J. Meteor. Res.    2014, Vol. 28 Issue (2): 308-322     PDF       
http://dx.doi.org/10.1007/s13351-014-3043-5
The Chinese Meteorological Society
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Article Information

LI Yuan, LIU Shuhua, WANG Shu, MIAO Yucong, CHEN Bicheng. 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
http://dx.doi.org/10.1007/s13351-014-3043-5

Article History

Received August 8, 2013;
in final form January 3, 2014
Comparative Study on Methods for Computing Soil Heat Storage and Energy Balance in Arid and Semi-Arid Areas
LI Yuan, LIU Shuhua , WANG Shu, MIAO Yucong, CHEN Bicheng       
Department of Atmospheric and Oceanic Sciences, School of Physics, Peking University, Beijing 100871
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.
Keywordssoil heat storage        harmonic method        conduction-convection method        temperature integral method        surface energy balance       
1. Introduction

In ideal conditions, the energy received and released by the earth's surface is equal. This tenet isone of the most basic principles of energy balance inthe earth system. L and surface energy balance closure is used as a criterion to judge the quality of observ ational data(e. g., to assess the accuracy of eddycorrelation data), and is crucial for accurate estimatesof surface CO2 and ev aporative fluxes based on theenergy balance equation. Improvement in scientificunderst and ing of mass and energy exchange betweenl and 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, observ ational assessments of the l and 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 observ ational 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 l and surface energy balance closure have been widely studied in recent decades.

L and surface energy imbalances are generally attributed to the following reasons: instrumental and observ ational 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 . Recent improvements in the accuracy of observ ationalinstruments 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 observ ational errors and have often increased estimatesof effective energy . Although these new developmentshave improved l and surface energy balance closure inmany 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 l and surface energyimbalance are thermal storage terms(Ochsner et al., 2007; Foken, 2008), including heat storage in vegetation, air, and soil. Canopy heat storage is particularlyimportant for ecosystems with tall, lush vegetation. V egetation photosynthesis also consumes energy, butcan typically be ignored because it has little effect onthe energy balance. The heat storage of the atmospheric surface layer is approximately zero under thequasi-steady assumption, and Sun et al. (1995)suggested that this heat storage term is small enough tobe ignored. The ground heat flux cannot be measureddirectly by using existing observ ational technology and is usually approximated by the shallow soil heat flux(even though significant differences may exist betweenthese two terms). Soil heat storage is generally thedominant heat storage term because the shallow soillayer above the heat flux plate often stores considerable heat. Ignoring soil heat storage could lead toa considerable energy imbalance. Shallow soil heatstorage 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 theeffects of heat conduction. Horton et al. (1983)ev aluated several common methods for calculating soil thermal diffusivity, including the amplitude method, thephase method, the arc tangent method, the logarithmic method, the numerical method, and the harmonicmethod. These different methods rely on different assumptions and therefore yield different results. Horton et al. (1983)also assessed the reliability of eachmethod and reported that the numerical and harmonicmethods were the most reliable. Upon comparing fiveof the six methods(except the numerical method), Verhoef et al. (1996)also judged the harmonic methodto be most reliable. Mo et al. (2002)provided furthervalidation for these methods. Wang et al. (2009)usedthe harmonic method and a temperature predictioncorrection method to calculate shallow soil heat storage observed during the "Heihe Comprehensive Observ ation Experiment". They reported that the energy closure rate was improved after modification ofthe soil heat flux using these two methods. Zuo etal. (2010)compared the results of harmonic, temperature prediction-correction, and temperature integralmethods for calculating the ground heat flux in observ ations from the SACOL(Semi-Arid Climate and Environment Observatory, Lanzhou University)station, and concluded that the harmonic and temperature prediction-correction techniques provided betterperformance.

Soil water is one of the most important factorsin the l and 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 movementwill 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 movementof liquid water in the soil. They also derived a onedimensional heat conduction convection equation bycoupling heat conduction and convection. Gao(2005)proposed a formula for calculating the soil heat fluxthat considers the effects of thermal convection processes.

Most conventional methods for estimating groundheat flux rely on knowledge of the temporal evolution of soil temperature. Wang et al. (2012)proposed a novel method that requires no information onsoil temperatures to supplement flux plate measurements. Wang(2012)extended this method to enablethe estimation of soil heat storage from a single depth 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. Thismethod is robust and preserves the accuracy of heatflux estimates in the face of reduced input information. The primary improvement over conventional methodsis in ease of use and expense, rather than accuracy(Wang, 2012; Wang et al., 2012).

