Geomorphological parameters of river basins

1.0       Definition of geomorphological parameters of a river basin

In the water cycle, in which a river basin is a fundamental part of the study of the response to the precipitation entering a basin, several processes that alter the runoff occur. The basin geomorphology, where climatology is the most important factor, the type and use of the soil, the vegetation cover or the level of urbanization are involved in these processes.

There are measurable parameters that consider the importance of these processes in order to establish comparisons and related basins in a preliminary way. The most studied geomorphological properties of a basin are presented below:

1.1       Area of the basin

It is an area of land where all precipitation converges into a common outlet through secondary streams or ravines that flow into a main stream. Waters from rainfall, lakes or melting-glaciers that have not infiltrated the ground is called surface runoff and flows from the higher points to lower points due to gravity. Whereas the underground runoff —waters that have been infiltrated by the ground—run underground in the same way. This is the most used parameter in the study of the basin runoff.

The delimitation of a river basin is carried out through an imaginary line called divortium aquarum, which separates the opposite slopes from the peaks, and the waters of the precipitations flow on both sides of the imaginary line towards the streams of the continuous basins. The components in a basin are shown below (see Figure 1-1).

Figure 1-1. Components in a basin

1.2       Length of the main stream

This parameter frequently coincides with the length of the longest stream being a very representative criterion for the length of a basin. It can be measured considering all the sinuosity of the stream or the length of its axis.

1.3       Perimeter of the basin

This is the length of the divortium aquarum that shapes the outline of the basin area. This parameter is useful to differentiate the shape of the basin when comparing basins of the same area; that is, if it is elongated or rounded.

1.4       Shape of the basin

In order to characterize the shape of a basin, we used several parameters related to the ratio of area, perimeter or length of the longest water stream, which is defined as the distance from the basin outlet to the further upstream. The most usual indices are:

a)    Gravelius compactness coefficient

It establishes the ratio of the perimeter of the basin to the perimeter of a circumference whose area is equivalent to the surface of the corresponding basin. This index represents the shape of the surface of the basin, according to its delimitation, and its influence on runoff and the hydrograph resulting from a precipitation (López Cadenas de Llano & Mintegui Aguirre, 1987).

Otherwise, this index is based on the comparison with an ideal circular basin with its radially arranged streams that flow into the central point (López Cadenas de Llano, 1998). It is expressed by the following equation:

When the Kc value is one, the basin will have an almost circular shape. This means that the floods will have greater coincidence because the times of concentration of the different points of the basin will be equal. The time of concentration consists in the necessary time for a drop of water that falls in the furthest point of the basin to reach the point of outlet. In very elongated basins, the Kc value exceeds 2 (see Figure 1-2).

Figure 1-2. Comparison of the shape of basins according to the compactness coefficient values.

b)    Form factor

This is one of the parameters that explains the elongation of a basin. It is defined as the ratio of a basin area to its length. The parameter is defined by the following expression:

It is a dimensionless parameter and the length of the basin can be considered according to three different criteria: the length of the main stream considering its sinuosity, the length of the main stream considering its axis, or the distance in a straight line between the control point of the basin and its furthest point. In this paper, the last distance is considered.

If the shape of the basin is fairly circular, then the Ff value will be close to one; whereas the elongated basins will have a lower Ff. In elongated basins, the discharges are of smaller volume because the main stream is longer than the secondary streams and the concentration times for precipitation events are different, as shown in Figure 1-3. This case is different to what happens with the compactness coefficient.

Figure 1-3. Influence of the configuration of the hydrological network in the discharges.

On the other hand, the following table shows the shape that a basin can adopt according to approximate ranges of the Form Factor (see Table 1-1).

