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Validation of remote sensing of bare soil ground heat ux Christiaan van der Tol ITC Faculty of Geo-Information Science and Earth Observation, University of Twente, Netherlands abstract article info Article history: Received 14 April 2011 Received in revised form 2 February 2012 Accepted 5 February 2012 Available online 8 March 2012 Keywords: Ground heat ux Soil heat ux Geostationary satellite Remote sensing MSG Energy balance Ground heat ux is an important component of the energy balance in bare soils or sparsely vegetated areas. This study presents the results of a validation experiment of a remote sensing method for ground heat ux. A heat diffusion model, calibrated to local soil heat ux soil temperature prole measurements at an eddy co- variance ux station in Spain, was used to validate the remote sensing method. The high energy balance clo- sure of 93% at the site, the high correspondence of modelled temperature prole data to observations, and agreement of retrieved thermal properties with literature data gave condence in the validation target. The remote sensing method makes use of retrieved radiometric temperatures and night-time net radiation. It was applied to eld radiometry measurements over bare soil and to MSG-SEVERI data (10% of the pixel of the eld site was covered by vegetation). Despite its simplicity, the remote sensing model applied to the eld radiometry performed well (slope of the regression against the validation target: 1.00, r 2 = 0.96). Good agreement was also found between the remote sensing method applied to eld radiometry and to satellite data (slope of the regression: 0.79, r 2 = 0.89). © 2012 Elsevier Inc. All rights reserved. 1. Introduction This paper focuses on the remote sensing of ground heat ux at the terrestrial earth surface. The ground heat ux at the surface, G 0 , is dened as the rate of heat exchange between the earth surface and the soil below (W m 2 , positive in downward direction). It is one of the main terms in the surface energy balance, beside the sen- sible heat ux to the air above the surface (H) and the latent heat ux for the evaporation of water (λE). Ignoring minor terms such as respiration, photochemistry, and heat storage changes in the canopy, the surface energy balance can be approximated as: R n ¼ H þ λE þ G 0 Wm 2 ; ð1Þ where R n is the net (absorbed minus emitted) radiation. Although the ground heat ux integrated over a 24-hour period is small compared to the other three terms, it is a signicant contributor to the instanta- neous energy balance uxes. This is particularly the case in areas with little vegetation, such as deserts (Heusinkveld et al., 2004), savannahs (Grote et al., 2008), and urban and paved areas (Voogt & Oke, 2003; Weber, 2006; Weber & Kuttler, 2005). For energy balance based esti- mates of the latent heat ux or the evaporation rate, knowledge on the ground heat ux is essential. Further relevance is that ground heat ux affects soil temperature, not only on a daily but also a seasonal time scale. The strong seasonal periodicity of soil tempera- ture at higher latitudes determines the earliest date of seed germi- nation that limits the length of the growing season (Bollero et al., 1996). The role of soil ground heat ux has been studied intensively in eld studies. In the two last decades, energy ux measurement sta- tions have been established worldwide, and many of these stations show a consistent energy balance closure problem: the energy uxes to and from the earth surface do not balance (Wilson et al., 2002). One of the obvious suspected causes of this lack of energy balance clo- sure was the estimation of ground heat ux. Although it became clear that an underestimate of ground heat ux could only partly explain the observed energy imbalance (Foken, 2008), it lead to careful con- sideration of a correct experimental setup. This includes taking care of close contact between heat ux plates and the soil, limiting the disturbance of the natural moisture and temperature prole, and using both temperature sensors (topsoil) and heat ux plate mea- surements (several cm deep) in the experimental design (Liebethal et al., 2005). Ground heat ux can locally be estimated accurately with eld in- strumentation in conjunction with a physical model that describes ground heat ux as a function of thermal properties of the soil. The representativeness of these measurements is a problem as ground heat ux may show signicant spatial variation due to differences in topography, soil characteristics and vegetation cover (Kustas et al., 2000). Remote sensing is an attractive tool to solve this problem, as it could provide estimates of ground heat ux representative to larger spatial scales. However, remote sensing products of ground heat ux are not operationally available yet. In most remote sensing energy Remote Sensing of Environment 121 (2012) 275286 Tel.: +31 53 4874282. E-mail address: [email protected]. 0034-4257/$ see front matter © 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.rse.2012.02.009 Contents lists available at SciVerse ScienceDirect Remote Sensing of Environment journal homepage: www.elsevier.com/locate/rse

Validation of remote sensing of bare soil ground heat flux

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Page 1: Validation of remote sensing of bare soil ground heat flux

Remote Sensing of Environment 121 (2012) 275–286

Contents lists available at SciVerse ScienceDirect

Remote Sensing of Environment

j ourna l homepage: www.e lsev ie r .com/ locate / rse

Validation of remote sensing of bare soil ground heat flux

Christiaan van der Tol ⁎ITC Faculty of Geo-Information Science and Earth Observation, University of Twente, Netherlands

⁎ Tel.: +31 53 4874282.E-mail address: [email protected].

0034-4257/$ – see front matter © 2012 Elsevier Inc. Alldoi:10.1016/j.rse.2012.02.009

a b s t r a c t

a r t i c l e i n f o

Article history:Received 14 April 2011Received in revised form 2 February 2012Accepted 5 February 2012Available online 8 March 2012

Keywords:Ground heat fluxSoil heat fluxGeostationary satelliteRemote sensingMSGEnergy balance

Ground heat flux is an important component of the energy balance in bare soils or sparsely vegetated areas.This study presents the results of a validation experiment of a remote sensing method for ground heat flux. Aheat diffusion model, calibrated to local soil heat flux soil temperature profile measurements at an eddy co-variance flux station in Spain, was used to validate the remote sensing method. The high energy balance clo-sure of 93% at the site, the high correspondence of modelled temperature profile data to observations, andagreement of retrieved thermal properties with literature data gave confidence in the validation target.The remote sensing method makes use of retrieved radiometric temperatures and night-time net radiation.It was applied to field radiometry measurements over bare soil and to MSG-SEVERI data (10% of the pixelof the field site was covered by vegetation). Despite its simplicity, the remote sensing model applied to thefield radiometry performed well (slope of the regression against the validation target: 1.00, r2=0.96).Good agreement was also found between the remote sensingmethod applied to field radiometry and to satellitedata (slope of the regression: 0.79, r2=0.89).

© 2012 Elsevier Inc. All rights reserved.

