Our study area on the Qianzhong Plateau (A=2193.14 km2) is the part of the Sancha River upstream of the Wujiang River, a branch of the Yangtze River in China (Fig. 1). The elevations of the study area vary between 1042 and 1846 m a.s.l. The climate type is north subtropical monsoon, with a high mountain influence. In recent decades, the mean annual rainfall amount is 1400 mm and peaks in the summer season during storm events and the annual average temperature is 15.6 ∘C (For data between 1961 and 2006). Strata from the Cambrian of the Lower Paleozoic Erathem to the Quaternary of the Cenozoic Erathem, except Silurian, Jurassic, and Cretaceous, all exhibit exposures. Among these exposures, the carbonate rocks of Permian and Triassic are most widely distributed, accounting for greater than 90 % of the study area (Table 2). Karst develops intensively. Thus, karst landforms, such as dolines, karren zones, and dry valley, are visible on the plateau, thus indicating that karstification is relatively high in the study zone with 23 underground rivers. The Yelanghu Reservoir, constructed in the study area in 1994, has become one of the main freshwater sources in Anshun, which supply drinking water to the city (Zhang et al., 2011). The Sancha River is the largest river in the study area and is considered to be the corrasion baselevel of the study area.

Data used in this study include 1:50 000 digital line graphic (DLG) data provided by the State Key Laboratory of Environmental Geochemistry (transformed into DEMs, with a resolution of 30 m, by using ArcGIS), geological data, hydrogeological data obtained through hydrogeological mapping, hydrogeological drilling, water quality tracing experiment based on geophysical prospecting, and high-resolution remote sensing image data (resolution of < 2 m). In 2012, precipitation in the study area is the data provided by the online observation of ecosystems and by research stations in China (Chinese Ecosystem Research Network (CERN), Puding). The aforementioned data sources are used in ArcGIS to establish a coordinate system that can be used to conduct spatial analysis. After the indoor extraction of KW based on the method previously presented, we conducted considerable field work to verify the boundary of small watershed on site.

By adopting the traditional method of automatic extraction, this step is completed by using the hydrological tools available in ArcGIS (Martz and Garbrecht, 1999). TIN is firstly established by using the digital line graphic (DLG) data and is converted to DEMs data, but DEMs data can also be obtained from existing data (such as ASTER DEMs and SRTM DEMs). Thereafter, flow distribution is conducted by using the commonly adopted D8 algorithm (Mark, 1984; O'Callaghan and Mark, 1984). However, in actual DEMs products, grids around the karst regions are higher than the depressions because of false data or the existence of “pits” or “sinks” in actual terrain. This phenomenon results in the retention of runoffs in depressions. Consequently, the extracted river network is discontinued and deviation errors occur in the flow direction and river network (Nikolakopoulos et al., 2006; Jiang et al., 2014b; Tarboton et al., 1991). Therefore, the pretreatment of DEMs data is necessary to fill the depressions in the data. After this process, the elevation value of the grid of the depression is equal to the elevation value of the surrounding lowest point. By modifying the elevation value specified previously, the elevation values of all grids in the DEMs are larger than or equal to that of the lowest outlet. In this manner, a DEM “with hydrological meaning” is generated and the continuity of the natural water system of the watershed extracted from DEMs data can be ensured (Li et al., 2003).

After filling the depressions, the elevation of each DEMs grid can be compared with its adjacent grids in 8 directions. The direction with the steepest slope is the direction of the runoff in this grid (Kiss, 2004; Jenson and Domingue, 1988). In ArcGIS, grids obtained after the calculation of the flow direction are marked as 1, 2, 4, 8, 16, 32, 64, and 128 to record the different flow directions of grids. On the basis of the determined flow directions of grids, the area of the upstream catchment of this grid is determined by calculating the number of grids whose upstream catchment flows directly or indirectly to the designated grid (Jensen, 1991). After generating an output raster of flow accumulation, the threshold of the grid where flows accumulated is selected as the area threshold of the upstream feeding area on the basis of the characteristics of climate in a certain region. The grid whose threshold is equal to the area threshold is adopted as the initial point of the watercourse. Grids with thresholds greater than the area threshold constitute the watercourse (Qiu et al, 2012). Furthermore, watershed and sub-watershed outlets can be defined by using the accumulated area raster. Thereafter, the watershed can be delineated and the watershed boundary can be converted to a vector polygon by using GIS tools (Khan et al., 2014).

