Modeling seasonal surface runoff and base flow based on the generalized proportionality hypothesis Xi Chen a,b , Dingbao Wang b,⇑ a Center for Sustainability and the Global Environment (SAGE), Gaylord Nelson Institute for Environmental Studies, University of Wisconsin, Madison, WI 53706, United States b Department of Civil, Environmental, and Construction Engineering, University of Central Florida, Orlando, FL 32816, United States article info Article history: Received 16 July 2014 Received in revised form 24 April 2015 Accepted 25 April 2015 Available online 5 May 2015 This manuscript was handled by Konstantine P. Georgakakos, Editor-in-Chief, with the assistance of Ashish Sharma, Associate Editor Keywords: Proportionality hypothesis Seasonal runoff Seasonal base flow SCS curve number method summary The proportionality hypothesis, originating from the curve number method at the event scale, is extended for modeling runoff in the water-limited and energy-limited seasons, respectively. The proposed seasonal runoff model includes three parameters for two separate seasons, which are wetting capacity, initial wet- ting and initial evaporation. The parameters for 203 watersheds from the United States are estimated, and the empirical relationships between the parameters and watershed properties, which include dura- tion of the season, duration, intensity and frequency of rainfall events, Normalized Difference Vegetation Index (NDVI) and soil saturated hydraulic properties, are obtained for applications in ungauged water- sheds. These empirical equations present physical controls on runoff at the seasonal scale besides climate seasonality. The Nash–Sutcliffe Efficiency coefficient of the seasonal runoff simulation for total runoff is higher than 0.5 in 86% (77%) of the study watersheds; while the surface runoff is 38% (46%) and the base flow is 92% (78%) in the energy-limited seasons (water-limited seasons). This paper shows the potential application of the proportionality hypothesis for estimating seasonal runoff, which is valuable for water resources planning and management. Ó 2015 Elsevier B.V. All rights reserved. 1. Introduction Reliable seasonal runoff prediction under a changing environ- ment provides key information for water resources management, particularly reservoir operations. The dominant controlling factors on rainfall partitioning vary with time scale, from long-term to sea- sonal scales. For mean annual water balance, runoff (Q) and evap- oration (E) are dominantly controlled by the long-term climate (Budyko, 1958, 1974). The climate indicator is defined as the ratio between atmospheric water demand and water supply, which is represented by the ratio between potential evaporation (E p ) and precipitation (P), and called climate aridity index (E p /P). Various functions have been developed to quantify the dependence of the evaporation ratio (E/P) or the runoff coefficient (Q/P) on E p /P (Turc, 1954; Pike, 1964; Fu, 1981; Choudhury, 1999; Zhang et al., 2001; Yang et al., 2008; Wang and Tang, 2014; Wang et al., 2015). Besides climate, the impacts of vegetation (Zhang et al., 2001; Gentine et al., 2012), soil storage (Milly, 1994a, 1994b; Potter et al., 2005) and seasonality (Hickel and Zhang, 2006; Yokoo et al., 2008; Gerrits et al., 2009) on mean annual water bal- ance have been studied as well. When the time scale is shortened to inter-annual and seasonal periods, climate seasonality and storminess, vegetation, and soil properties become increasingly important in rainfall partitioning (Sankarasubramanian and Vogel, 2002; Zhang et al., 2008; Donohue et al., 2012; Istanbulluoglu et al., 2012; Wang, 2012; Xu et al., 2013; Guo et al., 2014). Troch et al. (2009) found that vege- tation rain-use efficiency across different ecosystem types is related with the inter-annual water balance in the catchment. Wang and Alimohammadi (2012) found that the impact of soil water storage change became non-negligible at the annual scale, particularly in water-limited regions. Feng et al. (2012) found that soil water storage can compensate for the seasonality effects, espe- cially in dry regions. Xu et al. (2012) investigated the relationship between inter-annual rainfall partitioning and catchment vegeta- tion types, and concluded that catchments dominated by woody vegetation have a higher annual runoff ratio. A number of studies have been focused on simulating inter-annual variability of water balance. Jothityangkoon and Sivapalan (2009) explored the inter-annual rainfall-runoff relation- ship with a focus on seasonality and storminess. Chen et al. (2013) introduced storage change (DS) into Budyko’s framework to model seasonal evaporation. In their study, the available water, which is precipitation in the original Budyko framework, is replaced by the difference between precipitation and storage change, i.e., P  DS. http://dx.doi.org/10.1016/j.jhydrol.2015.04.059 0022-1694/Ó 2015 Elsevier B.V. All rights reserved. ⇑ Corresponding author. E-mail address: dingbao.wang@ucf.edu (D. Wang). Journal of Hydrology 527 (2015) 367–379 Contents lists available at ScienceDirect Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol