Comparative Study on Methods for Computing Soil Heat Storage and

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JOURNAL OF METEOROLOGICAL RESEARCH

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Comparative Study on Methods for Computing Soil Heat Storage and Energy Balance in Arid and Semi-Arid Areas

), LIU Shuhua

LI Yuan (

), WANG Shu ( and CHEN Bicheng ( ) ∗

(

), MIAO Yucong (

),

Department of Atmospheric and Oceanic Sciences, School of Physics, Peking University, Beijing 100871 (Received August 8, 2013; in final form January 3, 2014)

ABSTRACT Observations collected in the Badan Jaran desert hinterland and edge during 19–23 August 2009 and in the Jinta Oasis during 12–16 June 2005 are used to assess three methods for calculating the heat storage of the 5–20-cm soil layer. The methods evaluated include the harmonic method, the conduction-convection method, and the temperature integral method. Soil heat storage calculated using the harmonic method provides the closest match with measured values. The conduction-convection method underestimates nighttime soil heat storage. The temperature integral method best captures fluctuations in soil heat storage on sub-diurnal timescales, but overestimates the amplitude and peak values of the diurnal cycle. The relative performance of each method varies with the underlying land surface. The land surface energy balance is evaluated using observations of soil heat flux at 5-cm depth and estimates of ground heat flux adjusted to account for soil heat storage. The energy balance closure rate increases and energy balance is improved when the ground heat flux is adjusted to account for soil heat storage. The results achieved using the harmonic and temperature integral methods are superior to those achieved using the conduction-convection method. Key words: soil heat storage, harmonic method, conduction-convection method, temperature integral method, surface energy balance Citation: Li Yuan, Liu Shuhua, Wang Shu, et al., 2014: Comparative study on methods for computing soil heat storage and energy balance in arid and semi-arid areas. J. Meteor. Res., 28(2), 308–322, doi: 10.1007/s13351-014-3043-5.

1. Introduction In ideal conditions, the energy received and released by the earth’s surface is equal. This tenet is one of the most basic principles of energy balance in the earth system. Land surface energy balance closure is used as a criterion to judge the quality of observational data (e.g., to assess the accuracy of eddy correlation data), and is crucial for accurate estimates of surface CO2 and evaporative fluxes based on the energy balance equation. Improvement in scientific understanding of mass and energy exchange between land surface and the atmosphere is also a common basis for improving regional and global climate models (Twine et al., 2000; Wilson et al., 2002; Cava et al., 2008). However, observational assessments of the land

surface energy budget often contain significant imbalances. These imbalances may arise due to the complexity and non-uniformity of the underlying surface, or to the limits of observational technology and instrument precision. The magnitude of the energy imbalance may be as large as 30% in some cases (Foken and Oncley, 1995; Oncley et al., 2007). Problems in land surface energy balance closure have been widely studied in recent decades. Land surface energy imbalances are generally attributed to the following reasons: instrumental and observational errors, overestimates of available energy (i.e., the sum of net radiation and soil heat flux), underestimates of effective energy (i.e., the sum of sensible and latent heat), neglect of heat storage and advection, and surface non-uniformity and non-stationarity.

Supported by the National Science and Technology Support Program of China (2012BAH29B03) and National (Key) Basic Research and Development (973) Program of China (2009CB421402). ∗ Corresponding author: [email protected]. ©The Chinese Meteorological Society and Springer-Verlag Berlin Heidelberg 2014

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LI Yuan, LIU Shuhua, WANG Shu, et al.

Recent improvements in the accuracy of observational instruments and quality control techniques for turbulence data (such as coordinate rotation, plane fitting, high frequency response revisal, footprint analysis, density effect correction, and angle of attack revisal) have reduced the magnitude of instrumental and observational errors and have often increased estimates of effective energy. Although these new developments have improved land surface energy balance closure in many cases, the problem is not yet completely solved (Moore, 1986; Wilczak et al., 2001; Nakai et al., 2006; Wang et al., 2007; Foken, 2008). Many studies indicate that the main factors in land surface energy imbalance are thermal storage terms (Ochsner et al., 2007; Foken, 2008), including heat storage in vegetation, air, and soil. Canopy heat storage is particularly important for ecosystems with tall, lush vegetation. Vegetation photosynthesis also consumes energy, but can typically be ignored because it has little effect on the energy balance. The heat storage of the atmospheric surface layer is approximately zero under the quasi-steady assumption, and Sun et al. (1995) suggested that this heat storage term is small enough to be ignored. The ground heat flux cannot be measured directly by using existing observational technology and is usually approximated by the shallow soil heat flux (even though significant differences may exist between these two terms). Soil heat storage is generally the dominant heat storage term because the shallow soil layer above the heat flux plate often stores considerable heat. Ignoring soil heat storage could lead to a considerable energy imbalance. Shallow soil heat storage appears to be particularly important in arid and semi-arid regions due to strong surface heating (Heusinkveld et al., 2004; Finnigan, 2006). The traditional soil equation only considers the effects of heat conduction. Horton et al. (1983) evaluated several common methods for calculating soil thermal diffusivity, including the amplitude method, the phase method, the arc tangent method, the logarithmic method, the numerical method, and the harmonic method. These different methods rely on different assumptions and therefore yield different results. Horton et al. (1983) also assessed the reliability of each

