Comparison of Sensible Heat Fluxes Measured by a Large Aperture Scintillometer and Eddy Covariance System over a Heterogeneous Farmland in East China

Abstract

The sensible heat is an important component in surface energy partitioning over the land surface. This paper compared the sensible heat fluxes measured by a large aperture scintillometer system (LAS) and an eddy covariance system (EC) over a rice paddy with a patch of mulberry seedlings in the east China coastal region during the period from 13 September–11 October 2015. During the observation period, easterlies and northerlies prevailed, and 96% easterlies and northerlies had a speed of 0–6 m s⁻¹. The sensible heat fluxes measured by the two systems reflected that the value of H_LAS generally was inclined to be larger than H_EC with the average difference of 20.30 W m⁻², and the uncertainty for two instruments was less than 17 W m⁻². Analysis of the average footprint resulted that the mulberry seedling field always had a higher contribution to LAS than that to EC, which could be the reason that H_LAS was always larger than H_EC. During the days when the contributions of the mulberry seedling field to the two systems were close to each other, the sensible heat flux measurements of the two instruments were similar. The case analysis on typical sunny days showed that there would be larger sensible heat fluxes over the mulberry seedling field than in the rice paddy field especially under larger net radiation conditions.

1. Introduction

Farmland is a typical underlying surface and widely distributed around the world. In China, due to the family contract responsibility system, farmlands are divided into small pieces allocated to different families, and different crops may be planted within different farmland pieces upon the decision of the owners (e.g., Figure 1). Measurement of the sensible heat fluxes over these mixed-crop farmland fields can help to understand the energy distribution, which plays an important role in the local weather, water cycle and climate [1,2,3,4].

Traditionally, eddy covariance (EC), which is based on direct measurements of the product of vertical velocity fluctuations (w’) and scalar concentration fluctuations (c’), is considered as the standard method for sensible heat fluxes measurement [5,6,7,8,9]. However, recently, a new instrument, the large aperture scintillometer (LAS), was used in a number of field experiments and gradually widely used [10,11,12,13]. For LAS, sensible heat fluxes are derived from the line-integral of the structure parameter of the refraction index; the average of sensible heat fluxes is obtained over an area formed by the path length of the light beam of the scintillometer and a line in the upwind direction. In contrast to the EC system, the measurement range of LAS is extended to a few kilometers, which coincides with the common resolution of atmospheric numerical models and satellite remote sensing retrievals (i.e., several kilometers). The application of LAS over different surfaces has been evaluated in a number of experiments [11,14,15,16,17,18,19,20,21,22,23], and in some of the experiments, the LAS-derived sensible heat fluxes were compared with EC-derived sensible heat fluxes [14,15,16,20,24,25,26,27,28]. Over either a homogenous or a heterogeneous surface, these studies demonstrated that the fluxes measured by these two methods had a good consistency, and LAS was a reliable method for deriving the sensible heat fluxes over heterogeneous complex topography.

Field experiments were conducted over different farmlands, such as arid grassland [8] and rice paddy [6,29,30,31], with EC systems over the world. In this study, combined LAS and EC measurements were conducted over the selected heterogeneous farmland in Jiangsu province of China during the period from 13 September–11 October 2015. First, LAS sensible heat fluxes were compared with the EC system here to investigate their reliability and characteristics. Second, average footprints were calculated to analyze the statistical characteristic. Third and the last, the footprint model was used to assess LAS and EC measurements to understand the influence of the heterogeneity in typical sunny days. It is expected that the results found here will provide a reference for sensible heat fluxes’ analysis and/or LAS experiments over heterogeneous farmlands.

The study is organized as follows: Section 2 describes the observational site and micrometeorological measurement systems; Section 3 presents the data processing methods; Section 4 analyzes the results; and Section 5 summarizes and concludes the paper.

2. Observation Site and Micrometeorological Measurement Systems

2.1. Observation Site

The experimental site is at a farmland about 45 km from the east China coast (32.76° N, 120.47° E; 4 m above sea level). The site was generally flat, and around the site, there are some farmhouses (Figure 1). An LAS transmitter unit (marked A in Figure 1), a receiver unit (marked B in Figure 1), EC instruments (marked C in Figure 1) and an automatic meteorological station (AWS marked D in Figure 1) were installed at the site. At three meters east of the LAS optical path (the A-B line in Figure 1), there is a patch of mulberry seedlings with a north, west and east side length of 175 m, 175 m and 125 m, respectively. Additionally, there is a 70 m × 62 m poplar grove at the west of the LAS optical path (and at the north of the EC system). The rest of the areas are rice paddy fields. The experiment was carried out from 13 September–11 October 2015, and continuous sensible heat fluxes were derived by both the LAS and EC systems. During the observation period, the canopy height increased from 0.5 m–0.6 m for the rice paddy, from 0.15 m–0.4 m for the mulberry seedling field, and it remained about 12 m for the poplars in the grove, respectively.

2.2. Micrometeorological Measurement Systems

2.2.1. Large Aperture Scintillometer

The LAS instrument is manufactured by Rainroot Scientific Limited China (Beijing, China), and it has a similar observation principle to the LAS from Kipp&Zonen, but independently designed [32], and has an aperture diameter (D) of 0.15 m, operating at a near-infrared wavelength of 880 nm. The LAS receiver (marked B in Figure 1) and transmitter unit (marked A in Figure 1) were deployed at a height of 6 m on the tower over the paddy. The electromagnetic radiation was transmitted from north to south with an optical path of 470 m. Such a short path is caused by the limitation of the position of local villagers’ houses.

