Testing a distributed approach for modelling ... - Semantic Scholar

Hydrological Sciences—Journal—des Sciences Hydrologiques, 43(3) June 1998

425

Testing a distributed approach for modelling sediment delivery VITO FERRO Istituto di Genio Rurale, Facoltà di Agraria, Université di Reggio Calabria, Piazza San Francesco 4, 1-89061 Gallina di Reggio Calabria, Italy e-mail: [email protected]

PAOLO PORTO & GIUSEPPA TUSA Dipartimento ITAF, Sezione Idraulica, Facoltà di Agraria, Université di Palermo, Viale delle Scienze, 1-90128 Palermo, Italy

Abstract Both the theoretical basis of a distributed approach to sediment delivery and its agreement with basin sediment yield measurements are tested. At first, by using morphological data of five Apulian and four Calabrian basins, the applicability of a theoretically-based relationship for evaluating the sediment delivery ratio of each morphological unit SDRh into which a basin is divided, is verified. Using the morphological data of the nine investigated basins, the sediment delivery relationship, i.e. the relationship of the basin sediment delivery ratio SDRW and SDRh is tested. The analysis showed that the relationships, proposed by Ferro (1997), establishing the dependence of the a coefficient of the sediment delivery relationship on the median travel time and on a drainage density index are yet applicable. The influence of the scale of the basin topographic map on the sediment delivery distributed approach is also studied. The analysis showed that the ratio between the a coefficient and the median travel time is scale-invariable while the link between the coefficient a and the drainage density index has to be re-calibrated because the drainage density index is dependent on the map scale used. Finally, the predictive capability of the sediment delivery distributed model is validated using the sediment yield measurements carried out in three small Calabrian basins and in the Apulian Triolo basin. The analysis showed that the model accuracy is dependent on the temporal scale used and the model reliability increases from the event to the annual scale.

Validation d'une approche distribuée pour la modélisation de l'apport de sédiments Résumé Dans cet article les auteurs ont vérifié l'adéquation d'un modèle théorique fondé sur une approche distribuée tenant compte du mécanisme de transfert des sédiments en s'appuyant sur les données expérimentales de bassins versants. L'utilisation des données morphologiques relatives à neuf bassins situés dans le Sud de l'Italie a d'abord permis d'adapter une méthode théorique pour évaluer le coefficient d'apport solide SDRt de chaque unité élémentaire. Ensuite, le même critère de division morphologique a été utilisé pour vérifier la relation liant le coefficient d'apport solide SDRW de chaque bassin aux coefficients SDRt. En faisant l'hypothèse que cette dépendance peut être exprimée au moyen d'un coefficient a caractéristique du bassin versant, les relations entre ce coefficient et le temps de transfert moyen d'une part, les paramètres du réseau fluvial d'autre part ont également été vérifiées. La même analyse, conduite sur différentes cartographies, a permis d'établir que le rapport entre le coefficient a et le temps moyen de transfert est invariante d'échelle. Au contraire le rapport entre le coefficient a et les paramètres du réseau fluvial doit être calée chaque fois car les paramètres du réseau fluvial dépendent de l'échelle. Enfin, en utilisant les données d'apports solides à l'estuaire relatives à trois petits bassins calabrais et au bassin de la rivière Triolo situé dans les Pouilles, la capacité de prédétermination du modèle a été vérifiée.

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Vito Ferro et al.

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L'analyse a démontré que cette capacité dépend de l'échelle temporelle et qu'elle s'améliore très sensiblement lorsque l'on passe de l'échelle de l'averse à l'échelle annuelle.

