Evaluation of the Effect of Wind Velocity and Soil Moisture Condition on Soil Erosion in Andosol Agricultural Fields (Model Experiment)

Soil erosion by the wind is an important phenomenon in drastic soil degradation. In Japan, andosol agricultural field is eroded by the wind and agricultural productivity is significantly affected. The aim of this study was to evaluate the effect of wind velocity and soil moisture condition on the soil erosion in andosol agricultural fields. Also, we determined the timing and amount of irrigation water needed to prevent soil erosion by the wind with respect to the wind and soil moisture conditions. A numerical model to simulate airflow in bare andosol field was developed using a continuity equation and Navier Stokes equations. Wind tunnel experiments which described a bare andosol field were performed to measure the degree of soil erosion for four levels of soil moisture condition and five wind velocities. Using the measured amount of soil transferred by wind, the erodibility parameter in Bagnold’s method that quantifies soil erosion was estimated inversely for four soil moisture values. The amounts of soil erosion calculated using this parameter were in good agreement with the measured amounts. These results indicate that the soil moisture and wind conditions under which soil erosion occurs can be determined and the amount of soil erosion can be predicted. Using these conditions and the erodibility parameter, the amount of irrigation needed for the prevention of soil erosion was quantified and the effect of irrigation on soil erosion was evaluated.


Introduction
Soil degradation is a very serious environmental problem [1,2].The United Nations Environment Programme reported that the main cause of soil degradation is erosion by wind and water, which has damaged two billion hectares of agricultural fields [3].
Soil erosion by the wind is an important phenomenon in drastic soil degradation and it exacerbates desertification [4].The mechanism of soil erosion by the wind has been researched with respect to desertification control in arid or semi-arid areas.Bagnold [5,6] studied the motion of sand transferred by wind and developed a method to quantify the transferred amount using friction velocity.Kawamura [7] modified Bagnold's method and introduced the concept of critical friction velocity, which is the threshold for soil erosion.Also, wind tunnel experiment has been used as an effective method to clarify the soil erosion processes by wind [8][9][10].Using these methods, numerical models have been developed for predicting soil erosion by the wind on a relatively large scale [11][12][13][14].
The above-mentioned methods were developed for sandy and large-scale soil erosion by the wind in arid or semi-arid areas.However, the soil erosion by the wind also inflicts serious damage to agricultural fields located in relatively humid areas, such as Japan, because of the loss of fertile soil, seeds, and nursery plants [15,16].About 50% of Japanese agricultural fields are classified as andosol and the base materials of andosol are volcanic ash and humus [17].Andosol have high clay content, well-developed aggregate structures, high soil water retention, and high hydraulic conductivity, and are very fertile [18][19][20].However, the dry density and the resistance to the soil erosion are quite low [21].Various methods to protect andosol agricultural fields from the soil erosion by the wind include windbreak hedges and nets, ground cover plants, and mulching [15,16,[22][23][24][25].Because these methods are expensive, irrigation has been introduced to control soil moisture and prevent soil erosion by the wind [26].Kawata and Tsuchiya [27] evaluated the effect of soil moisture condition on sand movement and showed that controlling the moisture condition of the soil is important in the prevention of soil erosion by the wind.The effect of the soil moisture condition on erodibility was clarified by a wind tunnel experiment [28] and the soil erosion threshold parameters, including soil moisture condition and wind velocity in sandy soil were clarified by wind tunnel experiment [29].These studies showed that controlling the soil moisture condition is effective in preventing soil erosion by the wind in sandy fields; however, research on the prevention of erosion of soil with high clay content, including andosol, has not yet been performed and an optimal irrigation regime to prevent the soil erosion by the wind in andosol agricultural fields has not been developed.
The aim of this study was to evaluate the effect of wind velocity and soil moisture condition on soil erosion by the wind in andosol agricultural fields.Also, we determined the timing and amount of irrigation needed to prevent soil erosion by the wind with respect to the wind and soil moisture conditions.A numerical model to simulate airflow in bare andosol field was developed using a continuity equation and Navier Stokes equations.This method is effective for clarifying the micro-scale advection in the irrigated-soil surface and airflow distribution in the agricultural field considering the crop canopy [30,31].Wind tunnel experiments which described a bare andosol field were performed to measure the amount of soil erosion for four levels of soil moisture condition and five wind velocities to determine erodibility parameter.Using the erodibility parameter, scenario analyses were performed to quantify the amount of irrigation needed for the prevention of soil erosion and evaluate the effect of irrigation on soil erosion.