1. Introduction

This paper focuses on the remote sensing of ground heat flux atthe terrestrial earth surface. The ground heat flux at the surface, G0,is defined as the rate of heat exchange between the earth surfaceand the soil below (Wm−2, positive in downward direction). It isone of the main terms in the surface energy balance, beside the sen-sible heat flux to the air above the surface (H) and the latent heatflux for the evaporation of water (λE). Ignoring minor terms such asrespiration, photochemistry, and heat storage changes in the canopy,the surface energy balance can be approximated as:

Rn ¼ H þ λE þ G0 W m−2� �

; ð1Þ

where Rn is the net (absorbed minus emitted) radiation. Although theground heat flux integrated over a 24-hour period is small comparedto the other three terms, it is a significant contributor to the instanta-neous energy balance fluxes. This is particularly the case in areas withlittle vegetation, such as deserts (Heusinkveld et al., 2004), savannahs(Grote et al., 2008), and urban and paved areas (Voogt & Oke, 2003;Weber, 2006; Weber & Kuttler, 2005). For energy balance based esti-mates of the latent heat flux or the evaporation rate, knowledge onthe ground heat flux is essential. Further relevance is that groundheat flux affects soil temperature, not only on a daily but also a

rights reserved.

seasonal time scale. The strong seasonal periodicity of soil tempera-ture at higher latitudes determines the earliest date of seed germi-nation that limits the length of the growing season (Bollero et al.,1996).

The role of soil ground heat flux has been studied intensively infield studies. In the two last decades, energy flux measurement sta-tions have been established worldwide, and many of these stationsshow a consistent ‘energy balance closure problem’: the energy fluxesto and from the earth surface do not balance (Wilson et al., 2002).One of the obvious suspected causes of this lack of energy balance clo-sure was the estimation of ground heat flux. Although it became clearthat an underestimate of ground heat flux could only partly explainthe observed energy imbalance (Foken, 2008), it lead to careful con-sideration of a correct experimental setup. This includes taking careof close contact between heat flux plates and the soil, limiting thedisturbance of the natural moisture and temperature profile, andusing both temperature sensors (topsoil) and heat flux plate mea-surements (several cm deep) in the experimental design (Liebethalet al., 2005).

Ground heat flux can locally be estimated accurately with field in-strumentation in conjunction with a physical model that describesground heat flux as a function of thermal properties of the soil. Therepresentativeness of these measurements is a problem as groundheat flux may show significant spatial variation due to differences intopography, soil characteristics and vegetation cover (Kustas et al.,2000). Remote sensing is an attractive tool to solve this problem, asit could provide estimates of ground heat flux representative to largerspatial scales. However, remote sensing products of ground heat fluxare not operationally available yet. In most remote sensing energy

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276 C. van der Tol / Remote Sensing of Environment 121 (2012) 275–286

balance models for the calculation of evaporation, the ground heatterm is even neglected on a daily (24-hour) basis, and simple NDVI-based estimates are used for the instantaneous ratio of G0/Rn(Kalma et al., 2008; Kustas & Daughtry, 1990).

The main problem is that, while field-based estimates of groundheat flux make use of temperature measurements at different depthsin the soil, remote sensing only provides the surface temperature. Theuse of surface temperature has several disadvantages. First, the re-mote observations comprise both soil and vegetation temperatures,but for ground heat flux only the soil surface temperature is relevant.For this reason, separation of vegetation and soil skin temperatures isnecessary (see e.g. Jia et al., 2003). Second, contrary to most modelconceptualizations (discussed in Section 2), the soil–air interface isnot smooth, but rough. As a result, radiation may penetrate the soilstructure. Moreover, steep vertical gradients of bulk density, textureand soil moisture dominate the upper millimetres of the soil, result-ing in steep gradients of thermal properties. These effects conflictwith the commonly used assumption of an abrupt soil–air interface,with constant soil thermal properties in the vertical direction. Thusthe models may insufficiently reflect reality in the topsoil. Third,evaporation, condensation, melting and freezing may take place inthe upper few centimetres of soil (Cahill & Parlange, 1998; Holmeset al., 2008). The evaporation and subsequent diffusion of water va-pour to atmosphere through soil pores form a sink of latent heat. Itis mathematically possible to account for this loss by introducing asink term into the model (Rutten et al., 2010), but in practice the la-tent heat loss cannot be distinguished from the ground heat flux un-less vertical temperature profile data are available.

Despite these difficulties, several thermal remote sensing ap-proaches for ground heat flux in bare soils have been developed(Bennett et al., 2008; Tsuang, 2005; Verhoef, 2004). Murray andVerhoef (2007a,b) and Graham et al. (2010) resolved the problemof the temperature separation and developed techniques for estima-tion of ground heat flux below vegetation. Use was made of the factthat not the absolute temperature, but the amplitudes and phases ofthe variations are relevant. The methodology by Murray andVerhoef (2007a,b) has further been used to successfully derive spa-tially distributed ground heat flux measurements over SouthwestNiger using geostationary land surface temperature data of MSG-SEVERI (Verhoef et al., 2012). Surface temperature anomalies havealso been used for the detection of landmines using high-resolutionaerial images (Maathuis & Van Genderen, 2004), and the detectionof shallow groundwater using satellite thermal remote sensing(Alkhaier et al., 2001).

In this paper a remote sensing approach similar to Verhoef (2004)is applied to MSG-SEVERI data. The aim of this paper is to validate theremote sensing approach for the estimation of ground heat flux datafrom MSG-SEVERI using field data. In this way the error remainingafter calibration, caused by the model simplifications, can beevaluated.

Local temperature profile and energy balance data, collected at aneddy covariance tower in a sparsely vegetated, semi-arid area inSpain, are used to establish a validation target for the remote sensingapproach. The sparse vegetation, the homogeneous land cover andthe relatively long cloud-free periods made the site made a perfect lo-cation for a ground heat flux study. The remote sensing approach isapplied to both field radiometry and MSG-SEVERI data, thus makingit possible to focus both on the technique itself and on the effects ofcloud contamination and the representativeness of the satellitemeasurements.

2. Theoretical background

Heat flux into the ground is usually viewed as vertical heat diffu-sion from a horizontal plane source (the soil surface) into a homoge-neous medium of infinite depth (the soil). This general heat flux can

be described by two equations: the continuity equation for verticalheat transfer (Eq. 2) and the heat diffusion equation (Eq. 3):

cv∂T z; tð Þ

∂t ¼ −∂G z; tð Þ∂z ; ð2Þ

G z; tð Þ ¼ −λs∂T z; tð Þ

∂z ; ð3Þ

where T is soil temperature (°C or K), z is the depth into the soil (m,positive in downward direction), t is time (s), cv the volumetric heatcapacity (J m−3 K−1), G the ground heat flux at any depth (Wm−2)and λs the thermal conductivity of the soil (J m−1 s−1 K−1). CombiningEqs. (2) and (3) yields the general heat convection-diffusion equation(e.g. James, 1952; Tarara & Ham, 1997; Van Wijk & De Vries, 1963):

∂T∂t ¼ D

∂2T∂z2

; ð4Þ

where D=λs/cv is the heat diffusivity of soil (m2 s−1). Because groundheat flux has a strong periodic nature forced by solar radiation, sinoidalfunctions are chosen as boundary conditions to Eq. (4). A general solu-tion for periodic boundary conditions is:

