Use of GIS to calculate Hack Index as a basis for comparative geomorphologic
analysis between two drainage basins: a case study from SE-Brazil
Bráulio Magalhães Fonseca - Professor Assistente - IGC-UFMG- Address: Depto de Cartografia-IGCUFMG-Av. Antônio Carlos 6.627-CEP: 31270-90 - Belo Horizonte-MG-Brazil
E-mail: brauliomagalhaes@cart.igc.ufmg.br
Cristina Helena Ribeiro Rocha Augustin - Professora Titular-IGC- Address: Depto de GeografiaIGC-UFMGAv. Antônio Carlos 6.627-CEP: 31270-901 - Belo Horizonte-MG-BrazilE-mail: chaugustin@ymail.com
ABSTRACT
The Espinhaço Meridional is a Precambrian orogenic belt located in the southeastern
part of Minas Gerais State, in Brazil. It is formed by three litho-structural unities among
which the most important are the quartzites of the Espinhaço Supergroup. Occurring
mainly on the rocks of this Supergroup at the eastern side of the orogenic belt is the Rio
Jequitinhonha drainage basin. On the western side of the belt is the Rio Pardo drainage
basin, which runs partially over limestones from the Bambui Group. Both basins share
the similar tropical sub-humid climate conditions and a savanna type vegetation cover
(Cerrado). However, both present different landforms that we assume are the result of
variations to the litho-structural characteristics of their main geological formations. To
prove this, a Stream Length-Gradient Index (also known as Hack Index) was calculated
as an indicator for fluvial response to the geological stratum variation. Before
calculating the index, Geographical Information System (GIS) was used to integrate a
set of variables to enhance the outcome of the Hack Index application. The variables
needed to calculate the Hack Index (the topographic difference or the topographic
amplitude between the drainage channel and its length) were taken using the Terrain
Digital Model. The parameters were completely tabulated in the ArcGIS 9.2 Program.
The values calculated using the Hack Index were plotted individually in the middle
point of the drainage lines on the map, allowing the application of spatial oriented
statistics with the interpolation of isovalues. This transformed the representation of the
Hack index (calculated as points) in zones. The spatial distribution of the Index values
(Spatial Analyst and Geo-statistical Analyst) used through a geo-statistical interpolation
(Inverse Distance Weighting–IDW and Voronoi Diagram-VD) was essential as it
provided a basis for performing a comparative analysis with other variables such as
lithology and structure. The Index shows that the stream power in both basins is
different whilst also indicating that it could be related to underlying tectonics and
structural geological settings. While the Jequitinhonha River basin has developed over
predominantly homogeneous quartzite formation, the Pardo River basin partially cuts
through a limestone area. The results displayed variations of the Index values inside
each basin. For instance an increase at the index can be noted in the Pardo River where
erosive discordance occurs between the quartzite of the Espinhaço Supergroup and the
limestone of the Bambui Group. Whilst on the other hand, in the Jequitinhonha River
basin, the density of the quartzite formation faulting system seems to be a major
contributing factor to the degree of incision. These results suggest that much more
active dissection processes are taking place in the upper Jequitinhonha River than in the
Rio Pardo river basin. Therefore, the Hack index (using GIS as a tool) has proven to be
an important method of determining geomorphic differences between both basins, as
well as providing information that can be applied to the definition of variables and their
sampling in the field.
Key words: Hack Index, stream power, drainage basin, geomorphic differences, GIS
application, litho-structural influences.
1. Introducion
The Meridional Espinhaço mountain range (Fig. 1) is a Precambrian formation
associated with the Araçuaí orogenic belt deformed during the Brasiliana orogeny and
formed by three main litho-structural unities: the Espinhaço Supergroup, especially
quartzite which were folded and fractured, the remobilized crystalline embasement
(Gouveia, Porteirinha e Guanhães anticlinorium) and the rocks from Macaúbas Group
(PEDROSA SOARES, 1992).
The evolution of the landform presents, therefore, an important influence from these
litho-structural unities, due not only to their different responses to erosion rates, but also
to the differentiation in the types and intensity of the processes acting upon them along
time (AUGUSTIN, 1995). The ductile type of lithology from the Espinhaço Supergroup
was responsible for the occurrence of faulting systems that, together with the folded
strata, created a Sierra type of landscape.