INTRODUCTION Identifying areas of the landscape that are most sensitive or susceptible to erosion is necessary for the development of land management and soil conservation strategies, for maintaining soil productivity and developing a sustainable agriculture, and for reducing downstream sediment yield (Quine & Walling, 1993). These needs stimulated both the study of within-basin variability of the sediment delivery processes and the use of spatially-distributed models coupled with GIS (Ferro etal, 1994). The quantity of sediment which is transferred in a given time interval from eroding sources through the hillslopes and channel network to the basin outlet can be predicted by coupling a soil erosion model with a mathematical operator expressing the transport efficiency of the hillslope and the channel network (Walling, 1983; Bagarello et al., 1991). At the basin scale, a physically-based approach needs to divide the basin into individual fields (Kling, 1974; Richards, 1993) or morphological units (Bagarello et al., 1993), i.e. areas of clearly defined aspect, slope length and slope steepness, and to describe, in each area, the detachment, transport and deposition of particles (Meyer & Wischmeier, 1969; Nearing et al., 1989). The present difficulties of physically-based modelling, due to the need for numerous input parameters, the scale of basin discretization, the uncertainties of the selected model equations, etc., increases the attractiveness of & parametric approach, like RUSLE (Renard et al., 1994), coupled with a spatial disaggregation criterion of the sediment delivery processes (Ferro & Minacapilli, 1995). Sediment delivery processes have to be modelled by a spatially-distributed criterion since sediments are produced from different source areas throughout the basin. The distributed approach allows for within-basin variability and takes into account that: (a) low slope downstream areas have low delivery ratios (Boyce, 1975); (b) much of the sediment yield is produced in a small percentage of the total basin area; and (c) steep areas near main channels contribute to both erosion and sediment yield while steep fields remote from the channel network are characterized by local erosion but contribute little to sediment yield. Sediment transport in the basin hillslopes is a physical process distinct from transport within the channel network, therefore the corresponding sediment delivery processes have to be modelled separately (Atkinson, 1995). At the mean annual temporal scale, the channel component of the sediment delivery problem can be neglected according to Playfair's law (Boyce, 1975; Richards, 1993) establishing that over a long time a stream essentially transports all sediment delivered to it. Schumm (1972) assumes that in 100 years a stream will discharge essentially all of the sediment it receives; in other words the 100-year

Testing a distributed approach for modelling sediment delivery

All

average delivery ratio for streams is essentially 1 (Novotny & Chesters, 1989). For the floodplain system, Walling et al. (1986) measured significant sediment deposits while Wilkin & Hebel (1982), using the same measurement technique, found floodplain degradation. Leopold et al. (1964) suggested that sediments eroded from a drainage basin are only temporarily stored in floodplains and that floodplain aggradation is essentially balanced by degradation. For a small basin having an ephemeral channel network and with no welldeveloped floodplains, the delivery effects into the channel system can usually be neglected for modelling at the scale of individual events too. Under this hypothesis (mean annual temporal scale or small basin) Ferro & Minacapilli (1995) suggested that it was possible to take into account the within-basin variability of the sediment delivery processes by calculating the sediment delivery ratio, SDRj (kg kg"1), of each morphological unit into which the basin is divided. According to the authors, the SDRi coefficient is a measurement of the probability that the eroded particles arrive from the considered morphological unit to the nearest stream reach. In previous studies (Ferro & Minacapilli, 1995; Ferro, 1997), the analysis, carried out for 13 Sicilian and two Calabrian basins, of the empirical cumulative distribution function (cdf) of the travel time showed that the SDRt coefficient has the following expression: /„

SD^ = e x p ( - p ^ ) = e3cp

P

: exp P

I-r=

(1)

in which tpi is the travel time of each morphological unit (m), lpi (m) and spJ (m m"1) are the length and the slope of the hydraulic path from the considered morphological unit to the nearest stream reach, p (m"1) is a coefficient which is assumed constant for a given basin, Np is the number of morphological units localized along the hydraulic path, ALj and su are the length (m) and slope (m m4) of each j morphological unit localized along the hydraulic path (Fig. 1). The sediment balance equation, establishing that the sediment production of the basin outlet is equal to the sum of the sediment produced by all morphological units into which the basin is divided, yields the relationship between the basin sediment delivery ratio SDRW (kg kg"1) (Walling, 1983) and SDRt, known as the sediment delivery relationship. Ferro & Minacapilli (1995) showed that the sediment delivery relationship is independent of the soil erosion model and that the P coefficient can be estimated by the following equation using only morphological data: ^5s~S„

X ex p ^p PJ

SDR„ = -

J

(2)

I«S., in which /, and s, are the length (m) and slope (m m"1) of the /fh morphological unit,

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Fig. 1 Scheme used for calculating the navel time for each morphological unit.

