ZAGREB 1997. Frequency Distribution Curves as an Indicator of Evolutionary Trends in. Geomorphological Systems: A Case Study from the Northwestern Part.
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5 Figs.
3 Tabs.
ZAGREB 1997
Frequency Distribution Curves as an Indicator of Evolutionary Trends in Geomorphological Systems: A Case Study from the Northwestern Part of Hrvatsko Zagorje (Croatia) Zoran PEH
Key words: Geo morphological systems, 'I'hc rmoclynami cs or nOllcquilibrium sys te ms, Frequency di stribut ion curves, Hori zo ntal di ssection , Vertical dissec ti o n, HYPsoll1ctric iJ1l cg ral, Drainage den sit y, Slope, Erosional levels, Hrva tsko Zagorje, Croat ia.
Abstract Frequency (lislribulion curv es can be indicative of the dynamics
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PROCESSES CONCERNING DRAINAGE NETWORK horizontal dissection drainage density
-1.29 -2.72
2.74 2.99
0.61 0.15
-0.50 0.91
0.10 0.06
PROCESSES CONCERNING VERTICAL DIFFERENTIATION vertical dissection slope erosional levels hypsometric integral
-1 .68 -2.70 -3.55 -1.97
2.83 1.55 1.90 2.36
1.21 -1.19 -0.99 -0.32
1.78 1.57 2.73 0.20
0.06 0.13 0.13 0.08
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geomorphological processes in the landscape of the study area, it is logical to assume that they will mostly reflect the evolutionary trends of the obscrved geomorphological sys tems. Another group of geomorphological processes is distinguished by a normal frequency distribution curve of lluctuations, indicating structural stabilit y of the pertaining subsys tems, which is a consequence of their ability to maintain th ei r structural attributes in the existing regime of external forces. Such is the case of the subsystem of hypsometric integral (Fig. 4) and the subsystem of drainage density being integral parts of the fourth- and fifth -orde r drainage basin systems. System componenls fluctuate within the limits of the them10dy-
3
Fig. 4 Frcquency distribution hislogram of Ilucluations for the hypsometr ic integral, 3_5'1> order, in the area of Investigation.
namic branch, sustaining the existing stationary state. In other words, potential energy carried by the fluctuations is neithcr too high to spur cvolutionary changes, nor too low to bring about degeneration of the present structures. The normal frequency distribution curve of l1uctllations in the subsystem of drainage density supports the general concensus of opinion that drainage density in its present extent retlects a balance between the input and output of the hydrological cycle. Its pattem discloses a number of mutual adjustments providing for the maximum and most efficient surface runoff in the drainage basin (CHORLEY & KENNEDY, 1971)_ Conversely, the subsystem of the hypsometric integral (Fig. 4) reflects equilibrium tendencies in the processes
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Geologia Cromica 5011
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of denudation, erosion, transportation and aggradation. In lower-order drainage basins the balance is es tablished owing to the negative feedback between total relief and hypsometric integral (that is, among morphometric propert ies only). In the higher-order drainage basins lithology plays the role of moderator in the proce ss of mutual adjustment of the two morphometr ic variables - channel gradient and valley-side slope (PEH, 1992)_ Proce sses involved in shaping the slope subsystem (Fi g. 5) and the subsystem of erosional levels afe distingui shed by the progressive modification of the frequency distribution curve which shifts [rom normality toward s negative skeweness as the order increases. The
2
Fig. 5 Frequency distribuLion histogram of tlucIllations for the slope, 3_5 '10 order, in the area of investigation.
slope subsystem in the third -order drainage basin system is characterized by the normal distribution of fluctuations. In the fou rt h- and fifth-order drainage basin system the distribution is more negatively skewed (Fig. 5). The subsystem of erosional levels, which dissociates from the subsystem of vertical dissection in the fourthorder drainage basin system, is at this hierarchical level characterized by normal distribution of fluctuations, but becomes negatively skewed in the fifth -order drainage basin system. It can be stated that in this case only the m inority of system components in these basin subsystems oscillates in the proximity of the lower limit of the thermodynamic branch (that is , the probability of exceptionally high negat ive fluctuations is very small).
Pch: Frequcncy Distribution Curves as ,lTl Indicator or Evolution;)ry Trends in Geomorphologic;)1 Systems ...
