morphometric analysis of five river basins in the bulaloc and canipan quadrangles in s palawan

8/10/2019 Morphometric Analysis of Five River Basins in the Bulaloc and Canipan Quadrangles in S Palawan

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National Institute of Geological SciencesCollege of Science

University of the Philippines Diliman

A Morphometric Analysis of Five River Basins in the Bulaloc and Canipan Quadrangles in

Southern Palawan, Philippines

In partial fulfilment of the requirements for Geology 170 (Field Geology)

Submitted by

ANTONIO LORENZO M. MEDINA

ENID C. QUIAMBAO

DON PIETRO B. SALDAJENO

JOEL MARI C. VILLA, JR.

Submitted to

DR. CARLO A. ARCILLA

DR. MARIO A. AURELIO

Professors

PAOLO ANDRE D. BENAVIDESJOHN DALE B. DIANALA

SOFIA MARAH P. FRIAS

JOSE DOMINICK S. GUBALLAJOHN PAUL A. MENDOZA

LIKHA G. MINIMOJAMES CESAR A. REFRANLEONILA M. BRON-SIKAT

RUSSEL RAFFY M. ONGJASMIN CONSUELO D. URQUICO

RICHARD L. YBANEZInstructors


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ABSTRACT

This paper studies the morphometric parameters of the basins in the Bataraza and Rizal

municipalities of the province of Palawan. The morphometric analysis utilized the Horton-Strahler

method in determining relevant stream parameters which were then correlated to topographic and

lithologic factors. The study showed that drainage density has positive correlation with slope and has an

inverse relationship with permeability which was assessed by the constant of channel maintenance and

stream frequency. Bifurcation ratios appear to be negatively correlated with drainage density. This may be

due to topographic factors, differing stream lengths, and differing stream sinuosities.

INTRODUCTION

In previous studies, morphometric parameters have been widely used to analyze drainage systems

of different basins. Using these morphometric parameters is limited to the accuracy of digital elevation

models (DEMs), aerial photographs and other maps used in tracing all the streams that comprise a

drainage network. Parameters such as bifurcation ratios, linear aspects and areal aspects are useful in

correlating bedrock lithologies, dissection and geomorphic processes that shape the fluvial landscape of

the area.

The study area covers the municipalities of Rizal and Bataraza (Figure 2), located in the southern

region of Palawan (Figure 1). The study area consists of high, irregular mountains with narrow valleys

occurring in between them. The Bulanjao Range is the most prominent topographic feature of the area,

appearing to bisect the study area laterally. Streams on the western side of the Bulanjao Range drain to the

South China Sea while those in the eastern side drain to the Sulu Sea (Cabrera, 1985). The range is

surrounded by flatlands that are currently used for agricultural purposes which may be attributed to the

abundant river systems in these plains. The major streams in the study area include the Canipan River,

which flows parallel to the west of the ridge in the coastal plain, the Iwahig River situated east of the

Canipan quadrangle, and the Sumbiling River, located south of the Bulanjao Range. Field observations

combined with the use of several Geographic Information System (GIS) software were used to gather the

required morphometric parameters in the study area to conduct a Horton-Strahler drainage analysis.


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Figures 1 & 2.(Left) Map of Palawan showing the political boundaries of its municipalities. The study

area is boxed in red. (Right) A closer view of the bounded area in Figure 1 with the barangays covered in

the study.

REVIEW OF RELATED LITERATURE

A study on the relationship of drainage density with slope angle was conducted in Japan in 2004,

and two types were established under these conditions. Type 1 follows a downward sloping trendline,

where drainage density decreases with increasing slope value, and Type 2 follows a convex-upward dome-

shaped trend, where drainage density increases with slope angle up to a point where the slope angle

becomes high enough such that the drainage density begins to decrease again (Lin & Oguchi, 2004). The

Type 2 trend is characteristic of more mature watersheds than the Type 1 trend, and differences in the

stage of stream-net growth can also be attributed to the location and general inclination of the watersheds

being analyzed. Lin & Oguchi also proposed that the effects of geology seem to have a lesser weight than

the maturity of the watershed, as evidenced by their findings in the Usu and Kusatsu-Shirane areas.

Although previous studies suggested that therelationship between slope angle and drainagedensity

corresponds to dominant erosion types,this study has indicated that they correspondmore directly to the

stages of channelization (Lin & Oguchi, 2004).


