Open Access

Spatial variation of net radiation and its contribution to energy balance closures in grassland ecosystems

Ecological Processes20143:7

DOI: 10.1186/2192-1709-3-7

Received: 8 January 2014

Accepted: 20 February 2014

Published: 3 March 2014



Low energy balance closure (EBC) at a particular eddy-covariance flux site has increased the uncertainties of carbon, water, and energy measurements and has thus hampered the urgent research of scaling up and modeling analyses through site combinations in regional or global flux networks.


A series of manipulative experiments were conducted in this study to explore the role of net radiation (Rn) in the EBC in relation to spatial variability of vegetation characteristics, source area, and sensor type in three sites of the Inner Mongolian grassland of northern China.


At all three sites, the residual fluxes of EBC peaked consistently at 110 W m−2. The spatial variability in net radiation was 19 W m−2 (5% of Rn) during the day and 7 W m−2 (16%) at night, with an average of 13 W m−2 (11%) from eight plot measurements across the three sites. Large area measurements of Rn significantly increased by 9 W m−2 during the day and decreased by 4 W m−2 at night in the unclipped treatments. Net radiation decreased by 25 W m−2 (6% of Rn) at midday and 81 MJ m−2 (6%) during a growing season with heavier regular clipping than that in unclipped treatments. The Rn was lower by 11–21 W m−2 (~20–40% of Rn) measured by CNR1 than by Q7.1 at night, while there was only 6 W m−2 (~1–2% of Rn) difference during the daytime between these two types of commonly used net radiometers.


Overall, the inclusion of the uncertainty in available energy accounted for 65% of the ~110 W m−2 shortfalls in the lack of closure. Clearly, the unclosed energy balance at these three grassland sites remains significant, with unexplored mechanisms for future research.


Inner Mongolia Eddy-covariance Energy balance closure Net radiation Spatial variability Typical steppe


The energy balance of the terrestrial surface can be expressed by the first law of thermodynamics, which dictates conservation of energy as:
R n = H + LE + G + Q + ϵ

where Rn is the net radiation, H is the sensible heat flux, LE is the latent heat flux, G is the soil heat flux, Q is the sum of other heat fluxes on the surface (plants, water, etc.) with a small fraction converted to chemical energy through photosynthesis, and ϵ is any residual flux associated with errors. In grasslands, Q flux is relatively minor due to low and often neglected vegetation mass. If Q is small enough to ignore at a study site, the residual flux (ϵ = RnHLEG) should approximate to zero.

In-depth investigations on the energy balance and energy balance closure (EBC) of terrestrial ecosystems have been extensively revisited since the 2000s with rapid increases in the direct measurements of net exchanges of carbon and water using the eddy-covariance (EC) flux tower technology, in which the EBC plays a critical role in assessing the quality of flux measurements (Foken 2008; Oncley et al. 2007). Within the FLUXNET ( community, the EBC is considered a key indicator for evaluating the flux data quality of EC measurements (Baldocchi et al. 1996; Goulden et al. 1996; Mauder and Foken 2006; Wilson et al. 2002). The low EBC (i.e., higher portion of missing energy) triggers suspicions that trace gases are not being adequately measured. This would consequently hamper the use of flux data for model validations and/or up-scaling exercises (Turnipseed et al. 2002; Wilson et al. 2002). For example, Wilson et al. (2002) reported that the magnitudes of both CO2 uptake and respiration were underestimated when the energy imbalance was greater. Similarly, the amount of missing energy correlated negatively with the Bowen ratio (Chen et al. 2004), suggesting that the turbulent flux measurement had an error when the EBC was low.

The energy closure problem is frequently related to low turbulent energy and high available energy (H + LE < RnG), potentially due to underestimation of the turbulent energy and/or overestimation of the available energy. Foken (2008), in a review of the EBC problems, reported that the residuals of the EBC in daytime varied from 50–300 W m−2, suggesting that available energy could be 30% higher than turbulent energy (Wilson et al. 2002). In recent years, numerous efforts have been made to explain the specific reasons for the EBCs at diverse flux measurement sites (Oliphant et al. 2004; Sanchez et al. 2010). Yet, no universally valid theories for the underlying mechanisms have been accepted by the community. Herein, we describe the use of a net radiometer with sufficient replications and field installations among the many reasons for conducting this EBC study.

