Feb 24, 1974 - ratios of a basin depend firstly on precipitation inputs(Gomer,. 1994); but it is not so in a semi-arid climate: the spatial distribution of preliminary ...
Influence of antecedent precipitation index on the hydrograph shape
Influence of antecedent precipitation index on the hydrograph shape A. Benkhaled 1, B. Remini 2 and M. Mhaiguene 1 Université de Chlef, Algeria; 2Université de Blida, Algeria
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INTRODUCTION
The antecedent precipitation index (API) was first defined in the 1940s by M.A. Kohler. During this period of hydrology, scientists were seeking techniques which would simplify the relationships of rainfall and runoff. Various techniques which tried to conceptualise soil characteristics, through the application of infiltration theory and other models, were too complex, especially when trying to apply them to a very large basin. The Curve Number method of the US Soil conservation Service (SCS, 1972) is well-known. One considers the antecedent moisture by means of three classes, distributed from dry to wet. The API index influences the soil storage capacity. A significant quantity of precipitation brings the soil to a lower storage capacity; subsequent precipitation increases the runoff volume and the peak output. If the intensity of subsequent precipitations is high, it decreases baseflow and rise times. The two combined parameters produce steep hydrographs with significant peaks (Llamas, 1993). The interest in calculating an index of moisture generally arises at the time of modelling the output function. This index is regarded as an essential parameter of the rainfall-runoff relationship. Generally, storm characteristics can be determined from an adequate network of precipitation stations. However, determining soil moisture throughout the basin is difficult. Variations in soil and surface characteristics, vegetation differences and land use add to the complexity. When soil moisture data are not available, for reasons of operational management basin, one often uses: l
l l
base flow data from before the hydrograph begins to rise, which represents in an integral way the succession of the antecedent rains (whose infiltration generated baseflow); an index of the previous rains or IPA. The most recent rain has the greatest effect on soil moisture; satellite imagery, bringing information on the soil moisture (Crist and Cicone, 1984; Rimbert and Vogt, 1991).
The first index is seasonally sensitive and does not reflect changes due to previous precipitation. The second (API) provides good results. The variable API, from which the procedure is named, is a rough representation of the initial soil-moisture condition and can also be determined easily. It tries to utilise the accumulated precipitation and, at the same time, take into account evaporation and infiltration. By using the antecedent precipitation index, week of the year and storm precipitation and duration as parameters, Kohler and Linsley (1958) developed a relationship between storm runoff and precipitation by a graphical method of coaxial relations. It is based on the premise that if any important factor is omitted from a relation, then the scatter of points in a plotting of observed values of the dependent variable versus those computed by the relation will be at least partially explained. The API procedure is really a set of three variables relations arranged with common axes to facilitate computation. The API index for any day is equal to that of the previous day multiplied by the factor K. If any rain occurs, it is added to the index. The value k varies with physiographic basin characteristics, evaporation, temperature and humidity. It = I0 Kt
(1)
I0 is the initial value of the IPA, It is the reduced value after t days. K is a recessive factor ranging between 0.85 and 0.98 (Kohler et al., 1951) According to Casenave (1982), I Kn = ( I Kn-1 + Nh, n1) eat where I Kn I Kn-1 Nh, n-1 t and N at
(2)
: value of the index in mm before rain N : value of the index in mm before the rain n1 : height of rain in n1 mm : duration in hours between the two rains of row n-1 : : : coefficient of adjustment depending on the geographical factors.
