A modified topographic index that incorporates the hydraulic and physical properties of soil

Topography is an important land-surface feature affecting the soil moisture and runoff generation in a watershed. The topographic controls over the rainfall–runoff process are generally represented by the well-known topographic index ln(α/tanβ) (TI). In a topography-based water cycle simulation, the local water deficit which is the key factor to determine the point as unsaturated or saturated is physically linked to the local TI and the catchment mean soil moisture deficit. The saturated areas are generally defined as contributing areas generating subsurface flow or surface flow (Beven & Kirkby 1979; Beven 2012). Thus, TI is capable of predicting the propensity of any point in a catchment to generate runoff, and represent the effect of topography on the rainfall–runoff process.

In the past decades, because of the simple computation and its correlation with soil moisture and runoff generation, TI has been widely applied to various aspects of hydrology, agriculture, and environment. Hydrologists have made many efforts to modify TI to improve its physical significance and accuracy. These modifications mainly include amending the calculating method of accumulative upslope area (α) and the local slope (tanβ) (Feifei et al. 2004; Hjerdt et al. 2004); solving the problems resulting from digital elevation model (DEM), such as abnormal grids, optimal resolution, and boundary discretization (Cai & Wang 2006; Aryal & Bates 2008; Xu et al. 2008); trying to apply different types of down-slope transmissivity profile, such as the original exponential, the parabolic, and the linear profile (O'Loughlin 1986; Ambroise et al. 1996a; Sun et al. 2014). These modifications are mainly made on the basis of the classical TI which only considers the impacts of topography. Additionally, other modifications of TI focused on the impacts of soil heterogeneity since soil is an important factor in affecting the actual rainfall–runoff process (Famiglietti & Wood 1994; Ambroise et al. 1996b; Lei et al. 2016).

The influences of soil heterogeneity on the rainfall–runoff process were originally considered at the original construction of a soil topographic index ln(α/tanβ·T₀). However, specifying a spatial distribution for T₀ is generally much more problematic since there are not good enough measurement techniques for obtaining this parameter (Beven 2012), thus T₀ was omitted from ln(α/tanβ·T₀) by assuming the distribution of T₀ is spatially homogeneous, thus TI was formed. As the impacts of soil heterogeneity on the rainfall–runoff process still deserves attention, we tried to find another soil characteristic parameter D and integrate it into TI to construct a modified topographic index TI′. We supposed TI′ satisfies the two hypotheses that: (1) TI′ could correctly represent the effects of soil heterogeneity on the rainfall–runoff process; and (2) TI′ could improve the performance of the topography-based hydrological model.

During the selection of D, two requirements were necessary: (1) D should be directly or indirectly related to soil transmissivity and macroporosity which are two of the most important factors affecting soil water movement; and (2) as the field observed soil parameters are unavailable in our investigation, D should be closely related to soil texture to ensure the availability of its spatial distribution. Similarly, as the assumption that the transmissivity profile may be described by an exponential function of storage deficit, and with a value of T_o when the soil is just saturated to the surface (zero deficit) (Beven 2012), we assumed that the soil property characterized by D keep an exponential function of storage deficit as well, and when the soil is just saturated to the surface, it can be presented by the value of D. Therefore, the modified expression for TI′ can be defined as ln(α/tanβ·D). This paper aims to search for a relatively appropriate revised form of TI′ and test the two hypotheses mentioned above to prove the rationality of TI′.

The impacts of soil on the rainfall–runoff process are generally caused by multiple soil properties, thus D is not limited to one certain soil characteristic parameter. As satisfying the two requirements regarding D mentioned above, the saturated hydraulic conductivity (K_s) and the soil erodibility factor (K) were selected. K_s represents the hydraulic property of soil, it characterizes the soil capacity to conduct water flow. Soil with higher K_s value indicates a stronger ability to conduct water and consequently increase the soil moisture, and thus easier to generate runoff (Archer et al. 2013). K delegates the physical property of soil, it quantifies the soil's ability to resist water erosion, and soil with higher K value indicates a stronger ability to retain water and consequently easier to form runoff (Zhang et al. 2009). D can be defined as K_s, K, or K_s·K. The reason for the usage of the product of K_s and K, rather than the other forms, is to keep the exponentially correlated assumption. Thus, there are three optional revised forms for TI′ including ln(α/(tanβ·K_s) (TI1), ln(α/(tanβ·K) (TI2), and ln(α/(tanβ·K_s·K) (TI3).

YLX in northwestern China covers an area of 10,009 km², and is in a typical arid and semi-arid region located in the upper Heihe River Basin. WJB lies in the upper Huaihe River Basin, covers an area of 30,630 km², and is in the climate transition zone from humid to semi-humid. HQ is a typically humid watershed in the upper Nanshui River which is a tributary of the Yangtze River, and has an area of 2,660 km².