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method and reported that the numerical and harmonic methods were the most reliable. Upon comparing five of the six methods (except the numerical method), Verhoef et al. (1996) also judged the harmonic method to be most reliable. Mo et al. (2002) provided further validation for these methods. Wang et al. (2009) used the harmonic method and a temperature predictioncorrection method to calculate shallow soil heat storage observed during the “Heihe Comprehensive Observation Experiment”. They reported that the energy closure rate was improved after modification of the soil heat flux using these two methods. Zuo et al. (2010) compared the results of harmonic, temperature prediction-correction, and temperature integral methods for calculating the ground heat flux in observations from the SACOL (Semi-Arid Climate and Environment Observatory, Lanzhou University) station, and concluded that the harmonic and temperature prediction-correction techniques provided better performance. Soil water is one of the most important factors in the land surface energy balance of arid and semiarid ecosystems. Moisture movement generates thermal convection effects that influence the soil temperature. Although the soil water content of arid and semi-arid areas is relatively low, these effects still exist and neglecting the influences of moisture movement will introduce imbalances in the surface energy budget. Gao et al. (2003) showed that changes in soil temperature were connected with both soil heat conduction and heat convection caused by the vertical movement of liquid water in the soil. They also derived a onedimensional heat conduction convection equation by coupling heat conduction and convection. Gao (2005) proposed a formula for calculating the soil heat flux that considers the effects of thermal convection processes. Most conventional methods for estimating ground heat flux rely on knowledge of the temporal evolution of soil temperature. Wang et al. (2012) proposed a novel method that requires no information on soil temperatures to supplement flux plate measurements. Wang (2012) extended this method to enable the estimation of soil heat storage from a single depth

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measurement. The method is based on the fundamental solution of the one-dimensional heat equation and Duhamel’s principle. The only necessary thermal parameter is the soil thermal diffusivity, which can be assumed constant in the absence of measurements. This method is robust and preserves the accuracy of heat flux estimates in the face of reduced input information. The primary improvement over conventional methods is in ease of use and expense, rather than accuracy (Wang, 2012; Wang et al., 2012). Arid and semi-arid areas account for 30%–45% of the total global land area, and are the main land surface types in northern China. Arid and semi-arid areas are particularly sensitive to global climate change due to their geographic locations and the fragility of their ecosystems. Land-atmosphere interactions in these areas have important impacts on global redistribution of energy and global climate change (Fu and Wen, 2002; Huenneke et al., 2002). Deserts and oases are both common natural landscapes in arid and semi-arid areas; however, the underlying surfaces in desert hinterland, desert edge, and oasis regions are substantially different. Interactions between deserts and oases present special challenges for projecting and understanding regional climate changes. A number of recent studies have investigated the land surface energy balance over single underlying surface; however, few of these studies have considered the effects of different underlying surface types. We calculate the soil heat storage of different arid and semi-arid surfaces using the harmonic, conduction-convection, and temperature integral methods. The results reveal important differences in soil heat storage processes and land surface energy balance closure over different underlying surfaces. We analyze the energy balance after adjusting the shallow soil heat flux to account for differences in land surface type. 2. Data and instrumentation A portion of the observational data was obtained from the Badan Jaran desert hinterland (39◦ 46 N, 102◦ 9 E) and edge (39◦ 28 N, 102◦ 22 E) during 19–23

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August 2009. This dataset was collected under the National Basic Research and Development (973) Program of China “Energy and Water Cycle Experiment of Northwest China Typical Arid and Semi-arid Areas”. Another dataset was obtained from the Jinta Oasis (39◦ 59 N, 98◦ 56 E) in Gansu Province during 12–16 June 2005 under the “Energy and Water Cycle Field Experiment of the Oasis System” project of the Cold and Arid Regions Environmental and Engineering Institute (CAREERI), Chinese Academy of Sciences (CAS). All of the instruments used in the experiment were automated and calibrated before use. The observational data collected in the Badan Jaran desert were sampled as 30-min mean values with outliers eliminated during data quality control (Hu, 2004; Zuo et al., 2009). The observational data collected at the Jinta Oasis were sampled as 10-min means, and then averaged into 30-min means to facilitate direct comparison of the two datasets. This data processing only reduced the variability of the results and did not change the direction of the gradient or the accuracy of the calculations. All of the observations were taken under fine weather conditions. 3. Methodology Soil heat flux is one of the most important components of the surface energy balance, but direct measurement of this term is difficult. Calculation of soil heat storage is a necessary step in calculating soil heat flux. Intelligent adjustment of soil heat flux prior to its inclusion in the land surface energy balance equation may help to improve closure of the surface energy budget. 3.1 Methods for computing soil heat storage Three forms of heat transfer occur in soils: conduction, convection, and radiation. Radiative heat transfer at the surface is generally separated into short-wave and long-wave components. Short-wave radiation does not penetrate into the soil layer, and is reflected or absorbed at the surface. Long-wave radiation depends only on the temperature of an “infinitesimal” layer at the land surface. Because the

