Figure 1 shows a time series of the instantaneous horizontal wind velocity u and blown-sand impact count n measured at the Hasaki Beach; the median sand grain size d₅₀ at the beach was 0.2 × 10⁻³ m [22,31]. n shows a positive relationship with u during periods without any rainfall, but decreases significantly after a rainfall event. The sensor cannot detect the impact of blown sand if wet sand adheres to its surface after a rainfall event; however, it can detect the impact if this sand is subsequently removed by heavy rainfall. The sensor does not detect the impact of raindrops.

Many studies have shown that the vertical wind velocity profile in a wind tunnel is logarithmic [34,35]. In previous studies, the threshold wind velocity u_t has been estimated from both a wind profile law and Bagnold's [1] equation. The logarithmic wind profile law is expressed as: (1) u = u ∗ κ ln ( z u / z 0 s )

Here, u∗ is the wind shear velocity, κ is the von Kármán constant (= 0.4), z_u is the height at which u is measured, and z_0s is the saltation roughness length. Saltation is the hopping motion of sand grains and the primary mode of aeolian sand transport in beach intertidal and supratidal zones. Aeolian sand transport leads to an increase in the aerodynamic roughness length. u_t is obtained by substituting u∗ = u∗_t in Equation (1). The threshold wind shear velocity u∗_t is estimated from Bagnold's [1] equation: (2) u ∗ t = a σ − ρ ρ g dwhere a is the numerical transport rate coefficient (= 0.1), ρ is the air density, σ is the sand density (= 2,650 kg m⁻³), g is the gravitational acceleration, and d is the sand grain size. z_0s is estimated from the relation proposed by Charnock [36] and Chamberlain [37]: (3) z 0 s = c 0 u ∗ 2 2 gwhere c₀ is a constant (= 0.16 for saltation on beaches [38]).

Kubota et al. [30] performed experiments in a 20-m-long wind tunnel using the experimental setup that was employed by Hotta et al. [39]; the sand used in the experiments had a d₅₀ value of 0.25 × 10⁻³ m. The authors showed that the impact counts approached a constant value asymptotically at frequencies greater than 8 kHz. They also compared the sand mass flux q_s measured in the wind tunnel using an 8-kHz sensor [30] with q measured using a vertical-distribution-type sand trap [39]. q_s at the measurement height z_s was estimated from n using the following equation [22]: (4) q s ( z s ) = 2 σ d 50 3 n 3 d s 2 t 0where t₀ is the sampling period of n (= 1 s) and d_s is the diameter of the sensor (= 0.012 m). The vertical-distribution-type sand trap was developed by Hotta and Horikawa [40], and it can be used to measure the flux at 37 different heights in the range 0–0.505 m. q was corrected for trap efficiency. The wind tunnel experiments performed by Kubota et al. [30] and Hotta et al. [39] showed that q_s(z_s) for d₅₀ = 0.25 × 10⁻³ m was related to q(z_s) measured using the vertical-distribution-type sand trap [22], which was closely approximated as: (5) q ( z s ) = 10.57 q s ( z s )

The relationship between the sand flux at z_s, q(z_s) [kg m⁻² s⁻¹], and the total sand flux Q [kg m⁻¹ s⁻¹] is shown in Figure 2. Hotta et al. [39] employed the same wind tunnel as that used by Kubota et al. [30], with 0.17 m s⁻¹ < u∗ < 1.77 m s⁻¹ and 0.14 × 10⁻³ m < d₅₀ < 0.68 × 10⁻³ m. Here, only the data for d₅₀ = 0.25 × 10⁻³ m are shown. Q was found to be approximately proportional to q(z_s), as expressed by: (6) Q = A q ( z s )where the regression coefficient R² of the approximation was 0.96, 0.99, 1.00, 1.00, 0.99, 0.98, 0.97, and 0.97 for z_s = 0.005, 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, and 0.14 m, respectively. As shown in Figure 3, the constant A shows a positive relationship with z_s, and it can be expressed as: (7) A = B exp ( C z s )

The relationships between z_s and R² and between z_s and A (shown in Figures 2 and 3, respectively) indicate that z_s should be set in the range 0.02–0.08.