As the field observations of K_s and K are time-consuming, and K_s and K are sensitive to soil texture (Williams et al. 1983; Kaczmarek et al. 2016), the pedo-transfer function method (Sun et al. 2016) was applied to get the values of K_s and K. The soil property estimation module integrated in the SPAW hydrological model (Saxton & Rawls 2006) was applied to calculate K_s. K was calculated with the erosion productivity impact calculator (Williams et al. 1983). Since there are two layers for each soil type recorded in HWSD, the K_s and K values for each soil type are depth weighted. For the water bodies, the values of K_s and K were set as 1 to exclude them from soil. The statistics of the spatial distributions of K_s, K, and K_s·K in YLX, WJB, and HQ are shown in Table 1.

Hydro-meteorological data used in the simulation and evaluation of rainfall–runoff process were collected from the local hydrological or meteorological stations (shown in Figure 1). Considering data availability, for HQ, the daily precipitation and evapotranspiration data were obtained from the local precipitation and evaporation stations which were recorded in the book of Annual Hydrological Report for the P.R. of China. For YLX and WJB, the daily precipitation and evapotranspiration data were acquired from the local meteorological stations offered by China Meteorological Data Sharing Service System (CMDSSS). The observed daily discharges from the outlets of YLX, WJB, and HQ were collected from the Annual Hydrological Report of the P.R. of China. The study periods are 1995 to 2000 for YLX, 2001 to 2005 for WJB, and 2007 to 2011 for HQ.

It has been observed that saturated soils where rain falls are commonly adjacent to stream channels, and the dynamic contributing area can been regarded as the extension of stream systems to some extent (Beven & Kirkby 1979). Therefore, the detailed stream networks can reflect the distribution of the contributing areas to some extent. If the stream network extracted based on TI′ can reflect the flow tendency affected by soil heterogeneity (as mentioned earlier), the first hypothesis about TI′ can be proved.

The watershed delineation tool Terrain Analysis using Digital Elevation Models (TauDEM) was used to extract stream networks for YLX, WJB, and HQ. In the process of stream network extraction, flow direction is a fundamental and important factor affecting the final extracted result (Tarboton 1997), while flow direction is also a fundamental and decisive factor in TI. Thus the stream network can be extracted based on TI by using the same calculation algorithms of flow direction used in TI.

To extract the stream networks based on TI and TI′, we replaced the local slope in TauDEM by the tanβ expressed as Equation (2) and the tanβ·D expressed as Equation (5), respectively. During the extraction procedure for a certain watershed, the DEM used and other indispensable parameters, such as the location of watershed outlet and accumulated area threshold were fixed, so as to ensure the changes between the stream networks extracted based on TI and those extracted based on TI′ are only caused by the different inputs of soil parameters.

A previous study (Yan & Zhang 2014) demonstrated that the model efficiency improved when spatial heterogeneity of the watershed was considered. In order to test the second hypothesis about TI′, the daily rainfall–runoff process was simulated in the study watersheds. The efficiencies of the classical hydrological model TOPMODEL and the land surface hydrological processes model TOPX (Yong 2007) were evaluated. TOPX was applied in YLX and WJB, TOPMODEL was used in HQ as TOPMODEL was built for humid temperate areas (Beven 2012).

Both TOPMODEL and TOPX were built based on the concept of the topographic index. TOPX is a hydrological model constructed on the basis of the topographic index (TOP) and the water balance concept of the Xin'anjiang model (X). It applies the improved SIMTOP runoff-generation parameterization scheme, and the empirical unit hydrograph method, the linear reservoir equation, and the Muskingum method are applied for the routing of overland flow, base-flow, and channel flow, respectively (Yong 2007).

Combining the stream network changes illustrated in Figure 5 with the K_s, K, and K_s·K values listed in Table 3, it is clear that these streams turn from the places with lower K_s, K, and K_s·K to the places with higher K_s, K, and K_s·K. As mentioned in the section ‘Selection of soil characteristic parameter’, the lower values of K_s and K indicate weaker water conductivity and soil erodibility, while the higher values of K_s and K represent stronger water conductivity and soil erodibility. Thus, the natural phenomenon that the streams are more likely to form in the place with stronger water conductivity and stronger soil erodibility are correctly represented by these changes of stream networks. As the detailed stream networks can reflect the distribution of contributing areas to some extent (mentioned in the section ‘Extraction of stream networks based on TI and TI′’), it is concluded that for the places with stronger water conductivity and stronger soil erodibility it is easier to become contributing areas and generate runoff. It means that the impacts of soil properties on the rainfall–runoff process can be correctly represented by the incorporations of K_s, K, or K_s·K, and the first hypothesis about TI′ is tested to be correct.

