2.2. Data
The measurement levels, instruments, near-surface meteorological variables, turbulent fluxes, and surface radiation spectrum at the station are shown in
Table 1.
The observations of meteorological variables and turbulent fluxes used in this study covered the period from 5 January to 31 December 2010. The observations of wind speed and direction at 30-min intervals were acquired by a Metone 010C/020C sensor at a height of 10 m and using a CR1000 data logger. Observations of radiation at 30-min intervals were obtained used a CRN-1 mounted at a height of 1.5 m and with a CR1000 data logger. Observations of the air temperature at 30-min intervals were made using a Vaisala HMP45D sensor at heights of 0.5, 1, 2, 4, and 10 m, and with a CR1000 data logger. Observations of the soil temperature were acquired at 30-min intervals using Campbell 109L sensors at the surface soil (half of the sensor was above the surface) at heights of 10, 20, and 40 cm above the surface, and with a CR1000 data logger. Raw turbulent flux data were obtained using a Campbell CSAT3/Licor 7500 sensor at a height of 3.0 m and with a CR5000 data logger.
The raw turbulent data were processed to obtain 30-min interval turbulent flux averages using EddyPro (Eddy Covariance Processing Software) software (the parameters employed in EddyPro are shown in
Table 2). In addition, a series of quality control procedures were applied to the turbulent flux data, i.e., noise removal, coordinate rotation, stability testing, variance similarity analysis, and removal of out-of-correct-range data. The statistical analyses showed that the proportions of missing data and unqualified data (abnormally high or low data) were 8.2% and 28.5%, respectively. The unqualified data were excluded.
The Fourier transform infrared spectrometer (FTIR) was produced by Designs and Prototypes Company (USA). The instrument comprised of one Michelson interferometer, one detector, one black body, one electric current converter, one block reflector gold board, and one built-in individual computer. The computer program was used for sampling, processing, and the storage of samples on an individual computer. The FTIR had a fast recording speed, high signal-to-noise ratio, good sensitivity, and very little stray radiation, where the light flux = 0.016 cm
2 sr, spectral range = 2–16 µm, and spectral resolution = 2–24 cm
−1. The measurement results obtained had standard deviations less than 1% [
45].
The principle of FTIR involves converting the received infrared spectra
Ms(λ) into spectral power
Vs(λ) by using the internal photoelectric effect:
where
λ is the wavelength,
r(λ) is the linear response of the FTIR, and
M0(
λ,
Tinst) is radiation at the temperature of the FTIR. The FTIR was calibrated before measuring the radiation from the sample.
Ms(λ) is the sample radiation measured by the FTIR after calibration.
According to Kirchhoff’s law, for opaque objects such as surfaces, the sum of the absorptivity and reflectivity (Rs) is 1, and the absorptivity is equal to ε; thus,
The distance from the ground measurement sample to the sensor was less than 1 m, where the upward radiation could be treated as negligible at this distance and the atmospheric transmittance was considered to be 1. Thus, the radiation from the sample was expressed as:
where
is the radiation at temperature
Ts.
is the radiation that is reflected by environmental influences such as the atmosphere.
is the fallout radiation comprising downward radiation in the atmosphere reflected by the sample detected with the FTIR.
is black body radiation.
was obtained by transforming formula (3) [
45,
46], as follows,
In Equation (4), and were obtained by the FTIR. Thus, sample calibration was necessary before measuring and to ensure the accuracy of the measurements.
Therefore,
was converted into
:
where
and
are wavelength ranges with thermal infrared atmospheric window values of 8 and 14, respectively. In order to facilitate the computation, the integral equation was discretized as follows.
In fact, in order to improve the accuracy, the wavelength range interval of 8–14 µm was divided into 375 .
Land use is the same in all directions in TD (large scale), but the sand dunes are large and undulating near to the station. There is a flat and bare ancient riverbed SE (NW) of the station’s tower, which was consistent with the directions of 90% (70%) of the flux source area. The flux source area could be observed well in the windward direction (prevailing wind direction) [
47]. In this study, the bulk transfer coefficients (
Cd and
Ch) were calculated based only on data measured in the NNE–ESE wind directions (local dominant wind direction) (
Figure 1d–f). We then compared the results with those obtained in all wind directions.
The ground surface soil heat flux was calculated according to the soil temperature and moisture gradients [
48]. Due to errors in the land surface temperature during the sand dust season, the ground surface temperature was calculated using the observed ε and radiation values.
2.3. Theory and Methodology
According to many other observational studies [
49,
50], the energy balance closure is not achieved completely for different underlying types. The energy balance closure is usually formulated as:
, where
Rn is the net radiation flux,
G0 is the ground surface soil heat flux,
H is the sensible heat flux, and
LE is the latent heat flux. The ratio of the energy balance closure is usually formulated as:
. The energy balance is formulated relative to the residuals as:
.
H +
LE <
Rn −
G0 when
> 0, while
H +
LE >
Rn −
G0 when
< 0.
In the analysis,
was calculated from the observed surface solar radiation components [
51] using Equations (7) and (8):
where
is shortwave upward radiation,
is shortwave downward radiation,
is the mean of
(calculated using the weighted mean method), and the subscript
is the time index.