The constants B and C show a positive relationship with d₅₀ (Figure 4): (8) B = 89.7 d 50 + 0.0317and: (9) C = − 1.21 × 10 4 d 50 + 20.4

Finally, the following equation is derived from Equations (4)–(9): (10) Q = 7.05 σ d 50 3 n d s 2 t 0 ( 89.7 d 50 + 0.0317 ) exp [ ( − 1.21 × 10 4 d 50 + 20.4 ) z s ]

This equation suggests that Q can be estimated only if n, d₅₀, and z_s are measured by performing field experiments, although the equation was derived from observations made during 20-m-long wind tunnel experiments performed by Hotta et al. [39] and Kubota et al. [30] on a flat ground surface under steady wind conditions with u∗ < 1.8 m s⁻¹ and at a sensor height of 0.005 < z_s < 0.14.

Field measurements were performed at the Hasaki Beach using UD-101. The beach faces the Pacific Ocean and is located in Ibaraki Prefecture [35°50′25″N, 140°45′42″E; Figure 5(a)] [22,31]. The beach is of the dissipative type and has a foreshore slope ranging from 0.02 to 0.05 and a width of 100 m [Figure 5(b)]. d₅₀ is approximately 0.2 × 10⁻³ m along the backshore. Beach grasses grow around a small embryo dune at y = 50 m and around a longshore dune at y = 70 to 90 m just in front of the coastal forest area, where y is the onshore distance from the average shoreline position in 2004. The measurement point was located in a flat area between the embryo dune and backshore dune.

The annual wind direction is predominantly in the north-northeast direction [Figure 5(a)]. Winds are relatively weak in summer, except during typhoons, but strong in winter due to the presence of low-pressure systems. u, the wind direction θ, and n [the same data obtained by Udo [31], Figure 5(c)] were measured from 21 September to 3 December 2005. u and θ were measured at a height of 0.9 m above the measurement point (z = 0.9 m) using a three-axis ultrasonic anemometer (Delta Ohm; model: HD2003), while n was measured at z = 0.04 m using UD-101. Four UD-101 sensors were deployed, and they were directed toward the north, east, south, and west. The wind direction in the horizontal plane is expressed clockwise from north, from 0° to 360°. The data of u, θ, and n were recorded on a data logger system (FieldPoint cFP-2000, National Instruments) at a frequency of 1 Hz and were automatically downloaded on a weekly basis from the logger. The precipitation Pr was measured at 10-min intervals at the Choshi Meteorological Observatory (35°44′18″N, 140°51′24″E) by the Japan Meteorological Agency.

In addition, in this study, z_s was measured manually almost every day in order to calculate Q using Equation (10). The instantaneous z_s was calculated by linear interpolation. The z_s value of the sensor oriented toward the wind direction tended to be large and that of the sensor directed in the opposite direction tended to be small; for example, for north winds, the z_s value of the sensor directed northward tended to be large and that of the sensor directed southward tended to be small.

The measurement results are shown in Figure 6. Data could not be obtained from 28 October to 13 November 2005 because of network problems. Large amounts of sand were transported during the transport events on 24–26 September due to the impact of typhoon 0517, which resulted in a total precipitation of 39.5 mm; similar events involving the transport of a large amount of sand occurred on 11–12 October (period without rainfall); on 18–20 October (due to the impact of typhoon 0520), when the total precipitation was 6 mm; and on 14–15 November (period without rainfall) [31].

The Q value estimated from n was compared with that obtained using the conventional equations for a constant wind velocity in order to examine the accuracy of Q estimated from the UD-101 data. Here, the commonly employed equations of Bagnold [1], Kawamura [3], Owen [5], and Lettau and Lettau [6] (for Q_B, Q_K, Q_O, and Q_L, respectively) were used [13,16,41–43]: (11) Q B = c B d D ρ g u ∗ 3 (12) Q K = c K ρ g ( u ∗ − u ∗ t ) ( u ∗ + u ∗ t ) 2 (13) Q O = c O ρ g u ∗ ( u ∗ − u ∗ t ) ( u ∗ + u ∗ t ) (14) Q L = c L d D ρ g u ∗ 2 ( u ∗ − u ∗ t )