Inadequate spatial sampling of Rn, especially when patchy vegetation and complex terrains exist, has been examined as another possible reason for EBC issues (Malhi et al. 2004; Schmid 1997). An EC site is conventionally selected to meet the theoretical needs of a large, homogeneous, and flat landscape. While turbulent energy components (i.e., sensible and latent heat fluxes) have a footprint of an entire ecosystem (normally, 50–100 sensor heights in all directions) (Chen et al. 2004), net radiation and soil heat fluxes are sampled with a much smaller footprint, with about 100 m2 for Rn and 10−4 m2 for G. These mismatched measurement footprints would not be issues when the spatial variations of vegetation, soil, and topography are minimal (Schmid 1997); however, such ideal conditions rarely exist. To improve the EBC, one solution is to increase the sampling numbers of Rn and G (i.e., increasing the measurement footprint) within the larger footprint of the turbulent footprints (Schmid 1997; Shao et al. 2008).

This paper investigates how spatial variability in Rn affects EBCs through a detailed analysis of vegetation characteristics and source area effects. Measurements for this study were conducted at three experimental sites in Inner Mongolia along temperature and water gradients to produce more general results/conclusions. Three specific questions will be answered through inter-/intra-site comparisons and manipulative experiments: i) What is the magnitude of the spatial variability in Rn at the three EC measurement sites? ii) What are the potential causes of Rn variation within and between our sites? iii) What are the contributions of Rn to EBC at these sites due to its spatial variation caused by heterogeneous vegetation? To seek the answers, we designed three experiments in a typical grassland type of Inner Mongolia and applied a mobile energy flux measurement system, which consists of nine net radiometers and other meteorological sensors with three eddy flux towers to record spatially independent Rn and associated surface properties (e.g., vegetation and soil). We specifically hypothesize that the heterogeneity of vegetation structure plays an important role in the EBC due to its direct alterations of the outgoing (or reflectance) of short- and long-wave radiation that determine the magnitude of net radiation.


Site descriptions

Experiment 1 was designed to measure Rn at three EC measurement sites: Duolun (site I), Xilinhot (site II), and Dongwu (site III) of Inner Mongolia, northern China, during the growing season of 2006. Experiments 2 and 3 were conducted at site I during the growing season of 2007 in a manipulative plot that is approximately 1,000 m south of the EC tower (Table 1).
Table 1

Net radiometers and their deployments in the three experiments in this study


Period of measurement

Sensor used


1 Site I

Jul 9–29, 2006

Eight Q7.1 s; one CNR1

Q7.1 2 m; CNR1 4 m

  Site II

Jul 31–Aug 20, 2006

Eight Q7.1 s; one CNR1

Q7.1 2 m; CNR1 4 m

  Site III

Aug 21–Sept 15, 2006

Eight Q7.1 s; one CNR1

Q7.1 2 m; CNR1 3.5 m


Jun 3–30; July 26–Oct 31, 2007

Nine Q7.1 s

0.3–0.5 m above the canopy


Jul 13–21, 2007

Six Q7.1 s

Small 0.5 m; large 1.5 m

Site I (42° 02′ N, 116° 17′ E, 1,380 m asl) involved in Experiments 1 3 was located at the Shisanlitan Grassland Ecosystem Restoration Research Station in Duolun County, a semiarid agriculture-pasture transition area in southeastern Inner Mongolia. The site has a distinct continental climate with a mean annual relative humidity of 61% and a mean annual precipitation of 399 mm (375 mm in 2007), which falls primarily from May to October. The mean annual temperature is 3.3°C, with a mean monthly temperature ranging from −15.9°C in January to 19.9°C in July (1990–2004). Summers are relatively damp and warm while winters are rather cold, dry, and windy. The study site was flat with relatively homogenous vegetation within the landscape. The experimental manipulations were conducted in the Stipa krylovii grassland, which is the most dominant vegetation type in the region. The soils are chestnut soils and below 0.4 m, there is a mixture of sandy soil and gravel. The site has been fenced since 2001 to prevent large herbivores, such as cattle and sheep, from grazing on the grassland, as had previously occurred. The dominant species include Stipa krylovii, Artemisia frigida, and Potentilla acaulis.

Site II (43° 33′ N, 116° 40′ E, 1,120 m asl) is at the Inner Mongolian Grassland Ecosystem Research Station of the Chinese Ecosystem Research Network. The site is exposed to a temperate, semi-arid continental climate with a mean annual temperature of 2.6°C and mean monthly temperatures ranging from −18.8°C in January to 21.2°C in July over the past 30 years. The mean annual precipitation is 350 mm. The dominant wind direction is northwest with an average wind velocity of 3.4 m s−1 during the sampling period. Chestnut and dark chestnut soils are the zonal soil types (Chen et al. 2005). The dominant plant species are two perennial grass species, Leymus chinensis and Stipa grandis.