2.2.2. EC System

The EC instruments (marked C in Figure 1) were about 100 m to the west of the LAS optical path, including a H₂O analyzer (LI-7500, LI-COR Biotechnology, Lincoln, NE, USA) and a three-dimensional sonic anemometer (CSAT3, Campbell Scientific Inc., Edmonton, AB, Canada). The instruments were installed on a tower at the height of 10 m, and they measure three-dimensional wind speed components u, v, w, theta, the density of air, etc., at a sampling rate of 10 Hz.

2.2.3. Automatic Meteorological Station

The automatic meteorological station (AWS, marked D in Figure 1) was about 185 m to the east of the LAS optical path. The air temperature, humidity and wind speed sensors were placed at each height (3 m, 5 m, 8 m and 10 m) on the tower. A wind direction sensor was deployed at the height of 10 m. The radiometer, measuring upward and downward short and long wave radiations, was installed at a height of 3 m. Each of these sensors sampled at a rate of 1 Hz, and the measurements were averaged at 30-min intervals.

3. Data Processing Methods

3.1. Parameter Set

The aerodynamic roughness length (z₀) and the zero plane displacement height (d) were calculated through the gradient method with EC and AWS data. Based on the Monin–Obukhov (M–O) similarity hypothesis, the vertical wind profile is expressed as follows:

$$u=\frac{u_{*}}{\kappa }\ln \frac{z-d}{z_0}-{\mathsf{\Psi }}_m\left(\frac{z-d}{L}\right)+{\mathsf{\Psi }}_m\left(\frac{z_0}{L}\right)$$

(1)

where z is the height with respect to wind speed u, L is the Obukhov length derived by EC systems, $\kappa (=0.4)$ is the von Karman constant and $u_{*}$ is the friction velocity. The integrated stability correction function ${\mathsf{\Psi }}_m$ was given by Dyer [33]:

$${\mathsf{\Psi }}_m\left(\xi \right)=2\ln (\frac{1+x}{2})+\ln (\frac{1+x^2}{2})-2\arctan x+\frac{\mathsf{\pi }}{2}$$

(2)

$$x={(1-16\xi )}^{\frac{1}{4}}$$

(3)

$${\mathsf{\Psi }}_m(\xi )=-5\xi$$

(4)

where Equations (2) and (3) are valid under unstable conditions and Equation (4) is valid under stable conditions. Then, the fitting process was conducted on AWS-measured wind speed data, and the results showed that the mean of z₀ was 0.025 m; and d varied from 0.43 m on 13 September to 0.55 m on 11 October 2015. Besides, owing to the flat underlying surface, the LAS effective height (z_eff) was estimated to be its installation height of 6 m.

3.2. Data Process Scheme of EC

In this paper, we used EddyPro 5.2.1 (software developed by LI-COR Biotechnology) to process data measured by the EC system. The EddyPro software applied the following corrections: despiking algorithm [34], spectral corrections [35,36], compensation for density fluctuations [37], time lag compensation, double rotation for tilt correction, block averaging, statistical tests [34], etc. Then, the half-hour averages of heat fluxes were derived. As the sensible and latent heat fluxes were calculated, the Bowen ratio β could be derived as:

$$\mathsf{\beta }=\frac{H_{EC}}{L{E}_{EC}}$$

(5)

where H_EC is EC-derived sensible heat fluxes, and LE_EC is EC-derived latent heat fluxes. For the missing data or the results that β > 3 (unstable phase) during the observation period, the Bowen ratios were set up as the average β (=0.22). Then β can be used in the calculation of sensible heat fluxes from LAS.

3.3. Scintillometry Method

The intensity of fluctuations in the refractive index of air, which can be converted to the structure parameter of the refractive index ($C_n^2$) turbulence [38], could indicate the variation of atmosphere turbulence. LAS measures the intensity of optical fluctuations as the laser goes through a turbulent atmosphere. $C_n^2$ can be expressed as the function of the structure parameter of temperature ($C_T^2$) and humidity ($C_q^2$) [39]. Additionally, it is sensitive to the fluctuations of temperature more than humidity at a near-infrared wavelength [40]. Further, Odhiambo and Savage [41] verified that the sensible heat fluxes derived from the surface layer scintillometry (one kind of scintillometer that is similar to LAS in sensible heat fluxes’ measurements between 50 and 350 m) with the β-corrected $C_T^2$ has greater agreement with the EC-derived sensible heat fluxes than that without β correction. Following Odhiambo and Savage [41], $C_n^2$ is expressed as:

$$C_n^2=C_T^2{(\frac{-0.78\times {10}^{-6}P}{T^2})}^2{(1+\frac{0.03}{\mathsf{\beta }})}^2$$

(6)

where T is the air temperature (K), P is the atmospheric pressure (Pa) and β is the Bowen ratio derived from EC. Normally, the Bowen ratios were smaller than 1 (mean of 0.22 for this study) under rice paddy. The calculated $C_T^2$ could overestimate about 30% without the Bowen ratio correction. Therefore, this correction could not be neglect in this paper. The half-hourly average $C_n^2$ was calculated to match the averaging period of EC, and the noise was eliminated by using a criterion of $X(t)<\overline{X}-4\sigma$ or $X(t)>\overline{X}+4\sigma$, where $X(t)$ is the measurement, $\overline{X}$ is the mean over the interval and $\sigma$ is the standard deviation. Besides, the mathematical relationship of $C_n^2$ and the variance of the natural logarithm of light intensity was not established, and the measurement should be eliminated when the LAS signal is saturated (with higher turbulence intensity). Based on Ochs and Hill [42], the threshold value of $C_n^2$ for LAS signal saturation is set to $5.87\times {10}^{-12}{\mathrm{m}}^{-2/3}$ in our experiment.

Then, according to the M-O similarity hypothesis, the following equation can be derived:

$$\frac{C_T^2{(z_{eff}-d)}^{\frac{2}{3}}}{T_{*}^2}=f_T(\frac{z_{eff}-d}{L})$$

(7)

where $T_{*}$ is the surface layer temperature scale parameter, z_eff is the LAS effective height, d is the zero plane displacement, L is the Obukhov length and f_T is a universal dimensionless function of the temperature structure parameter. Several forms of f_T have been proposed from different experiments [43,44,45,46,47,48,49]. This paper adopts the function of Andreas (1988) [45]:

$$f_T(\frac{z_{eff}-d}{L})=4.9{(1-6.1\frac{z_{eff}-d}{L})}^{-\frac{2}{3}} \text{for the unstable condition},$$

(8)

$$f_T(\frac{z_{eff}-d}{L})=4.9(1+2.2{(\frac{z_{eff}-d}{L})}^{\frac{2}{3}}) \text{for the stable condition}.$$

(9)

The friction velocity $u_{*}$ and the Obukhov length $L$ were calculated as:

$$u_{*}=\frac{\kappa u}{\ln \frac{z_{eff}-d}{z_0}-{\mathsf{\Psi }}_m(\frac{z_{eff}-d}{L})+{\mathsf{\Psi }}_m(\frac{z_0}{L})}$$

(10)

$$L=\frac{u_{*}^{2}T}{gk{T}_{*}}$$

(11)

where $\kappa (=0.4)$ is the von Karman constant, and $g(=9.8{\mathrm{m}\mathrm{s}}^{-2})$ is the acceleration of gravity. u is the wind speed at the height of z_eff. Owing to the different heights of LAS and EC, u was obtained through neutral-condition log-law correction of the EC-measured wind speed.

The surface layer is considered as unstable when these following inequalities were satisfied:

$$\{\begin{array}{l}{H}_{EC}>0{\mathrm{W}\mathrm{m}}^{-2}\\ R_n>10{\mathrm{W}\mathrm{m}}^{-2}\end{array}$$

(12)

where R_n is net radiation. The surface layer parameters $T_{*}$, $u_{*}$ and L are solved using an iterative calculation of Equations (2)–(4) and (6)–(11), then area-averaged H_LAS can be calculated through the $T_{*}$ (based on $C_n^2$) and $u_{*}$ (sensitive to the local roughness):

$$H_{LAS}=-\rho C_P{u}_{*}{T}_{*}$$

(13)

where $\rho$ is the air density and $C_P$ is the specific heat capacity of air at constant pressure. Similar to Gruber and Fochesatto [50], the convergence of this iterative calculation was identified through the fixed-point method [50]. Combining Equations (2)–(4) and (6)–(11), the recursive function was:

$$\frac{z_{eff}-d}{L}=M\frac{{\left(\ln \frac{z_{eff}-d}{z_0}-{\mathsf{\Psi }}_m(\frac{z_{eff}-d}{L})+{\mathsf{\Psi }}_m(\frac{z_0}{L})\right)}^2}{f_T{\left(\frac{z_{eff}-d}{L}\right)}^{1/2}}$$

(14)

where under unstable conditions:

$$M=-\frac{\mathrm{g}\left(z_{eff}-d\right)\sqrt{C_T^2{\left(z_{eff}-d\right)}^{2/3}}}{T\kappa u^2}$$

(15)

Equation (14) using fixed-point recursion under unstable conditions is seen in Figure 2. As the relationship of M and $\left(z_{eff}-d\right)/L$ is monotonic, the iterative calculation was applicable to derive sensible heat fluxes from LAS measurement under unstable conditions.

3.4. Calculation Uncertainty

The uncertainty of EC-derived sensible heat fluxes was also calculated through Finkelstein and Sims’ [51] method; the results under unstable conditions are shown in Figure 3a with the increase of H_EC; the uncertainty of H_EC could increase from almost zero to about 17 W m⁻²; and the mean uncertainty was 5.46 W m⁻².

Even if turbulence is being sampled above an extremely flat field, for LAS, the uncertainty in z will still be present. The uncertainty of LAS should be assessed before comparison. The sensitivity function for the sensible heat flux H_LAS under unstable conditions was given by Gruber et al. [52]:

