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

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

Kozue Yuge * and Mitsumasa Anan

Department of Environmental Sciences, Faculty of Agriculture, Saga University, Saga 8408502, Japan; [email protected] * Correspondence: [email protected]; Tel.: +81-952-28-8756

Received: 8 December 2018; Accepted: 31 December 2018; Published: 8 January 2019

Abstract: 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.

Keywords: soil degradation; soil erosion; soil loss; soil moisture condition; computational ﬂuid dynamics (CFD); wind tunnel experiment; irrigation regime

1. 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 [8–10]. Using these methods, numerical models have been developed for predicting soil erosion by the wind on a relatively large scale [11–14]. 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,

Water 2019, 11, 98; doi:10.3390/w11010098 www.mdpi.com/journal/water Water 2019, 11, 98 2 of 11 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 [18–20]. 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 [15,16,22–25]. 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.

2. Methodology

2.1. 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 ∂v + = 0 (1) ∂x ∂z ∂u ∂u ∂u 1 ∂p ∂ ∂u ∂ ∂u + u + v = − + K + K (2) ∂t ∂x ∂z ρ ∂x ∂x a ∂x ∂z a ∂z ∂v ∂v ∂v 1 ∂p ∂ ∂v ∂ ∂v + u + v = − + K + K (3) ∂t ∂x ∂z ρ ∂z ∂x a ∂x ∂z a ∂z where u and v are the wind velocities in the horizontal and vertical directions (m s−1), respectively, ρ is −3 −1 −2 the air density (=1.293 kg m ), p is the air pressure (g m s ), Ka is the eddy diffusion coefficient (m2 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 Figure1. Equation (2) can be 1 approximated by Equation (4) using the MAC method for node [(i + 2 )h, kh]:

∆t ui+ 1 k l+ = ui+ 1 k l + ∆tLi+ 1 k l − (Pi+1,k,l − Pi,k,l) (4) 2 , , 1 2 , , 2 , , h where h is the interval of staggered mesh shown in Figure1, 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. Water 2019, 11, x FOR PEER REVIEW 3 of 12

Δ = + Δ − t ()− u 1 u 1 tL 1 Pi+1,k,l Pi,k,l i+ ,k,l +1 i+ ,k,l i+ ,k,l (4) 2 2 2 h

where h is the interval of staggered mesh shown in Figure 1, i and k are the node numbers of the wind Watervelocities2019, 11 ,in 98 the horizontal and vertical directions, respectively, and l is the node number of time.3 of 11

v 1 1 i,k + k + 2 2

P h i,k

u 1 u 1 i− ,k i+ ,k 2 2 v 1 1 i,k − k − 2 2 h 1 1 i − i + 2 2 FigureFigure 1. 1.Schematic Schematic of of the the staggered staggered mesh. mesh.

1 Similarly,Similarly, Equation Equation (3) (3) can can be be approximated approximated as as Equation Equation (5) (5) for for node node [ih [,(ihk, (+k +2 )½)h)]:h)]: Δ = + Δ −∆tt ()− vi k+ 1 l+v =1 vi k+ 1vl +1 ∆tMtMi k+ 1 l1− (PPii,k,k++11,,ll −PiP,ki,,lk,l ) (5)(5) , 2 , 1i,k + ,l +1, 2 ,i,k + ,l , i,2k +, ,l h 2 2 2 h where P = p/ρ. L 1 and M 1 are deﬁned as follows: where P = p/ρ. iL+ 21,k,l and Mi,k+ 2 ,1l are defined as follows: i+ ,k,l i,k + ,l 2 2

