Impact of Human Development on the Phenomenon of Surface Runoff Crossing Adjacent Watershed Boundaries

Abstract

The concept of watersheds, also called catchments, is fundamental to both flood mitigation and water resource management, as it greatly aids in the calculation of overland flow attributes. Watershed boundaries are typically determined by elevation, as water adheres to the geological characteristics of watersheds under natural circumstances and does not cross watershed boundaries. However, advances in human development have caused elevation and land usage changes, and boundaries between adjacent watersheds in downstream areas with flat terrain have become unclear and unstable. This study chose the Kaoping River watershed and Donggang River watershed as the study area, to investigate the cross-watershed runoff phenomenon under different return period rainfall. Based on land use surveys of the study area, the area in proximity to the boundary between the two watersheds was highly developed, with land primarily used for agriculture, buildings, and transportation. As the study area was highly developed, cross-watershed runoff was observed, even in the 2-year return period rainfall simulation case. The size and depth of the areas where cross-watershed runoff occurred became stable in the simulation cases, with return periods of 25 years or greater due to the surrounding high-elevation terrain obstructing further surface runoff development. Thus, when planning for flood mitigation, cross-watershed runoff from adjacent watersheds must also be considered, in addition to normal surface runoff.

1. Introduction

Taiwan is situated in the Pacific Northwest and has some of the highest levels of typhoon activity in the world [1,2]. According to statistics from Taiwan’s Central Weather Administration (CWA), an average of 3~4 typhoons strike Taiwan each year. Heavy wind and rainfall brought by typhoons cause massive economic losses and endanger the lives of the general population. The Intergovernmental Panel on Climate Change (IPCC) has stated in its Sixth Assessment Report (AR6) that the influence of climate change will cause the difference in rainfall between wet and dry seasons to become even more pronounced for most areas around the globe [3]. Extreme weather disasters have become a major global threat [4], and the prevention and mitigation of damage caused by heavy rain disasters have become an issue of high importance worldwide.

Watersheds, areas determined by natural hydrological boundaries, are considered to be important areal units in environmental decision-making [5]. In past studies, rainfall–runoff simulations considered each watershed as an independent area during the simulation [6,7,8]. A watershed is an area composed of a mainstream and all the mainstream’s tributaries inside a geographical area [5,9]. Watersheds vary in size, with areas usually decided by geographical characteristics, such as the topography, terrain, and runoff direction. All tributaries in the watershed eventually converge into the mainstream and exit the watershed through a single outlet, such as a river, lake, or ocean [9]. Hydrological phenomena are closely related to watershed characteristics. The concept of watersheds is extremely important to hydrology, environmental science, and water resource management. Understanding watershed characteristics can help us better understand water flow phenomena and aid river management agencies in water resource management and usage. The boundaries of watersheds or catchment areas were usually determined by elevation [5]. However, rapid urbanization has caused massive land usage and surface elevation changes [10,11,12,13], and the boundaries between adjacent watersheds have become unclear and irregular. Hence, defining a clear boundary for downstream areas of different watersheds has become very difficult [14].

In most circumstances, water adheres to geographical characteristics and, thus, does not flow across different watersheds. The most common cause of water crossing watershed boundaries is the manual transfer of water, called interbasin water transfer [15,16,17]. Interbasin water transfer can be achieved by building infrastructure, such as canals, reservoirs, tunnels, or pipelines, to transfer water from one watershed to another [18,19]. Issues that interbasin water transfer can address include differences in water resource requirements, the need to improve irrigation, water shortages, and other environmental, economic, or political concerns. In addition to interbasin water transfer, water crossing watershed boundaries can also occur in downstream areas during typhoons and heavy rain events [14]. When only a single watershed is considered, this phenomenon causes possible inaccuracies in runoff simulation results and potential inundation maps. Inaccurate data renders real-time disaster relief manpower and equipment allocation ineffective, when misjudgment occurs during disaster prevention, damage assessment, and disaster response. It is crucial to consider adjacent watersheds when performing the aforementioned actions.