At site III (45° 33′ N, 116° 59′ E, 840 m asl), the mean annual precipitation is 259 mm and the mean annual temperature is 1.4°C, with mean monthly temperatures ranging from −20.8°C in January to 21.1°C in July over the past 30 years. The growing season usually begins in mid-May and ends in late September. The mean wind direction is southwesterly from June 1 to September 30, with an average wind velocity of 3.1 m s−1 during the sampling period. The experimental plot is very flat and homogenous with degraded typical grasslands. The dominant species are Salsola collina and Leymus chinensis. For further site information, see Shao et al. (2008).

Experiment 1: Spatial variability of Rnwithin the EC footprints

All of the EBC terms in Eq. (1) were directly measured at each of the EC towers (Zhang et al. 2007). Rn was measured by four-component net radiometers CNR1 (Kipp & Zonen, Delft, the Netherlands). The open path EC tower included a fast response three-dimensional ultrasonic anemometer (CSAT3, Campbell Scientific Inc. (CSI), Logan, UT, USA) installed 3 m above the ground and a LI7500 InfraRed Gas Analyzer (IRGA, LiCor Inc., Lincoln, NE, USA) to obtain the LE and H. We arbitrarily laid out a 50 × 50 m2 plot around the three EC towers to install the mobile energy balance (EB) system, which consists of eight stations in an orthogonal layout with 12.5 m intervals in the four cardinal directions. That is, two stations were installed at distances of 12.5 and 25 m from the center point in each direction. Each station was equipped with a Q7.1 net radiometer (Radiation Energy Balance System (REBS), Seattle, WA, USA) mounted 2.0 m above the ground, two heat flux transducers (HFT3.1, REBS) buried at 0.025 m depth to measure soil heat flux (G0), and one custom-made T-type copper-constantan thermocouple to measure soil temperature at 0.05 m depth (Ts). The mobile EB system also included four water content reflectometers (model CS616, CSI) in the four directions at a depth of 0.025 m (upper pole) to record soil volumetric water content (θ), and three E-type chromel-constantan thermocouples to measure soil surface temperature (T0). Soil bulk density (ρb), from surface to 0.05 m depth, was measured in four replicates in each direction at each site. Ts, T0, θ, and ρb were used to calculate the soil layer heat storage (S) above the two HFT3.1 s. The sum of G0 and S is soil heat flux (G). All the Q7.1 s were corrected by using the same wind speed derived from an anemometer (05103, CSI) that was mounted at 2 m above the ground at each site. Data was collected at 10 s intervals and compiled as 30 min averages with a CR10X datalogger (CSI). The prevailing wind directions were northwest for sites I and II, and southwest for site III, with average wind velocities of 3.5, 3.4, and 3.1 m s−1 from June 1 to September 30 for sites I, II, and III, respectively. A footprint analysis was performed using the method of Stannard (1997, Eqn. (18), P382), showing that, at all three tower sites, approximately 99% of measured scalar fluxes originated within 500 m of the tower and approximately 97% originated with 250 m.

Experiment 2: Vegetation influence

To assess the influence of vegetation on Rn, a precision manipulative experiment initiated in 2003 near site I but outside the EC tower footprint was used. The experiment was planned in a single-factor design with five clipping treatments and five replications on the grassland: remaining shoot height 0.02 (M2), 0.05 (M5), 0.10 (M10), 0.15 m (M15), and without clipping (M0, control). Three replicate microclimatic stations were installed in each of the M2, M10, and M0 treatments, for a total of nine stations. Continuous measurements of micrometeorological variables began on June 3 (DOY 154) throughout the growing season, 2007. After four years of continuous clipping, the dominant species changed from heterogeneous tall-stature bunchgrass Stipa krylovii grassland (treatment M0) to homogeneous short-stature semi-shrub Artemisia frigida grassland (treatment M2). The cover, biomass, and biomass-per-cluster in Stipa krylovii, leaf area index, green biomass, height, and litter weight in the communities of M2 plots were consistently less than those of M10 and M0 plots (Table 2).
Table 2

Vegetation characteristics at growing seasonal peak time for clipping treatments where Experiments 2 and 3 were conducted


Vegetation cover (%)

Leaf area index

Living biomass (g m−2)

Litter (g m−2)

Stand dead (g m−2)

Average height of vegetation (m)