L 1 i+ 2 ,k,l L ( u +u 2 u +u 2) + 1 i+ 1 k l i+ 3 ,k,l i− 1 k l i+ 1 k l i ,k1,l 2 , , 2 2 , , 2 , , = −2 h 2 − 2 2 2 u u +u + u v +vu + u u +u v +v i+ 1 k l1 i+ 1 k+ 3l ik+ 1 l  i+ 1k+ 1 l i1+ 1 k l i+ 1 k− l i k− 1 l i+ k− 1 l − 1 1  2 i,+, ,k,l 2 , i+1, ,k·,l , 2 ,  i−1, ,k,l2 , −i+ ,k2,l, ,  2 , 1, · , 2 , 1, 2 , = −h  2 2 2  − 2 2 2  2 2 h u2 −u 2u −u (6)  i+ 3 ,k,l i+1 k l  i+ 1 k l i−1 k l 1 2 2 , , 2 , , 2 , , + h Ka i+1,k,l h  − Ka i,k,l h   u −u Ku ++Ku +Kv +Kv i+ 1 ,ku+1,l i++1 ,uk,l v + v  1 a+ i,1k+1,l a i++11,k+ 1,l a i + 1,1 k,l a+ i,k,l+ 1 2 + 1 2 + 1 − − 1 + − 1 + h1  i ,k,l i ,k 14,l i,k ,l i 1,k · ,l i h ,k,l i ,k 1,l i,k ,l i 1,k ,l  −  2 2 ⋅ 2 2 − 2 2 ⋅ 2 2  u −u h 2 2 i+ 1 k l i+ 1 k− l 2 2 Ka i,k,l +Ka i+1,k,l +Ka i+1,k−1,l +Ka i,k−1,l 2 , , 2 , 1,  −  4 · h  − − (6)  u 3 u 1 u 1 u 1   i+ ,k,l i+ ,k,l i+ ,k,l i− ,k,l  1 2 2 2 2 M + 1 K + − K i+ 2 ,k,l a i 1,k,l a i,k,l  h u +u h v +v u h +u v +v  i+ 1 k l i+ 1 k+ l i k+ 1 l i+ k+ 1 l i− 1 k+ l i− 1 k l i− k+ 1 l i k+ 1 l 1 2 , , 2 , 1, , 2 , 1, 2 , 2 , 1, 2 , , 1, 2 , , 2 , = − h  2 · 2 − 2  · 2 − ( v +v 2 v +v 2) u 1 u 1  Ki,k+ 1 ,l +i,k+K3 ,l + Ki,k+ 1 ,l i+,k−K1 ,l i+ ,k +1,l i+ ,k,l − 1 1 a i,k2+1,l 2a i+1,k +−1,l a i2+1,k,l 2 a i,k,l 2 2 +h  2 2 ⋅ h 4 h  v −v (7) K +K +K +K i+1,k+ 1 ,l i,k+ 1 ,l + 1 a i,k+1,l a i+1,k+1,l a i+1,k,l a i,k,l · 2 2 h 4 h − u 1 u 1  + + + v 1 −v i+ ,k1,l i+ ,k −1,l KK a i,k,l +K a i+1,k,l+K K a +i+1K,k −1,l K ai,k i+,k −1,l,l i−1,k+ ,l  −− a i−1,k+1,l a i,k+1,l a i,k,l a i−1,k,l · 2 ⋅ 2 2 2  4 4 h h v −v v −v  i,k+ 3 ,l i k+ 1 l i k+ 1 l i k− 1 l 1 2 , 2 , , 2 , , 2 ,  + h Ka i,k+1,l h − Ka i,k,l h

Because the continuity equation, Equation (1), holds when t = (l + 1)∆t, the following equation can be introduced: 1 ui+ 1 k l+ − ui− 1 k l+ + vi k+ 1 l+ − vi k− 1 l+ = 0 (8) h 2 , , 1 2 , , 1 , 2 , 1 , 2 , 1

Substituting Equations (4) and (5) into Equation (8) yields the following equation: hn o n o 1 + − ∆t − − + − ∆t − h ui+ 1 ,k,l ∆tLi+ 1 ,k,l h (Pi+1,k,l Pi,k,l) ui− 1 ,k,l ∆tLi− 1 ,k,l h (Pi,k,l Pi−1,k,l) 2 2 2 2 (9) n ∆t o n ∆t oi + v 1 + ∆tM 1 − (Pi,k+1,l − Pi,k,l) − v 1 + ∆tM 1 − (Pi,k,l − Pi,k−1,l) = 0 i,k+ 2 ,l i,k+ 2 ,l h i,k− 2 ,l i,k− 2 ,l h Water 2019, 11, 98 4 of 11