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effects of radiation do not penetrate into the soil layer, radiative heat transfer can be neglected in the soil heat budget. 3.1.1 Harmonic method (HM) Soil heat transfer occurs mainly via molecular transmission. Bhumralker (1975) presented the heat conduction equation ∂2T ∂T =k 2, ∂t ∂z

(1)

where T is the soil temperature, t is time, z is depth, λ and k = is the soil thermal diffusivity (with λ the Cv soil thermal conductivity and Cv the soil thermal capacity). The soil thermal diffusivity k is a weak function of soil water content and can be approximated as constant across the depth of the soil layer (Wang, 2012; Wang et al., 2012). Changes of soil temperature with time can be expressed as the superposition of n harmonics. The initial boundary condition is defined as T (z, 0) = T0 − γz,

z 0,

(2)

where T0 is the average temperature of the soil surface, γ is the lapse rate of soil temperature with depth, and z is the soil depth. Hillel (1982) parameterized the diurnal forcing at the surface as a pure sinusoidal function. The upper boundary condition in this case is T (t)|z=0 = T0 + A sin(ωt) when t > 0, where A is the 2π is the angular velocity of the amplitude and ω = p earth rotation (p = 24 h is the harmonic period of land surface temperature). The diurnal forcing is not a true sine function, which can be accounted for by replacing the upper boundary condition with the Fourier series T (t)|z=0 = T0 +

n

Ai sin(iωt + ϕi ),

t > 0,

(3)

i=1

where Ai is the amplitude of harmonic i and ϕi is the initial phase of harmonic i. This formula indicates that variations in the land surface temperature consist of two parts: the constant T0 and n superimposed sine waves. The periods of these sine waves are p, p/2, . . ., p/n, respectively, with the corresponding amplitudes A1 , A2 , . . ., An . Here, we assume that the initial phases ϕi and the soil temperature below 1-m

depth are all constants. We can then use the variable separation method to solve the heat conduction equation (Eq. (1)). This approach yields T (z, t) = T0 − γz +

n

Ai exp(−Bi z)

i=1

· sin(iωt + ϕi − Bi z),

(4)

with Bi = iω/2k. The parameters in Eq. (4) are derived by using the least squares method to find an optimal fit to soil temperature measurements at two depths. We can then obtain the harmonic soil heat flux formula as G(z, t) = kCv γ + kCv

n

√ Ai 2Bi exp(−Bi z)

i=1

· sin(iωt + ϕi + π/4 − Bi z).

(5)

Miao et al. (2012) fitted harmonic models of different orders and found that the accuracy of the second-order harmonic model (n = 2) was already sufficient for most purposes. Accordingly, we use the second-order harmonic for simplicity and ease of computation. 3.1.2 Conduction-convection method (CM) Moisture movement in the soil produces heat convection, which in turn affects the soil temperature. The convective heating Qv caused by the vertical movement of water through a unit area of soil per unit time can be expressed as Qv = Cw wθΔT,

(6)

where w is the water permeability in unit of m s−1 (positive upward), Cw is the liquid water thermal capacity, θ is the soil water content, and ΔT is the vertical gradient of water temperature. Using the second law of thermodynamics, the soil heat balance can be expressed as ∂T ∂T ∂2T = ka 2 + W , ∂t ∂z ∂z

(7)

where ka is the thermal diffusivity (including only heat Cw conduction) and W = wθ can be understood as the Cv liquid water flux density (in m s−1 ). Equations (1) and (7) are equivalent when W = 0 (i.e., the conductionconvection equation reduces to the traditional heat

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conduction equation in soils with low water content). Gao et al. (2003) derived a first-order harmonic analytical solution to the conduction-convection equation (Eq. (7)):

method is the difference between the soil heat fluxes at two different layers: S = G1 − G2 ,

(8) (9)

∂T − Cv Wa ΔT, Qt = Qd + Qw = −Cv ka ∂z

(11) (12) (13)

Qd = −Cm k[−γ − M Aexp(−M z) × sin(ωt

0 G0 = Gz + Cv z

∂Tz dz, ∂t

(18)

where G0 is the ground heat flux, Gz is the soil heat flux observed at a heat flux plate at depth z, Tz is the temperature profile in the soil between z and the land surface, and t is time. The soil heat storage can then be calculated as 0 ∂T dz, (19) S = Cv z ∂t ∂T can be approximated using a finite differwhere ∂t ence scheme. The soil heat storage can be written as S=