Numerical Model to Simulate Airflow over a Bare Soil Field
Airflow over a bare soil field can be described by the following continuity equation and Navier-Stokes equations: ∂u ∂x where u and v are the wind velocities in the horizontal and vertical directions (m s −1 ), respectively, ρ is the air density (=1.293 kg m −3 ), p is the air pressure (g m −1 s −2 ), K a is the eddy diffusion coefficient (m 2 s −1 ), t is time (s), x is the fetch (m), and z is the height (m).To solve Equations ( 2) and (3), the Marker And Cell (MAC) method [32] was used on the staggered mesh shown in Figure 1.Equation ( 2) can be approximated by Equation (4) using the MAC method for node [(i + 1 2 )h, kh]: where h is the interval of staggered mesh shown in Figure 1, i and k are the node numbers of the wind velocities in the horizontal and vertical directions, respectively, and l is the node number of time.
where h is the interval of staggered mesh shown in Figure 1, i and k are the node numbers of the wind velocities in the horizontal and vertical directions, respectively, and l is the node number of time.Similarly, Equation (3) can be approximated as Equation (5) for node [ih, (k + ½)h)]: ( ) where P = p/ρ.
are defined as follows: Similarly, Equation (3) can be approximated as Equation (5) for node [ih, (k + 1  2 )h)]: where P = p/ρ.L i+ 1 2 ,k,l and M i,k+ 1 2 ,l are defined as follows: Because the continuity equation, Equation (1), holds when t = (l + 1)∆t, the following equation can be introduced: Substituting Equations ( 4) and (5) into Equation (8) yields the following equation: Water 2019, 11, 98 4 of 11 From Equation (9) we get R i,k,l in Equation ( 10) is defined as follows: D i,k,l is defined as follows: The Successive Over-Relaxation (SOR) method [33] can be used to estimate P using the wind velocity field when t = n∆t.

Eddy Diffusion Coefficient
The Eddy coefficient that appears in Equations ( 2) and (3) can be estimated as The parameter λ, can be represented as the following equations using Karman constant κ. λ = κz (14)

Boundary Condition
To set the boundary conditions for the wind velocity on the soil surface, we need to provide the wind velocity and pressure at virtual node A (Figure 2).The wind velocity in the vertical direction is 0 at the soil surface.We assumed that the wind velocity in the vertical direction at node C' was the same at node C. The wind velocity in the horizontal direction at node A was set the same as that at node B but in the opposite direction.Substituting these data into Equation (3) yields P A at node A: Water 2019, 11, x FOR PEER REVIEW 5 of 12 The parameter λ, can be represented as the following equations using Karman constant κ.

Boundary Condition
To set the boundary conditions for the wind velocity on the soil surface, we need to provide the wind velocity and pressure at virtual node A (Figure 2).The wind velocity in the vertical direction is 0 at the soil surface.We assumed that the wind velocity in the vertical direction at node C' was the same at node C. The wind velocity in the horizontal direction at node A was set the same as that at node B but in the opposite direction.Substituting these data into Equation (3) yields PA at node A: Figure 2. Boundary conditions of wind velocity and pressure fields.