From Equation (9) we get

1 2 P + = P + + P − + P + + P − − h R (10) i,k,l 1 4 i 1,k,l i 1,k,l i,k 1,l i,k 1,l i,k,l

Ri,k,l in Equation (10) is deﬁned as follows:

D 1 = i,k,l + − + − Ri,k,l Li+ 1 ,k,l Li− 1 ,k,l Mi,k+ 1 ,l Mi,k− 1 ,l (11) ∆t h 2 2 2 2

Di,k,l is deﬁned as follows:

∂u ∂v 1 Di,k,l = + = ui+ 1 k l − ui− 1 k l + vi k+ 1 l − vi k− 1 l (12) ∂x ∂z h 2 , , 2 , , , 2 , , 2 , The Successive Over-Relaxation (SOR) method [33] can be used to estimate P using the wind velocity ﬁeld when t = n∆t.

Water2.2. Eddy2019, 11 Diffusion, x FOR PEER Coefﬁcient REVIEW 5 of 12 The Eddy coefﬁcient that appears in Equations (2) and (3) can be estimated as ∂ = λ2 u Ka 2 ∂u (13) Ka = λ ∂z (13) ∂z The parameter λ, can be represented as the following equations using Karman constant κ. The parameter λ, can be represented as the following equations using Karman constant κ. λ = κz (14) λ = κz (14)

2.3.2.3. Boundary Boundary Condition Condition ToTo set set the the boundary boundary conditions conditions for for the the wind wind veloci velocityty on on the the soil soil surface, surface, we we need need to to provide provide the the windwind velocity velocity and and pressure pressure at virtual node A (Figure2 2).). The The wind wind velocity velocity in in the the vertical vertical direction direction is is 0 0at at the the soil soil surface. surface. We We assumed assumed that that the the wind wind velocity velocity in thein the vertical vertical direction direction at node at node C’ was C’ thewas same the sameat node at node C. The C. wind The wind velocity velocity in the in horizontal the horizontal direction direction at node at Anode was A set was the set same the as same that as at that node at B node B but in the opposite direction. Substituting these data into Equation (3) yields PA at node A: but in the opposite direction. Substituting these data into Equation (3) yields PA at node A:

= − 2KavCC (15) P P=A PPB− (15) A B hh

vc C

B PB

u1 u2 v=0 Soil surface

A PA

-u1 -u2 vc C'

FigureFigure 2. 2. BoundaryBoundary conditions conditions of of wind wind velocity velocity and and pressure pressure fields. ﬁelds.

2.4. 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] ρ = 3 q b u* (16) g where b is the soil erodibility determined by the soil surface condition, g is gravitational acceleration −2 −1 (9.81 m s ), and u* is the friction velocity (m s ), which can be estimated using the wind velocity obtained by solving Equations (1)–(3) and the following equation:

d u u u = υ (17) * dz u where υ is the kinematic viscosity of air (m2 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).

Water 2019, 11, 98 5 of 11

2.4. 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]

ρ 3 q = b u∗ (16) g where b is the soil erodibility determined by the soil surface condition, g is gravitational acceleration −2 −1 (9.81 m s ), and u* is the friction velocity (m s ), which can be estimated using the wind velocity obtained by solving Equations (1)–(3) and the following equation: r d|u| u u∗ = υ (17) dz |u| where υ is the kinematic viscosity of air (m2 s−1). Figure3 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 horizontalWater 2019, 11 wind, x FOR velocity PEER REVIEW at the vicinity of the soil surface which is calculated from Equations (1)–(3).6 of 12

Wind

1 m q (g m-1 s-1)