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A drainage pattern analysis was conducted on the Foix Canyon System in the Mediterranean Sea

to determine the role of gullies in its evolution (Tubau et al., 2013). The primary method used was the

Horton-Strahler analysis, and parameters such as drainage density, stream frequency and drainage area

relief patterns were utilized alongside it. The main process responsible for canyon head growth and

across-flank transport of material from the continental shelf is the formation of a large dendritic network

extending from the canyon thalweg up to the canyon rim. These are called rim gullies. Toe gullies form

smaller pinnate networks restricted to the lower portion of the canyon flanks. These are intepreted as the

morphological expression of the rejuvenation of rim gullies and the canyon itself (Tubau et al., 2013).

The drainage system anomaly of 15 basins in the Zagros folded belt in Iran was studied via a

morphometric analysis (Bahrami, 2013). The methodology of the study consisted of the computation of

various factors including drainage density and bifurcation ratio. The study concluded that the elongation

and tilting of the basins are associated with varying rates of uplift, folding and anticline hinge spacing,

which are controlled by the tectonic activity in the Zagros belt.

Pakhmode et al. (2003) evaluated the drainage network of the Kurzadi river basin by analyzing

morphometric parameters including stream-order analysis, bifurcation ratio, length ratio, drainage density,

constant of channel maintenance, length of overland flow and stream frequency and integrating these data

into hydrogeological mapping. Domains of high surface permeability typically indicate relatively higher

length ratios and lower drainage density and stream frequency (Pakhmode et al., 2003).It was then

concluded that the sub-basins with higher values of the constant of channel maintenance and length of

overland flow, and lower values of drainage density and stream frequency indicate higher permeability to

infiltration.

Tolessa et al. (2013) examined the morphometric parameters of the Tandava River Basin in India

through a Horton-Strahler analysis alongside Schumms methods. Stream order versus the logarithm of

the stream count, drainage density, stream frequency, drainage texture, bifurcation ratio, elongation ratio,

circulatory ratio were calculated for the analysis. Drainage density was correlated with subsoil permeability

and vegetation thickness, while stream frequency was correlated with drainage density. The bifurcation

ratio was then correlated with the area lithology and structures, and elongation ratio with hardness and


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slope. The conclusion was that the Tandava River Basin had medium drainage density, coarse texture

ratio, and low elongation ratio.

METHODOLOGY

Watershed Delineation

The delineation of stream basins was executed in ArcGIS 10 by using a 90m SRTM DEM map

obtained from PHILGIS (Figure 3). The processing was based on flow accumulation and flow direction

of the streams as generated by the hydrogeology tool in ArcGIS 10. Five stream-nets were produced in

the study area as shown in Figure 4. The geometry of the sub-basins is generally characterized by a single

drainage network which is topographically controlled as evidenced by the radiating streams from areas of

high elevation.

Figure 3.3D slope shader 90m STRM DEM map of the study area as bounded by the box.Map generated by GlobalMapper.

Linear and Areal Morphometric Parameters

ArcGIS 10 was also used to measure the stream lengths of individual segments to be able to

calculate various morphometric parameters including drainage density, stream frequency, length ratio,

texture ratio and bifurcation ratio. These parameters, along with the stream orders, will be the main

factors that will evaluate the drainage network of each basin.


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Figure 4.Stream-nets delineated in the study area. A number wasassigned to a basin for presentation of results.

The Strahler (1952) method of assigning stream orders was employed in the study. This method

explains that two streams of the same order must combine to form a stream that is one order higher.

First-order streams are designated as the tributaries which combine to form higher order stream channels.

The highest order stream carries all the discharge of water that was transported by lower order streams.

Horton (1945) defined the drainage density (Dd) as the total length of streams in a basin divided

by the area of the basin, as shown by the equation

= (1)


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The bifurcation ratios of each order for each basin were calculated using number of streams of

each order counted using ArcGIS 10.1 .

Horton (1945) also proposed the Law of Stream Numbers, Law of Mean Stream Lengths, and

Law of Total Stream Lengths, given respectively by Equations (3), (4), and (5).

= (3)

= (4)

= (5)where Nu= number of streams of order u

Rb= bifurcation ratio

RL= length ratio

Lmu= mean length of streams of order u

Lu = total length of streams of order u

s = highest stream order in the basin

u = stream order of interest

The values of log(Nu), log(Lmu), and log(Lu) were calculated and plotted versus u for each basin

using Microsoft Excel 2013. A best-fit line was made for each plot, and by taking the R2values of the

best fit lines, the accuracy of the best-fit lines approximation was examined.The graphs are shown in the

Results and Discussion section.

