A Remote Sensing Method for Estimating Surface Air Temperature and Surface Vapor Pressure on a Regional Scale

This paper presents a method of estimating regional distributions of surface air temperature (Ta) and surface vapor pressure (ea), which uses remotely-sensed data and meteorological data as its inputs. The method takes into account the effects of both local driving force and horizontal advection on Ta and ea. Good correlation coefficients (R2) and root mean square error (RMSE) between the measurements of Ta/ea at weather stations and Ta/ea estimates were obtained; with R2 of 0.77, 0.82 and 0.80 and RMSE of 0.42K, 0.35K and 0.20K for Ta and with R2 of 0.85, 0.88, 0.88 and RMSE of 0.24hpa, 0.35hpa and 0.16hpa for ea, respectively, for the three-day results. This result is much better than that OPEN ACCESS Remote Sens. 2015, 7 6006 estimated from the inverse distance weighted method (IDW). The performance of Ta/ea estimates at Dongping Lake illustrated that the method proposed in the paper also has good accuracy for a heterogeneous surface. The absolute biases of Ta and ea estimates at Dongping Lake from the proposed method are less than 0.5Kand 0.7hpa, respectively, while the absolute biases of them from the IDW method are more than 2K and 3hpa, respectively. Sensitivity analysis suggests that the Ta estimation method presented in the paper is most sensitive to surface temperature and that the ea estimation method is most sensitive to available energy.