Figure 3. Definition of wind erosion amount q in Equation (16). Figure 3. Definition of wind erosion amount q in Equation (16). 3. Wind Tunnel Experiment 3. Wind Tunnel Experiment To estimate the parameter b in Equation (16), we performed a wind tunnel experiment. A schematicTo estimate of the the wind parameter tunnel is b shown in Equation in Figure (16),4. Therewe perfor is a suctionmed a wind fan at tunnel the end experiment. of the wind A tunnel.schematic In theof the wind wind tunnel, tunnel we is show reproducedn in Figure a bare 4. There andosol is a fieldsuction (N fan 32◦ at14 the0, E end 130 of◦30 the0) aswind shown tunnel. in FigureIn the5 wind which tunnel, was located we reproduced in Kagoshima a bare Prefecture, andosol field southwest (N 32°14 of′, E Japan. 130°30 This′) as fieldshown was in locatedFigure 5 onwhich a windy was andlocated hillside in Kagoshima of a mountain Prefecture, and had southwest a great riskof Japan. of the This soil erosionfield was by located the wind. on a Potato windy wasand cultivated hillside of ina mountain this field fromand had February a great to risk May of andthe soil the erosion field surface by the was wind. bare Potato in the was other cultivated period. Averagein this field peak from wind February gust speed to May from and 2008 the to field 2017 whichsurface was was measured bare in the in other the nearest period. meteorological Average peak stationwind gust (N 31 speed◦160, Efrom 130 ◦2008180) wasto 2017 about which 20.1 mwas s− 1meas[34].ured The in wind the velocitynearest meteorological was relatively highstation from (N −1 December31°16′, E 130°18 to April′) was in this about area 20.1 except m s during [34]. The typhoons wind [velocity34]. The was peak relatively wind gust high speed from of December >13.9 m s− to1 −1 (HighApril windin this in area Beaufort except scale) during was typhoons recorded [3 in4]. 98 The days peak in 2017wind [ 34gust]. We speed sampled of >13.9 distributed m s (High surface wind soilin Beaufort in this field scale) and was performed recorded the in soil 98 particledays in analysis2017 [34]. (pipet We method)sampled anddistributed dry density surface measurement. soil in this Afield test and of the performed soil water the retention soil particle curve analysis (Figure (pip6) inet the method) drying and process dry density by suction measurement. plate method A test and of centrifugingthe soil water method retention was performedcurve (Figure using 6) thein undistributedthe drying process soil sample by suction of 100 plate cm3. method Distributed and 3 andcentrifuging undistributed method soil was samplings performed were using performed the undistributed at three kitty-cornered soil sample of points100 cm of. Distributed the field. The and ratesundistributed of clay, silt soil and samplings sand were were 23.7%, performed 3.5% andat thre 72.8%,e kitty-cornered respectively. points The dryof the density field. The of the rates soil of underclay, silt natural and sand conditions were 23.7%, was 0.993.5% g and cm −72.8%,3. The respectively. volumetric waterThe dry content density of of the the air-dried soil under soil natural was −3 3 −3 0.026conditions m3 m− was3. We 0.99 filled g cm rectangular. The volumetric tanks (0.15 water m × content0.14 m of× the0.09 air-dried m) with air-driedsoil was 0.026 andosol m samplem . We atfilled the dryrectangular density oftanks 0.99 (0.15 g cm m−3 ×and 0.14arranged m × 0.09 m) 99 tankswith air-dried with andosol andosol soil sample tightly at in the the dry wind density tunnel of −3 as0.99 shown g cm in and Figure arranged7. During 99 tanks the experiment, with andosol the soil wind tightl flowedy in the at constantwind tunnel velocities as shown of 2.0, in Figure 4.0, 6.0, 7. −1 8.0,During and 9.5the m experiment, s−1 at a height the ofwind 0.4 mflowed for 1 h,at respectively.constant velocities Soil erosion of 2.0, was 4.0, measured6.0, 8.0, and using 9.5 am particle s at a counterheight of (PS2, 0.4 Shineim for Technology1 h, respectively. Co., Ltd., Soil Kobe,erosion Hyogo, was measured Japan) and using custom-built a particle soil counter sampling (PS2, devices Shinei madeTechnology of 40-denier Co., Ltd., net andKobe, 60-mm-diameter, Hyogo, Japan) and 100-mm-long custom-built vinyl soil chloridesampling pipe. devices The made particle of 40-denier counter wasnet setand at 60-mm-diameter, a height of 0.1 m and100-mm-long the sampling vinyl devices chloride were pipe. placed The downstreamparticle counter at heights was set of at 0.10, a height 0.25, 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 m3 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 m3 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 m3 m−3, respectively. As shown in Figure 6, the volumetric water content of 0.250 m3 m−3 is approximately the same as the depletion of moisture content for optimum growth (pressure head of about 3 × 103 cm). The average amount of soil erosion was measured by weighing the soil captured in the three sampling nets after three repetitions of experiment.