Arid and semi-arid areas account for 30%-45% ofthe total global l and area, and are the main l and surface types in northern China. Arid and semi-arid areasare particularly sensitive to global climate change dueto their geographic locations and the fragility of theirecosystems. L and -atmosphere interactions in these areas have important impacts on global redistribution ofenergy and global climate change(Fu and Wen, 2002; Huenneke et al., 2002). Deserts and oases are bothcommon natural l and scapes in arid and semi-arid areas; however, the underlying surfaces in desert hinterl and , desert edge, and oasis regions are substantially different. Interactions between deserts and oasespresent special challenges for projecting and underst and ing regional climate changes. A number of recent studies have investigated the l and surface energybalance over single underlying surface; however, fewof these studies have considered the effects of differentunderlying 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 differencesin soil heat storage processes and l and surface energybalance closure over different underlying surfaces. Weanalyze the energy balance after adjusting the shallowsoil heat flux to account for differences in l and surfacetype. 2. Data and instrumentation

A portion of the observ ational data was obtainedfrom the Badan Jaran desert hinterl and (39° 46'N, 102° 9'E) and edge(39° 28'N, 102° 22'E)during 19-23August 2009. This dataset was collected under theNational Basic Research and Development(973)Program of China "Energy and Water Cycle Experimentof Northwest China Typical Arid and Semi-arid Areas". Another dataset was obtained from the JintaOasis(39° 59'N, 98° 56'E)in Gansu Province during12-16 June 2005 under the "Energy and Water Cycle Field Experiment of the Oasis System" project ofthe Cold and Arid Regions Environmental and Engineering Institute(CAREERI), Chinese Academy ofSciences(CAS).

All of the instruments used in the experimentwere automated and calibrated before use. The observational data collected in the Badan Jaran desert weresampled as 30-min mean values with outliers eliminated during data quality control(Hu, 2004; Zuo et al., 2009). The observ ational data collected at the JintaOasis were sampled as 10-min means, and then averaged into 30-min means to facilitate direct comparisonof the two datasets. This data processing only reducedthe variability of the results and did not change thedirection of the gradient or the accuracy of the calculations. All of the observ ations were taken under fineweather 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 soilheat storage is a necessary step in calculating soil heatflux. Intelligent adjustment of soil heat flux prior toits inclusion in the l and surface energy balance equation may help to improve closure of the surface energybudget. 3. 1 Methods for computing soil heat storage

Three forms of heat transfer occur in soils: conduction, convection, and radiation. Radiative heattransfer at the surface is generally separated intoshort-wave and long-wave components. Short-waveradiation does not penetrate into the soil layer, and is reflected or absorbed at the surface. Long-waveradiation depends only on the temperature of an"infinitesimal" layer at the l and surface. Because the effects of radiation do not penetrate into the soil layer, radiative heat transfer can be neglected in the soil heatbudget. 3. 1. 1 Harmonic method(HM)

Soil heat transfer occurs mainly via moleculartransmission. Bhumralker(1975)presented the heatconduction equation

where T is the soil temperature, t is time, z is depth, and is the soil thermal diffusivity(with ¸ thesoil thermal conductivity and Cvthe soil thermal capacity). The soil thermal diffusivity k is a weak function of soil water content and can be approximatedas 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 aswhere 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 isT(t)jz=0 = T0 + A sin(ωt)when t > 0, where A is theamplitude and is the angular velocity of theearth rotation(p = 24 h is the harmonic period of l and surface temperature). The diurnal forcing is not a truesine function, which can be accounted for by replacingthe upper boundary condition with the F ourier serieswhere Ai is the amplitude of harmonic i and φi isthe initial phase of harmonic i. This formula indicates that variations in the l and surface temperatureconsist of two parts: the constant T0 and n superimposed sine waves. The periods of these sine waves arep, p=2, ..., p=n, respectively, with the correspondingamplitudes A1, A2, ..., An. Here, we assume that theinitial phases φi and the soil temperature below 1-mdepth are all constants. We can then use the variable separation method to solve the heat conductionequation(Eq. (1)). This approach yieldswith . The parameters in Eq. (4)arederived by using the least squares method to find anoptimal fit to soil temperature measurements at twodepths. We can then obtain the harmonic soil heatflux formula asMiao et al. (2012)fitted harmonic models of differentorders and found that the accuracy of the second-orderharmonic model(n = 2)was already sufficient for mostpurposes. 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 Qvcaused by the verticalmovement of water through a unit area of soil per unittime can be expressed as

