Long-Term water balance of a bare soil with slope in Chuncheon, South Korea

ae E. YANG, Hyun-il LEE Department of Biological Environment, Kangwon National University, Chuncheon, South Korea * Correspondence: maydin08@yahoo.com 1. Introduction Quantification of water balance components is of major importance in the assessment of soil hydrology, especially under bare-field conditions. There are numerous methods for direct quantification of elements of the soil–water balance. Instead of working with an in situ measurement method, many researchers prefer using a simulation model for estimating the rates of the components. However, the models are structured based on simplifications of the real systems, although soil is a very complex environment. Soil evaporation, drainage, soil water storage, and runoff are strongly interdependent. Quantification of evaporation from bare soils is critical in the physics of land-surface processes because soil evaporation is an important component of the water balance and the surface energy balance (Bittelli et al., 2008; Allen, 2011; Xiao et al., 2011). Agam et al. (2004) concluded that latent heat flux played a major role in the dissipation of the net radiation during dry seasons. The evaporation from the soil is also the link between atmosphere and soil surface in the water cycle, and it is a key issue in the hydrologic processes that are linked to water fluxes in the soil (Romano and Giudici, 2009; Vanderborght et al., 2010). Evaporation from a bare soil surface is a complex process, including the multiphase transport of soil water to evaporation surface (Alvenas and Jansson, 1997; Konukcu et al., 2004). Therefore, the evaporation process should be assessed in order to adopt feasible management practices. On the other hand, many models have been developed to represent the rainfall-runoff processes (Yoo and Park, 2008; Hwang et al., 2009). The rainfall-runoff process is mainly developed based on elements of topography such as slope, flow-path and drainage density, soil texture and depth, and surface roughness conditions (Jung et al., 2011). In surface runoff studies, data collection and process knowledge mostly originate from the plot scale (Kirkby, 2001), although models often operate at the catchment scale (Cerdan et al., 2004). At the plot scale, surface runoff depends on the surface characteristics (gradient and soil properties), rainfall intensity, and the antecedent soil water conditions (Eilers et al., 2007). The role of initial soil water content in runoff generation was emphasized by several authors (Karnieli and Ben-Asher, 1993; Fitzjohn et al., 1998; Descroix et al., 2002; Castillo et al., 2003). Special attention has been paid to the reduction of soil infiltration capacity due to increasing levels of soil moisture (Cerda, Abstract: Water balance components of a bare soil with slope varying from 5% to 30% in Chuncheon, South Korea, were simulated using the E-DiGOR model, which proposed an interactive way to quantify runoff, drainage, soil water storage, and evaporation. Daily computations were carried out during the period of 1980 to 2009 for the identified soil-topography-climate combination. A strong correlation between measured pan evaporation and calculated potential soil evaporation was observed (R2 = 63.8%, P < 0.01) based on the monthly data of the past 30 years (hereafter ‘long-term’). When examining long-term dynamics of simulated soil evaporation, monthly mean potential and actual soil evaporations ranged from 9.1 and 9.0 mm in December to 110.5 and 75.2 mm in June and July, respectively. The ratio of actual to potential soil evaporation (Ea/Ep) had a close linkage with soil water content. The higher the soil water amount, the greater the Ea/Ep ratio was. A nonlinear relationship between rainfall and surface runoff was obtained at a given slope. Excess surface runoff and subsurface flow (percolation + interflow) occurred throughout the rainy months from July to September, with peaks in July. The ratio of direct surface runoff to rainfall increased with the natural logarithm of slope. The long-term mean annual direct surface runoff and subsurface flow at the maximum slope were 408.1 and 437.6 mm, respectively. Furthermore, mean annual surface runoff from the slope of 30% was approximately 2 times higher than that from the slope of 5%. Key words: Runoff, soil water storage, evaporation, E-DiGOR model Received: 27.01.2013 Accepted: 17.06.2013 Published Online: 13.12.2013 Printed: 20.01.2014 Research Article 81 AYDIN et al. / Turk