Introduction
Surface air temperature (Ta) and surface air vapor pressure (ea), as measured at standard meteorological shelter height (about 2 m), are two primary descriptors of terrestrial environmental conditions [1].They can not only indicate near surface atmospheric condition, but also reflect surface energy balance situations.They are the most basic parameters in the land-atmosphere system.Almost all models involving the land-atmosphere system, such as the global climate model, hydrological model, land surface model, crop growth model, weather forecasting model, etc., need Ta and ea as inputs.Therefore, accurate estimations of Ta and ea play important roles in the study of the land-atmosphere system.
Generally, Ta and ea at the field scale can be easily acquired from standard meteorological stations.However, this provides only limited information about spatial patterns over wide areas, because they are strongly affected by surface properties, which vary greatly in both time and space [1,2].As a result, the measurements of Ta and ea at meteorological stations are unrepresentative at the regional scale.For acquiring spatial distributions of Ta and ea, three kinds of methods were primarily used at present. 1. Geostatistical method.This method uses geostatistical models to interpolate the measurements of Ta and ea obtained from meteorological stations and get the spatial maps of them.The inverse distance weighted method (IDW), the kriging interpolation method, the linear method and the spline interpolation method are the typical examples of this kind of method.The geostatistical method has been widely used by many researchers for many years [3,4].The advantage of this kind of method is that it can be easily used on the basis of the observations of Ta and ea.However, because it has not considered the effects of local land surface on near-surface atmosphere through longwave radiation, heat and vapor exchange between land surface and atmosphere, the method would produce large errors when applied to a large heterogeneous surface [4,5].Additionally, when the density of meteorological stations is sparse in the study area, the precision of the method would decrease because of the lack of observation data [1].Furthermore, the station-based interpolation techniques suffer from the arbitrary location of weather stations [6], and different interpolation methods can produce different results [7,8].
2. Vertical lapse method.This method is often used to estimate air temperature in mountainous areas where there are large elevation variations.By assuming a specified lapse rate, typically a value, such as 6.0 or 6.5 °C/km [9], Ta with adjustments for elevation is estimated according to the geolocation of the study area.Obviously, the determination of the value of the lapse rate is the key for the method.However, there are significant variations in lapse rates under different meteorological conditions and in different seasons.If the lapse rate is poorly determined, large errors of Ta estimates will be produced [10].
3. Remotely-sensed land surface temperature (LST)-based method.As is well known, there is a close relationship between air temperature and land surface temperature [11].With the developments for the ability to get spatial estimates of LST at high temporal and spatial resolution, many methods were presented to derive Ta from LST.For example, some studies [12,13] use nighttime satellite LST products to estimate daily minimum Ta.Some studies [2,14,15] derive daily maximum Ta from satellites through the vegetation index-temperature method (VI-T method), which assumes that the surface temperature of a fully-vegetated canopy equals its ambient air temperature.Shamir and Georgakakos [16] derived Ta at four times using four instantaneous LST from the Moderate Resolution Imaging Spectroradiometer (MODIS).In addition, because the difference between LST and maximum Ta is mainly controlled by the surface energy balance [13], some Ta estimation methods based on the surface energy balance were developed.For example, Pape et al. [17] developed a model for simulating Ta variations in high mountain landscapes at a high temporal resolution of one hour; Sun et al. [18] built a quantitative relationship between LST and Ta based on the crop water stress index and aerodynamic resistance.Surface energy balance is a complex system depending on many environmental factors, such as solar radiation, cloud-cover, wind speed, soil moisture and land surface type [19].Therefore, an under parameterization problem is encountered when estimating Ta with this method.Additionally, the surface energy balance non-closure problem was widely observed at flux sites [20], which brings additional uncertainty to this method.
As for the estimation of ea at the regional scale, the geostatistical method is also widely used, like the estimation of Ta.The conventional interpolation methods include IDW, spline and kriging, Thiessen polygons and least-squares polynomial regression.Establishing an empirical function between a vapor pressure-deficient (VPD) and remotely-sensed parameter is also a common method of estimating ea.For example, Granger [21] modelled VPD as a function of saturated vapor pressure (es) and the long-term average of Ta.Hashimoto et al. [22] estimated the spatial distribution of VPD with a simple linear relationship between it and LST retrieved from MODIS.With the availability of satellite total precipitable water (TPW) products, some studies have used TPW to estimate ea by establishing the regression functions between TPW and ea or air-specific humidity, such as the approaches presented by Sobrino et al. [23] and Recondo et al. [24].However, the relationship between TPW and ea is empirical, which can only apply to the specific area by the limitation of the training dataset.
As stated above, most approaches for estimating Ta and ea at present are based on statistical or empirical methods.In physics, two forces control Ta and ea.One is the turbulent flow exchange, including vertical turbulent diffusion/exchange and horizontal advection.The other is the radiation effect, which mainly indicates the heating effect of surface longwave radiation on near-surface atmosphere.Vertical turbulent diffusion/exchange and the radiation effect are primarily determined by the local meteorological conditions and surface properties.However, horizontal advection is mainly related to the environmental and meteorological conditions at the regional scale.On a windy day, horizontal advection may play a greater role with respect to air temperature and vapor pressure; while in calm weather, local environmental conditions may dominate Ta and ea by the influence of the radiation effect and vertical turbulent diffusion/exchange.
The objective of this paper is to develop a method that takes into account the effects of both local driving forces and horizontal advection on the near-surface atmosphere, for estimating regional distributions of Ta and ea.For a clear description, the method for air temperature is called advection-energy balance for air temperature (ADEBAT), and the method for vapor pressure is called advection-energy balance for air water vapor pressure (ADEBAV) in the paper.Section 2 describes the derivations of the ADEBAT method and the ADEBAV method.The study area and the data are introduced in Section 3. Section 4 provides the results of the Ta and ea estimates.The conclusions are given in Section 5.

