3. Situación actual
3.3 Aspectos económico-financieros
3.3.5 Tasas y tarifas
Few studies focusing on rainfall-runoff separation modelling in terraced slopes are available.
An innovative theoretical approach applied to terraces was introduced by Van Dijk and Bruijnzeel (2004). The authors investigated the spatially variable infiltration model (Yu et al., 1997) and proposed an event-based model of rainfall infiltration and surface runoff. In the spatially variable infiltration model (SVI; Yu et al., 1997a) the infiltration-excess rainfall (Q’ in mm/hour) is calculated as the difference between the rainfall intensity (R) and the infiltration rate (I(R)) assuming an exponential trend of maximum infiltration rates, represented by the average maximum infiltration rate (Im in mm/hour):
Theoretically, Im is reached when the entire area under consideration generates runoff (Yu et al., 1997a).
To avoid the need for high-resolution rainfall intensity data, an exponential depth–rainfall intensity distribution for individual storms was proposed and tested by Van Dijk (2002). It is characterized by storm depth P (mm) and depth-averaged rainfall intensity R (mm/hour), calculated for n time intervals making up a storm as
(1.10) Based on the exponential rainfall distribution, an expression was derived relating storm runoff depth (Qtot) to P, and Im (see Van Dijk, 2002):
(1.11) where SI (mm) is initial excess infiltration and Im is the average maximum infiltration rate.
The bench terraces examined are comprised of three segments with contrasting infiltration characteristics (Figure 1.7).
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Figure 1.7 General layout of back-sloping bench terraces, the three component sections and their intersection with the subsoil (dark shaded). A hydrologically defined terrace unit is shown lightly shaded (Van DiI Jk and Bruijnzeel, 2004).
The theoretical runoff response from the entire terrace is therefore found by weighting the infiltration characteristics of each segment by its relative area:
(1.12) where FA,i is the relative area, and Im,i (mm/hour) the maximum average infiltration rate associated with segment i. Similarly, overall runoff depth is given by the equation:
(1.13)
where SI,i (mm) is the initial additional infiltration on segment i. If the resulting distribution of maximum infiltration rates over the entire terrace remains exponential the corresponding spatially averaged value (mm hour-1) is given by:
(1.14) However, in most cases the distribution of infiltration rates of the total area will no longer conforms to an exponential distribution. If Equations 1.9 or 1.11 are used with calculated from Equation 1.14 to predict instantaneous runoff rates or event runoff totals, respectively, the results will be different from those calculated with the corresponding Equations 1.12 and 1.13 for the entire terrace, respectively. This is illustrated in Figure 1.8(a,b) for combinations of relative area and Im for the three segments of a representative bench terrace. Instead of using an value calculated with Equation 1.14, an ‘apparent’ value may be chosen such that it best fits infiltration rates over the range of observed rainfall intensities (Figure 1.8a,b).
Total runoff depth from the composite area is hence described by (see Equation 1.11):
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(1.15) where denotes an ‘effective’ spatially averaged storage term and ε is the error that is introduced by the approximation.
Figure 1.8 The combined response of the three terrace sections expressed as the relationship between (a) rainfall intensity (R) and infiltration rate (I(R);Equation (1.12)) and (b) depth-averaged rainfall intensity ( ) and runoff coefficient (rc; Equation (1.13)). Cumulative contributions by the three sections are shown by dashed lines, whereas solid lines indicate the relationships for the combined response using area-weighted average values of . Relative area values of 5, 16 and 79% and Im values of 20, 70 and 200mmhour-1 were used for the central drain, riser and bed, respectively. (Van DiI Jk and Bruijnzeel (2004)).
Van DiI Jk and Bruijnzeel (2004) validated and tested the theory developed in Van Dijk (2002) using a data set of rainfall intensity, runoff depth and runoff rates from small to medium-sized (1–231m2) erosion plots. These measurements were collected in bench-terraced hillslopes in volcanic upland terrain in West Java, Indonesia. These bench terraces comprise a terrace riser and a terrace bed with a central drain (Figure 1.7). Totals of measured rainfalls and associated surface runoff coefficients have been analyzed for the terrace beds and risers and for the terrace units.
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Runoff coefficients associated with bare terrace riser sections (12–28%) were not higher than those for bare terrace beds (16–26%), despite the difference in slope gradient and subsoil exposure. However, runoff from terrace beds with appreciable vegetation cover was generally less than that from bare plots, especially under mixed cropping (0.1–24%). Similarly, runoff from terrace risers with vegetation cover was generally less than half (0.6–13%) that from bare risers, whereas unweeded risers with variable degrees of cover showed intermediate values (8–20%). The storm-based equations were used successfully to model runoff depths and maximum effective runoff rates for individual events. Resulting values for maximum average infiltration rate (Im) varied between 18 and 443mm/hour and reflected effects of vegetation or mulch cover and soil compaction. The authors concluded that the SVI model and the derived equations provide a robust and accurate method for predicting runoff at the investigated scale.
As reported in Gallart et. al (2009) “The modelling of Mediterranean mountain areas is often seen as a complex challenge and an unresolved problem for which model improvements are required”. These authors carried out modelling exercises in the Vallcebre small research basins, located in the Eastern Pyrenees (Latron et al., 2009) in order to both improve the understanding of the hydrological processes and test the adequacy of some models in such Mediterranean mountain conditions. One of these exercises consisted of the analysis of the hydrological role of the agricultural terraces using the TOPMODEL topographic index. This last is defined as
where a is the local upslope area draining through a certain point per unit contour length and tanb is the local slope in radians.
The results showed that the frequently saturated areas had a bi-modal distribution of topographic index values, one mode attributed to the general topography of the basin and the other (with lower values) to the role of terraces. The terraces promoted the formation of saturated areas in drier conditions than those expected by the main topography. Furthermore, the analysis of the response time of these basins demonstrated a delay of flows when compared with the response times expectable for saturated overland flow in basins of similar size (Gallart et al., 2005a).