Here, D is the reference sand grain diameter (= 0.25 × 10⁻³ m) and c_B, c_K, c_O, and c_L are constants with values of 1.8, 2.78, 0.25 + w₀/3u∗ (where w₀ is the fall velocity), and 4.2, respectively. The sand transport rate was estimated to be zero when u∗ < u∗_t. u∗ was estimated from Equation (1) using the measured value of u; u∗_t was obtained using Equation (2) and w₀ was determined from Rubey's [44] equation: (15) w 0 = ( s − 1 ) g d ( 2 3 + 36 ν 2 ( s − 1 ) g d 3 − 36 ν 2 ( s − 1 ) g d 3 )where s is the relative density of the sand (= σ/ρ) and ν is the kinematic viscosity of air. These equations were derived for a constant wind velocity, and hence, Q estimated using the UD-101 data was averaged over 10 min. The 10-min mean sand flux Q_mean during periods without rainfall was compared to Q_B, Q_K, Q_O, and Q_L.

Figure 7 shows a comparison of Q_mean values obtained from n with Q_B, Q_K, Q_O, and Q_L values derived from the equations given above, for periods without rainfall. Data for n = 0 and u∗ < u∗_t (i.e., u < 4.05 m s⁻¹) were excluded. Q_mean showed a clear positive relationship with Q_B, Q_K, Q_O, and Q_L, and the estimated values followed the order Q_O < Q_B < Q_L < Q_K. The best agreement was observed between Q_mean and Q_O when 0.02 < Q_mean < 0.10 and between Q_mean and Q_B when Q_mean > 0.10.

Figure 8 shows double logarithmic plots of Q_mean versus Q_B, Q_K, Q_O, and Q_L for east-northeast (15° < θ_mean < 105°), south-southeast (105° < θ_mean < 195°), west-southwest (195° < θ_mean < 285°), and north-northwest (285° < θ_mean < 375°) winds. For small Q_mean values, i.e., less than 0.01 kg m⁻¹ s⁻¹, the Q_mean value was overestimated by Q_B, Q_K, Q_O, and Q_L. The probable causes for the overestimation are the low measurement accuracy of n for small Q_mean, the low estimation accuracy of z_0s for small u∗, variations in the wind velocity, and the high moisture content at the beach surface. Raupach [38] showed that c₀ in Equation (3) depended on u∗, especially for small u∗. A decrease in the instantaneous wind velocity below the threshold velocity, even when the mean wind velocity is greater than the threshold velocity, can lead to an overestimation. The moisture content of the backshore is nonzero even during periods without rainfall because of the proximity of the backshore to the sea. Udo et al. [22] demonstrated that the sand transport flux at a height, q_mean, decreased by more than one order of magnitude when the moisture content increased during rainfall periods.

Table 1 lists the linear regression relationships between Q_mean estimated from n and Q_B, Q_K, Q_O, and Q_L for the east-northeast, south-southeast, west-southwest, and north-northwest winds (see Figure 8). While a strong correlation was observed for the north-northwest wind (in the longshore direction), a clear correlation was not observed in the case of the other winds because only a small number of Q_mean values were greater than 0.01 kg m⁻¹ s⁻¹. Udo [31] showed the dependency of q_mean on θ_mean and that q_mean was high when θ_mean was in the longshore direction (especially in winter); however, q_mean was low when θ_mean was seaward (in late summer and winter) and was even lower when θ_mean was landward (in spring and autumn). The differences between Q_mean and Q_B, Q_K, Q_O, and Q_L were found to be independent of θ_mean.

Hotta and Horikawa [40] performed field experiments at beaches by using a trench-type trap and a vertical-distribution-type trap to estimate the aeolian sand transport rate and showed that the possible ranges of c_B and c_K are 0.5−2.0 and 1.0–3.0, respectively. This result suggests that the actual values of Q_B and Q_K are possibly one-third of those shown in Figures 7 and 8. All the field results showed that the sand transport rate estimated using the new method together with the UD-101 data was of the same order as that estimated using the conventional equations, although several differences were observed between the aeolian sand transport rate in the wind tunnel and that in field experiments [38,40,45,46]. The new method is useful for the direct estimation of the sand transport rate in a field analysis. Further analysis using the UD-101 data can provide additional insights into aeolian sand transport mechanisms in fields.