Introduction

Chinese Loess Plateau is well-known for its serious soil erosion largely caused by cultivation of marginal lands and destruction of natural vegetation (Shi and Shao 2000; Lu and van Ittersum 2004). As a vast semiarid and high-risk region of desertification, this region has been a great concern not only in China but also in the world. In the process of desertification, serious soil erosion has occurred on the Loess Plateau since the 17th century (Wang and Takahashi 1999; Bo and Long 2002). Soil and water loss has seriously depleted land resources and degraded the eco-environment in the Loess plateau (Shi and Shao 2000). Revegetation is recognized as an important means to control soil erosion and protect land from desertification (Bu et al. 2002; Jia et al. 2010). Although water is a key factor for restoration of vegetation (Li 1983; Huo et al. 2008), however, scarce and uneven distribution of rainfall in addition to intense evapotranspiration causes the deficiency of annual water resources (Zheng et al. 2005; Kimura et al. 2005a) which hampering restoration of vegetation in the Loess Plateau (Yang 1996).

The northern Loess Plateau is a fragile ecological environment in China due to severe soil erosion and serious ecosystem degradation (Yang and Shao 1998; Tang 2000), and tendency of desertification at the northern region has become more severe than that at the southern region in the Loess Plateau due to the long-term water and wind crisscross erosion compounded by low precipitation. Ecological restoration and sustainable agriculture are hardly guaranteed by the limited water resources at the wind–water erosion crisscross region of the northern Loess Plateau.

Guaranteeing agricultural production and ecological restoration in the Loess Plateau relies on available water resources (Chen et al. 2007). Researches on water budget are significant for estimating seasonal water resources and hydrological circle within a basin. Meanwhile, runoff is a basic hydrological factor when estimating water budget, thereby, clarification of runoff characteristics is also important for further studies on hydrological circle and estimating water resources. The conventional studies related to water resources have been conducted at the wind–water erosion crisscross region on the northern Loess Plateau. Kimura et al. (2004, 2007) estimated the moisture availability over the Liudaogou Catchment using new indices with surface temperature; Zhu and Shao (2008) characterized variability and the pattern of upper soil moisture by field experiment; Fan et al. (2010) evaluated the soil water balance during vegetative restoration; Hu et al. (2011) characterized the spatio-temporal variability behavior of land surface soil water. Research focusing on evapotranspiration also has been conducted at this catchment such as by Kimura et al. (2005b, 2007), Wang et al. (2010). Compared to research findings related to soil water and evapotranspiration, the runoff characteristics and water budget are still poorly understood due to lack of the studies even though such studies are significant for assessing the available water resources of the study location. This study was therefore conducted at the Liudaogou Catchment with the aims to reveal the main runoff characteristics and to estimate the water budget of the wind–water erosion crisscross region on the northern Loess Plateau.

Materials and methods

Study area

The Liudaogou Catchment (110°21′–110°23′E longitude and 38°46′–38°51′N latitude, area: 6.89 km2) (Fig. 1) was chosen as the study location because it represents diversified landscape types in terms of geology, morphology, soil, hydrology and climatic conditions, and it represents a certain number of different land use patterns of the wind–water erosion crisscross region on the northern Loess Plateau environment (Huo et al. 2008; Zhu et al. 2008). This catchment is situated at the elevation ranging from 1,094.0 to 1,273.9 m above sea level. Average annual rainfall is 430 mm with uneven seasonal distribution, more than 70 % of the total rainfall is received in the rainy season from June to September. Annual potential evapotranspiration generally exceeds 1,000 mm. Terrain is considerably complicated, many gullies in various scales spread around the main river channel. Due to excessive pasturage, serious land erosion has occurred and the natural bush is severely damaged and there is almost no large area of distribution. Vegetation cover only accounts for about 25 % of the total basin area (Jiang et al. 2005; Fan et al. 2006).