In this study, we focused on the measurements in sunny and dry weather. In order to calibrate the radiation, the FTIR had to be calibrated every 10–20 min to a black body. The temperature of the cold black body was 10 °C lower than the environmental temperature, whereas the temperature of the hot black body was 10 °C higher than the surface temperature. After setting the temperatures of the cold black body and the hot black body, radiation spectrum data were measured for the cold and hot black body and saved. The accuracy achieved for the black body emissivity was 0.994–0.998 ± 0.002 and the accuracy of the temperature was ±0.1 °C. Thus, the error caused by the black body was less than 0.004. The temperature fluctuations according to the interferometer remained within 0.1 °C and the calibration error for the black body was less than 0.002 [
46]. In order to reduce the interference in the instrument’s noise signal, we set the spectrum stacking number at 10 times and the average values were obtained.
In this study, we performed three steps to minimize the error during operation in order to obtain the surface emissivity spectrum with high accuracy: (1) we measured the cold black body, hot black body, and diffuse reflection radiation from a gold plate; (2) we measured the surface radiation; and (3) we repeated step (1). These three steps were performed as quickly as possible, where we limited the time to 10 min for each group of measurements. Radiation correction was performed in steps (1) and (3) to evaluate the influence of the environment over time on the surface spectral radiation, thereby reducing the error. The surface temperature of the diffuse gold plate was measured using a thermoelectric coupling thermometer. In general, the average value was taken based on five measurements.
For the desert surface, Korb et al. [
45] suggested that the maximum emission rate for the band fitted (black body radiation spectrum fitted to the surface radiation spectrum) at 7.45–7.65 µm is 0.95. By using this method to obtain the surface radiation temperature, the surface emission spectra were acquired for a thermal infrared window at wavelengths of 8–14 µm in the TD with high efficiency and accuracy.
We used the physically-based and semi-empirical methods of Yang et al. [
11] to calculate
. The computed surface sensible heat (
Hsfc) was compared with the observed surface sensible heat (
Hobs) to fit the
values.
Hsfc can be obtained from:
, where
Cp [=1004 J kg
−1 K
−1] is the heat capacity of air at constant pressure,
is the air density (kg m
−3),
T0 is the aerodynamic surface temperature (K),
Ta is the air temperature (K), and
rh is the aerodynamic resistance for heat (s m
−1) (
).
, where Pr is the Prandtl number (=1 if
z/
L ≥ 0 and 0.95 if
z/
L < 0),
is the Obukhov length,
u* is the frictional velocity (m s
−1);
is the frictional temperature;
and
are the integrated stability correction function for momentum transfer and temperature profiles, respectively;
k (=0.4) is the von Kármán constant,
and
are the upward longwave radiation and downward longwave radiation, respectively.
σ (5.677 × 10
−8 W m
−2 K
−4) is the Stefan–Boltzmann constant near neutral (i.e.,
T0 =
Ta). The difference between
Hsfc and
Hobs is sensitive to the value of
. Using an iterative algorithm (
values from 0.8 to 1.0 with a step width of 0.001), the
value was derived by minimizing the root mean square (RMS) between the calculated
Hsfc and observed
Hobs.
In the analysis,
z0m was estimated using Equations (9) to (11):
where
z is the observed height (m) and
d is the displacement height (m), which was negligible in our study with no vegetation coverage.
According to Dyer ([
52], parameters 16 and 5 in Equations (10) and (11) are consistent with
k = 0.40, while
u is the average wind velocity (m s
−1). Under unstable conditions [
12,
53], the following equation can be used:
where,
.
Under stable conditions [
54,
55], the equation is as follows.
The value of
z0h is difficult to determine because it cannot be measured directly, but it is possible to derive
z0h from the equations for
Hobs [
23], where it can be obtained from the flux-gradient relationships in a surface layer based on Monin–Obukhov (M–O) similarity theory [
56]. The following equation can be used.
Under unstable conditions:
Under stable conditions:
where
and
.
In the analysis, we employed the same procedure used by Yang et al. [
11] for data quality control, as follows: (1) excluding periods when the absolute value of
W m
−2, which corresponds to the time with a low solar elevation angle when the observation error was large; (2) excluding periods when
, which is physically unrealistic; and (3) excluding data from sandy, rainy, and snowy periods for
Cd and
Ch.
In our analysis,
Cd and
Ch were calculated using two methods. First, we followed the Eddy correlation method using Equation (15):
where
τ is the surface stress (kg m
−1 s
−2).
The other method for calculating
Cd and
Ch is based on M–O similarity theory where
Cd and
Ch are expressed as [
57,
58]:
where
Ψm(
z/
L) and
Ψh(
z/
L) are the integration forms of the M–O similarity functions
φm and
φh at the station, respectively, and the equation is:
where Δ is the difference symbol,
z1 and
z2 are the height above ground (in this analysis,
z1 = 2 m,
z2 = 4 m),
θ∗ is the turbulent temperature scale, and
θ is the potential temperature.
The lack of observations across the whole TD prevented us from capturing the spatial distributions of these surface parameters based on in situ observations alone, so we also compared our site observations with the values of
and
from remote sensing products. This comparison allowed us to use in situ observations to calibrate the remote sensing products and to produce improved surface parameter estimates over a large spatial domain. In this analysis, Landsat 8 data from NASA were used to compare the observation data for
and
. The empirical method described by Qin et al. [
59] was used to calculate
and
from the Landsat data. We only used data from 19 August 2013 at 11:00 (Local time), which was a sunny day. The solar elevation angle at the station was 59.05° at 11:00 on 19 August 2013.