1 Introduction

The Tibetan Plateau (TP) is located in the central eastern Eurasian continental mass and contains the world’s highest average elevation (circa 4,000 m), with some surface features reaching into the mid-troposphere. It comprises an extensive landmass extending from subtropical to middle latitudes and spans >25° longitude (Fig. 1). Because of its topographic character, the plateau surface absorbs large quantities of solar radiation energy and undergoes dramatic seasonal changes in its surface heat and water fluxes (e.g., Ye and Gao 1979; Ye 1981; Yanai et al. 1992; Ye and Wu 1998; Ma and Tsukamoto 2002; Hsu and Liu 2003; Yang et al. 2004; Ma et al. 2005; Sato and Kimura 2007; Ma et al. 2008; Xu et al. 2008; Cui and Graf 2009; Zhong et al. 2010). Many studies have found that the east Asian monsoonal climate and the middle Asian dry climate in summer are intensified by TP mechanical and thermal forcing (e.g., Liu et al. 2007). This heat source enhances the Asian monsoon and further influences precipitation in China and east Asia (e.g., Yanai et al. 1992; Wu and Zhang 1998; Zhao and Chen 2001; Duan et al. 2005; Duan et al. 2011).

Fig. 1
figure 1

The location and landscape of the Tibetan Plateau

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The surface heating field has been defined as (Ji et al. 1986):

$$ {H}_{\mathrm{f}}={R}_{\mathrm{n}}-{G}_0=H+\lambda E $$
(1)

where R n is net radiation flux, G 0 is surface soil heat flux, H is sensible heat flux, and λE is latent heat flux. When H f > 0, the land surface is a heat source for the atmosphere; otherwise, the land surface is a heat sink for the atmosphere. Therefore, net radiation flux, soil heat flux, sensible heat flux, and latent heat flux are very important components in the distribution of the surface heating field over the TP.

Some researchers have focused upon determining net radiation flux, soil heat flux, sensible heat flux, and latent heat flux by using in situ data (e.g., Ji et al. 1986; Ma and Tsukamoto 2002; Ma et al. 2005; Ma and Ma 2006). Regional distributions of net radiation flux, soil heat flux, sensible heat flux, and latent heat flux over the TP have already been measured by some researchers (e.g., Ma et al. 2002, 2006), though results remain on a mesoscale. In order to understand the effect of the TP on climate change over China, east Asia, and even globally, the regional distribution of net radiation flux, soil heat flux, sensible heat flux, latent heat flux, and the surface heating field over the whole TP has to be accurately determined.

Remote sensing from satellites, in conjunction with data from sparse field experimental stations, offers the possibility of determining the regional distribution of land surface heat fluxes (net radiation flux, soil heat flux, sensible heat flux, and latent heat flux) and the surface heating field over a heterogeneous land surface. The objective of this study is to explore the feasibility of upscaling the point and mesoscale net radiation flux, soil heat flux, sensible heat flux, latent heat flux, and surface heating field to yield distributions quantifiable on a plateau-wide scale with the aid of NOAA (National Oceanic and Atmospheric Administration) Advanced Very High-Resolution Radiometer (AVHRR) data, Moderate Resolution Imaging Spectroradiometer (MODIS) data, and in situ data.

2 Theory and scheme

The general concept governing the methodology is shown in Fig. 2. The surface reflectance for short-wave radiation r 0 and surface temperature T sfc are retrieved from AVHRR and MODIS data by using land surface observations of surface temperature, surface albedo, and aerological observations of the profiles of water vapor content; wind speed and direction as observed by a radiosonde system; a wind profiler and tethered balloon; the radiative transfer model MODTRAN (Berk et al. 1989); and atmospheric correction. The MODTRAN model computes downward short-wave and long-wave radiations at the surface (Ma and Tsukamoto 2002). After collation of these results, the regional surface net radiation flux R n(x,y) can be determined. The regional soil heat flux G 0(x,y) is estimated using R n(x,y) and field observations (Ma et al. 2002). The regional sensible heat flux H(x,y) is estimated using T sfc(x,y) and surface and aerological data captured with the aid of the so-called “tile approach” (Ma et al. 2010). The regional latent heat flux λE(x,y) is calculated as the residual value of the energy budget theorem for land surface heating. The surface heating field H f(x,y) is derived from R n(x,y) and G 0(x,y) by using Eq. (1) on a regional scale.