Fig. 1
figure 1

Position of the study location and layout of field observation management. a Location of Loess Plateau in China and the Liudaogou Catchment in Loess Plateau. b Position of the Liudaogou Catchment. c Layout of field observation management

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Data acquisition

The data used for analysis were obtained mainly through field observations. Hydrological and meteorological observations were conducted on the Liudaogou Catchment. Hydrological observations included rainfall, groundwater level, soil water content, discharge of surface flow in river channel, and groundwater outflow. The tipping rain gauge [Model number: 7852 M-L10, Dimensions: φ165 × 240H (mm)] was used for rainfall observation and rain gauge of this type records data once for every 0.2 mm rainfall. Groundwater level (phreatic water) and the depth of the surface flow were observed by water level recorder (Groundwater level, HM-910-02-309, Sensez co. ltd.; Surface flow, KADEC21-MZPT, KONA System co. ltd.). Discharge of groundwater outflow was observed by a flow meter (Model number: KENEK-VE20). Observation on soil water content was conducted by soil moisture sensor (Model number: S-SMC-M005, HOBO Data Loggers). As the groundwater level was relatively stable, the measurement interval was set to 1 h. The measurement interval of the surface flow observation was set to 5 min considering the ephemeral runoff was significantly influenced by rainfall intensity. To estimate the surface flow, the water level data were converted into discharge data. Manning’s mean velocity formula was applied to the conventional method for data transformation from water level to discharge (Eq. 2). Meteorological observations such as temperature, sunshine duration, wind speed, atmospheric pressure, and air humidity were also carried out at a meteorological station which was set up at the upstream of the Liudaogou Catchment. Layout of the field observation management was represented in Fig. 1c. Field observation was conducted since May in 2004, however, data deficiency in various degrees existed during the observed period due to influence by uncertain factors.

Numerical model for runoff calculation

The results on hydro-geological survey indicate that topsoil is loose loess with thickness of about 10–15 cm on the slope, subsequent to the topsoil, the soil profile is hard yellow ocher with thickness down to 20 m depth, the groundwater table (phreatic water) exists below the second soil layer. The under stratum is sandstone formed in the Jurassic period of Mesozoic. Model of the vertical profile of soil on the slope was therefore considered to be composed of two layers (Fig. 2). As there is no loose topsoil in the river channel, the set up of the soil layer from the ground surface to the groundwater table in the model was the single layer. Model lumping of the general hydro-geological conditions of the Liudaogou Catchment is depicted in Fig. 2.

Fig. 2
figure 2

Model lumping of hydro-geological conditions of the Liudaogou Catchment

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Ephemeral runoff is restrictively generated only for intensive rainfall in the rainy season at the wind–water erosion crisscross region of the Loess Plateau. In this study, surface runoff was estimated using rainfall-runoff numerical model. Various models on rainfall-runoff calculation have been conventionally proposed such as the prior representative models: System Hydrologic European (SHE, Abbott et al. 1986), Institute of Hydrology Distributed model (IHDM, Calver and Wood 1995), Topographic Kinematic Approximation and Integration (TOPKAPI, Ciarapica and Todini 2002), Soil and Water Assessment Tools (SWAT, Neitsch et al. 2000) and etc. Delfs et al. (2013) proposed a practical model in which coupled surface/subsurface flow model accounting for air entrapment and air pressure counterflow. To achieve accurate numerical calculation on runoff at the study location and to provide a practical numerical model for rainfall-runoff process for the Liudaogou Catchment, a numerical model was originally developed based on kinematic wave theory combined river channel network for rainfall-runoff process calculation for the distributive basin (Huang et al. 2008). The kinematic wave equations are used widely in calculating the rainfall-runoff process as it is physically based and utilizes physical parameters to characterize a basin. Kinematic model is also applied to describe the features of infiltration and subsurface lateral flows (Mariza et al. 1992; Yomoto and Mohammad 1992; Chua Lloyd et al. 2008). Sarkar and Dutta (2012) used the kinematic form of Darcy’s equation to formulate subsurface flow. To apply the kinematic model, lumping of the basin is necessary because of the physical characteristics, such as surface condition, roughness, and slope. So, characterization of the study area is required before the lumping (Huang et al. 2013).