Wind 3.0m 0.5m

2.5m 1.0m Soil

Fan

Figure 4. Schematic of the wind tunnel.

Water 2019, 11, x FOR PEER REVIEW 6 of 12

Wind

1 m q (g m-1 s-1)

Figure 3. Definition of wind erosion amount q in Equation (16).

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 cm3. 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 m3 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 WaterTechnology2019, 11, 98 Co., Ltd., Kobe, Hyogo, Japan) and custom-built soil sampling devices made of 40-denier6 of 11 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 and 0.40 m. The experiments were performed at four values of volumetric water content: 0.026, 0.100, experiments were performed at four values of volumetric water content: 0.026, 0.100, 0.170, and 0.250 0.170, and 0.250 m3 m−3 (2.6, 10.0, 17.0, and 25.0%). At ﬁrst, we performed the measurement at the m3 m−3 (2.6, 10.0, 17.0, and 25.0%). At first, we performed the measurement at the volumetric water 3 −3 volumetriccontent of water 0.026 contentm3 m−3 and of 0.026 we added m m theand water we and added mixed the the water water and to mixed soil sample the water evenly to soilto make sample 3 −3 evenlythe soil to water make thecondition soil water of 0.100, condition 0.170, ofand 0.100, 0.250 0.170, m3 m and−3, respectively. 0.250 m m As, respectively.shown in Figure As shown6, the in 3 −3 Figurevolumetric6, the volumetricwater content water of 0.250 content m3 of m 0.250−3 is approximately m m is approximately the same as the the depletion same as the of depletionmoisture of 3 moisturecontent contentfor optimum for optimum growth (pressure growth (pressure head of about head of3 × about 103 cm). 3 × The10 averagecm). The amount average of amountsoil erosion of soil erosionwas measured was measured by weighing by weighing the soil the captured soil captured in the inthree the threesampling sampling nets after nets three after threerepetitions repetitions of ofexperiment. experiment.

Wind 3.0m 0.5m

2.5m 1.0m Soil

Fan Water 2019, 11, x FOR PEER REVIEW 7 of 12 Water 2019, 11, x FOR PEER REVIEW Figure 4. Schematic of the wind tunnel. 7 of 12 Figure 4. Schematic of the wind tunnel.

Figure 5. Condition of bare andosol field. FigureFigure 5. 5.Condition Condition of bare bare andosol andosol field. ﬁeld.

100000100000

1000010000

10001000

100100 Pressure head (cm) head Pressure Pressure head (cm) head Pressure

1010

11 0.00.20.40.60.00.20.40.6 3 -3 VolumetricVolumetric water content (m3 m-3))

FigureFigureFigure 6. Soil 6. 6. Soil waterSoil water water retention retention retention curve curvecurve of ofofandosol andosolandosol whic whichwhich was was used used in in thethe the windwind wind tunneltunnel tunnel experiment. experiment. experiment.

Water 2019, 11, 98 7 of 11 Water 2019, 11, x FOR PEER REVIEW 8 of 12 Water 2019, 11, x FOR PEER REVIEW 8 of 12

