Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Hydrol. Earth Syst. Sci. Discuss., 9, 4919–4941, 2012 Hydrology and www.hydrol-earth-syst-sci-discuss.net/9/4919/2012/ Earth System HESSD doi:10.5194/hessd-9-4919-2012 Sciences © Author(s) 2012. CC Attribution 3.0 License. Discussions 9, 4919–4941, 2012 This discussion paper is/has been under review for the journal Hydrology and Earth System Factors affecting the Sciences (HESS). Please refer to the corresponding final paper in HESS if available. runoff coefficient G. Del Giudice et al. Factors affecting the runoff coefficient Title Page Abstract Introduction G. Del Giudice, R. Padulano, and G. Rasulo Conclusions References Federico II University, Department of Hydraulic, Geothecnical and Environmental Engineering, Tables Figures Via Claudio 21, 80125, Naples, Italy Received: 31 March 2012 – Accepted: 4 April 2012 – Published: 17 April 2012 J I Correspondence to: G. Del Giudice ([email protected]) J I Published by Copernicus Publications on behalf of the European Geosciences Union. Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion 4919 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Abstract HESSD The runoff coefficient ϕ is a crucial parameter for flood peak discharge estimate in ungauged drainage basins. Tables and graphs generally allow the determination of ϕ 9, 4919–4941, 2012 in a somewhat empirical way that can lead to inconsistency in application; therefore, it 5 is important to identify other parameters that can be utilized to assess ϕ more directly. Factors affecting the In the present paper, focusing on Southern Continental Italy, a simple analytical ex- runoff coefficient pression between runoff coefficient ϕ and soil potential maximum retention S is pro- posed; moreover, an improvement of this expression is provided by considering the G. Del Giudice et al. pre-event moisture condition of the watershed through the use of a climatic factor. At 10 this aim, the US Soil Conservation Service classification for soil permeability has been adopted, that allows the evaluation of S, according to its relationship with the runoff Title Page curve number CN, as a function of soil type, land use and antecedent soil moisture Abstract Introduction condition (AMC). Conclusions References 1 Introduction Tables Figures 15 One of the most commonly adopted methods for regional flood frequency analysis is J I the “index flood” (Darlymple, 1960; Riggs, 1973); in accordance with it and whatever statistical method is used to evaluate its probability distribution, the annual maximum J I flood-peak discharge QT , with return period T , can be written as: Back Close QT = ξQKT (1) Full Screen / Esc 20 where (i) ξQ is the index flood of the examined site, usually the mean or modal value, Printer-friendly Version depending on the probability distribution model used, and (ii) KT is a dimensionless growth factor, related to the return period and to the adopted probability model. Interactive Discussion Hydrological similitude criteria (Penta et al., 1972; Rossi et al., 1982; Cunnane, 1988; Hoskings et al., 1997) are based on the identification of homogeneous regions within 25 which the probability distribution of annual maximum flood peak discharge is invariant 4920 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (uniqueness of the growth factor KT ), whereas the index flood, representing the scale factor, depends on the characteristics of each watershed. HESSD Therefore, for basins where no direct measurements are available, the main technical 9, 4919–4941, 2012 problem is to evaluate the flow index ξQ. One of the most popular methods literature 5 provides to estimate the index flood in ungauged watersheds is the kinematic runoff model (Eagleson, 1972), whose physically based relation is: Factors affecting the runoff coefficient ϕ · I (A,d,T ) · A ξ = A (2) Q 3.6 G. Del Giudice et al. 3 −1 2 where: (i) ξQ is the index flood (in m s ); (ii) A is the watershed area (in km ); (iii) IA (A, −1 d, T ) is the mean rainfall intensity over the basin (in mmh ), whose return period T is Title Page 10 the same as the index flood, and whose duration, d, is equal to the concentration time Abstract Introduction TC of the watershed; (iv) ϕ is the runoff coefficient, that is the ratio between effective and total rainfall. Conclusions References In order to estimate the Intensity-Duration-Frequency (IDF) Curves, representing the Tables Figures maximum point rainfall intensity IP (d, T ) as a function of duration d and return period 15 T (Koutsoyiannis et al., 1998), many methods can be applied (Chow et al., 1998). Conversely, only a few empirical relations are available in literature (Eagleson, 1972) J I for Areal Reduction Factor (ARF) estimate, namely the ratio between IA (A, d, T ) and J I IP (d, T ): I (A,d,T ) Back Close ARF(A,d,T ) = A (3) IP(d,T ) Full Screen / Esc 20 Moreover, a large number of empirical relations can be applied to evaluate T in accor- C Printer-friendly Version dance with watershed geo-morphological features (Chow et al., 1998), whereas tables and graphs allow the determination of ϕ from different parameters assumed as rep- Interactive Discussion resentative of watershed soil permeability. Because of the above mentioned multiple choices, results can be very different depending on the various formulas and tables 25 adopted, which are quite different from each other. 4921 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | In the present paper, using the annual maximum flood-peak discharge data of river gauging stations within the Southern Continental Italy watersheds, some analysis are HESSD provided in order to obtain the main factors affecting the runoff coefficient ϕ as well 9, 4919–4941, 2012 as to propose a simple analytical expression for its better estimation within ungauged 5 basins. Factors affecting the runoff coefficient 2 Data sources G. Del Giudice et al. The annual peak flood values were taken from “Pubblicazione n.17” published by the SIMN (Servizio Idrografico e Mareografico Nazionale) for the gauged river sections located within the river basins of Southern Continental Italy. These values have been Title Page 10 already processed by the Operative Units of National Group for Prevention from Hydro- geological Disasters (GNDCI), within the special project on “Flood Evaluation” (VAPI) Abstract Introduction supported by the National Research Council (CNR) of Italy. The data reliability tests Conclusions References allowed to reject some data in addition to those already eliminated within the VAPI project. Indeed, in some cases it was found that some drainage basins presented an Tables Figures 3 −1 2 15 anomalous unit discharge (m s km ) if compared to the watersheds belonging to the same river but situated upstream or downstream. J I Table 1 shows, for each region of Southern Continental Italy, the number and charac- teristics of gauged river sections monitored by the SIMN, once data reliability test were J I carried out. Although Southern Continental Italy corresponds to about one fifth of the Back Close 20 whole national surface area, the available data are only 50. Table 1 also shows index Full Screen / Esc floods for each basin, namely the expected value, µQ, computed as an arithmetic mean of annual peak floods over the number of year of recorded data; this was preferred to the modal value, since the former is coupled with the extreme probability distribution Printer-friendly Version widely used in Italy, named TCEV (Two-Component Extreme Value) model (Rossi et al., Interactive Discussion 25 1984). However, using the modal value would be equally suitable, since it’s closely re- lated to the mean. In order to estimate time of concentration, TC, the Giandotti formula (Eq. 4) (Giandotti, 1934), most commonly used in Italy, was adopted. ARF, previously 4922 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | defined in Eq. (3), was estimated with the empirical formula of Eagleson (1972) (Eq. 5) by using the dimensional coefficients C1, C2 and C3 calibrated for Southern Continental HESSD Italy basins (Versace et al., 1989; Rossi, Villani, 1994; Claps et al., 1994). Equation (5) 9, 4919–4941, 2012 does not depend on the return period whose effect is still negligible in the investigated 5 basins (Rossi, Villani, 1994). √ Factors affecting the 4 A + 1.5L T = (4) runoff coefficient C p 0.8 Hm − H0 G. Del Giudice et al. C3 ARF(A,d) = 1 − (1 − e−C1A) · e−C2d (5) where: (i) TC is the watershed concentration time (in h); (ii) A is the drainage basin area Title Page 2 10 (in km ); (iii) L is the length of the longest watercourse to the drainage basin outlet (in Abstract Introduction km); (iv) Hm is the mean drainage basin elevation (in m); (v) Ho is the drainage basin outlet elevation (in m). Conclusions References Because the VAPI project provides the IDF Curves for maximum point rainfall for Tables Figures each region, the expected runoff coefficient ϕo, for each watershed, was computed by 15 inverting Eq. (2) and considering d = TC: J I µQ ϕo = (6) ARF(A,TC) · µ[IP(TC)] · A J I where µ[IP(TC)] is the expected value of IDF curve for maximum point rainfall. Back Close Full Screen / Esc 3 Problem definition Printer-friendly Version Although the computed ϕo values contain errors due to different causes including the 20 specific rainfall-runoff model adopted as well as the reliability of hydrological data mea- Interactive Discussion surement, they were assumed to be the most precise estimations that could be ob- tained with the available data; hence, they will be referred to as “observed runoff coef- ficient” ϕo. 4923 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Since these values definitely depend on soil permeability, the geological formations outcropping in each watershed and the corresponding land cover were defined, in order HESSD to give each of these combinations a permeability assessment identified through the 9, 4919–4941, 2012 “estimated runoff coefficient” value, ϕe, by minimizing the objective function of error: N X 2 Factors affecting the 5 E = (ϕ − ϕ ) (7) o,i e,i runoff coefficient i=1 G.