J Agric For 1997). Some authors have pointed out that antecedent soil water content in hydrological response is secondary in importance compared with the soil surface characteristics, especially soil crusting phenomena. Other studies have described relations between rainfall characteristics and soil texture and the effects of initial soil moisture on runoff (Casenave and Valentin, 1992; Castillo et al., 2003). Changes in the soil water content greatly deal with evaporation; however, the calculation of actual soil evaporation poses a serious dilemma (Aydin et al., 2012a). A reasonable estimation under wet conditions is to set evaporation equal to potential evaporation (Croke et al., 2000). However, the evaporation from bare soils depends not only on the atmospheric conditions but also on the soil properties (Aydin et al., 2005). To improve a rainfall-runoff model, one generally has to analyze all the model components and devise better alternatives for the components that may degrade the model performance (Kim et al., 2006). Over the last decade a new model, E-DiGOR, has been developed (Aydin, 2008, 2012). It provides the descriptions of water balance components at the scale of a single farm field. Since rainfall-runoff models are poorly responsive to potential evaporation (Oudin et al., 2005), the computed actual soil evaporation is used as an input to soil water balance to obtain a realistic estimation of the antecedent soil water storage (Aydin, 2012). The hydrological components of a nearly level sandy loam soil in Chuncheon, South Korea, over 30 years were previously computed by Aydin et al. (2012a) using the E-DiGOR model. The present study was carried out in the same location to simulate the water balance components of a bare soil possessing different levels of slope. 2. Materials and methods 2.1. Description of the model The model with the acronym E-DiGOR was developed by Aydin (2008) to predict soil evaporation, drainage, and water storage based on physical features. The model has been improved recently to also estimate the surface runoff from bare soils (Aydin, 2012). In principle, the E-DiGOR model can successfully simulate soil–water balance (Onder et al., 2009; Aydın and Keçecioğlu, 2010; Aydin et al., 2012b) at plot scales. More precisely, the model simulates the components at point scale, and then the homogeneous conditions are assumed over a plot by scaling up that point situation. In order to estimate soil evaporation and drainage rates, the applicability of the E-DiGOR model to a wide range of environments has been demonstrated by different researchers using field-based measurements (Aydin, 2008; Aydin et al., 2008; Kurt, 2011). In general, soil evaporation is modeled via potential evaporation (e.g., from the Penman–Monteith equation) with a surface resistance of zero (Wallace et al., 1999; Aydin et al., 2005): Ep = (Rn Gs )+86.4cp / ra ( + ) , (1) where Ep is potential soil evaporation (kg m–2 day–1 ≈ mm day–1), Δ is the slope of vapor pressure-temperature curve (kPa °C–1), Rn is the net radiation (MJ m –2 day–1), Gs is the soil heat flux (MJ m–2 day–1), r is the air density (kg m–3), cp is the specific heat of air (kJ kg–1 °C–1 = 1.013), r is the vapor pressure deficit of the air (kPa), ra is the aerodynamic resistance (s m–1), r is the latent heat of vaporization (MJ kg–1), r is the psychrometric constant (kPa °C–1), and 86.4 is the factor for conversion from kJ s–1 to MJ day–1. A simple model, referred to as the Aydin equation for estimating actual evaporation from bare soils, was tested by Aydin et al. (2005) under different environmental conditions: Ea = Log Log ad Log tp Log ad Ep (2) If |Ψ|≤|Ψtp|, then Ea = Ep or Ea/Ep = 1. For |Ψ|≥|Ψad|, Ea = 0. Remember that Ep ≥ 0. Here, Ea and Ep are actual and potential evaporation rates (mm day–1), respectively; |Ψtp| is the absolute value of soil water potential (matric potential) at which actual evaporation starts to drop below potential one (cm of water); |Ψad| is the absolute value of soil water potential at air-dryness (cm); and |Ψ| is the absolute value of soil water potential at the surface layer (cm). Although the Aydin equation appeared to be useful, the objective measurement of soil water potential near the surface of the profile was difficult, especially at the drier upper layer. In order to overcome this difficulty, the following equation can be used for estimating the soil water potential at the top surface layer (Aydin et al., 2008): = (1/ )(10 Ep) 3 2( fc ad )(Davt / ) 1/2 (3) where Ψ is soil water potential (cm of water) at the top surface layer, α is a soil-specific parameter (cm) related to flow path tortuosity in the soil, ΣEp is cumulative potential soil evaporation (cm), θfc and θad are volumetric water content (cm3 cm–3) at field capacity and air dryness, respectively, Dav is average hydraulic diffusivity (cm2 day–1) determined experimentally, t is time (day), and π is 3.1416. 