lithological conditions. Because of poor constraints from palaeogeographical data the results should be interpreted carefully, mainly from the point of view of dating. The model works with absolute ages, however only resultant sequences and ratios are credible. Therefore, we interpret the results only in terms of basic geological stages (Miocene - Pliocene - Quaternary).

Some problematic results of the simulations can be caused not only by inappropriate settings of climatic, tectonic or lithological conditions, but also by limitations of the version of the CHILD model used. Inability to simulate the accumulation of sediments in the detachment-limited option caused absence of creation of prolluvial and colluvial sediments affecting the topography of foothills. Instead of alluvial cones and colluvium on the foothills an extensive flat surface was created. This can explain e.g. abundance of remnants of the river-side level in the SW part of Zobor in simulation 3 (Figure 12).

Other limitations that may affect the river network include: (1) insufficient sensitivity to the lithological data (represented only by TIN points) if the computational TIN is insufficiently dense and/or by (2) inability to set spatially differentiated infiltration and saturation (simulating an excessively dense river network in areas with permeable rocks). These limitations may lead to: (1) formation of unreal extensive remnants of planation surfaces, or conversely (2) remnants too denuded by the influence of a very dense river network.

Many other factors conditioned differences between the modelled and real surfaces: the problematic representation of hillslope processes, the simple setup of uplift pattern with creation of very inclined fault slopes, the possibility to set only one value of input parameters for the whole territory, etc.

On the other hand, the real planation surfaces have not been mapped ideally and therefore not all differences have to be caused by a failure of the modelling. We have found out that several narrow ridges at the same altitude in the Zobor and Jelenec part of the Tribeč Mts. could probably be remnants of the intramontane level even though they were not mapped [28]. Simulations show that a significant part of the river-side level in the Tribeč Mts. is probably a former intramontane level integrated into the riverside level but not recognised [28]. In all simulations several modelled remnants of the river-side level were formed only during the Quaternary uplift in regard to the local erosion base. This supports the idea of formation of individual bevels of pediments shaped at the same time at different altitudes [19].

A good landscape evolution model can be considered as a concentrated expression of geomorphological theory. But necessary simplifications transform it to a physically based hypothesis. From this point of view, we only tested whether the combination of the assumed process model and the hypothesized geomorphic evolution scenario is sufficient to explain the observed morphology. Failure of geomorphic presumption as well as its confirmation should therefore be considered only as indicative and not final proof.

5 Conclusions

Findings concerning (1) functionality of the CHILD model and (2) development of investigated territory can be concluded. The CHILD model provides an appropriate tool to test hypotheses about landscape evolution of the area at the scale of mountain belts. Setting the resistances of rocks influenced rates of fluvial erosion, and setting vertical tectonic movements for each point of the computing network is a significant advantage of CHILD. Thus, anyone can work with a variety of tectonic scenarios in an investigated area.

However, important limits occurred in our modelling of the mountain development:

1. Limited density of the computing grid, and a necessity to generalize lithology of the territory;

2. Impossibility of spatial differentiation of settings of rainfall, infiltration and permeability of the rocks;

3. Insufficient representation of various mechanisms of regolith formation, and use of only one value of the transport coefficient K_d, for the whole territory;

4. Absence of a specific module for sheet erosion (significant for the creation of pediments during drier climatic conditions), etc.

The quality of input data also limits modelling of long term evolution. The advantages of the storm generator were not fully exploited because of lack of constraints from the palaeoclimate data. Great lithological diversity and poor knowledge of palaeoclimatic changes excluded use of field measurement for determination of the detachment rate coefficient K_br. However, the proposed method of K_br estimation on the basis of plausible manifestation of rock resistance in the landforms (Table 1) could be sufficient for this type of modelling. Successful calibration by real land surface character confirms that limitations due to lack of palaeoclimatic constraints can be compensated by determination of the K_br value in this way and it is an advantage of this approach.

Despite these limitations, modelling confirms our capability to test regional geomorphic hypotheses at least at a provisional level. Results of simulations reject an assumption of dominant Pliocene tectonic uplift of the whole territory (as was supposed by Mazúr [15]), and suggest the possibility of existence of a Late Miocene initial planation surface (intramontane level) in both Tribeč Mts. and Pohronský Inovec Mts. ([25] vs. [36]). The modelling supports also the following hypotheses:

1. Exhumation of a significant (west) part of the Tribeč Mts. from below Neogene sediments [28].

2. Recent composition of tectonic blocks reflects Neogene extensional tectonic with a character of gravitational collapse [36],

3. More or less zonal character of the Quaternary uplift with maximum in the east, which is in accordance with the new morphostructural subdivision of the Western Carpathians [17],

4. Creation of the most extensive remnants of river-side level in both mountains by incorporation of less uplifted intramontane level into river-side level as supposed in Minár [29].

Modelling offered also some further non-trivial explanations (new regional hypotheses):

1. Success of modelling in the east part of this territory indicates that preservation of extensive remnants of the intramontane level here is a consequence of delayed (Quaternary) tectonic uplift,

2. Partial failure of modelling in the Zobor and Jelenec partsofthe Tribeč Mts. indicates very young (Quaternary) uplift of the territory that could be confirmed by a follow-up stage of modelling and AFT analyses.