EMPIRICAL DETERMINATION OF THE AVERAGE ANNUAL RUNOFF COEFFICIENT IN THE MEDITERRANEAN AREA

Runoff estimation in ungauged basin is a challenge for the hydrological engineers and planners. For an y hydrological study on an ungauged basin, a methodol ogy has to be appropriately selected for the determination of runoff at its outlet. Several meth ods have been used to estimate the basin runoff production. In this study the empirical Kennessey m ethod to determine average annual runoff coefficien t, RC, is tested on 61 Sicilian basins characterized b y ifferent climate conditions, surface permeabilit y, mean slope and vegetation cover. A comparison between ob served and calculated RC showed that a calibration of the Kennessey model could be necessary. The slight and not satisfying improvement of the calibrated mo del suggested that the main factors accounted for the K ennessey method could not be enough to describe mea n runoff production. So the analysis has been focused on researching empirical relations between RC and other variables which could play a significant role n RC estimation. Finally, the best result on RC e stimate was obtained by a simple linear regression for two Sicilian sub-zones, by considering only two main climatic parameters, average annual rainfall depth and average annual temperature.


INTRODUCTION
One of the central problem in hydrology deals with the estimation of average annual runoff production at basin scale. Runoff estimation in ungauged basin is a challenge for the hydrological engineers and planners. The problem becomes much more essential in arid and semiarid regions (D'Asaro and  as population increases and land use have continues to change, furthermore, in all those regions, such as Sicily, where the problem of water scarcity is particularly nearby so to be arduous water resources planning. Several methods are available for estimation of runoff (SCS, 1972). Most of them are based on the estimate of the average annual runoff coefficient, RC. RC can be defined as the fraction of the average annual precipitation that does not infiltrate into the soil and is not transferred back to the atmosphere through evapotranspiration. Thus, runoff coefficient represents the fraction of the precipitation, in excess of the deep percolation and evapotranspiration, which becomes surface flow and ends up in either perennial or intermittent surface water bodies.
Because of difficulties on modeling spatial variability of topography, geology, soil type and vegetation, as well in climate fluxes such as rainfall, infiltration and evapotranspiration, simple empirical approaches to determine average annual Runoff Coefficient (RC) have been widely applied (Barazzuoli et al., 1988;Santos and Hawkins, 2011). Between the simple empirical models the Kennessey method (Kennessey, 1930) provides RC values by accounting for the main factors wherefrom RC is influenced: Climate characteristic, surface permeability, mean slope and vegetation cover. After computing a climatic aridity index which, the method involves calculating RC as simple addition of three partial runoff coefficients related to the same components, according to empirical tabled values proposed by Kennessey (1930).

AJAS
This study, after applying Kennessey model for 61 Sicilian basins and after a not satisfying attempt to calibrate it on the base of rainfall and runoff data, aims to provide an empirical and reliable tool to determine average annual runoff coefficient in Sicily.

Study Area
The study has been carried out in Sicily, the greatest island of the Mediterranean sea, covering 25,700 km 2 (Fig. 1). Sicily is 62% hilly, principally in the inner areas of the island, 24% mountainous, mainly in the north and 14% plain in the coastal areas.
The mean annual rainfall P varies in the mountain ranges from 600 to 1,600 mm, whereas in the rest of island P goes from 300 to 800 mm.
The mean annual temperature T is approximately 14-15°C, with lower T in the mountain ranges (8-13°C and even 4-5°C at Mt. Etna) and higher T in the costal and urban areas (18-19°C) (Agnese et al., 2008;Grillone et al., 2009;. The study here presented has been carried out for 61 Sicilian gauged basins, quite uniformly distributed all over the region (Fig. 1). Table 1 reports main characteristics of the considered basins (D'Asaro and . Firstly, each basin has been characterized in terms of climate, morphology, land use; same indications of soil permeability were also available from previous study (Fierotti et al., 1988).

Observed Average Annual Runoff Coefficient
For the 61 considered basins, daily measurements rainfall data and discharge data about in the period 1940 -1997 are available (D'Asaro and . Spatial variability of rainfall into the basins has also considered for evaluating annual rainfall depth, by using data collected in 130 pluviometric stations. Observed average runoff coefficient, RC obs , were computed as the ratio between average annual runoff volume, Q and average annual rainfall depth, P (Table 1).