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 ¢T is the vertical gradient of water temperature. Using the secondlaw of thermodynamics, the soil heat balance can beexpressed aswhere ka is the thermal diffusivity(including only heatconduction) and W = can be understood as theliquid water flux density(in m s-1). Equations(1) and (7)are equiv alent when W = 0(i. e., the conductionconvection equation reduces to the traditional heat conduction equation in soils with low water content).

Gao et al. (2003)derived a first-order harmonicanalytical solution to the conduction-convection equation(Eq. (7)):

where the amplitude A M = and N = A1 and A2 are the amplitudes of soil temperature variations at the depths z1 and z2, and φ1 and φ2are the phases of soil temperature variations at depths z1 and z2 . In this work, wetake z1 = 5 cm and z2 = 20 cm.

Fan and Tang(1994)calculated the heat flux using a correlation form of the conduction-convectionmethod:

where Qt is the total heat flux, Qd is the conduction heat flux, Qw is the convective heat flux, and × W . Using Eq. (8), and

The soil heat storage calculated using eitherthe harmonic method or the conduction-convectionmethod is the difference between the soil heat fluxesat two different layers:

3. 1. 3 Temp er ature inte gr al method(TIM)

Based on the first law of thermodynamics, the integral form of one-dimensional heat conduction equation is

where G0 is the ground heat flux, Gz is the soil heatflux observed at a heat flux plate at depth z, Tz is thetemperature profile in the soil between z and the l and surface, and t is time. The soil heat storage can thenbe calculated aswhere can be approximated using a finite difference scheme. The soil heat storage can be written as3. 2 Expression of energy balance closure

We assume that the l and surface is horizontal and uniform and the atmosphere is in a steady state. Using the energy conserv ation and conversion laws and considering soil heat storage, the l and surface energybalance equation can be expressed as

where Rn is the net l and surface radiation flux, H isthe l and surface sensible heat flux, LE is the l and 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 usingthe sensible and latent heat fluxes observed near thesurface. Sensible and latent heat fluxes were observedduring the campaign in the Badan Jaran desert hinterl and and edge, but were not directly observed during the campaign at the Jinta Oasis. We use the aerodynamic method(Liu et al., 2009; Liu et al., 2010)tocalculate the sensible heat flux and latent heat fluxfrom the gradients of observ ations that were taken atthe Jinta Oasis. Rnis calculated from the radiationbalance equation aswhere Rsd is the total downward short-wave radiation reaching the surface, Rsu is the amount of shortwave radiation reflected by the l and surface, Rld is thedownward flux of long-wave radiation from the atmosphere, and Rlu is the upward flux of long-wave radiation from the l and surface. Rsd, Rsu, Rld, and Rlu have been directly observed.

Several approaches may be used to assess the imbalance in the l and surface energy budget. These different approaches may yield different results even forthe same dataset. We use an ordinary linear regression(OLR)method to analyze the imbalances in theenergy budgets calculated for the Badan Jaran deserthinterl and , Badan Jaran desert edge, and Jinta Oasis. In this method, the slope of the linear regressionbetween the quantities(H+LE) and (Rn - G - S)isused to represent the energy balance closure rate. Energy closure is accomplished if the slope of the linearregression 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 validatedagainst observ ational data. The shallow soil heat fluxwas adjusted to the l and surface energy balance and the energy balance closure rate was analyzed. Thedetailed results of this analysis are presented and discussed in the following section. 4. 1 Soil heat storage4. 1. 1 Analysis of observational data

The soil water content at 5-cm depth was smallest in the Badan Jaran desert hinterl and and largest atthe Jinta Oasis, with the Badan Jaran desert edge inbetween(Fig. 1). The surface type in the Badan Jar and esert hinterl and was s and , with a surface albedo ofapproximately 0. 33. The surface type at the BadanJaran desert edge was sparse desert reeds, with a vegetation height of about 0. 6 m and a surface albedo of0. 23(Ma et al., 2012). The most common soil typesat Jinta Oasis were irrigated silty soil, moist meadowsoil, and aeolian s and y soil. The surface was engagedas farml and . The typical crop in this area is wheat, but in mid June 2005, the primary crop was an initialgrowth of cotton. The surface albedo at Jinta Oasiswas 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 arounda soil particle increases the absorption path of solar radiation. Greater soil moisture typically correlates withsmaller albedo. The surface albedo at Jinta Oasis waslower 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.
Fig. 1. Time series of soil water content at 5-cm depth.