R2values of the best fit lines were treated as a measure of how closely the basins obey Hortons

laws. The basins were compared on their degree of obedience to Hortons laws based on the R2values of

the best fit lines. The rationale for this is discussed in the Appendix.

RESULTS & DISCUSSION

Linear Aspect

Morphometric analysis was started with the division of the basin into five sub-basins, with their

perimeters and areas calculated from ArcGIS (Table 1).


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Sub-basin Area (km2) Perimeter (km)

1 60.08723088 42.50837581

2 68.88788012 57.17145037

3 103.960319 50.08501351

4 81.23358186 49.09494727

5 136.5596901 38.27103616

Table 1.Area and perimeters of the sub-basins in the study area.

Sub-basinNo.

Number of Streams per Order

N1 N2 N3 N4 N

1 26 6 2 1 35

2 17 4 1 0 22

3 28 10 2 0 40

4 16 4 1 0 215 39 13 3 1 56

TOTAL 126 37 9 2 174

Table 2.Summary of the number of streams in each stream order per basin.

Drainage basin analysis was started with the assignment of stream orders to the streams in the

five sub-basins, according to Strahlers stream orders, up to the fourth order. A total of 174 streams were

counted, with first-order streams comprising 72.41% of all streams, second-order streams 21.27% of all

streams, third-order 5.17% of all streams and fourth-order 1.15% of all streams (Table 2).

Sub-

basin

Stream Length (km) Total

Length

(km)L1 Lx1 L2 Lx2 L3 Lx3 L4 Lx4

1 43.350 1.667 7.821 1.303 17.224 8.612 2.599 2.599 70.995

2 40.095 2.359 11.714 2.928 18.864 18.864 - - 70.673

3 66.833 2.387 23.950 2.661 30.258 15.129 - - 121.042

4 42.312 2.645 18.543 4.636 13.690 13.690 - - 74.546

5 83.071 2.130 32.984 2.537 29.022 9.674 18.649 18.649 163.726

Table 3.Stream Lengths of the sub-basins arranged by their stream orders.

Slope steepness can be a factor in the stream lengths. Ideally, areas with steeper slopes will have

shorter basins. Sub-basin 3, which is situated in an area with sharp slopes, shows the shortest stream


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lengths. Consequently, sub-basin 5 has the longest stream length since it is located in an area with gentle

slopes. Stream lengths of the sub-basins are shown in Table 3.

Figure 5.Stream order vs. log total stream length

Figure 5 shows the relationship between the logarithm of the total stream length and stream

order. Upon inspection, it is concluded that the stream-net conforms to Hortons law of stream length.

The total stream length decreases as stream order increases, which is expected. Note that only sub-basins

4 and 5 have best-fit lines, as the curves for the other three basins are too far from linear to prove useful

in approximating the data points.

Table 4. Stream frequency, drainage density and constant of channel maintenance values for the sub-

basins in the study area.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

1 2 3 4

log(totalstreaml

ength)

Stream Order

log(total stream length) vs Stream Order

Red Basin

Blue Basin

Orange Basin

Cyan Basin

Green Basin

Sub-basinNo.

Area (km2)Stream Frequency

(km-2)Drainage Density

(km-1)Drainage

TypeConstant of Channel

Maintenance (km)

1 60.08723 0.582486487 1.181529831 M 0.846360349

2 68.88788 0.319359515 1.025910169 M 0.974744212

3 103.9603 0.38476219 0.521435348 M 1.917783296

4 81.23358 0.258513776 0.917669505 M 1.089716935

5 136.5597 0.410077088 1.198935531 M 0.834073204


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Areal Aspect

The overall drainage density of the study area is 1.111491502 km-1which indicates a medium

density basin based on the Deju (1971) quantification of drainage densities. Table 4 lists all the drainage

density values computed for each sub-basin. The drainage density of sub-basin 3 is significantly lower

than those of the other four which may be attributed to the high permeability and abundant vegetative

cover of alluvium in the south-eastern area of the Canipan Quadrangle. Sub-basin 4 is covered by most

alluvium too but the very low relief of the area allows the drainage network to form as part of the eastern

coastal plain.