Cv [T (zi , t + Δt) − T (zi , t − Δt)]Δz. (20) 2Δt z

3.2 Expression of energy balance closure We assume that the land surface is horizontal and uniform and the atmosphere is in a steady state. Using the energy conservation and conversion laws and considering soil heat storage, the land surface energy balance equation can be expressed as Rn = H + LE + G + S,

+ϕ − N z) − N Aexp(−M z) (14)

and ΔT = T (z2 , t) − T (z1 , t) = −γz2 +Aexp(−M z2 ) × sin(ωt + ϕ − N z2 ) + γz1 −Aexp(−M z1 ) × sin(ωt + ϕ − N z1 ).

(17)

0

where Qt is the total heat flux, Qd is the conduction heat flux, Qw is the convective heat flux, and θ(z) − θ(z + Δz) × W . Using Eq. (8), Wa = θ1 − θ2

× cos(ωt + ϕ − N z)],

(CM).

(16)

3.1.3 Temperature integral method (TIM) Based on the first law of thermodynamics, the integral form of one-dimensional heat conduction equation is

(10)

Tmax − Tmin , M = where the amplitude A = 2 √ W 2 + W 2 + W 4 + 16ka2 ω 2 , and N = 2ka 4k √a 2ω . A1 and A2 are the ampli W 2 + W 4 + 16ka2 ω 2 tudes of soil temperature variations at the depths z1 and z2 , and ϕ1 and ϕ2 are the phases of soil temperature variations at depths z1 and z2 . In this work, we take z1 = 5 cm and z2 = 20 cm. Fan and Tang (1994) calculated the heat flux using a correlation form of the conduction-convection method: ∂T , Qd = −Cv ka ∂z Qw = −Cv Wa ΔT,

(HM),

S = Qt1 − Qt2 ,

T (z, t) = T0 − γz + Aexp(−M z) · sin(ωt + ϕ − N z), (z1 − z2 )2 ω ln(A1 /A2 ) , ka = (ϕ2 − ϕ1 )[(ϕ2 − ϕ1 )1 + ln2 (A1 /A2 )] ω(z1 − z2 ) 2 ln2 (A1 /A2 ) , W = ϕ2 − ϕ1 (ϕ2 − ϕ1 )2 + ln2 (A1 /A2 )

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(15)

The soil heat storage calculated using either the harmonic method or the conduction-convection

(21)

where Rn is the net land surface radiation flux, H is the land surface sensible heat flux, LE is the land surface latent heat flux, G is the ground heat flux, and S is the soil heat storage between the heat flux plate and the surface. H and LE can be approximated using the sensible and latent heat fluxes observed near the surface. Sensible and latent heat fluxes were observed during the campaign in the Badan Jaran desert hinterland and edge, but were not directly observed during

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the campaign at the Jinta Oasis. We use the aerodynamic method (Liu et al., 2009; Liu et al., 2010) to calculate the sensible heat flux and latent heat flux from the gradients of observations that were taken at the Jinta Oasis. Rn is calculated from the radiation balance equation as Rn = (Rsd − Rsu ) + (Rld − Rlu ),

(22)

where Rsd is the total downward short-wave radiation reaching the surface, Rsu is the amount of shortwave radiation reflected by the land surface, Rld is the downward flux of long-wave radiation from the atmosphere, and Rlu is the upward flux of long-wave radiation from the land surface. Rsd , Rsu , Rld , and Rlu have been directly observed. Several approaches may be used to assess the imbalance in the land surface energy budget. These different approaches may yield different results even for the same dataset. We use an ordinary linear regression (OLR) method to analyze the imbalances in the energy budgets calculated for the Badan Jaran desert hinterland, Badan Jaran desert edge, and Jinta Oasis. In this method, the slope of the linear regression between the quantities (H+LE) and (Rn − G − S) is used to represent the energy balance closure rate. Energy closure is accomplished if the slope of the linear regression is 1 and the intercept is 0. 4. Results and discussion The three methods introduced above (HM, CM, and TIM) were tested and the results were validated against observational data. The shallow soil heat flux was adjusted to the land surface energy balance and the energy balance closure rate was analyzed. The detailed results of this analysis are presented and discussed in the following section.