Quantification of Soil Erosion by the Wind
The amount of soil particles transferred by wind, q (g m −1 s −1 ), can be quantified as [1] 3 * where b is the soil erodibility determined by the soil surface condition, g is gravitational acceleration

Quantification of Soil Erosion by the Wind
The amount of soil particles transferred by wind, q (g m −1 s −1 ), can be quantified as [1] where b is the soil erodibility determined by the soil surface condition, g is gravitational acceleration (9.81 m s −2 ), and u * is the friction velocity (m s −1 ), which can be estimated using the wind velocity obtained by solving Equations ( 1)-( 3) and the following equation: where υ is the kinematic viscosity of air (m 2 s −1 ). Figure 3 describes the definition of q in Equation ( 16).The amount of soil particles transferred by wind was defined as the total soil mass blown across the line AB perpendicular to the wind direction in per unit and second [1].The amount of soil erosion by the wind can be estimated as q using the horizontal wind velocity at the vicinity of the soil surface which is calculated from Equations ( 1)-( 3).

Wind Tunnel Experiment
To estimate the parameter b in Equation ( 16), we performed a wind tunnel experiment.A schematic of the wind tunnel is shown in Figure 4.There is a suction fan at the end of the wind tunnel.In the wind tunnel, we reproduced a bare andosol field (N 32°14′, E 130°30′) as shown in Figure 5 which was located in Kagoshima Prefecture, southwest of Japan.This field was located on a windy and hillside of a mountain and had a great risk of the soil erosion by the wind.Potato was cultivated in this field from February to May and the field surface was bare in the other period.Average peak wind gust speed from 2008 to 2017 which was measured in the nearest meteorological station (N 31°16′, E 130°18′) was about 20.1 m s −1 [34].The wind velocity was relatively high from December to April in this area except during typhoons [34].The peak wind gust speed of >13.9 m s −1 (High wind in Beaufort scale) was recorded in 98 days in 2017 [34].We sampled distributed surface soil in this field and performed the soil particle analysis (pipet method) and dry density measurement.A test of the soil water retention curve (Figure 6) in the drying process by suction plate method and centrifuging method was performed using the undistributed soil sample of 100 cm 3 .Distributed and undistributed soil samplings were performed at three kitty-cornered points of the field.The rates of clay, silt and sand were 23.7%, 3.5% and 72.8%, respectively.The dry density of the soil under natural conditions was 0.99 g cm −3 .The volumetric water content of the air-dried soil was 0.026 m 3 m −3 .We filled rectangular tanks (0.15 m × 0.14 m × 0.09 m) with air-dried andosol sample at the dry density of 0.99 g cm −3 and arranged 99 tanks with andosol soil tightly in the wind tunnel as shown in Figure 7.During the experiment, the wind flowed at constant velocities of 2.0, 4.0, 6.0, 8.0, and 9.5 m s −1 at a height of 0.4 m for 1 h, respectively.Soil erosion was measured using a particle counter (PS2, Shinei Technology Co., Ltd., Kobe, Hyogo, Japan) and custom-built soil sampling devices made of 40-denier net and 60-mm-diameter, 100-mm-long vinyl chloride pipe.The particle counter was set at a height of 0.1 m and the sampling devices were placed downstream at heights of 0.10, 0.25, and 0.40 m.The experiments were performed at four values of volumetric water content: 0.026, 0.100, 0.170, and 0.250 m 3 m −3 (2.6, 10.0, 17.0, and 25.0%).At first, we performed the measurement at the volumetric water content of 0.026 m 3 m −3 and we added the water and mixed the water to soil sample evenly to make the soil water condition of 0.100, 0.170, and 0.250 m 3 m −3 , respectively.As shown in Figure 6, the

