Comparative application of two erosion models to a basin

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1 Hydrologicaî Sciences-Joumal~(les Sciences Hydrologiques, 47(2) April Comparative application of two erosion models to a basin V. HRISSANTHOU Department of Civil Engineering, Demoeritus University of Thrace, Xanthi, Greece vhrissan@civil.duth.gr Abstract Two mathematical models were used to estimate the annual sediment yield resulting from rainfall and runoff at the outlet of the Nestos River basin (Toxotes, Thrace, Greece). The models were applied to that part of the Nestos River basin (838 km") which lies downstream of three dams. Both models consist of three submodels: a simplified rainfall-runoff submodel, a physically-based surface erosion submodel and a sediment transport submodel for streams. The two models differ only in the surface erosion submodel: that of the first model is based on the relationships of Poesen (1985) for splash detachment and splash transport, while the corresponding submodel of the second model is based on the relationships of Schmidt (1992) for the momentum flux exerted by the droplets and the momentum flux exerted by the overland flow. The degree of conformity between the annual values of sediment yield at the basin outlet according to both models is satisfactory. Key words sediment yield; basin outlet; mathematical models; rainfall-runoff model; soil erosion model; Nestos River basin, northeastern Greece Application comparative de deux modèles d'érosion à un bassin versant Résumé Deux modèles mathématiques ont été utilisés pour estimer le débit solide annuel résultant de la précipitation et de l'écoulement à la sortie du bassin versant du fleuve Nestos (Toxotes, Thrace, Grèce). oles modèles ont été appliqués à la partie du bassin versant du fleuve Nestos (838 km") qui se trouve en aval de trois barrages. Les deux modèles se composent de trois sous-modèles: un sous-modèle simplifié pluiedébit, un sous-modèle à bases physiques de l'érosion de surface et un sous-modèle de transport des sédiments dans les cours d'eau. Les deux modèles diffèrent seulement au niveau du sous-modèle de l'érosion de surface. Celui du premier modèle se base sur les relations de Poesen (1985) de détachement et de transport par éclaboussure, tandis celui du deuxième modèle se base sur les relations de Schmidt (1992) de quantité de mouvement des gouttes et de quantité de mouvement de l'écoulement de surface. L'accord entre les valeurs annuelles de débit solide, à la sortie du bassin versant, et les résultats de chacun des deux modèles est satisfaisant. Mots clefs débit solide; exutoire; modèles mathématiques; modèle pluie-débit; modèle d'érosion de sol; bassin versant du fleuve Nestos, Nord-Est de la Grèce NOTATION a A b Anax Ci C CN Dso DR slope gradient ( ) considered area (m~) width of the considered area (m) concentration of suspended particles at transport capacity (m J total sediment concentration by weight (ppm) soil cover factor curve number median particle diameter (m) sediment delivery ratio (%) m') Open for discussion until I October 2002

2 280 V. Hrissanthoa E dimensionless coefficient E p potential évapotranspiration (mm) f friction factor g gravity acceleration (m s"") h runoff height (mm) or generally flow depth (m) i energy slope IN deep percolation (mm) k, k' proportionality coefficients KE rainfall kinetic energy (J m"~) n index for the time step of the variables N rainfall amount (mm) q runoff rate per unit width (nr 1 s~' m" 1 ) q cr runoff rate per unit width at initial erosion (nr 1 s" 1 m" 1 ) q f sediment transport per unit width by runoff (nr' s" 1 m" 1 ) q r downslope splash transport per unit width (kg m" 1 ) q,f available sediment discharge per unit width (kg m" 1 s" 1 ) q rs mass of detached particles per unit area (kg m"") q, sediment transport capacity by overland flow per unit width (nr 1 s" 1 m" 1 ) or (kg s" 1 m" 1 ) r rainfall intensity (m s" 1 ) r L. entrainment ratio r s soil resistance to drop detachment (J kg" 1 ) 5* available soil moisture (mm) Smax maximum available soil moisture (mm) u mean flow velocity (m s" 1 ) u critical mean flow velocity (m s" 1 ) u r mean fall velocity of the droplets (m s" 1 ) u* shear velocity (m s" 1 ) w terminal fall velocity of sediment particles (m s" 1 ) x factor depending on the soil slope gradient Y A annual value of sediment yield at the basin outlet (t) YD annual value of surface erosion volume for the whole basin (t) P factor proportional to the square of the mean fall velocity of the raindrops (Jm~ 2 mm" 1 ) v kinematic viscosity of the water (nr s" 1 ) p water density (kg m" J ) p x sediment density (kg nr 1 ) q>. critical momentum flux (kg m s"") (fy momentum flux by the overland flow (kg m s"") cp r momentum flux by the droplets (kg m s" 2 ) INTRODUCTION The Nestos River flows through two European countries, Bulgaria and Greece, and discharges its water into the Aegean Sea. The basin area of the Nestos River is about 5760 km". In the Greek part of the Nestos River, two dams have already been con-