The constant of channel maintenance is simply the inverse of the drainage density and is

indicative of the permeability of the bedrock. As expected and in line with the interpretation of the

drainage densities previously, sub-basins 3 and 4 registered the highest constant of channel maintenance

values. The relatively higher constants of channel maintenance of sub-basins 3 and 4 basically suggest that

large areas are needed to maintain 1 km of the stream channel which relate to their high permeability.

Figure 6. Lithologic map of the area overlain with the streams and stream-nets used in the study. Map

generated in QGIS.


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For stream frequencies, the overall value for the entire study area was calculated to be 0.386402

km-2. The values for stream frequency and drainage density indicate a positive correlation between the

two variables although their exact relationship cannot be accurately delineated with the data presented in

this paper. However, it may be said that the high values of stream frequency are related to the size of the

area covered in the Bulanjao Range which is a high relief and low permeability area.

The areas of the delineated stream nets generally cover a range of lithologies as shown in Figure

6. The stream head of all sub-basins are located in the topographic highs in the area where bedrock is

composed of ophiolitic rocks (ultramafic and volcanic rocks). The streams located in the ophiolitic

terrane of the Bulanjao Range shows a radial pattern. These streams then drain and incise through the

clastic rocks (for sub-basins 1 & 2) or through alluvial deposits (for sub-basins 3 & 4). Streams cutting

through the clastic rocks generally show a trellis pattern which indicates structural control by differential

erosion of folded sedimentary rocks. These clastic rocks are part of the Panas Formation which were

turbidites that underwent folding during the obduction of the Palawan Ophiolite onto the Palawan

Continental Block in the Early Miocene to Late Oligocene (Aurelio et al., 2013). Isolated or intermittent

streams occur frequently in the flat lying coastal plains (Cabrera, 1985) as seen in sub-basins 3 & 4. The

drainage network of sub-basin 5 is more complex than the others as it consists of a wide variety of

lithologies and the area covers the transition of the flat-lying plain to the sandstone areas at higher

elevation. The topographic control explains why the streams drain directly from the interbedded

sandstone area into the flat lying plains instead of also cutting through the massive sandstones.

Bifurcation Ratio

Mean Rbis lower for sub-basins 1 and 5, and higher for sub-basins 2, 3 and 4 (Table 5). Higher

bifurcation ratio can mean greater flood risk, since there are a large number of lower-order streams that

flow into a small number of higher-order streams, possibly causing the higher-order streams to overflow.

Thus, sub-basins 2, 3 and 4 may be more susceptible to flooding than sub-basins 1 and 5.

Analysis of bifurcation ratios is complex because of the diversity of lithologies, which cause

variations in bifurcation behavior within sub-basins. Although the mean Rbof sub-basin 5 is low at only

3.444, it can be seen from Figure 6 that bifurcation and stream density are high in the interbedded


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sandstone area of sub-basin 5, but bifurcation is low in areas of covered by alluvium in the same sub-

basin. Topographic control may be the cause of this difference; the interbedded standstones are located

in a mountainous region above the low-lying areas covered by alluvium, so most of the lower-order

branches of the stream are found in the topographically higher interbedded sandstone region. These

streams flow down to the higher-order, less branched streams in the lowland alluvium areas. Difference

in permeability may also play a role; the interbedded sandstones are probably less permeable than the

alluvium, thus causing greater bifurcation and stream density in the region of interbedded sandstones.

Since the low-lying alluvium region occupies a substantially larger percentage of the area of sub-basin 3

than the topographically higher interbedded sandstone, the mean Rbfor the entire sub-basin is low.

Mean Rb is low in sub-basins 1 and 5 despite their high drainage densities. This implies that

many of the streams in the two sub-basins are long, but do not bifurcate very much. This leads to large

total stream lengths (and therefore high drainage densities), but low mean Rb. On the other hand, sub-

basin 3 has a high mean Rbdespite having a low drainage density. This implies that most of the streams

in sub-basin 3 are short and bifurcate frequently, leading to a low total stream length (and therefore low

drainage density), but large Rb.

From the data, it appears that bifurcation ratio is negatively correlated with drainage density. The

basins with larger bifurcation ratios have lower drainage densities, and vice versa. This may be because the

basins with larger bifurcation ratios have numerous short streams, while the basins with lower bifurcation

ratios have fewer but longer and more sinuous streams. This may also be due to topographic factors.