Previous studies (Wolock & Price 1994; Lin et al. 2010) have shown that it should not be concluded that coarse resolution is an inappropriate source of topographic information for topography-based watershed models. Moreover, considering the large spatial scale of soil data, the resolutions of the input data, i.e., the precipitation, evapotranspiration, and the mean topographic indices, were set as 1 km. As there are a large variety of soils in each study watershed, the exponential decline of transmissivity could be valid (Beven 1982). Similarly, we assumed the exponentially correlated assumption of K_s, K, and K_s·K were valid in YLX, WJB, and HQ.

To achieve relatively better compatibilities between the models and the study areas, the calibrations and validations of the TOPMODEL and TOPX were performed in the study watersheds. Using the data of the first three years of the corresponding study periods, TOPMODEL and TOPX were calibrated with the method of trial-and-error. The model validation for each study watershed was investigated with the data of the remaining two or three years of the corresponding study periods. The results of the calibrations and validations showed adaptive applications for TOPX in YLX and WJB, and for TOPMODEL in HQ. The calibrated parameters for TOPX and TOPMODEL are listed in Table 4.

The daily rainfall–runoff processes during the entire study periods were simulated with the different inputs of TI and TI′ in YLX, WJB, and HQ. During the simulations, the corresponding calibrated parameters and input data for each watershed were fixed, to ensure that the changes of simulated results are only caused by the different inputs of TI and TI′, with soil being the only controlling factor for the changes of the simulated flows. The other possible impacting factors such as topography, vegetation, land use, dams, and reservoirs can be excluded.

The simulated daily and mean monthly stream flows of TOPMODEL and TOPX based on TI, TI1, TI2, and TI3 were evaluated and are shown in Table 5. The CEs and Rs of the simulated mean monthly stream flow are obviously improved compared with the CEs and Rs of the simulated daily results. For the simulated daily stream flow, based on TI1, the CEs in the three study areas are equal to (in WJB) or lower than (in YLX and HQ) the corresponding CEs based on TI; based on TI2, comparing with that based on TI, the CEs in WJB and HQ are decreased, only in YLX the CE improves by 0.007 but its R is reduced by 0.007; based on TI3, the REs in YLX, WJB, and HQ are increased by 0.039, 0.011, and 0.007, respectively, but both the CEs and Rs are improved, the CEs are increased by 0.063, 0.019, and 0.003, respectively. For the simulated mean monthly stream flow, compared with the other simulated results based on TI, TI1, and TI2, the CEs and Rs based on TI3 are improved the most, the CEs in YLX, WJB, and HQ are increased by 0.036, 0.006, and 0.001, respectively. The performances of TOPMODEL and TOPX based on TI3 are all improved in the three study watersheds. TI3 is suitable for the topography-based hydrological modeling in different climatic regions. Therefore, the second hypothesis about TI′ is proved and TI3 is recommended for the revised form of TI′.

Although the incorporation of K_s·K affects the distribution of topographic index evidently (shown in Figure 3), the topography-based hydrological models are sensitive to the mean of the topographic index distribution (Wolock & Price 1994; Lin et al. 2010), which may weaken the performance improvements of the topography-based models. Although the improvements based on TI3 were minor in the study watersheds, they were confirmed with the minor changes of the extracted stream networks. TI3 can quantify the impacts of soil on the rainfall–runoff process. It is useful to improve the physical mechanism of topography-based hydrological simulation.

Aiming at quantifying the impacts of soil on rainfall–runoff process, K_s and K were selected and incorporated into TI to construct TI′. In order to select the proper expression for TI′ and test the rationality of TI′, the extracted stream networks based on TI and TI′ in different climatic watersheds were analyzed. The extracted results showed that the incorporation of K_s·K would not cause any unacceptable or abrupt changes on the stream networks. The changes of the stream networks between those extracted based on TI and those extracted based on TI3 were capable of reflecting the tendency that the points show greater potential to be saturated to become contributing areas if their underlying soils have higher soil hydraulic conductivities and stronger soil erodibilities. ln(α/(tanβ·K_s·K) (TI3) was found suitable for the daily rainfall–runoff simulation in different climatic regions. The performances of the topography-based TOPMODEL and TOPX based on TI3 were all improved, and the extent of the performance improvements are in proportion to the soil spatial heterogeneities. Although the incorporation of K_s·K evidently affected the distribution of the topographic index, the topography-based hydrological models are sensitive to the mean of the topographic index distribution, which may weaken the performance improvements of the topography-based models. Although the improvements were minor, the incorporation of K_s·K to TI can quantify the impacts of soil hydraulic and physical properties on rainfall–runoff process, and it is useful in improving the physical mechanism of topography-based hydrological simulation. As the two hypotheses were satisfied for TI′, TI3 was recommended for the modified expression of TI′.

This work was supported by the National Natural Science Foundation of China (No. 41175088), the National Basic Research Program of China (973, No. 2010CB951404) and the Joint Program on Space Technology for Disaster Mitigation in Asia (No. Y3YI2701KB). We are very grateful to Zhang Jingnan from the Hydrology Institute of Hohai University for assisting with the hydrological simulations.