Figure 2 shows the soil heat fluxes observed at5- and 20-cm depths at the three sites. The observedfluxes had obvious diurnal variations. The soil heatfluxes at 5-cm depth varied substantially from day today, while the soil heat fluxes at 20-cm depth variedmuch more smoothly . The diurnal variations of soilheat fluxes at 20-cm depth had smaller peaks, smalleramplitudes, and larger phase lags than the diurnalvariations at 5-cm depth. These differences illustratethat the amplitude of soil heat flux decays with depth, while the phase becomes delayed. The soil heat flux at 5 cm cannot be used as a direct measure of theground heat flux, but must be supplemented by thesoil heat storage terms in the l and surface energy balance equation.

Fig. 2. Time series of soil heat fluxes measured at 5-cm depth (G5) and 20-cm depth (G20) at the (a) Badan Jaran desert hinterland, (b) Badan Jaran desert edge, and (c) Jinta Oasis.
4. 1. 2 Analysis of model results

Soil thermal capacity is needed to calculate soilthermal storage regardless of the numerical methodused. The soil thermal capacity at each measurement site can be obtained using the heat conduction equation. These heat capacities are 0. 69×10-6J(m3K)-1for the Badan Jaran desert hinterl and , 0. 80×10-6 J(m3K)-1for the Badan Jaran desert edge, and 0. 92×10-6J(m3K)-1for the Jinta Oasis. The HM and CM also require the soil thermaldiffusion, which is calculated according to the detailedmethod provided by Miao et al. (2012). The mainparameters for each method are listed in Tables 1-6.

Table 1. Amplitudes for the harmonic method

Table 2. Phases for the harmonic method

Table 3. Thermal diffusivity for the harmonic method

Table 4. Amplitudes for the conduction-convection method

Table 5. Phases for the conduction-convection method

Table 6. Thermal diffusivity and liquid water flux density for the conduction-convection method

Figure 3 shows soil heat storage at each site calculated using the HM, CM, and TIM methods, as well asthe measured value of soil heat storage between 5- and 20-cm depths. The soil heat storage varies substantially on the diurnal timescale. The daily variationsof soil heat storage calculated using the three methods show good agreement with the variations in themeasured values. The HM method provides the closest fit because the iterative method of calculating soilthermal diffusivity makes the fullest use of the measurements. The CM method underestimates the soilheat storage at night. This underestimate may be attributable to the error inherent in assuming the soilmoisture flux density W to be constant throughoutthe day(Dai et al., 2009). During daytime, especiallyunder fine weather conditions, soil moisture moves upward because of surface ev aporation(i. e., W > 0). Surface ev aporation abates with the decrease of surface temperature at night, so soil moisture moves fromshallow layers to deeper layers(i. e., W < 0). Ignoringthese variations in soil water flux density induceserrors in the calculated soil heat storage. The valuesof soil heat storage calculated by using the HM and CM are closer to the observed values; however, neitherof these methods is able to capture fluctuations in soilheat storage on smaller timescales. The diurnal amplitude of the soil heat storage calculated using the TIMmethod is larger, and the maxima are significantlyhigher, but the time series captures these small-scalefluctuations. A comprehensive and objective comparison of the performance of these three methods in thiscase requires a more quantitative analysis.

Fig. 3. Time series of soil heat fluxes measured at 5-cm depth (G5) and 20-cm depth (G20) at the (a) Badan Jaran desert hinterland, (b) Badan Jaran desert edge, and (c) Jinta Oasis.