Governing equations

The governing equations include equations of continuity, motion of one-dimensional surface flow (Eqs. 1 and 2), and infiltration flow (Eqs. 3 and 4) (used for the first layer in slope sector, Fig. 2).

$$\frac{\partial h}{\partial t} + \frac{\partial q}{\partial x} = r - f_{1}$$
(1)
$$v = \frac{1}{n}R(h)^{\frac{2}{3}} I^{\frac{1}{2}}$$
(2)
$$\lambda \frac{{\partial \overline{h} }}{\partial t} + \frac{{\partial \overline{q} }}{\partial x} = f_{1} - f_{2} - ET$$
(3)
$$\overline{v} = k\overline{I}$$
(4)

where, h is depth of water (m), q is unit width flow discharge (m2 s−1), x is distance in flow direction (m), \(\Delta t\) is unit time (s), v is velocity of flow (m s−1), r is effective rainfall (m s−1), f 1 is mean infiltration velocity of the first soil layer (m s−1), b is width of the river channel (m), n is coefficient of the roughness (s m−1/3), R is hydraulic radius (m), I is gradient of riverbed, λ is soil effective porosity, \(\overline{h}\) is depth of infiltration flow (m), \(\overline{q}\) is the discharge of infiltration flow of the unit width (m2 s−1), \(\overline{I}\) is gradient of the groundwater table of the first layer, f 2 is the mean infiltration velocity of the subsequent soil layer (m s−1), ET is the evapotranspiration (m s−1), \(\overline{v}\) is velocity of infiltration flow (m s−1), k is coefficient of permeability (m s−1).

The equations for calculation in the second soil layer were analogous with those of the first soil layer. Only the footnote number and the sectional form are replaced. The equations for the river channel are similar to those for the slope. Only some factors in the equations were replaced, which resulted in variation of the equations in forms.

Difference scheme

As the governing equations characterize the transfer of the boundary condition from upstream to downstream, the upstream difference scheme was used (Japan Society of Mechanical Engineers 1988). According to the upstream difference scheme, the continuity equation of the surface flow (Eq. 1) and the continuity equation of the groundwater flow (Eq. 3) were discretized as follows:

$$h_{i}^{n + 1} = h_{i}^{n} + {\text{d}}t(r - f_{1} - \frac{{q_{i}^{n} - q_{i - 1}^{n} }}{{{\text{d}}x}})$$
(5)
$$\overline{h}_{i}^{n + 1} = \overline{h}_{i}^{n} + \frac{{{\text{d}}t}}{\lambda }(f_{1} - f_{2} - \frac{{\overline{q}_{i}^{n} - \overline{q}_{i - 1}^{n} }}{{{\text{d}}x}})$$
(6)

where, n is time step, i is spatial step in flow direction, and other factors correspond to those previously mentioned.

Initial and boundary conditions

As the initial condition, the discharges of the surface and groundwater flows were assumed as 0 at the upstream end (the origin of the flow) of each slope sector. In the process of the calculation, boundary condition was set to the calculation on infiltration velocity in the first and second soil layers which is given by water depth of the surface flow and infiltration flow in the first layer, respectively. For example, the infiltration velocity of the first layer (f 1) in Eq. (1) was equal to the depth of water (h i ) divided by the unit of time (dt) (h i /dt) when h i /dt < f 1.

Model validation

Validity of the numerical model for rainfall-runoff calculation at the Liudaogou Catchment was tested and verified in previous studies (Huang et al. 2008, 2011). The numerical results showed excellent fit with the observed data (Fig. 3). The discharge was observed at the surface flow observation point (Fig. 1c). The difference between the calculated flow (C-flow in Fig. 3) and the observed flow (O-flow in Fig. 3) was <3 %. The model was therefore applied to rainfall-runoff calculation at the Liudaogou Catchment.

Fig. 3
figure 3

The simulated results of the surface flow (O-flow observed flow discharge, C-flow calculated result). a 11 Aug. 2004. b 29 Aug. 2008

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Numerical calculation for rainfall-runoff was carried out for 5 years (2005–2009); the numerical results of runoff were used for estimating annual runoff rate and evaluating water budget of the Liudaogou Catchment.