The Derivation of the ADEBAT Method
At the field scale, two local physical processes result in Ta: (1) the heating effect of land surface longwave radiation on near-surface air; in the daytime, LST is usually higher than Ta, because of the strong surface absorption of solar radiation; in this condition, Ta increases by absorbing surface longwave radiation; (2) the effect of vertical turbulent flow, meaning the vertical heat exchange between surface and near-surface atmosphere.The two processes illustrate the reason why there is a very close relationship between LST and Ta.In the paper, the two processes are called the local driving force of Ta.
Neglecting systematic sampling errors, systematic instrument bias, low and high frequency loss of turbulent fluxes and energy sinks, horizontal advection of heat and water vapor is regarded as the primary reason for the non-closure of the surface energy balance [20,25,26].When the effects of the factors mentioned above on the surface energy balance closure are neglected and in a situation in which there is no horizontal advection, the surface energy budget is balanced, namely surface energy balance closure.In this case, Ta is dominated by local driving force and can be derived as Equation (4) according to the surface energy balance equation (Equation (1)), the heat diffusion equation (Equation ( 2)) and the definition of the Bowen ratio (Equation (3)). (1) where Rn is the net radiation.H and LE are sensible heat flux and latent heat flux, respectively.G is soil heat flux.ra is aerodynamic resistance.ρCp is the volumetric heat capacity of air.T0 is aerodynamic temperature and is usually replaced by LST in applications [27,28].β is the Bowen ratio.
On the contrary, under the condition that there is obvious horizontal advection, like in windy weather, horizontal movement of the air mass would have a great influence on Ta.In this case, similar Ta would be observed at a regional scale, and the local driving force becomes less dominant.In practice, the surface energy balance is not closed in most cases [20], which means both the local driving force and horizontal advection have influences on Ta.
For a constant air column in a closed system, its temperature is mainly determined by the available energy (Rn−G), meteorological conditions and surface properties.When there is air from outside coming into the closed system, the air temperature would be changed through air mixing.When the air temperature outside is higher than that in the closed system, Ta in the closed system would increase.Conversely, it would decrease.This kind of effect of exotic air on Ta is like the effect of the horizontal advection.Assuming that the inner and the exotic effects on Ta agree with the linear mixture theory and using Vawl and Vajd to express the air volume coming into the closed system from outside and the original air volume in the closed system, respectively, Equations ( 5) and ( 6) were established.
where Vazs is the total air volume and equals the sum of Vawl and Vajd.Tazs is the final air temperature.
In practice, it is the real air temperature observed at the meteorological station.Tawl is the air temperature affected by horizontal advection.Tajd is the original air temperature in the closed system, which is the air temperature under the condition of surface energy balance closure and is controlled by the local driving force.f is the volume percentage, ranging from 0 to 1, which represents the weight of the effects of horizontal advection on Tazs.From Equation ( 5), it can be seen that f = 0 means there is no horizontal advection (surface energy balance closure), and Tazs is totally controlled by the local driving force; while f = 1 means that there is no local driving force and that Tazs is totally controlled by horizontal advection.
In most cases, f is between 0 and 1.
Estimating Tazs is the purpose of this paper.Obviously, three parameters of f, Tawl and Tajd must be calculated first to estimate Tazs.

The Calculation of Tajd
The surface energy balance equation describes the relationship between surface energy components well under the condition of surface energy balance closure.On the basis of this, Ta under the condition of surface energy balance closure can be derived as Equation ( 4).Therefore, Tajd can be calculated from Equation (4) in which Ta is Tajd.
For calculating Tajd, ra in the condition of no horizontal advection needs to be determined.In the study, a value of ra of 65 s/m, which is determined by a lab experiment, was used to compute Tajd.In the experiment, radiometric soil surface temperature (Ts), ea and evapotranspiration for bare soil with saturated soil water content were measured in a no-wind condition.Then, ra was retrieved in terms of Equation (7).
where es is surface saturated vapor pressure, which is calculated by Equation (8).rs is surface resistance and equals zero for soil with saturated soil water content; γis the psychrometer constant.
where T0 is aerodynamic temperature.In the study, T0 is replaced by Ts [29,30].An empirical method presented by Zhang et al. [31] was used to estimate β.
where A is an empirical coefficient and equals 0.66 according to the literature.P is a simplified thermal inertia defined as: T02 is the surface temperature at satellite overpass time.T01 is the daily minimum surface temperature usually occurring at the time before sunrise.t2 and t1 are the times when T02 and T01 occur. is the average net radiation from t1 to t2.Pmax and Pmin are the maximum and the minimum thermal inertia, respectively, for a given fractional vegetation cover (fv), which are determined by the trapezoid space formed by the scatter plot of remotely-sensed vegetation index (VI) versus LST.
Rn and G were estimated by Equations ( 11) and (12).
where σ is the Stefan-Boltzmann constant.α is surface albedo.ε is surface emissivity.Rld is downward longwave radiation.