Wind Tunnel Experiment
To estimate the parameter b in Equation ( 16), we performed a wind tunnel experiment.A schematic of the wind tunnel is shown in Figure 4.There is a suction fan at the end of the wind tunnel.In the wind tunnel, we reproduced a bare andosol field (N 32 • 14 , E 130 • 30 ) as shown in Figure 5 which was located in Kagoshima Prefecture, southwest of Japan.This field was located on a windy and hillside of a mountain and had a great risk of the soil erosion by the wind.Potato was cultivated in this field from February to May and the field surface was bare in the other period.Average peak wind gust speed from 2008 to 2017 which was measured in the nearest meteorological station (N 31 • 16 , E 130 • 18 ) was about 20.1 m s −1 [34].The wind velocity was relatively high from December to April in this area except during typhoons [34].The peak wind gust speed of >13.9 m s −1 (High wind in Beaufort scale) was recorded in 98 days in 2017 [34].We sampled distributed surface soil in this field and performed the soil particle analysis (pipet method) and dry density measurement.A test of the soil water retention curve (Figure 6) in the drying process by suction plate method and centrifuging method was performed using the undistributed soil sample of 100 cm 3 .Distributed and undistributed soil samplings were performed at three kitty-cornered points of the field.The rates of clay, silt and sand were 23.7%, 3.5% and 72.8%, respectively.The dry density of the soil under natural conditions was 0.99 g cm −3 .The volumetric water content of the air-dried soil was 0.026 m 3 m −3 .We filled rectangular tanks (0.15 m × 0.14 m × 0.09 m) with air-dried andosol sample at the dry density of 0.99 g cm −3 and arranged 99 tanks with andosol soil tightly in the wind tunnel as shown in Figure 7.During the experiment, the wind flowed at constant velocities of 2.0, 4.0, 6.0, 8.0, and 9.5 m s −1 at a height of 0.4 m for 1 h, respectively.Soil erosion was measured using a particle counter (PS2, Shinei Technology Co., Ltd., Kobe, Hyogo, Japan) and custom-built soil sampling devices made of 40-denier net and 60-mm-diameter, 100-mm-long vinyl chloride pipe.The particle counter was set at a height of 0.1 m and the sampling devices were placed downstream at heights of 0.10, 0.25, Water 2019, 11, 98 6 of 11 and 0.40 m.The experiments were performed at four values of volumetric water content: 0.026, 0.100, 0.170, and 0.250 m 3 m −3 (2.6, 10.0, 17.0, and 25.0%).At first, we performed the measurement at the volumetric water content of 0.026 m 3 m −3 and we added the water and mixed the water to soil sample evenly to make the soil water condition of 0.100, 0.170, and 0.250 m 3 m −3 , respectively.As shown in Figure 6, the volumetric water content of 0.250 m 3 m −3 is approximately the same as the depletion of moisture content for optimum growth (pressure head of about 3 × 10 3 cm).The average amount of soil erosion was measured by weighing the soil captured in the three sampling nets after three repetitions of experiment.conditions was 0.99 g cm .The volumetric water content of the air-dried soil was 0.026 m m .We filled rectangular tanks (0.15 m × 0.14 m × 0.09 m) with air-dried andosol sample at the dry density of 0.99 g cm −3 and arranged 99 tanks with andosol soil tightly in the wind tunnel as shown in Figure 7.During the experiment, the wind flowed at constant velocities of 2.0, 4.0, 6.0, 8.0, and 9.5 m s −1 at a height of 0.4 m for 1 h, respectively.Soil erosion was measured using a particle counter (PS2, Shinei Technology Co., Ltd., Kobe, Hyogo, Japan) and custom-built soil sampling devices made of 40-denier net and 60-mm-diameter, 100-mm-long vinyl chloride pipe.The particle counter was set at a height of 0.1 m and the sampling devices were placed downstream at heights of 0.10, 0.25, and 0.40 m.The experiments were performed at four values of volumetric water content: 0.026, 0.100, 0.170, and 0.250 m 3 m −3 (2.6, 10.0, 17.0, and 25.0%).At first, we performed the measurement at the volumetric water content of 0.026 m 3 m −3 and we added the water and mixed the water to soil sample evenly to make the soil water condition of 0.100, 0.170, and 0.250 m 3 m −3 , respectively.As shown in Figure 6, the volumetric water content of 0.250 m 3 m −3 is approximately the same as the depletion of moisture content for optimum growth (pressure head of about 3 × 10 3 cm).The average amount of soil erosion was measured by weighing the soil captured in the three sampling nets after three repetitions of experiment.