Results and discussion for runoff

Mechanism of runoff generation

Mechanism of runoff generation for saturated topsoil

Soil water content was also measured on the cross-section on which the surface flow was observed (Fig. 4). Figure 5 depicts the temporal process of rainfall, variation of soil water content at different depths and runoff on 15–16 August 2008. Rainfall amount is 86.2 mm, rainfall duration is 1,335 min, and the maximum rain intensity was 2.0 mm × 5 min−1. During the lag from rainfall start and runoff generation, as the rain intensity was lower than unsaturated infiltration velocity of the topsoil, rainfall was entirely infiltrated into soil by assuming evapotranspiration was 0. Soil water content at the depth of 5 cm in both sides began to increase at the different time point, respectively. Soil water content at the depth of 20 cm increased later than that of the depth of 5 cm, however, soil water content at 50 cm always remained stable before runoff generation. Runoff was generated by rain intensity of 0.6 mm × 5 min−1. At the time of runoff came into being, soil water content at the depth of 20 cm increased distinctly, whereas at the depth of 50 cm, its change was not clear. As rain intensity of 1.2 mm × 5 min−1 once occurred before runoff generation and the lag between start of rain and runoff generation was more than 10 h, topsoil attained saturation when runoff was generated (Fig. 5). Additionally, before the runoff generation, the accumulated amount of infiltration was 27.0 mm which was given by the initial loss assuming no evaporation. As the porosity of the topsoil was 0.30–0.35 at the surface flow, observed location thickness of the topsoil was estimated to be about 8 cm.

Fig. 4
figure 4

Schematic drawing of the surface flow and soil water content observed section

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Fig. 5
figure 5

Mechanism of runoff generation due to a long duration and low intensity rainfall (15–16 Aug. 2008) (arrow points out to the time when the runoff occurred)

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Another representative long duration with low intensity rainy event occurred on 14–15 August 2004 (Fig. 1, ESM only). In this rainy event, the rain duration was 735 min, total rainfall was 44.2 mm, and the maximum intensity was 0.8 mm × 5 min−1 before runoff generation. Runoff was generated by rain intensity of 0.6 mm × 5 min−1. Before runoff generation, rainfall of 22.6 mm was infiltrated into the soil. Topsoil was inferred to attain saturated conditions because the lag from rainfall start to runoff generation was more than 10 h. Therefore, mechanism of saturation excess runoff can be concluded that the topsoil attained saturation and rain intensity is ≥0.6 mm × 5 min−1.

Mechanism of runoff generation for unsaturated topsoil

Figure 6 depicts temporal process of rainfall, variation of soil water content and runoff which occurred on 29 August 2008. Rainfall was mainly concentrated between the time periods of 14:00–15:00 with an average intensity over 5.0 mm × 5 min−1. Runoff was immediately generated by a rain intensity of 4.2 mm × 5 min−1 at the time point of 10 min after rainfall started. Soil water content at various depths still remained relatively stable when runoff was being generated. Mechanism of runoff generation caused by high intensity rainfall can be simply generalized to postulate that runoff is consequentially generated by high rain intensity in spite of soil water content in the topsoil.

Fig. 6
figure 6

Mechanism of runoff generation caused by a short duration and high intensity rainfall (29 Aug. 2008)

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Three rainfall-runoff events that occurred on 11 August in 2004, 15 August in 2005, and 9 June in 2006 were chosen to evaluate the relationship between intensity of rain and runoff generation under unsaturated topsoil. The rainfall duration, rainfall amount, the maximum intensity, and the factors related to runoff generation are listed in Table 1. In all of the three rainfall events, runoff started immediately when intensity of rain attained 2.6 mm × 5 min−1. The lag time from the starting of rainfall to onset of runoff generation was <20 min and the topsoil was still unsaturated. Mechanism of the infiltration excess runoff therefore can be inferred that is the rain intensity ≥2.6 mm × 5 min−1.

Table 1 Index of rainfall of runoff events for unsaturated condition
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Figures 5 and 6 also show that ephemeral runoff is unstable and the magnitude was significantly influenced by intensity of rain. Runoff normally maintained transitory existence and disappeared soon after the rain ceased.