Figure 7. Installation condition of measurement devices and andosol sample in the wind tunnel Figure 7. Installation condition of measurement devices and andosol sample in the wind tunnel experiment.Figure 7. Installation condition of measurement devices and andosol sample in the wind experiment.tunnel experiment. 4. Results and Discussion 4.4. Results Results and and Discussion Discussion 4.1. Relationship between Soil Moisture Condition, wind Velocity, and Amount of Soil Erosion 4.1.4.1. Relationship Relationship between between Soil Soil Moisture Moisture Conditio Condition,n, wind wind Velocity, and Amount of Soil Erosion Figure 8 shows the relationships between volumetric water content, wind velocity, and the FigureFigure 88 shows shows the the relationships relationships between between volumetric volume watertric water content, content, wind velocity,wind velocity, and the and amount the amount of soil erosion measured by the sampling nets. The relationship between the wind velocity amountof soil erosion of soil measurederosion measured by the sampling by the sampling nets. The ne relationshipts. The relationship between between the wind the velocity wind velocity and the and the amount of soil erosion shows that there was no soil erosion when the wind velocity was 2.0−1 andamount the amount of soil erosion of soil erosion shows thatshows there that was there no was soil no erosion soil erosion when thewhen wind the velocity wind velocity was 2.0 was m s2.0 . m s−1. The amount of soil erosion increased gradually with the wind velocity, with a significant rate mThe s−1 amount. The amount of soil oferosion soil erosion increased increased gradually gradually with with the the wind wind velocity, velocity, with with a signiﬁcant a significant rate rate of of increase between 4.0 and 6.0 m− s1−1 for all soil moisture conditions. Wind velocity of 6.0 m s−11 at a ofincrease increase between between 4.0 4.0 and and 6.0 6.0 m m s s−1for for all all soil soil moisture moisture conditions. conditions. WindWind velocity velocity ofof 6.06.0 mm ss−1 atat a a height of 0.4 m corresponds to a velocity of 14 m s−−1 1at a height of 10 m. Soil erosion was significant heightheight of of 0.4 m corresponds to a velocity of 14 m ss−1 atat a a height height of of 10 10 m. m. Soil Soil erosion erosion was was significant signiﬁcant when the soil moisture content was 0.026 m3 m−3 3(air-dried sample). The amount of soil erosion when the soil moisture contentcontent waswas 0.0260.026 mm3 mm−3 (air-dried(air-dried sample). sample). The The amount amount of of soil soil erosion erosion decreased with the increase in the soil moisture content. Soil transfer by wind was inhibited when decreaseddecreased with thethe increaseincrease inin the the soil soil moisture moisture content. content. Soil Soil transfer transfer by by wind wind was was inhibited inhibited when when the the volumetric water content reached 0.1703 m3− m3 −3. thevolumetric volumetric water water content content reached reached 0.170 0.170 m m3 m. −3. 1.0 1.0 Volumetric water content (m3 m-3) 0.8 Volumetric water content (m3 m-3) 0.8 0.026 0.026 0.100 0.100 0.6 0.170 0.6 0.170 0.250 0.4 0.250 0.4

Amount of soil erosion of(g) Amount soil 0.2 Amount of soil erosion of(g) Amount soil 0.2

0.0 0.0 0246810 0246810 Wind velocity (m s-1) Wind velocity (m s-1)

FigureFigure 8. 8. RelationshipsRelationships between between volumetric volumetric water water content, content, wind wind velocity, velocity, and and amount amount of of soil soil erosion. erosion. Figure 8. Relationships between volumetric water content, wind velocity, and amount of soil erosion. 4.2. Parameter Estimation for Quantiﬁcation of Soil Erosion 4.2. Parameter Estimation for Quantification of Soil Erosion 4.2. ParameterThe accuracy Estimation of this for simulation Quantification model of Soil was Erosion veriﬁed the using the simulated and measured soil The accuracy of this simulation model was verified the using the simulated and measured soil moistureThe accuracy conditions of [this31]. simulati The frictionon model velocity was was verified estimated the using using the the simulated simulated and wind measured velocity soil in moisture conditions [31]. The friction velocity was estimated using the simulated wind velocity in the 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 horizontal direction from Equations (1)–(3) and used to quantified the soil erosion amount by