Figure 4 shows scatter plots of calculated and measured values of soil heat storage for each of thethree measurement sites. At the Badan Jaran deserthinterl and site, the fitting coefficient is closest to 1 forthe HM results(0. 9409), while the correlation coeffi-cient is highest for the TIM results(0. 9297). At theBadan Jaran desert edge site, the fitting coefficientsare closer to 1 for HM(0. 9004) and CM(1. 0354), while the correlation coefficients are highest for HM(0. 9080) and TIM(0. 8934). At the Jinta Oasis site, the fittingcoefficient is closest to 1 for CM(0. 9072), while thecorrelation coefficient is highest for TIM(0. 9141). Thefitting coefficient of the HM results gradually departsfrom 1 with increasing soil water content, while the fitting coefficient of the CM result gradually approaches1 under the same conditions. This difference arises because CM considers the heat convection effects of soilwater, while the HM does not. TIM, which is based onenergy conserv ation, correlates well with the measuredvalues at all three sites; however, the fitting coefficientfor TIM is greater than 1 and the magnitude of theerror is larger. Whereas HM uses a second-order harmonic model, CM uses a true sine function to estimatesoil heat storage. This limits the accuracy of the CMcalculation, so the correlation coefficients for CM areonly 0. 48-0. 70.

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.

Three statistics are used to further illustrate thedifferences between observ ations and calculations ofsoil heat storage using the three methods: the averagedeviation(Biss), the st and ard deviation(SEE), and the relative st and ard deviation(NSEE). These statistics are defined as:

where n is the total number of samples and S and S0are the calculated and measured values of soil heatstorage, respectively . The results are listed in Table 7.
Table 7. Average deviation, standard deviation, and relative standard deviation for values of soil heat storage calculated at each site

The errors are smallest for calculations using HMfor the Badan Jaran desert hinterl and and edge sites, while TIM performs better than CM. The HM calculation is also most accurate for the Jinta Oasis site, butCM performs better than TIM in this case. Based onthese statistics, the calculation using HM is superior 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 inthe l and surface energy balance equation(Eq. (21))have been introduced in Section 3. 2. The followingsection presents an analysis of these four fluxes as observed at the measurement sites.

The accuracy of radiation observ ations has grea-tly improved over the past 10-15 years with the adventof the global surface radiation reference station network(BSRN). The four-component radiometer usedto measure the net surface radiation Rn at these experiment sites is accurate to within §5%. The errorin the observ ations is r and om. Under normal maintenance conditions, the net radiation observ ations arethe most accurate among the four energy budget components.

The turbulent fluxes H and LE were collected using eddy correlation methods. The sampling frequencywas 10-20 Hz, and the observ ations were then averaged into 30-min means. The instrument performedconsistently well during these experiments. The soil heat flux G was observed by using a soilheat flux plate at a depth of 5 cm(denoted by G5). Heat flux measurements using this instrument are gen-erally accurate to within ±3%. Errors in these observations are not a primary reason for imbalance in theobserved energy budget.

Figure 5 shows measurements of Rn, H, LE, and G5 over the 5-day measurement periods at the BadanJaran desert hinterl and and desert edge(19-23 August 2009) and at Jinta Oasis(12-16 June 2005). Allfour terms have obvious diurnal variations, with positive anomalies during daytime and negative anomaliesat night. The phase of diurnal variations in G5 lagsslightly behind the phase of diurnal variations in Rn, H, and LE; in other words, the energy fluxes are notsynchronous. We therefore need to consider the role ofsoil heat storage between the soil heat flux plate and the l and surface to close the surface energy budget.

Fig. 5. Time series of the net radiation flux at the surface (Rn), the latent (LE) and sensible (H) heat fluxes, and the soil heat flux (G5) measured at the (a) Badan Jaran desert hinterland, (b) Badan Jaran desert edge, and (c) Jinta Oasis sites.
4. 2. 2 Analysis of model results

Figure 6 shows the observed soil heat fluxes at 5-cm depth(G5) and ground heat fluxes(G0)adjustedbased on soil heat storage calculated by using the threemethods described in Section 3. 1. G0(HM)is calculated by using Eq. (5) and G0(CM)is calculated bydirectly using Eqs. (11)-(15)with the parameter values listed in Tables 3-8. F or G0(TIM), the soil heatstorage from 5-cm depth to the l and surface is calculated by using Eq. (20) and the ground heat flux iscalculated by Eq. (18). The amplitudes of the calculated ground heat fluxes are larger than the measuredsoil 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 thecalculated values match well with the observed heatfluxes. The results indicate that these three methodsprovide a reliable means of calculating soil heat storage and adjusting soil heat flux for energy balance closure.