T z; tð Þ ¼ Ak exp Kzþ i Kzþωktð Þð Þ þ Bk exp −Kz−i Kz−ωktð Þð Þ: ð5Þ

In this equation, ω=(2π/N) is the radial frequency (s−1), N is thelength of the time series (s), i is the imaginary unit, K ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikω= 2Dð Þ

p, A

and B are integration coefficients (°C or K), and k is an integer in thedomain [0,∞]. For N, a period covering a complete cycle of solar radi-ation, such as a full day or a full year, is commonly used. Similar toearlier studies (Heusinkveld et al., 2004; Verhoef, 2004), only thereal part of the first n+1 solutions (n harmonics plus the mean tem-perature, k=1) is selected from Eq. (5) and summed up in the formof a Fourier composition:

T z; tð Þ ¼Xnk¼0

Ak sin ωkt−Kzð Þ þ Bk cos ωkt−Kzð Þð Þ exp −Kzð Þ: ð6Þ

Eq. (6) is used in the literature (e.g. Verhoef, 2004) as a solutionfor the soil temperature as a function of time and depth: periodicforcing by solar radiation at z=0 causes a temperature wave thatpropagates downward with an exponential decay in amplitude andan increasing time lag.

With Eq. (6) one can reconstruct the temperature time series atany depth analytically. The ground heat flux G is consequently solvedfrom either Eq. (2) or Eq. (3). If Eq. (3) is used, then one needs to es-timate λs, either from a model (e.g. Lu et al., 2007), or from a mea-sured ground heat flux time series by calibration, after which theheat flux at the surface G0 is calculated as G(0,t). If Eq. (2) is used,then the ground heat flux is calculated by integration of observedheat storage changes over depth:

Gz ¼ cv ∫∞

s¼z

∂T∂t ds: ð7Þ

Because the depth over which soil temperature and heat capacitycan be measured is finite, this method is commonly used in conjunc-tion with a flux bottom boundary condition at zb (e.g. Sauer et al.,2003; Weber, 2006). The heat flux at the surface is calculated as:

G0 ¼ Gzbþ cv ∫

zb

s¼0

∂T∂t ds: ð8Þ

If temperature is measured in a profile, then a numerically discreteform of the integration (i.e. discrete steps ds) is used. The volumetric

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heat capacity cv can be estimated as a function of bulk density, textureand soil moisture with a model (Van Wijk & De Vries, 1963).

Both methods require temperature measurements in the soil,preferably at multiple depths for estimating the diffusivity (Horton&Wierenga, 1983). These data may be available at dedicated researchsites, but they cannot be obtained through remote sensing. An ex-pression for the ground heat flux at the surface as a function of radio-metric surface temperature is obtained by combining Eqs. (3) and (6)(Verhoef, 2004):

G0 tð Þ ¼ ΓXnk¼0

ffiffiffiffiffiffiffiffiffiffiffiffikω=2

qAk−Bkð Þ sin ωktð Þ þ Ak þ Bkð Þ cos ωktð Þð Þ; ð9Þ

where Γ ¼ cv⋅ffiffiffiffiD

pis the thermal inertia of the soil (J m−2 K−1 s−1/2).

In the literature, an alternative way to obtain Eq. (9) can be found aswell, in which the right hand side of Eq. (4) is expressed as a half-order time derivative of temperature (Bennett et al., 2008; Wang &Bras, 1999). The thermal inertia can be calculated using models(Murray & Verhoef, 2007a,b) or by calibration against night timemeasurements of net radiation, assuming that during windless nights,ground heat flux equals net radiation (see e.g. Price, 1977, 1985;Verhoef, 2004).

In this research, Eqs. (2) and (3) were both used to obtain field es-timates of ground heat flux as a function of time and depth. The heatflux at the surface obtained in this way was used to validate the re-mote sensing implementation of Eq. (9), as outlined in Section 6.

3. Site description

The experimental site (Fig. 1) is located in the gently undulating,80-km2 sized Sardon River catchment in the Castilla y León provincein the West of Spain (located between 41°02′ and 41°09′ N, and 6°06′and 6°14′ W). The elevation of the catchment ranges from 740 to840 m above mean sea level. The geology is dominated by fracturedgranite rock, covered with a few decimetres (on the slopes) to a fewmetres (in the valleys) of weathered material and poorly developedloamy sand (Lubczynski & Gurwin, 2005), with a composition of21% gravel, 62% clay, 12% silt and 5% clay. Analysis of 16 ring samplesshowed that the soil, except in the riverbed, was rather homogeneouswith a mean porosity of 0.443 (standard deviation 0.005), and meanbulk density of 1480 kg m−3 (standard deviation 10 kg m−3)(Cisneros, 2011). The land is extensively used for cattle grazing. The

Fig. 1. Left: true colour Quickbird image (bands 3, 2, 1 as RGB) of the study site in Sardon, Swith flux source density for windy (4.1 m s−1), unstable conditions (z/L=−0.166) observeof metres. The (fire) colour intensity resembles the relative contribution of the area to the othe tower (accessed December 2011). The location of the tower is indicated by the circle.

land cover consists of sparsely distributed broad-leafed deciduousoak trees (Quercus ilex and Quercus pyrenaica) covering 10% of thearea, some annually pruned by farmers to reduce water losses. Theheight of the trees range from 4 to 6 m; some taller trees (up to10 m) are found close to the riverbed. Furthermore, the shrub ScotchBroom (Cytisus scoparius) is present, and in the spring (March–May),grasses sprout, which turn brown for lack of water and disappear as aresult of cattle grazing by early June.

The annual rainfall in the area is about 500 mm, and the potentialevapotranspiration 1800 mm y−1 (Lubczynski & Gurwin, 2005). Fluxtower estimates of actual evapotranspiration ranged from 0.2 mm d−1

in September to 3.5 mm d−1 in April.

4. Field instrumentation

A 10-m tall reticulated tower was erected on 10 June 2009, sup-porting a range of equipment to measure the energy balance and car-bon dioxide fluxes (Fig. 2). The tower is positioned on a slightlyelevated point in the landscape (41°07′02″N, 6°08′49″W), in thenorthern part of the catchment, 270 m east of the Sardon River. Thelocal topographic slope is 2°. The land cover of sparse oak trees (seeSection 3) stretches for 6 km to the north, 2.5 km to the east, 30 kmto the south and 4.5 km to the west. The slightly elevated positionof the site (744 m amsl, 5 m above the river valley) in combinationwith the height of the tower made that the instrumentation was lo-cated well above the trees (Fig. 2). A footprint analysis followingHsieh et al. (2000) in combination with Detto et al. (2006) (for thelateral component) and another following Kljun et al. (2004) showedthat in typical wind conditions, 80% of the turbulent heat fluxes pick-ed up by the instruments originates from an area with a radius of600 m around the tower (Rwasoka, 2010). No shrubs or trees werepresent in a radius of 17 m surrounding the tower (Fig. 1), such thatthe downward pointing radiometer and the soil contact measure-ments presented below concern bare soil. The turbulence measure-ments are thus inevitably representative for a larger area than thesoil profile measurements.

