The hydrological processes of small watersheds are closely related to water resource
theory, land surface ecology, and soil erosion. Severe soil and water loss in the loess
hilly–gully region of the Loess Plateau has attracted much concern. Small watersheds are
the basic unit for soil and water conservation. Models of hydrologic processes for small
watersheds could serve as an important aid for soil and water conservation, water resource
optimization and flood prediction.
In this study, by taking the hilly-gully regions of the Loess Plateau as the study area,
the establishment of hydrological process models for different-scale watersheds during a
single rainfall event was studied. In Qiaozi-West watershed (W1-b, 1 km 2 ), the model
establishment, calibration and validation for watershed infiltration, runoff, and flow routing
were studied. In the watersheds of Luoyugou (W100, 100 km 2 ), Lvergou (W10, 10 km 2 ),
Qiaozi-East (W1-a, 1 km 2 ) and Qiaozi-West (W1-b, 1 km 2 ), the Hydraulic Geometry
theory was introduced to study the measuring method of watershed runoff. Preliminary
conclusions of the study are summarized as follows:
(1) A method was developed for modifying NRCS-CN model. By introducing steady
infiltration to the NRCS-CN model, the modified NRCS-CN (MCN) model was developed.
The steady infiltration rates for the study watershed were determined as 4.8 mm h -1 by
using observed initial abstraction, and 4.2 mm h -1 by using calculated initial abstraction.
Both of the MCN and NRCS-CN models were used to simulate watershed runoff process
for the study events. The results showed that the simulation of watershed infiltration and
runoff by the MCN model was better than that of NRCS-CN model by using either calibrated steady infiltration rate, especially in simulating larger infiltration, runoff events;
the infiltration simulation using steady infiltration rate of 4.8 mm h -1 was superior to that
using 4.2 mm h -1 for MCN model.
(2) Based on Qiaozi-West watershed rainfall-runoff process data, watershed DEM,
soil and land use digital maps, the initial abstraction ratio of the NRCS-CN model was
determined by Back Calculation (BC) and Event Analysis (EA) methods. The initial
abstraction ratios were determined as 0.1 and 0.17 by using BC and EA methods,
respectively. Using three initial abstraction ratio values of 0.1, 0.17 and 0.2, runoff
amounts for the study watershed were predicted by NRCS-CN model. Considering both of
error analyses and curve fitting results, the value of 0.1 was indicated as the appropriate
value of the initial abstraction ratio for the NRCS-CN model in Qiaozi-West watershed.
(3) The observed flow velocity data from the measuring weirs at watershed outlets
were fitted with the discharge rate, using both Hydraulic Geometry power function and
logarithmic function models for the Luoyugou (W100, 100 km 2 ), Lvergou (W10, 10 km 2 ),
Qiaozi-East (W1-a, 1 km 2 ) and Qiaozi-West (W1-b, 1 km 2 ) watersheds. The coefficient of
determination (R 2 ) and model efficiency coefficient (E) were used to evaluate model
calibration and validation results, respectively. The effect of watershed scale on the model
parameters was examined by using model calibration results from W100, W10 and W1-a
watersheds. It was found that the parameter k (flow velocity for unit discharge rate) in the
power function model was negatively correlated with watershed size, while parameter m
(rate of change of flow velocity) had an opposite correlation with watershed size compared
with parameter k. In the logarithmic function model, parameter e (rate of change of flow
velocity) had no significant correlation with watershed size, while parameter d (flow
velocity for unit discharge rate) was negatively correlated with watershed size, similar to
parameter k The calibration results from the two paired watersheds (W1-a and W1-b) were
used for exploring the effect of watershed land use on the model parameters. The
parameter k in the power function model for W1-a watershed was significantly higher than
that of W1-b watershed (P<0.001). The parameter m for the two paired watersheds showed
no significant difference. The parameter e in the logarithmic function model for W1-b
watershed was higher than that of W1-a watershed, however the difference was not
significant (P<0.05). The parameter d for W1-a watershed was significantly higher than that of W1-b watershed (P<0.05). Another data set from the study watersheds was used to
test the two function models. The results showed that both of the model functions yielded
acceptable results, nevertheless the power function model generally showed superior
performance to the logarithmic function model for the wide value range of flow velocity.
(4) By using GIS tools, the Qiaozi-West (W1-b) watershed was dissected as 11 slopes,
which were connected by a channel. The runoff for each slope in the watershed was
calculated using NRCS-CN model based on watershed rainfall process input for the year
1987–2006. A new conceptual method was developed and used to calculate flow routing of
the runoff from each slope, to derive watershed hydrograph. The predictions for the three
important hydraulic variables: runoff, peak discharge rate and time to peak were examined.
The absolute error for runoff depth prediction varied from -0.08 to 7.4 mm, the mean was
0.35 mm; the relative error changed from 8% to -103%, the mean was -1%. The maximum
absolute and relative errors for peak discharge rate prediction were -1.85 m 3 s -1 and -63%,
and the mean were -0.02 m 3 s -1 and 10%, respectively. For the prediction of time to peak,
the maximum absolute and relative errors were 0.99 h and -109%, and the mean were -0.09
h and -17%. Moreover, the slopes of linear fitting for peak discharge rate and time to peak
were 1.09 and 1.04 (both close to 1), with coefficients of determination (R 2 ) both close to 1
(0.99 and 0.97). For runoff prediction, the slope and R 2 values for the linear fitting were
0.83 and 0.78. The root mean square error (RMSE), model efficiency coefficient (E), and
coefficient of residual mass (CRM) were calculated for the simulations of each hydraulic
variable. It was shown that the simulation of peak discharge rate was best, followed by that
of time to peak, and runoff.
(5) A new method was suggested to accurately measure the discharge from the
watersheds by measuring the flow velocity and using the relationship between flow
velocity and discharge rate. The power function of flow velocity-discharge rate was
established by deriving the inverse function of Hydraulic Geometry power function, taking
the discharge rate as the dependent variable with flow velocity as the independent variable.
The inverse power function model was tested by the flow velocity-discharge rate data from
the measuring weirs of Luoyugou (W100), Lvergou (W10), Qiaozi-East (W1-a) and
Qiaozi-West (W1-b) watershed outlets. According to the calculation of coefficients of
determination (R 2 ), the model calibration of W100 was best, followed by those of W1-a, W10 and W1-b. Based on model efficiency coefficient (E) calculation results, the
simulation accuracy of W1-a watershed was highest, followed by those of W100, W10 and
W1-b. The study indicated that the derived power function could be used to determine
discharge rate at study watershed outlets. Therefore, a new method was developed for
measuring discharge rate given the measurement of the flow velocity instead of flow depth.
The results of the study contribute to better understanding watershed hydrological
cycle, and could supply basic tools for the study of water resource optimization, soil
erosion, and sediment transport for the small watersheds on the Loess Plateau.
Key words: watershed; infiltration; rainfall–runoff process; Hydraulic Geometry;