Occurring on the eastern side of the Sierra is the Jequitinhonha river basin with 2.054
Km2 linked to the Brazilian coastal dynamics (Fig. 1). On the western border is the Rio
Pardo drainage basin, with 2.029 Km2, belonging to the São Francisco drainage basin
(Fig. 1). The Pardo basin is predominantly formed by quartzite from the Espinhaço
Supergroup on its eastern portion and by limestone from the Bambui Group on its
western one. The relief is dominated by quartzite outcrops intercalated by pediments
like type of landform. The Jequitinhonha basin, on the eastern portion of the Sierra, is
also characterized by quartzite outcrops, however the outcrops arise from scarps and the
rivers valleys present deep incisions, with steep valley walls. Variations in their
landforms which can also be observed in field situation have been assumed as resulting
from the differences in the litho-structural setting. It apparently induces a more vigorous
drainage incision in the Jequitinhonha basin, although a more intense dissolution of
limestone was expected to account for a more active dynamic of the Pardo basin.
By aiming to analyze and verify if the two basins in fact present differences in the
intensity of their erosion, a Hack Index (Stream Length-gradient Index), proposed by
John T. Hack in 1973 and denominated by Etchebehere et al. (2004) as the “declivityextension index” was used. Because this index is easily and rapidly obtained it has been
largely used for appraising geological and landform differences, as it gives a basis to
compare rivers of various extension and physiographic characteristics, besides making it
possible to draw inferences related to the geological and geomorphologic development
of the study areas. The Index was used, for example, by Mayer et al. (1983), in studying
the movement of the Stafford Fault in the northeast of Virginia State, USA; by Keller
(1977) and Keller et al. (1984) to identify very active “tectonic cells” in certain parts of
California; by Seeber et al. (1983) to detect neotectonic activities in the Himalaya; by
McKeown et al. (1988) to infer physiographic expression of a series of seismic
registration in the mountain range of Ozark in the State of Arkansas, USA; by
Etchebehere et al. (2004; 2006), to identify tectonic deformations in the Rio dos Peixes,
São Paulo State, Brazil; by Della Seta et al. (2008), to access a morphotectonic analyses
in small drainage basins from central Italy, among other examples.
On the basis of empiric evidence, Hack (1957a, p. 87-90) observed that the value of the
product declivity of the channel (S) by its length (L) is directly related to river
competency. During his study in the Potomac River, Hack discovered the rivers of this
basin have the following relation:
where M represents the average size of the load particles in the river bed. There is a
functional relation between these variables: an increase in the particle size deposited in
the river bed corresponds to an increase also in the value of the product SL. In other
words, in the Hack Index (HACK, 1957a, p. 71; HACK et al., 1959, p. 4; HACK,
1973). Therefore, assuming that the river competency is directly related to the energy
operating in its system, it is acceptable to regard the Hack Index as a measure or as an
indicator of the energy at work in a river and, therefore as a basis of geomorphic
comparison between them (ETCHEBEHERE et al, 2004, 2006; KELLER et al,
1996).We assume in this study that the Hack Index values can be more meaningful
when interpreted in a comparative way. Therefore, a comparative analysis between the
two drainage basins, Pardo and Jequitinhonha rivers was done with the objective of
evaluating the energy present in the drainage systems. The results were interpreted in
terms of their significance for indicating different geomorphic evolution between the
two orders of the Espinhaço mountain range.
2. The study area
The Espinhaço Meridional is an orogenic belt that occurs in the eastern portion of
Minas Gerais State, Brazil (Fig. 1). It was submitted to a main compressive tectonic
event during the Brasiliana orogeny that ended at app. 560 Ma, with tension from east to
west (KNAUER, 2007) and direction of deformation N-S, generating elevations and
scarps that formed today’s sequence of sierras, named locally. It is formed by three
main geological unities, from which the quartzite, from the Supergroup Espinhaço are
stratigraphically located on the top of the depositional sequences that were
metamorphosed during the Upper Proterozoic. Below them occur schist, also deformed
by the same event and the remobilized crystalline basement, exposed by erosion in the
Gouveia Depression.