82 AYDIN et al. / Turk J Agric For In a very dry range (in which the flow is entirely vapor), either resistance models or a Fickian equation should be used (Konukcu, 2007) to estimate water transport through the slow process of moisture diffusion. Minimum water potential at a dry soil surface can be derived from the Kelvin equation (Brown and Oosterhuis, 1992; Aydin et al., 2005; Aydin, 2008): ad = RgT mg lnHr , (4) where Ψad is the water potential for air-dry conditions (cm of water), T is the absolute temperature (K), g is the acceleration due to gravity (981 cm s–2), m is the molecular weight of water (0.01802 kg mol–1), Hr is the relative humidity of the air (fraction), and Rg is the universal gas constant (8.3143 × 104 kg cm2 s–2 mol–1 K–1). A new approach that requires rainfall depth intensity, slope steepness, soil water deficit, and saturated hydraulic conductivity data is used for estimating surface runoff from bare soils (Aydin, 2012): Q = P × {1/2 × [log√Sp + exp(–Ds/P)]}(Ks/Im) (5) where Q is the direct surface runoff (Kim and Lee, 2008) or rainfall excess in dimension length (mm) facilitating comparisons among precipitation, percolation, storage, and evaporation; P is rainfall (mm); Sp is slope steepness (%); Ks is saturated hydraulic conductivity (mm h–1); Im is maximum intensity of rainfall (mm h–1); and Ds is deficit of saturation (mm), which means the saturated water amount minus the antecedent water amount. A simplified approach is implemented to derive the portion of rainfall infiltrating into soil: U= P – Q, (6) where U is infiltrated rainfall (mm) representing rainwater uptake by soil (Rubin, 1966). The soil water storage (S) on a considered day can be imposed on the difference between infiltrated rainfall (in case) and actual evaporation on the consecutive day. Symbolizing this produced variable as W, the following expression can be written (Aydin, 2008): W(j) = S(j–1) + U(j) – Ea(j) (7) If W(j) < θfcZ, then S(j) = W(j) If W(j) ≥ θfcZ, then S(j) = θfcZ. Initial soil water amount between the soil surface (0) and a given depth (Z) is calculated by integrating water content of individual soil layers (∫ 0 z θi dz). Here, θi is the initial water content (cm3 cm–3) of each layer. In the present study, it was assumed that no impervious barrier existed throughout a profile depth of 120 cm. The drainage term used by Aydin (2008) for nearly level soils has been adopted as subsurface flow for sloping land when soil water content exceeds the field capacity. The cumulative subsurface flow including vertical movement (percolation) and lateral flow (interflow) through the profile until day j can be expressed as follows: F ( j) = 0 z dz+ U ( j) Ea ( j) S( j) , (8) where ΣF is cumulative subsurface flow (mm) out of the storage depth from the first day of the simulation period, ΣU is total infiltrated rainfall (mm), and ΣEa is cumulative actual soil evaporation (mm). Thus, from the differences between the consecutive days, subsurface flow rates (F = mm day–1) can be easily calculated, if any, as: F ( j) = F ( j) F ( j 1) . Aydin and Polat (2010) developed a computer program (runoff module not included) for the functional implementation of the model described above. The input variables of the computer program are climate data (sunshine duration, air temperature, relative humidity, wind speed, and precipitation) and soil properties (albedo, tortuosity, average diffusivity for drying soil, volumetric water content at field capacity, profile depth, and initial water content of the profile). 2.2. Study location The study site, Chuncheon (37°54′N, 127°44′E, 76.8 m a.s.l.), is located in a basin formed by the Soyang River, South Korea (Figure 1). Chuncheon has cold winters and hot summers. Daily climate data including pan evaporation for the study area were obtained from the Korea Meteorological Service. Based on the meteorological data for the period of 1980–2009, the mean annual temperature and relative humidity at the site were 11.1 °C and 71%, respectively. The mean annual precipitation was 1329.2 mm during the same period, and over 60% of precipitation occurred in summer. Water balance components of a sandy loam soil with slope varying from 5% to 30% were simulated. Daily computations of bare soil evaporation, soil water storage, direct surface runoff, and subsurface flow (if any) were carried out for the period of 1980 to 2009. In this study, it was assumed that no impervious barrier existed throughout a profile depth up to 120 cm. Volumetric water content at field capacity and saturation were taken as 0.18 and 0.41 cm3 cm−3, respectively. The other soil parameters for model calibration were compiled from literature (Aydin et al., 2012a). 