Kennessey Method
The Kennessey method let to estimate the average runoff coefficient as a function of three main basin components: slope component, Ca, Permeability component, Cp and vegetation component, Cv. For each of the three components, partial runoff coefficients have to be evaluated, according to their description reported in Table 2. Partial runoff coefficient is assigned to the basin, once the basin De Martonne aridity index, Ia, is evaluated.
According to the physical meaning of each component, partial runoff coefficient increases with increasing of slope, with decreasing of soil permeability and by passing from forest land use to bare rock.
Furthermore, partial runoff coefficient increases with increasing Ia, i.e., by passing from dry to wet climate basin conditions. Once the partial runoff coefficients are identified, the basin RC is evaluated by their simple addition, after weighting with the basin homogeneous area fractions, where homogeneity has to be intended for each of the 39 classes of Table 2 (13×3).
To determine the De Martonne aridity index, Ia, for the 61 considered Sicilian basins, Ia map of the Sicilian Region has been extracted from the "Atlante Climatologico della Sicilia" (SIAS, 2002). Ia map has been developed on rainfall data and temperature data from 1965 to 1994, collected for 55 thermo-pluviometric stations e 124 pluviometric stations distributed all over the region.
To determine basins area fractions, for slope component and particularly for the corresponding area fractions associated to the four slope classes of Table  2, 100 m resolution Digital Elevation Model (DEM) of Sicily has been used.
With reference to the permeability component, it has to be observed that soils of Sicily are characterized by a large variety, going from less to more developed pedologic types (Fierotti et al., 1988). This is due to the different geolithological formations, sedimentary to volcanic to metamorphic, which characterizes the Sicilian Region, as a consequence soil permeability can be considered the most arduous component to determine. For the purpose of this study, in view of the very small spatial scale of this investigation, soil permeability has been roughly estimated by the pedological map mentioned above, by considering a mixed of the qualitative indications there reported (soil depth, soil structure and texture).
Differences in land cover were accounted by the average Normalized Difference Vegetation Index (NDVI) obtained in a previous study for the Sicily, by using NOAA satellite images, for the period 1988-2005 (Bono et al., 2007). Thus, in this study seasonal variability of the vegetation component was not taken into account for the estimation of the average runoff coefficient. Figure 2 reports the four classes of NDVI considered in this study and associated to the vegetation components of the Kennessey method.   The determination of the average runoff coefficient of each basin, according to Kennessey method, RC K , is therefore obtained by adding the partial runoff components of Table 2, weighted with the homogeneous area fractions derived by intersecting the four different thematic maps: Acclivity (Ca), permeability (Cp), vegetation (Cv) and climate condition (Ia).

Calibration of the Kennessey Method
Partial runoff coefficients of the Kennessey method ( Table 2) were also calibrated by minimizing the Root Mean Square Error (RMSE) between observed, RC obs and calculated RC K , setting up the above discussed expected trend of partial RC by varying with the classes of each component. Table 3, analogously to Table 2, reports the partial runoff coefficients obtained by calibrating the Kennessey method based on the observed RC values.
Firstly, Table 3 shows that partial RC is completely unaffected by vegetation component and it is generally weakly influenced by the other components.
Particularly, slope and permeability components result weakly influenced in the down-left side of the

RESULTS AND DISCUSSION
Results of the comparison between observed runoff coefficients RC obs and estimated ones by the Kennessey method are presented in Fig. 3. The pairs (RC obs , RC K ) are almost dispersed around the line of perfect agreement, indicating a clear overestimating/ underestimating of the Kennessey method for the Sicilian environment for small/high RC values. Figure 3 also reports a comparison between observed RC, RC obs and calculated RC with the calibrated Kennessey method, RC K,c , obtained by using partial runoff coefficients of Table 3. As expected, calibration strongly improves RC estimation (see R and RMSE in Fig. 3), but showed that results are still slights and not at all satisfactory, so to suggest that the components accounted for the RC in the Kennessey method could not be enough to describe mean runoff production. Thus, the analysis has been focused on researching empirical relationships between RC obs and other variables which could play a significant role on RC estimation. In particular, average annual rainfall, average annual temperature, average annual evapotranspiration, vegetation indexes, surface basin, main aspect and distance from coast line, mean altitude and height, distance from basin outlet to cost, as regression variables were also considered.
Finally, the best result on RC estimate was carried out by a stepwise regression. In the final relationship, that follows, RC is a function of only the two main climate parameters, average annual rainfall depth, P (mm) and average annual temperature, T (°C) Fig. 1: RC = -0.06+0.000411P+0.0012 T (1a) for the north sub-zone 1 of Sicily RC = 1.09+0.000411P-0.0707 T (1b) for the south sub-zone 2 of Sicily The relationships (1), which show a good fitting of the data with a multiple regression coefficient equal to 0.846 and RMSE = 0.086 (Fig. 3), can be usefully used in Sicilian ungauged watersheds. Using the maps of average annual rainfall depth, P (mm) and average annual temperature, T (°C) furnished by SIAS (2002), the Equations (1) were applied to figure out the RC map for Sicily (Fig. 4). RC values are higher in the north-east part of the island (0.3÷0.5), with values higher than 0.6 in areas with higher elevation, whereas lower values are in the south part of the island ( Fig. 1 and 4).

AJAS
Future work could improve Equations (1) inserting watersheds' morpho-climatic and hydrologic characteristics here not considered.

CONCLUSION
After applying Kennessey method to 61 Sicilian basins, a comparison between observed and calculated RC showed that a calibration of the model was necessary. The slight and not satisfying improvement of the calibrated model suggested that the components accounted for the RC estimation could not well explain mean runoff production. So the analysis has been focused on researching empirical relationships between RC obs and other variables which could play a significant role on RC estimation. In particular, mean annual precipitation, mean altitude and height, mean potential evapotranspiration, surface, main aspect and distance from coast line, were also considered. Finally, a regional relationship to estimate mean annual runoff production, involving only the two main climate parameters, the average annual rainfall depth and the average annual temperature, is proposed for Sicily Region.
The collecting of watersheds' morpho-climatic and hydrologic characteristics here not considered could improve the RC estimation.

ACKNOWLEDGEMENT
This study is a result of the full collaboration of all the authors.