The site was fenced for protection against cattle, but great carewas taken to limit the disturbance of the radiometer measurements.A total of 8 adjustable guy lines ensure stability of the tower andkeep the equipment level. At the top of the tower, a CNR1 four com-ponent radiometer (Kipp and Zonen, Delft, The Netherlands), aCSAT3 sonic anemometer (Campbell Scientific Inc., Utah, USA) and a

pain, acquired on 9 August 2009, showing the location of the eddy flux tower overlaind at solar noon (GMT) of 26 September 2010. Coordinates are in UTM and have the unitbserved sensible heat flux. Right: a Google Earth aerial overview of the surroundings of

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Fig. 2. View from the tower taken in different azimuth directions (top), photograph of the flux tower (bottom left), and some of the instrumentation (bottom right).

278 C. van der Tol / Remote Sensing of Environment 121 (2012) 275–286

LI7500 gas analyser (Licor Biosciences, Nebraska, USA) recording at10 Hz, and a WXT520 ‘multi weather sensor’ (Vaisala Oyj, Helsinki,Finland) were mounted. The multi weather sensor provided windspeed and direction, air temperature and humidity, rainfall and hailrate, and air pressure. At a distance of 1 m south of the tower, a HFP01heat flux plate (Hukseflux, The Netherlands) was buried 10 cm depth.Two other heat flux plates were buried at 1 cm depth, but the data ofthese sensors were later discarded as it was recognized that flux platesinstalled close to the surface disturb the natural energy and soil waterflow. In addition, two TCAV-L average temperature sensors (CampbellSci.) were installed at 2 and 7 cmdepth in the soil, at several decimetresfrom the heat flux plates. Each sensor consists of four small probeswhichwere installed ~7 cm apart, at the samedepth, of which the aver-age temperature was recorded. All equipment was connected to aCR5000 datalogger (Campbell Sci.). After a start-up period, the equip-ment has been operational since August 2009, with a two-month inter-ruption in the winter of 2009–2010. The software AltEddy (www.climatexchange.nl/projects/alteddy/) of the Alterra institute (Wagenin-gen University, The Netherlands) was used to process 30-minute inter-val turbulent heat fluxes. The following corrections were carried out:2-D axis rotation (Moore, 1986), Webb correction (Webb et al.,1980), spike detection and removal, frequency response correctionand Burba's correction for the instrument temperature (Burba etal., 2008). Only data with steady state conditions and well developedturbulence were used, following a procedure described by Foken etal. (2004) (Eqs. (9.6) and (9.9) therein).

On 12 September 2010 a more detailed soil temperature profilewas installed consisting of 11 calibrated HOBO TMC termistors(10kΩ NTC's) connected to three HOBO4 dataloggers (Onset, USA),recording at 10 minute intervals. Ten sensors were inserted in tight,horizontal holes drilled at 1, 2, 3, 4, 5, 6, 8, 10, 12.5 and 15 cm depthin an excavated pit close to the heat flux plates. The full width ofthe pit of 25 cm was used, and the sensors were placed at horizontaldistances of 5–20 cm in order to limit the disturbance of the soil pro-file by the presence of sensors. One sensor was fixed on the surfaceand covered with soil dust only. Because of the relative large size ofthe sensors (0.5×2.5 cm), direct radiation effects on the soil surfacesensor could not be eliminated entirely. The sensors delivered continu-ous data between 24 September and 7 December 2010. The data fromthe deepest sensor, at 15 cmdepth, were discarded due tomalfunction-ing of the sensor. The overlapping period with both high quality turbu-lence data and detailed soil temperature profile measurements was24 September to 4 October 2010. At a distance of 100 m west of theflux tower, soil moisture measurements were carried out at severaldepths.

5. Satellite data collection

Five MeteoSat Second Generation (MSG) products, notably albedo(α), incoming shortwave radiation (Rsi, in Wm−2), incoming long-wave radiation (Rli, in Wm−2), land surface temperature (LST, in°C) and emissivity, were downloaded from LSA SAF (http://landsaf.meteo.pt/), for 5 May to 17 August 2010, thus covering relativelywet and dry conditions. The products have a spatial resolution of3×3 km, and a temporal resolution of 15 min (Geiger et al., 2008b),except for albedo and emissivity, which have a daily resolution(Geiger et al., 2008a). It should be noted that the emissivity productis still an internal product that is not fully operational yet. The productsare corrected for the effects of atmospheric water vapour (ECMWF) andozone concentration (TOMS). The incoming shortwave radiation (0.3–4.0 μm) is calculated from top-of-canopy albedo and radiative transfermodels for clear and cloudy conditions separately. The incoming long-wave radiation (4.0–100 μm) is calculated with the model of Josey etal. (2003), using forecasts of 2 m temperature, 2 m dew point tempera-ture and total columnwater vapour (ECMWF), cloudmask and effectivecloudiness as input. In this study, the broadband bi-hemisphericalproduct was used for albedo, calculated with BRDF models for thesolar noon. The land surface temperature product is calculated witha split window algorithm.

6. Methodology

6.1. Temperature profile method

The heat diffusivity model was calibrated using temperature pro-file measurements for the period between 25 September and 4 Octo-ber 2010. The coefficients Ak and Bk for this period were calculated byFourier decomposition of the measurements at 8 cm depth (see Ap-pendix A). For n (the number of harmonics) a sixth of the numberof measurements in the time series, rounded of to the nearest integerbelow (i.e. 8 per day) was used; this makes it possible to capturehigh-frequency variations in temperature while maintaining an ac-ceptable computation time. The diffusivity D was subsequently calcu-lated by minimizing the sum of the least square differences betweensimulated and measured temperatures at all other depths, resultingin a single, profile-averaged value for D. The surface temperaturewas excluded from this analysis due to susceptibility to measurementerrors and model flaws close to the surface. This procedure is differ-ent from earlier studies where the Arctangent method was used(e.g. Verhoef et al., 1996). The current method allows fitting the tem-perature time series to all data points at all depths simultaneously.

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The thermal diffusivity λs was solved from Eq. (3) by linear regres-sion of the measured ground heat flux at 10 cm depth against themodelled vertical gradient at this depth. Finally, the ground heatflux was calculated by extrapolation of the calibrated model to thesurface.