3 Comparative application of two erosion models to a basin 281 structed, while a third is under construction. The construction of the dams and, therefore, the creation of the corresponding reservoirs implies that a decrease in the sediment yield will occur at the basin outlet, in relation to that before the construction of the dams, due to reservoir sedimentation. It is worth mentioning that an ecologically interesting delta exists at the basin outlet and the sediment deposition regime of the delta is quantitatively influenced by the reservoir sedimentation. This study aims to estimate the annual sediment yield, due to rainfall and runoff, at the outlet of the Nestos River basin. The main physical processes quantified in the study are: runoff resulting from rainfall, surface soil erosion due to rainfall and runoff, inflow of soil erosion products into streams, and sediment transport in streams. The quantification of the above chain of physical processes leads to the computation of sediment yield at the basin outlet. Particular analysis is undertaken for soil erosion models, although the other physical processes are also modelled. Two model categories for predicting soil erosion are the empirical and the physically-based models, respectively. Representative empirical models are those based on the Universal Soil Loss Equation (USLE), or on modified forms of this equation. Modified forms of the classical USLE were applied in the past by the author for estimating sediment yield at the outlets of the sub-basins of a large basin in central Europe (Hrissanthou, 1988, 1990). In spite of the empirical nature of the USLE and the fact that this equation was initially developed for small agricultural fields, the computed annual values of sediment yield at the basin outlet were satisfactory, compared with the corresponding measured values. Santos et al. (1997) developed an empirical sheet erosion equation, in the form of the Musgrave equation, for a semiarid region. Johnson & Julien (2000) quantified upland erosion with a modified Kilinc & Richardson equation, and combined this empirical equation with St Venant equations for overland flow. In the physically-based models, the soil surface is subdivided into rills and interrill areas, while the soil erosion process is broken down into physical subprocesses. Equations describing the physical subprocesses of soil erosion are given in Foster (1982). Hairsine & Rose (1992a,b) considered three main physical processes which take place during the sheet and rill flow: runoff entrainment, deposition and runoff reentrainment. Lopes (1987) considered the physical processes of detachment by rainfall impact, detachment by shear stress and deposition. In another model category (Das & Agarwal, 1990; Sharma et al, 1993), the mobilized sediment, which is computed with empirical or physically-based equations, is convoluted with the Instantaneous Unit Sediment Graph (IUSG). The convolution aims at the identification of the variation with time of sediment yield at a basin outlet. In the present study, two erosion models that are more recent than USLE are used: one based on the relationships of Poesen (1985) and the other based on the relationships of Schmidt (1992). A common feature of all three erosion models (USLE, Poesen, Schmidt) is that they were verified by measurements in experimental fields. Both surface erosion models (Poesen, Schmidt) are combined with the same simplified rainfall-runoff model and the same stream sediment transport model. In this way, two mathematical models arise that differ only in the surface erosion submodel. At this point, it must be noted that the lack of sediment yield data at the outlet of Nestos River basin is the main reason for applying two different mathematical models to this basin. The individual submodels are described below.

