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Hydrological Sciences-Journal-des Sciences Hydrologiques, 42(5) October 1997

633

Further remarks on a distributed approach to sediment delivery

VITO FERRO htituto di Genio Rurale, Facoltâ di Agraria, Université di Reggio Calabria, Piazza San Francesco 4, 89061 Gallina de Reggio, Italy Abstract In this paper the sediment delivery relationship, i.e. the relationship between the basin sediment delivery ratio SDRW and the sediment delivery ratio SDRj of each morphological unit, i, into which a basin is divided, is firstly tested using morphological data (length, steepness and area of each unit) from six Sicilian and three Calabrian basins. Then a coefficient a of the sediment delivery relationship is related to several channel network parameters affecting the sediment transport efficiency. Finally, the spatial distribution of l37Cs activity measured in a small Australian basin is used for validating the predictive capability of the proposed distributed approach to sediment delivery.

Des observations complémentaires sur l'approche distribuée des processus d'apport de sédiments Résumé Dans cette note, on a d'abord établi une formule exprimant la production de sédiments, c'est à dire la relation entre le coefficient de production de sédiments à l'échelle d'un bassin complet SDRW et le coefficient de production SDRt de chacune des unités morphologiques selon lesquelles il a été divisé, en utilisant les données morphologiques (longueur, pente et aire de chacune des unités) de six bassins siciliens et trois bassins calabrais. Ensuite le coefficient a de la formule de production de sédiments a été exprimé en fonction de paramètres du réseau fluvial qui conditionnent l'efficacité du transport des sédiments. Enfin la distribution spatiale de l'activité en caesium-137, mesurée dans un petit bassin australien, a été utilisée pour établir la capacité de prévision de l'approche distribuée des processus d'apport de sédiments.

INTRODUCTION The prediction of the quantity of sediment which is transferred, in a given time interval, from eroding sources through a channel network to a basin outlet can be undertaken by coupling a soil erosion model with a mathematical operator expressing the sediment transport efficiency of the hillslope and of the channel network. If the process is studied at the mean annual temporal scale, a sediment lag between basin sediment yield and soil loss exists and is usually represented by the spatially lumped concept of basin sediment delivery ratio SDRW (Walling, 1983). The sediment delivery ratio SDRW generally decreases with increasing basin size because average slope decreases with increasing basin size and large basins also have more sediment storage sites located between sediment source areas and the basin outlet (Boyce, 1975). At the mean annual temporal scale, SDRW generally assumes values less than unity (ASCE, 1975; Renfro, 1975; Bagarello et ai, 1991); at the storm scale, eroded sediment can be deposited in the hillslopes or in the channel network Open for discussion until 1 April 1998

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and can be reworked in a following event yielding sediment delivery ratio values greater than one. Since sediment is produced from different source areas distributed throughout a basin, sediment delivery processes have to be modelled by a spatially distributed criterion. For modelling the spatial disaggregation of the sediment delivery processes the basin has to be discretized into morphological units (Bagarello et al, 1993), i.e. areas of clearly defined length and steepness. Sediment transport on the basin hillslopes is a physical process distinct from transport within the channel network. Therefore hillslope and channel sediment delivery processes have to be considered and modelled separately (Atkinson, 1995). At the mean annual temporal scale the sediment delivery problem can be simplified if the channel component is neglected. According to Playfair's law of stream morphology (Boyce, 1975; Richards, 1993) over a long time a stream must essentially transport all sediment delivered to it. In other words, the transport capacity of the river flow is not a limiting factor and sediment delivery losses occur at the hillslope scale only. The delivery effects into the channel system can be neglected for small basins in which well-developed floodplains do not exist. Under this hypothesis, Ferro & Minacapilli (1995) suggested taking into account the within-basin variability of the sediment delivery processes by calculating the sediment delivery ratio SDRt of each morphological unit into which the basin is divided. According to those authors, the SDR[ coefficient, which is a measure of the probability that the eroded particles are transferred from the morphological unit under consideration to the nearest stream reach, can be expressed as follows: /„

= exp -P

SDR,=exd-ptp,

= exp -p

./ = ! . S: :

(1)

in which tpi is the travel time of each morphological unit, lpJ and spi are the length and the slope of the hydraulic path (Fig. 1), /? is a coefficient which is assumed constant for a given basin, Np is the number of morphological units localized along the hydraulic path, and Au and stJ are the length and slope of each of the j morphological areas. The sediment balance equation, indicating that the sediment yield at the basin outlet is equal to the sum of the sediment produced by all morphological units into which the basin is divided, allows the relationship SDRW = (J3) to be obtained. Ferro & Minacapilli (1995) showed that this relationship is independent of the soil erosion model and that the p coefficient can be estimated by the following equation using only morphological data: (

,

L exp -P;=1

^N

tf-Vs..