83 AYDIN et al. / Turk J Agric For 3. Results The evaporation rate from pans filled with water (Epan) is widely used to estimate reference evapotranspiration (Xu et al., 2006) and potential soil evaporation (Ep). The relation between Epan and calculated Ep has been demonstrated using their monthly values (from April to October) of 30 years (Figure 2). On the basis of the scatter diagram, it was observed that there were 3 different clusters. Therefore, cluster analysis (clustering with squared Euclidean distance) was done using SPSS 20.0 to form similar groups of data. Three different groups of potential soil evaporation data (ranges: 37–47, 44–111, and 94–132 mm) and corresponding pan evaporation quantities were obtained. However, the pairs of data were best fitted to a linear relationship based on the statistical trials. Monthly mean precipitation, air temperature (average, minimum, and maximum) and potential and actual soil evaporations for a period of 30 years are depicted in Figure 3. Potential soil evaporation was higher than the actual rate. It is very well known that potential evaporation is mainly related to the evaporative power of the atmosphere. However, the actual evaporation from bare soils depends not only on the atmospheric conditions Seoul Chuncheon Kangwon National University (Campus) N not scaled ~30% 5%~ 6 % 11%~14 % Bare-Soil Strip Hobby-Terrace Farming Figure 1. Location of the study area and slope range. y = 1.0844x R² = 0.6388 25 50 75 100 125 150 25 50 75 100 125 150 Po te nt ia l s oi l e va po ra tio n (m m /m on th ) Pan evaporation (mm/month) Figure 2. The relation between observed pan evaporation and calculated potential soil evaporation based on monthly data of 1980 to 2009. 387,3 –10 –5 0 5 10 15 20 25 30 0 40 80 120 160 200 240 280 320 1 2 3 4 5 6 7 8 9 10 11 12 A ir te m pe ra tu re (° C) Pr ec ip ita tio n (m m ) Month Pp Tmax Tavr Tmin 0 25 50 75 100 125 1 2 3 4 5 6 7 8 9 10 11 12 So il ev ap or at io n (m m ) Month Potential Actual Figure 3. Monthly mean precipitation (Pp), air temperature (average [Tavr], minimum [Tmin], and maximum [Tmax]), and soil evaporation over a period of 30 years starting from 1980. 84 AYDIN et al. / Turk J Agric For but also on the soil properties, particularly soil wetness. The lower the evaporative demand of the atmosphere was, the lower the rates of both potential and actual soil evaporations were, even for wet soil conditions. In this study, potential soil evaporation was computed from the Penman–Monteith equation using daily climate data such as radiation, air temperature, wind speed, and humidity (or vapor pressure deficit). Evaporation could take place at any temperature; however, higher temperature usually increased soil evaporation. The ratio of actual to potential soil evaporation (Ea/Ep) was closely related to soil water storage (Figure 4). A graphical illustration of monthly mean direct surface runoff versus rainfall for the period of 1980 to 2009 is shown in Figure 5. Surface runoff increased strongly with increasing rainfall, and a nonlinear relationship between rainfall and runoff appeared. In terms of surface runoff, an obvious difference among slopes was observed. To better understand the influence of slope on water flow, monthly mean surface runoff and subsurface flow for different levels of slope are given in Figure 6. Excess surface runoff and subsurface flow occurred during rainy months. On the other hand, slope steepness significantly affected the ratio of surface runoff to rainfall (Figure 7). In order to prove interannual variations of the elements, annual quantities of water balance components for 30 years are summarized in the Table. Surface runoff and subsurface flow varied with precipitation and slope, and they showed higher interannual variations than actual soil evaporation. 