Table 1-1. Approximate ranges of the Form Factor

Source: Pérez, 1979

1.5       Drainage system

The drainage system is constituted by a main stream and its tributary streams. The longer the main stream, the more branches the drainage network will have. The most representative parameters are:

a)    Order of the streams

There are several criteria to establish the stream order to quantify the magnitude of the drainage network in direct surface runoff. The criterion used in this paper is based on the Strahler model, which assigns a number to each of the tributary streams in an increasing way, starting in the water divide line until reaching the main stream so that the final number indicate the order of the drainage network in the basin (see Figure 1- 4 ).

The highly dissected basins have a high stream order and the soils are relatively impermeable; hence, the response to a storm is rapid (Aparicio, 1996).

Figure 1-4. Branch of a main stream according to the Strahler model.

b)    Bifurcation ratio

It is a parameter that results from the relationship between the number of streams of a given order and the number of streams of the next higher order. Its ratio is the following:

Very high values of this ratio, which is determined to steep slopes, easily eroded soils. In addition, these basins present a wide hydrographic network with many tributary streams with rapid response to precipitations (Aparicio, 1996).

1.6       Drainage density

This parameter measures the total length of the irregular and regular watercourses of the basin and the total area of ​​the basin. It expresses the capacity to drain a given volume of water (López Cadenas de Llano, 1998). This parameter is very representative with respect to the topography of the basin in the studies.

Minimum values ​​of this relationship are related to regions with lowly erodible soil materials, poor vegetation cover and flat slopes. Whereas high values ​​point to precipitations that intervene quickly on river discharge. Generally, these regions have impermeable soil and strong slopes. It is expressed with the following equation:

Referential values are shown below (see Table 1-2).

Table 1-2. Approximate ranges of Drainage Density

Source: IBAL, 2009

1.7       Mean distance of surface runoff

This parameter shows the average distance that water from precipitation will have to cover to reach a nearby stream. The formula is as follows:

1.8       Frequency of rivers

This parameter relates the total sum of all stream orders (i.e.  the total number of all the rivers in the basin) to the total area. It shows the value of the number of rivers per Km².

1.9       Elevation of lands

The analysis of the variations in the elevation of lands with respect to sea level is a characteristic that influences the result of the slope of a basin. The most representative parameter is the following:

a)    Mean elevation of the basin

This value allows representing climatic and natural aspects that are interrelated with the basin through a climate pattern of the area (ANA, 2010). Its formula is the following:

b)  Hypsometric curve

The hypsometric curve is represented by a very important characteristic curve of a basin under study. This curve represents the elevations in meters above sea level on the axis of ordinates, and the percentage of the basin area that is above the indicated elevation on the axis of abscissas. It characterizes the relief (Ministry of Agriculture and Food, 1978). 

It is worth mentioning that, entering 50% of the area on the abscissa axis, we can obtain the mean elevation of the basin that intercepts with the hypsometric curve.

c)  Frequency Polygon for elevations

The frequency polygon diagram represents, on the ordinate axis, the partial percentage of the area of ​​a basin under study, and on the abscissa axis, the altitudes in meters above sea level included within that percentage.

The frequency polygon is a complement of the hypsometric curve and allows determining the most frequent altitudes in a basin through the highest percentage in the diagram.

1.10     Equivalent rectangle

It is the geometric transformation of the basin into an ideal rectangle that has the same area and perimeter. In this rectangle, the level curves become parallel lines to the minor side, these being the first and the last level curve, respectively (Ministry of Agriculture and Food, 1978). The sides of the equivalent rectangle have the following ratio:

1.11     Declivity of the streams

A greater declivity of the streams generates, as consequence, a faster rapidity of water runoff into the same streams. The most representative parameter is the following:

a)    Mean slope of the main stream

The influence of the topographic configuration in the erosion process of a basin and the formation of high discharges is presented according to the steeper or lower degrees of slope (López Cadenas de Llano, 1998). There are several criteria to define this parameter. The ratio of the assumed criterion is shown below:

Reference values are shown below (see Table 1 -3).