Correlation between rainfall factors and runoff rate

Some rainfall-runoff events were randomly selected to estimate the relationships between rainfall factors and runoff rate, and the results are listed in Table 1 (ESM only). The regression curve of average intensity of rain and runoff rate of the events in Table 2 are shown in Fig. 7. The curve indicates that high correlation (>0.87) exists between average intensity of rain and runoff rate. Both relationships between rainfall duration and runoff rate and amount of rainfall and runoff rate were also evaluated, there is no conspicuous relationship between rainfall duration and runoff rate (Fig. 2, ESM only), as well as between amount of rainfall and runoff rate (Fig. 3, ESM only). Therefore, among rainfall factors of average rain intensity, rainfall duration and amount of rainfall, average intensity is a key factor which impacts runoff rate of every runoff event.

Fig. 7
figure 7

Relationship between average rain intensity and runoff rate

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Annual runoff rate

Calculation of rainfall-runoff was carried out using numerical method (Eqs. 1–4), model lumping: Fig. 2) for 5 years (2005–2009). Data processed covered the period in which there was runoff generation. The results of annual precipitation, runoff and runoff rate are summarized in Table 2.

Table 2 Index of annual precipitation and runoff rate
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In 2005, because the precipitation was less than the annual mean and few intensive rainfall events occurred which resulted in three surface runoff events with low runoff rates. In 2006, though the amount of precipitation was evidently lower than the annual mean, due to concentrated rainfall mainly in the rainy season and the high occurrence of intensive rainfall events, there has been relatively high runoff. In 2007, precipitation was slightly more than the annual mean and its annual distribution approximately represented the normal year as most part was received in the rainy season in the form of several intensive rainfall events with relatively high intensity, therefore, runoff rate in 2007 was approximately equated to the annual mean value. In 2008, though precipitation was visibly higher than annual mean and was approximate to that of 2007, owing to lack of heavy rainfall event, runoff rate was less than that of 2007. In 2009, precipitation was approximate to that of 2008 but runoff rate was higher than that of 2008 due to differences in seasonal rainfall distribution between 2008 and 2009.

Mean annual precipitation in given years (2005–2009) was 439 mm which was approximately equal to the annual mean (430 mm a−1), while the average runoff rate was 11.0 %. Based on results of average annual runoff rates for 5 years (2005–2009), annual runoff rate at the study location can be estimated as 10–15 %.

Annual water budget

Water budget equation

Water budget relationship at the earth’s surface is complex and dynamic. The relationship involves interactions between atmosphere, surface, soil, plant and groundwater. Main components of the hydrologic circle are precipitation, runoff, infiltration, and evapotranspiration (Eagleson 1970; Huang et al. 2001). Analysis of the water balance is the basis for realizing the scientific evaluation and appropriate allocation of the water resources in a basin (Zhu et al. 2008). The results of the field observation and numerical results of the surface runoff for 5 years (2005–2009) were used for estimating the annual water budget of the Liudaogou Catchment. To emphasize target value of each water budget component, the unit area of 1 km2 was selected as the index area. Considering habitant water consumption at the study location, a new factor U was added to the common water budget formula (Eq. 5).

$$P = R + \Delta W + E + U$$
(5)

where, P is the precipitation, R is the runoff which includes surface runoff and groundwater outflow, ΔW is the change of water storage in a basin which manifests in variation of soil water content and the change of groundwater, its annual mean value is approximate to 0, E is evapotranspiration, U is the habitant water consumption, it includes domestic water and irrigation water at the Liudaogou Catchment.

The general distribution of water to components of water budget in the study location is depicted by a schematic illustration shown in Fig. 8. In the natural state, the water resources in a catchment maintain a normal sustainable state and keep a dynamic balance. However, if the water balance in a basin is distributed by water resources development and by human activities, such as groundwater overdraft for farmland irrigation, the change of water storage, ΔW, will lead to negative value or deficit state (Todd and Mays 2005; Yu 2008).