The study area is located on the southern part of the Espinhaço mountain range, below
parallel 170 S, known as Espinhaço Meridional, exclusively placed in Minas Gerais
State. The ruptile characteristics of quartzite favored the fracturing and faulting of these
rocks. This, coupled with a relatively expressive yearly average precipitation around
1400mm, creates a condition of water retention. That makes the southern part of the
Sierra an important area of water recharge and location of an expressive number of
headwaters. The two drainage basins of this study occur at either side of the Sierra do
Espinhaço: Pardo River at the western side and Jequitinhonha at the eastern side, both
however sharing the same watershed (Fig. 1, 2).
The most recurrent landforms of the Espinhaço Meridional are scarps, faults, residual
synclines and anticlines structures with SW-NE directions following the main
deformational direction (SAADI, 1995). They form sequences of ridges know as sierras
that were eroded by a dense river system of small rivers that explore the faulting and
deformational features to dissect the inherited geological background (AUGUSTIN,
1995). This explains why the drainage always follows the main geological lineaments.
The western border of the Espinhaço mountain range is marked by an erosive escarp
with an average break of slope of 500m that changes to a faulting-escarp on the
southern sequence of this border (Fig. 1).
Fig. 1- Location of the study area: on the western border, the Pardo River basin; on the
eastern, the Jequitinhonha River.
The Pardo River flows down this sharp escarp through canyons that drain into the
Velhas River, before entering the São Francisco River. The basis of the escarp along the
entire border indicates the contact of the Espinhaço mountain range and its geological
sequences are approximately 500m above and the metapelites of the Bambui Group are
below (Fig. 1).
The eastern border of the Espinhaço where the Jequitinhonha basin occurs is marked by
structural windows associated with trust folds and also by less resistant lithologies
exposed by an efficient vertical down cutting by the drainage system (Fig. 1). The result
is the occurrence of a more discontinuous escarp, partially dissected by valleys that
drain to the Jequitinhonha, Mucuri and Doce rivers (Fig.1).
The annual rainfall average in both basins is approximately the same: 1400mm
concentrated during the summer months, from October to March. Annual average
temperatures are also similar: 220C, characterizing this climate as Tropical sub-humid,
with two well defined seasons.
Vegetation cover varies from forested savanna, grass bushed savanna (cerradão), its
degraded savanna type (cerrado degradado), occurring in areas dominated by rocks of
the granite complex and metabasic and basic intrusions, to an altitudinal Prairie, and
rupestrian grassland on the outcrops and riparian forest along the rivers (AUGUSTIN,
1995).
3. Materials and Methods
The Hack Index was obtained using SRTM images (special resolution of 30m) and over
these images the model (D8) of drainage extraction was used and the Sthraler (1957)
hierarchy was applied. The Index was calculated for the entire extension of the river
(whole slope vs length index), taking the total altimetric amplitude represented by the
difference between the altimetric values of the rivers head until its mouth, as well as the
natural logarithm (Ln) of the total river extension, suggested by McKeown et al. (1988)
and Etchebehere et al. (2004). Only 2nd order channels or higher orders represented in a
topographic map of IBGE (1977) (scale 1:00.000, the only scale available for the study
area) were used to calculate the Index, making a total of 120 channels for the Pardo
basin and 194 for the Alto Jequitinhonha.
Field work was carried out to localize and to measure by GPS the main representative
knick points that form waterfalls (28 waterfalls). There were, however, difficulties in
accessing some of these areas, thereby limiting the sampling to 15% of the possible
points, identified on the basis of the Hack maximum values.
The Hack Index was calculated for stream of 2nd and higher orders with both studied
basins that are represented on a 1:100.000 topographic scale (IBGE, 1977) using the
mathematic equation:
. It can also be represented as
,
where L is the length of the maximum segment of the river, taken from its head until the
mouth;
is the variation of height of this segment, and
is its horizontal distance,
thereby representing the average declivity of the segment. The parameters were
measured after Hack´s definition as represented below (Fig. 2).
It is important to note that the segment taken for the Hack Index calculation must be
long enough to allow for variations in the declivity of the small channels (rapids and
pounds). Further, any unit of measurement may be used; providing that a pattern is
followed for the calculation.