It suggests that the potential energy in specific parts of a system is so low that existing structures (landforms) undergo spontaneous degenerat ion in the places where its magnitudc falls below some critical value necessary for maintaining the stationary state. A reason for this can be found either in the unfavourable mechanical properties of the underlying bedrock (high permeability and low cohesion of rock and soil material), or in varying rates of uplift that affect some major tectonic blocks in the area of invcstigation. If the fonner is case, the vallcy-sidc slopes tend to form lower angles due to ineffective st ream downcutting (caused chiefly by relatively high infiltration capacity), which is most conspicuously reflected in higher-order and larger drainage basins (fourth- and, particularly, fifth-order). In the latter, denudation processes give way to aggradation processes when the uplift only slightly exceeds or evcn tends to be lowcr than the rales of denudation. As an example, in the subsystem of erosional levels onc of the key variables - thc main-valley mouth (which is also the mouth of a referring drainagc basin) - represents an overt indicator of uplift and subsidence that can be helpful in disclosing "act ive" and " inactive" gcologic struc tures in a landscape. Obviously, due 10 their relative lag in respect of the gene ral uplift typical for the study area (PRELOGOYIC, 1975), some tectonic blocks have considerably lower potential energy with respect to the surrounding area, inducing the processes of aggradation and development of "inactive" geologic structures. Both cxamples show that the energy expenditure in these subsys tems occurs mostly at the lowcr hierarchical levels (PEH, 1992, 1994).
4. CONCLUSIONS Examples presented in this study show that varioLls landforms in the fluvial landscape, such as the north western part of Hrvatsko Zagorje, can pursue different evolutionary schcmes which can be discerned from the corresponding frequency dist ributions of rIuetuations. The thermodynamic th eory of non-equilibrium states and related fluctuations as the source of instability is the kcy clement in the interpretation of evolutionary trends in gcomorphological systems and their subsystems. This results from utilizing new insights in fundamenta l physics in the geolog ical sciences. It has been shown in this study that thrce types of frequency distribution curves exist which, in a thermodynamic se nsc, can be indicative of equil ib rium and non -equilibrium relationships between driving and resisting forces in land forming processes. They show how landforms try to adjust themselves with minimum internal change to the external driving forces. The example of the processes responsible for the development of the subsystem of drainage density and subsystem of hypsome tric integral is presented. Non-normal freque ncy distribution of systcm parameters indicatcs non-equilibrium conditions which give
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rise to non -linear relationships between process and form and, accordingly, to structural instability within specific subsystems. Such a case is demonstrated by both the positive and negative skew of distribut ion frequency curves. Positivc skew is indicativc of structural changc which is the response to strong energy inputs from the sys tem surroundings. The loss of structural stability and emergence of new and more complex landforms is the final result which spurs landscape evolution. An example of this was shown by thc processes accounting for drainage network expansion (horizontal dissection) and, to some extent, by the proccsses of valley incision (vertical dissection). Negative skew, on the contrary, can suggest structural changes distinguished by the lack of energy in a system, which is insufficient to reinstatc thc original equilibrium conditions and, thus , to sustain existing landforms. This case predicts the downward path to landscape degeneration, that is, its involution. Such a case is exemplified by the processes affecting valley-slope angles and erosional levels. Although the re levant space and time scales have been taken into consideration, this st udy has been put into a frame which, in a geomorphological and geological sense, could not be strictly viewed upon as regional. However, the results point to distinct evolutionary laws that rule the development of a fluvial landscape in the temperate climate zones. Further investigations should therefore be directed toward the spatial evalua tion of thermodynamically specified geomorphol ogical parameters with assistance of the relevant maps ("process maps", PEH, 1994). Attention should also be paid to the concept of geomorphological thresholds and boundary values delimiting landform stability. This would allow individual landforms and their evo lutionary (or, contrari ly, degenerative) changes to be directly related to geological struclurcs, lithological characteristics and tectonic activity. Acknowledgments During preparation of this paper the author benefitted greatly from critical comments by Prof. Eduard PRELOGOYTC (Faculty of Mining, Geology and Petrolcum Engineering, University of Zagreb, Croatia) which were cxt remely valuable. His help is grateful ly acknowledged. Also, the author is greatly indebted to Prof. Simon PIRC (Institute of Geology, Unive rsi ty of Ljubljana, Slovenia) for his thoughtful reviews and useful comments on earlier drafts of the manuscript. Thanks are also due to all my colleagues who supported me in this erfort.
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Manuscript received Ma rch 15, 1995. Revis ed manuscript accepted April 28, 1997.