Number of species


54 ± 2a

0.34 ± 0.02a

66 ± 8a

48 ± 8a

25 ± 4a

0.04 ± 0.01a

15 ± 1a


49 ± 2a

0.38 ± 0.02a

76 ± 10a

58 ± 17a

24 ± 1a

0.09 ± 0.01b

14 ± 2a


48 ± 5a

0.48 ± 0.02b

112 ± 7b

130 ± 14b

177 ± 19b

0.23 ± 0.02c

12 ± 1b

M2, M10, and M0 showed biomass removal by clipping shoots at heights of 0.02 m, 0.10 m, respectively, once a year in late August since 2003 and no clipping. Values (mean ±1 SE) designated by the same letter (a, b, or c) are not significantly different at P = 0.05 among treatments.

The 25 10 × 20 m2 plots were randomly assigned for treatment types and placed with 4 m gaps between the adjacent plots. A push mower (Yard-man 160CC, USA) was used to clip the vegetation in late-August once a year and plants were allowed to grow until the next clipping. The nine stations were distributed randomly avoiding the edge effects (Chen et al. 1992).

Experiment 3: Influence of the source area

The size of the source area under a radiometer can also be critical, since a large source area will often include more diverse land surfaces. Three paired Q7.1 net radiometers were randomly selected for July 12–20, 2007, with one Q7.1 raised to 1 m higher than the others during a four-day study period (Table 1).

The source area of a radiometer with a hemispherical windshield can be calculated as:
A = 1 R / h 2 + 1 1
where A is the relative contribution to the measured flux signal from a partial source area (centered below the net radiometer) of radius R for net radiometer height above the canopy of h (Stannard et al. 1994). When R/h = ∞, A = 1. In Experiment 2, as R/h > 10, ≈99% contributed from each of the measured clipping plots; while in Experiment 3, R/h = 3.3, therefore A = 92%. The plot area in our study was large enough for all three experiments. Experiment 1 was conducted in the summer of 2006 with the new eight factory calibrated Q7.1 s. These Q7.1 s were moved to the three sites (I, II, and III) in turn, and then an inter-comparison was conducted before Experiments 2 and 3. At this time, nine Q7.1 s were randomly divided into three groups and operated side by side. Descriptions of net radiometer deployments of Experiments 1 3 are listed in Table 1. In addition to the factory calibration of Q7.1 at the beginning of Experiment 1, a one week field inter-comparison (Halldin and Lindroth 1992) was also conducted during Experiment 2 (Table 3).
Table 3

One week inter-comparison between the Q7.1 net radiometers before Experiments 2 and 3 in 2007


OLS slope


r 2

1, 2




1, 3




2, 3




4, 5




4, 9




5, 9




6, 7




6, 8




7, 8




Mean (SE)

0.99 (0.00)

0.20 (0.34)

1.00 (0.00)

§In the first column, the first value is the independent variable and the second value is dependent variable when making the linear regression; r2 is the coefficient of determination.

Eddy-covariance data processing

The July to September raw 10 Hz time series data from the EC measurements were processed off-line using the EC_Processor software package ( (Noormets et al. 2007; 2010) for sites I, II, and III, respectively, which were corrected by the double rotation method. The turbulent fluxes were adjusted for fluctuations in air density using the Webb-Pearman-Leuning expression (Webb et al. 1980). A series of data quality controls were used in the EC_Processor; for example, data quality was judged by atmospheric stability. Obvious outliers were removed, such as anomalous or spurious data that were caused by sensor malfunction, sensor maintenance, rainfall events, IRGA calibration, power failure, etc. A friction velocity u* (Goulden et al. 1996) of <0.15 m s−1 was used in this study (Zhang et al. 2007). Following these quality tests, the remaining data were classified as ‘good data’ to be submitted for analysis. Consequently, 52%, 42%, and 40% of the July–September growing season H and LE data obtained from our EC systems of sites I, II, and III, respectively, were discarded in Experiment 1. We did not intend to gap-fill the data and only the ‘good data’ were used in this energy balance closure analysis.