The accuracy of the Index is dependent on a consistent relation between the length of a
channel and its drainage area, as observed by Hack (1973), which occurs in the vast
majority of natural fluvial systems. Therefore, when calculating the Index it is important
to ensure that the channel length of the most representative river (the longest one)
begins at its head and continues up to its mouth without interruptions, even when
junctions occur. Hack pointed out that the results at the catchment areas usually present
anomalies because they do not directly respond to the kinetic energy of the rivers, but to
other processes, so one may not need to consider them.
Extra care must also be taken to calculate the Index due to the fact that the product, SL,
corresponds to a tangent in a specific point of the longitudinal profile in semi-log scale.
So, when an average declivity of a segment is calculated using the formula
, what is
in fact measured is a secant of the profile, and thus represents an error. Hack (1973)
indicates that this error is a function of the ratio , being that the smaller the ratio, the
larger is the error; the error becomes non significant only when this ratio reaches the
value of 2.0 or 1.0. Therefore,
should be always smaller than L.
The variables for calculating the Hack Index in this work (height differences or
altimetric amplitude of a drainage channel and its length) were extracted from a Digital
Terrain Model (DTM). The parameters were tabulated on the ArcGIS 9.2 Program by
associating each vector representing water flow from the study basins. The Hack Index
values were plotted individually as points, at the middle point of each drawn drainage
line (ETCHEBEHERE et al., 2004), making the use of spatial statistics possible, and the
interpolation of the Index isovalues to zones. To perform the statistics the extensions of
Spatial Analyst and Geostatistical Analyst were used.
Interpolation was achieved using the Inverse Distance Weighting (IDW) which allows
the information of a point to be weighted during the process, so that specific data from a
point will have less influence over another as the distance between them increases
(DAVIS, 1986). The IDW, represented in the equation below was used to generate a
continuous surface using the Hack Index as a basis which is calculated using points,
making it possible to identify zones that are drained by the same water flows, or rivers
with the same energetic power:
z

1
zi
i 1
di
n
1
i 1
di 
n

where z corresponds to estimated values; n is the size of the sampling; zi the known
values and di refers to distance between the known and estimated values (zi and z).
The Voronoi Diagram, on the other hand, is an abrupt interpolator also known as the
Polygons of Voronoi or as Thiessem Polygons, which is used to calculate the area of
influence of each average point of the Hack Index and was useful to determine the
closest region around a point (LEE et al., 2000). The Voronoi Diagram, shown in Fig. 3
is formed by irregular polygons, with one polygon for each sampled variable to be
modeled. A polygon covers the limits of the nearest region compared to all other
samples. The advantage of this model is precisely the possibility it offers to determine
the area of influence of each sample by the distance:
Fig. 3 –Representation of the Diagram of Voronoi.
The Veronoi Diagram was in this study used in the following manner: taking into
account a group S of n points in a plan, we tried to determine for each point p of S
which region V(p)of the points in a plan that are the nearest of p, in comparison with
another point in S. In this case, the group S represents the values calculated through the
Hack Index (plotted at the middle point of the river). In the case of the study area, the
plan represents the areas drained by Alto Jequitinhonha and Pardo River as the regions
V(p) represent the areas drained by channels with the same energy and that are subject
to the influence of p.
4. Results and Discussion
To allow a better observation of the energetic dynamics of the drainage basins and to
detect alterations in the rivers as a result of, for instance, differences on the geological
setting along their valley and to appraise sediment load or even tectonic activities, the
first step is to transform the Hack Index into spatial dimension. In the present case we
followed procedures similar to those carried out by Etchebehere et al. (2004) that
interpolated curves of isovalues from the Hack Index to examine anomalies of the
drainage system of the Peixe river, Presidente Prudente, SP, Brazil.
The points representing the values calculated for the Hack Index are presented below
(Fig. 4).
FIG. 4- The middle points of the drainage lines plotted over the
corresponding rivers ordered by Sthraler (1957) hierarchy.
The values of the surfaces obtained using the IDW interpolator, were calculated using
the real Hack values as the basis.
From the 28 knick points sampled in the field (Fig. 5), two of them were located outside
the study area; 5 were located in the Pardo River and 21 in the Alto Jequitinhonha basin.
Some of the break of slope in the Alto Jequitinhonha are near each other and are not
located on the map (Fig. 5) due to its scale.