4 282 V. Hrissanthou RAINFALL-RUNOFF SUBMODEL A simplified water balance model is used for the computation of the runoff, h, in a sub-basin (Giakoumakis & Tsakiris, 1992). As is well known, a part of the rainfall water can be stored in the root zone of the soil. If S max is the maximum available soil moisture and S the available soil moisture for the time increment, n, the difference (S nmx -S ) represents the soil moisture deficit for the time increment considered. It is obvious that the available soil moisture, S, increases through the rainfall, N, and decreases through the potential évapotranspiration, E p, the deep percolation, IN, and the runoff, h. The water balance equation is written as: S,'^S^+N^E,,,, (1) The runoff, h, and the deep percolation, IN, for the time step n can be evaluated as follows: If S ' < 0 then S = 0, h on = 0 and IN,, = 0 If 0 < S ' < S max then S = S \ h = 0 and IN,, = 0 lfs '>S max then S = S max, h 0l, = k(s,' -S max ) and IN = k'{s ' -S max ) where k' = 1 - k The maximum available soil moisture, S max, is estimated by the following relationship of the US Soil Conservation Service (SCS, 1972): 6, mas = 25.4[(l 000 ICN)-\ OJ (2) where CN is the curve number depending on the soil cover, the hydrological soil group and the antecedent soil moisture conditions (0 < CN 100). The potential évapotranspiration, E p, is estimated by the radiation method improved by Doorenbos & Pruitt (1977). For this purpose, the following meteorological data are required: mean daily temperature, sunlight hours per day, mean daily relative humidity and mean daily wind velocity. FIRST SURFACE EROSION SUBMODEL The following relationships of Poesen (1985) are used for estimating surface erosion: q rs =C(KE)r; 1 cos a (3) q r =^ra [o.301sina Z) 50^ - 22 (l^e" 2 ' 42sina )J (4) In the model of Poesen, a more detailed consideration of the rainfall erosion, in relation to the USLE, is attempted, e.g. splash detachment, upslope and downslope splash transport. However, the correlation of the influencing parameters of the erosion remains empirical exactly as in the USLE. The variables r x, a and C are the "passive" factors of the detachment process because they refer to the soil surface, while KE is the "active" factor because it refers to the rainfall inducing detachment.

5 Comparative application of two erosion models to a basin 283 A comparison between equation (3) and the classical USLE, which delivers soil loss due to rainfall detachment, indicates a correspondence between the influencing factors of the detachment process: the rainfall erosivity factor of the USLE, which is a function of rainfall kinetic energy and rainfall intensity, corresponds to KE; the soil erodibility factor of the USLE, which depends on the soil properties, corresponds to r s ; and the topographic factor of the USLE, which is a function of slope gradient and slope length, corresponds to a. The original relationship of Poesen for splash detachment is valid for bare soils. Therefore, an additional factor is necessary to express the decrease of splash detachment because of the vegetation. It is believed that the dimensionless vegetation factor, C, of the USLE is appropriate to express the vegetation influence. The rainfall kinetic energy, KE, is given by (Poesen, 1985): KE = pw (5) The resistance of the soil material, r s, can be given by (Poesen, 1985): r s = InD 50, for m < > 50 < m (6) It is evident from the empirical equations (5) and (6) that the variables KE and r, can be estimated in a simple way, because rainfall and soil particle size data are usually available. Empirical equations, incorporated into models describing a chain of physical processes with numerous parameters, constitute an useful tool. Often, the use of empirical equations in physically-based models is unavoidable. The sediment transport by runoff, qj, can be expressed as follows (Nielsen et al., 1986): <?/ = r e q, (7) where the entrainment ratio, r e = 1 for noncohesive soils, while for cohesive soils r e < 1 and q, is the sediment transport capacity by overland flow (m J s" 1 nt 1 ). Equation (7) clarifies that sediment transport originating from runoff erosion is a part of, or equal to, sediment transport capacity by overland flow. In a modified form of the USLE, taking into account erosion by both rainfall and runoff (Foster et al., 1977), the runoff erosivity factor is a function of runoff volume per unit area and peak runoff rate per unit area. From these remarks it was concluded that soil detachment due to rainfall and runoff should be calculated by the above mentioned form of the USLE, while sediment transport due to rainfall and runoff should be computed by equations (4) and (7), respectively. The well-known formula of Engelund & Hansen (1967) for sediment transport capacity by streamflow was modified especially for overland flow (Nielsen et al, 1986): q, = 0.04 ^ /','! Ï 3 i' 3 (8) " <P,.p-l)V -D 5(l n V > The friction factor,/ is given by (Engelund & Hansen, 1967): f = 2ghj/u 2 (9) where h (m) is the flow depth.