Fig. 2
figure 2

The diagram of parameterization procedure to determine net radiation flux, soil heat flux, surface heating field, sensible heat flux, and latent heat flux by combining AVHRR and MODIS data with field observations

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2.1 Net radiation flux

The regional net radiation flux is derived using:

$$ {R}_{\mathrm{n}}\left(x,y\right)=\left(1-{r}_0\left(x,y\right)\right){K}_{\downarrow}\left(x,y\right)+{L}_{\downarrow}\left(x,y\right)-{\varepsilon}_0\left(x,y\right)\sigma {T}_{\mathrm{sfc}}^4\left(x,y\right) $$
(2)

where r 0(x,y) is surface reflectance at position (x, y), ε 0(x,y) is surface emissivity, T sfc(x,y) is surface temperature, K ↓(x,y) is incoming short-wave radiation flux density, and L ↓(x,y) is incoming long-wave radiation flux. Surface emissivity of ε 0(x,y) is a function of vegetation coverage. It is derived from the model suggested by Valor and Caselles (1996). The incoming long-wave radiation flux L ↓(x,y) and the incoming short-wave radiation flux K ↓(x,y) in Eq. (2) are directly calculated from the radiative transfer model MODTRAN by using aerological observations of the profiles of water vapor content, wind speed and direction as observed by a radiosonde system, a wind profiler, and a tethered balloon (Ma and Tsukamoto 2002). The surface reflectance and surface temperature in Eq. (2) are derived in different ways, dependent upon differing sets of remote sensing data. They have been derived using the methodology proposed by Zhong et al. (2010).

2.2 Soil heat flux and surface heating field

The regional soil heat flux G 0(x,y) is determined by (Choudhury and Monteith 1988):

$$ {G}_0\left(x,y\right)={\rho}_{\mathrm{s}}{c}_{\mathrm{s}}\left[\left({T}_0\left(x,y\right)-{T}_{\mathrm{s}}\Big(x,y\right)\right]/{r}_{\mathrm{s}\mathrm{h}}\left(x,y\right) $$
(3)

where ρ s is soil dry bulk density, c s is soil specific heat, T s (x,y) stands for soil temperature at a determined depth, and r sh (x,y) represents soil heat transfer resistance.

G 0(x, y) cannot be directly mapped from satellite measurements through Eq. (3). The difficulty lies in deriving r sh(x,y) and T s(x,y) (Bastiaanssen 1995; Wang et al. 1995; Ma and Tsukamoto 2002; Ma et al. 2002, 2006; Gao et al. 2010). In order to calculate the values of G 0(x, y) solely from remote sensing data, these values have to be proportional to another term within the energy balance equation. A good candidate for this proportional term is R n(x,y) (e.g., Jackson et al. 1985; Choudhury et al. 1987; Kustas and Daughtry 1990; Bastiaanssen 1995; Ma and Tsukamoto 2002; Ma et al. 2006; Gao et al. 2010). Based on the in situ data gathered in the TP, Ma et al. (2002) proposed an equation to derive regional soil heat flux G 0(x,y) from regional net radiation flux R n(x,y) for the TP, thus:

$$ {G}_0\left(x,y\right)=0.35462\left(\pm 0.00235\right){R}_{\mathrm{n}}\left(x,y\right)-47.79008\left(\pm 0.70005\right) $$
(4)

Equation (4) is based on the in situ data gathered from the different land surface types of the TP, and R n(x,y) in Eq. (4) is similarly dependent upon surface type. Equation (4) has therefore been used in this study to determine the regional distribution of soil heat flux in the TP area.

The regional surface heating field H f(x,y) may then be derived from Eq. (5) after the determination of R n(x,y) and G 0(x,y), thus:

$$ {H}_{\mathrm{f}}\left(x,y\right)={R}_{\mathrm{n}}\left(x,y\right)-{G}_0\left(x,y\right) $$
(5)

2.3 Sensible heat flux and latent heat flux

The sensible heat flux H is estimated with a bulk transfer equation written in the form (Montheith 1973):

$$ H=\rho {c}_{\mathrm{p}}\frac{T_{\mathrm{sfc}}-{T}_{\mathrm{a}}}{r_{\mathrm{a}\mathrm{h}}} $$
(6)

where r ah is aerodynamic resistance for heat transfer between land surface and reference height, T sfc is the surface temperature, T a is the air temperature at the reference height, ρ is the air density, and c p is the air specific heat at constant pressure.