Influenced by regional tectonic activities, the datum plane significantly affects the hydrological and geomorphic processes within a certain region (Fitzpatrick, 1998). The corrasion baselevel is usually at the level of the adjacent large river instead of the sea level in most parts of a karst region. As such, the erosion baselevel is associated with the sea level through the trunk stream (Li and Cui, 2004). The regional tectonic uplift and strong downcutting of the river cause the formation of relatively independent water-bearing blocks locally. In most cases, independent recharge, runoff, and discharge areas exist in each block, which leads to the exposure of subterranean rivers or karst springs around the discharge datum plane in karst regions (Yang, 1982). As a result, the place where subterranean rivers or karst springs is exposed can be turned into a perpetual open channel because the corrosion baselevel of this area in karst regions can be used to determine the exit of watersheds (shown in Fig. 2a). The main watercourse of a large river in the region is considered to be the regional corrasion baselevel line (shown in Fig. 2b). In this manner, the line linking corrosion baselevel and corrasion baselevel is the regional corrosion and corrasion baselevel line (shown in Fig. 2c). In watershed management, the intersection of the corrosion and corrasion baselevel line and the main watercourse of the large river is considered to be the exit of the KW (shown in Fig. 2d).

As stated in Sect. 3.2, the watercourse of the large river, which can be extracted automatically based on the DEMs, is the trunk stream of the watershed in the downstream area of the regional corrosion and corrasion baselevel in karst regions. By contrast, the main watercourse is often characterized by the alteration of open channels and subterranean streams in the upstream area of the corrosion and corrasion baselevel because of the effects of the lithologic characteristics and structure of stratum, fault, and folding. In the area of subterranean streams, the error rate of the automatic extraction of trunk stream based on the DEMs is high. Thus, the manual correction of the trunk stream of ATW can be conducted from the upstream watercourse to the exit of KW by using terrain data, high-resolution images, and hydrogeological data. The correction process is shown on the left of Fig. 3. In the upstream area of (1) ATW featuring clastic rocks, the trunk stream is the surface runoff that enters the carbonatite area at site a. The trunk stream turns into a subterranean river and flows to the (2) area. At site b, the subterranean river encounters the water-resisting layer of clastic rocks and flows to (3) the ATW area through sunken pipes. Finally, the subterranean river flows out of the surface at b in the (4) ATW area. The trunk stream reaches the exit of the KW and enters the watercourse of the regional large river (corrasion baselevel). According to the high-resolution images, no overland runoffs exist in the automatically extracted areas where the trunk stream flows through in the eastward direction of a in the (1) ATW, the eastward direction of b in the (2) ATW, and the southward direction of c in the (3) ATW. The hydrological processes of these areas are dominantly underground processes. Thus, manual correction is necessary on the topographic trunk stream extracted automatically in these areas to obtain the trunk stream on the basis of the dual structure of the surface and underground in the KW.

After the determination of the trunk stream of the surface and underground in KW, determining the flow direction of each hydrogeological unit in the area it flows through becomes an important step for the extraction of KW. In non-karstic terrains, groundwater divides are assumed to directly underlie the surface topographic divides as determined from contour maps and aerial photographs (Ford and Williams, 2007). However, in karst areas, groundwater flow is significantly independent of topography but is often guided by geological formations and structures (Nico and David, 2007). Therefore, in areas without carbonatite, the flow direction is determined on the basis of the surface terrain. By contrast, in carbonatite areas, the flow direction is determined by considering the lithological characteristics and the combination of strata, fault, and structure and by conducting geophysical survey, tracing experiment, and model simulation (Rugel et al., 2016). On this basis, the distribution of watershed in the area with permeable strata in karst carbonatite is determined.