High bifurcation ratio is more likely to occur in the topographically higher regions of the study area, since

the more numerous, low-order streams from the mountains flow down to the less numerous, high-order

streams in the lowlands. For the same reason, low bifurcation ratio is more likely to occur in the

topographically lower regions of the study area. Most of the area of sub-basins 1 and 5 are in

topographically lower regions, thus they tend towards lower bifurcation ratios, while most of the area of

sub-basins 2, 3, and 4 are in topographically higher regions, which thus they tend towards higher

bifurcation ratios.


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Sub-basinNo.

Stream Order,u

No. of Streams, Nu Rb Mean Rb

1

1 26 4.333

3.1112 6 3

3 2 24 1 -

2

1 17 4.25

4.1252 4 4

3 1 -

3

1 28 2.8

3.92 10 5

3 2 -

4

1 16 4

42 4 4

3 1 -

5

1 39 3

3.4442 13 4.333

3 3 4

4 1 -

Table 5. Summary of the individual and average bifurcation ratios of each sub-basin.

Horton Analysis

The values of log(Nu) for each stream order uwere calculated and graphed in Figure 7. Values of

R2 for each of the basins are shown in the graph. Sub-basin 4 has an R2 value of 1, which indicates

perfect adherence to Hortons Law of Stream Numbers. Sub-basin 1 has the lowest R2 value, which

indicates that it is the least adherent to Hortons Law of Stream Numbers.

The values of log(Lmu) for each stream order uwere calculated and graphed in Figure 8. Values

of R2 for each of the basins are shown in the graph. Sub-basin 4 has the highest R2value, which indicates

that it is the most adherent to Hortons Law of Mean Stream Lengths. Sub-basin 1 has the lowest R2

value, which indicates that it is the least adherent to Hortons Law of Mean Stream Lengths.

The values of log(Lu) for each stream order uwere calculated and graphed in Figure 9. Values

of R2 for each of the basins are shown in the graph. Sub-basin 4 has the highest R2value, which indicates

that it is the most adherent to Hortons Law of Total Stream Lengths. Sub-basin 2 has the lowest R2

value, which indicates that it is the least adherent to Hortons Law of Mean Stream Lengths.


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Horton analysis shows that sub-basin 4 has the highest R2values for the plots of the logarithm of

stream order, mean stream length, and total stream length vs. stream order. Sub-basin 1 had the lowest R2

values for the logarithm of stream order vs. stream order and logarithm of mean stream length vs. stream

order plots, and sub-basin 2 had the lowest R2 values for the logarithm of the total stream length vs.

stream order plot.

Figure 7. Graph of log(Nu) versus u for all five sub-basins in the study area. R2values shown for each

sub-basin.


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Figure 8. Graph of log(Lmu) vs ufor all five sub-basins in the study area. R2values are shown for each

sub-basin.

Figure 9. Graph of log(Lu) versus u for all five sub-basins in the study area. R2values are shown for

each sub-basin.


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Based on the properties of Hortons equations shown in the Appendix, Hortons Laws are most

applicable to a river basin where the lower-order streams are numerous and short, and the higher-order

streams are few and long. Conversely, the applicability of Hortons Laws decreases if lower-order streams

are relatively few and long and higher-order streams are relatively plenty and short. This is supported by

the R2data, which indicate that sub-basin 4 is the one that has the highest R2values. Sub-basin 4 has

relatively more short lower-order streams, and less long high-order streams. In contrast, sub-basins that

have low R2 values, such as sub-basins 1 and 2, have long and relatively few lower-order streams, and

have relatively short higher-order streams.

CONCLUSION

All of the five sub-basins are comprised mostly of first-order streams, accounting for 72.41% of

the total number of streams. Sub-basin 5 is the largest sub-basin in area and consequently has the largest

total stream length. Results of plotting the logarithm of the total stream length vs. stream order show that

slope angle is inversely proportional to stream length.

The basin was identified as a medium-type density basin based on Dejus density classification of

drainage systems. Drainage density has a positive correlation with stream frequency and an inversely

related relationship with constant of channel maintenance which were observed in the low drainage

density, high constant of channel maintenance and low stream frequency values for sub-basins 3 and 4

while the other way around were observed in sub-basins 1 and 2. Sub-basin 5 does not conform to this

trend due to numerous changes in lithologies and a complex characterization of relief. However, it was

observed that the ophiolitic rocks in the Bulanjao Range correspond to steeper slopes, higher stream

frequency, higher drainage density and lower permeability and show radial pattern of streams, and the

clastic rocks around the range are generally more permeable due to gentler slopes, lower stream frequency

and lower drainage density. The clastic rocks in the western side of the range were known to be folded

turbidites which allowed formation of trellis stream patterns. Intermittent streams were observed in the

eastern coastal plain of the area.