For comparison, the ground heat flux at the surface was also calcu-lated by integration of heat storage changes over the upper 10 cm ofthe soil with a numerically discrete version of Eq. (8):

G0 tð Þ ¼ G0:1 tð Þ þ cvXMi¼1

∂T∂t Δzi; ð10Þ

where i refers to the sensor at depth zi, M is the number of sensors inthe profile, and Δzi is the corresponding representative depth inter-val, estimated as the half of the distance between the sensor aboveand below sensor i. It should be noted that the individual Δzi valuesare sensitive to inaccuracies in measurement depth due to the smalldistances between the sensors of 1 to 2 cm. The temperature gradientover time (∂T/∂ t), was calculated by Fourier decomposition of themeasurements at each depth separately (once including, and once ex-cluding the surface temperature) and differentiating analytically to t.The volumetric heat capacity of the soil, cv, was subsequently calcu-lated as the ratio of diffusivity over thermal conductivity, and forG0.1 the measured heat flux at 10 cm depth was used.

These two approaches, the analytical using Eq. (3) and the numeri-cal integration using Eq. (10), are expected to yield similar results asboth the data and the underlying model are identical. The only differ-ence is in the way the data are handled: in the numerical method, thetemperature series at each depth is used separately, while in the analyti-cal method themodel is fitted to themeasurements at all depths simul-taneously. By fitting the model at once, misplaced sensors or erroneousmeasurements can easily be identified by a large deviation from themodelled time series.

The relatively short period time series of ground heat flux calculatedfrom the temperature profile data was extended by using the (long-term) measurements of temperature at two depths. As it is difficult tomaintain the depth of the sensors for a long period of time, the actualdepths of these sensors, one year after installation, were re-calculatedby comparison with the model that was calibrated with the tempera-ture profile data. The depths at which the modelled temperature timeseries resembled the observations best were used. These depths werecalculated by searching the smallest mean square difference betweenmodelled and observed temperatures. The temperatures at the two(recalculated) depths were finally used to estimate ground heat fluxfor the entire time series of flux tower data for the year 2010 by Fourierdecomposition at one depth and calculation of D by using the seconddepth. It is acknowledged that the longer time series may suffer frompossible drift in the measurement depths as a result of wind and rainsplash erosion.

6.2. Energy balance residual method

Ground heat flux was solved as the residual of the surface energybalance (Eq. 1), making use of the measurements of the other compo-nents with the flux tower. The energy balance provides an indepen-dent means of assessing the ground heat flux. Applying this methodis in fact a test of the measurement setup including the turbulentheat fluxes, as errors in these fluxes propagate into the ground heatflux estimate. In the energy balance, heat storage in the air betweenthe ground and the height of the eddy covariance system (10 m)are neglected, as well as horizontal advection of heat, and otherminor energy sinks and sources such as soil respiration.

6.3. Remote sensing method

Fourier decomposition was applied to the radiometric surfacetemperature measurements, and Eq. (9) was used to calculate groundheat flux at the surface. The radiometric surface temperature was cal-culated from measured longwave radiation using Stefan–Boltzmann'sequation. The emissivity was calculated for 25 September to 4 Octo-ber 2010 by minimizing the quadratic error between observed andestimated upward longwave radiation, Rlo (W m−2). The estimatedRlo was computed as:

Rlo ¼ 1−εð ÞRli þ εσT40; ð13Þ

where Rli is the incoming longwave radiation (Wm−2), σ is Stefan–Boltzmann's constant (5.67 ∙108 W m−2 K−4) and T0 surface temper-ature (K). For T0 , the measured as well as the modelled surface tem-perature derived from the soil profile were used, and the resultscompared. It was further assumed that the calculated emissivity wasvalid for the entire year 2010. The thermal inertia Γ was calibratedagainst night time net radiation, assuming that ground heat flux duringthe night equals net radiation (or: assuming that sensible plus latentheat fluxwere negligible). The fieldmeasurements showed that this as-sumption is reasonable, although it is acknowledged that eddy covari-ance measurements during stable conditions (at night time) can beuncertain. This procedure is similar to Verhoef (2004), but here, allavailable measurements during the night were included in the calibra-tion procedure, which was carried out by minimizing the sum of thesquare error between all data points of modelled ground heat flux andmeasured night time net radiation (Appendix A). The calculation wascarried out for individual days separately, thus resulting in one valuefor Γ per day. Days were defined as the period between sunsets ratherthan between midnights.

The procedure was repeated for the satellite remote sensing data.The data from the pixel of interest (the pixel of the tower) wereextracted for each image. Outgoing long wave radiation was calculatedfrom LST and emissivity with Stefan–Boltzmann's equation. Net radia-tion was calculated from the radiation balance:

Rn ¼ 1−αð ÞRsi þ Rli−Rlo ð14Þ

where α is the broadband albedo, and Rsi incoming shortwave radiation(Wm−2). The components of the radiation balance were compared tofield measurements individually. Gaps in the data caused by cloud con-tamination caused difficulties in retrieving the thermal inertia for somenights. For nightswith less than 7 cloud-free images, the thermal inertiaof the previous day was used. The threshold of 7 was chosen afterseveral tests of artificially decreasing the number of night-time datapoints and evaluating the quality of the retrieval. In an operationalmode, this procedure could be replaced by a more quantitative data as-similation algorithm.

7. Results and discussion

7.1. Temperature profile method

The individual fluxes for an example day and the energy balanceclosure of the flux tower data are shown in Fig. 3 for illustration pur-pose. The ground heat flux in this figure was calculated with the ana-lytical heat profile method. The left panel shows the observed diurnalcycle of the energy balance fluxes for a typical clear sky day in Sep-tember 2010. The ground heat flux at midday consumes 45% of net ra-diation, while latent heat flux consumes less than 15%. The right panelof Fig. 3 shows the energy balance closure for the period for which thesoil temperature profile measurements overlapped with the fluxtower measurements (25 September to 4 October 2010). The closurewas 93% during this period (r2=0.98). The energy balance closure for

Page 6: Validation of remote sensing of bare soil ground heat flux

0 6 12 18 0−100

0

100

200

300

400

500

time(hours)

Flu

x (W

m−

2)

Rn

H

λEG0

0 200 400 600

0

200

400

600

Rn (W m−2)

λE +

H +

G0 (

W m

−2)

y = 0.931 x

r2 = 0.98

Fig. 3. Left: diurnal cycle of net radiation Rn, sensible heat flux (H), latent heat flux (λE) and ground heat flux (G0, analytical model calibrated to the temperature profile data) mea-sured at the flux tower on 29 September 2010 versus time of the day (GMT). Right: a scatter plot of sensible, latent heat and ground heat flux versus net radiation for 25 Septemberto 4 October 2010. The 1:1 line, a linear regression line forced through the origin and the coefficient of determination are given in the graph.

280 C. van der Tol / Remote Sensing of Environment 121 (2012) 275–286

the measurement period from 31 January to 4 October 2010, thus in-cluding the extended ground heat flux time series calculated fromtemperature measurements at two depths only, was 88% (r2=0.95)(not shown).