Data analysis

We analyzed the energy balance residual and applied linear regression to explore the spatial variability in Rn contributing to EBC in Experiment 1. First, the data from 12, 16, and 17 days at sites I, II, and III, respectively, were compiled into 30 min averages to illustrate the residual fluxes of EBC (i.e., ϵ). Then, the data was examined using an ordinary least square (OLS) linear regression by relating dependent turbulence energy (H + LE) and independent available energy (RnG). The mean values of the 30 min Rn and G from eight replicated measurements were calculated at each site. The mean values of Rn were used to compare the closures resulting from Q7.1 with those from CNR1 at the EC towers. The maximum and minimum values were used to illustrate the spatial variability of Rn and its contribution to the EBC. The mean values of G from sixteen replications were used to calculate the EBC. Rainy days were deliberately avoided, because the turbulent flux instruments would not work well at those times. For Experiments 2 and 3, all the 30 min experimental periods data were also integrated and examined on a diurnal scale. The paired T- test (SPSS 13.0 software) was used to analyze Rn deployment by height to find its contribution to the EBC. Rn differences among treatments/plots were used to examine the influences of vegetation and source area.


Spatial variability of Rn

The ϵ averaged 19 W m−2 (i.e., 5% of Rn) during the day and 7 W m−2 (16%) at night across the three sites due to the spatial variability in Rn (Table 4 and Figure 1). The daytime ϵ were 48, 68, and 67 W m−2 due to the maximum Rn for sites I, II, and III, respectively, and 33, 48, and 47 W m−2 due to the minimum Rn (Table 4 and Figure 1). Altogether, the spatial variability in Rn contributing to the EBC was approximately 13 W m−2 or 11% of the daily mean Rn (Table 4). A 4% OLS slope difference (0.88 and 0.92) was found from the replicated Rn sampling (i.e., spatial variability). The OLS slopes for sites I, II, and III were 0.97, 0.93, and 0.86 for the minimum Rn, respectively, and 0.95, 0.89, and 0.81 for the maximum Rn. The wet site (i.e., site I) had the highest OLS slopes for both day and night.
Table 4

Energy balance closure residuals ( ϵ , W m −2 ) resulted from the spatial variability in R n at the three grassland sites (I, II, and III)






Day and night


38 to 54 (3)

−10 to −1 (20)

33 to 48 (3)

−7 to 2 (20)

13 to 25 (12)


65 to 87 (5)

1 to 7 (13)

48 to 68 (5)

1 to 7 (14)

25 to 38 (9)


57 to 80 (6)

−11 to −4 (16)

47 to 67 (6)

−6 to 1 (15)

20 to 34 (11)


20 (5)

7 (16)

19 (5)

7 (16)

13 (11)

Average row shows the mean ϵ spatial variability of the three sites. The number in brackets is the percentage of ϵ/Rn; §Day and night refer to 9:00–15:00 and 21:00–3:00 h, respectively. Data are derived from Experiment 1.
Figure 1

Uncertainties in energy balance closure residuals ( ϵ ) due to spatial variability in R n . The upper and lower bounds of the gray band derived from the maximum and minimum Rn of the eight treatments, respectively. Site I (a), II (b), and III (c). Data are derived from Experiment 1.

The daytime ϵ was higher than that at night, but the portion to Rn was greater at night in all three sites. The daytime ϵ was 33 to 68 W m−2 with the portion to Rn being 3% to 5%, while the nighttime ϵ was −7 to 7 W m−2 with the portion to Rn being 14% to 20% (Table 4).

Sensor influence

The Rn values from the Q7.1 and CNR1 net radiometers were different and varied by time. The residual fluxes of the EBC (i.e., ϵ) were similar between the two radiometers during the day but higher (less negative) from the Q7.1 at night in all three sites (Figure 2). In the daytime, especially from 9:00 to 15:00 h, only 6 W m−2 (~1% of Rn) difference among the three sites was found. However, larger differences appeared at night, reaching up to 21 W m−2 (~40% of Rn) at sites I and III, whereas at site II, the difference was 11 W m−2 (~20% of Rn).The OLS linear regression showed similar results, with 10% OLS slope difference for the Q7.1 measurements (0.91) and the CNR1 (0.81) across the three sites (Figure 3). The Q7.1 provided an OLS slope of 0.84 to 0.97, while the CNR1 had slopes of 0.73 to 0.88.
Figure 2

Energy balance closure residuals ( ϵ ) derived from Q7.1 and CNR1 measurements in R n . Site I (a), II (b), and III (c). Data are derived from Experiment 1; 30 min averages data from 12, 16, and 17 days at sites I, II, and III, respectively, were compiled into a one-day scale, the same as in Figure 1.
Figure 3

Comparisons of 30 min values of turbulent ( H+LE ) vs. available energy ( R n G ). Data derived from Q7.1 “(Left)” and CNR1 “(Right)” determined Rn with the ordinary least square (OLS) linear regression equation of (H + LE) = k (RnG) + i (k, slope, i intercept, coefficient of determination, r2 are also shown). The solid line shows OLS linear regression fit. Site I (a, d), II (b, e), and III (c, f). Data are derived from Experiment 1.