In order to determine the regional distribution of sensible heat flux H(x,y) over the TP, the “tile approach” (Ma et al. 2010) is used here. In the “tile approach,” the reference height z ref is taken within the surface layer (SL). Then, using satellite measurements at the surface and the SL observations on a “tile” at and below the reference height (e.g., 20 m), the heat flux over a heterogeneous landscape is estimated. Firstly, surface reflectance r 0, surface temperature T sfc, vegetation coverage P v, and surface emissivity ε 0 at the surface are derived from satellite measurements. Secondly, SL observations on a “tile” of wind speed u, air temperature T a, and specific humidity q at the reference height are made. Zero-plane displacement d 0, aerodynamic roughness length z 0m and thermodynamic roughness length z 0h, excess resistance for heat transportation kB −1, and the like in the SL below the reference height over the i-tile are used to estimate the regional sensible heat flux H(x,y) (Fig. 2).

Hence, in mathematical terms:

$$ \begin{array}{r}\hfill {H}_1\left(x,y\right)=\rho {c}_{\mathrm{p}}\frac{\left[{T}_{\mathrm{sfc}}\left(x,y\right)-{T}_{\mathrm{a}1}\right]}{r_{\mathrm{a}\mathrm{h}1}},\\ {}\hfill {H}_2\left(x,y\right)=\rho {c}_{\mathrm{p}}\frac{\left[{T}_{\mathrm{sfc}}\left(x,y\right)-{T}_{\mathrm{a}2}\right]}{r_{\mathrm{a}\mathrm{h}2}}\\ {}\hfill \dots \kern1em \dots \\ {}\hfill {H}_{\mathrm{n}}\left(x,y\right)=\rho {c}_{\mathrm{p}}\frac{\left[{T}_{\mathrm{sfc}}\left(x,y\right)-{T}_{\mathrm{a}\mathrm{n}}\right]}{r_{\mathrm{a}\mathrm{h}\mathrm{n}}}\end{array}, $$
(7)

Therefore, H over the whole TP may be derived from:

$$ H\left(x,y\right)={\displaystyle \sum_{i=1}^na(i){H}_i\left(x,y\right)}, $$
(8)

where a(i) is the fractional ratio of each “tile” for the TP as determined from satellite images and land cover maps. H 1(x,y), H 2(x,y)…, and H n(x,y) are the sensible heat flux calculations on each “tile”; T a1, T a2…, and T an are air temperature measurements at the reference height on each “tile”; and r ah1, r ah2 …, and r ahn are aerodynamic resistance for heat transfer between land surface and the reference height on each “tile”. r ah1, r ah2 …, and r ahn are determined from the eddy diffusion coefficients for heat transport between the land surface and the reference height (Ma et al. 2010).

The regional latent heat flux λE(x,y) is derived as the residual value of the energy budget theorem for land surface heating based on the zero horizontal advection conditions, i.e.,

$$ \lambda E\left(x,y\right)={R}_{\mathrm{n}}\left(x,y\right)-H\left(x,y\right)-{G}_0\left(x,y\right) $$
(9)

3 Cases study and validation

Four sets each of AVHRR data and MODIS data for the TP area were used in this study (as the TP covers a large proportion of southwest China, several satellite images are needed to make a composition of the whole plateau image here). They were collected on 17 January 2003 (winter), 14 April 2003 (spring), 23 July 2003 (summer), and 16 October 2003 (autumn).

Inputting the AVHRR, MODIS, and in situ data, the distributions of net radiation flux, soil heat flux, sensible heat flux, latent heat flux, and the surface heating field are derived using Eqs. (2)–(9). Figures 3 and 5 show surface heating field and latent heat flux distribution maps for the TP. Figures 4 and 6 show their distribution frequencies. The surface heating field and latent heat flux distribution maps are based on 3,012 × 1,517 pixels with a size of 1 × 1 km. The derived net radiation flux, soil heat flux, sensible heat flux, latent heat flux, and surface heating field have been further validated by station measurements. In situ data collected at four CAMP/Tibet stations, viz.: D105 (33.06° N, 91.94° E; elevation of 5,039 m; sparse meadow land cover); NPAM (31.93° N, 91.71° E; elevation of 4,620 m; grassy marshland land cover); BJ (31.37° N, 91.90° E; elevation of 4,509 m; sparse meadow land cover); and ANNI (31.25° N,92.17° E; elevation of 4,480 m; grassy marshland land cover) were used for the validation in 2003. In Fig. 7, the satellite-derived results are validated against the station measurements. Since it was difficult to determine the locations of the four stations, the values of a 5 × 5-pixel rectangle surrounding the determined Universal Transfer Macerator (UTM) coordinates are compared with the in situ data. In Fig. 1, the derived results are validated against the measured values collected in the field. The absolute percentage difference (APD) quantitatively measures the difference between the derived results (H derived(i)) from satellite and measured values (H measured(i)) and:

Fig. 3
figure 3

The distribution maps of surface heating field over the Tibetan Plateau area. a AVHRR results and b MODIS results

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Fig. 4
figure 4

The frequency distribution of surface heating field over the Tibetan Plateau area. a AVHRR results and b MODIS results

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$$ APD=\frac{\left|{H}_{derived(i)}-\left.{H}_{measured(i)}\right|\right.}{H_{measured(i)}}. $$
(10)

where i represents different derived or measured values of R n, G 0, H, and λE at four the validation sites (i = 1…4).