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approximately 0.33. The surface type at the Badan Jaran desert edge was sparse desert reeds, with a vegetation height of about 0.6 m and a surface albedo of 0.23 (Ma et al., 2012). The most common soil types at Jinta Oasis were irrigated silty soil, moist meadow soil, and aeolian sandy soil. The surface was engaged as farmland. The typical crop in this area is wheat, but in mid June 2005, the primary crop was an initial growth of cotton. The surface albedo at Jinta Oasis was approximately 0.19 (Chen et al., 2006; Ao et al., 2008). Soil moisture is an important factor in determining surface albedo, as the presence of water around a soil particle increases the absorption path of solar radiation. Greater soil moisture typically correlates with smaller albedo. The surface albedo at Jinta Oasis was lower than the albedo at the other two locations because the soil water content was highest. The differences in albedo indicate that the underlying surfaces at the three sites have different physical characteristics. Figure 2 shows the soil heat fluxes observed at 5- and 20-cm depths at the three sites. The observed fluxes had obvious diurnal variations. The soil heat fluxes at 5-cm depth varied substantially from day to day, while the soil heat fluxes at 20-cm depth varied much more smoothly. The diurnal variations of soil heat fluxes at 20-cm depth had smaller peaks, smaller amplitudes, and larger phase lags than the diurnal variations at 5-cm depth. These differences illustrate that the amplitude of soil heat flux decays with depth, while the phase becomes delayed. The soil heat flux

4.1 Soil heat storage 4.1.1 Analysis of observational data The soil water content at 5-cm depth was smallest in the Badan Jaran desert hinterland and largest at the Jinta Oasis, with the Badan Jaran desert edge in between (Fig. 1). The surface type in the Badan Jaran desert hinterland was sand, with a surface albedo of

Fig. 1. Time series of soil water content at 5-cm depth.

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Fig. 2. Time series of soil heat fluxes measured at 5cm depth (G5) and 20-cm depth (G20) at the (a) Badan Jaran desert hinterland, (b) Badan Jaran desert edge, and (c) Jinta Oasis.

at 5 cm cannot be used as a direct measure of the ground heat flux, but must be supplemented by the soil heat storage terms in the land surface energy bal-

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ance equation. 4.1.2 Analysis of model results Soil thermal capacity is needed to calculate soil thermal storage regardless of the numerical method used. The soil thermal capacity at each measurement site can be obtained using the heat conduction equation. These heat capacities are 0.69×10−6 J (m3 K)−1 for the Badan Jaran desert hinterland, 0.80×10−6 J (m3 K)−1 for the Badan Jaran desert edge, and 0.92×10−6 J (m3 K)−1 for the Jinta Oasis. The HM and CM also require the soil thermal diffusion, which is calculated according to the detailed method provided by Miao et al. (2012). The main parameters for each method are listed in Tables 1–6. Figure 3 shows soil heat storage at each site calculated using the HM, CM, and TIM methods, as well as the measured value of soil heat storage between 5- and 20-cm depths. The soil heat storage varies substantially on the diurnal timescale. The daily variations of soil heat storage calculated using the three methods show good agreement with the variations in the measured values. The HM method provides the closest fit because the iterative method of calculating soil thermal diffusivity makes the fullest use of the measurements. The CM method underestimates the soil heat storage at night. This underestimate may be attributable to the error inherent in assuming the soil moisture flux density W to be constant throughout the day (Dai et al., 2009). During daytime, especially under fine weather conditions, soil moisture moves upward because of surface evaporation (i.e., W > 0). Surface evaporation abates with the decrease of surface temperature at night, so soil moisture moves from shallow layers to deeper layers (i.e., W < 0). Ignoring these variations in soil water flux density induces errors in the calculated soil heat storage. The values of soil heat storage calculated by using the HM and

Table 1. Amplitudes for the harmonic method Day 1 2 3 4 5

Badan Jaran desert hinterland A1 A2 –11.40 1.82 –10.36 1.82 –8.83 1.63 –8.82 2.07 –8.05 1.92

Badan Jaran desert edge A1 A2 –9.82 1.36 –6.33 1.09 –7.03 1.01 –8.17 1.39 –6.38 1.36

Jinta Oasis A1 A2 –6.51 0.95 –6.97 1.61 –6.89 1.19 –6.40 1.27 –6.73 1.59

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Table 2. Phases for the harmonic method Day 1 2 3 4 5

Badan Jaran desert hinterland ϕ1 ϕ2 0.10π –0.08π 0.09π –0.02π 0.08π –0.10π 0.08π –0.10π 0.09π –0.05π

Badan Jaran desert edge ϕ1 ϕ2 1.90π –0.30π 1.92π –0.17π 1.92π –0.23π 1.93π –0.18π 1.91π –0.15π

Jinta Oasis ϕ1 0.09π 0.08π 0.08π 0.07π 0.10π

ϕ2 –0.10π –0.07π –0.05π –0.02π 0.05π

Table 3. Thermal diffusivity for the harmonic method Day 1 2 3 4 5

Badan Jaran desert hinterland k (10−7 m2 s−1 ) 7.88 7.67 7.64 7.32 7.11

Badan Jaran desert edge k (10−7 m2 s−1 ) 4.70 4.47 4.96 3.88 4.01

Jinta Oasis k (10−7 m2 s−1 ) 5.91 6.02 5.92 5.58 5.76

Table 4. Amplitudes for the conduction-convection method Day 1 2 3 4 5

Badan Jaran desert hinterland A1 A2 11.44 4.02 10.66 3.60 9.15 3.10 9.27 3.02 8.99 2.51