$$S_{H,z}=\frac{\begin{array}{c}-z(u){(z(u)+6.1z{(u)}^2\stackrel{⌣}{\Lambda }{(6.1{\zeta }^2-\zeta )}^{1/4})}^{-5/3}\\ \cdot (1+12.2z(u)\stackrel{⌣}{\Lambda }{(6.1{\zeta }^2-\zeta )}^{1/4})G(u)\end{array}}{\begin{array}{c}\{\left[{\displaystyle \underset{0}{\overset{1}{\int }}{(z(u)+6.1z{(u)}^2\stackrel{⌣}{\Lambda }{(6.1{\zeta }^2-\zeta )}^{1/4})}^{-2/3}G(u)\mathrm{d}u}\right]\\ +6.1\stackrel{⌣}{\Lambda }{(6.1{\zeta }^2-\zeta )}^{1/4}\cdot \left[{\displaystyle \underset{0}{\overset{1}{\int }}{(z(u)+6.1z{(u)}^2\stackrel{⌣}{\Lambda }{(6.1{\zeta }^2-\zeta )}^{1/4})}^{-5/3}z(u)G(u)\mathrm{d}u}\right]\\ -\frac{4{(6.1{\zeta }^2-\zeta )}^{3/4}}{\stackrel{⌣}{\Lambda }}\cdot {\left[{\displaystyle \underset{0}{\overset{1}{\int }}{(z(u)+6.1z{(u)}^2\stackrel{⌣}{\Lambda }{(6.1{\zeta }^2-\zeta )}^{1/4})}^{-2/3}G(u)\mathrm{d}u}\right]}^{5/2}\}\end{array}}$$

(16)

$$\zeta =\frac{z-d}{L}$$

(17)

$$\stackrel{⌣}{\Lambda }={\left(\frac{\kappa g\sqrt{C_T^2}}{u_{*}^{2}T\sqrt{4.9}}\right)}^{3/4}$$

(18)

where $z(u)$ is the height of the beam along the relative path position u. The weight function from Hartogensis et al. [53] is as follow:

$$G(u)=16{\mathsf{\pi }}^2{K}^{2}L{\displaystyle \underset{0}{\overset{\infty }{\int }}k{\varphi }_n(k){\sin }^2\left[\frac{k^{2}Lu(1-u)}{2K}\right]\cdot {\left[\frac{2J_1(x_1)J_2(x_2)}{x_1{x}_2}\right]}^2\mathrm{d}k}$$

(19)

where L is the optical path length, $K=2\pi /\lambda$ is the optical wavenumber, k the turbulent spatial wavenumber, ${\varphi }_n(k)=0.033k^{11/3}$ the three-dimensional spectrum of the refractive index in the inertial range and $J_1(x_1)$ and $J_2(x_2)$ are Bessel functions of the first kind, first order with $x_1=kDu/2$ and $x_2=kD(1-u)/2$, where D is the aperture diameter. Combining Equations (16)–(19), the uncertainty of LAS-derived sensible heat fluxes could be calculated through:

$${\sigma }_H=H_{LAS}{\displaystyle \underset{0}{\overset{1}{\int }}\frac{{\sigma }_z(u)}{z(u)}}{S}_{H,z}\mathrm{d}u$$

(20)

where ${\sigma }_z(u)$ is the uncertainty of z through relative path position u. With the zero plane displacement height varied from 0.43–0.55 m, the difference of 0.12 m may indicate the uncertainty of z. The uncertainty of LAS-derived sensible heat fluxes is shown in Figure 3b with the mean of 0.74 W m⁻².

3.5. Footprint Analysis

The flux footprint provides a means of estimating both the source area and the relative contribution of each surface element to the measured fluxes. In this paper, the flux footprint model was calculated through [54]:

$$f_{LAS}={\displaystyle \underset{x_1}{\overset{x_2}{\int }}G(u)f}\left(x-x\prime ,y-y\prime ,z\right)\mathrm{d}x$$

(21)

where $G(u)$ is the weight function and $x_1$ and $x_2$ are the position of transmitter and receiver of LAS, respectively. ($y$) and $x\prime$($y\prime$) are the point in the optical path and in the up-wind areas, respectively. $f$ is the point-flux footprint model from Kormann and Meixner [55].

4. Results

4.1. Meteorological Conditions

Temporal variations of wind speed, air temperature, relative humidity, surface atmospheric pressure and precipitation from 12 September to 11 October 2015 was showed in Figure 4 and Figure 5. During the observation period, the wind speed (WS) showed obvious diurnal variation, and the maximum WS occurred at noon every day with a value varying from 1.95–10 m s⁻¹ on different days (Figure 4a). Between the height of 10 m and 3 m, the WS difference was always less than 1 m s⁻¹. The overall average WS was 2.43 m s⁻¹ at 10 m, 2.21 m s⁻¹ at 8 m, 1.94 m s⁻¹ at 5 m and 1.72 m s⁻¹ at 3 m, respectively. The highest value of WS was 10 m s⁻¹ at the height of 10 m at 10:30 on 29 September. Combined with Figure 5, it is easy to find that the prevailing winds were easterlies at the observation height of 10 m in this site. During the daytime, more than 62 percent of winds were easterlies (including southeasterlies and northeasterlies), and only 21 percent of winds were westerlies (including southwesterlies and northwesterlies). At night, about 51 percent of winds were from the east, and 26 percent were from the west. The air temperature (Figure 4b) also significantly varied with a diurnal cycle. Most of the values were between 283 K and 298 K, and the overall average air temperature was 291.62 K at 10 m, 291.75 K at 8 m, 291.95 K at 5 m and 292.03 K at 3 m, respectively. As the height increased, the air temperature slightly decreased, but the temperature difference between the highest and lowest levels was less than 0.5 K at daylight. Driven by the variation of the surface net radiation, the highest and lowest temperature often occurred at 14:00 and 2:00, respectively. The maximum and minimum temperatures were 298.17 K and 283.88 K (caused by a strong precipitation process) at 14:30 on 18 September and at 5:30 on 2 October, respectively. Relative humidity (RH) also varied largely between mostly 50% and 100% during a day. Generally, the maximum RH (Figure 4c) followed the minimum air temperature at about 2:00, while the minimum RH corresponded to the maximum air temperature at about 14:00. It is noteworthy that RH was also influenced by other factors such as precipitation, advective flow, transpiration and turbulent intensity. The variation of atmospheric pressure is presented in Figure 4d. During the observation period, the value of atmospheric pressure varied from 1020.92 hPa (at 9:30 on 13 September) to 1006.44 hPa (at 12:30 on 23 September) and then increased to 1019.86 hPa (at 10:30 a.m. on 29 September). Later, because the air mass transited from northwest, the pressure went sharply down to 1005.18 hPa (at 4:00 a.m. on 1 October) and finally picked up to 1025.19 hPa (at 9:30 a.m. on 4 October). Combined with the wind speed and wind direction from 29 September–1 October, it could be found that a low pressure moved from west to the east of the site. Meanwhile, the values of pressure varied significantly and had two maximums and minimums during the diurnal cycle. The first low value and high value were usually at about 3:00 a.m. and 10:00 a.m.; the second low value and high value were usually at about 14:00 and 20:00. The temporal variation of precipitation is shown in Figure 4e; there were four obvious precipitation processes: 22–23 September (32.9 mm), 29 September (24.3 mm), 30 September–1 October (34.3 mm) and 7–8 October (4.5 mm).