4. Discussion It is known that both pan evaporation and potential soil evaporation basically are the function of evaporative demand of the atmosphere. Passing an ideal line (1:1 line) or a line without an intercept through data is a common approach for comparing such identical variables, although evaporation calculated by models has some inaccuracy. However, a wider scatter of data or a shift to one side from 0 0.2 0.4 0.6 0.8 1 185 190 195 200 205 210 215 1 2 3 4 5 6 7 8 9 10 11 12 Ea /E p So il w at er st or ag e ( m m /1 20 cm ) Month Storage Ea/Ep Figure 4. Monthly mean soil water storage along with the ratio of actual (Ea) to potential (Ep) soil evaporation based on daily data of 30 years. 0 25 50 75 100 125 150 0 100 200 300 400 Su rfa ce ru no  (m m /m on th ) Rainfall (mm/month) 5% sloping 10% sloping 15% sloping 30% sloping Figure 5. The relation between rainfall and direct surface runoff based on monthly mean data of 30 years for different slopes. –240 –200 –160 –120 –80 –40 0 40 80 120 160 1 2 3 4 5 6 7 8 9 10 11 12 m m Month 5% sloping 10% sloping 15% sloping 30% sloping subsurface ow surface runo y = 0.0676ln(x) + 0.018 R² = 0.9997 0.10 0.15 0.20 0.25 0 5 10 15 20 25 30 35 Q /P Slope (%) Figure 6. Monthly mean direct surface runoff and subsurface flow (percolation + interflow) over a period of 30 years starting from 1980. Figure 7. The relation between slope and the ratio of direct surface runoff to rainfall (Q/P) based on the average data of 30 years. 85 AYDIN et al. / Turk J Agric For Table. Annual precipitation (Pp), actual soil evaporation (Ea), direct surface runoff, and subsurface flow in Chuncheon (Pp and Ea were previously reported by Aydin et al. 2012a). Year Pp(mm) Ea (mm) Land slope (%) 5 10 15 30 5 10 15 30 Surface runoff (mm) Subsurface flow (mm) 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 1037.5 1630.8 927.6 1153.7 1342.2 1191.5 1021.6 1513.2 1064.1 1219.2 2069.2 1298.0 1101.5 1161.0 930.9 1593.1 1185.7 1175.7 1707.6 1586.9 1154.9 1108.0 1177.7 1865.8 1404.0 1334.2 1659.4 1374.9 1439.4 1446.9 466.2 477.0 442.3 508.8 475.1 482.2 489.9 480.2 446.6 507.8 500.1 492.1 500.5 500.4 447.0 486.4 448.5 458.7 506.5 477.3 473.5 396.9 504.9 528.4 484.2 492.4 502.9 519.7 510.1 496.0 138.8 264.6 115.5 165.8 233.2 175.6 136.9 235.7 177.7 152.5 374.0 244.5 151.1 164.4 121.0 257.9 189.3 179.8 274.8 306.4 155.0 174.5 162.0 326.6 205.3 206.6 299.3 200.5 244.6 283.1 195.1 363.0 164.5 232.8 306.9 246.9 194.0 329.5 233.9 213.8 510.5 319.8 210.0 227.6 170.5 349.7 256.6 250.1 384.5 407.8 212.5 236.2 225.8 446.0 288.1 289.1 401.8 281.4 332.7 373.3 227.4 420.3 190.7 271.6 349.2 287.6 225.6 384.4 266.5 249.5 590.2 363.4 244.4 262.7 199.2 403.2 295.4 290.9 447.7 465.4 246.1 271.7 261.7 515.6 335.4 337.3 460.6 328.4 382.8 423.0 281.6 518.0 235.0 332.1 420.2 350.4 276.1 477.8 321.3 309.2 725.4 435.6 303.3 321.5 244.9 494.3 359.1 360.6 553.8 561.6 303.5 332.2 319.6 633.3 416.0 418.9 559.6 406.8 465.7 504.9 435.2 895.0 362.3 489.1 626.4 531.0 395.5 809.6 452.6 534.1 1191.9 561.1 449.1 495.8 368.1 848.0 547.0 538.2 927.7 799.7 525.0 543.6 503.2 1013.5 713.3 633.5 859.8 654.0 684.2 666.7 378.9 796.6 313.3 422.1 552.7 459.7 338.4 715.8 396.4 472.8 1055.4 485.8 390.2 432.6 318.6 756.2 479.7 467.9 818.0 698.3 467.5 481.9 439.4 894.1 630.5 551.0 757.3 573.1 596.1 576.5 346.6 739.3 287.1 383.3 510.4 419.0 306.8 660.9 363.8 437.1 975.7 442.2 355.8 397.5 289.9 702.7 440.9 427.1 754.8 640.7 433.9 446.4 403.5 824.5 583.2 502.8 698.5 526.1 546.0 526.8 292.4 641.6 242.8 322.8 439.4 356.2 256.3 567.5 309.0 377.4 840.5 370.0 296.9 338.7 244.2 611.6 377.2 357.4 648.7 544.5 376.5 385.9 345.6 706.8 502.6 421.2 599.5 447.7 463.1 444.9 Avg. 1329.2 483.4 210.6 288.5 333.3 408.1 635.1 557.2 512.4 437.6 86 AYDIN et al. / Turk J Agric For the ideal line can be observed in the linear relationship, which indicates the existence of overestimation or underestimation. In the lower range of evaporative demand of the atmosphere, potential soil evaporation (Ep) was underestimated when compared with pan evaporation, and almost all dots in the cluster were below the diagonal. Conversely, under high evaporative conditions, Ep was usually overestimated (Figure 2). In spite of this fact, the scatter of data was usually good over the whole range. A significant correlation between measured pan evaporation and calculated potential soil evaporation was observed (R2 = 63.8%, P < 0.01) since the pan responded in a similar fashion to the same climatic factors affecting potential evaporation from the other surfaces. However, several factors (radiation reflection from the surfaces; heat storage and transfer within and/or through the sides of mediums; differences in