Badan Jaran desert edge A1 A2 9.56 2.12 6.65 1.45 7.40 1.32 8.44 1.74 6.87 1.46

Jinta Oasis A1 6.67 7.77 7.61 7.15 7.52

A2 2.04 2.17 2.11 2.00 2.19

Table 5. Phases for the conduction-convection method Day 1 2 3 4 5

Badan Jaran desert hinterland ϕ1 ϕ2 1.10π 0.82π 1.00π 0.77π 1.08π 0.77π 1.08π 0.77π 1.07π 0.73π

Badan Jaran desert edge ϕ1 ϕ2 1.00π 0.71π 0.92π 0.48π 0.92π 0.51π 0.93π 0.59π 0.91π 0.54π

Jinta Oasis ϕ1 1.09π 1.08π 1.08π 1.07π 1.10π

ϕ2 0.76π 0.73π 0.74π 0.75π 0.79π

Table 6. Thermal diffusivity and liquid water flux density for the conduction-convection method Day 1 2 3 4 5

Badan Jaran desert hinterland ka (10−7 m2 s−1 ) W (10−6 m s−1 ) 10.20 1.95 9.29 1.54 9.54 1.75 10.35 2.37 10.44 1.43

Badan Jaran desert edge ka (10−7 m2 s−1 ) W (10−6 m s−1 ) 7.07 2.95 5.02 0.90 5.62 1.37 5.80 3.04 5.56 2.41

CM are closer to the observed values; however, neither of these methods is able to capture fluctuations in soil heat storage on smaller timescales. The diurnal amplitude of the soil heat storage calculated using the TIM method is larger, and the maxima are significantly

Jinta Oasis ka (10−7 m2 s−1 ) W (10−6 m s−1 ) 7.24 1.43 6.61 1.40 7.11 1.90 7.69 2.34 8.04 2.30

higher, but the time series captures these small-scale fluctuations. A comprehensive and objective comparison of the performance of these three methods in this case requires a more quantitative analysis. Figure 4 shows scatter plots of calculated and

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the correlation coefficients are highest for HM (0.9080) and TIM (0.8934). At the Jinta Oasis site, the fitting coefficient is closest to 1 for CM (0.9072), while the correlation coefficient is highest for TIM (0.9141). The fitting coefficient of the HM results gradually departs from 1 with increasing soil water content, while the fitting coefficient of the CM result gradually approaches 1 under the same conditions. This difference arises because CM considers the heat convection effects of soil water, while the HM does not. TIM, which is based on energy conservation, correlates well with the measured values at all three sites; however, the fitting coefficient for TIM is greater than 1 and the magnitude of the error is larger. Whereas HM uses a second-order harmonic model, CM uses a true sine function to estimate soil heat storage. This limits the accuracy of the CM calculation, so the correlation coefficients for CM are only 0.48–0.70. Three statistics are used to further illustrate the differences between observations and calculations of soil heat storage using the three methods: the average deviation (Biss), the standard deviation (SEE), and the relative standard deviation (NSEE). These statistics are defined as: n

storage between 5- and 20-cm depths at the (a) Badan Jaran desert hinterland, (b) Badan Jaran desert edge, and (c) Jinta Oasis measurement sites. Calculations have been performed using the harmonic (HM), conductionconvection (CM), and temperature integral (TIM) methods.

measured values of soil heat storage for each of the three measurement sites. At the Badan Jaran desert hinterland site, the fitting coefficient is closest to 1 for the HM results (0.9409), while the correlation coefficient is highest for the TIM results (0.9297). At the Badan Jaran desert edge site, the fitting coefficients are closer to 1 for HM (0.9004) and CM (1.0354), while

|S − S0 |

, n

n

(S − S0 )2 SEE = i=1 , n−2

n (S − S )2

0

NSEE = i=1 , n (S0 )2

Biss =

Fig. 3. The measured and calculated values of soil heat

i=1

(23)

(24)

(25)

i=1

where n is the total number of samples and S and S0 are the calculated and measured values of soil heat storage, respectively. The results are listed in Table 7. The errors are smallest for calculations using HM for the Badan Jaran desert hinterland and edge sites, while TIM performs better than CM. The HM calculation is also most accurate for the Jinta Oasis site, but CM performs better than TIM in this case. Based on these statistics, the calculation using HM is superior

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Fig. 4. Scatter plots of calculated and measured values of soil heat storage at the (a1 –a3 ) Badan Jaran desert hinterland, (b1 –b3 ) Badan Jaran desert edge, and (c1 –c3 ) Jinta Oasis measurement sites. (a1 –c1 ) HM, (a2 –c2 ) CM, and (a3 –c3 ) TIM. Table 7. Average deviation, standard deviation, and relative standard deviation for values of soil heat storage calculated at each site Statistics Biss SEE NSEE (%)