The results show that: (1) the derived net radiation heat flux (R n), soil heat flux (G 0), sensible heat flux (H), latent heat flux (λE), and surface heating field (H f) derived from MODIS and AVHRR data for the TP are in close accordance with the land surface status; the wide range in values reflects highly contrasting surface features (forests, grasslands, meadows, marshlands, farmland, deserts, desertification zones, snowy mountains, rivers, glaciers, lakes, etc.) in this region (Figs. 1, 3, 4, 5, and 6). One low-value center, located in the desert/desertification zone of the Qaidam Basin, was clearly identifiable in the derived latent heat flux images (Figs. 5 and 6); (2) the derived net radiation flux, soil heat flux, sensible heat flux, latent heat flux, and surface heating field values across the TP are very close to the field measurements. The difference between the derived results and the field observations’ APD is less than 10 % (Fig. 7) because accurate surface reflectance and surface temperatures were determined, and the processes within the atmospheric boundary layer were considered in greater detail when determining sensible heat flux values; (3) the mean surface heating field values over the TP increase from January to April and from April to July, decreasing from October to January. They are 303.4 W m−2, 370.3 W m−2, 459.9 W m−2, and 335.67 W m−2 for the AVHRR data and 302.1 W m−2, 375.5 W m−2, 467.1 W m−2, and 346.9 W m−2 for the MODIS data. The mean latent heat flux values across the TP also increase from January to April and from April to July, decreasing from October to January. They are 161.8 W m−2, 237.5 W m−2, 380.4 W m−2, and 219.1 W m−2 for the AVHRR data and 170.9 W m−2, 243.6 W m−2, 395.0 W m−2, and 225.8 W m−2 for the MODIS data; and (4) as a rule, the derived results from AVHRR images were in agreement with those from MODIS images when the imaging time was the same. The results collected from the MODIS procedure were usually superior to the AVHRR data, which had an average APD of 5.4 % (net radiation flux), 8.0 % (soil heat flux), 6.3 % (surface heating field), 6.5 % (sensible heat flux), and 6.9 % (latent heat flux), while the values for the MODIS data were 4.9 % (net radiation flux), 7.3 % (soil heat flux), 5.5 % (surface heating field), 5.0 % (sensible heat flux), and 5.7 % (latent heat flux) (Fig. 7).

Fig. 5
figure 5

The distribution maps of latent heat flux over the Tibetan Plateau area. a AVHRR results and b MODIS results

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Fig. 6
figure 6

The frequency distribution of latent heat flux over the Tibetan Plateau area. a AVHRR results and b MODIS results

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Fig. 7
figure 7

Comparison of derived results with field measurements for the net radiation flux, surface heating field, sensible heat flux, and latent heat flux over the Tibetan Plateau area, together with a 1:1 line. a AVHRR and b MODIS

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4 Concluding remarks

In this study, the regional distributions of net radiation heat flux, soil heat flux, sensible heat flux, latent heat flux, and the surface heating field over the heterogeneous landscape of the TP are derived with the aid of AVHRR, MODIS, and in situ data. Compared with reliance upon field measurements alone, the proposed methodology has proven to provide a better approach for deriving related land surface heat flux (net radiation heat flux, soil heat flux, sensible heat flux, and latent heat flux) and the surface heating field over a heterogeneous landscape. It forms a sound basis for the further study of water–heat exchange processes on heterogeneous land surfaces.

Deriving regional net radiation heat flux, soil heat flux, sensible heat flux, latent heat flux, and the surface heating field over a heterogeneous landscape is not straightforward. The parameterization methodology presented in this research is still developing, as only a single set of values from a specific time on a specific day is used in this research. In order to establish more accurate regional values of net radiation heat flux, soil heat flux, sensible heat flux, latent heat flux, and surface heating field values and to delineate their seasonal and annual variations over the TP, there is a need for more field observations, more accurate radiation transfer models for determining surface reflectance and temperatures, and more satellite data such as that provided by the Landsat-5 TM, GMS (Geostationary Meteorological Satellite), ATSR (Along Track Scanning Radiometer), and MODIS systems.