Vegetation influence

With an increase in clipping intensity, Rn decreased during most of the daytime throughout the growing season (Figure 4). At midday, the average Rn values were 413, 395, and 388 W m−2 for the M0, M10, and M2 treatments over the growing season, respectively. The Rn in M2 was nearly 6% lower than in M0 treatments both at midday and by daily total. Over the growing season, the total Rn were 1409, 1331, and 1328 MJ m−2 for M0, M10, and M2, respectively, i.e., in the heavily mowed treatment (M2) decreased by another 6% (or about 81 MJ m−2) as compared to the reference.
Figure 4

Half-hourly differences of R n between unclipped control and clipped treatments. (M0–M2) means shoots clipped at 0.02 m and (M0–M10) at 0.10 m. Each value is the average of growing season from 3 June to 31 October, 2007. Data are derived from Experiment 2.

Source area influence

The size of observed Rn source, changed by deploying Q7.1 at different heights, did not show a significant influence in M2 and M10, but did in M0 treatments (Figures 5 and 6). With M0 treatment, the Rn difference was 9 W m−2 during the day (9:00–15:00 h, P <0.0001) and 4 W m−2 at night (21:00–3:00 h) between the two heights. In M2 and M10 treatments, however, the Rn differences were generally <2 W m−2 throughout the day.
Figure 5

Net radiometer deployment heights vs. R n results (half-hourly data integrated into a diurnal scale). Diff height means Rn differences between the two Q7.1 s deployed above the canopy by 0.5 and 1.5 m, respectively. Same height means both of the two Q7.1 s deployed above the canopy by 0.5 m. M0, M10, and M2 refer to unclipped areas and areas with shoots clipped at 0.10 and 0.02 m at the end of each growing season, respectively. Data are derived from Experiment 3.
Figure 6

Net radiometer deployment heights vs. R n results with Figure 5 half-hourly data integrated into a diurnal scale.



The primary focus of this study was to seek potential sources of missing Rn energy within the EBC at multiple sites where vegetation structure had been manipulated. In the last 15 years, much has been done to increase the accuracy of the radiation measurements (Foken 2008; Kohsiek et al. 2007; Wilson et al. 2002). The regression slope of the comparisons remained constant over the sampling period for the three treatments, suggesting that the Q7.1 is a stable sensor (Table 3). Further evidence showing small differences (Figures 5 and 6) at the M2 among Q7.1 radiometers (0.5 W m−2 during 9:00–15:00 h and 1 W m−2 between 21:00–3:00 h) are likely due to the more homogeneous vegetation. Clearly, the error related with the different Q7.1 could be reduced with good maintenance. However, in the early evening, the Q7.1 can produce occasional spikes (Figures 5 and 6).

Spatial variability of Rnand the EBC

The spatial variability of the Rn measured from multiple Q7.1 sensors was 19 W m−2 (5% of Rn) during the day and 7 W m−2 (16%) at night, with a daily average of 13 W m−2 (11%) or a 4% OLS slope. This variability might be due to the differences in vegetation structure, soil characteristics, and microclimates among the eight plots at each site. However, the spatial variability in available energy is still smaller to account for the lack of closure. The turbulent flux is systematically lower by 110 W m−2 at peak time than the available energy (Figures 1 and 2). The uncertainty in Rn could contribute to a systematic error of about 20 W m−2 (21 ± 3 W m−2 at midday across the three sites), or 5% of Rn which is in consistent with the report by Twine et al. (2000) of 6% of midday and mid-season Rn at a grass site in Oklahoma. The uncertainty in soil heat flux could contribute another 50 W m−2 (53 ± 11 W m−2) of error to the available energy (Shao et al. 2008). Altogether, the inclusion of the uncertainty in available energy accounted for about 65% of the 110 W m−2 (111 ± 10 W m−2) shortfall in the lack of closure. Clearly, the unclosed energy balance at these three grassland sites remains real and there remain unexplored mechanisms. Yet, it is unlikely that improper measurement of Rn during the daytime is responsible for the energy imbalance because both CNR1 and Q7.1 were in relative accordance during the course of the study (see also Turnipseed et al. 2002).