After completing the steps presented in Sect. 3.4, the watershed distribution of all karst hydrogeological units is almost completely determined. Corrections on several divides extracted automatically are imperative to enable the boundary of the dividing area to reflect the karst hydrological process more accurately. Two conditions must be considered in the process of correction. (1) The divide runs through areas featuring clastic rocks (not carbonatite) with water-resisting layers or slopes where the terrain changes significantly. Considering the fact that the hydrological process of these areas is mainly characterized by surface runoffs, the watershed boundary of KW is considered to be the watershed boundary of ATW; i.e. correction on the automatically extracted divide is not needed. (2) In carbonatite areas characterized by underground corrosion where vertical permeation and subsurface runoff are the dominant hydrological processes (negative relief develops well in these areas and peak cluster depression is the main topographic feature), correction of ATW boundary and watershed distribution is completed by using hydrogeological data and high-resolution images and by using the flow direction determined in Sect. 3.4. In this regard, an example is shown in Fig. 4. A depression with no surface runoff is observed in the dividing area between KW 1 and KW 2, and the hydrological process is absolutely different from that of surface terrain. Underground runoffs in the depression flows through A′ (terrain peak) and sunken pipes in karst carbonatite areas and accumulates in KW 1. However, the true divide goes through the water-resisting layer of clastic rocks where B′ is located. Accordingly, we conducted manual correction on the watershed divide on the basis of the features of the underground hydrological process.

From the perspective of quantity, 22 small KWs are extracted in the study area. Compared with those based on DEMs, the number of watersheds was reduced by seven (Fig. 5), a decrease of 24 %. For the watershed boundary, the total length of the boundaries of small watersheds on the surface obtained based on the DEMs in the study area is 1381.47 km. The total length of the boundaries of KWs is 1004.18 km. The length of the boundaries shared by these two types is 394.36 km, accounting for 28.5 % of surface watershed boundaries and 39.27 % of KW boundaries.

In terms of the superimposition of watersheds, the number of watersheds that reached the level of coupling is nine in ATW and KW. The number of watersheds without any coupling is also nine, and the number of approximate coupling is four (Table 3). Furthermore, except for watershed 3#, at least two pairs of superimposition of surface watersheds are observed in all the other small KWs.

The linear correlation between the water flow of subsurface runoff (or karst spring) in normal seasons (from May to October), which is 1 of the 13 rivers with water flow obtained previously, and the area of the upstream catchment is examined. In KW, the linear correlation coefficient (R2) between the water flow in normal seasons and the area of the upstream catchment is 0.84 (Fig. 6). In addition, Table 4 shows the proportions of atmospheric precipitation in the upstream catchment area of 13 subterraneous rivers (or karst springs) that are converted into subsurface runoffs. The values of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and total RATW are all greater than 100, thus indicating that the upstream catchment areas extracted automatically are small. Accordingly, the RKW values of 13 subsurface runoffs (or karst springs) are all less than 100, thus indicating that the small KW that we extracted is reasonable.

The automatic delineation of watersheds is extensively accepted and applied by hydrologists, geologists, and ecologists internationally because of the convenience in the acquisition of data source and automation in the extraction process (Verdin and Verdin, 1999). However, in karst areas, wherein the eco-hydrogeological principles are complex and significant differences exist in the dual structure of the surface and underground (Yang, 1982). This study has presented a novel approach to overcome faults of the traditional method of delineation watersheds in karst areas, by combining hydrogeological principles and DEMs. The method proposed in this study not only had similar advantages of accurate expression of terrain and quick automation as the traditional automatic extraction method but also considered the specific eco-hydrogeological principles in karst areas.