Fig. 8
figure 8

Diagram of annual water budget at the study location

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Each component of annual water budget

Precipitation

For a closed basin, the total water inflow refers to the precipitation received during the period of analyzes. Thus, average annual precipitation of 430 mm is the total water inflow to the study location in a normal year.

Runoff

Annual runoff includes surface runoff and groundwater outflow.

Average annual surface runoff rate for 5 years (2005–2009) was estimated at 11.0 % based on the numerical results of runoff calculation. As mean annual precipitation for the 5 years (2005–2009) was 439 mm, which is almost equal to the annual mean, surface runoff rate of 11.0 % was adopted as the annual runoff rate in the normal year and it is equivalent to rainfall of 47.3 mm a−1.

Observation of groundwater outflow was carried out and the observational point was as shown in Fig. 1c. Groundwater flow occurs at the phreatic zone and its discharge gradually increases from the observational position to the downstream. Discharge of groundwater flow was observed using a flow meter and the observed results indicated that the groundwater outflow was relatively stable at the observational point and did not show distinct change in spite of seasonal changes. The mean discharge throughout the observed time was about 1.77 × 103 cm3 s−1. However, groundwater outflow seasonally ceased in winter from December to the end of February due to the upper ground was frozen.

The Liudaogou Catchment can be treated as hydro-geological homogeneous model due to its uniform ground condition (Zheng et al. 2005). The groundwater flow is therefore considered to be uniformly generated from each tributary. On account of the catchment area of the discharge observed point is 1.04 km2, discharge of groundwater outflow from the unit area is estimated to be 1.70 × 103 cm3 s−1 and its annual amount is 4.04 × 104 m3 a−1 (converted to millimeter, 40.4 mm a−1).

Change of water storage

According to actual investigation at the study location, deep groundwater generally lies at depth of dozens of meters or even over a hundred meters from the ground surface. On the other hand, annual rainfall is mainly concentrated to the rainy season during which intense evapotranspiration consumes most of the soil water. Therefore, deep groundwater cannot get effective recharge from rainwater infiltration (Fan 2005). Annual water storage was thought to vary mainly with variation of the soil water content and change of the shallow groundwater (phreatic water).

The soil water content data were provided by the previous research activities at the same study location (Kimura et al. 2005b ). The observed point was shown in Fig. 1c. In the study location, evapotranspiration impacts the infiltration to the maximum depth of 60 cm from the ground surface and the soil water content remains relatively stable below this depth (Fan 2005). The observational depth of the soil water content was 4, 10, 26, 34, 42, 50, 58 66 cm and at the maximum depth of 100 cm. The results of the average soil water content at various depths indicate that mean soil water content maintained the same level at the beginning and end of each year such as on 1st January 2005, 2006 and 2007, soil water content is 0.0761, 0.076 and 0.0764 cm3 cm−3, respectively (Fig. 4, ESM only). Therefore, annual water storage response to variation of soil water content can be estimated to be 0.

Observation of shallow groundwater was carried out at a site (well No. 1) as shown in Fig. 1c. The observed results of groundwater fluctuation and mean monthly groundwater change during the observed time represents that groundwater maintains the same level at the annual corresponding time such as on 16 March 2005 and 2006, groundwater level was 1.465 and 1.467 m, respectively, and groundwater change is approximately 0 at the beginning and end of each year (Fig. 5a, b, ESM only). Thus, annual groundwater change remains constant.

Based on the analysis results of annual variation of soil water content and groundwater change, annual change of water storage is approximately 0 at the study location.

Water consumption

Water consumption in the Liudaogou Catchment includes domestic water and irrigation water.

Irrigation water was provided by two reservoirs, large and small as shown in Fig. 1c. The large reservoir supplied 70 % of the annual irrigation water requirement and the small one supplied 30 % of the balance requirement. The irrigation period was from late April to September almost covering the whole growing season. Amount of irrigation water withdrawal is roughly estimated by the change of the water level in the reservoirs. Method for estimating irrigation water withdrawal is to evaluate fall of water level from the original water level in the large reservoir as shown in Fig. 6a (ESM only). Monthly distribution of the irrigation water withdrawal from the large reservoir is shown in Fig. 6b (ESM only) which represents the irrigative process and the amount of irrigation water remained same in all 3 years (2006–2008). Based on the estimated irrigation water withdrawal from the large reservoir, amount of irrigation water provided by the small reservoir in the corresponding year was estimated to be 1.0 × 104 m3 (in 2006 and 2007) and 1.06 × 104 m3 (in 2008). The total irrigated area is 20.6 hm2 which is equivalent to 3.0 hm2 km−2 in the Liudaogou Catchment and annual amount of irrigation water is 5.1 mm of annual precipitation.