The model results for temperature are illustrated in Fig. 4, show-ing the diurnal cycle of measured (symbols) and modelled tempera-ture (lines) for different depths on 28 September 2010. For 8 cmdepth, the modelled temperatures follow the measurements accu-rately, as these measurements were subjected to Fourier decomposi-tion. The model accurately reproduced the temperature series at theother depths too, except for the temperatures at the surface and at1 cm depth. For all other depths, the differences between the mea-sured and modelled values at one depth were smaller than the differ-ences between the measurements of two adjoining sensors, indicatingthat the error in the installation depthwas less than 1 cm. This was alsothe case when the data of any other depth (instead of 8 cm) were usedas a starting point for the Fourier decomposition.

At the surface and at 1 cm depth, the model may insufficientlyrepresent the actual physical processes, as discussed earlier. The sur-face at the field site was rather rough due to the presence of 21% ofgravel. The 1-week average temperature appeared to consistently in-crease with depth-typical for early autumn conditions-, but the ob-served surface temperature did not follow this trend: it was higher

0 6 12 18 0

10

20

30

400 cm

0 6 12 18 0

10

20

30

401 cm

0 6

10

20

30

402 cm

0 6 12 18 0

10

20

30

40

Time (hrs)

T(o C

) T

(o C)

5 cm

0 6 12 18 0

10

20

30

40

Time (hrs)

6 cm

0 6

10

20

30

40

Tim

8 cm

Fig. 4. Diurnal cycles of measured and simulated temperatures in the temperature profile foposition. All depths except the surface temperature were used in the calibration of the diff

than the average temperature at 1 cm depth. This raised the questionwhether the different albedo of the surface sensor may have causedthe sensor temperature to deviate from the temperature of the sur-rounding soil, although this effect was minimized by covering thesensor with fine dust. For these reasons, the surface temperaturewas excluded from the calibration data set. A separate test revealedthat including the surface temperature would result in significant de-viations of model and measurements for all depths (not shown).

The calibration resulted in a diffusivity of 0.57 ∙10−6 m2 s−1, heatcapacity cv of 1.80 ∙106 J m−3 K−1, and a thermal conductivity of1.03 Wm−1 K−1. A comparison with experimental data reportedelsewhere shows that these values are realistic. For example,Ochsner et al. (2001) observed similar values for these three param-eters for sandy loam at a soil moisture content of about 20%. Invertinga simple model of VanWijk and De Vries (1963) for heat capacity as afunction of soil moisture yields a similar soil moisture content of 17%.Verhoef et al. (1996) observed values ranging from 0.4⋅10−6 to1.5 ∙10−6 m2 s−1 for diffusivity and 0.5 to 1.5 Wm−1 K−1 for ther-mal conductivity of a bare soil in the Sahel. These ranges corre-sponded to dry (low values) to relatively wet conditions (highvalues). The values also agree with values reported by Verhoef(2004) for a sandy loam soil in England during the dryer part of theyear.

12 18 0 0 6 12 18 0

10

20

30

403 cm

0 6 12 18 0

10

20

30

404 cm

12 18 0

e (hrs)

0 6 12 18 0

10

20

30

40

Time (hrs)

10 cm

0 6 12 18 0

10

20

30

40

Time (hrs)

12.5 cm

r 28 September 2010 (GMT). The data for 8 cm depth were used for the Fourier decom-usivity D.

Page 7: Validation of remote sensing of bare soil ground heat flux

0 6 12 18 0 6 12 18 0 6 12 18 0

−100

0

100

200

300

time (hours)

G0

(W m

−2 )

G0

G0, remote, field radiometer

G0 energy balance

Fig. 5. Ground heat flux estimated with the temperature profile approach, the energybalance residual and the remote sensing measurements versus time (GMT), usingflux tower and temperature profile data for three consecutive days (27, 28 and 29 Sep-tember 2010).

281C. van der Tol / Remote Sensing of Environment 121 (2012) 275–286

The results of the two different approaches for the temperatureprofile based G (analytical using Eq. (3) and numerical usingEq. (10)) agreed well (G0,numerical=1.012⋅G0,analytical, r2=0.996),confirming the consistency of the model and measurements. In thefollowing, the results of the analytical model are used exclusively.

The re-calculation of the depths of the earlier installed sensors at 2and 7 cmdepth resulted in a best fit betweenmodel andmeasurementsat a depth of 5.2 and 8.1 cm, respectively. These rather significant devi-ations are possibly the result of changes in the micro-topography afterrainfall in winter or wind deposition. After recalculation of the depths,the estimates of G based on the two depths only correlated well withthe estimates based on the complete profile (G0, 2 depths=0.977 G0,profile,r2=0.934).

7.2. Remote sensing method with field radiometer data

For the remote sensing method it was necessary to first calculatethe emissivity. The emissivity estimated from simulated and the mea-sured contact surface temperature, T0, resulted in ε=0.905 andε=0.833, respectively. In the calculations hereon, ε=0.905 as calcu-lated from the simulated temperature measurements was used. Thisvalue is in agreement with earlier reported values for bare soil ther-mal emissivity (e.g. Schmugge et al., 1998; Ten Berge, 1990). Becausethe ground heat flux is a function of the daily amplitudes rather thanthe absolute values, it showed low sensitivity to emissivity within the

−100 0 100 200 300

−100

0

100

200

300

G0,ground

Rn−

H−

λE

y = 1.11 x

r2 = 0.93

n = 177

RMSE = 32 W m−2

Fig. 6. Scatter plots of half-hourly ground heat flux estimated with the energy balance and th(G0, ground), for 25 September to 4 October 2010.

range of 0.8 to 1.0. Fig. 5 shows for three typical example days (27 to30 September 2010) the ground heat flux calculated with the ground(profile) method, the energy balance residual and the remote sensingmethod, and Fig. 6 presents the results for 25 September to 4 Octoberin scatter plots. One may expect that the problems with the surfacetemperature illustrated in Fig. 4 propagate into the remote sensingmethod. However, the remote sensing method agrees remarkablywell with the other methods, despite uncertainly in the model con-cept for the surface, uncertainty in the emissivity and the assumptionthat measured night time net radiation equals ground heat flux. Theoverall correspondence between the profile and the remote sensingmethods was rather good (G0,remote=1.00 ∙G0,ground, r2=0.96 for thedetailed profile – Fig. 4-, and G0,remote=0.85 ∙G0,ground and r2=0.91for entire 2010 – not shown-).

7.3. Comparison with the energy balance residual

The ground profile method matches well with the energy balanceresidual method (Fig. 6), despite the difference in representative areabetween turbulent fluxes and ground measurements. The satellitemeasurements are representative to an area that is similar to that ofthe eddy flux tower footprint. Kustas et al. (2000) studied the spatialvariation of ground heat flux at the scale of metres for a sand dunearea, and found large spatial differences of up to 300Wm–2 for sensorsplaced on slopes of different aspect and areas with different vegetationcover. The land cover and topography in the present study were morehomogeneous and the vegetation cover fraction ismuch lower. Soil tex-turewas homogeneous except for the river beds. Consequently, the spa-tial variability of ground heat flux is expected to be lower in the currentstudy.