Overall, 73% of Taiwan’s population is at risk of encountering over three types of natural disasters, the highest percentage in the world [20]. According to Taiwan’s Ministry of Agriculture, Taiwan’s agricultural industry loses approximately USD 24 million annually due to natural disasters, such as heavy rain, typhoons, earthquakes, and cold waves, with damage from typhoons and heavy rain being the most severe. Flood disasters are often related to an inability to release surface runoff fast enough. The disaster prevention ability can be improved if runoff characteristics are better understood. To investigate the phenomenon of cross-watershed runoff in downstream areas, this study used the PHD model with different return periods to simulate the exchange of runoff over watershed boundaries in different precipitation scenarios. The simulation results were used to further understand which rainfall conditions may cause cross-watershed runoff and the effects of human development on the phenomenon.

2. Materials and Methods

2.1. Study Area

This study chose the Kaoping River watershed and the adjacent Donggang River watershed, both located in southwestern Taiwan, as the study area. The Kaoping River watershed is the largest in Taiwan, with an area of 3320 km². Kaoping River is the second longest river in Taiwan, with its mainstream originating from Yu Shan, and being 171 km in length. The Donggang River watershed is located south of the Kaoping River watershed, with an area of 480 km², or approximately 1/7 of the Kaoping River watershed. Donggang River’s mainstream originates from the mountainous areas of the Pingtung district. The elevation of both watersheds is higher in the northeastern direction, with the elevation gradually decreasing toward the southwestern direction. The distribution and relative positions of the elevation are shown in Figure 1. The elevation distribution of the boundary between the two watersheds and the surrounding area is shown in Figure 2. The area from the estuary to approximately 37 km in the upstream direction is relatively flat, with an elevation below 100 m. However, the elevation rapidly increases to about 1700 m, once the hilly and mountainous regions are reached. The area within 500 m from the watershed boundary line shows that the watershed boundary line does not have the highest relative elevation. The Kaoping River watershed generally has a higher elevation than the Donggang River watershed if the C-C′ area in Figure 2 is overlooked.

2.2. Land Use

This study collected land use survey data on the study area from 2021 and 2007, as shown in

Table 1. The land use condition of the study area in 2021.

Land Use	Kaoping River Watershed		Donggang River Watershed
	Area (km2)	Percentage of Watershed Area (%)	Area (km2)	Percentage of Watershed Area (%)
Agriculture	493.88	14.9%	264.72	55.3%
Forests	2180.34	65.7%	100.85	21.1%
Transportation	56.22	1.7%	23.56	4.9%
Water	168.57	5.1%	12.22	2.6%
Buildings	107.07	3.2%	39.97	8.4%
Public Facilities	22.56	0.7%	8.32	1.7%
Recreation	13.50	0.4%	8.87	1.9%
Mining/Salt Production	5.75	0.2%	0.32	0.1%
Others	270.33	8.1%	19.61	4.1%

and

Table 2. The land use condition of the study area in 2007.

Land Use	Kaoping River Watershed		Donggang River Watershed
	Area (km2)	Percentage of Watershed Area (%)	Area (km2)	Percentage of Watershed Area (%)
Agriculture	572.51	17.3%	284.51	59.5%
Forests	2235.64	67.4%	90.87	19.0%
Transportation	49.8	1.5%	19.58	4.1%
Water	127.45	3.8%	10.8	2.3%
Buildings	97.74	2.9%	36.36	7.6%
Public Facilities	10.98	0.3%	7.42	1.6%
Recreation	19.81	0.6%	8.01	1.7%
Mining/Salt Production	4.59	0.1%	0.22	0.1%
Others	199.7	6.0%	20.67	4.3%

, and Figure 3. According to the more recent 2021 land use survey results, the Kaoping River watershed is mainly composed of forests, covering about 2180 square kilometers, or about 65.7%, of the watershed. Agricultural usage occupies about 494 square kilometers, or about 14.9%, of the watershed and is mainly located in the downstream area. Buildings are mainly located on both sides of the Kaoping River’s downstream area and cover about 107 square kilometers (3.2%) of the Kaoping River watershed. The Donggang River watershed, on the other hand, is mainly used for agriculture, with agricultural land located primarily in the mid and downstream areas of the Donggang River, covering about 265 square kilometers (55.3%) of the watershed. Forests cover about 101 square kilometers (21.1%) of the watershed and are mainly situated in the Donggang River’s upstream area. Buildings in the Donggang River area are also located downstream and cover about 40 square kilometers (8.4%) of the Donggang River watershed.