There is a natural association between the points/areas of break of slopes and an
increase in the Hack Index, as a result of more energy being liberated in the river
channel.
The comparative analyses between both basins using the Hack Index show that higher
values are occurring predominantly in the Alto Jequitinhonha River than compared to
the Pardo river basin, (Fig 5). The higher values are therefore better distributed in
spatial terms in the Alto Jequitinhonha basin.
Fig 5. – Spatial distribution of Hack Index with the use of the IDW interpolator.
The smallest values are those occurring on the drainage divide of both basins, which is
normally the case due to the effect of dispersion of erosion at the summit area.
The Voronoi interpolator was also applied using the average values of the parameter
considered for the calculation of the Hack Index (Fig. 6). Both interpolators show a
good representation of the used parameter, but the Voronoi Diagram was able to
individualize a more representative, clearer and more identifiable number of areas under
the influence of the Hack Index in the Alto Jequitinhonha basin (Fig. 6).
Fig. 6 - Spatial distribution of the Hack Index using Voroni Diagram for the study area.
This occurs as the abrupt Voroni interpolator favors the optimization of the field
observations, due to the fact that it allows the delimitation of exact areas of influence of
the Index. Therefore, the results are presented as a grouping of areas (polygons) where
the energy is more pronounced (Fig. 6).
The results of the Voroni Diagram (Fig. 6) also show that the energy concentrated along
the Alto Jequitinhonha main valley, although it is not regularly distributed along it, was
interrupted in some of the main channel segment. Fig. 6 allows the observation that the
area of the Prado River with higher energetic values correspond to an affluent, with
convergence W-L, of the main river that shows a S-N direction at this segment.
The overall results seem to indicate an important litho-structural influence in both
basins (Fig. 7).
Fig. 7 - Lithology and structure of the study area. (COMIG, 1996).
In the Pardo River it is possible to identify a close relation between the most significant
Hack Index and a lithological contact of the metadiamictite of the Macaúbas Group and
the quartzite of the Espinhaço Supergroup (Fig. 7). Apparently the significant change
that occurs from quartzite of Espinhaço Supergroup to the limestones of the Bambui
Group does not result in an exceptional erosive energy within the Pardo river basin, of
that can be observed in the figures 5 and 6 of this area. There is an increase as shown by
the yellow color in Fig. 6 (Voronoi Diagram), but it does not reach the values of the
Alto Rio Jequitinhonha (229-332).
Overall, the Alto Jequitinhonha basin is geologically more homogeneous than the Pardo
basin (Fig. 7). The basin is formed mainly by orthoquartizte and meta-conglomerates of
the Sopa Brumadinho Formation, from the Espinhaço Supergroup (Fig. 7). However,
differently from the other basin, this shows an intense presence of structural and
morphological lineaments, which can affect the energy within the drainage system. A
similar situation was reported by Miller (1991) in studying the influences of the geology
on the break of slopes, also known as kidnickpoints in river beds litho logically
homogenous. Miller concluded that the thickness of the geological strata and the
distribution of these slope breaks were strongly related to the frequency of fractures in
the rocks that are intercepted by the channels as well as to the height of the strata in
relation to the direction of the river flow. These features create an increase in the
velocity of the river flow, speeding up their erosive work, which can be captured by the
Hack Index measurements. It is not, however, totally out of the question to assume that
the higher values of the Hack index for the Alto Jequitinhonha basin are related to a
neo-tectonic reactivation linked to the fact that the Jequitinhonha River flows to the
Atlantic Ocean and is more related to the dynamic of the eastern Brazilian coast.
5. Conclusion
The Hack Index allowed comparison between two drainage basins of approximately the
same area, located at the Espinhaço Mountain range, in Minas Gerais State, Southeast
Brazil: the Pardo River and the Alto Jequitinhonha river basins.
This comparison is based on the differences of energy detected by the Index and it is
expected to reflex the erosive energy involved in the drainage basins. To enhance the
Hack Index, its values were transformed from point to spatial representation using the
Inverse Distance Weighting (IDW) interpolator and the Veronoi Diagram. Both methods
showed very good results allowing a better visualization of the spatial distribution of the
Index thereby facilitating its analysis and making it possible to associate the causes of
their variation.