Hydrology: Science & Practice for the 21st Century. Volume I © 2004 British Hydrological Society
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A. Benkhaled, B. Remini and M. Mhaiguene According to Hansmann (1994) at = 0.09 It is accepted that in a moderate zone, the rainfall-runoff ratios of a basin depend firstly on precipitation inputs(Gomer, 1994); but it is not so in a semi-arid climate: the spatial distribution of preliminary moisture is therefore fundamental (Vogt and Gomer, 1993). In such climates, the variability of initial moisture constitutes a significant and non constant parameter in the modelling of the runoff and the associated processes. The nature of the marny rock and scarce precipitation do not allow the formation of saturated zones, close to the surface. But, as the catchment area is never wetted in a uniform way, the distribution of soil moisture cannot be perfectly constant. It should be noted that one can introduce the API parameter into the precipitation and soil factors, because the API represents a height of rainfall which fell in an interval from a preceeding time and at the same time the preliminary state of saturation from the soil. The measurement of soil moisture is generally difficult and little practised in Algeria. This study, undertaken in the basin of the Ouahrane river, subjected directly to the climatic risks of the orographical barrier located on the southern frontage of the area, aims to identify the process responsible for irrationality of these risings and the conditions for their appearance. Among the latter is soil moisture which denotes the capacity for absorption as the runoff coefficient. This fact means that any search or use for a runoff model requires knowledge of the soil moisture before precipitation, or at least that of an index representative of this moisture.
SETTING
On the arid semi basin of Ouahrane Wadi, like much of nearby north Algerias basins, the rise in floods is sudden and brutal, being able to cause considerable damage. These types of floods are defined with precision in space and time, and the more violent ones occur between the beginning of September and the end of November. They can, however, occur more tardily, at the beginning of February. The catchment area of the Ouahrane river extends to 270.15 km2 and is located in the northern part of the large basin of Cheliff (Figure 1). Ouahrane river is a small tributary of the Cheliff river. This basin is controlled by three rainfall stations and a gauging station. The basin is limited to the east by the basin of the Fodda river, to the west by the Ras river, in the north by the basin of the Allala river, and in the south by the basin of the Sly river. It extends between longitudes 1° and 1°3 E and between the latitudes 36° and 36°24 N. The average annual temperature is 18°C. Climate
The catchment area of the Ouahrane river is influenced by the Mediterranean climate, with a mean inter-annual precipitation of 389 mm. The spatial distribution of precipitations indicates two rainfall sections opposing two different sectors: The sector of Ouled Farès receiving less than 400 mm of rain, which is located at the lower regions, below 200 m. It occupies nearly 40% of the catchment area. The sector of Benairia located at more than 350 m, where
Méditerrannée Sea Ouahrane basin
Fig. 1 Map of Ouahrane catchment area
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Influence of antecedent precipitation index on the hydrograph shape the annual mean rainfall varies between 280 and 740 mm. This sector occupies approximately 60% of the basin.
Resources of Algiers over the period 1974 to 1990. RESULTS
Geology
The catchment area of the Ouahrane river is characterised by an impermeable marny substratum covering 80% of the basin area. These localised tender lithological formations in the north of the basin are continuously subjected to a strong mechanical erosion, contrary to the formations located in the southern part of the basin, consisting of conglomerate and red sand and characterised by average permeability.
The analysis of the statistical shape coefficients for each hydrograph enables us to note that for the steep shape of the hydrograph rise, the spread is positive (A p > 0), i.e. there is a strong distribution, and a positive skewness (C S > 0), i.e. there is an asymmetry on the right-hand side of the hydrograph for the majority of floods (Table 2). For the flat shape of hydrograph rise, we have a negative spread, i.e. there is a weak distribution and an asymmetry on the right (A p < 0, C S > 0).
Land use
The main agricultural activity is mixed farming and the cultivation of cereals in the catchment area of the Ouahrane river. Data
Twenty-three events were used in this study. The values of the API were calculated from rainfall data (Table 1). The timesteps are 5, 10, 20 and 30 days. The flow discharges were obtained from the services of the National Agency of Hydraulic
DISCUSSION
The types of runoff occurring on a drainage basin and their spatio- temporal variations will have an important effect on the hydrological relationships applying to that basin. Variations in the these runoff processes and their relative magnitude from basin to basin will thus fundamentally affect similar relationships between the hydrological responses of basins (Pilgrim, 1983). The simplest division of runoff types is between direct storm runoff and base flow.
