Comparison with erosion plot data. The Sierra de Enguera Soil Erosion Experimental Station
The model described above is compared with data for runoff from the site of El Teularet in the Sierra de Enguera, SSE of Valencia, Spain (Cerda et al., 2017; 2018). The Sierra de Enguera range within the Massís del Caroig in Eastern Spain (750 m.a.s.l., 38° 55′ N, 00° 50′ W) was selected to establish the Sierra de Enguera Soil Erosion and Degradation   Research Station (Figure 8). This is a rainfed and rangeland use region in the Eastern part of the Iberian Peninsula. The climate is typical Mediterranean with a mean annual temperature of 12.7 °C as registered in the nearby meteorological station of Las Arenas Enguera (5 km from the study area). Mean annual rainfall is 540 mm and the soil texture is Clay loam and the soil is a Typic Xerorthent (Soil Survey Staff, 2014). The use of herbicides (glyphosate) was applied following the strategy of the farmers of the Sierra de Enguera. They applied herbicides when weeds were present with the objective to maintain the soil bare.
A set of five plots under different agriculture and forest managements were established between 2002 and 2003, and the first measurements took place in January 2004. The data used in this investigation were collected from 2004 to 2014 from plots treated with herbicide to suppress vegetation growth. Plots were bounded with aluminium sheets, 1 mm thick and 50 mm high, to achieve plots of different sizes (1×1; 1×2; 1×4; 2×8 and 3×16 m2) (Figure 8 ). Plots having different areas were obtained varying both plot lengths and widths and were established in an area having aq gradient of 5%. Runoff (mm), sediment concentration (g L-1) and soil loss (g m-2) were measured after each rainfall event. More than 6 hours without rainfall was used as the threshold to distinguish rainfall events. Runoff was collected from each plot by a 0.15 m wide and 0.15 m deep gutter. The collected runoff was conveyed, by a 0.4 m diameter pipe, into containers with storage capacities of 125, 250, 375, 600 and 1000 L for the 1, 2, 4, 16 and 48 m2 plots, respectively. Runoff volume was recorded after each major rainfall event.
The measurements of daily rainfall and runoff provided over 300 runoff measurements from 450 rain days. When it was not possible to measure runoff after every rainfall event, events between successive runoff measurements have been combined into a single ‘effective rainfall’. Preliminary correlation showed that, for smaller events, runoff was proportional to the third power of rainfall. Effective rainfall over successive events was therefore calculated as [Σ(r3)](1/3), giving appropriately greater weight to the largest rainfall in the sequence. With this consolidation, measurable runoff was compared with the effective rainfall for 220 events.
Following equations (5) and (6) proposed above, the plot runoff and storage were estimated for all events and for the fourplot lengths (1,2,4,8 and 16m). With these data, it was found that the best fit between observed and estimated runoff was obtained for = 2. A value for the storage threshold, Θ was then fitted for each of the plot lengths. With these values, Figure 9(a) shows the level of agreement between observed and estimated runoff for the 220 events and four plot lengths. 90% of the data points lie within the lines drawn around the 1:1 line. Figure 9 (b) shows the non-linear relationship found between the storage threshold, Θ and plot length. With no data on storm duration, it is difficult to compare directly with equation (1) above, though both show a diminishing increase in threshold with increasing plot length.
Values for the storm threshold have been selected to optimise estimates of runoff, and Figure 9(c) shows their impact on estimates of storage. Here the solid curves indicate the estimated storage [from equation (5)]. The plotted points are binned values, each the average for ten sequential values of ranked storm rainfall. The upper grey line is the 1:1 line, which has been seen to be the asymptotic state for small rainfalls [equation (2) above]. These curves should be visually compared with the forms of figures 6(b) and 6(d) above, suggesting that the field data lies closer to the constant duration (m = 2.8) than to the constant intensity storm model (m = 4.7). The consistent behaviour of the proposed storm runoff model provides some confidence in proposing equations (5) and (6) as a viable alternative to the widely used runoff model encapsulated in the SCS curve number approach.