The results of the application of these procedures to the study basins pointed out that a
higher energy is involved in the incision of the Alto Jequitinhonha River located at the
eastern part of the Espinhaço when compared to the Pardo River that occurs on the
western limits of the same mountain range. Although it runs over rocks that
lithologically favor erosion, like limestones, is the Alto Jequitinhonha that shows the
presence of higher Index values, which are also better distributed along the valley. The
most representative Index values in the Pardo basin are related to the contact between
two main lithologies: the metadiamictites from Macaubas Group and the limestones
from the Bambui Group. Otherwise, the index is much less representative than those in
the Alto Jequitinhonha, which can be associated with the occurrence of geologic
lineaments, that increases break of slopes, different thickness of the strata that can speed
up or slow down erosion rates, and mainly the frequency of rock fractures that tend to
intercept the channels creating conditions for the occurrence of water falls and other
break of slopes. These features create the increase in the velocity of the river flow,
speeding up their erosive work what can be captured by the Hack Index measurements.
It can also be assumed that this energy is related to a more dynamic evolution of the
Jequitinhonha River linked to the more tectonic mobile eastern Brazilian coastal system.
It is also important to call to attention that the Hack Index can be calculated taking the
basins of each segment in hierarchy as proposed by Strahler as the basis for the
calculation. In this case the drainage area for each segment would substitute the
geostatistical interpolators, which can reduce the generalization of the data and help the
spatial analysis of the drainage basins to a systemic basis.
Acknowledgement: we to thank The Fundação de Amparo à Pesquisa do Estado de
Minas Gerais (FAPEMIG) for the financial support for the realization of this research
(CRA APQ 0165209).
5. Bibliography
ABREU, A.A. de. Análise Geomorfológica: Reflexão e Aplicação – Uma contribuição
ao conhecimento das formas de relevo do Planalto de Diamantina. São Paulo. 1982.
ALMEIDA ABREU, P.A. O Supergrupo Espinhaço da Serra do Espinhaço Meridional
Minas Gerais: o rifte, a bacia e o orógeno. Geonomos. 3(1) : 1-18, 1995.
AUGUSTIN, C.H.R.R. Geoökologische Studien im Südlichen Espinhaço Gebirge bei
Gouveia, Minas Gerais, Brasilien Unter Besonderer Berucksichtigung der
Landschaftsentwicklung. Tese de Doutorado: 324 p. Universidade de Frankfurt,
Frankfurt, Alemanha, 1995.
COMIG. Projeto Espinhaço. Belo Horizonte, Cia. Mineradora de Minas Gerais.
(including 23 geologic maps, escale 1:100.000). (1996).
DAVIS, J. C. Statistics and data analysis in geology. Second Edition, John Wiley &
Sons. 1986. 646 p.
DELLA SETA, TROIANI, M. The use of the Stream Length –Gradient index in
morphotectonic analysis of small catchments: A case study from Central Italy.
Geomorphology 102, p.159–168, 2008.
ETCHEBEHERE, M.L.C.; SAAD, A.R.; PERINOTTO, J.A.J.; FULFARO, V.J.
Aplicação do Índice "Relação Declividade-Extensão - RDE" na Bacia do Rio do Peixe
(SP) para detecção de deformações neotectônicas, Revista do Instituto de Geociências
da USP - Série Científica, v.4, n.2, p. 43-56, 2004.
ETCHEBEHERE, M.L.C.; SAAD, A. R.; SANTONII, G.; CASADO, F. C.;
FULFARO, V. J. Detecção de prováveis deformações neotectônicas no vale do rio do
Peixe, Região Ocidental Paulista, mediante aplicação de índices RDE (Relação
Declividade-Extensão) em segmentos de drenagem. Revista UNESP – Geociências,
v.25, n. 3, p.271-287, 2006.
FONSECA, B. M.; AUGUSTIN, C.H.R.R. O Uso do Geoprocessamento para o
Mapeamento Geomorfológico da Serra do Espinhaço Meridional In: VII Simpósio
Nacional de Geomorfologia/II Encontro Latino Americano de Geomorfologia, 2008,
Belo Horizonte.
