Runoff Estimation in Ungauged Watershed and Sensitivity Analysis According to the Soil Characteristics: Case Study of the Saint Blaise Vallon in France

Abstract

Water Resources Research announced that, as a result of global warming, the amount of extreme torrential rain globally has increased steadily since the middle of the last century. To cope effectively with climate change, it is important to use consistent and scientific water information of water resources. In this study, we use a hydrological analysis of the Saint Blaise Vallon area to indicate how the damage from natural disasters that may come in the future may be minimized. In addition, a hydrological analysis and a numerical simulation model were implemented to estimate runoff and runoff coefficients derived from a heavy rainfall event that caused serious damage to river flooding. A runoff sensitivity analysis was conducted according to the soil parameters. In particular, a method using the hydrological model and the hydrological sensitivity analysis were applied to the target watershed, and the results of the peak outlet discharge were analyzed in time series so that they could be used for flood prediction and disaster management. In addition, the flood discharge and runoff coefficients during the flooding of the target watershed were presented through the study.

1. Introduction

Water is the most important natural resource for human life. However, due to repeated and steady human activities, such as urbanization, industrial development, and population growth, the climate has changed substantially. Water Resources Research announced that, as a result of global warming globally, the amount of extreme torrential rain has increased steadily since the middle of the last century [1]. To cope effectively with climate change, it is important to use systematic and scientific water-resource information [2].

Flooding accidents in rivers due to torrential rains and floods occur frequently around the world due to climate change [3,4,5]. In particular, various hydrological analysis studies related to flood forecasting are being conducted to reduce the occurrence of flood damage in rivers [6,7].

In the case of watersheds with water level and flow measurement facilities, the accuracy of flood discharge prediction according to rainfall can be improved. However, in the case of an unmeasured watershed, it is difficult to accurately estimate flood discharge, and due to uncertainty, it is inevitably vulnerable to flood preparation. For runoff analysis of unmeasured watersheds, studies using various statistical analysis techniques such as hydrological image, a convolutional neural network (CNN), multiple linear regression, and the kriging method * were performed [8,9]. Numerous studies have been conducted to estimate runoff, and the MIKE SHE and HEC-HMS models have been the most widely used [10,11,12].

According to the International Disaster Database, 2020, the Var River Basin in France suffered from floods in 1994, 2000, 2011, 2015, and 2019. In addition, heavy rainfall in 2020 caused significant flood damage in the Saint-Martin-Vésubie area of the Var River Basin, as shown in Figure 1.

In this study, we use a hydrological analysis of the Saint Blaise Vallon watershed in France to determine how to minimize the damage from natural disasters that may occur in the future. However, Saint Blaise Vallon is a mountainous and ungauged area. An ungauged district refers to an area that has not been observed for several different reasons, such as social, political, cost, or technological aspects [13]. Accordingly, the Saint Blaise Vallon district is classified as an unmeasured area. The accurate calculation of runoff from mountainous areas is one of the most complicated hydrological processes. Therefore, it is essential to consider the three main controlling factors, the vegetation, the contemplation of land use, and the climate. Different combinations of these factors determine the amount and nature of complex runoff in mountainous areas [14].

To interpret natural disasters, measured hydrological data are required, but the Saint Blaise Vallon watershed is an ungauged area, so there is a limitation to the hydrological data that can be collected. For the hydrological analysis of ungauged areas, it is essential to use topographical data that can be extracted from satellite-image data rather than measured data [15,16,17,18]. In the past, the hydrological analysis of ungauged areas has been impossible. However, as topographical data such as the digital elevation model (DEM), soil type, and land-use type became available for collection, the hydrological prediction of ungauged areas became possible. In particular, MIKE SHE and MIKE 11 have been applied in various studies for the analysis of watershed runoff [19,20,21,22,23].

In this study, the hydrological analysis model (MIKE SHE) and hydraulic model (MIKE 11) were used to calculate the runoff and runoff coefficients depending on the frequency of precipitation in the Saint Blaise Vallon area.

The importance of this study lies in the hydrological analysis of the unmeasured watershed, and it suggests a way to improve the uncertainty in the runoff prediction. Sensitivity analysis has been widely used in the field of hydrological analysis [24,25,26], and it has the feature of being able to suggest the minimum and maximum range of analysis results due to the factor determination value through sensitivity analysis.

2. Materials and Methods

2.1. Hydrological Model

In the past, the hydrological analysis of ungauged areas was impossible; however, as topographical data such as DEM, land use, and soil type became available, together with satellite photography, the hydrological prediction of ungauged areas became possible. Hydrological analysis enables the prevention of future flood damage by estimating runoff in ungauged areas using DEM, soil type, land use, and precipitation data.

A typical distributed hydrological model, MIKE SHE, was used in this study. MIKE SHE [27] is an integrated hydrological model. All components of the hydrological cycle, such as surface flow, evapotranspiration, groundwater flow, and infiltration, are incorporated into the model. It is also a physically distributed hydrologic model because it can handle parameters that have related characteristics of the watershed such as soil type, vegetation type, distribution of topography, and geology. In addition, it can manage spatial variability in both physical characteristics and meteorological conditions [28]. The MIKE SHE model consists of a number of modules, wherein each module represents a specific hydraulic flow process. The modules of MIKE SHE used in this study are topography, overland flow, precipitation, river flow, land use, unsaturated flow, and saturated zone. As mentioned above, MIKE SHE calculates the rainfall–runoff process in the watershed in a fully distributed and integrated manner and generates river flows that consider overland flow, interflow, and base flow (Figure 2).

MIKE SHE models the following processes of the hydrological system (Figure 2): interception, snow melt, infiltration, subsurface flow in the saturated and unsaturated zones, evapotranspiration, surface flow, and flow in channels and/or ditches. The spatial variation of input data is represented in a network of grid squares that constitute the basic computational unit of the model. Each grid square is discretized in the vertical into a series of layers. The river network is assumed to run along the boundaries of the grid squares [29].

Rainfall interception is modeled using the Rutter accounting procedure, which considers the maximum storage capacity of the vegetation canopy. The zero-inertia approximations to the St. Venants equation were solved numerically in two dimensions for overland flow and in one dimension for channel flow. The one-dimensional Richards’ equation, applied to a representative grid square, was solved numerically for the pressure head variation, which in turn is converted to the moisture content through the soil moisture-retention curve [29].

Hydrological models simulate the motion of water and the transport of mass and account for both spatial and temporal variations [30] after a system boundary is defined. As the boundary information defined for a catchment, the movement of water can be clarified through inter-relationships between each hydrological component and the inter-relationship could be generalized as Equation (1) [31,32]:

P + GW_i = SW_o + ET + GW_o + ∆ST

(1)

where, P = precipitation; GW_i = groundwater inflow from adjacent catchments; accordingly, GW_o = groundwater outflow from the catchment; SW_o = surface water outflow; ET = evapotranspiration; ∆ST = changes in soil storage

2.2. Status of Study Area

2.2.1. Study Area

The Var River is in the southeastern part of France. The controlling drainage-basin area is approximately 2800 km². The Var River is one of the main rivers in the French Mediterranean Alps region. The basin elevation is 0–3100 m above sea level, with a steep slope distributed along the branches located in the middle and upper areas of the catchment [33]. There are five major tributaries (Upper Var, Vésubie, Estéron, Tinée, and Lower Var) that cross five sub-catchments in this basin. The specific study area is located in the Lower Var, which is a sub-catchment in the Var River Basin called Saint Blaise Vallon. Figure 3 shows the location of the Var River, and Figure 4 represents the specific scope of this study.

Figure 4 (right) is the topography of Saint Blaise Vallon. A 5 m resolution of DEM is provided by the city hall of Nice (Métropole Nice Côte d’Azur), and the topography is presented using the ArcGIS and MIKE toolbox. The elevation of the highest point is 1411 m and the lowest point is 85 m. Input topography has a significant impact on runoff estimation [34].

Figure 5 is the geological setting of the Var basin and its subbasins. White lines delimit the sampled subbasins; colored squares represent sampling points, and red hashed areas indicate the presence of quartz-bearing rocks.

Table 1. Geographical information of Saint Blaise Vallon area [34].

Location	Area	Sub-Watershed Length	Average Slope	Longest Flow Path
Saint Blaise Vallon	17.4 km2	30,402 m	23.7°	12,312 m

shows the physical characteristics of the Saint Blaise Vallon area. The average slope in this area is 23.68°. As reported by the Nashua Regional Planning Commission, the definition of a steep slope is when the slope is higher than 15°. Therefore, the Saint Blaise Vallon area can be described as having a steep slope, which leads to sudden runoff.

2.2.2. Soil Characteristics

For soil types in this study area, soil data with a high resolution (500 m × 500 m) were obtained from the U.S. Department of Agriculture (USDA).

Table 2. Adapted soil hydraulic parameter values in MIKE SHE [34,36].

Soil Hydraulic Parameters	Clay	Sand	Silt
Water content at saturation (kg/kg)	0.56	0.38	0.51
Water content at field capacity (kg/kg)	0.36	0.18	0.31
Water content at the wilting point (kg/kg)	0.22	0.08	0.11
Saturated hydraulic conductivity (m/s)	5.0 × 10−6	1.0 × 10−3	2.0 × 10−5

shows the soil types according to the serial number. Based on the USDA data, the Saint Blaise Vallon area consists of silt, clay loam, and silty clay loam. However, in a previous study [14] that included the same area, the optimized soil types of the Var area were described as sand, clay, silt, and loam. As a result, the soil type proposed in this study was regarded as the true distribution. In addition, field surveys indicate that the Saint Blaise Vallon area in the downstream part can be assumed to be sand rather than silty clay loam. The soil-distribution process was therefore improved. Figure 6 shows the improvement of the soil-type distribution in the study area.

In this study area, the main soil type was clay, accounting for 71%. Figure 7 shows the percentages of each soil type. It is expected that the runoff estimated will be mostly affected by the hydraulic parameters of the sandy soil.

The soil hydraulic parameters shown in Table 2 were adapted from previous research [36].

2.2.3. Land Use

The land use applied in this study was based on satellite photographs provided by the city hall of Nice Côte d’Azur. The land-use data (see Figure 8) comprises satellite photographs, delineation, mapping, and the implementation of land use.

The land use provided by the city hall covered the entire Cote d’Azur area. A total of 788 different types of land use were identified in the Saint Blaise Vallon region. In this study, the 788 land uses were classified into eight major types of land use and applied to the MIKE SHE hydrological model. Figure 9 shows the reclassified land use in the sub-watershed.

The values applied to the MIKE SHE model by land use are shown in

Table 3. Land-use value according to the vegetation [34].

	Vegetation	LAI	ROOT	KC (−)
1	Residential Area	0.8	100	1.2
2	Grass	1.1	300	1.0
3	Grass + Tree	1.0–4.0	300–700	1.0
4	Forest B	7.0	800	1.0
5	Forest C	5.0	800	1.0
6	Forest M	6.0	800	1.0
7	Agriculture	1.5–5.0	200–1000	1.0
8	Water Body	0.8	100	1.2

. These values are the leaf area index (LAI) and root (ROOT) and crop coefficients (KCs) and were provided by the University of Nice Sophia Antipolis laboratory. The LAI is the mean of leaves per unit of ground area. The typical range of LAI in mid-latitude forests or shrublands is between 3 and 6 [38]. This depends on the type of vegetation and the season. A small LAI value reduces leaf density, which results in a reduction in canopy evaporation. The range of LAI in this study was a minimum of 0.8 and a maximum of 7.0.

ROOT is the root depth (in mm) of the crop or vegetation type. The simulated range of root depth was 100 to 1000 mm. KC is the crop coefficient. The simulation used a KC value in the range of 1.0 to 1.2.

The Strickler coefficient is a value that indicates the resistance to flow. This is determined by the characteristics of the land-use type. Ma (2018) suggested the Stricker coefficient shown in

Table 4. Strickler Coefficient [34,36].

Land-Use Type	Strickler Coefficient (m1/3/s)
Residential Area	50.0
Grass	2.5
Grass + Tree	2.5
Forest B	2.0
Forest C	2.0
Forest M	2.0
Agriculture	25.0
Water	20.0

through a comparison of the measured flow rate and the model flow rate result from the Var river basin.

In the hydrological model, the Strickler coefficient values used were 2.0, 2.5, 20.0, 25.0, and 50 m^1/3/s, depending on the land-use type. When transferred to the Manning n values, these values became 0.5, 0.4, 0.05, 0.04, and 0.02, respectively.

2.2.4. Meteorological Characteristics

In this study, all meteorological information was obtained from the National Meteorological Administration of France [39,40]. The average annual precipitation and monthly precipitation in the Var River Basin are approximately 1154 mm and 96 mm, respectively [13]. Most of the Var River Basin consists of mountainous areas, where precipitation varies greatly by region [41]. Rainfall stations in the Saint Blaise Vallon area are only at Nice airport. There is no data for Carros and Levens before 2020. Figure 10 shows the locations of the rainfall stations near the Saint Blaise Vallon area.