4.2. Turbulent Heat Fluxes

The variations of H_LAS, H_EC, LE_EC and net radiation (Rn) are shown in Figure 6. The maximum of Rn varied from 200 W m⁻² (on cloudy days) to near 700 W m⁻² (on sunny days). The maximum of Rn in this period was 682.3 W m⁻² at 11:30 on 16 September, and the average of the daily maximum of Rn was 489.3 W m⁻². Because of the occurrence of the clouds, there were always some fluctuations near the peak of Rn. The H_LAS and H_EC varied significantly from very low values to about 130 W m⁻² and about 90 W m⁻², respectively. The values of H_LAS were always larger than the corresponding H_EC, and the difference is mostly experienced in the central part of the day, while towards the beginning and end of the diurnal cycle, the fluxes converged. Considering the uncertainty of the two systems’ derived sensible heat fluxes shown in Figure 3, the uncertainty (<17 W m⁻² for EC) was always smaller than the difference between LAS and EC shown in Figure 6; this may indicate that the differences are not caused by the uncertainty of two instruments. The maximums of H_LAS and H_EC were 125.36 W m⁻² (at 10:30 on 6 October) and 93.36 W m⁻² (at 14:00 on 10 October), respectively; and the averages of the daily maximum of H_LAS and H_EC were 80.14 W m⁻² and 59.84 W m⁻², respectively. The same as other experiments [22,56], the sensible heat fluxes had a similar diurnal variation pattern with net radiation. The LE also showed an evident diurnal variation pattern with the average daily maximum of 383.71 W m⁻².

The relationship of H_LAS and H_EC is shown in Figure 7 with negative values omitted. The red points and the corresponding bars represent the median values binned at 5 W m⁻² of the H_EC interval and the interquartile ranges, respectively. The median of H_LAS was 13.09 W m⁻² greater than the median of H_EC on average when H_EC was at the range of 0–80 W m⁻². For the data where H_EC exceeded 80 W m⁻², the sample numbers were too small to exactly estimate the relationship between H_LAS and H_EC. Overall, H_EC shows that the sensible heat fluxes varied from 0 to about 80 W m⁻² on the rice paddy fields in eastern China during the maturity period of rice, and it is similar to the measurement during the rice growth period [31].

4.3. The Effects of Winds and Associated Footprint on H_LAS and H_EC

To clarify the reason that H_LAS tended to be larger than H_EC during the observation period, the effects of wind direction, speed and the associated footprint (the model of Kormann and Meixner [55]) are investigated in this subsection.

Figure 8a–d shows the observed H_LAS and H_EC under different wind directions, and Figure 8e–h presents the corresponding average footprint under each wind direction condition. Under easterlies, westerlies, southerlies and northerlies, the number of data points is 157, 30, 38 and 116, respectively; and the maximum H_LAS (H_EC) values are 125.36 (85.56), 95.38 (93.35), 69.51 (81.54) and 84.45 (77.72) W m⁻², respectively. The average H_LAS (H_EC) values are 55.09 (31.96), 50.83 (35.05), 39.59 (27.97) and 33.72 (25.66) W m⁻², respectively. The mulberry seedling field contributions to the footprint of H_LAS (H_EC) are 40.14% (26.66%), 0.07% (0%), 17.31% (0.14%) and 27.23% (1.57%), respectively; while the contributions from the grove field to the footprint of H_LAS and H_EC are always very small, with a maximum of 4.24% for H_LAS and 1.57% for H_EC when westerlies prevailed.

It should be noted that the H_LAS − H_EC regression slope (1.46) was specifically large when easterlies prevailed, while when winds were from other directions, the H_LAS − H_EC regression slopes were closer to one (1.17, 1.17 and 1.1 for westerlies, southerlies and northerlies, respectively). Therefore, the heterogeneity caused by the mulberry field, which was at the east side of the LAS and EC observation instruments, could play a significant role.

Since the easterlies and northerlies conditions dominated the observation period, the observed sensible heat fluxes and associated mulberry seedling field contributions under the two conditions are analyzed in detail here. First, it is found that when the wind direction switched from northerlies to easterlies, the average H_LAS increased from 33.72–55.09 W m⁻² associated with the average mulberry seedling field contribution from 27.23–40.14%. Second, the average H_EC increased from 25.66–31.96 W m⁻² associated with the average mulberry seedling field contribution from 1.57%–26.66%. Third, similar average mulberry seedling field contributions to LAS under northerlies (27.23%) and to EC under easterlies (26.66%) yielded similar average sensible heat flux observations (33.72 W m⁻² for LAS and 31.96 W m⁻² for EC). Based on this evidence, it can be concluded that, under the same meteorological condition and for the same area, the mulberry seedling field generally produces more sensible heat flux than the rice paddy; and the different mulberry seedling field contribution to LAS and EC is the substantial cause of the difference between the H_LAS and the H_EC.

To clarify the physical mechanism giving the origin to the difference of two instrument under unstable conditions, the factors derived from sensible heat fluxes (shown in Equation (13)) were compared here under north wind and east wind conditions. Under unstable conditions, the LAS-EC regression slope (k), determination coefficient (Rs), mean square error (RMSE) and mean air density ($\rho$), mean friction velocity ($u_{*}$), mean temperature scale parameter ($T_{*}$) were calculated (

Table 1. Comparison of the LAS and EC measured factors derived for sensible heat fluxes under unstable conditions. The LAS-EC regression slope (k), determination coefficient (Rs), mean square error (RMSE), mean air density ($\rho$), mean friction velocity ($u_{*}$), mean temperature scale parameter ($T_{*}$) are shown in this table.

Wind Direction	Factors	k	Rs	RMSE	LAS Mean	EC Mean
East	$\rho$ (kg m−3)	1.01	0.60	9.82 × 10−5	1.20	1.18
	$u_{*}$ (m s−1)	0.60	0.20	0.015	0.26	0.38
	$T_{*}$ (K)	1.97	0.11	0.025	−0.21	−0.079
North	$\rho$ (kg m−3)	1.02	0.66	9.13 × 10−5	1.20	1.17
	$u_{*}$ (m s−1)	0.51	0.41	0.0048	0.20	0.37
	$T_{*}$ (K)	1.6	0.25	0.013	−0.16	−0.067

RMSE: square error of factors’ regression; LAS: averaged measurement from LAS; EC: averaged measurement from EC;

). First, it is clear that the air density measured from two instruments has a small bias here both under east (1.20 kg m⁻³ for LAS and 1.18 kg m⁻³ for EC) and north wind conditions (1.20 kg m⁻³ for LAS and 1.17 kg m⁻³ for EC). Additionally, the differences were small such that they had a slight influence (less than 3%) on sensible heat fluxes. Second, it is found that when the wind direction switched from northerlies to easterlies, the average $u_{*LAS}$ ($u_{*EC}$) increased from 0.20 (0.37)–0.26 (0.38) m s⁻¹, and the average $T_{*LAS}$ ($T_{*EC}$) decreased from −0.16 (−0.067)–−0.21 (−0.079) K associated with the average mulberry seedling field contribution from 27.23% (1.57%)–40.14% (26.66%). Third, under the similar average mulberry seedling field contributions (27.23% for LAS under northerlies and 26.66% for EC under easterlies), the absolute value of average $T_{*LAS}$ was significantly larger than the absolute value of $T_{*EC}$ while $u_{*LAS}$ was smaller than $u_{*EC}$. This results in a similar value on the average sensible heat flux for two instruments. Therefore, it can be concluded that the mulberry seedling field had significant influence not only on $u_{*}$, but also on $T_{*}$. The difference of sensible heat fluxes derived from two instruments could be attributed to the different $u_{*}$ and $T_{*}$ from the two instruments.

Further, measurements under east and north wind conditions were selected to analyze the influence of wind speeds and the associated footprint. The wind speeds are categorized by 0–2, 2–4 and 4–6 m s⁻¹, while the condition is which wind speeds are larger than 6 m s⁻¹ is not considered here due to their infrequent occurrence. For different wind speed conditions under east (north) wind directions, Figure 9a,b shows the observed H_LAS and H_EC, and Figure 9c–h presents the corresponding averaged footprints. Under easterlies of 0–2, 2–4 and 4–6 m s⁻¹, the footprint extended more eastward when the wind speed increased, and the corresponding contributions of the mulberry seedling field were 53.51% (19.21%), 41.07% (28.25%) and 35.23% (26.71%) for LAS (EC), respectively. Generally, with the increase of the speed of easterlies, the mulberry seedling field contributed less for LAS, but more for EC. When the east winds were at speed of 0–2, 2–4 and 4–6 m s⁻¹; the average H_LAS (H_EC) were 33.87 (21.50), 47.76 (30.17) and 69.91 (37.69) W m⁻², respectively. Following the increasing of wind speed category, the contributions from the mulberry seedling field to LAS and EC became closer to each other, but the difference between the average H_LAS and H_EC became larger, which was probably caused by the larger sensible heat fluxes’ difference over the mulberry seedling field and rice paddies under higher wind speeds and larger average net radiation (the average net radiation was 320.05, 363.24 and 395.75 W m⁻² for 0–2, 2–4 and 4–6 m s⁻¹).

