STUDY ,OF MAXIMUM FLOODS 1.N SMALL BASïNS OF TORRENTIAL TYPE

Rafael HERAS Dr. Civil Engineer

Angel LARA Civil Engineer

ABSTRACT

The methodology of study is summarized for small b= sins of torrential character and it is applied to one of the gu- llies of the Gran Canaria island, considering the geological and geomorphological conditions of the basin and also the principal physical characteristics of the same one. In relation to all these physical characteristics and of a statistical complete study of in- tensities, the hydrogram is established for different hypothesis and the type of hydrogram is studied more unfavorable in relation in relation to the duration-intensity-frequency curves of maximum precipitations in 24 hours.

RESUMEN

S:e resume la metodologia de estudio para pequeñas cuencas de carácter torrencial y se aplica a uno de los barrancos d e la isla de Sran Canaria, teniendo en cuenta las condiciones geo- lógicas y geomorfológicas de la cuenca y también las principales c z racteristicas físicas de la misma. En función de todas estas carac- terísticas y de un estudio estadístico completo de intensidades, se establecen los hidrogramas para distintas hipótesis y se estudia el hidrograma tipo más desfavorable en función de las curvas duración- intensidad-frecuencia de precipitaciones máximas en 24 horas.

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1. Generalities

This method has been applied to the Tirajana gully, which is one of the most important in the south zone of the Gran Canaria island. The high part of their channel is formed by a big number of gullies which have its origin to an altitude of about 1,700 m., following the receiver basin a direction sensibly north-west-southeast. The maximum longitude of the channel is 27 km. and the total area of the basin is 71,4 km2. Its location in the island is reflected in the graph number 1.

2. Geology of the basin of the Tirajana gully

The region where the Tirajana gully is located is the southeast of the Gran Canaria island.

For its location, it participates of the geological characteristic of the half south of this island, appearing on the surface the most ancient complex which have taken part in its formation, such as are the Ancient Basalt of the Serie I, of basaltic alkaline-olivinical composition and formed by sub- parallel running out with pyroclasts intercalated, the Trachysienite complex with ignimbrites associated, of rhyolithical, panthelithical and trachyphenol- ithical compositions, and the Phonolithical serie, composed in this zone by running out, pius, end ignimbrites, frequently with laminar parting parallel to the direction of the flow.

All these series are located principally in the middle zone of the gully, existing also in form of little cropping out, principally phonolithic and trachysienite, in the high part of the basin. O n the other hand, all the mentioned series are practically impermeable in the process of infiltration from the surface and, particularly, the series of Basalts I and Trachysienite Complex, forming the majority of the substratum on which are seated the most recent superficial formations.

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The series Pre-Roque Nublo and Roque Nublo, which have its maximum power in the interior of the island appearing largely disseminated in the Tirajana gully, specially in its middle and high zones.

The said series are composed lithologically by angular fragments constituting xenolithical agglomerate with intercalations of tephrithical lavas, basaltical running out and sediments. In these series, of moderate permeability, a quick fall in the level of water is produced, being therefore, its pondage coefficient very law.

The most modern basaltical serie that appear on the surface, is the correspondent to the Basalts II, of basaltical olivinical composition and constituted by aa and pahoehoe lavas, more permeable than the previous formations. These lavas cover principally the northcast zone of the fully disseminating also in smaller proportion in its middle zone.

Finally, this basin present a genuine characteristic which is distinguished from the contiguous ones, since that a big part of its surface occupied by sedimental formations, of which, the avalanches of various ages constitute the principal cropping out of the zone of heading, while the low zone of the basin is covered by deposits of recent alluviums, with bigger porosity and higher permeability.

3. Physical Data

In order to know the characteristics of the basin to use them fundamentally in the estimation of its velocity of propagation of maximum flood, it has been calculated for the same one, the following characteristics:

, longitudinal section . surface . perimeter . equivalent rectangle , hypsometrical curve . index of compactness . index of slope

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The values obtained have been the following:

surface perimeter

17.4 k m 2 57.5 k m

compac tnes s equivale nt index rectangle

1.90 L = 26. 10 1 = 2.74

slope index

O. 263

4. Maximum floods

4. 1. General planning

The principal probleme presented is the absolute lack of direct data of gauging with sufficient extension and guarantee, as much in the studied basin as in the rest of the island, therefore it is not possible to study the flood from the direct data of maximum flows neither by comparison with others basins, affinitive basins hydrologically. Therefore, using the maximum available data, it has been performed the complete study of floods by empirical and hydrometrical methods, constrasting each one of the estimated parameters with data obtained by direct procedures in the Gran Canaria gully.