Table 5. Statistics from 1982 to 2016 at Nice airport station [40].

Return Period (Year)	5	10	20	30	50	75	100
Rainfall Intensity (mm/h)	44.3	53.3	61.9	66.7	72.7	77.4	80.7

shows historical statistics data from 1982 to 2016 at Nice airport rainfall station.

Table 6. Monthly average precipitation [39].

Month [mm]	Nice Airport 1981–2000	Carros 2020	Levens 2020
January	69	25.3	15.2
February	44.7	0.4	1.6
March	38.7	76	81.9
April	69.3	44.5	36.6
May	44.6	153.7	173
June	34.3	138.1	99.9
July	12.1	2.4	24.3
August	17.8	9.2	9.8
September	73.1	16.3	10.8
October	132.8	64.3	204.6
November	103.9	6.4	7
December	92.7	124.8	130.1
Total Amount	733	661.4	794.8

shows average monthly precipitation at each rainfall gauge.

The maximum return period data from Meteo France was 100-year. With this return period, rainfall intensity was approximately 80.7 mm/h.

The average monthly precipitation data are from the meteorological administration of France. For Carros and Levens, the collection of precipitation data began in 2020, and at Nice airport, it began in 1981. As of 2020, annual precipitation for Carros and Levens were 661.4 mm and 794.8 mm, respectively. For Nice airport, the average annual precipitation was 733 mm (1981–2000). This is approximately 57–68% of the average annual precipitation in the entire Var River Basin.

The calculation methods for the total precipitation volume, discharge, and runoff coefficient are as follows. The total precipitation volume is (the sum of the specific year return period of precipitation) × 1/1000 × (the catchment area). The total discharge volume is (the average hourly discharge) × 3600 × (the total number of simulation hours).

3. Results and Discussion

3.1. Hydrological Analysis

The DEM used to derive the topographic results had a 10 m resolution. The return period precipitation used in this model was 10-, 25-, 50-, 75-, 100-, and 162-year (PMP, probable maximum precipitation) return periods. Figure 11 shows the result of peak runoff for different return periods of precipitation occurring in the Saint Blaise Vallon area using MIKE SHE model. With 162-year return period precipitation, the peak discharge occurred as 29.65 m³/s.

For the values of major factors in the hydrological analysis model of the target watershed, the conditions used were from a previous study of the Var river watershed analysis. Based on this, the probably maximum flood (PMF) of the target watershed was calculated, and the results of runoff discharge for each return period of precipitation are shown in Figure 11.

Table 7. Parameter results for various return periods of precipitation [34].

Return Period	10-Year	25-Year	50-Year	75-Year	100-Year	162-Year
Sub-Watershed Area (m)	17,460,000	17,460,000	17,460,000	17,460,000	17,460,000	17,460,000
Total Precipitation Volume (m3)	3,449,085	4,116,043	4,598,246	4,866,924	5,076,444	5,423,077
Total Discharge Volume (m3)	2,089,406	2,559,438	2,937,849	3,162,668	3,348,006	3,648,916
Peak discharge at 3rd peak (m3/s)	2.51	6.21	12.83	17.99	26.36	29.65
Runoff Coefficient	0.606	0.622	0.639	0.650	0.660	0.673

shows the parameter results for various return periods of precipitation.

A hydrological analysis was conducted using several different return period precipitation data. The total discharge volume during the 10-year precipitation was 2,089,406 m³, and the total volume of precipitation was 3,449,085 m³. This means that 61% of water is overland runoff, and 39% of water is infiltrated to the underground. Compared with the maximum return period precipitation, the total volume of discharge during the 162-year precipitation was 3,648,916 m³, and the total volume of precipitation was 5,423,077 m³. This means that 67% of water is overland flow, and 32% of water is infiltrated.

As a result of six return period hydrological analyses, the Pearson r value of total precipitation volume and total discharge volume was 0.99, and the r values of total precipitation volume and peak discharge was 0.96. It was found that the correlation between the mutual factors was high.

In the case of an unmeasured watershed, it is impossible to evaluate the accuracy of the hydrological analysis result because there is no actual data. Therefore, it is necessary to propose the results of hydrological analysis according to the range of the main factors used through sensitivity analysis.