Under northerlies, the footprint extended northward with the wind speed increase. The contributions of the mulberry seedling field were 36.41% (1.03%), 27.66% (1.24%) and 22.09% (2.28%) for LAS (EC) with wind speed increasing from 0–2 to 4–6 m s⁻¹. When the north winds were at speeds of 0–2, 2–4 and 4–6 m s⁻¹, the average net radiation was 281.92, 291.74 and 362.09 W m⁻², respectively. Additionally, the average H_LAS (H_EC) were 32.39 (23.08), 27.78 (23.81) and 44.54 (30.91) W m⁻², respectively. The results show that the larger mean net radiation also corresponds to the higher wind speed.

4.4. Case Analysis

The sensible heat fluxes vary under different weather conditions (net radiation, wind, etc.) during the observation period (Figure 6). To investigate the mechanisms of the fact that H_LAS were inclined to be larger than H_EC, three typical sunny days (28 September, 2 and 5 October, marked as yellow in Figure 6) were selected to analyze the possible impact of the varied wind conditions (i.e., direction and speed) on the measured sensible heat fluxes. During the three days, the daily variation of net radiation was similar, so that the impact of net radiation on sensible heat fluxes could be omitted. Besides, LAS and EC measurements can have higher reliability when the values of sensible heat fluxes are relatively large under the free convective conditions. Therefore, only the data collected between 10:00 and 15:00 were used here, and the EC system measurements were very low depending on where it was placed compared to the core of the thermal motion during this time period. During 10:00 and 15:00 on the three days, Rn, H_LAS and H_EC were always larger than 400, 50 and 30 W m⁻², respectively. The 10:00–15:00 averages of net radiation (Rn_avg), latent heat fluxes (LE_avg), wind speed (WS_avg) and sensible heat fluxes (H_LASavg and H_ECavg) were calculated (

Table 2. Comparison of temporal mean (10:00–15:00) LAS-derived and EC-derived sensible heat fluxes with different weather and footprint conditions on some sunny days. The mean value of net radiation (Rn_avg), latent heat fluxes (LE_avg), wind speed (WS_avg), wind direction (WD), LAS- and EC-derived sensible heat fluxes (H_LASavg and H_ECavg) and the contribution of the mulberry seedling field for the LAS and EC systems (K_LASmavg and K_ECmavg) are shown in the table.

Date	Rnavg	LEavg	WSavg	WD	HLASavg	HECavg	KLASmavg	KECmavg
	(W m−2)	(W m−2)	(m s−1)	-	(W m−2)	(W m−2)	-	-
28 September	499.74	360.77	5.68	East	79.92	60.79	33.78%	36.05%
2 October	497.95	350.06	3.12	West	55.24	47.03	3.06%	0%
5 October	494.84	364.84	2.91	East	76.12	41.64	45.15%	21.92%

). Further, with the footprint model of Kormann and Meixner [55], the averages of the mulberry seedling field contributions for LAS (K_LASmavg) and EC (K_ECmavg) measurements during 10:00 and 15:00 were calculated based on their weighted area proportions of the calculated footprint source area.

4.4.1. Effects of Different Wind Directions

2 and 5 October were chosen to distinguish the effects of different wind directions on the sensible heat fluxes, because the values of Rn_avg, LE_avg and WS_avg on the two days were very similar to each other, but not the WD (Table 2). Table 2 shows that H_LASavg was larger than H_ECavg on 5 October, but close to H_ECavg on 2 October, and the LAS-measured sensible heat fluxes were larger on 5 October than on 2 October. Figure 10a,b further confirms that on 5 October, H_LAS was always larger than H_EC, while on 2 October, their variations were similar to each other. During the two days (2 and 5 October), the calculated footprint areas were at the west and east of the instruments, respectively (Figure 10c,d). Please be reminded that there was a mulberry seedling field at the east of the optical path (green trapezoid in Figure 10c,d) and a poplar grove at the west (blue rectangle in Figure 10c,d). The grove contributed little during the two days; footprint analysis shows that the contribution of the grove to H_LAS or H_EC was smaller than 1.5%. However, during 10:00–15:00 on 2 and 5 October, the mulberry seedling field contributed 3.06% and 45.15% to H_LAS, 0% and 21.92% to H_EC, respectively. In other words, on 2 October, H_LAS and H_EC were generally from the homogenous rice paddies; while on 5 October, the mulberry seedling field affected H_LAS and H_EC greatly, and the influence was different for the two instruments. Generally, under the same meteorological condition (i.e., wind, downward short and long wave radiation), the sensible heat fluxes were homogeneous over a uniform underlying surface such as a rice paddy field [18], which is supported by the observation on 2 October when the footprints of LAS and EC were both over the rice paddy field. However, when the footprints of LAS covered more the mulberry seedling field than that of EC on 5 October, H_LAS and H_EC diverged drastically. On 5 October, based on the fact that the mulberry seedling field accounted for more weight in footprints for LAS than that for EC, it can be concluded that the mulberry seedling field contributed more sensible heat fluxes to LAS than that to EC. On the other hand, on 5 October, the H_LAS was larger than H_EC, while it can be further deduced that the mulberry seedling field generated more sensible heat fluxes than that rice paddy field. Therefore, due to the influence of the mulberry seedling field at the east side of the instruments, the sensible heat fluxes obtained by LAS were generally larger on the days with easterlies than on the days with westerlies. Alfieri and Blanken [57] found that a single point measurement (EC systems) is not sufficient to accurately describe this sand-sagebrush environment where the components of the surface energy budget can differ substantially across short distances. Meanwhile, EC could not capture the large-scale motions, which were beyond its footprint [58]. The difference between LAS and EC might have been caused by the large-scale turbulence at the experimental site.