6 284 V. Hrissanthou SEDIMENT INFLOW INTO STREAMS The available sediment on the soil surface equals the sum "downslope splash transport + sediment transport by runoff. The sediment quantity reaching a stream from the respective basin area is controlled by the following: - If the available sediment in the stream basin exceeds the overland flow sediment transport capacity, deposition occurs on the basin soil, and the sediment transported to the stream equals sediment transport capacity. - If the available sediment in the basin is less than overland flow sediment transport capacity, and if the flow's erosive forces exceed the resistance of the soil to detachment by flow, detachment occurs; in this case sediment transported to the stream is equal to the available sediment. SECOND SURFACE EROSION SUBMODEL According to Schmidt ( 1992), the erosive impact of droplets and overland flow is proportional to the momentum flux contained in the droplets and the flow, respectively. The momentum flux exerted by the falling droplets, (p r, is given by: (p r =CrpAu r sin a (10) According to equation (10), the "active" factors of the rainfall erosion process are r and u r, while the "passive" factors are C, A and a. For the soil cover factor, C, in equation (10), an analogous remark to that for equation (3) is valid. The fall velocity of the droplets, u r, is a function of the rainfall intensity, r, according to: w,,=4.5r <U2 (11) The momentum flux exerted by the overland flow, %, is given by: (p f = qpbu (12) The mean flow velocity u can be obtained from the well-known Manning formula. The available sediment discharge, q rt, due to rainfall and runoff, in the soil area considered, is given by: where q rl. =( )10 ~ 4 (13) = (<p,. +q> / )/(p. E>\ (14) The critical momentum flux, q\ T, which designates the soil credibility, can be calculated from: (p. =q a pbu (15) Equation (14) suggests the concept of a critical situation characterizing the initiation of sediment motion on the soil surface. However, this concept is mostly encountered in stream bed load formulas.

7 Comparative application of two erosion models to a basin 285 The sediment supply to a stream is estimated by means of a comparison between the available sediment in the corresponding basin area and the sediment transport capacity by overland flow as described in the previous section. The sediment transport capacity by overland flow, q t (kg s' ] m" 1 ), is computed as follows: <1< =c ram p J 9 (16) According to equation (16), the sediment transport capacity by overland flow consists only of suspended load, while equation (8) of the first surface erosion submodel includes both bed load and suspended load. On the other hand, Yalin (1963) assumed that the mechanism of sediment transport by a shallow flow, e.g. by the overland flow, is similar to the mechanism of bed load transport in channels. The concentration, c max, is calculated by: 19,+9, n7, Cmm= (17) x p s Aw~ Equation (17) is obtained from the equilibrium condition between the vertical component of the total momentum flux (cp,. + <pj) and the critical momentum flux of the suspended particles. If the critical momentum flux is exceeded, the particles do not remain in suspension. The equilibrium condition is valid when the sediment transport capacity is achieved. The structure of most of the above equations indicates that the model of Schmidt is based on fundamental physical concepts. Nevertheless, some basic variables, e.g. u r and q r f, are evaluated by empirical equations, e.g. (11) and (13), respectively. STREAM SEDIMENT TRANSPORT SUBMODEL The sediment yield at the outlet of a stream can be computed by the concept of sediment transport capacity by streamflow using the