The bifurcation ratios appear to be negatively correlated with drainage density. This is probably

due to topographic factors; the sub-basins with low bifurcation ratios are mostly lowland areas, while the


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sub-basins with high bifurcation ratios are mostly highland areas. The highland areas with high relief have

greater bifurcation than the lowland areas with low relief. But the sub-basins with low bifurcation ratios

have longer and more sinuous streams, which gives them high drainage densities.

Using R2 as a measure of adherence to Hortons Laws, it was found that the sub-basins with

short but numerous lower-order streams and long but few higher-order streams have greater adherence to

Hortons Laws than the sub-basins with longer and fewer lower-order streams, and shorter and more

numerous higher-order streams.

REFERENCES

Aurelio, M.A., Forbes, M.T., Taguibao, K.J.L., Savella, R.B., Bacud, J.A., Franke, D., Pubellier, M., Savva,

D., Meresse, F., Steuer, S., & Carranza, D. (2014). Middle to Late Cenozoic tectonic events in

south and central Palawan (Philippines) and their implications to the evolution of the south-

eastern margin of South China Sea: Evidence from onshore structural and offshore seismic data.

Marine and Petroleum Geology, In Press, 1-16.

Bahrami, S. (2013). Analyzing the drainage system anomaly of Zagros basins: Implications for active

tectonics. Tectonophysics, 608, 914-928.

Blue Marble Geographics. (2014) Global Mapper 15. www.globalmapper.com

Cabrera, R. (1984). Report on the Geological Appraisal and Assessment of Guano and Phosphate Rock Deposits in

Southern Palawan (Technical Report).Manila: Bureau of Mines.

Deju, R. (1971). Regional hydrology fundamentals.New Jersey: Gordon & Breach Publishing Group.

ESRI. (2011). ArcGIS Desktop: Release 10. Redlands, CA: Environmental Systems Research Institute.

Hassen, M. B., Deffontaines, B., & Turki, M. M. (2014). Recent tectonic activity of the Gafsa fault

through morphometric analysis: Southern Atlas of Tunisia.Quaternary International, 338, 99-112.

Horton, R. (1932). Drainage basin characteristics. Bulletin of the American Geophysical Union, 13, 350-361.


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Lin, Z., & Oguchi, T. (2004). Drainage density, slope angle, and relative basin position in Japanese bare

lands from high-resolution DEMs. Geomorphology, 63(3-4), 159-173.

Pakhmode, V., Kulkarni, H., & Deolankar, S. (2003). Hydrological-drainage analysis in watershed-

programme planning: a case from the Deccan basalt. Hydrogeology Journal, 11, 595-604.

QGIS Development Team. (2014). QGIS Geographic Information Information System. Open Source

Geospatial Foundation Project. http://qgis.osgeo.org.

Schumm, S. A. (1956). Evolution of drainage basins and slopes in Bundland Amboy-New Jersey. Bulletin

of the Geological Society of America, 67, 597-646.

Strahler, A. N. (1952). Dynamic basis for geomorphology. Bulletin of the Geological Society of America, 63, 923-

938.

Strahler, A. N. (1952). Statistical analysis in geomorphic research. The Journal of Geology, 62, 1-25.

Tolessa, A., Rao, J., & Babu, V. (2013). Morphometric analysis of the Tandava river basin, Andhra

Pradesh, India. International Journal of Advanced Remote Sensing and GIS, 2(1), 56-69.

Tubau, X., Lastras, G., Canals, M., Micallef, A., & Amblas, D. (2013). Significance of the fine drainage

pattern for submarine canyon evolution: The Foix Canyon System, Northwestern Mediterranean

Sea. Geomorphology, 184, 20-37.