4.4.2. Effects of Different Wind Speed

28 September and 5 October were chosen to distinguish the effects of different wind speeds on the sensible heat fluxes, because the values of Rn_avg, LE_avg and WD in the two days were very similar to each other, but not WS_avg (Table 2). Table 2 shows that H_LASavg was larger than H_ECavg not only on 28 September but also on 5 October, and the sensible heat fluxes obtained by the two instruments were larger on 28 September than on 5 October. Figure 11a,b further confirms that H_LAS was always larger than H_EC on 28 September and 2 October, but their differences decreased with larger wind speeds. During the two days (28 September and 5 October), the calculated footprint areas are both at the east of the instruments (Figure 10d and Figure 11b). Still, there was the mulberry seedling field at the east of the optical path (green trapezoid in Figure 10d and Figure 11b). During 10:00–15:00 on 28 September and 5 October, the mulberry seedling field contributed 33.78% and 45.15% to H_LAS, 36.05% and 21.92% to H_EC, respectively. Generally, the sensible heat fluxes were homogeneous over the rice paddy field (discussed above). Meanwhile, for EC, the mulberry seedling field contributed more sensible heat fluxes on 28 September than on 5 October, and EC obtained larger values on 28 September. Therefore, it can be reconfirmed that the mulberry seedling field generates more sensible heat fluxes than that rice paddy field. Due to the influence of the mulberry seedling field at the east side of the instruments, the sensible heat fluxes obtained by EC were increased while LAS-derived sensible heat fluxes were almost invariable under greater wind speeds conditions when the weather was dominated by prevailing easterly wind. Due to the influence of the mulberry seedling field at the east side of the instruments, the sensible heat fluxes obtained by EC were increased while LAS-derived sensible heat fluxes were almost invariable under larger wind speeds conditions when the weather was dominated by prevailing easterly wind. The different phenomenon of LAS and EC might be caused by the difference of the measurement theory between two instruments. The LAS-derived sensible heat fluxes are based on M-O similarity equations; while EC measured turbulence directly and required a certain level of mechanical turbulence present in the flow. The error by using M-O similarity equations under a heterogeneous underlying surface may affect the accuracy of the LAS-derived sensible heat fluxes, and the EC measurement under low wind conditions may also be erroneous.

5. Conclusions

This study compared sensible heat fluxes measured by a large aperture scintillometer and an eddy covariance system over a rice paddy in the coastal region of east China during the period from 13 September–11 October 2015. Through the comparison of the two sets of data, it can be found that the majority of the values of H_LAS were larger than H_EC, and the daily maximum of H_LAS (H_EC) during the period was about 100 (80) W m⁻².

First, the daytime sensible heat fluxes and corresponding average footprints under different wind direction conditions were compared. During the observation period, east wind and north wind prevailed, and the footprint analysis showed that under larger contribution conditions of the mulberry seedling field, the average H_LAS was always larger than H_EC. The consistent measurements of sensible heat fluxes by the two instruments often correspond to the consistent contributions from the mulberry seedling field for the two instruments’ source areas. That is, the mulberry seedling field has significantly affected the sensible heat fluxes’ observation of the two systems, and the influence is not only on $u_{*}$, but also on $T_{*}$. The difference of the sensible heat fluxes derived from the two instruments could be attributed to the different $u_{*}$ and $T_{*}$ from the two instruments.

Under easterlies and northerlies, with increasing wind speed, which always corresponded to larger net radiation, the footprint extended more eastward and northward, respectively; and the mulberry seedling field’s contributions to the two instruments became more similar to each other; but the difference between H_LAS and H_EC became larger. It is also concluded that the difference of the sensible heat fluxes over the mulberry seedling field and over rice paddies increased with the average net radiation conditions.

Finally, the H_LAS was generally larger under easterlies than under westerlies conditions. Footprint analysis showed that, under easterlies, the source areas of instrument were rice paddies together with a mulberry seedling field. Additionally, under westerlies, the source areas were basically rice field. This confirmed that the sensible heat fluxes over the mulberry seedling field were larger than the value over the rice paddies field. For LAS, the contribution of the mulberry seedling field was larger, and that made the LAS-derived sensible heat fluxes larger than those that were EC derived on east wind conditions. Through the comparison of sensible heat fluxes measured by the two instruments under different east wind speed conditions, it is found that under east wind conditions, the enlargement of H_EC is consistent with the increasing contribution of the mulberry seedling field for EC. This confirms that there were larger sensible heat fluxes over the mulberry seedling field than over the rice paddy again.

This paper found that during the observation period, the sensible heat fluxes over the mulberry seedling field were larger than over the rice paddy field especially under larger net radiation conditions. Additionally, the heterogeneity caused by the different crops in nearby fields played an important role in the sensible heat fluxes’ observation by the LAS and EC systems. This paper shows an example of using the two observation systems (LAS and EC) to expose the effect of surface heterogeneity. More detailed analysis of the variation of sensible heat fluxes over each kind of crop in east China will be carried out with further observation experiments.