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Equationthe horizontal (16). The direction parameter from b Equations in Equation (1)–(3) (16), andsoil usederodibility, to quantiﬁed was estimated the soil inversely erosion amount using the by amountEquation of (16).soil erosion The parameter due to wib innd Equation shown in (16), Figure soil 8 erodibility,and the esti wasmated estimated amount inversely of soil erosion using theby Equationamount of(16). soil Table erosion 1 presents due to windthe re shownsults of inthe Figure inverse8 and estimation the estimated of b. Using amount the values of soil erosionin Table by 1, theEquation amount (16). of Tablesoil erosion1 presents was the estimated results of for the the inverse four estimationlevels of soil of moistureb. Using thecondition. values inFigure Table 19, comparesthe amount the ofamounts soil erosion of soil was erosion estimated estimated for theusing four b from levels Table of soil 1 and moisture the measured condition. amounts Figure for9 fourcompares wind velocities. the amounts Root of mean soil erosion squareestimated errors (RMSE) using determinedb from Table using1 and the the measured measured and amounts estimated for datafour windunder velocities. four wind Root velocities mean square shown errors in (RMSE)Figure determined9 were 0.0001, using 0.0007, the measured 0.0005, andand estimated 0.0007, respectively.data under four The wind results velocities show that shown the inestimated Figure9 were amounts 0.0001, of 0.0007,soil erosion 0.0005, at and the 0.0007,four levels respectively. of soil moistureThe results condition show that were the in estimated good agreement amounts with of soil th erosione measured at the amounts four levels for offour soil wind moisture velocities condition and thatwere parameter in good agreement b is effective with for the predicting measured the amounts amountfor of soil four erosion wind velocities due to wind. and that parameter b is effective for predicting the amount of soil erosion due to wind. Table 1. Inversely estimated parameter b. Table 1. Inversely estimated parameter b. Volumetric Water Content Volumetric Water Content Parameter b (m3 m−3) Parameter b (m3 m−3) 0.0260.026 0.03520.0352 0.1000.100 0.01400.0140 0.1700.170 0.00420.0042 0.2500.250 0.00300.0030

0.0020 (a) 4.0 m s -1 0.008 (b) 6.0 m s -1

0.0015 Measured 0.006 Measured

) Estimated ) Estimated -1 -1 s s

-1 0.0010 -1 0.004 (g m (g m (g 0.0005 0.002 Amount of soil ofAmount soil erosion ofAmount soil erosion 0.0000 0.000 0.026 0.100 0.170 0.250 0.026 0.100 0.170 0.250 Volumetric water content (m3 m-3) Volumetric water content (m3 m-3)

0.008 (c) 8.0 m s -1 0.008 (d) 9.5 m s -1

0.006 Measured 0.006 Measured

) Estimated ) Estimated -1 -1 s s

-1 0.004 -1 0.004 (g m (g m (g 0.002 0.002 Amount of soil ofAmount soil erosion ofAmount soil erosion 0.000 0.000 0.026 0.100 0.170 0.250 0.026 0.100 0.170 0.250 Volumetric water content (m3 m-3) Volumetric water content (m3 m-3)

Figure 9. Comparison of estimated and measured amounts of soil erosion. (a) 4.0 m s−1,(b) 6.0 m s−1, (c) 8.0 m s−1,(d) 9.5 m s−1

4.3. QuantificationFigure 9. Comparison of Timing of estimated and Amount and ofmeasur Irrigationed amounts Waterto of Prevent soil erosion. the Soil (a) Erosion4.0 m s−1, (b) 6.0 m s−1, (c) 8.0 m s−1, (d) 9.5 m s−1 As shown in Figure8, the soil erosion was significant when the wind velocity was over 6.0 m s −1 − 4.3.and Quantification the volumetric of Timing water contentand Amount was <0.170of Irrigation m3 m Water3. At to thePrevent Japanese the Soil meteorological Erosion 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 As shown in Figure 8, the soil erosion was significant when the wind velocity was over 6.0 m s−1 0.4 m corresponds to 14 m s−1 at 10 m using logarithmic law for wind velocity. The threshold of wind and the volumetric water content was <0.170 m3 m−3. At the Japanese meteorological observatory, the velocity that caused significant soil erosion was this value and it could be an indicator for initiating wind velocity is generally measured at an altitude of 10 m. Wind velocity of 6.0 m s−1 at a height of irrigation to prevent soil erosion. 0.4 m corresponds to 14 m s−1 at 10 m using logarithmic law for wind velocity. The threshold of wind Scenario analyses were performed to estimate the amount of irrigation water needed to increase velocity that caused significant soil erosion was this value and it could be an indicator for initiating the volumetric water content from 0.026 and 0.100 m3 m−3 to 0.170 m3 m−3 for the prevention of soil irrigation to prevent soil erosion.