To understand the effects of human development on the study area, this study compared the land use survey data from 2021 to the data from 2007. The percentage of agricultural land was reduced the most in both watersheds, with 2.4% of agricultural land in the Kaoping River watershed and 4.2% of agricultural land in the Donggang River watershed repurposed for other uses. The ‘others’ land use type, including wetlands, grasslands, and bare land, had the highest increase in the Kaoping River watershed, by 2.1% of the entire watershed. The second largest land use increase in the Kaoping River watershed was the water land use type, i.e., land used for hydrological infrastructure, increasing by 1.3% of the entire Kaoping River watershed. The Donggang River watershed, on the other hand, saw the most significant increase in the forest land use type and the second most significant increase in the transportation land use type, at 2.1% and 0.8%, respectively, of the whole watershed.

2.3. Physiographic Drainage–Inundation (PHD) Model

To understand the distribution of rainfall and runoff across space and time, this study used the physiographic drainage–inundation (PHD) model to simulate runoff. The PHD model is widely used to simulate rainfall–runoff in Taiwan, when assessing flood vulnerability [21], nature-based solutions for flood mitigation [22], and potential inundation analysis [23]. Its governing equation is shown as follows [24]:

$$A{s}_i\frac{d{h}_i}{dt}=P{e}_i+{\displaystyle \sum _k{Q}_{i,k}\left(h_i,h_k\right)}$$

(1)

where $A{s}_i$ is the area of cell $i$; $Q_{i,k}$ expresses the discharge from cell $k$ into cell $i$, with positive values indicating the discharge flows from cell $k$ into cell $i$, and negative values indicating the discharge flows from cell $i$ into cell $k$; $h_i$ represents the water level of cell $i$ at time $t$; $h_k$ represents the water level of cell $k$ at time $i$; $P{e}_i$ denotes the effective rainfall volume per unit of time in cell $i$, and is equal to the effective rainfall per unit of time in cell $i$ multiplied by the area of cell $i$.

Effective rainfall can be calculated using the Soil Conservation Service Curve Number (SCS-CN) method, the equation of which is shown as follows [25]:

$$P^{\prime }=\frac{{(P-I_a)}^2}{(P-I_a)+S}$$

(2)

$$S=\frac{25400-254CN}{CN}$$

(3)

where $P^{\prime }$ is the effective rainfall; $P$ represents the total rainfall; $I_a$ denotes the initial abstraction, including depression storage, interception, and evapotranspiration; $S$ is the potential maximum retention after runoff begins; $CN$ being the dimensionless curve number that is determined by various conditions of the watershed, such as soil type, vegetation cover type, land use, hydrologic condition, antecedent moisture condition, and climate type [25]. In this study, $I_a=0.2S$, while $CN$ is between 25 and 98.

Grid cells mainly exchange flow, via either weir or river flow types. The conditions and equations for both types are listed below.

2.3.1. River Flow Type

It is assumed that no local obstacles exist between two grids. In that case, discharge can be seen as an overland flow, and the Manning equation can be used to calculate the flow between the boundaries of two adjacent cells. From the perspective of cell $i$, the discharge from cell $k$ is expressed by:

$$Q_{i,k}=\frac{h_k-h_i}{\left|h_k-h_i\right|}\cdot \Phi (\overline{h_{i,k}})\cdot \sqrt{\left|h_k-h_i\right|} for \frac{\partial Q_{i,k}}{\partial h_i}\le 0$$

(4)

$$Q_{i,k}=\Phi (h_k)\cdot \sqrt{\left|h_k-h_i\right|} for \frac{\partial Q_{i,k}}{\partial h_i}>0$$

(5)

in which $\overline{h_{i,k}}$ is the water level on the boundary of cell $i$ and cell $k$:

$$\overline{h_{i,k}}=h_k+(1-\alpha )h_i, 0\le \alpha \le 1$$

(6)

and $\Phi (h)$ can represents the following equation:

$$\Phi (h)=\frac{A\left(h\right)R{\left(h\right)}^{2/3}}{n\sqrt{\Delta x}}$$

(7)

where $\Delta x$ is the distance between the center of cell $i$ and cell $k$; $n$ denotes Manning’s roughness coefficient between the two cells; $A$ and $R$ represents the hydraulic area and radius at the border between the two cells, respectively; $\overline{h_{i,k}}$, obtainable via linear interpolation, is the water level of the boundary between cell $i$ and cell $k$; $\alpha$ is the weighting coefficient, ranging from 0 to 1. When $h_k>h_i$ and $h_i$ is decreasing, we can assume that $\alpha =1$ in Equation (6) to negate the influence of $h_i$, and calculate the discharge from cell $k$ to cell $i$ using Equation (5).

2.3.2. Weir Flow Type

In addition to the river flow type, the weir flow type can also be used. However, to treat the border as a broad-crested weir, neighboring cells must be divided by natural or artificial structures, such as banks, levees, reservoir dams, roadways, or field ridges. If the aforementioned condition is fulfilled, the weir formula can be used to obtain the flow between the two cells. When $h_k>h_i$, the flow types can be further divided into two subtypes, the free weir and the submerged weir, with the equations shown as follows:

• Free weir

$$\left(h_i-h_w\right)<\frac{2}{3}\left(h_k-h_w\right), Q_{i,k}={\mu }_{1}b\sqrt{2g}{(h_k-h_w)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$

(8)

2.

Submerged weir

$$\left(h_i-h_w\right)\ge \frac{2}{3}\left(h_k-h_w\right), Q_{i,k}={\mu }_{2}b\sqrt{2g}(h_i-h_w){(h_k-h_i)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$

(9)

in the two equations above, $h_w$ is the weir height, or the roadway, levee, or ground height at the boundary; $b$ is the effective width of the weir top, which is equivalent to the intersection length of two adjacent cells; $g$ is the gravitational constant; ${\mu }_1$ and ${\mu }_2$ are the weir coefficients of the free and submerged weirs, respectively. Under normal circumstances, ${\mu }_1=0.36~0.57$. This study chose the values ${\mu }_1=0.4$ and ${\mu }_2=2.6{\mu }_1$ [26].

2.4. Model Certification and Verification

The two watersheds in the study area were divided into computational cells based on obtained data on aspects such as the terrain, topology, land use, and hydrological recording station locations, as shown in Figure 4. The Kaoping River watershed was divided into 6542 cells, with cell areas ranging from 0.06 to 597.76 hectares. The Donggang River watershed was divided into 5794 cells, with cell areas ranging from 0.03 to 457.32 hectares. The number of cells in the study area totals 12,336.

After the cells were built, the 2016 Megi typhoon was used as a certification case, and the Nash–Sutcliffe efficiency coefficient (NSE) was used to test and verify the results. The equation for the NSE can be expressed as follows [27]:

$$NSE=1-\frac{{\displaystyle {\sum }_{t=1}^T{(y_o^t-y_m^t)}^2}}{{\displaystyle {\sum }_{t=1}^T{(y_o^t-{\overline{y}}_o)}^2}}$$

(10)

where ${\overline{y}}_o$ is the mean of the observed water level; $y_o^t$ expresses the observed value at time $t$; $y_m^t$ is the simulated value at time $t$.

The upper and lower limits of the NSE are 1 and −∞, respectively. The closer the NSE value is to 1, the more simulation results match the reality. However, in practice, the presence of any extreme negative values, regardless of the reason for their presence, causes the NSE value to become an extreme negative value. Hence, this study adopted a normalized version of the Nash–Sutcliffe efficiency coefficient (NNSE). As it is normalized, the NNSE has upper and lower limits of 1 and 0, respectively, and is more effective when evaluating the performance of model simulation. The relationship between the NSE and NNSE can be shown as follows [28,29]:

$$NNSE=\frac{1}{2-NSE}$$

(11)

The observed water levels and simulated results are shown in Figure 5. Excluding the NNSE value of 0.689 that occurred at observing station (D) due to lost data, all the NNSE values exceeded 0.8, which shows that the PHD model can effectively simulate runoff in the study area.

2.5. Boundary Conditions

To further understand the flow conditions between adjacent watersheds under precipitation in different return periods, this study calculated the precipitation for 2, 5, 10, 25, 50, and 100-year return periods, using a parameter from the Horner formula obtained from rainfall stations in the study area. A histogram on the precipitation and the Thiessen mean rainfall for each return period is shown in Figure 6.

3. Results and Discussion

3.1. Discussion on the Cross-Watershed Runoff Phenomenon on the Boundary between Adjacent Watersheds

Figure 7 shows the inundation area (areas with inundation over 30 cm) in the study area in proximity to the border between the Kaoping River watershed and the Donggang River watershed, and

Table 3. Maximum inundation depth and area near the watershed border for different return periods.

Watershed	Return Period	Maximum Inundation Depth (m)				Total Inundation Area (ha)
		0.3–0.5	0.5–1.5	1.5–2.0	>2.0
Kaoping River Watershed	2 years	261.92	275.73	3.18	17.34	558.17
	5 years	289.08	449.93	30.85	18.85	788.71
	10 years	255.46	540.40	46.57	28.30	870.73
	25 years	267.28	702.89	99.34	48.14	1117.65
	50 years	241.07	695.46	127.39	64.86	1128.78
	100 years	206.21	728.35	133.55	64.86	1132.97
Donggang River Watershed	2 years	188.75	145.06	46.28	15.91	396.00
	5 years	394.96	256.72	49.71	50.67	752.06
	10 years	396.47	371.50	55.19	77.92	901.08
	25 years	384.80	432.57	84.40	110.09	1011.86
	50 years	379.12	456.66	78.03	119.11	1032.92
	100 years	395.04	434.65	93.33	132.49	1055.51

shows the maximum inundation depth of the zone within 500 m in both directions of the aforementioned border. According to the digital elevation model (DEM), the Kaoping River watershed has a slightly higher overall elevation than the Donggang River watershed, when comparing the areas in proximity to the border.

Cross-watershed runoff in this study could be roughly divided into two areas: the estuary area and the area about 30 km upstream of the estuary. When the rainfall return period was 2 years, the estuary cross-watershed runoff area stretched from the estuary to about 3 km in the upstream direction, and the maximum inundation depths in the area were between 0.5 m and 1.5 m. On the other hand, the upstream area had a length of about 3 km and maximum inundation depths from 0.3 m to 0.5 m. As the return period rainfall amount increased, the area where cross-watershed runoff occurred increased, and the maximum inundation depth near the boundary between the two watersheds also increased. When the return period was 5 years, the estuary area extended to about 9 km upstream of the estuary and had maximum inundation depths between 0.3 m and 2.0 m. The upstream area also increased to about 7 km long and had maximum inundation depths ranging from 0.3 m to 1.5 m. However, the attributes of the areas where cross-watershed runoff occurred stabilized when the return period was increased to 25 years and above. The estuary area stretched from the estuary to about 12 km in the upstream direction, with maximum inundation depths ranging from 0.5 m to 2.0 m in most parts of the area and exceeding 2 m in a few places, while the upstream area extended in length to 10.5 km and had maximum inundation depths ranging from 0.3 m to 1.5 m. The lack of change in the cross-watershed runoff area attributes, when comparing 50 and 100-year return period simulations to the 25-year return period simulation, showed that the size and depth of the areas where cross-watershed runoff occurs stopped changing with the increase in rainfall after the return period exceeded 25 years. The size and depth of the cross-watershed runoff areas remained relatively unchanged, and the runoff volume was not enough to affect areas with a higher elevation.

The runoff direction during the initial stages of rainfall for all return periods was mainly decided by the elevation. The slight elevation difference between the two watersheds caused surface runoff to enter the Donggang River watershed from the Kaoping River watershed. Also, as the inundation depth caused by the 2-year return period rainfall did not exceed the boundary elevation in the E-E′ zone in Figure 2, cross-watershed runoff was not prominent in the E-E′ zone when under 2-year return period rainfall, and the Kaoping River watershed had a distinctly larger inundation area there. As the return period increased, the difference in the inundation area of the two watersheds decreased. The reduction in the inundation area difference showed that runoff primarily flowed in the direction of the Kaoping River watershed to the Donggang River watershed when the return period was below 25 years. However, with the geographical features being relatively flat near the boundary between the two watersheds and the differences in elevation relatively small, elevation failed to become the decisive factor in the runoff direction when the rainfall increased. The water level differences between the two watersheds decreased as the rainfall increased, and the flow direction became more dependent on which watershed had a higher upstream water level rising speed.

3.2. Discussion on the Effect of Different Land Use Types on the Cross-Watershed Runoff at the Boundary between Adjacent Watersheds

According to the runoff simulation results, cross-watershed runoff was notable in two areas of the study area. The first area, near the estuary, had a surface elevation mostly below 10 m. The second area, the upstream area, had surface elevations ranging from 45 m to 100 m. To investigate the causes of the phenomenon, this study overlaid the land usage distribution with the 25-year return period simulation results, with the results shown in Figure 8. It can be deduced from Figure 8 that cross-watershed runoff mainly occurred in developed areas, used for agriculture, buildings, and transportation.

Elevation changes occur during human land development. The irrigation requirement that water flows evenly across all parts of the agricultural area and effectively drains away is the cause of elevation adjustments via land leveling, when agriculture is the prominent land use type. When buildings are the primary land use type, grading, the process of reshaping land at a construction site, also causes elevation changes, when constructors attempt to adjust the building lot and slope of the construction site to ensure that buildings fulfill their original design purpose. However, elevation adjustments change natural runoff directions, blocking original flow directions or causing runoff to discharge into different areas, which, in turn, causes stagnant water in some previously non-inundated areas. The presence of buildings also increases impervious areas, which lowers infiltration rates and increases surface runoff. Increased runoff increases the flood risk in neighboring zones without supporting water storage facilities, such as detention and retention ponds.

Human development significantly changes the surface elevation, flattening slopes and preventing clear watershed boundaries from forming. In other words, the cross-watershed runoff phenomenon may be more pronounced in areas with a high level of development. Thus, possible surface runoff from adjacent watersheds must be considered when conducting integrated flood mitigation management or evaluating multiple watersheds simultaneously.

4. Conclusions

This study used two adjacent watersheds in southern Taiwan, the Kaoping River watershed and the Donggang River watershed, as the study area and used the PHD model to simulate the maximum inundation depth when the study area was subjected to 2, 5, 10, 25, 50, and 100-year return period rainfall, to investigate the cross-watershed runoff phenomenon that occurs during the rainfall–runoff process.

The simulation results show that when the return period was 2 years, i.e., when the Thiessen mean rainfall was approximately 500 mm, cross-watershed runoff occurred in two areas inside the study area: the area near the estuary and the area about 30 km upstream of the estuary. When the return period was 25 years, i.e., when the Thiessen mean rainfall was about 1300 mm, the size and depth of the areas where cross-watershed runoff occurred became relatively stable, as the flow volume was insufficient to affect higher elevation areas. The DEM data showed that the elevation of the Kaoping River watershed was slightly higher than the Donggang River watershed in both of the cross-watershed runoff areas, causing runoff during the initial stages of rainfall to flow from the Kaoping River watershed to the Donggang River watershed. When the rainfall increased, the difference in the water level between the two watersheds decreased, and the flow was no longer limited to the direction from the Kaoping River watershed to the Donggang River watershed, but was more dependent on the water level rising speed of the two watersheds’ upstream areas.

According to land use surveys of the study area, cross-watershed runoff mainly occurred in developed regions, for e.g., land used for agriculture, buildings, and transportation. The correlation between cross-watershed runoff-prone areas and developed regions showed that development changes the runoff behavior, with behavior changes especially significant in highly developed urban areas, which causes the cross-watershed runoff phenomenon to occur. Cross-watershed runoff causes flood mitigation strategies in the related watersheds to fall short of flood protection design standards. When conducting integrated flood mitigation management in the future, runoff from adjacent watersheds must also be considered, in addition to the normal runoff from a watershed. The proposed change should help achieve Goal 11 (Sustainable Cities and Communities) and Goal 13 (Climate Action) of the Sustainable Development Goals (SDGs), by reducing the damage from natural disasters and increasing the resilience and sustainability of human settlements.