The multiple methods from the geography, topography, hydrology, and hydrogeology were used conformably in the five steps of delineation KW. The work extends previous studies on watershed delineation using 3S (GIS, RS, and GPS) and digital terrain data (Hollenhorst et al., 2007; Seyler et al., 2009). In these studies, watershed delineation has the following advantages: (i) the DEMs data (e.g. the Shuttle Radar Topography Mission DEMs and the Advanced Spaceborne Thermal Emission and Reflection Radiometer – global digital elevation model) is easy available (Jarihani et al., 2015); and (ii) Surface morphology analysis based on DEMs is accurate in the digital mapping to ditch, slope, mountain divide, and drainage network, with the advantages of high automation and wide spatial scale from the global to the nano - or microscales (Wilson and Gallant, 2000).

On the other hand, in the research fields of karst hydrology and karst hydrogeology, the study of watershed delineation most concentrated on delineation the catchment area of a single spring (Table 1) (e.g. Fontaine de Vaucluse Spring in the southeastern karst region of France; St. Ivan karst spring in the centre of the Istria peninsula of Croatia; Ombla karst spring in Croatia) or a ground runoff (e.g. Cuatrociénegas of Mexico) using geophysical and geochemical methods (Bonacci, 2001; Wolaver et al., 2008). In these cases it is reliable that determined the catchment area of the ground runoff on the surface, but expensive and impracticable that the methods are applied to a greater geographical spatial scales. Therefore, this study has combined the above two advantages to delineate KW based on the dual structure of the surface and subsurface, and this integrative delineation KW framework can be applied to map karstic catchments in multi-scales.

In the field of topography, the key of watershed delineation is the extraction of drainage network that can be divided into different rank, accordingly, the rank of the watershed can be divided respectively (Fürst and Hörhan, 2009). Moreover, one of the most critical issues in deriving drainage networks from DEMs is the location of the channel head in the Arc-Hydrology tool (Vogt et al., 2003). Therefore, whatever a contributing area threshold to generate headwater can be defined and then the vary drainage network and watershed can be delineated.

However, Karst landscapes are influenced by three main factors: the geological setting, the influence of events within the Quaternary (the last ca. 1.8 million years), and recent processes (usually taken to cover events within the Holocene or the last ca. 10 000 years) (Viles, 2003). In some areas, with the affection from the lithology and geological tectonic movement, and the domination from the Earth's crust uplift and the long-term corrosion (as described the above Sect. 3.2), runoffs often enter into ground conduits (Pitty, 1968). Then the inconsistency can be developed between the delineation watershed area by only considering the surface topography and the physical hydrological process (Fig. 3). Obviously, the watershed should not be further divided in such karst areas. This study has proposed that the minimum unit of the river basin in karst regions should be the watershed whose exit is the corrosion and corrasion baselevel, which ensures the coincident hydrological process of the dual structure of surface and subsurface.

The method of delineation KW in this study has proposed karst based on the dual structure of surface and subsurface and should be used in the karst areas where a wide range of closed surface depressions, a well-developed underground drainage system, and a strong interaction between circulation of surface water and groundwater is typical (Bonacci, 2009). In contrast, (i) for the karst area covered by glaciers (e.g. northern Tibet, high alpine, cordillera), the karst solution processes are unlikely to be an important factor in karst landform development because of low solubilities and/ or low secondary porosity (Zhang, 1996; Plan et al., 2009; Viles, 2003); (ii) for steep slope in karst areas (e.g. the eastern Tibet plateau), the karst hydrological processes are dominated by surface runoff and the development degree of underground karst processes is low. In the above two areas, a watershed can be delineated by traditional method on the basis of the surface topography.

Moreover, the small watershed extracted by using the new method has a better application value in the management of regional water resources, ecological construction, and management of land utilization. On that account, this method can be utilized by fellow scientists and government managers from around the world. Furthermore, on the basis of the method proposed in this study, our subsequent study will be focused on further promotion of the level of automation in KW extraction.