Badan Jaran desert hinterland HM CM TIM 9.60 16.54 13.63 12.34 19.83 18.89 52.09 83.72 79.73

Badan Jaran desert edge HM CM TIM 10.90 22.07 19.24 13.07 29.70 25.57 30.34 68.91 59.33

regardless of the underlying surface. 4.2 Energy balance 4.2.1 Analysis of observational data The definitions for Rn , H, LE, and G as terms in

HM 14.20 17.02 61.76

Jinta Oasis CM 19.89 23.46 85.13

TIM 20.53 28.60 96.06

the land surface energy balance equation (Eq. (21)) have been introduced in Section 3.2. The following section presents an analysis of these four fluxes as observed at the measurement sites. The accuracy of radiation observations has grea-

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tly improved over the past 10–15 years with the advent of the global surface radiation reference station network (BSRN). The four-component radiometer used to measure the net surface radiation Rn at these experiment sites is accurate to within ±5%. The error in the observations is random. Under normal maintenance conditions, the net radiation observations are the most accurate among the four energy budget components.

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The turbulent fluxes H and LE were collected using eddy correlation methods. The sampling frequency was 10–20 Hz, and the observations were then averaged into 30-min means. The instrument performed consistently well during these experiments. The soil heat flux G was observed by using a soil heat flux plate at a depth of 5 cm (denoted by G5). Heat flux measurements using this instrument are gen-

Fig. 6. Unadjusted and adjusted soil heat fluxes at the (a) Badan Jaran desert hinterland, (b) Badan Jaran desert Fig. 5. Time series of the net radiation flux at the sur-

edge, and (c) Jinta Oasis sites. The adjusted values (G0)

face (Rn ), the latent (LE) and sensible (H) heat fluxes, and

rely on calculations using the harmonic (HM), conduction-

the soil heat flux (G5) measured at the (a) Badan Jaran

convection (CM), and temperature integral (TIM) meth-

desert hinterland, (b) Badan Jaran desert edge, and (c)

ods.

Jinta Oasis sites.

taken at 5-cm depth.

The unadjusted values (G5) are raw observations

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erally accurate to within ±3%. Errors in these observations are not a primary reason for imbalance in the observed energy budget. Figure 5 shows measurements of Rn , H, LE, and G5 over the 5-day measurement periods at the Badan Jaran desert hinterland and desert edge (19–23 August 2009) and at Jinta Oasis (12–16 June 2005). All four terms have obvious diurnal variations, with positive anomalies during daytime and negative anomalies at night. The phase of diurnal variations in G5 lags slightly behind the phase of diurnal variations in Rn , H, and LE; in other words, the energy fluxes are not synchronous. We therefore need to consider the role of soil heat storage between the soil heat flux plate and the land surface to close the surface energy budget. 4.2.2 Analysis of model results Figure 6 shows the observed soil heat fluxes at 5cm depth (G5) and ground heat fluxes (G0) adjusted based on soil heat storage calculated by using the three methods described in Section 3.1. G0 (HM) is calculated by using Eq. (5) and G0 (CM) is calculated by directly using Eqs. (11)–(15) with the parameter values listed in Tables 3–8. For G0 (TIM), the soil heat storage from 5-cm depth to the land surface is calculated by using Eq. (20) and the ground heat flux is calculated by Eq. (18). The amplitudes of the calculated ground heat fluxes are larger than the measured soil heat fluxes at 5-cm depth with a slight phase lead. These results are in line with the universal law mentioned in Section 4.1. The diurnal variations of the calculated values match well with the observed heat fluxes. The results indicate that these three methods provide a reliable means of calculating soil heat storage and adjusting soil heat flux for energy balance closure. Figure 7 shows linear regression fits of (H+LE) and (Rn − G) using the unadjusted soil heat fluxes at 5-cm depth and the ground heat fluxes adjusted using calculations of soil heat storage. This plot illustrates the discrepencies from energy balance closure over the different underlying surfaces. The regression parameters and correlation coefficients are listed in Table 8. The slope of the linear regression between (H+LE) and (Rn − G) is closer to unity after adjusting the soil heat flux regardless of location. The en-