following relationships (Yang & Stall, 1976): loge, = log ^^ log v w + fl og^ og-]logf^- Mc '- / w J \w w (18) w 2.5 \og(n*d 5(j /v)-q if 1.2<u*D 5 o/v<70 (19) w 2.05 ifu* >5o/v>70 (20) Equation (18) was determined from the concept of unit stream power (rate of potential energy expenditure per unit weight of water, symbolized with the product, ui) and dimensional analysis. The variable, u cr, in equation (18) suggests that a critical situation is considered at the beginning of sediment particle motion, as in most sediment transport equations. Equations (18), (19) and (20) are frequently used by the

8 286 V. Hrissanthou author for estimating sediment transport capacity by streamflow owing to the fact that these equations were verified in natural rivers. The sediment yield at the outlet of a stream can be estimated by a similar concept to the sediment supply to the stream from surface erosion: if the available sediment in the stream exceeds sediment transport capacity by streamflow, deposition occurs and the sediment outflow is equal to sediment transport capacity; if the available sediment is less than streamflow sediment transport capacity, bed detachment may occur and the sediment outflow is equal to the available sediment. APPLICATION TO THE NESTOS RIVER BASIN Both mathematical models described above were applied to that part of the Nestos River basin which lies downstream of the dams. The area of this part of the Nestos basin is about 838 km 2, consisting of forest (48%), bush (20%), cultivated land (24%), urban area (2%) and an area with no significant vegetation (6%). The highest altitude of the considered basin part is about 1600 m. The length of the Nestos River in this part is about 55 km. The basin was divided into 20 natural sub-basins (area: between 13 and 67 km") for more precise calculations. The division of the basin into subareas by means, for example, of a quadrangular grid, has the disadvantage that the sides of the quadrangles are not natural boundaries of the subareas. A natural sub-basin has only a single outlet, but a square may have more than one outlet (Hrissanthou, 1990). Monthly rainfall data were available for 11 years ( ) from eight rainfall stations. The mean annual rainfall at these stations amounts to 814 mm. For every month of the 11 years, mean daily values of air temperature, relative air humidity and sunlight hours, from a meteorological station located near the basin outlet, were also available. Mean daily values of wind velocity for two years only were obtained from the same meteorological station. However, the wind velocity data were used exclusively for estimating a correction factor of the potential évapotranspiration (Doorenbos & Pruitt, 1977). The physiographic characteristics of the basin were taken from topographic and geological maps. The submodels described in the previous sections were applied to each sub-basin separately and for every month of a certain year. This way of working renders necessary the assumptions that uniform conditions exist over a sub-basin and that steady-state conditions exist throughout each month for the runoff, erosion and sediment transport processes. Application of the rainfall-runoff submodel The rainfall-runoff submodel is applicable on a long-term basis, e.g. on a monthly basis, because it is based on a water balance equation (equation (1)). Performing the calculations on a monthly time basis may be justified by the fact that the rainfall in most rain days of a year in Greece is not particularly high. Furthermore, it is usual to express the évapotranspiration in monthly or annual values, because the évapotranspiration in this case can also be calculated empirically with a good approximation.