Table 1. Values of API index 5, 10, 20 and 30 days for the 27 selected floods. Date
Rainfall (mm)
API (mm) 5 days
API (mm) 10 days API (mm) 20 days
API (mm) 30 days
24-02-74 02-04-74 29-04-74 18-10-74 05-03-75 02-02-76 05-02-76 01-05-76 28-09-76 23-01-77 19-10-78 20-09-79 13-01-81 25-02-82 02-09-82 13-10-86 09-12-86 23-12-86 08-11-87 01-01-88 19-03-89 04-06-89 03-01-90
23.9 20.3 18.9 43.6 40.7 22.0 78.1 43.0 33.1 27.7 31.8 21.2 25.2 34.5 57.4 44.5 37.7 30.6 21.2 29.9 26 25.2 19.9
53.0 172.3 13.7 37.2 31.2 19 39.5 16.1 7.4 0 51.5 3.7 6.2 27.6 3.7 0.5 3.8 10.4 0 15.8 1.1 0 31.8
83.5 180.4 26.7 48.6 31.2 62.5 73.5 16.9 7.4 0 51.5 3.7 6.2 85.1 4.2 6.2 12.0 17.2 0 15.8 1.1 3.5 31.8
113.1 199.8 208.7 54.0 31.2 62.5 84.5 41.2 7.4 81.8 119.5 3.7 259.8 110.2 4.2 40.9 43.6 123.3 7.5 25.8 21.6 4.4 40
101.4 186.0 88.6 52.1 31.2 62.5 84.5 28.6 7.4 35.3 119.5 3.7 117.4 85.7 4.2 40.6 15.7 111.4 0.6 17.6 1.1 4.4 31.8
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A. Benkhaled, B. Remini and M. Mhaiguene Table 2. Statistical parameters of the selected floods. Believed Standard Mean N° deviation
Mode
Median
Variation coefficient
Spread
Skewness
Observations
01 02 03 04 05 06 07 08 09 10 12 13 14 15 16 20 21 22 23 24 25 26 27
6.25 2.17 2.19 2.17 2.54 11.44 6.13 11.50 3.54 61.25 0.19 234.6 6.86 2.92 1.48 0.19 1.46 0.45 0.25 4.10 1.56 0.91 1.46
5.70 16.88 15.25 15.13 5.80 93 22.70 40.50 19.90 59.86 0.35 94.57 5.70 12.42 3.87 0.35 0.86 0.94 0.19 3.41 13.94 8.34 9.60
0.88 0.83 0.79 0.78 1.10 0.96 0.64 1.28 0.97 1.30 0.62 0.79 1.28 0.85 0.85 0.65 1.99 1.80 1.75 0.92 1.20 0.18 0.31
1.01 0.78 1.42 1.41 1.15 0.35 1.13 0.51 0.10 0.82 -0.52 1.64 0.82 0.84 -1.01 -0.52 -1.40 1.12 -0.88 0.98 1.01 0.90 0.90
1.48 -0.75 0.18 0.16 1.53 1.03 0.33 1.45 0.94 0.89 0.85 0.21 0.89 0.56 1.47 0.85 1.61 1.53 1.57 1.15 0.69 -1.68 -1.34
A p > 0, C S > 0 A p > 0, C S < 0 A p > 0, C S > 0 A p > 0, C S > 0 A p > 0, C S > 0 A p > 0, C S > 0 A p > 0, C S > 0 A p > 0, C S > 0 A p > 0, C S > 0 A p > 0, C S > 0 A p < 0, C S > 0 A p > 0, C S > 0 A p > 0, C S > 0 A p > 0, C S > 0 A p < 0, C S > 0 A p < 0, C S > 0 A p < 0, C S > 0 A p > 0, C S > 0 A p < 0, C S > 0 A p > 0, C S > 0 A p > 0, C S > 0 A p > 0, C S < 0 A p > 0, C S < 0
8.59 16.128 12.77 11.63 12.05 134.16 16.67 128.17 24.08 94.54 0.27 98.63 34.77 11.40 2.58 0.19 1.98 2.88 1.51 35.76 15.15 11.84 8.79
9.75 19.31 16.10 14.82 10.97 140.18 25.93 100.14 24.83 72.54 0.34 99.65 27.18 12.88 3.02 0.29 0.94 1.59 0.86 38.92 14.94 13.20 9.75
The suddenness of the flood rise is one of the outstanding characteristics of the hydrology of this Mediterranean basin. In addition, the rainfall depth is not a factor determining the start of the rise, and the flows can remain very low for a long time, in spite of significant precipitations. The floods of February 1976, October 1978, September 1979 and September 1982, are examples of these hydrological processes (Table 3). On September 03, 57.4 mm fell before the flow of 5 m3 s-1, considered as the flood flow, was reached; the API was low (3.7 mm). Flows remain very low for all this period. Conversely, on October 19, 1978, 33.8 mm was enough; here, the value of the API was high compared to the first value (51.5 mm). One could make the same comments for the floods of February 04, 1976 and September 79. For the first, a significant rainfall (62.6 mm) fell, to reach a peak of 93.16 m3 s-1, noting that the value of the API was low (3.7 mm) whereas for the second (February 04, 1976), 22.0 mm was sufficient to reach a peak of 56.5 m3 s-1, but the value of the API was higher (19.0 mm). This is true under completely different moisture conditions in the basin. Once started, the rise is significant and continuous, even if the intensities are low as it was the case in October 1978 (intensity < 10 mm/h generally). If the intensities are stronger,