turbulence, temperature, and humidity of the air immediately above the respective surfaces; etc.) may produce considerable differences in loss of water from a water surface and from a cropped (Allen et al., 1998) or wet soil surface. Potential soil evaporation (Ep) was higher during May to August due to the higher evaporative power of the atmosphere (Figure 3). Conversely, Ep rates were lower during the winter season. However, the actual soil evaporation was related to rainfall patterns and consequently soil wetness, in addition to atmospheric demand. Monthly mean potential and actual soil evaporations ranged from 9.1 and 9.0 mm in December to 110.5 and 75.2 mm in June and July, respectively. When the soil is wet, initially evaporation occurs at the potential rate. With time, the soil surface becomes progressively drier, and the drying front moves into the soil with a time-lag (Gowing et al., 2006; Aydin, 2008). When the soil becomes drier, water cannot be supplied to the soil surface fast enough to meet the evaporative demand, and so the rate of actual evaporation declines. However, during the winter season, the only limitation was evaporative demand of the atmosphere, even for wet soil conditions, since climate data such as radiation, air temperature, humidity, and wind speed affect the magnitude of evaporation. Evaporation could take place at any temperature; however, high evaporation could occur at high temperatures (Figure 3). Since temperature can imply the characteristics of other climate data, it is included in both radiation (diabatic) and aerodynamic (adiabatic) components of the Penman– Monteith model. However, the sensitivity analysis of the model is not among the aims of the present study (see Aydın and Keçecioğlu, 2010). In practice, the water stored in a bare soil without any shallow water table is changed with infiltrated rainfall as input and actual evaporation and drainage as outputs. During rainy days, soil water may temporarily increase up to the saturation. When the water content of the soil reaches the field capacity, water can generally drain through the soil profile. Under such wet conditions, the rate of actual soil evaporation is equal or closer to the potential one. However, the water storage decreases continuously during the dry days due to evaporative losses. In Chuncheon, the soil is not dry during the winter season but evaporation is very low due to atmospheric demand. In other words, soil water is lost as much as the atmosphere allows. During summer, the precipitation is high but water loss via evaporation from soil is also high. Thus, in winter months the soil is usually wetter when compared with other seasons, except rainy days. Briefly, there was a mutual relation between the soil water storage and the ratio of actual to potential soil evaporation (Ea/Ep). The pattern of monthly mean Ea/Ep ratio was consistent with soil water amount (Figure 4). Initially evaporation from a wet soil proceeds at the potential rate. As stated before, when the soil surface becomes drier, water cannot be supplied from the deeper layers to the surface fast enough to meet the higher evaporative demand of the atmosphere even in rainy seasons. Therefore, the Ea/Ep ratio was high in the winter months due to lower Ep, and low in the other seasons because of higher Ep. It should be noted that one can set evaporation equal to potential evaporation only during the winter season in the study area. According to Kim and Lee (2008), it is an advantage if a method considers the effects of rainfall as well as the antecedent soil water condition on runoff during a given day. However, the E-DiGOR model does not consider the effect of slope on soil evaporation, as most models do. From a larger perspective, it can be thought that the relationship between land slope and actual soil evaporation may be weak but significant. On the other hand, it is clear that soil water content has the greatest effect on actual evaporation and consequently on subsurface flow and surface runoff production when water content exceeds field capacity of the soil. In general, the rainfall-runoff relationship is determined by the depth and intensity of rainfall, watershed characteristics (soil type, topography, land use, and cover), farming system, soil water status, and soil conservation techniques (Istanbulluoglu et al., 2006). On the other hand, the confidence in a model can be gained through simulation of measured data. Therefore, the runoff submodel of the E-DiGOR was calibrated and validated using observational