Relationship between Soil Moisture Condition, wind Velocity, and Amount of Soil Erosion
Figure 8 shows the relationships between volumetric water content, wind velocity, and the amount of soil erosion measured by the sampling nets.The relationship between the wind velocity and the amount of soil erosion shows that there was no soil erosion when the wind velocity was 2.0 m s −1 .The amount of soil erosion increased gradually with the wind velocity, with a significant rate of increase between 4.0 and 6.0 m s −1 for all soil moisture conditions.Wind velocity of 6.0 m s −1 at a height of 0.4 m corresponds to a velocity of 14 m s −1 at a height of 10 m.Soil erosion was significant when the soil moisture content was 0.026 m 3 m −3 (air-dried sample).The amount of soil erosion decreased with the increase in the soil moisture content.Soil transfer by wind was inhibited when the volumetric water content reached 0.170 m 3 m −3 .

Parameter Estimation for Quantification of Soil Erosion
The accuracy of this simulation model was verified the using the simulated and measured soil moisture conditions [31].The friction velocity was estimated using the simulated wind velocity in the horizontal direction from Equations ( 1)-( 3) and used to quantified the soil erosion amount by

Relationship between Soil Moisture Condition, wind Velocity, and Amount of Soil Erosion
Figure 8 shows the relationships between volumetric water content, wind velocity, and the amount of soil erosion measured by the sampling nets.The relationship between the wind velocity and the amount of soil erosion shows that there was no soil erosion when the wind velocity was 2.0 m s −1 .The amount of soil erosion increased gradually with the wind velocity, with a significant rate of increase between 4.0 and 6.0 m s −1 for all soil moisture conditions.Wind velocity of 6.0 m s −1 at a height of 0.4 m corresponds to a velocity of 14 m s −1 at a height of 10 m.Soil erosion was significant when the soil moisture content was 0.026 m 3 m −3 (air-dried sample).The amount of soil erosion decreased with the increase in the soil moisture content.Soil transfer by wind was inhibited when the volumetric water content reached 0.170 m 3 m −3 .

Relationship between Soil Moisture Condition, wind Velocity, and Amount of Soil Erosion
Figure 8 shows the relationships between volumetric water content, wind velocity, and the amount of soil erosion measured by the sampling nets.The relationship between the wind velocity and the amount of soil erosion shows that there was no soil erosion when the wind velocity was 2.0 m s −1 .The amount of soil erosion increased gradually with the wind velocity, with a significant rate of increase between 4.0 and 6.0 m s −1 for all soil moisture conditions.Wind velocity of 6.0 m s −1 at a height of 0.4 m corresponds to a velocity of 14 m s −1 at a height of 10 m.Soil erosion was significant when the soil moisture content was 0.026 m 3 m −3 (air-dried sample).The amount of soil erosion decreased with the increase in the soil moisture content.Soil transfer by wind was inhibited when the volumetric water content reached 0.170 m 3 m −3 .

Parameter Estimation for Quantification of Soil Erosion
The accuracy of this simulation model was verified the using the simulated and measured soil moisture conditions [31].The friction velocity was estimated using the simulated wind velocity in the horizontal direction from Equations ( 1)-( 3) and used to quantified the soil erosion amount by

Parameter Estimation for Quantification of Soil Erosion
The accuracy of this simulation model was verified the using the simulated and measured soil moisture conditions [31].The friction velocity was estimated using the simulated wind velocity in the horizontal direction from Equations ( 1)-( 3) and used to quantified the soil erosion amount by Equation ( 16).The parameter b in Equation ( 16), soil erodibility, was estimated inversely using the amount of soil erosion due to wind shown in Figure 8 and the estimated amount of soil erosion by Equation ( 16).Table 1 presents the results of the inverse estimation of b.Using the values in Table 1, the amount of soil erosion was estimated for the four levels of soil moisture condition.Figure 9 compares the amounts of soil erosion estimated using b from Table 1 and the measured amounts for four wind velocities.Root mean square errors (RMSE) determined using the measured and estimated data under four wind velocities shown in Figure 9 were 0.0001, 0.0007, 0.0005, and 0.0007, respectively.The results show that the estimated amounts of soil erosion at the four levels of soil moisture condition were in good agreement with the measured amounts for four wind velocities and that parameter b is effective for predicting the amount of soil erosion due to wind.Equation ( 16).The parameter b in Equation ( 16), soil erodibility, was estimated inversely using the amount of soil erosion due to wind shown in Figure 8 and the estimated amount of soil erosion by Equation ( 16).Table 1 presents the results of the inverse estimation of b.Using the values in Table 1, the amount of soil erosion was estimated for the four levels of soil moisture condition.Figure 9 compares the amounts of soil erosion estimated using b from Table 1 and the measured amounts for four wind velocities.Root mean square errors (RMSE) determined using the measured and estimated data under four wind velocities shown in Figure 9 were 0.0001, 0.0007, 0.0005, and 0.0007, respectively.The results show that the estimated amounts of soil erosion at the four levels of soil moisture condition were in good agreement with the measured amounts for four wind velocities and that parameter b is effective for predicting the amount of soil erosion due to wind.