We designed a large scale plot (50 × 50 m2) with 8 Q7.1 s and 16 soil heat flux plates to quantify the spatial variability in Rn and G approximately to match with the source area with H and LE. The mean Rn and G stood reasonably well for the large-scale realities. There still existed 47 ± 16, 50 ± 13, and 70 ± 15 W m−2 of the energy balance at midday that could not be explained at sites I, II, and III, respectively. Even with all of the spatial uncertainties included, an imbalance of ~20 W m−2 still existed, perhaps due to other instrumental, operational, and flow based errors (Finnigan 2008). Examples of these errors are H, LE, or both of the turbulent fluxes at either low- and/or high-frequency and mean vertical or horizontal advection of scalar quantities. Moore et al. (1986) and Massman (2000) reported that the low and/or high frequency spectral losses were another reason from turbulence measurements caused the imbalance of energy balances. In the literature, flux loss was typically 5% to 10% for sensible and latent heat fluxes (Moore 1986). In our three sites, the average midday H + LE was nearly 300 to 400 W m−2, so the spectral loss perhaps reached 15 to 40 W m−2, which is also important in EBC. Gash and Dolman (2003) and van der Molen et al. (2004) argued that turbulence energy from sonic anemometer (co)sine errors was a potential source, while Aubinet et al. (2000) and Foken et al. (2001) pointed out that the time lag among different energy flux measurements need to be considered. Twine et al. (2000) also calculated that the uncertainties from Rn and G could only account for half of their imbalance 130 W m−2 in grassland at midday.

Sensor differences

The domes on the Q7.1 sensor might have a low thermal transmissivity resulting in underestimated incident thermal sky radiation (Twine et al. 2000). Additionally, the CNR1 measured a wider spectrum of wavelengths than Q7.1, which could also introduce additional bias, particularly in the nighttime. There is no doubt that this discrepancy would lead to a large variation in ϵ at night. In this study, the Rn of the CNR1 were significantly lower (10 to 20 W m−2) at night than those of the Q7.1, with the OLS slope varying approximately 4% (Figure 2). Kohsiek et al. (2007) compared these two types of radiometer and found a similar difference at night (15 W m−2). In our study, the regression slope remained constant during the study period at all three sites (1.04 ± 0.02), using the value of Q7.1 as the independent variable. This suggests that the calibrations of the two instrument types remained constant (Turnipseed et al. 2002), with regression slopes of 1.00 ± 0.01 in the daytime (9:00–15:00 h) and 1.31 ± 0.07 at night (21:00–3:00 h). Nighttime measurements of Rn, however, showed substantial discrepancies between the two sensors – close to 1.25 reported by Turnipseed et al. (2002) in a forest where the authors suspected as an error in the ‘long-wavelength measurement of one or both radiometers’. Other authors (Halldin and Lindroth 1992; Hodges and Smith 1997; Oncley et al. 2007) also noticed the discrepancies between different instruments. The magnitudes of nocturnal turbulent heat fluxes are typically underestimated with the EC method, as turbulence is generally low. The underestimation (less negative) of nocturnal Rn value from Q7.1 would further increase EBC. Thus, this difference must be taken into account when comparing and calculating EBC among or within sites.

The different EBC could also occur at different time scales. On a half-hourly scale, for example at site I, it showed the same daytime EBC between CNR1 and Q7.1, while the ϵ value determined by the Q7.1 was closer to zero at night. Therefore, we conclude that Q7.1 measurements provided much ‘better closure’ (Figure 2a) because of the underestimation of the magnitude of Rn with the Q7.1 during night-time. However, on a daily scale, it seemed that CNR1 provided better measurements. On a typical day (July 11), the daily imbalance yielded 1.44 MJ m−2d−1 using Q7.1 but only 0.63 MJ m−2d−1 using CNR1.

Due to the difference between the Q7.1 and CNR1, a method in comparing the EBCs within and among sites at a specific period from 9:00 to 15:00 h during the daytime would be useful to provide definite results both in residual and OLS regression methods. This is because during this period, the sensors (net radiometer, sensible and latent heat measurements) usually worked in their best conditions (e.g., high friction velocity). Different kinds of gap-filling strategies (Falge et al. 2001) in H and LE usually impede further EBC analysis. Furthermore, in the early morning and evening when net radiation is changing most rapidly, the magnitude of storage heat in the soil, air, and biomass can approach that of Rn (Moore and Fisch 1986). In addition, toward midday, the storage heat is less important (McCaughey 1982). Using this method, the effect of differences between instruments would be partially avoided.