Water 2019, 11, x FOR PEER REVIEW 10 of 12

Scenario analyses were performed to estimate the amount of irrigation water needed to increase the volumetric water content from 0.026 and 0.100 m3 m−3 to 0.170 m3 m−3 for the prevention of soil 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 m3 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 m3 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 m3 m−3. The difference between the amounts of soil erosion for 0.170 and 0.250 m3 m−3 is relatively small. These results indicate that the optimal volumetric water content to prevent soil erosion is 0.170 m3 m−3. 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 m3 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 Water 2019, 11, 98 9 of 11 =0.170 m3 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 erosionprevent and thethe inhibitivesoil erosion effect by the of irrigation wind. on soil erosion was evaluated as shown in Table2. Using parameterBergamettib shown inet Tableal. reported1, the soilthat erosionthe soil amountserosion by for the 1 wind hour was in the reduced study siteby a (Figurerain event5) was at a sand estimatedagricultural with the field wind in Niger velocity [36]. of 6.0,They 8.0 clarified and 9.5 that m s− the1, respectively, soil transport when was the reduced wind directionespecially was during perpendicularthe first 10–15 to the min long following side (100 the m)beginning of the study of the ﬁeld rain shownevent, and in Figure almost5 .no The significant volumetric sand water transport contentoccurred increased after from30 min. 0.026 They to also 0.100 showed m3 m− that3 and this the inhibition amount ofeffect soil lasted transferred no longer by thethan wind 12 h wasafter the reducedend almostof the rain by halfevent when (cumulative 3 mm of rainfall irrigation of 20 was mm). applied. Optimal With irrigation an additional amount 3 mm for prevention of irrigation, of the the volumetricsoil erosion water by the content wind could increased be estimated to 0.170 min 3ourm− study,3 and thehowever, amount optimal of soil ir transferredrigation duration by the also windshould was greatly be determined reduced comparedto enhance with the theirrigation amount effe whenct on the soil volumetric erosion prevention. water content Also was the 0.026irrigation andeffect 0.100 mon3 mthe− 3prevention. The difference of the between soil erosion the amountsby the wind of soil should erosion be clarified for 0.170 taking and 0.250 into maccount3 m−3 the is relativelytemporal small. changes These of soil results moisture indicate conditions that the after optimal irrigation. volumetric water content to prevent soil erosion is 0.170 m3 m−3. Table 2. Irrigation water amount for the prevention of soil erosion with respect to soil moisture and Tablewind 2. Irrigation conditions. water amount for the prevention of soil erosion with respect to soil moisture and wind conditions. Volumetric Irrigation Hourly Amount of Soil Erosion (kg h−1) −1 VolumetricWater Water ContentIrrigation Water Water Amount Hourly Amount of Soil Erosion (kg h ) 3 −3 Content (m (mm 3 m) −3) Amount (mm)(mm) u = 6.0u =(m 6.0 s −(m1) s−1) u =u 8.0 = 8.0 (m s(m−1 )s−1) u u= 9.5= 9.5 (m (m s− 1s)−1)

0.0260.026 0.5880.588 1.1931.193 1.9271.927 3.2 0.1003.2 0.234 0.474 0.765 0.100 0.234 0.474 0.765 0.1702.6 2.6 0.069 0.141 0.227 0.170 0.069 0.141 0.227 2.6 0.2502.6 0.051 0.103 0.167 0.250 0.051 0.103 0.167

5.Arimori Conclusions 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 m3 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 Figure9 and Table2, 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 m3 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.

5. 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. Water 2019, 11, 98 10 of 11

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 m3 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.

Author Contributions: The methodology for the experiments was a joint effort of K.Y. and M.A. K.Y. and M.A. were responsible for carrying out the experiments and analyzing the experiment data. K.Y. developed the numerical model. K.Y. wrote the first draft of the paper, and M.A. contributed to reviewing and editing the manuscript. Funding: This research received no external funding. Acknowledgments: We want to thank project staffs of Kyushu Regional Agricultural Administration Office of Ministry of Agriculture, Forestry and Fisheries of Japan for their technical support for this work. We also thank the editors and three anonymous reviewers for their constructive suggestions and comments for improvement of the paper. Conflicts of Interest: The authors declare no conflict of interest.

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