Suj is the area of the ith morphological unit (m2) and Nu is the number of morphological units into which the basin is divided. For each basin, the pairs (P, SDRJ calculated by equation (2) using SDRW values ranging from 0 to 1 can be represented by the following relationship: SDRw=exp(-\000a$)

(3)

in which the constant, a (m), is estimated by the least squares method. For a given p value, high a values correspond to basins characterized by small sediment delivery ratio (SDRJ values and therefore Ferro (1997) suggested that a could be used as an indicator of the hillslope sediment transport efficiency. The progress of the sediment delivery distributed modelling is also dependent on the availability of measurements able to establish the link between the eroded soil leaving an individual morphological unit and the patterns of erosion and deposition occurring along the hydraulic path from the considered area to the nearest stream reach. Tracer techniques are useful to overcome the problems due to representativeness of plot measurements at hillslope and basin scale and to spatial variability. The most widely used tracer, which possesses the greatest potential in sediment yield studies, is the radionuclide caesium-137 (Ritchie & McHenry, 1990; Walling & Quine, 1991, 1992). Caesium-137 data were used to validate erosion model comparing the caesiographic map, i.e. the map plotting the lines (isocaes) of equal B7 Cs activity (Bq m"2), with the soil erosion spatial distribution simulated by the model (De Roo & Walling, 1994). Ferro (1997), for validating the SEdiment Delivery Distributed (SEDD) approach based on RUSLE (Renard et al., 1994; McCool et al, 1989) and the sediment delivery ratio SDRh suggested the comparison of the sediment yield Yt (t) of


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each morphological unit with the corresponding caesium-137 loss LCs, (mBq): ZCs,= Cs r e / -

(4)

'CsAS,

in which ,37Cs, is the caesium-137 concentration (mBq m2) of the i morphological unit calculated taking into account all isocaes falling into the considered morphological unit and Csre/ is the 137Cs input measured in an undisturbed site (with no erosion or deposition). The analysis, carried out for a small Australian basin (Morris & Loughran, 1994), showed a good correlation between Yt and LCs(. Recently the predictive capability of the SEDD model was also positively verified for a Sicilian basin (Ferro et al., 1998) by comparing the calculated sediment yield and the 137-caesium spatial distribution obtained by a kriging interpolation procedure based on 129 sampling sites uniformly distributed over the basin area. In this paper, both the theoretical basis of the sediment delivery distributed approach and its agreement with basin sediment yield measurements will be tested. At first, by using morphological data of five Apulian and four Calabrian basins, the applicability of equation (1) will be verified. Then the dependence of the a coefficient, appearing in the sediment delivery relationship (equation (3)), on the median travel time and on a drainage density index will be tested. The influence of the scale of the basin topographic map on the sediment delivery distributed approach will also be investigated. Finally, using the sediment yield measurements carried out in three small Calabrian basins and in the Triolo (Apulian) basin, the predictive capability of the SEDD model will be validated.

TESTING THE RELATIONSHIP BETWEEN HILLSLOPE SEDIMENT DELIVERY PROCESSES AND CHANNEL NETWORK PARAMETERS For studying the cdf of the travel time tpJ of each morphological unit, five Apulian basins (Casanova, Celone, Salsola, Triolo and Vulgano) and four Calabrian basins (Ciappetta, Coccari, Tombino and Valli Cupe) were selected. Table 1 lists the name, drainage area, Sw (km2), number of stream sources (magnitude) p., the median value Table 1 Characteristic data of investigated basins. Basin Casanova Celone Salsola Triolo Vulgano Ciappetta Coccari Tombino Valli Cupe

s«,2

(km ) 52.3 85.8 43.0 53.8 94.0 10.1 9.7 3.9 4.9

LI

40 35 29 14 34 92 35 31 76

t,„ (m) 3648.3 2647.3 2847.6 2803.8 10 486.8 633.6 779.4 392.5 495.9

a (m) 2.952 2.412 2.254 3.950 9.432 0.420 0.626 0.388 0.324

P* 1

(m- ) 0.00019 0.00025 0.00024 0.00023 0.00020 0.00106 0.00089 0.00177 0.00142

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cCASANOVA o CELONE

x CIAPPETTA o COCCARI A TOMBINO . VALU CUPE

oSALSOLA D TRIOLO .VULGANO

c

-30000

-----

i

6 1

-20000

-10000

- 6 ••

0

-6000

-4000

-2000

-tp,i [m] -tp.i M Fig. 2 Cumulative distribution function of the -tpJ variable (a) for the Apulian and (b) for the Calabrian basins.