runoff data obtained by Çelik (1998) from measurements made with a runoff collection system during 28 rainfall events for a slope of 30%. It was observed that after calibration, the estimated surface runoff reflected the measurements sufficiently (number of pairs = 28, R2 = 67.7%, P < 0.01), although the model outputs were inconsistent in the range of lower runoff (data not shown). Unknown rainfall intensity was considered to be the main 87 AYDIN et al. / Turk J Agric For reason for the less satisfactory prediction of small runoff volumes. The precision of results was still sufficient to estimate the runoff when considering the range of events selected for the comparisons. A nonlinear relationship between rainfall and surface runoff in Chuncheon was existent at a given slope (Figure 5). By comparing the extension of the trend lines from about 149 mm of rainfall to 309 mm and 387 mm of rainfall in Figure 5, it can be observed that increases in rainfall cause wider intervals among the rainfall-runoff lines belonging to different slopes. This pattern can be attributed to the reduced deficit of soil saturation and consequently the increased surface runoff, drastically so on steep slopes. In other words, the water amount (antecedent soil water plus rainfall) exceeding soil saturation caused a proportional increase in runoff. As noticed by Singh and Woolhiser (1976) and Yoo and Park (2008), surface runoff is generally recognized as a nonlinear process, and therefore nonlinear models are more applicable. Similarly, Kim et al. (2009) reported that increases in rainfall may potentially result in substantial and nonlinear increases in runoff and soil loss in Chuncheon. In contrast, Istanbulluoglu et al. (200), examining the SCS-CN method, noticed that the calculated runoff rates versus rainfall were fitted linear curves. Excess surface runoff and subsurface flow occurred during rainy months (from July to September), with peaks in July (Figure 6). Similar runoff trends in the same region have been reported by Kim et al. (2005) investigating rainfall and runoff time series at the Soyanggang Dam catchment. The runoff module of the E-DiGOR model has been designed to compute direct surface runoff only during the rainfall season. However, precipitation consists of rainfall and snow in Chuncheon from mid-December to mid-March. The evaluation of separate effects of rainfall, snow coverage, and snowmelt on runoff is difficult, and therefore the runoff includes some errors during this period. However, this fractionation could be neglected because the runoff volume was considered to be small (see Figure 6). Slope strongly affected the ratio of surface runoff to rainfall (Figure 7). Haggard et al. (2005) mentioned that some other studies showed similar responses to slope. The relationship between the ratio of direct surface runoff to rainfall and slope showed a nonlinear function. In other words, the ratio explained above increased with the natural logarithm of slope. As stated by Haggard et al. (2005), the natural logarithmic relationship between slope and the ratio of surface runoff to rainfall suggested that surface runoff production would continue to increase at greater slopes. The maximum subsurface flow and surface runoff were computed at the slopes of 5% and 30%, respectively (Figures 6 and 7). A decrease in runoff on the slopes could lead to an increase in subsurface flow, as also reported by Cerdan et al. (2004). The results showed that slope considerably increased surface runoff generation when holding the other factors constant, except rainfall and antecedent water content of the soil. Regarding the latter factor, Istanbulluoglu et al. (2006) reported that antecedent moisture conditions from the previous 5 days influenced the surface runoff rates remarkably; however, its influence was not regular due to the distribution of precipitation within the particular month. Some other runoff and erosion models commonly used are taking the effect of slope on rainfall-runoff relationship into account. For example, in the EUROSEM (Morgan et al., 1998), MEFIDIS (Nunes et al., 2005), and SiB2 (Wang et al., 2009) models, surface flow is determined by kinematic wave approach using Manning’s equation, which is related to slope (the square root of slope), surface roughness coefficient, and water depth. The RUSLE (Renard et al., 1997) and WEPP models also use a slope geometry or profile (the physical characteristics of a slope such as slope gradient, length, and shape), which can determine the characteristics