9 Comparative application of two erosion models to a basin 287 However, it has to be emphasized that performing the calculations on an event basis is the best way for the quantification of the runoff process, provided that pertinent detailed data are available. The required input data for the rainfall-runoff submodel are summarized as follows: (monthly) rainfall amount, mean daily temperature, sunlight hours per day, mean daily relative humidity, mean daily wind velocity, altitude, latitude, land use, and hydrological soil group. The proportionality coefficient, k, of the rainfall-runoff submodel was determined on the basis of the empirical assumption that the runoff coefficient (ratio of rainfall excess to rainfall) is 40%. Application of the first surface erosion submodel As far as the time basis of the calculations for the erosion process is concerned, the same remark is valid as for the runoff process. The additional input data for the first erosion submodel, with reference to the rainfall-runoff submodel, are: soil slope gradient, sub-basin area, soil cover factor, main stream length of the sub-basins, grain diameter, sediment and water density. The factor (3 (equation (5)) was taken as equal to 12.5 J m"~ mm" 1 (Poesen, 1985). The entrainment ratio, r e (equation (7)), was determined by testing different values of r e and comparing the sediment yield values of both mathematical models at the basin outlet. After trial computations, r e was taken as equal to 0.1. However, the above manner of r e determination has as a consequence that this parameter loses its physical meaning in relation to soil cohesion and becomes rather an arithmetic calibration factor. Application of the second surface erosion submodel The additional input data for the second erosion submodel, with reference to the first erosion submodel, are: roughness coefficient and critical erosion velocity of the soil surface. According to Schmidt (1992), x (equation (17)) is an empirical factor that must be determined by calibration. Nevertheless, the derivation of equation ( 17) implies that the value of factor x depends on the soil slope gradient (x = 1/sina). After this remark, x was taken as equal to Application of the stream sediment transport submodel Only the main stream of each sub-basin was considered in the sediment transport submodel for streams, because numerous unavailable data for the geometry and hydraulics of the entire stream system would otherwise be required. A sediment routing plan is necessary in order to specify the sediment motion from sub-basin to sub-basin (Akritidis & Tsoumanis, 1998). The additional input data for the stream sediment transport submodel, with reference to the foregoing submodels, concern the main stream of each sub-basin:

10 288 V. Hrissanthou baseflow, bottom slope, bottom width, bed roughness, diameter of suspended particles, grain diameter of bed material, and kinematic viscosity of water. In general, the input data of both mathematical models concerning soil and bed characteristics were evaluated by means of topographic maps, geological maps and relevant tables. Equation (18) for stream sediment transport capacity was tested successfully in natural streams with a certain range of bed width, water depth, bed slope and grain size. However, in the present case study, the bed slope of the main stream of each subbasin exceeds the application limit of the Yang formula. COMPUTATIONAL RESULTS The monthly values of sediment yield at the basin outlet resulting from both models for a certain year were added together to produce the annual value of sediment yield, YA, due to surface and stream erosion. The ratio of YA to YD, the annual surface erosion volume for the whole basin, is called the sediment delivery ratio, DR. The computer results from both mathematical models for YA, YD and DR for the years are given in Table 1. Model 1 includes the erosion submodel of Poesen and model 2 includes the erosion submodel of Schmidt. Table 2 gives the mean value and the standard deviation (SD) of the variables YA, YD and DR for both models. The ratio of YA values (model 1 /model 2) for the given years varies between 0.9 and 1.2, while the ratio of YD values (model 1/model 2) varies between 0.9 and 1.5. It may readily be seen from Table 1 that DR has high values sometimes the maximum value is 100%, if the annual erosion volume is relatively low (see e.g. 1983, 1985, 1990). This means that a high percentage of the erosion products reaches the basin outlet, if the erosion volume has relatively low values. Table 1 Computational results for YA, YD and DR for different years. Year Model 1: YA(t) YD(t) DR (%) JJ Model 2: YA(t) YD(t) DR (%) Table 2 Mean value and standard deviation (SD) of the variables YA, YD and DR. ModeTH Model 2: YA (t) YD (t) DR (%) YA (t) YD (t) DR (%) Ivfem ^H^r] Î91ÔÔ SD

11 Comparative application of two erosion models to a basin 289 Fig. 1 Arithmetic values (t km"") of surface erosion in each sub-basin for February 1987 according to both models. Th sub-basin number is encircled; values are given for model 1/model 2. In general, the differences in the structure of the erosion submodels contribute to the discrepancies between the corresponding annual values of surface erosion in the whole basin and sediment yield at the basin outlet according to both models. Moreover, the size order of the arithmetic difference between the values of sediment transport capacity by overland flow according to both models is quite high. It is notable that sediment transport capacity by overland flow is a key concept in the model running. Figure 1 shows arithmetic values (t km""") of surface erosion in each sub-basin, using February 1987 as an example, according to both models. The first value refers to model 1 and the second to model 2. The deviation between the erosion volumes according to both models is relatively satisfactory in the most sub-basins; but in five sub-basins (3, 8, 9, 18 and 19), the ratio of the erosion volumes (model 1/model 2) is less than 0.5 or greater than 2.4. The very low values of the erosion volume in subbasins 13, 14, 17 and 20, according to model 1, are due to the fact that no runoff erosion, but only rainfall erosion, occurs in these sub-basins. Here, it has to be added that, generally, rainfall erosion is a very small part of runoff erosion according to both models, provided that runoff erosion exists. In the same sub-basins (13, 14, 17 and 20), the erosion volume, according to model 2, is practically zero, because no runoff erosion occurs. It is noticeable that model 2 does not deliver erosion quantities if no runoff takes place, although rainfall erosion may exist (see equations (13) and (14)). In

12 290 V. Hrissanthov Fig. 2 Percentage of the erosion volume in each sub-basin in relation to the total erosion volume of the whole basin for February 1987 according to both models. The sub-basin number is encircled; values are given for model 1/model 2. sub-basin 1, the erosion volume according to model 2 is also zero because (p r + % is less than (p. (see equation (14)). In Fig. 2, the percentage of surface erosion in each sub-basin in relation to the total erosion of the whole basin for the same month (February 1987), also according to both models, is illustrated. Again, the first value refers to model 1, while the second refers to model 2. As far as the deviation between the percentages according to both models is concerned, the same comment written above for the absolute values of the erosion quantity is valid. A comparison of the arithmetic results in Table 1 and Fig. 1 renders obvious that the corresponding annual values of surface erosion, according to both models, deviate less than the monthly values. This situation is caused by the integrating effect obtained through use of a large basin and long (annual) simulation period. The addition of the computed monthly values to produce the annual value of surface erosion in the whole basin and sediment yield at the basin outlet compensates for the errors existing in the monthly values. A sensitivity analysis showed that the rainfall volume and the parameter CN (curve number) influence the monthly sediment yield at the basin outlet more strongly than the other input data, in both models. This result highlights the importance of the hydrological submodel for the quantification of soil erosion and sediment transport.

13 Comparative application of two erosion models to a basin 291 GENERAL REMARKS The most important drawbacks of the modelling chain are as follows: (a) The temporal development of the physical processes over the considered time period is not followed. The models compute only total values of runoff, soil erosion and sediment transport. (b) The equations used for soil erosion and sediment transport were not adapted to local conditions; in particular, the equations for soil erosion were developed for small experimental fields. (c) Snowmelt runoff, gully and bank erosion were neglected. CONCLUSIONS (a) The lack of sediment yield data at the outlet of the considered basin was the main reason for applying two different mathematical models to the basin. (b) The small deviation between the annual sediment yield values of both models at the basin outlet is an encouraging indication for the size order of the computed sediment yield. (c) In