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ergy closure rate for the Badan Jaran desert hinterland site increases by 3.83% when HM is used to adjust G, by 2.94% when CM is used, and by 3.83% when TIM is used. The correlation coefficient also increases by 0.0373, 0.0084, and 0.0337, respectively. HM and TIM provide a greater improvement than CM. The energy closure rate for the Badan Jaran desert edge site increases by 3.19%, 3.11%, and 5.97%, respectively, while the correlation coefficient changes by 0.0042, –0.0145, and 0.0335, respectively. For this site, TIM provides the largest improvement. The energy closure rate for the Jinta Oasis site increases by 1.39%, 1.49%, and 1.74%, respectively, while the correlation coefficient changes by 0.007, 0.006, and –0.011, respectively. The differences in the results among the three methods for this site are not significant. Overall, the energy closure rate after adjustment is better than before adjustment. The soil heat fluxes adjusted using HM and TIM provide better closure rates than those adjusted using CM. The diurnal variations of soil heat flux do not follow a pure sine curve. HM uses a second-order harmonic model to simulate diurnal variations in heat flux, and is therefore more accurate than CM (which uses first-order harmonic model). The results summarized in Fig. 7 and Table 8 illustrate that errors in the energy balance have different magnitudes over different underlying surfaces. The energy balance closure rate at the Badan Jaran desert hinterland site is approximately 80%, while the closure rates at the Badan Jaran desert edge and Jinta Oasis sites are only about 55%. Even after accounting for soil heat storage, the energy budgets at the latter two sites are still far from being closed. This suggests that the reasons for energy imbalance may vary substantially for different underlying surfaces. In further research on energy balance closure, we must consider other factors in addition to soil heat storage. Each underlying surface type may have unique features that contribute to energy imbalance. 5. Conclusions Three methods for estimating soil heat storage

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Fig. 7. Linear regressions between the (H+LE) and (Rn − G) terms of the energy balance equation over the (a1 –a4 ) Badan Jaran desert hinterland, (b1 –b4 ) Badan Jaran desert edge, and (c1 –c4 ) Jinta Oasis measurement sites. (a1 –c1 ) The unadjusted observations, (a2 –c2 ) HM, (a3 –c3 ) CM, and (a4 –c4 ) TIM. Table 8. Energy balance closure metrics after adjusting for soil heat storage

Unadjusted HM CM TIM

Badan Jaran desert hinterland Closure rate R2 0.7927 0.8744 0.8310 0.9117 0.8221 0.8828 0.8331 0.9081

have been evaluated for revealing their potential to improve energy balance closure over arid and semiarid surface types. The analysis is based on observations collected at measurement sites in the Badan Jaran desert hinterland, the Badan Jaran desert edge, and Jinta Oasis. Soil heat storage between 5- and 20cm depths has been calculated using the HM, CM, and TIM methods. The soil heat flux at 5-cm depth has been adjusted based on the results of these calculations, and the resulting land surface energy balance has been analyzed. The conclusions are as follows.

Badan Jaran desert edge Closure rate R2 0.5067 0.8434 0.5386 0.8476 0.5378 0.8289 0.5664 0.8769

Jinta Oasis Closure rate R2 0.5346 0.8272 0.5485 0.8342 0.5495 0.8332 0.5520 0.8162

(1) The soil heat storage calculated using HM is closest to the measured value because this method makes the fullest use of measurements in estimating soil thermal diffusivity. HM also benefits from the use of a second-order harmonic model of daily variations in soil heat flux. CM couples heat conduction and convection; theoretically, this method should provide a more accurate representation of heat transfer processes in the soil than the other methods. CM applied in this work neglects diurnal variations in soil water flux density, and therefore underestimates nighttime

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soil heat storage. CM also simulates the diurnal cycle of soil heat storage using a sine function, which limits the accuracy of the calculation. TIM calculates soil heat storage based entirely on energy conservation laws, so the calculation is consistent with observed fluctuations; however, the diurnal amplitude is larger than observed and the peak values are substantially higher. (2) The relative performance of each method varies according to the soil water content of the underlying surface. The minimum errors are achieved using HM. Moreover, the HM calculations are the most accurate for the three surface types considered here. The results using TIM are better than those using CM for the Badan Jaran desert sites, but the results using CM are superior to those using TIM for the Jinta Oasis site. (3) Accounting for soil heat storage in estimates of ground heat flux improves energy balance closure rates at all three surface sites relative to unadjusted measurements collected at 5-cm depth. However, these improvements are an order of magnitude smaller than the total land surface energy imbalance (0.01–0.05 compared to 0.2–0.5). The energy closure rate is especially low for the Badan Jaran desert edge and Jinta Oasis measurement sites. This result indicates that soil heat storage is just one among many factors that cause imbalance in observations of the energy budgets of arid and semi-arid surfaces. Future work on this topic must consider other factors in addition to soil heat storage, such as vertical thermal advection within the surface layer. Due to data limitations, we have not discussed these aspects in this study. We will treat them in depth as observational data becomes more abundant in the future. REFERENCES Ao Yinhuan, L¨ u Shihua, Zhang Yu, et al., 2008: Contrast analyses of the soil condition of the different ground surface over Jinta Oasis. Acta Energiae Solaris Sinica, 29, 465–470. (in Chinese) Bhumralker, C. M., 1975: Numerical experiments on the computation of ground surface temperature in an atmospheric circulation model. J. Appl. Meteor., 14, 1246–1258.

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