2.5

5

1000 P Fig. 3 Sediment delivery relationship (a) for the Apulian Celone basin and (b) for die Calabrian Tombino basin.

of the variable X,/si 5 , representing the median travel time t,„ (m) into the morphological unit, and the a coefficient of equation (3) for each investigated basin. Figure 2 shows that for the investigated basins the relationship between the logarithm of the empirical frequency F, of non-exceedence of the travel time tpJ, InF,, and the variable ~tpi is approximately linear for each basin. Consequently, equation (1) was assumed to be applicable for evaluating SDR^ Figure 3 shows, as an example for the Apulian Celone basin (Fig. 3(a)) and for the Calabrian Tombino basin (Fig. 3(b)), values of p and SDRW calculated using equation (2), using SDR„ values ranging from 0 to 1, and the fitted equation (3). The analysis, for the basins listed in Table 1, confirmed the suitability of equation (3) to represent the sediment delivery relationship.


431

1

«APULIA 0 CALABRIA

2-

•

* ci O O

o

• •

og 0-

L

O

1

100 75 50 S„ [km2] Fig. 4 Values of the variable lOOOap* for the investigated basins. 0

25

For a given i morphological unit, if SDRt is assumed equal to the empirical frequency F, of non-exceedence of the travel time tpi, equation (1) gives: P,=-

-lnF,

(5)

By using the cdf of the defined (3, variable, each basin is characterized by the median value p* (m1). Figure 4 confirms that, for the investigated basins, the variable lOOOap* is largely independent of the basin area, Sw, and assumes a median value equal to 0.62 (Ferro, 1997). The only exception is the Vulgano basin because it is characterized by flatter hillslopes (higher travel time values) than the other basins investigated. Ferro (1997) showed that the sediment transport efficiency of the hillslope, which is represented by the a coefficient (small SDRW values correspond to high a values), decreases for increasing tn values according to the following equation: a = 0.001116 fw

(6)

Figure 5 confirms the applicability of equation (6) also for the nine investigated basins. Taking into account the definition and calculating criterion of tpJ, Ferro (1997) suggested that in addition to basin size and slope the sediment transport efficiency is affected by some properties describing the river network such as the total length of streams or the number of stream sources. In fact, the shortest travel paths from the considered morphological area to the first stream reach correspond to stream networks which are more and more branching (having high drainage density values). Ferro (1997), comparing basins having different size and following Shreve's (1966, 1967) scheme, which represents the channel network as a branching tree with neither lakes nor islands, suggested the following equation in which the drainage density index (2LI—\)ISW appears:

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Vito Ferro et al.

100

"~

7 /

10

• / "3 o

0.1

7

0.1

|

• APULIA

|

O CALABRIA

1

10

100

measured |m|

Fig. 5 Comparison between measured a values (Table 1) and those calculated using equation (6). 100

B

10

•% o

i

~~

o/

• APUUA O CA1.ABRIA

r

0.1 0.1

1

10

100

measured [m] Fig. 6 Comparison between measured a values (Table 1) and those calculated using equation (7).

2ja.-l

a = 0.2491 + 0.00095 / „ - 0.0102

(7)

Figure 6 clearly shows that equation (7) can also be applied to the Apulian and Calabrian basins investigated.

THE INFLUENCE OF MAP SCALE ON SEDIMENT DELIVERY DISTRIBUTED MODELLING The estimation accuracy of the morphological variables, such as area, slope length, slope steepness, stream length and number of stream sources, depends on the scale of


433

the available maps. Previous analyses (Ferro & Minacapilli, 1995; Ferro, 1997) were developed only using basin topographic maps at the scale 1:25 000. For testing the influence of the map scale on sediment delivery distributed modelling, nine Calabrian and eight Sicilian basins were selected. For the Calabrian basins, topographic maps at a scale of 1:10 000 were available while maps at a scale of 1:50 000 were used for the Sicilian basins. Table 2 lists the basin name, the drainage area Sw (km2), the magnitude ji, the median travel time tm, the a coefficient and the p* value for each investigated basin.