Fig. 6. Unadjusted and adjusted soil heat fluxes at the (a) Badan Jaran desert hinterland, (b) Badan Jaran desert edge, and (c) Jinta Oasis sites. The adjusted values (G0) rely on calculations using the harmonic (HM), conductionconvection (CM), and temperature integral (TIM) methods. The unadjusted values (G5) are raw observations taken at 5-cm depth.

Table 8. Energy balance closure metrics after adjusting for soil heat storage

Figure 7 shows linear regression fits of(H+LE) and (Rn - G)using the unadjusted soil heat fluxes at5-cm depth and the ground heat fluxes adjusted usingcalculations of soil heat storage. This plot illustratesthe discrepencies from energy balance closure over thedifferent 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 energy closure rate for the Badan Jaran desert hinterl and site increases by 3. 83% when HM is used to adjustG, by 2. 94% when CM is used, and by 3. 83% whenTIM is used. The correlation coefficient also increasesby 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 siteincreases by 3. 19%, 3. 11%, and 5. 97%, respectively, while the correlation coefficient changes by 0. 0042, -0. 0145, and 0. 0335, respectively . F or this site, TIMprovides the largest improvement. The energy closure rate for the Jinta Oasis site increases by 1. 39%, 1. 49%, and 1. 74%, respectively, while the correlationcoefficient changes by 0. 007, 0. 006, and -0. 011, respectively . The differences in the results among the threemethods for this site are not significant.

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.

Overall, the energy closure rate after adjustmentis better than before adjustment. The soil heat fluxesadjusted using HM and TIM provide better closurerates 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 simulatediurnal variations in heat flux, and is therefore moreaccurate than CM(which uses first-order harmonic model).

The results summarized in Fig. 7 and Table 8illustrate that errors in the energy balance have different magnitudes over different underlying surfaces. The energy balance closure rate at the Badan Jar and esert hinterl and site is approximately 80%, while theclosure rates at the Badan Jaran desert edge and JintaOasis sites are only about 55%. Even after accountingfor soil heat storage, the energy budgets at the lattertwo sites are still far from being closed. This suggeststhat the reasons for energy imbalance may vary substantially for different underlying surfaces. In furtherresearch on energy balance closure, we must considerother factors in addition to soil heat storage. Eachunderlying surface type may have unique features thatcontribute to energy imbalance. 5. Conclusions

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

(1)The soil heat storage calculated using HM isclosest to the measured value because this methodmakes the fullest use of measurements in estimatingsoil thermal diffusivity . HM also benefits from the useof a second-order harmonic model of daily variationsin soil heat flux. CM couples heat conduction and convection; theoretically, this method should providea more accurate representation of heat transfer processes in the soil than the other methods. CM appliedin this work neglects diurnal variations in soil waterflux density, and therefore underestimates nighttime soil heat storage. CM also simulates the diurnal cycle of soil heat storage using a sine function, whichlimits the accuracy of the calculation. TIM calculatessoil heat storage based entirely on energy conserv ation laws, so the calculation is consistent with observedfluctuations; however, the diurnal amplitude is largerthan observed and the peak values are substantiallyhigher.

(2)The relative performance of each methodvaries according to the soil water content of the underlying surface. The minimum errors are achieved usingHM. Moreover, the HM calculations are the most accurate for the three surface types considered here. Theresults using TIM are better than those using CM forthe Badan Jaran desert sites, but the results usingCM are superior to those using TIM for the Jinta Oasis site.

(3)Accounting for soil heat storage in estimates ofground heat flux improves energy balance closure ratesat all three surface sites relative to unadjusted measurements collected at 5-cm depth. However, these improvements are an order of magnitude smaller than thetotal l and surface energy imbalance(0. 01-0. 05 compared to 0. 2-0. 5). The energy closure rate is especiallylow for the Badan Jaran desert edge and Jinta Oasismeasurement sites. This result indicates that soil heatstorage is just one among many factors that cause imbalance in observ ations of the energy budgets of arid and semi-arid surfaces. F uture work on this topic mustconsider other factors in addition to soil heat storage, such as vertical thermal advection within the surfacelayer. Due to data limitations, we have not discussedthese aspects in this study . We will treat them indepth as observ ational data becomes more abundantin the future.

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