ACKNOWLEDGMENTS

We would like to thank the NIGS faculty who guided us in properly executing this research as beginners,

and for being understanding enough to extend the deadline multiple times. We are also grateful to our

adviser Sir Richard Ybaez who helped us in choosing this topic and suggesting the proper software for

our analysis.
http://en.wikipedia.org/wiki/Warren_Yba%C3%B1ezhttp://en.wikipedia.org/wiki/Warren_Yba%C3%B1ez


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APPENDIX A

Tables of the Lengths of Individual Stream Segments

SUB-BASIN 1

N1 Length (km) N2 Length (km)

1 01 4.211515504 2 01 1.246042275

1 02 1.007762492 2 02 0.610496691

1 03 1.70381097 2 03 2.682607689

1 04 1.75318132 2 04 1.132953457

1 05 1.523829033 2 05 2.056931357

1 06 5.314933114 2 06 0.092233647

1 07 3.279319435

1 08 0.827221859 N3 Length (km)

1 09 0.753009423 3 01 6.8119020841 10 0.725758201 3 02 10.41261425

1 11 2.987493175

1 12 3.4730053 N4 Length (km)

1 13 1.354245142 4 01 2.598824107

1 14 1.007887248

1 15 0.998577978

1 16 1.016672272

1 17 0.95091169

1 18 0.769804147

1 19 0.9253082911 20 0.869820373

1 21 2.913784656

1 22 1.053570113

1 23 1.427222429

1 24 1.194405798

1 25 1.020255351

1 26 0.286944853

SUB-BASIN 2


1 01 1.704775319 2 01 4.689319735

1 02 2.006812045 2 02 4.009035499

1 03 1.695060634 2 03 2.23240774

1 04 1.577462461 2 04 0.782983659

1 05 3.44583634

1 06 2.413509295 N3 Length (km)

1 07 3.424501619 3 01 18.8641553

1 08 2.912677061

1 09 2.3892560261 10 4.385554299


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1 11 4.397037248

1 12 0.838501505

1 13 1.425581156

1 14 1.528998096

1 15 2.351023273

1 16 2.180444528

1 17 1.417843926

SUB-BASIN 3


1 01 1.374986267 2 01 3.02003692

1 02 0.719853877 2 02 2.823875243

1 03 5.243230723 2 03 4.054510644

1 04 4.602731011 2 04 2.540641719

1 05 4.743012789 2 05 2.578658181

1 06 1.774542854 2 06 1.706659312

1 07 1.740110633 2 07 3.809027731

1 08 0.912066717 2 08 2.610373249

1 09 1.057666367 2 09 0.806550467

1 10 1.457376652

1 11 2.953407792 N3 Length (km)

1 12 1.955238601 3 01 18.8641553

1 13 1.297066094 3 02 11.39409633

1 14 2.759563118

1 15 2.173934342

1 16 1.709126772

1 17 1.997477587

1 18 2.179057835

1 19 3.352784093

1 20 1.980953319

1 21 4.168775214

1 22 2.849090128

1 23 2.245812895

1 24 2.2866664681 25 4.733516017

1 26 1.720480265

1 27 0.738995673

1 28 2.105534841

SUB-BASIN 4


1 01 2.182991612 2 01 2.607731776

1 02 1.939066533 2 02 3.7568209571 03 1.376148738 2 03 5.531694504


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1 04 1.489630106 2 04 6.646690446

1 05 1.573511863

1 06 1.65628691 N3 Length (km)

1 07 1.792103487 3 01 13.69034127

1 08 1.611591289

1 09 4.227686392

1 10 3.065635129

1 11 0.795400932

1 12 1.447361856

1 13 3.658486381

1 14 8.340069312

1 15 2.281466397

1 16 4.874864959

SUB-BASIN 5


1 01 1.346302314 2 01 3.494269163

1 02 2.291689636 2 02 0.368192055

1 03 1.981713461 2 03 2.190653903

1 04 1.729651102 2 04 0.39136827

1 05 1.008118316 2 05 1.625572354

1 06 0.839627892 2 06 1.994641318

1 07 1.384070328 2 07 2.759876016

1 08 0.640392203 2 08 2.322917175

1 09 0.826181883 2 09 1.073087742

1 10 6.984872249 2 10 5.757814432

1 11 1.521920498 2 11 0.832076615

1 12 1.151649748 2 12 2.057976379

1 13 3.12314786 2 13 8.115314432

1 14 2.826851206

1 15 1.201392931 N3 Length (km)

1 16 2.03274468 3 01 7.013117411

1 17 1.480118833 3 02 13.9912021

1 18 1.954706815 3 03 8.0179336391 19 1.035045874

1 20 3.066942031 N4 Length (km)