Quantification of Timing and Amount of Irrigation Water to Prevent the Soil Erosion
As shown in Figure 8, the soil erosion was significant when the wind velocity was over 6.0 m s −1 and the volumetric water content was <0.170 m 3 m −3 .At the Japanese meteorological observatory, the wind velocity is generally measured at an altitude of 10 m.Wind velocity of 6.0 m s −1 at a height of 0.4 m corresponds to 14 m s −1 at 10 m using logarithmic law for wind velocity.The threshold of wind velocity that caused significant soil erosion was this value and it could be an indicator for initiating irrigation to prevent soil erosion.

Quantification of Timing and Amount of Irrigation Water to Prevent the Soil Erosion
As shown in Figure 8, the soil erosion was significant when the wind velocity was over 6.0 m s −1 and the volumetric water content was <0.170 m 3 m −3 .At the Japanese meteorological observatory, the wind velocity is generally measured at an altitude of 10 m.Wind velocity of 6.0 m s −1 at a height of 0.4 m corresponds to 14 m s −1 at 10 m using logarithmic law for wind velocity.The threshold of wind velocity that caused significant soil erosion was this value and it could be an indicator for initiating irrigation to prevent soil erosion.
Scenario analyses were performed to estimate the amount of irrigation water needed to increase the volumetric water content from 0.026 and 0.100 m 3 m −3 to 0.170 m 3 m −3 for the prevention of soil Water 2019, 11, 98 9 of 11 erosion and the inhibitive effect of irrigation on soil erosion was evaluated as shown in Table 2. Using parameter b shown in Table 1, the soil erosion amounts for 1 hour in the study site (Figure 5) was estimated with the wind velocity of 6.0, 8.0 and 9.5 m s −1 , respectively, when the wind direction was perpendicular to the long side (100 m) of the study field shown in Figure 5.The volumetric water content increased from 0.026 to 0.100 m 3 m −3 and the amount of soil transferred by the wind was reduced almost by half when 3 mm of irrigation was applied.With an additional 3 mm of irrigation, the volumetric water content increased to 0.170 m 3 m −3 and the amount of soil transferred by the wind was greatly reduced compared with the amount when the volumetric water content was 0.026 and 0.100 m 3 m −3 .The difference between the amounts of soil erosion for 0.170 and 0.250 m 3 m −3 is relatively small.These results indicate that the optimal volumetric water content to prevent soil erosion is 0.170 m 3 m −3 .the wind occurred were evaluated as <28% and >8 m s , respectively by field measurement in an andosol field [35].The volumetric water contents of 0.026, 0.100, 0.170 and 0.25 m 3 m −3 which were adopted as the experimental conditions in this study corresponds to soil moisture content of 2.6, 9.9, 16.8, 24.8%, respectively.As shown in Figure 9 and Table 2, the thresholds of soil moisture content and wind velocity for soil erosion by the wind can be specified as 16.8% (volumetric water content =0.170 m 3 m −3 ) and 14 m s −1 (at the height of 10 m), respectively.The method introduced in this study enables precise determination of these thresholds and optimization of soil moisture management to prevent the soil erosion by the wind.Bergametti et al. reported that the soil erosion by the wind was reduced by a rain event at a sand agricultural field in Niger [36].They clarified that the soil transport was reduced especially during the first 10-15 min following the beginning of the rain event, and almost no significant sand transport occurred after 30 min.They also showed that this inhibition effect lasted no longer than 12 h after the end of the rain event (cumulative rainfall of 20 mm).Optimal irrigation amount for prevention of the soil erosion by the wind could be estimated in our study, however, optimal irrigation duration also should be determined to enhance the irrigation effect on soil erosion prevention.Also the irrigation effect on the prevention of the soil erosion by the wind should be clarified taking into account the temporal changes of soil moisture conditions after irrigation., respectively by field measurement in an andosol field [35].The volumetric water contents of 0.026, 0.100, 0.170 and 0.25 m 3 m −3 which were adopted as the experimental conditions in this study corresponds to soil moisture content of 2.6, 9.9, 16.8, 24.8%, respectively.As shown in Figure 9 and Table 2, the thresholds of soil moisture content and wind velocity for soil erosion by the wind can be specified as 16.8% (volumetric water content =0.170 m 3 m −3 ) and 14 m s −1 (at the height of 10 m), respectively.The method introduced in this study enables precise determination of these thresholds and optimization of soil moisture management to prevent the soil erosion by the wind.