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which is frequently the case, the rise of the flood is very fast, giving, for example on February 07, 1976 (when 78.1 mm fell with strong intensities) 45.3 m3 s-1to 397.5 m3 s-1 in five hours. As with the previous events, (February 05, 1976, September 76 and September 79) the important flows occurred only when a certain threshold of saturation was exceeded. During the flood of February 05, 1976, the first rainy episode, which took place before the soil was saturated, involved only one rise of 46.9 m3 s-1. The second, when the soil is saturated, causes a 10 times greater discharge. These results, in themselves, are not surprising. It is well known that the runoff coefficient increases progressively with precipitation, because of the extension of saturated surfaces, or through the progressive closing of the soil surface which involves a decrease in infiltrability. The characteristics of floods of January 1977 and January 1988 given in Table 3 are very different, thus the weakness from the runoff coefficient and the brevity of the flood in spite of significant precipitations (68.6 mm and 27.7 mm respectively for these floods). However, there is an influence of the lower API where the soil presents a relatively dry condition.
Influence of antecedent precipitation index on the hydrograph shape Table 3. Characteristics of selected floods. Date
API (mm)
Rainfall (mm)
Basic flow (m3 s-1)
Rising time Peak flow (hours) (m 3 s-1)
Ratio initial max Flow / basic flow
Ratio final Hydrograph max Flow / shape final flow
23-27/02/74 02-05/04/74 29/04-01/05/74 18-20/10/74 05-07/03/75 28/02-04/03/79 02-04/02/76 05-09/02/76 01-03/05/76 28-30/09/76 23-26/01/77 19-22/10/78 20-22/09/79 13-15/01/81 25-27/02/82 03-06/09/82 06-09/11/87 31/12/87-05/01/88 13-16/10/86 09-12/12/86 23-30/12/86 19-21/03/89
53.0 172.3 13.7 37.2 31.2 123.5 19.0 39.5 16.1 7.4 0.0 51.5 3.7 6.2 27.6 3.7 0.0 15.8 0.5 3.8 10.2 1.1
23.9 20.3 18.9 43.6 40.7 101.5 22.0 78.1 43.0 33.1 27.7 31.8 21.2 25.2 34.5 57.4 21.2 29.9 44.5 37.7 30.6 26
2.82 1.70 1.5 0.157 0.31 5.42 7.1 2.92 0.677 0.133 0.086 5.95 0.02 0.184 0.482 0.002 0.0 0.012 0.072 0.04 0.186 0.009
10.00 7.30 1.50 1.05 1.16 9.0 6.0 8.0 1.40 5.0 8.0 1.40 1.10 3.10 5.00 2.30 1.16 2.50 6.00 5.20 30.00 3.00
9.87 11.08 10.66 9.61 8.01 58.97 7.95 27.6 18.26 24.34 5.33 26.22 14.24 3.43 3.51 9.91 3.49 5.05 27.4 10.20 13.06 8.35
7.507 7.09 3.11 5.46 5.97 34.40 3.40 19.9 4.08 19.44 1.55 17.96 10.96 2.14 2.92 5.77 2.22 3.37 10.99 3.25 4.15 1.79
The floods of December 1986 and March 89 give a better example of the influence of the low value of the API, in spite of a significant sum of precipitations (90 mm and 127.6 mm). Here still, it is the temporal distribution of the rainy episodes rather than their characteristics in themselves, which is responsible for the exceptional peak discharge. Indeed, although the intensities were fairly strong, they cannot, alone, explain the importance of the peak flow, as for example at the beginning of the rainy episode of the 01 to 03 May 1976 where a strong intensity