3.2. Sensitivity Analysis

Collecting data on the sensitivity of soil properties is useful for model development and application purposes. This can lead to more accurate values, better understanding, and thus, reduced uncertainty in the results. A sensitivity analysis shows how a given simulation model output depends on the input parameters.

To determine which parameters were the most sensitive in generating the model output, a sensitivity analysis was performed by changing the soil-property values by up to ±30% of their original value. Then the simulated value of peak runoff was compared to the original value.

First, the suggested value by Ma (2018) [35] was used as the standard to determine the factor that responds most sensitively to the soil parameters and has the greatest influence on the runoff change. Water content at saturation (${\mathsf{\theta }}_s$), water content at wilting point (${\mathsf{\theta }}_r$), field capacity water content (${\mathsf{\theta }}_e$), and saturated hydraulic conductivity (Ks) were adjusted upward by 30% to find sensitive soil parameters.

In the hydrological numerical simulation model, ${\mathsf{\theta }}_s$ is the water content of the soil, which is equal to the porosity. ${\mathsf{\theta }}_e$ is the water content at which the vertical flow becomes negligible. This is the water content that is reached when the soil can freely drain. However, it is higher than the residual saturation, which is the minimum saturation obtained from laboratory tests. ${\mathsf{\theta }}_{r }$ means the lowest water content in which plants can extract water from the soil. The saturated hydraulic conductivity (Ks) refers to the infiltration rate and has a (m/s) dimension.

Usually, soil parameters are obtained based on laboratory experiments with field samples. There are previous studies on field capacity (FC) and wilting point (WP) equations [34,42,43,44,45,46].

Table 8. Suggested FC and WP equation from previous research [34,42].

Gupta, S. C. and W. E. Larson [43]
FC	θ = 0.003075 × SA + 0.005886 × SI + 0.008039 × CL + 0.002208 × OM − 0.1434 × BD
WP	θ = −0.000059 × SA + 0.001142 × SI + 0.005766 × CL + 0.002228 × OM + 0.02671 × BD
SA, sand (%); SI, silt (%); CL, clay (%); OM, organic matter (%); BD, bulk density (g/cm3).
Rawls, W. J. et al. [44]
FC	θ = 0.2576 − 0.0020 × SA + 0.0036 × CL + 0.0299 × OM
WP	θ = 0.026 + 0.005 × CL + 0.0158 × OM
SA, sand (%); SI, silt (%); CL, clay (%); OM, organic matter (%)
Oliveira, L. B. et al. [45]
FC	θ = 0.000333 × SI + 0.000387 × CL
WP	θ = 0.000038 × SA + 0.000153 × SI + 0.000341 × CL − 0.030861 × BD
SA, sand (g kg−1); SI, silt (kg kg−1); CL, clay (kg kg−1); OM, organic matter (kg kg−1); BD, bulk density (kg dm−1)
Reichert, J. M. et al. [46]
FC	θ = 0.106 + 0.29 × (CL + SI) + 0.93 × OM − 0.048 × BD
WP	θ = −0.04 + 0.15 × CL + 0.17 × (CL + SI) + 0.91 × OM + 0.026 × BD
SA, sand (kg kg−1); CL, clay (kg kg−1); OM, organic matter (kg kg−1); BD, bulk density (kg dm−3).

shows the previous research equations for FC and WP. Table 8 shows the suggested FC and WP equations from previous researches.

During the sensitivity analysis, only a single parameter was changed at a time, while the others remained unchanged during each sensitivity simulation. Figure 12 shows the peak discharge results for increases of the ${\mathsf{\theta }}_s$, ${\mathsf{\theta }}_e$, ${\mathsf{\theta }}_r$, and Ks parameters.

From the results in

Table 9. Standard soil parameter values [34,36].

	Water Content at $\mathbf{Saturation} \left({\mathsf{\theta }}_{\mathit{s}}\right)$	Field Capacity $\mathbf{Water} \mathbf{Content} \left({\mathsf{\theta }}_{\mathit{e}}\right)$	Water Content at $\mathbf{Wilting} \mathbf{Point} \left({\mathsf{\theta }}_{\mathit{r} }\right)$	Ks (m/s)
Sand	0.38	0.18	0.08	1.0 × 10−3
Clay	0.56	0.36	0.22	5.0 × 10−6
Silt	0.51	0.31	0.11	2.0 × 10−5
Peak Discharge: 29.65 m3/s

and

Table 10. 30% Increased water content at saturation. (${\mathsf{\theta }}_s$ [34].

	Water Content at $\mathbf{Saturation} \left({\mathsf{\theta }}_{\mathit{s}}\right)$	Field Capacity $\mathbf{Water} \mathbf{Content} \left({\mathsf{\theta }}_{\mathit{e}}\right)$	Water Content at $\mathbf{Wilting} \mathbf{Point} \left({\mathsf{\theta }}_{\mathit{r} }\right)$	Ks (m/s)
Sand	0.494	0.18	0.08	1.0 × 10−3
Clay	0.728	0.36	0.22	5.0 × 10−6
Silt	0.663	0.31	0.11	2.0 × 10−5
Peak Discharge: 7.01 m3/s

, it can be seen that the most sensitive soil parameters that have a significant influence on peak runoff are ${\mathsf{\theta }}_s$ and ${\mathsf{\theta }}_e$ in the study area. The peak runoff of ${\mathsf{\theta }}_{r }$ and Ks were 30.04 m³/s and 31.67 m³/s, respectively. There is no substantial change compared to the original peak runoff result.

For ${\mathsf{\theta }}_s$, when the 162-year return period of precipitation was applied, the peak discharge was 7.01 m³/s (see Table 10), which was 76% lower than the original peak discharge runoff of 29.65 m³/s (see Table 9).

Table 11. 30% increased water content at field capacity $\left({\mathsf{\theta }}_e\right)$ [34].

	Water Content at $\mathbf{Saturation} \left({\mathsf{\theta }}_{\mathit{s}}\right)$	Field Capacity $\mathbf{Water} \mathbf{Content} \left({\mathsf{\theta }}_{\mathit{e}}\right)$	Water Content at $\mathbf{Wilting} \mathbf{Point} \left({\mathsf{\theta }}_{\mathit{r} }\right)$	Ks (m/s)
Sand	0.38	0.234	0.08	1.0 × 10−3
Clay	0.56	0.468	0.22	5.0 × 10−6
Silt	0.51	0.408	0.11	2.0 × 10−5
Peak Discharge: 67.16 m3/s

shows 30% increased water content at field capacity and its peak discharge result.

For ${\mathsf{\theta }}_e$, the maximum runoff discharge was 67.16 m³/s (see Table 11). This is 127% higher than the original peak runoff discharge (see Table 9).

3.3. Sensitivity Analysis for Water Content at Saturation and Field Capacity

The most sensitive soil parameters were found to be ${\mathsf{\theta }}_s$ and ${\mathsf{\theta }}_e$. A sensitivity analysis was performed on ${\mathsf{\theta }}_s$ and ${\mathsf{\theta }}_e$ to determine how the runoff is affected by these values.

Table 12. Change range of water content at saturation $\left({\mathsf{\theta }}_s\right)$ [34].

Range	−30%	−20%	−10%	Standard	10%	20%	30%
Sand	0.266	0.304	0.342	0.38	0.418	0.456	0.494
Clay	0.392	0.448	0.504	0.56	0.616	0.672	0.728
Silt	0.357	0.408	0.459	0.51	0.561	0.612	0.663
Peak Discharge [m3/s]	76.76	69.07	53.82	29.65	14.7	9.2	7.01
Total Discharge Volume [m3]	5,427,160	4,961,485	4,344,082	3,648,917	3,000,136	2,509,572	2,137,722
Runoff Coefficient	1.0	0.915	0.801	0.673	0.553	0.463	0.394

shows the peak discharge, total discharge volume, and runoff coefficient when ${\mathsf{\theta }}_s$ changes from 30% less to 30% more than the standard. Table 12 shows the range of change in water content at saturation and its discharge results.

The change range of ${\mathsf{\theta }}_s$ was increased in 10% steps from 30% less to 30% more than the standard to perform the sensitivity analysis. The runoff was 76.76 m³/s when ${\mathsf{\theta }}_s$ was 30% lower, and the lowest flow rate was 7.01 m³/s when ${\mathsf{\theta }}_s$ was 30% higher. The runoff coefficients were 1 and 0.394, respectively. The total discharge volume was 5,427,160 m³, and 2,137,722 m³, respectively, which was approximately 60% lower than the peak discharge volume.

Table 13. Range of change in water content at field capacity $\left({\mathsf{\theta }}_e\right)$ [34].