Bergametti et al. reported that the soil erosion by the wind was reduced by a rain event at a sand agricultural field in Niger [36].They clarified that the soil transport was reduced especially during the first 10-15 min following the beginning of the rain event, and almost no significant sand transport occurred after 30 min.They also showed that this inhibition effect lasted no longer than 12 h after the end of the rain event (cumulative rainfall of 20 mm).Optimal irrigation amount for prevention of the soil erosion by the wind could be estimated in our study, however, optimal irrigation duration also should be determined to enhance the irrigation effect on soil erosion prevention.Also the irrigation effect on the prevention of the soil erosion by the wind should be clarified taking into account the temporal changes of soil moisture conditions after irrigation.The result indicated that the method introduced here is effective to quantify and save the irrigation water for prevention of soil erosion by the wind.Arimori et al. reported that soil moisture content and the wind velocity when the soil erosion by the wind occurred were evaluated as <28% and >8 m s −1 , respectively by field measurement in an andosol field [35].The volumetric water contents of 0.026, 0.100, 0.170 and 0.25 m 3 m −3 which were adopted as the experimental conditions in this study corresponds to soil moisture content of 2.6, 9.9, 16.8, 24.8%, respectively.As shown in Figure 9 and Table 2, the thresholds of soil moisture content and wind velocity for soil erosion by the wind can be specified as 16.8% (volumetric water content =0.170 m 3 m −3 ) and 14 m s −1 (at the height of 10 m), respectively.The method introduced in this study enables precise determination of these thresholds and optimization of soil moisture management to prevent the soil erosion by the wind.
Bergametti et al. reported that the soil erosion by the wind was reduced by a rain event at a sand agricultural field in Niger [36].They clarified that the soil transport was reduced especially during the first 10-15 min following the beginning of the rain event, and almost no significant sand transport occurred after 30 min.They also showed that this inhibition effect lasted no longer than 12 h after the end of the rain event (cumulative rainfall of 20 mm).Optimal irrigation amount for prevention of the soil erosion by the wind could be estimated in our study, however, optimal irrigation duration also should be determined to enhance the irrigation effect on soil erosion prevention.Also the irrigation effect on the prevention of the soil erosion by the wind should be clarified taking into account the temporal changes of soil moisture conditions after irrigation.Arimori et al. estimated that the irrigation amount to prevent the soil erosion by the wind is 2-10 mm using water budget model [26] and the irrigation amount estimated in this study were smaller.The result indicated that the method introduced here is effective to quantify and save the irrigation water for prevention of soil erosion by the wind.
Arimori et al. reported that soil moisture content and the wind velocity when the soil erosion by the wind occurred were evaluated as <28% and >8 m s −1 , respectively by field measurement in an andosol field [35].The volumetric water contents of 0.026, 0.100, 0.170 and 0.25 m 3 m −3 which were adopted as the experimental conditions in this study corresponds to soil moisture content of 2.6, 9.9, 16.8, 24.8%, respectively.As shown in Figure 9 and Table 2, the thresholds of soil moisture content and wind velocity for soil erosion by the wind can be specified as 16.8% (volumetric water content = 0.170 m 3 m −3 ) and 14 m s −1 (at the height of 10 m), respectively.The method introduced in this study enables precise determination of these thresholds and optimization of soil moisture management to prevent the soil erosion by the wind.
Bergametti et al. reported that the soil erosion by the wind was reduced by a rain event at a sand agricultural field in Niger [36].They clarified that the soil transport was reduced especially during the first 10-15 min following the beginning of the rain event, and almost no significant sand transport occurred after 30 min.They also showed that this inhibition effect lasted no longer than 12 h after the end of the rain event (cumulative rainfall of 20 mm).Optimal irrigation amount for prevention of the soil erosion by the wind could be estimated in our study, however, optimal irrigation duration also should be determined to enhance the irrigation effect on soil erosion prevention.Also the irrigation effect on the prevention of the soil erosion by the wind should be clarified taking into account the temporal changes of soil moisture conditions after irrigation.