of 44.00 mm h-1 in 13 minutes caused a peak of 81.3 m3 s-1. Usually, such strong intensities are the prerogative of summer storms which do not reach a state of saturation of the basin, whereas the autumn rains responsible for substantial storms, have generally only relatively moderate intensities as in the case for the flood of October 1978. The intensity is lower than 15 mm h-1 but the basin presents a soil relatively wet. The API index was 51.5 mm. For the floods of February and April 1974, the value of the API was high (53.0 mm and 172.3 mm respectively). The soil surface was relatively wet and the rainfall had a low intensity (8.28 mm h - and 9.0 mm h -1); the peak discharge is not
24.1 53.2 43.3 32.7 40.4 437 56.5 397.5 81.3 280 1.20 200 93.16 33.86 8.65 78 5.38 8.90 137 54.88 32 23.22
steep flat steep steep steep steep steep steep steep steep flat steep steep steep flat steep flat steep steep steep steep steep
significant (24.1 m3 s-1) though the values of the API are high in comparison with those of September 1979. The variability of storm runoff processes can also be illustrated on the basin under different conditions. Several results indicated that runoff occurs from only part of the basin in smalls storms or under dry antecedent conditions, but that the whole of the drainage basin contributes runoff in large storms and under wet antecedent conditions. The effect of runoff occurring on areas from the basin outlet is illustrated in Figure. 2. This hydrograph rise (N°1) occurred on a very wet basin after about 100 mm of rain in the previous two days. This flood represents the influence of two significant parameters during production of a significant peak flow, intensity and rainfall depth. Initially, the API was high (123.5 mm), the total amount of precipitations is 101.5 mm with moderate intensities. The two combined parameters cause a peak flow (437.5 m3 s-1) without common measurement with the others floods. This hydrograph shape is typical of events where antecedent conditions have been wet. The high peak, time base and steep recession were the significant characteristics of floods occurring under these conditions. The hydrograph rise (N° 2 ) shown in Figure 3 occurred for
85
60
400 350 300 250
50
3/s )
200 150 100
3/s )
500 450
D é bit Q
A. Benkhaled, B. Remini and M. Mhaiguene
40
D é bit
30 20 10
50 0
0 0
50
100
150
0
20
Temps (heure) Fig. 2 Hydrograph rise to February, 28 1979
60
80
100
Fig.3 Hydrograph rise to April, 02 1974. (High API High precipitation)(High API Low precipitation)
1.2
90 80
1
3/s )
70
3/s )
40
Temps (heure)
0.8
60 50
0.6
D é bit Q
40 30
D é bit
0.4
20
0.2
10 0
0 0
50
100
150
0
Temps (heure)
50
100
Temps (heure)
Fig. 4 Hydrograph rise to September, 02 1982
Fig. 5 Hydrograph rise to June , 02 1977. (Low API High precipitation)(Low API Low precipitation)
500 450 400 1
3/s )
350 300 250
D é bit
200 150
4
2
3
100 50 0 0
20
40
60
80
100
120
140
Temps (heure) Série1
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Série2
Série3
Série4
Fig. 6 Typical hydrographs for Ouahrane river 1 high API High Precipitation 2 high API Low Precipitation 3 Low API High Precipitation 4 Low API Low Precipitation