SDR,., =

(2)

ÏX?s?S„

Further remarks on a distributed approach to sediment delivery

635

stream hydraulic path

Ipj -Xj+?v2+X 3 Aj

A-2

A-3

Fig. 1 Scheme for calculating the travel time of a morphological unit.

in which Xj and st are the length and the slope of the ith morphological unit, Suj is the area of the z'th morphological unit and Nu is the number of morphological units into which the basin is divided. For each basin, the pairs {ft, SDRJ calculated by equation (2) using SDRW values ranging from 0 to 1 can be represented by the following fitted relationship: SZ)/îw=exp{-1000ap)

(3)

in which a is a constant estimated by least squares. For a given j3 value, high a values correspond to basins characterized by low sediment delivery ratio SDRW values; in other words the a coefficient can be used as an "indicator" of hillslope sediment transport efficiency. In this paper the sediment delivery equation (3) is tested by analysing six Sicilian basins, with 21 sub-basins, and three Calabrian basins. Then, using the morphological data for the basins investigated by Ferro & Minacapilli (1995), the a coefficient values are also related to several channel network parameters affecting sediment transport efficiency. Finally, the spatial distribution of 137Cs activity measured in a small Australian basin is used for validating the predictive capability of the proposed sediment delivery distributed approach.

THE SEDIMENT DELIVERY RELATIONSHIP AND CHANNEL NETWORK PARAMETERS For testing the sediment delivery relationship of equation (3) six Sicilian (Fig. 2) and three Calabrian basins were selected . For each basin and sub-basin, the name, the

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corresponding drainage area Sw (km2) and the number Nu of morphological units are listed in Table 1.

1

MAZZARRA

2

ARANCIA

3

ELICONA

*

IIMETO

5

ZAPPULLA

6

ROSMARINO

?

ORETO

«

IATO

9

FA5TAIA a La Chinta

10

BELICE DESTRO a Piana dtgll Albantsi

11

BELICE SINISTRO a Garcia

12

SAIA a P r i n i

13

IMERA MERIDIONALE a Petralla

Fig. 2 Sicilian basins investigated in this research.

Table 1 Basin characteristics. Basin Sub-basin Arancia lato lato 1 Iato2 lato 3 Iato4 Lordo Mazzarrà Mazzarrà l Mazzarrà 2 Mazzarrà 3 Mazzarrà 4 Metramo Oreto Oreto 1

sw 2

(km ) 25.0 153.6 15.6 31.4 52.3 131.3 10.3 82.4 29.2 24.0 18.3 15.6 14.0 120.1 16.1

K 133 918 82 193 355 794 73 646 169 130 140 91 104 773 125

a 0.91 1.51 1.99 2.00 1.21 1.37 1.06 0.97 0.66 1.20 0.77 1.10 0.92 1.27 0.85

P* 0.000531 0.000365 0.000242 0.000318 0.000509 0.000371 0.000631 0.000585 0.000573 0.000558 0.000761 0.000640 0.000624 0.000581 0.000815

Basin Sub-basin Oreto 2 Oreto 3 Pristeo Rosmarino Rosmarino 1 Rosmarino 2 Rosmarino 3 Rosmarino 4 Rosmarino 5 Zappulla Zappulla 1 Zappulla 2 Zappulla 3 Zappulla 4 Zappulla 5

sw 2

(km ) 22.6 25.2 12.4 96.6 30.8 16.5 60.2 12.2 74.5 137.7 30.5 39.7 56.7 59.6 10.7

K

a

P*

156 166 89 478 129 106 309 49 368 773 160 219 306 357 66

0.90 1.34 0.75 1.49 1.90 2.20 1.59 1.96 1.63 1.29 1.25 1.22 1.32 1.24 1.34

0.000861 0.000512 0.000850 0.000434 0.000318 0.000391 0.000399 0.000360 0.000393 0.000557 0.000611 0.000544 0.000546 0.000539 0.000512

Further remarks on a distributed approach to sediment delivery

0

2

4

637

6 1000 p

Fig. 3 Sediment delivery relationship for the Metramo basin.

Figure 3 shows, as an example for the Calabrian Metramo basin, values of /? and SDRW calculated by equation (2), using SDRW values ranging from 0 to 1, and the fitted equation (3). For all basins listed in Table 1, the analysis confirmed the suitability of equation (3) to represent the sediment delivery relationship. Table 1 also lists the a value of each investigated basin or sub-basin and values of a parameter ft* defined below. For a given morphological unit i, the probability that the eroded particles arrive into the nearest stream reach is assumed proportional to the probability of nonexceedence of the travel time tpi (Ferro & Minacapilli, 1995). According to this concept the following relationship is deduced from equation (1): P, =

-In F

(4)

in which F, is the empirical frequency of non-exceedence of the travel time tpJ. For a given basin, the empirical cumulative frequency distribution (CDF) of the travel time tpJ of each morphological unit is calculated. Then by using the CDF of the defined f5\ variable (equation (4)), each basin is characterized by the median fl\ value, /?*, obtained for a frequency value F{fi\) equal to 0.5 (Table 1). Figure 4 confirms that, for the basins investigated, the variable 1000a/?* is largely independent of the basin area Sw and assumes a median value equal to 0.62. The sediment transport efficiency of the hillslopes increases for decreasing values of the median travel time of the morphological units into which the basin is divided. According to the definition and criterion for calculating the morphological unit travel time, the sediment transport efficiency is affected by basin size and slope and some properties describing the river network such as the total length of streams or the number of stream sources. In fact, when the basin size, described by basin area or main channel length, increases the hydraulic paths increase too; in other words the sediment transport efficiency decreases because there is an increase in both the probability that the

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1.5 1.25 Calabria

*

1

Sicily

o m o 0.75 9 Ê f