4. 2. Empirical methods

In the formation of maximum floods intervenes multiple causes, whose possibility of coincidence characterizes the risk. The surface of the receiver basin is one of the causes among the principal ones, since there exists a good correlation between the basin area and the maximum flood.

Using formulas that could tie directly the flows of floods with the surface of the basin and others in which intervene others hydrological parameters.

A m o n g the existing formulas it has been used those which are in the joined chart; these formulas has been selected in relation to the hydro- logical characteristics of the basin in the present study. In the mentioned

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SANTI

GREAGER

FORTI

ZAPATA

chart it has been given, in the same way, the values which are the result of its application.

423 (Tr = 500 años) KUICKLING 255 (Tr = 100 anos)

520 (Tr = 500 años) TURAZZA 820 (Tr = 500 anos)

626 (Tr = 500 años) HERAS 780 (Tr = 500 anos)

272 (Tr.= 100 años) G. QUIJANO 292 (Tr = 100 anos)

The big dispersion of the results obtained of the same ones can be observed.

4. 5. Hydrometrical method

This method consists in trying to reproduce the meteorological phenomenon and, in this case, we will use the method of the isochronal curves, to which it is necessary to discompose the surface of the basin in some zones (si, s2, . . . sn) limited by lines (isochrones) in which the water fallen in one of these ones delays in arriving to the point in wich w e estimate the flood, sucesive times of value t, 2t, . . . , being our case t half hour.

The velocity of the water if fixed by experimental and empirical methods, in relation to the physical data, fundamentally of the longitudinal section and index of slope, and other characteristics peculiar of the basin (vegetation, geology and so on). In our case, w e have fixed as velócity 6 km/hour in the low zone of the basin, up to an altitude of 600 m., above sea level, and 7 km/hour in the high part. Once fixed this one, the pointe are obtained from which delays in arriving the water to the place studied a same time and with which, as contour line of a topographical elevation, we can draw the isochronical lines obtaining simultaneously the concentration time, that in our case is of 4.3 hours.

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If we contrast this time with the one given by any of the empii ical formulas existing (for example, Giandotti), we obtain a difference, by an excess of about 1 hour. This appreciable difference is justified by the quantity of sediment load which carry the floods in this type of gullies, and produce a disminution in the mean velocity of propagation. The incidence of the considered velocity in the flood peak is small, and so is only influenced by the concentration time.

The isochrones once obtained, multiplying the area encircled among the same ones by the intensity of precipitation and the supposed runoff coefficient, the flow is obtained in the studied point due to the precipitation in each one of the zones.

They are, therefore, necessary the data of maximum intensities of precipitations in the basin for a determined period of recurrence. To realize the statistical study of the intensity we will use from among the several laws of distribution of frequencies which are applied in hydrological problems, Gumbel’s law, which is used principally for distributions of m a x i m u m values. This law has been applied to the usable series of the interior stations of the basin and to a series of stations of lap. All of them can be seen in the graph number 1. The maximum annual values of precipitation in 24 hours for several periods of recurrence are reflected in the charts numbers 1, for the stations of the interior of the basin, and number 2, for the exterior ones.

In order to adjust the distribution of the values of maximum precipitation in 24 hours and considering the probability of coincidence of said values, the Gumbel’s law has been applied to the monthly data in all the stations, for October, november, december, january, february and march, resulting to be the months of October and november the most unfavourable in relation to the floods, as it is deducted of the observation of the chart number 3.

Also, to contrast the distribution of maximum values in the basin, the isomaximum curves has been designed with the values of maximum precipitation in 24 hours to times of recurrence of 50, 100 and 500 years for the maximum maximorum annual values and for the maximum values of October (which is the month of maximum intensity). These isomaximum curves can be seen in the graphs numbers 5 up to 10 and have served like contrast of the values obtained by Gumbel and also to adjust the mean intensity of precipitation and its variation with the time.