Range	−30%	−20%	−10%	Standard	10%	20%	30%
Sand	0.126	0.144	0.162	0.18	0.198	0.216	0.234
Clay	0.252	0.288	0.324	0.36	0.396	0.432	0.468
Silt	0.217	0.248	0.279	0.31	0.341	0.372	0.403
Peak Discharge [m3/s]	9.8	12.88	18.72	29.65	45.42	58.74	67.16
Total Discharge Volume [m3]	2,591,835	2,881,583	3,235,739	3,648,917	4,080,355	4,489,669	4,860,854
Runoff Coefficient	0.478	0.531	0.597	0.673	0.752	0.828	0.896

shows the peak discharge, total discharge volume, and runoff coefficient when the ${\mathsf{\theta }}_e$ value changes from 30% less to 30% more than the standard.

The range of change in ${\mathsf{\theta }}_e$ was also adapted in the same way as ${\mathsf{\theta }}_s$ to perform the sensitivity analysis. The runoff discharge was 67.16 m³/s when ${\mathsf{\theta }}_e$ was 30% more, and the lowest flow discharge was 9.8 m³/s when ${\mathsf{\theta }}_e$ was 30% less than the standard. The runoff coefficients were 0.896 and 0.478, respectively. The total runoff discharge volume was 4,860,854 m³ and 2,591,853 m³, respectively, which was approximately 46% lower than the peak discharge volume. In the simulation of the hydrology model in the Saint Blaise Vallon sub-watershed, the two-layer method was applied in the unsaturated flow numerical simulation because it requires less data for an ungauged basin. The soil physical characteristics, including water content at saturation, wilting point, field capacity, and hydraulic conductivity were used for soil-characteristic sensitivity analysis in the hydrology model.

Among them, the physical characteristics of the soil that had significant influence on the runoff discharge were water content at saturation and field capacity. Figure 13 and Figure 14 show the water content at saturation and field capacity discharge variation, respectively.

4. Conclusions

In this study, the runoff and runoff coefficients of ungauged areas were calculated using DHI MIKE series to predict and prevent future flood damage due to continuous climate change in the Saint Blaise Vallon region. The rainfall runoff discharge in the unmeasured basin was calculated by performing hydrological analysis on the various return periods for extreme precipitation.

Although flash floods have caused damage in many mountainous areas, it is difficult to estimate the amount of runoff in unmeasured watersheds, and accurate prediction is impossible. Therefore, a method for estimating the amount of runoff that can improve the prediction accuracy and reduce uncertainty in the unmeasured watershed was suggested. The proposed method and the range of sensitivity factors used can be applied to all unmeasured watersheds and can be used for flood protection in mountainous area.

The proposed runoff calculation method is an improved approach from the runoff calculation based on past empirical formulas and case studies. In addition, the research results can contribute to the establishment of flood protection measures in the Saint Blaise Vallon region. In particular, in order to reduce research uncertainty, the range of hydrological factor values proposed by previous studies was compared and specifically limited so that they could be continuously used in future research.

By using high-resolution DEM, it contributed to more accurate runoff calculation, and through runoff with diversified return periods, it could be utilized for flood protection and planning in the watershed. In particular, the range of possible runoff was limited by applying the parameters of water content at saturation, wilting point, field capacity, and hydraulic conductivity to various ranges, thereby resolving the uncertainty of runoff analysis results.

Water content at saturation and field capacity were selected as the most sensitive factors in the runoff discharge of the Saint Blaise Vallon region. The sensitivity analysis result of this study is expected to be used when adjusting the runoff range when accurate measurement data is collected in the target area in the future and can be used as basic data for accurate hydrological analysis.

According to the sensitivity analysis results, the runoff sensitivity ranges of water content at saturation and filed capacity were calculated. The runoff coefficient can be used as an index of the flood area for extreme rainfall based on the derived runoff. The results of the runoff analysis vary depending on the values of the factors used in the hydrological analysis. And it is expected that the sensitivity analysis results of this study can be utilized in other basins similar to this target area.

If data collection for the Saint Blaise Vallon catchment becomes sufficient in the future, it is predictable that the accuracy of the simulation model will improve through comparison with observed data. In particular, it is important to improve the soil-parameter estimation method and to secure real hydrological data from the target area. It is expected that the accuracy of this study can be improved when measuring the actual runoff discharge in the target area for the correction of the hydrological model set-up.

Through this study, a numerical analysis methodology was proposed for estimating hydrologic runoff in watersheds of mountainous regions. In the future, it can be used to reduce the uncertainty of hydrological analysis in similar basins.