7.4. Evaluation of retrieved thermal properties

Although the interest of this study is on ground heat flux ratherthan the thermal properties of the soil alone, it is useful to comparethe present results to established relations between thermal proper-ties and soil moisture. Thermal properties obtained from remotesensing have long been used to classify soils and to retrieve soil mois-ture (e.g. Idso et al., 1975; Pratt & Ellyett, 1978). One can make use ofthe fact that cv increases linearly (Van Wijk & De Vries, 1963) and λs

logarithmically with soil moisture (Johansen, 1977). The diffusivity D(=λs/cv) initially increases and later decreases with progressive dry-ing of the soil.

Variations in thermal properties are attributed to soil moisture inthis study, because the measurements were carried out at a fixed lo-cation (with constant bulk density and texture). Soil moisture content

−100 0 100 200 300

−100

0

100

200

300

G0,ground

G0,

rem

ote,

fiel

d ra

diom

eter

y = 1.00 x

r2 = 0.96

n = 413

RMSE = 20 W m−2

e remote sensing approach (G0, field radiometer) versus the temperature profile approach

Page 8: Validation of remote sensing of bare soil ground heat flux

282 C. van der Tol / Remote Sensing of Environment 121 (2012) 275–286

was estimated by inverting the model of Van Wijk and De Vries(1963), using volumetric heat capacity derived from the long fielddata time series (Eq. B6). The obtained soil moisture is representativefor the top layer of the soil where the temperature sensors are, i.e.5–8 cm depth. Soil moisture was also obtained from remote sensingderived thermal inertia, following Lu et al. (2009) (Appendix B).The soil moisture obtained in this way is representative for thesurface.

Fig. 7 compares the time series of the retrieved thermal propertiesand soil moisture with other field observations. The middle panelshows the diffusivity and thermal conductivity from the field data(i.e. the temperature sensors and heat flux plate) as well as the ther-mal inertia calculated from the remote sensing data for 2010. Allthree properties exhibit temporal variations, apparently in responseto rainfall events (top panel). The observed ranges of values of 0.4to 1.2 Wm−1 K−1 for λs and 0.3 ∙106 to 1.2 ∙106 m2 s−1 for D corre-spond roughly to soil moisture values of about 5% to 25% accordingto experimental data of Ochsner et al. (2001). The range of values ofdiffusivity and the responses to rainfall events also agree qualitativelywith observations in the Sahel in 1991 and 1992 (Verhoef et al.,1996). The response of remotely derived Г to rainfall is less pro-nounced than that of the D and λs derived from field data. A possibleexplanation is that the surface temperature, and thus the thermal in-ertia, is also indirectly affected by soil moisture through variations inemissivity and soil evaporation. These effects were not explicitlyaccounted for in the model and may blur the relation with soilmoisture.

The values for soil moisture content estimated from the thermalproperties are presented in the bottom panel, together with mea-sured soil moisture content in a nearby station, 100 m west of theflux tower at 25 cm depth. It should be noted that these data can

0

20

40

Rai

n (m

m d

−1 )

0.5

1

1.5

2

2.5

10−

6 D, λ

, 10−

3 Γ

10−6 D

λs (J m

10−3 Γ

50 100 1500

10

20

30

40

50

DOY

θ (%

)

from soil tempfrom thermal measured at 2

Fig. 7. Top: measured daily rainfall at the flux tower versus Julian day of the year 2010 (misductivity (λs), calculated with the model from sensors at 2 depths and heat flux at 10 cm dsoil moisture content (θ) at 25 cm depth, measured ~100 m west of the flux tower, topsoil sture calculated from thermal conductivity with Van Wijk and De Vries (1963).

only be qualitatively compared, as they refer to different depths.The estimated subsoil moisture varies around 10% with upward ex-cursions following rainfall events. In the driest period of the year (be-tween Julian days 180 and 250), the soil moisture of the topsoil dropsto 1–5%. The seasonal cycle and the range of values of calculated soilmoisture are realistic, which in turn indicates that the retrieved ther-mal properties used for the calculation of ground heat flux wererealistic.

7.5. Remote sensing method with satellite data

A comparison between the input data of the satellite and field dataof radiation is shown in Figs. 8 and 9. For this comparison, all half-hourly data were linearly interpolated to the 15-minute time stepsof the satellite land surface temperature data. Fig. 8 shows the incom-ing and outgoing shortwave and long wave radiation for a typicalclear example day (23 July 2010) and Fig. 9 the components of the ra-diation balance as scatter plots of satellite versus field measurements.Close agreement between satellite and ground data was observed, de-spite the fact that the satellite data cover an area of 9 km2 with ~10%of vegetation (pixel size of 3×3 km), whereas the radiometer in thefield measured a much smaller, bare soil area (~100 m2 for outgoingradiation). Differences in the definitions of the product also play arole. For example, there is a difference in the spectral range overwhich the shortwave radiation is measured: 0.303 to 2.8 μm for thefield radiometer and 0.3 to 4.0 μm for the satellite, and a differencein the long wave radiation: 5.0–50 μm for the field radiometer and4.0 to 100 μm for the satellite. Fortunately the contributions of thenon-overlapping parts of the thermal spectrum are negligible. Thedifference in outgoing shortwave radiation around sunrise and sunsetis caused by the fact that the MSG product of albedo is defined at solar

(m2s−1)−1K−1)

(J m−2 K−1 s−1/2)

200 250

2010

erature data (subsoil)inertia (surface)5 cm depth

sing values indicated by the symbol ‘x’). Middle: daily diffusivity (D) and thermal con-epth, and thermal inertia (Г) calculated from field radiometric measurements. Bottom:oil moisture calculated according to Lu et al. (2009) from thermal inertia, and soil mois-

Page 9: Validation of remote sensing of bare soil ground heat flux

0 3 6 9 12 15 18 21 24−200

0

200

400

600

800

1000

Rsi

(W

m−

2 )

0 3 6 9 12 15 18 21 240

50

100

150

200

250

Rso

(W

m−

2 )

0 3 6 9 12 15 18 21 24280

290

300

310

320

330

340

350

time, GMT (hours)

Rli (

W m

−2 )

0 3 6 9 12 15 18 21 24350

400

450

500

550

600

time, GMT (hours)

Rlo

(W

m−

2 )

Fig. 8. Incoming shortwave (Rsi), outgoing shortwave (Rso), incoming longwave (Rli) and outgoing longwave radiation measured with the satellite (symbols) and measured in thefield (solid line) versus time (GMT) for 23 July 2010.

