DEM-based numerical modelling of runoff and soil erosion processes in the hilly–gully loess regions

Abstract

For sake of improving our current understanding on soil erosion processes in the hilly–gully loess regions of the middle Yellow River basin in China, a digital elevation model (DEM)-based runoff and sediment processes simulating model was developed. Infiltration excess runoff theory was used to describe the runoff generation process while a kinematic wave equation was solved using the finite-difference technique to simulate concentration processes on hillslopes. The soil erosion processes were modelled using the particular characteristics of loess slope, gully slope, and groove to characterize the unique features of steep hillslopes and a large variety of gullies based on a number of experiments. The constructed model was calibrated and verified in the Chabagou catchment, located in the middle Yellow River of China and dominated by an extreme soil-erosion rate. Moreover, spatio-temporal characterization of the soil erosion processes in small catchments and in-depth analysis between discharge and sediment concentration for the hyper-concentrated flows were addressed in detail. Thereafter, the calibrated model was applied to the Xingzihe catchment, which is dominated by similar soil erosion processes in the Yellow River basin. Results indicate that the model is capable of simulating runoff and soil erosion processes in such hilly–gully loess regions. The developed model are expected to contribute to further understanding of runoff generation and soil erosion processes in small catchments characterized by steep hillslopes, a large variety of gullies, and hyper-concentrated flow, and will be beneficial to water and soil conservation planning and management for catchments dealing with serious water and soil loss in the Loess Plateau.

Appendix: List of symbols

RS :

The infiltration excess runoff (mm/min)

PE :

The precipitation minus evaporation (mm/min)

F :

The infiltration rate (mm/min)

P :

The precipitation (mm/min)

f _t :

The infiltration rate at time t (mm/min)

f _c :

The constant or equilibrium infiltration rate after soil has been saturated or minimum infiltration rate (mm/min)

f ₀ :

The initial infiltration rate (mm/min)

k _d :

A decay constant specific to the soil (dimensionless)

K _c :

The concentration routing coefficient (dimensionless)

v :

The cross-sectional velocity (m/s)

q :

The overland discharge per unit width (m²/s)

h :

The water depth in meters (m)

r _e (t):

The rainfall excess rate, or lateral inflow rate (mm/min)

l ₁ :

The length of loess slope (m)

l ₂ :

The length of gully slope (m)

l ₃ :

The length of groove (m)

T :

The duration of a storm event (min)

x :

The streamwise distance (m)

t :

Time (min)

S _f :

The friction-induced head loss per unit length between the moving fluid and the bed (m/m)

S ₀ :

The slope of the overland surface (m/m)

S :

The slope of the flow surface (m/m)

f :

The Darcy–Weisbach friction loss coefficient (dimensionless), which can be determined from the Moody diagram

g :

The local gravitational acceleration, ≈ 9.8 m/s²

R :

The hydraulic radius (m)

n :

The Manning’s roughness (dimensionless)

σ, λ :

Constant

θ :

A weighting factor in the Preissmann implicit scheme (dimensionless)

ε :

A weighting factor in the Preissmann implicit scheme (dimensionless)

Ks :

The hydraulic roughness coefficient

η ₁ :

A distance related coefficient $\left( \frac{1}{m} \right)$

γ :

The bulk density of clear water (kg/m³)

γ _s :

The bulk density of dry sediment (kg/m³)

γ _m :

The bulk density of wet sediment (kg/m³)

e ₁ :

The soil erosion rate of a loess slope (kg/s)

α ₁ :

The degree (or angle) of a loess slope (°)

$W_{f1}$ :

The effective power of soil erosion of the loess slope per unit area (W)

τ _o :

The shear stress (N/m²)

τ _c :

The critical yield stress (N/m²)

V :

The average cross-sectional velocity of surface flow (m/s)

A :

A non-dimensional coefficient

$A_{1} = \frac{A}{{g \cdot \eta_{1} \cdot tg\alpha_{1} }}$ :

A sediment erosion model coefficient for loess slope erosion (s²)

γ :

The bulk density of the flow

SC :

The sediment concentration (kg/km³)

Q _h :

The discharge of the clear-water flow (m³/s)

Q _c :

The discharge of the muddy flow (m³/s)

J ₁ :

The loess slope (‰)

J ₀ :

The slope of the surface flow (‰)

e ₂ :

The gully slope erosion rate (kg/s)

$\zeta_{2}$ :

The energy coefficient for gully soil erosion (dimensionless)

h ₂ :

The flow depth of the gully (m)

J ₂ :

The slope of the gully (‰)

α ₂ :

The degree (or angle) of the gully slope (°)

$A_{2} = \zeta_{2} A_{1} ,$ :

A sediment erosion model coefficient for gully slope erosion

$W_{s3}$ :

The power of soil erosion of the groove per unit area (W)

$\eta_{3}$ :

A distance related coefficient $\left( \frac{1}{m} \right)$ for groove erosion

e ₃ :

The groove soil erosion rate (kg/s)

ω :

The settling velocity (cm/s)

$W_{f3}$ :

The actual power of soil erosion of the groove per unit area (W)

U _* :

The friction velocity (m/s)

h ₃ :

The groove depth (m)

J ₃ :

The groove slope (‰)

κ :

The Karman constant

$\zeta_{3}$ :

The energy coefficient for groove soil erosion (dimensionless)

C :

A dimensionless coefficient

B ₀ :

A dimensionless coefficient

A ₃ :

A sediment erosion model coefficient for groove erosion

CE :

The model efficiency measure (dimensionless)

$\sigma_{e}^{2}$ :

Variance of model residuals (dimensionless)

$\sigma_{o}^{2}$ :

Variance of observations (dimensionless)