of flow across the surface (Zhang, 2005). Similarly, the MEDALUS model (Kirby et al., 1998) provides a relationship between slope gradient and unit catchment area for runoff and erosion simulation. A direct comparison among the model results obtained under different conditions may not be reasonable because rainfall characteristics, scale, slope profile, soil properties, ground cover, etc. need to be taken into account to explain variability in outputs. For example, Mourinou et al. (2012) showed that the processes generating runoff on plots of 50 and 150 m2 were identical and significantly different from the unit plot of 1 m2. The best way to compare the performance of different models is to test them at the same time in the same locations. Precipitation, surface runoff, and subsurface flow had noticeable interannual variations (Table). Actual soil evaporation showed comparatively less interannual variations than runoff. The 30-year average direct surface runoff and subsurface flow (percolation + interflow) at the maximum slope were 408.1 and 437.6 mm/year, respectively. Direct surface runoff increased with increases in slope, while subsurface flow decreased. The long-term mean annual surface runoff from the slope of 30% was approximately 2 times higher than that from the slope of 5%. Accurate estimation of the soil’s physical and hydrological parameters is essential when operating a soil hydrological model. Some popular and comprehensive models compute runoff using kinematic wave equations or an approximation to kinematic wave solutions obtained for a range of rainfall intensity distributions, hydraulic roughness, and infiltration parameter values (Flanagan and Livingston, 1995; Morgan et al., 1998). The runoff module 88 AYDIN et al. / Turk J Agric For of the E-DiGOR model developed for bare soils uses all relevant parameters, such as rainfall depth-intensity, slope steepness, soil water deficit, and saturated hydraulic conductivity. However, it does not consider infiltration and surface roughness parameters. Infiltration is a cumbersome process and roughness may change during storms. The primary disadvantage of the E-DiGOR model is that it cannot provide flow and transport dynamics in individual soil layers, since it acts like a single-layer model. For example, preferential flow or impervious barriers may be active in some soil profiles. In addition, the model does not take into account surface crusting conditions and their reflection on water balance components. However, there is no single tool to be applicable to all processes. In practical situations, much simpler but not necessarily less precise models are required (Aydin et al., 2005). The E-DiGOR model is described in relatively simple equations, and it requires readily available input parameters. Another advantage of the model is that the computed actual soil evaporation is used as input to soil water balance to have a realistic estimation of the antecedent soil water storage for the runoff submodel. Briefly, the main advantage of the E-DiGOR model is to calculate direct surface runoff, drainage, actual soil evaporation, and soil water storage in an interactive way, since these components are strongly interdependent (Onder et al., 2009; Aydin, 2012). Nevertheless, due to several reasons such as preferential flow (Xevi et al., 1997; Hansen et al., 2007), surface roughness (Cerdan et al., 2001), and neglected upward fluxes (Onder et al., 2009), simulated quantities should be interpreted cautiously. Unknown rainfall intensity restricts the application and predictive potential of the runoff module of the E-DiGOR model, like most runoff models requiring intensity data of high temporal resolution (van Dijk et al., 2005). As reported by Nunes et al. (2005), the model calibration and validation must rely on measured events for several environments. Nevertheless, our results can be considered satisfactory in the context of the limitations posed on the information provided by the inputs to the model. In conclusion, the outputs indicated a very clear distinction between wet and dry spells, as well as higher and lower evaporative demands of the atmosphere. Once the soil was fully charged with water or soil water content reaching field capacity, the rate of actual soil evaporation was equal or closer to that of the potential one. This means that soil water content has the greatest effect on actual evaporation, and consequently subsurface flow and surface runoff production. 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