283C. van der Tol / Remote Sensing of Environment 121 (2012) 275–286

noon, while the diurnal cycle of albedo as present in the field data isnot accounted for. The satellite product for emissivity provides a con-stant value of 0.964, while in the ground data analyses a constant

0 500 10000

200

400

600

800

1000

Rsi field

(W m−2)

Rsi

sat

ellit

e (W

m−

2 )

y = 0.99 x

r2 = 0.96

200 250 300 350 400 450200

250

300

350

400

450

Rli field

(W m−2)

Rli

sate

llite

(W

m−

2 )

y = 1.01 x

r2 = 0.79

Fig. 9. Scatter plots of satellite versus field measured 15-minute interval incoming shortwavdiation for 1 May to 17 August 2010. Regression lines are forced through the origin.

value of 0.905 was assumed. The MSG product was corrected usingclimatic values for visibility and aerosol concentrations for atmo-spheric correction, with their own uncertainties. Taking into account

0 50 100 150 200 2500

50

100

150

200

250

Rso field

(W m−2)

Rso

sat

ellit

e (W

m−

2 )

y = 0.91 x

r2 = 0.95

300 400 500 600250

300

350

400

450

500

550

600

650

Rlo field

(W m−2)

Rlo

sat

ellit

e (W

m−

2 )

y = 0.99 x

r2 = 0.97

e (Rsi), outgoing shortwave (Rso), incoming longwave (Rli) and outgoing longwave ra-

Page 10: Validation of remote sensing of bare soil ground heat flux

−200 0 200 400 600 800−200

0

200

400

600

800

Rn field

Rn

sate

llite

y = 0.98 x + 28.9

r2 = 0.99

−200 −100 0 100 200 300−200

−100

0

100

200

300

G0, remote, field radiometer

G0,

rem

ote,

sat

ellit

e

y = 0.79 x

r2 = 0.89

Fig. 10. Scatter plots of satellite versus field measurements of 15-minute interval net radiation (Rn) (left) and remote ground heat flux G0, remote (right). To illustrate the bias insatellite derived net radiation, the regression of net radiation was not forced through the origin.

284 C. van der Tol / Remote Sensing of Environment 121 (2012) 275–286

all these differences in measurement technique between the groundand the satellite data, the correlation between the two can be consid-ered high.

The individual components of the radiation balance measuredwith the satellite agree fairly well with field data, and so does net ra-diation (Fig. 10, left panel). However, a positive bias is present in thesatellite data of net radiation, also during the night, when shortwaveradiation is absent. The bias during the night can be explained by thedifference in long wave radiation. Since thermal inertia is calibratedagainst night-time net radiation, the difference in longwave radia-tion of 29 W m−2 affects the estimates of ground heat flux.

Fig. 10 also shows a comparison between the remote sensingbased G0 using radiometric tower data and versus satellite data(right panel). Ground heat flux calculated with satellite data is 21%lower than ground heat flux calculated with the field radiometerdue to the observed differences in night-time net radiation. Despitethis difference, the coefficient of determination is rather high(r2=0.89). It should be emphasized that the field radiometer viewed~100 m2 of bare soil, versus 9 km2 of sparse vegetation for the satel-lite sensor.

8. Conclusion

It was shown by validation with detailed field measurements thatremote sensing estimates of ground heat flux over bare soil yields ac-curate results, despite problems associated with the use of surfacetemperature and the model conceptualization of the soil surface. Acomparison between the remote sensing methods applied to field ra-diometry and to MSG satellite data showed that the retrieval of satel-lite based ground heat flux is feasible. This study focussed on an MSGpixel with a vegetation cover area of only 10%. For more densely vege-tated areas, other techniques such as Verhoef et al. (2012) are moresuitable.

Acknowledgement

This research was supported by internal funds of the ITC faculty ofthe University of Twente. Logistics in the field were provided by theUniversity of Salamanca. I am grateful to Alain Pascal, LeonardoReyes, Donald Rwasoka, Guido Turricchia, Ernico Balugani and CesarCisneros for the fruitful cooperation in the field, to Ben Maathuis,Wout Verhoef, Gabriel Parodi and Anne Verhoef for constructive dis-cussions on the subject, and the anonymous reviewers for theircomments.

Appendix A. Scripts used in the data processing

The Fourier decomposition of time series (Eq. 6) was carried out intwo steps. First, a matrix was created containing the n harmonics ofthe Fourier series:

X ¼1 1

sin 1ωt−K1zð Þ exp −K1zð Þ cos 1ωt−K1zð Þ exp −K1zð Þ… …

sin nωt−Knzð Þ exp −Knzð Þ cos nωt−Knzð Þ exp −Knzð Þ

2664

3775 ðA1Þ

Second, the coefficients A and B were calculated by linear regres-sion of the harmonics, multiplied by coefficients, with the measuredtime series:

A0 BA1 B1… …An Bn

2664

3775 ¼ X0X

� �−1X0T ðA2Þ

where T is a vertical vector of (temperature) measurements. All analyseswere carried out using the software Matlab:

The calibration of the diffusivity was carried out by the leastsquare algorithm ‘lsqnonlin’. The temperature time series at alldepths are simulated using an initial value for D. The (squared) differ-ence between the simulated and measured temperature time serieswas used as objective function for minimization. A similar procedure,but for minimizing the squared difference between night time net ra-diation and night time ground heat flux was used to calibrate Γ withthe remote sensing approach:

G0 −GAM*dXdz0matrix(N,K,omega,t,k)*C0;Er Rn (nighttime)-G0 (nighttime);

Page 11: Validation of remote sensing of bare soil ground heat flux

285C. van der Tol / Remote Sensing of Environment 121 (2012) 275–286

Appendix B. Application of the model of Lu et al. (2009)

Soil moisture is calculated as a function of the Kerstan number Ke

(Eq. 10) in Lu et al., 2009):

θ ¼ v 1− ln Keð Þ2:95

� �1=−0:16ðB1Þ

Where v is the porosity and

Ke ¼Γ−Γsat

Γsat−Γdry; ðB2Þ

Γsat ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiλsatcv;sat

q; ðB3Þ

Γdry ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiλdrycv;dry

qand ðB4Þ

λsat ¼ λq1−vλw

v; ðB5Þ

where λq is the conductivity of quartz (7.7 Wm−1 K−1) and λw theconductivity of water (0.594 Wm−1 K −1). The saturated and drycv was calculated with Van Wijk and De Vries (1963), for saturated(θ=v) and dry conditions (θ=0), respectively:

cv ¼ 1:92 1−vð Þ þ 4:18θð Þ106: ðB6Þ

For λdry, a value of 0.3 Wm−1 K−1 was used, such that the valueof Гdry calculated with Eq. (B4) agreed with an empirical function de-veloped by Murray and Verhoef (2007a,b):

Γdry ¼ 1062:4vþ1010:8: ðB7Þ

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