HACK, J. T.; YOUNG, R.S. Intrenched meanders of the North Fork of the Shenandoah
River, Virginia: U.S. Geol. Survey Prof. Paper 354-A, 10 p., 1959,
HACK, J. T. Stream-profile analysis and stream-gradient index. Journal of Research of
the United States Geological Survey, v. 1, n. 4, p. 421-429, 1973.
HACK, J. T. Studies of longitudinal stream profiles in Virginia and Marylan: U.S Geol.
Survey Prof. Paper 294-B, p. 45-97 [1957; 1958].
IBGE. Cartas do Brasil do IBGE – Carbonita - 1:100.000. Rio de Janeiro, IBGE 1978.
IBGE. Cartas do Brasil do IBGE – Corinto - 1:100.000. Rio de Janeiro, IBGE 1978.
IBGE. Cartas do Brasil do IBGE – Curvelo - 1:100.000. Rio de Janeiro, IBGE 1978.
IBGE. Cartas do Brasil do IBGE – Diamantina - 1:100.000. Rio de Janeiro,IBGE, 1978.
IBGE. Cartas do Brasil do IBGE – Presidente Kubitch - 1:100.000. Rio de Janeiro,
IBGE 1978.
IBGE. Cartas do Brasil do IBGE – Rio Vermelho - 1:100.000. Rio de Janeiro, IBGE
1978.
KELLER, E.A., Adjustment of drainage to bedrock in regions of contrasting tectonic
framework [abs.]: Geological Society of America Abstracts with Programs, v. 9, no. 7,
p. 1046, 1977.
KELLER, E.A., ROCKWELL, T.K. Tectonic geomorphology, Quaternary chronology,
and paleoseismicity, In Costa, J.E., and Fleisher, P.l, eds. Developments and
applications of geomorphology: New York, Springer-Verlag, p. 203-239, 1984.
KNAUER, L.G. O Supergrupo Espinhaço em Minas Gerais: considerações sobre sua
estratigrafia e seu arranjo estrutural. Geonomos. 15(1): 81-90, 2007.
LANDIM, P.M. B. Análise estatística de dados geológicos. Editora UNESP 226 p.,
1997.
LEE, I.; GAHEGAN, M. Interative analysis using Voronoi diagrams: algorithms to
support dynamic update from a generic triangle-based data structure. Scientific
Literature Digital Library, 2000.
LEOPOLD, L.B., WOLMAN, M.G., MILLER, J.P. Fluvial processes in
geomorphology: San Francisco, W.H Freeman and Co., 522 p, 1964.
MAYER L., WENTWORTH, C.M., Geomorphic differences east and west of the
Stafford fault system, northeastern Virginia [abs.]: Southeastern Section, Geological
Society of America, v.15, no. 2: p. 56, 1983.
McKEOWN, F.A. et al. Analysis of stream-profile data an inferred tectonic activity,
Eastern Ozark Mountains region U. S. Geological Survey Bulletin, n. 1807, p. 1-39,
1988.
PEDROSA-SOARES, A.C.; NOCE, C.M.; VIDAL, P.; MONTEIRO, R.;
LEONARDOS, O.H. Toward a new tectonic model for the Late Proterozoic Araçuaí
(SE Brazil) - West Congolian (SW Africa) Belt. Journal of South American Earth
Sciences, 6: 33-47, 1992.
PFLUG, R. Die präkambrische Miogeosynklinale der Espinhaço- Kordilliere, Minas
Gerais, Brasilien. - Geol. Rundschau, Bd. 56, p. 825 – 844, 1965.
RENGER, F. Evolução dos conceitos geológicos da Serra do Espinhaço. In: SIMP.
GEOL. MINAS GERAIS, 1, Diamantina, Anais... Belo Horizonte, SBG/MG, Bol. 1, p.
9-28, 1979.
SAADI, A. A. Geomorfologia da Serra do Espinhaço em Minas Gerais e suas margens.
Geonomos, Revista de Geociências, 3(1):41-63, 1995.
SEEBER, L.; GORNITZ, V.M. River profiles along the Himalayan arc as indicators of
active tectonics: Tectonophysics, v. 92, p. 335-367, 1983.
STHRALER, A.N. Quantitative analysis of watershed geomorphology. Trans.
American Geophysical Union, v.38, p. 913-920, 1957.