Potential causes of Rnmeasurements for non-closure

In addition to the spatial variability resulting from vegetation, radiometer type and source area could also be responsible for inaccurate Rn measurements. In the unclipped plot, Rn might be higher due to a lower albedo in comparison to the clipped one (Li et al. 2006). The Student’s t-test, with a 0.05 level of significance, was used in previous studies to examine the differences between samples from the different clipping treatments (Shao et al. 2012). The maximum contrast in vegetation was found between sample treatments M0 and M2 with the latter having less leaf area index and green biomass (Table 2). This explained the 6% difference in Rn that was recorded in Experiment 2 (Figure 4), and also the peak difference of ~10 to 20 W m−2 between M0 and M2 in Experiment 3 (Figure 6) in our grassland sites. Similarly, a higher Rn in grazed compared to ungrazed management in desert steppe was also observed (Shao et al. 2013). Further, the reduced Rn energy input from the atmosphere by clipping or grazing land-use types has important implications for global warming studies and ecosystem modeling.

The source area experiment indicated that Q7.1 deployment needs to be high enough to record reliable Rn, especially under heterogeneous surface. The typical deployment height of 1.5 to 2.0 m seemed to be inadequate to integrate across vegetation heterogeneity (Stannard et al. 1994). An error would appear with low installation height of radiometers because the sensor could not receive the representative long- and short-wave reflections from the surface. However, Lloyd et al. (1997) pointed out that as the height of the net radiometer increases, the measurement would be degraded by long-wave losses in the air layer between the surface and the measurement height.

From Figure 3, comparing sites II and III with I, when the LE was larger the energy closure was better. We speculate that the mismatch between the energy fluxes (Shao et al. 2008) and the underestimated LE (Dugas et al. 1991) at our arid sites may be responsible for this imbalance. Since sensible heat fluxes between both systems compared better than latent heat fluxes (Schlesinger et al. 1996), we agree with the view that the instrument could cause bigger error when LE was lower (Stannard et al. 1994); this point needs to be studied further. The closure issue becomes even more important upon consideration of the long-term water balance. Twine et al. (2000) summed over a period of 15 days from 4 EC systems and drew a conclusion that evapotranspiration would be significantly overestimated by calculating LE as the residual of the energy budget; this is also supported by others (Dugas et al. 1991; Kampf et al. 2005; Nie et al. 1992). Thus, in our study, it is a risk to use the EC residual method to estimate LE since there were more uncertainties from Rn, G, S, and other heat sinks, especially when LE is smaller or under a certain spatial scale. This coincided with previous studies (Twine et al. 2000; Wilson et al. 2002) indicating that each flux should be analyzed separately.


Net radiation contributions to the EBC were examined through three experiments in grassland where EC towers had been installed since 2005. A large scale plot (50 × 50 m2) with 8 Q7.1 s and 16 soil heat flux plates was firstly designed to quantify the spatial variability in Rn and G approximately to match with the source area with H and LE. The spatial variabilities of vegetation, source area, and sensor type in grassland played critical roles in the EBC of our study sites. Despite the fact that net radiation (estimated too high) and soil heat (estimated too low) could not be excluded, the spatial variability quantity in net radiation is less than that in soil heat flux, and the sum of these two energy fluxes (i.e., available energy) accounted for 65% of the missing energy. The other portion of missing energy remains at large, nearly 40 W m−2 at the daytime peak time. More effort under different conditions (e.g., winter, spring, and fall when different phenological vegetation exist, different weather conditions, and long temporal scales) must be made in a similar way to reach a comprehensive understanding of EBC. For example, from this study, we noticed also that the EBC was better under conditions of higher soil moisture, higher LE, higher vegetation cover, lower H, and lower latitude. However, further work needs to be performed to systematically explore the mechanisms or empirical relationships.



Energy balance


Energy balance closure




Soil heat flux


Sensible heat flux


Ordinary least square


Sum of other heat fluxes on the surface

R n

Net radiation


Soil layer heat storage


Soil surface temperature


Residual flux associated with errors


Volumetric water content

ρ b

Soil bulk density.



This study was supported by the Natural Science Foundation of China (31170454, 31229001, 31130202), the State Key Basic Research Development Program of China (2013CB956600), the NASA-NEWS Program (NN-H-04-Z-YS-005-N), and the USCCC. We would like to thank Asko Noormets for “EC processor” software, and Xin Li and Zhichun Yan for their assistance in fieldwork. We greatly appreciate the editorial support from Valerie Pinkerton, Lisa Delp Taylor, and Alona Gutman.

Authors’ Affiliations

Department of Environmental Sciences, University of Toledo
Key Laboratory of Vegetation and Environmental Change, Institute of Botany, The Chinese Academy of Sciences
School of Life Science, Shanxi University


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