Domestic water normally includes water supply for residents and cattle. The domestic water is supplied by an artesian well at the upstream of the Liudaogou Catchment (well No. 2 in Fig. 1c). Groundwater in this well also belongs to the phreatic water. Based on the observed result of water level in well No. 2 (the data is discontinuous) and actual investigation on local water utilization, amount of daily domestic water requirement was 200 m3 and this increased to 300 m3 in summer from July to September. Total annual domestic water was estimated to 12 mm of annual precipitation.

Evapotranspiration

Evapotranspiration generally refers to the sum of evaporation from ground surface and transpiration from vegetation. In view of the complicated geomorphological features of the study location such as the bare land, the crops, and various types of vegetation, actual evapotranspiration is difficult to estimate accurately. Based on hydrological principle for water budget in a closed basin, its annual change of water storage is 0 and the water output consists of evaporation and runoff (Zhu et al. 2008; Li et al. 2011). Based on the estimated results of annual variation of the soil water content and groundwater change, which are both equal to 0 at the study location, annual evapotranspiration was approximately estimated by subtracting surface runoff, groundwater outflow, and water consumption from annual precipitation. And it is 324.2 mm over the unit area.

Index of annual water budget

Index (%) of annual water budget is listed in Table 3. Total annual runoff (surface and groundwater), annual water consumption, and annual change of water storage account for 20.4, 4.0 and 0 % of the total annual precipitation, respectively, while annual evapotranspiration represents 75.6 % of the annual precipitation. From view point of the total hydrological cycle, annual irrigation water use can generally be regarded as a part of evapotranspiration (Fig. 8) which resulted in evapotranspiration attaining 76.8 % of the annual precipitation. Domestic water can be considered as a part of groundwater outflow (Fig. 8) with the result that annual runoff accounted for 23.2 % of the annual precipitation.

Table 3 Components of annual water budget (unit area: 1 km2)
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Precipitation is supposed to be utilized efficiently by means of the proper methods, however, it is viewed as impossible under the current conditions. In view of the existing conditions at the wind–water erosion crisscross region on the northern Loess Plateau such as complex landform, intense evapotranspiration in summer and the underdeveloped economy, efficient utilization of precipitation and the surface runoff is difficult. Therefore, the shallow groundwater combined with its outflow becomes the significant available water resources for agricultural production and people’s daily lives.

Conclusions

In this study, the observed hydrological data and numerical results of the surface flow were used for evaluating the main runoff characteristics and annual water budget for the Liudaogou Catchment on the northern Loess Plateau. Some conclusions were drawn as follows:

For the characteristics of ephemeral runoff:

  1. (1)

    Mechanisms of runoff generation were clarified by analyzing the representative rainfall combined with runoff and change of soil water content in the same period. The conditions of runoff generation for saturated topsoil and unsaturated topsoil are intensity of rain ≥0.6 mm × 5 min−1 and ≥2.6 mm × 5 min−1, respectively.

  2. (2)

    A relatively high correlation existed between the runoff ratio and average rainfall intensity, runoff ratio was proportional to the average rainfall intensity.

  3. (3)

    Based on the annual runoff rate of 2005–2009 which achieved by numerical analysis of the rainfall-runoff, annual runoff rate of the Liudaogou Catchment was estimated to be 10–15 %.

For annual water budget:

Annual runoff, evapotranspiration, change of water storage, and water consumption accounted for 20.4, 75.6, 0 and 4 % of annual precipitation, respectively. Evapotranspiration is much more predominant than other hydrological factors in annual hydrological circle at the wind–water erosion crisscross region on the northern Loess Plateau.