24
2 Similarity of Model Experiments
λ SB =
S p
S B
=
4.26 × 10
6
121.53
= 35,053
(2.8)
Calculated in the same manner, the soil loss scale numbers of the Model Da and
Model Db were 9.01 × 10
5 and 1.95 × 10
6 , respectively. The relative ratio of erosion
extent between the Model Da (or Model Db) and Model B, R DB , was calculated by
solving Eqs. (2.3) and (2.4) simultaneously. Consequently, the relative ratio of the
Model Da and Model Db to Model B was 2.5 and 1.16, respectively.
2.5.3 Validation of Soil Loss Scale Number
The rainfall-erosion data for the natural watershed, especially those after constructing
dams, are so scarce that the reliability of the SSPM had to be verified by comparing
the experimental results for the Model Da and Model Db with those for the Model
B.
To validate the soil loss scale number as R DB = 1. The Model Da was used to
predict the amount of soil loss in the Model B when check dams were constructed
in an orderly fashion. Thus, R DB, the relative ratio of the Model Da to Model B was
2.5 in these experiments. All soil losses in the model experiments were converted to
prototype values by multiplying the soil loss scale number. The error of soil loss in
the Model Da caused by the difference of the rainfall intensities was counteracted by
Eq. (2.6). The relative differences in soil loss for the corresponding rainfall events
between the Model B and Model Da, which represent the accuracy of the SSPM,
were calculated using the following equation:
e = (S p D − S p B ) × 100%/S p B
(2.9)
where e is the relative differences of soil losses; S p D is the soil loss at the prototype
scale that was transferred from the Model Da, S P D = S D × λ SD ; S p B is the soil loss
at the prototype scale that was transferred from the Model B, S p B = S B × λ SB .
Consequently, the amount of soil loss in the Model Da was very close to that in the
Model B, and the difference between the two models was less than 50% (Table 2.3),
except that in the first rainfall event. The intensity of the first rainfall in the Model Da,
2.70 mm/min, was 63.9% more intense than the designed intensity resulting from
human error, 1.65 mm/min.
To validate the soil loss scale number as R DB ≈ 1. The Model Db was used to
predict the soil loss in the Model B when the check dams were built in an orderly
fashion. The value of R DB was 1.16 in these experiments. All soil losses in the
model experiments were converted to the prototype values by multiplying the soil
loss scale number. The soil loss error in the Model Db caused by the difference of
rainfall intensities was counteracted using Eq. (2.6). Thus, the amount of soil loss
in the Model Db was close to that in the Model B, and the difference between two
2 Similarity of Model Experiments
λ SB =
S p
S B
=
4.26 × 10
6
121.53
= 35,053
(2.8)
Calculated in the same manner, the soil loss scale numbers of the Model Da and
Model Db were 9.01 × 10
5 and 1.95 × 10
6 , respectively. The relative ratio of erosion
extent between the Model Da (or Model Db) and Model B, R DB , was calculated by
solving Eqs. (2.3) and (2.4) simultaneously. Consequently, the relative ratio of the
Model Da and Model Db to Model B was 2.5 and 1.16, respectively.
2.5.3 Validation of Soil Loss Scale Number
The rainfall-erosion data for the natural watershed, especially those after constructing
dams, are so scarce that the reliability of the SSPM had to be verified by comparing
the experimental results for the Model Da and Model Db with those for the Model
B.
To validate the soil loss scale number as R DB = 1. The Model Da was used to
predict the amount of soil loss in the Model B when check dams were constructed
in an orderly fashion. Thus, R DB, the relative ratio of the Model Da to Model B was
2.5 in these experiments. All soil losses in the model experiments were converted to
prototype values by multiplying the soil loss scale number. The error of soil loss in
the Model Da caused by the difference of the rainfall intensities was counteracted by
Eq. (2.6). The relative differences in soil loss for the corresponding rainfall events
between the Model B and Model Da, which represent the accuracy of the SSPM,
were calculated using the following equation:
e = (S p D − S p B ) × 100%/S p B
(2.9)
where e is the relative differences of soil losses; S p D is the soil loss at the prototype
scale that was transferred from the Model Da, S P D = S D × λ SD ; S p B is the soil loss
at the prototype scale that was transferred from the Model B, S p B = S B × λ SB .
Consequently, the amount of soil loss in the Model Da was very close to that in the
Model B, and the difference between the two models was less than 50% (Table 2.3),
except that in the first rainfall event. The intensity of the first rainfall in the Model Da,
2.70 mm/min, was 63.9% more intense than the designed intensity resulting from
human error, 1.65 mm/min.
To validate the soil loss scale number as R DB ≈ 1. The Model Db was used to
predict the soil loss in the Model B when the check dams were built in an orderly
fashion. The value of R DB was 1.16 in these experiments. All soil losses in the
model experiments were converted to the prototype values by multiplying the soil
loss scale number. The soil loss error in the Model Db caused by the difference of
rainfall intensities was counteracted using Eq. (2.6). Thus, the amount of soil loss
in the Model Db was close to that in the Model B, and the difference between two