With regard to the runoff coefficient, there is hardly no data for maximum maximorum flows, therefore considering the impermeability of the middle and high zone and the greater permeability of the low zone, we estimate some runoff coefficients of O. 85, O. 80 and O. 50, respectively, for each one of the three considered zones. To estimate these coefficients, which could be reached in strong floods which would be produced after several days

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of considerable precipitation, it has been realize studies with all usable data and considering the physical, geological and geomorphological characteristics of the basin, detached in high, middle and low zones, it has been obtained mean runoff coefficient of O. 78 that seems to be reasonably adjusted to the characteristics of this basin.

The duration of the storm is an important factor in the determination of the maximum flood, the maximum value of the peak flow is used to obtain with durations of storm about the concentration time. In our case, we have supposed durations of storm of 1, 2, 3, 4, 5, 6 and 8 hours. The precipitation for the several hypothesis has been estimated in relation to the distribution of the maximum precipitation in 24 hours for smaller periods, obtained from the short available data, which have been contrasted with direct measures, obtaining the following values:

Duration of the storm (hours)

the precipitation in 24 hours 35 43 57 69 75 ao 86

1 2 3 4 5 6 8 Precipitation in percentage of

Although it is considered little representative the compiled data of maximum intensities in several stations of the basin in study, the said values are kept, putting us in security side. At the same time and in order to procure greater aproximation to the actual phenomenon, we can consider three stretch of different mean intensity coincident with the high, middle and low zones, previously mentioned in the estimation of the runoff coefficients.

For the different hypothesis of duration of the flood, the intensity, together, is distributed in the time in such a manner that in the hydrograms of duration 1 and 2 hours it is considered all the unitary intensity estimated and for 3 or more hours it has been supposed uniform intensity during the two first hours and decreasing in a 20% each hour more of duration until reaching a minimum of a 20% in the storm of 6 or more hours.

The isochrone curves used in the calculation of the hydrograms as well as the different zones considered can be seen in the graph number 11, and the hypothesis that the storm i s produced simultaneously in all the basin has been made since that the hypothesis that began in the head waters and goes displacing in the direction of the gully appears excessively unfavourable for the climatological conditions of the basin. Once the runoff values, intensity of precipitation and duration of the storm, are fixed, we can obtain the flows due to each zone and the accumumulated of these ones give the flows that would reach the sea in each moment, supposing an infinite time of rain. Displacing horizontally this curve in the time of duration of rain and calculating the curve difference of the two, we obtain the actual flows that reach in each moment.

In relation to the study realized it has been considered the hypothesis (i), applying in all of them some runoff coefficients of O. 80, O. 85 and O. 50 for each one of the different zones considered and the distribution of intensities already cited for durations higher than two hours.

A s summary of the hydrograms obtained, in the graphs numers 12 up to 15 figure the correspondent to a duration of storm of 4 hours and periods of recurrence of 100 and 500 years, the same for the m a x i m u m - maximorum values of precipitation, as for the m a x i m u m of October. In the chart number 4 appears the distribution of intensities in space and time for these hypothesis.

C ONCLUSIONS

As a result of the calculations realized by the different methods and considering that the hydrograms obtained must be affected by a reducent coefficient in relation to the hypothesis of calculation, in which it has been considered some m a x i m u m values of the runoff coefficient and some m a x i m u m intensities which must be reduced due to the non-coincidence of the distribution in the space and time of m a x i m u m values in all the stations, w e obtain the results that can be seen in the annexed chart.

The hydrogram type estimated figure in the graph number 16.

The statistical study of m a x i m u m precipitation in 24 hours has been realized in the period of 21 years, 1949-50 - 1969-70 and the data of the usable stations has been contrasted and, generally, it appears to have enough guarantee, but by the extension of the period used, resulted as a risk to extrapolate for times of recurrence higher than 100 years.

The results obtained are conditioned by the empirical-theorical methods used, due to the absolute lack of series of m a x i m u m flows, although w e estimate that the m a x i m u m difference with the actual values will not exceed 15%.

The study is only related to m a x i m u m values of flood and in it has not been considered the effect of the solid flows.

of hydrograms with durations of storm of 1, 2, 3, 4, 5, 6 and 8 hours. (1)

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