Conclusions
To evaluate the effect of wind velocity and soil moisture condition on soil erosion by the wind in andosol agricultural fields, we developed a numerical model that simulates airflow in bare soil fields.
We then performed a wind tunnel experiment using a replica bare soil field to measure the amount of soil erosion under four levels of soil moisture condition and five wind velocities.The experimental results indicated that soil erosion is significant when the wind velocity at a height of 0.4 m is over 6.0 m s −1 (which corresponds to 14 m s −1 at a height of 10.0 m) and the volumetric water content decreases to <0.170 m 3 m −3 .Using the measured amount of soil transferred by wind the parameter b in Bagnold's method that quantifies soil erosion was estimated inversely for four soil moisture values.The amounts of soil erosion calculated using this parameter was in good agreement with the measured amounts.These results indicate that the conditions under which soil erosion occurs can be determined and the amount of soil erosion can be predicted.Using these conditions and the erodibility parameter, the amount of irrigation needed for the prevention of soil erosion was quantified and the effect of irrigation on soil erosion was evaluated.The results of this study can be used to predict the occurrence of soil erosion and to optimize the irrigation used to prevent soil erosion.

Figure 1 .
Figure 1.Schematic of the staggered mesh.

Figure 1 .
Figure 1.Schematic of the staggered mesh.

Figure 2 .
Figure 2. Boundary conditions of wind velocity and pressure fields.

Figure 4 .
Figure 4. Schematic of the wind tunnel.

Figure 6 .Figure 5 . 12 Figure 5 .
Figure 6.Soil water retention curve of andosol which was used in the wind tunnel experiment.

Figure 6 .Figure 6 .
Figure 6.Soil water retention curve of andosol which was used in the wind tunnel experiment.

Figure 7 .
Figure 7. Installation condition of measurement devices and andosol sample in the wind tunnel experiment.

Figure 8 .
Figure 8. Relationships between volumetric water content, wind velocity, and amount of soil erosion.

Figure 7 .
Figure 7. Installation condition of measurement devices and andosol sample in the wind tunnel experiment.

Water 2019 , 12 Figure 7 .
Figure 7. Installation condition of measurement devices and andosol sample in the wind tunnel experiment.

Figure 8 .
Figure 8. Relationships between volumetric water content, wind velocity, and amount of soil erosion.

Figure 8 .
Figure 8. Relationships between volumetric water content, wind velocity, and amount of soil erosion.

Table 2 .
Irrigation water amount for the prevention of soil erosion with respect to soil moisture and wind conditions.

Table 2 .
Irrigation water amount for the prevention of soil erosion with respect to soil moisture and wind conditions.Arimori et al. reported that soil moisture content and the wind velocity when the soil erosion by the wind occurred were evaluated as <28% and >8 m s −1

Table 2 .
Irrigation water amount for the prevention of soil erosion with respect to soil moisture and wind conditions.

Table 2 .
Irrigation water amount for the prevention of soil erosion with respect to soil moisture and wind conditions.