both models, the proportionality factor (k) of the hydrological submodel was determined on the basis of an assumption. Additionally, the entrainment ratio (r e ) of the first model was determined by means of the arithmetic results of the second model. All remaining parameters were estimated by means of tables and topographic or geological maps. Therefore, both mathematical models are applicable to basins for which rainfall and other meteorological data on the one hand, and topographic as well as geological maps on the other, are available. The climatic and soil particularities of a basin can be represented arithmetically by the parameter values. (d) It must be stressed that an "average behaviour" of the basin with reference to soil erosion and sediment transport is quantified by the models described above. REFERENCES Akritidis, I. & Tsoiunanis, K, (1998) Compulation of sediment quantity in the Neslos River basin downstream of the dams. Diploma Thesis. Democritus University of Thrace. Greece (in Greek}. Das. Ci. & Aearwal. Â. (1990) Development of a conceptual sediment nraph model. Trans. Am. Soc. Agrie. Engrs 33(1) Doorenhos..1. & Pruilt, W. (). (1977) Crop water requirements. FAO. Irrigation and Drainage Paper 24 (revised). FAO, Rome. Italy. Fngclund, F. & I lansen, F. ( 1967) A Monograph on Sediment Transport in Alluvial Streams. Teknisk Forlag. Copenhagen, Denmark. Foster, Ci. R. (1982) Modeling the erosion process. In: Hydrologie Modeling of Small Watersheds (éd. bv C. T. liaan. ii. P. Johnson & D. L. Brakensiek) Monograph no. 5, Am. Soc. Agrie. Kngrs, Michigan, USA. Foster, G, R-, Meyer, L. D. &. Onstad, C. A. (1977) A runoff erosivity factor and variable slope length exponents for soil loss estimates. Trans. Am. Soe. Agrie. Engrs 20(4), Giakoumakis, S. & Tsakiris, G. (1992) Soil erosion modeling in the northern region of the Mornos River basin, in: flydroteehniea (ed. by Greek Hydrotechnieal Union) (Proc. Larissa Symp., November 1992). vol (in Greek). Greek Hydrotechnieal Union, Thessaloniki. Greece. Hairsine. P. B. & Rose, C. W. (1992a) Modeling water erosion due to overland How us inn physical principles. 1. Sheet How. Wat. Resoiir. Res. 28(1) Hairsine. P. B. & Rose. C. W. ( 1992b) Modeling water erosion due to overland How usinn physical principles, 2. Rill flow. Wat. Resour. Res. 28(1),

14 292 V. Hrissanthou Mrissanthou, V. (1988) Simulation model for the computation of sediment yield due to upland and channel erosion from a large basin. In: Sediment Budgets (éd. bv M. P. Bordas & D. E. Walling) (Proc. Porto Alegre Svmp., December 1988), IAHS Publ. no Hrissanthou, V. (1990) Application of a sediment routine model to a Middle European watershed. Wat. Résout: Bull. 26(5), Johnson, B. E. & Julien, P. Y. (2000) The two-dimensional upland erosion model CASC2D-SED. In: The Hydrology Geomorphology Interface: Rainfall Floods. Sedimentation. Land Use (ed. bv M. Hassan, O. Slavmaker & S. Berkowicz) (Proc. Jerusalem Conf., May 1999), IAI IS Publ. no " Lopes, V. E. (1987) A numerical model of watershed erosion and sediment yield. PhD Thesis, University of Arizona, Tucson, Arizona, USA. Nielsen, S. A., Storm, B. & Styczen, M. (1986) Development of distributed soil erosion component for the SI IE hvdrological modelling svstem. In: Proc. Int. Conf. on Water Quality Modelling in the Inland Natural Environment (Bournemouth, UK), BIIRA, Bedford, UK. ' Poesen,.1. (1985) An improved splash transport model. Z. Geomorphol 29(2), I. Santos, C. A. G., Suzuki, K., Watanabe, M. & Srinivasan. V. S. ( 1997) Developing a sheet erosion equation for a semiarid region. In: Human Impact on Erosion and Sedimentation (ed. bv D. E. Walling & J.-E. Probst) (Proc. Rabat Svmp., April-May 1997), laiispubl.no Schmidt,.1.(1992) Predicting the sediment yield from agricultural land using a new soil erosion model. In: Proc. Fifth Int.. Symp. on River Sedimentation (ed. by P. Earsen & N. liisenhaucr) (Karlsruhe, Germany), Institute of Hydraulic Structures and Agricultural Engineering, University of Karlsruhe, Germany. Sharma, K. D., Dhir, R. P. & Murthy,.1. S. R. (1993) Modelling soil erosion in arid zone drainage basins. In: Sediment Problems: Strategies for Monitoring. Prediction and Control (ed. bv R. E. Hadlev & T. Mizuvama) (Proc. Yokohama Symp., July 1993 ), IAHS Publ. no SCS (Soil Conservation Service) (1972) National Engineering Handbook. Section of Hvdrologv, SCS, Washington DC, USA. Yalin, S. ( 1963) An expression of bed-load transportation../. Hydraul. Div. ASCE 89(3), Yang, C. T. & Stall,.1. B. (1976) Applicability of unit stream power equation. J. Hydraul Div. ASCE 102(5), Received 2 October 2000-, accepted 15 October 2001