1 21 2.10981456 4 01 18.64909921

1 22 0.725902504

1 23 3.664643485

1 24 3.751138201

1 25 1.308376854

1 26 1.081099061

1 27 1.876695852

1 28 1.1834532341 29 0.907957248


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22

1 30 1.68471248

1 31 1.587863219

1 32 1.295223925

1 33 2.299800233

1 34 3.246831919

1 35 4.466074874

1 36 2.203146695

1 37 5.312732749

1 38 1.753906556

1 39 4.184638815


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APPENDIX B

R2of Best Fit Lines of log(Nu), log(Lmu), and log(L) vs. u as a Measure ofAdherence to

Hortons Laws

In the Methodology section, it was asserted that a linear relationship between x and log(y) must

imply an exponential relationship between x and y. In order to prove that this assertion is valid, let us

prove that an exponential relationship between x and y is a necessary and sufficient condition for a linear

relationship between x and log(y).

An exponential equation is any equation of the form:

= (6)

where a is an arbitrary constant, and b is a constant which serves as the base of the exponential

function. If a > 0 and b > 1, the function represents exponential growth. If a > 0 and 0 < b < 1, the

function represents exponential decay.

Let us first prove that an exponential relationship between x and y is a sufficient condition for a

linear relationship between x and log(y). We assume an exponential relationship, and show that it must

inevitably lead to the conclusion that x and y are linearly related. Taking the logarithm of both sides in

Equation (6), we get:

log()= log()= ()=[log()]

log()=[log()] (7)

Since a and b are both constants, log(ab) is also a constant. Equation (7) is of the form y = mx +

b1, with m = log(ab) and b1= 0 (we use b1instead of b to avoid confusion with the b used in Equations

(6) and (7)). Therefore, for any variable y dependent on a variable x, an exponential relationship between

y and x is a sufficient condition for a linear relationship between log(y) and x.

Now let us prove that an exponential relationship between y and x is a necessary condition for a

linear relationship between log(y) and x. We first assume a linear relationship between log(y) and x, and


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show that it must inevitably lead to the conclusion that y and x are exponentially related. Let us set up the

equation:

log()= (8)

which mathematically states that log(y) is linearly related to x. Raising both sides to the power of 10 in

order to remove the logarithmic term, we get:

= 10+=(10)(10)

= (10)(10) (9)

Since b1and m are constants, 10b1and 10mare also constants. Thus, Equation (9) is of the same

form as Equation (5), with a = 10b1and b = 10m. Therefore, Equation (9) is an exponential function, and

we have proven that an exponential relationship between y and x is a necessary condition for a linear

relationship between log(y) and x.

Combining this with our two findings, we have proven that an exponential relationship between

y and x is a necessary and sufficient condition for a linear relationship between log(y) and x. In other

words, y and x are exponentially related if and only if log(y) and x are linearly related.

From this finding, we can infer that deviations from linearity in a graph of log(y) versus x must

imply deviations from an exponential relationship between y and x. We can infer that the lower the value

of R2in the best fit line of a graph of log(y) versus x, the greater the deviation from exponential behavior

between y and x. It turns out that Hortons laws of stream numbers, mean stream lengths, and total

stream lengths are exponential functions, as we shall show.

Hortons laws of stream numbers, mean stream lengths, and total stream lengths are given

respectively by Equations (3), (4), and (5) in the Methodology section.

= (3)


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= (4)

= (5)

By rearranging the terms, Equations (3), (4), and (5) can be expressed respectively in the forms:

= ()( ) (10)

=

(11)

= (

)()

(12)

Equations (10), (11), and (12) are of the same form as Equation (6). Therefore they are

exponential functions relating Nuto u, Lmuto u, and Luto u, respectively. Because we asserted that R2of

the best fit line of a graph of log(y) versus x can be taken as a measure of how closely y and x follow

exponential behavior, we can infer that R2of the best fit lines of log(Nu), log(Lmu), and log(Lu) versus u

can be taken as a measure of how closely the drainage basin obeys Hortons laws of stream numbers,

mean stream lengths, and total stream lengths. The higher the R2, the more closely Hortons laws are

obeyed, and thus the more accurate the calculations based on Hortons laws. The lower the R2, the less

obedient the basin is to Hortons laws, and thus the less accurate the calculations based on Hortons laws.

morphometric analysis of five river basins in the bulaloc and canipan quadrangles in s palawan

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