Table 1-3. Approximate ranges of the mean slope of the main stream

Source: IBAL, 2009

1.12     Declivity of land

a)    Mean slope of the basin

This index represents a mean value of all the slopes that make up the different topographic zones of the basin. To a large extent, it determines the speed of the surface runoff. There are several criteria for calculating the mean slope. The following table shows the topography adopted by a basin according to approximate ranges of its mean slope (See Table 1 -4).

Table 1-4. Approximate ranges of the mean slope of the basin

Source: Pérez, 1979

1.13     Coefficient of torrentiality

This parameter results from the ratio between the number of first-order water streams to the area of the basin. The greater the number of first-order streams and smaller the area, the torrentiality of the basin will be greater (Romero Díaz, A., 1987). This result means that water travels a short distance to go to the streams and the speed of discharge is greater. Its ratio is shown as follows:

1.14     De Martonne coefficient

This parameter is the ratio between the mean elevation of the basin, which is calculated by the hypsometric curve, to its area (Martonne, 1940). It scores high for basins with high peaks, and low in basins where flat lands predominate with similar areas. Its ratio is shown as follows:

As an example, we present these summary tables that show the geomorphological parameters of a basin under study called sub-basin Yauli:

Table 1-5. Number of streams according to order and bifurcation ratio in the sub-basin

Yauli

Source: Personal

Table 1-6.  Geomorphological characteristics in the sub-basin Yauli

Source: Personal

Geographical map of the sub-basin Yauli

BIBLIOGRAPHIC REFERENCES

Aparicio, F.  (1996).  Fundamentos de Hidrología de Superficie (Fundamentals of Surface Hydrology).  4th. Edit.  Mexico.  Editorial Limusa S.A.  PP 303.

López Cadenas de Llano & Mintegui Aguirre  (1987).  Hidrología de Superficie (Surface Hydrology).  Escuela de Técnica Superior de Ingenieros de Montes.  Madrid, Spain.  Edit. Salazar.  PP 222.

López Cadenas de Llano  (1998).  Restauración Hidrológica Forestal de Cuencas y Control de Erosión (Forest Hydrological Restoration of Basins and Erosion Control).  Ingeniería Medioambiental, TRAGSATEC, Ministry of Environment.  Madrid, Spain.  Edit. Mundi Prensa.  PP 945.

Martonne, E.  (1940).  Traité de Geographie Physique.  Armand Colin, Paris.

Ministerio de Agricultura y Alimentación (Ministry of Agriculture and Food) (1978).  Estudio de los Parámetros Geomorfológicos de una Cuenca (Geomorphological Parameters Study of a Basin).  Technical bulletin No. 2.  Peru.  PP 32.

Perez, J.  (1979). Fundamentos del ciclo hidrológico (Fundamentals of the Hydrological Cycle).  Universidad Central de Venezuela.  Facultad de Ingeniería Departamento de Meteorología e Hidrología.  Caracas, Venezuela.  PP 38.

Autoridad Nacional del Agua  (2010).  Evaluación de Recursos Hídricos Superficiales en la Cuenca del Río Mantaro (Evaluation of Surface Water Resources in the Mantaro River Basin) Retrieved from: http://www.ana.gob.pe/media/390314/evaluacion%20rh%20superficiales%20rio%20mantaro.pdf

IBAL S.A.  (2009).  Plan de Ordenación y Manejo Ambiental de la Microcuenca de las Quebradas Las Panelas y La Balsa (Environmental Management Plan of the Microbasin of Las Panelas and La Balsa ravines).  Retrieved from: http://www.cortolima.gov.co/sites/default/files/images/stories/centro_documentos/estudios/cuenca_panelas/DIAGNOSTICO/2.2ASPECTOS_BIOFISICOS.pdf

Romero Díaz, A.  (1987). Morfometría de Redes Fluviales: Revisión crítica de los parámetros más utilizados y aplicación al Alto Guadalquivir (Morphometry of River Networks: Critical review of the most used parameters and application to the Alto Guadalquivir).  Papeles de Geografía No. 12, 47-62. Retrieved from:  http://revistas.um.es/geografia/article/view/42391/40741