Influence of antecedent precipitation index on the hydrograph shape wet conditions but lower rainfall was derived from a flood less than half as large. Recession flows after an event with this condition have much lower discharges and flatter slopes than those after extreme wet conditions. An opposite case of this hydrograph type is shown in Figures 4 and 5, where one can see the lower peak flow, the short time base and the flatter recession limb (N° 3 and N° 4). Runoff volumes of events after dry periods are generally small fractions of the rainfall, whereas they are almost equal to half the rainfall for the events after wet antecedent conditions (Figure 6). On the other hand, from the available graphic results, it seems that the start of the hydrograph rise is different for the two conditions mentioned above. Under wet conditions before the rise, the magnitude of hydrograph rise is very significant whereas it is lower for dry initial conditions. CONCLUSION
The influence of antecedent precipitation index upon storm runoff depends upon the extent to which it has been considered. Through the API index it is possible to provide a simple and good method of understanding runoff processes. The first conclusion is that the API for five days is a better index. Recognition of this fact seems to be an important step for the remaining analysis. The exceptional rise which could be observed during the first days of March 1979 seems to validate the well-known hydrological process of contributing areas. The importance of the peak flow and thus the shape of the hydrograph depends on the high rains that occur once that saturation is reached. Finally, it arises from this study that the API index which characterises the state of soil moisture is a significant factor in the transformation process of rainfall into flows.
REFERENCES Casenave, A. 1982. Le mini simulateur de pluie- conditions dutilisation et principes de linterprétation des mesures. Cahiers Orstom. Serie hydrolog. 19(4). Crist, E.P. and Cicone, R.C. 1984. Application of the Tasseled Cap concept to simulated Thematic Mapper Data. Photogramm. Engin.&Rem. Sens., 50(3). Gomer, D. 1994. Ecoulement et érosion dans des petits bassins versants à sols marneux sous climat semi aride méditérranéen. Thèse de docteur ingénieur . Université Technique de Karlsruhe Hansmann, W. 1994. Beschreibung des Infiltrationsverhaltens von Mergelböden under semiaridem Klima im Noreden Algeriens. Vertieferarbeit Institut für Wasserbau und Kulturtechnik. Kohler, A.M. 1944. The use of crest stage relation in forecasting the rise and fall of the flood hydrograph. U.S.Weather Bureau. Kohler, A.M. and Linsley, K.R. 1951. Predicting the runoff from storm rainfall. U.S Weather Bureau Research Paper N° 63. Linsley, K.R, Kohler, A.M. and Paulhus, H.L.J. 1982. Hydrology for engineers. Mc Graw Hill. Llamas, J. 1993. Hydrologie générale : principes et applications. Ed. Gaêtan Morin Pilgrim, D.H. 1983. Some problems in transferring hydrological relationships between small and large drainage basins and between regions. J. hydrol, 65, 4972. Rimbert, S. Vogt, T. 1991.Données satellitaires et paysages factoriels. Spatial analysis and population. D. Pumain (Ed). J. libbey. Paris. Soil Conservation Service SCS. 1972. National Engineering Handbook. Section 4, Hydrology. U.S Departement of Agriculture, Washington D.C. Vogt, T. and Gomer, D. 1993. Determination of runoff and soil erosion under semiarid conditions using GIS to integrate Landsat TM, DEM and hydrological field data from the Oued Mina project, Algeria. Proc. Workshop on soil erosion in semi arid Mediterranean areas. Taormina, 28-30 October. Consiglio nazionale delle ricerche. Roma.
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