Table 2 Characteristic data of basins with different map scales. Basin

Map scale

Lordo Mangiafico Metramo Molaro Piètre Blanche Salariace Salito Salito2 Torbido Belice D Elicona Jato Mazzarrà Oreto Rosmarino Timeto Zappulla

1:10 1:10 1:10 1:10 1:10 1:10 1:10 1:10 1:10 1:50 1:50 1:50 1:50 1:50 1:50 1:50 1:50

(a) o

S„ (km2) 12.7 3.22 19.4 11.6 12.9 4.1 1.8 1.0 2.4 342.6 52.3 123.0 109.1 108.2 99.1 87.2 139.8

000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000

p 491 88 152 370 551 134 50 25 80 293 81 72 114 57 97 136 228

o (b)

1 • LORDO o MANGIAFICO A METRAMO A MOLARO o SALITO

-1.5

Jr8Jf 2P

° °

A

/

J •

«

'

A

-3000

p*(nr') 0.001604 0.001304 0.001568 0.002694 0.001863 0.002636 0.001775 0.003219 0.001702 0.000236 0.000222 0.000241 0.000419 0.000373 0.000225 0.000256 0.000340

,_

• BELICE D. o ELICONA

AlATO A MAZZARRA'

m Jf

i 1/ 1 *" AJ '

A A

Jr

-4.5

1r~

* A*

a (m) 0.37 0.46 0.34 0.22 0.32 0.25 0.32 0.16 0.32 4.01 2.83 2.33 1.5 1.86 2.17 1.15 1.81

. ROSMARINO o TIMETO o

G

t,n (m) 353.2 409.5 356.3 209.1 362.1 158.1 255.6 138.3 328.3 2598.1 1525.5 2216.5 1494.3 1575.8 3056.5 1025.4 1955.1

3

~

a »

»

Ô

9

»

a O

A

-2000

-1000

0

-15000

-10000

-5000

- tp,i [m]

-1„ ; [m] Fig. 7 Cumulative distribution function of the -t , variable for basin maps (a) at a scale of 1:10 000 and (b) at a scale of 1:50 000.

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Vito Ferro et al.

Figures 7(a) and (b) show that for the investigated basins, both at a scale of 1:10 000 (Fig. 7(a)) and at a scale of 1:50 000 (Fig. 7(b)), the relationship between the logarithm of the cumulative frequency Fh lnF„ and the variable -tpi is approximately linear for each basin. Consequently the mathematical shape of the relationship between SDRt and tpi (equation (1)) is assumed to be scale-invariable even if P is scale-dependent. Figure 8 shows, for the Mangiafico basin at a scale of 1:10 000 (Fig. 8(a)) and for the Belice D basin at a scale of 1:50 000 (Fig. 8(b)), values of p and SDRW calculated from equation (2), using SDRW values ranging from 0 to 1, and the fitted equation (3). The analysis confirmed, for all basins listed in Table 2, the suitability of equation (3) to represent the sediment delivery relationship. In other words, even the sediment delivery relationship can be assumed to be map scale-invariable.

1 i1

-

! J MANGIAFICO |

- '-— fb) 0.8

BELKT D

v —

—

"

j~

- —

J 0.4 - —

0.2 •

"

0 •

1

0.2 -

"^r»~ "

^——- •

-

- —^ _

_.

» __?__.

0 .

•

-

!

•

~

• — - » - — ,

1000 p 1000 P Fig. 8 Sediment delivery relationship (a) for the Mangiafico basin and (b) for the Belice D basin.

Figure 9 shows that equation (6) is still useful to represent the relationship between the a coefficient and the median travel time tm. In particular, the basins at a scale of 1:50 000 are characterized by tm values falling in the same range (50010 000 m) of the median travel time values measured for the basins at a scale of 1:25 000, while the basins at a scale of 1:10 000 have the lowest tm values (less than 500 m). In other words, Fig. 9 shows that the ratio altm is scale-invariable. Equation (7) was derived (Ferro, 1997) using basins having median travel time values ranging from 620 to 2014 m and drainage density index, (2u - 1)/5W, values ranging from 1.22 to 32.2 km"2, while for the 63 investigated basins, at different map scales (1:10 000, 1:25 000 and 1:50 000), the range of tm values was 138-10 487 m and that of (2u - 1)/5W values was 0.5-85.3 km-2. Since in this investigation the two morphological variables tm and (2u. - 1)1 Sw are characterized by a wider range than the one used by Ferro (1997) to derive equation (7), this empirical relationship was re-calibrated and the following


435

100 • (Ferro, Minacapiili, 1995) o (Ferro, 1997) n Apulia a Calabria • 1 : 10,000 o Î : 50,000 —eq.(6)

1

o

y •