The Calculation of f and Tawl
In the study, meteorological measurements of air temperature, wind speed and wind direction at weather stations were used to calculate fi and Tiawl.i represents the pixel at which air temperature is to be estimated.The procedures of estimating them at pixel i are: 1. Selecting two weather stations nearest to pixel i.The two stations must have similar wind speed and wind direction.Here, similar wind speed and wind direction is assumed to have similar horizontal advection.The pixels at which the two weather stations are located are represented as Pixel 1 and Pixel 2. Under the assumption that horizontal advection is the same over a regional area, the horizontal advection at pixel i is the same as that at Pixel 1 and Pixel 2. As a result, T1awl = T2awl = Tiawl, f1 = f2 = fi.
2. Calculating the Tajd map with Equation (4) based on ra and the remotely-sensed data of Rn, G and LST; 3. At Pixel 1 and Pixel 2, the following two equations can be established based on Equation ( 5): T1azs and T2azs are the observed air temperatures at Pixel 1 and Pixel 2. T1ajd and T2ajd are the air temperatures affected by the local driving force at Pixel 1 and Pixel 2, which is obtained from Step (2).Because T1awl = T2awl = Tiawl, f1 = f2 = fi, f and Tawl at pixel i can be estimated from Equations ( 13) and (14).

The Derivation of the ADEBAV Method
The idea of the method of estimating air vapor pressure is similar to that of air temperature.The local driving force and horizontal advection are also the primary factors influencing near-surface vapor pressure.When there is no horizontal advection, ea under the condition of surface energy closure can be estimated from Equation (17), which is deduced from Equations ( 1), ( 3) and (7).
1 (17) The parameters have the same meanings with the above descriptions.
Under the condition that there are both effects of the local driving force and horizontal advection, ea can be expressed as Equation (19) in terms of the linear mixture theory.
1 (18) where eazs is the real vapor pressure and eawl, eajd are the vapor pressures affected by horizontal advection and the local driving force, respectively.
Equation (17) gives the estimation of vapor pressure under the condition of surface energy balance closure, so eajd can be calculated from it in which ea is eajd.The methods of calculating Rn, G, β and ra are the same as that used in calculating Tajd; see Section 2.1.1.The VI-T trapezoid method was used to acquire rs [32], which is formed by the scatter plot of VI versus T under a full range of vegetation cover and soil moisture availability and has been widely used to infer soil moisture and to quantify land surface evaporation [33][34][35][36].In the trapezoid method, the dry edge is the uppermost line of the VI-T space, the pixels on which are taken as surfaces with the largest water stress (soil water content reaches wilting point), and thereby, rs is largest on the dry edge.The wet edge is the lowest line of the VI-T space, the pixels that represent surfaces without water stress, and thereby, rs is smallest on the wet edge.An isopleth line within the trapezoid space has the same soil surface moisture availability.According to this, rs for every pixel was interpolated in terms of the LST difference between the pixel and the dry edge and the LST difference between the pixel and the wet edge; see Equation (18).
where Tmax and Tmin are the corresponding maximum and minimum surface temperatures at the dry and wet edges, respectively, for a given fv.rs_max and rs_min are the maximum and minimum surface resistance, respectively.rs_min equals zero when the soil water content is saturated.For sandy loam, which is the dominant soil type in the North China Plain (the study area in the paper), the wilting point at a depth of 0-20 cm is about 0.07 v/v, and the saturated water content at a depth of 0-20 cm is about 0.3 v/v [37,38].
According to the studies of Camillo [39] and Sun [40], rs_max for sandy loam was set as 140 s/m in the study when soil water content reached the wilting point.
The procedures of the calculation of f and eawl for pixel i are the same as that in calculating Tawl; see Section 2.1.2.Air temperature is replaced by vapor pressure.The formulas of f and eawl for pixel i are: where the subscripts of 1 and 2 represent the two selected weather stations determined by Step (1).
It should be noted that Ta and ea estimated with this method are the air temperature and the water vapor pressure instantaneously at the satellite overpass time, because remotely-sensed data of Rn, G and LST are the important inputs of the method, which can only represent the values at the satellite overpass time.

The Study Area and the Dataset
The study area is located in the North China Plain and ranges from 35.0°N to 38.3°N in latitude, from 116.0°E to 118.5°E in longitude.The land use in the area is dominated by the rotating cropping of winter wheat and summer maize.Millet, soybean and cotton are also scatter planted in summer.According to the traditional tillage practice, winter wheat is sown in early October, harvested in early or mid-June next year, and summer maize is planted in early to mid-June and harvested at the end of September.The soil types are mostly sandy loam.Annual precipitation is about 600 mm, more than 50% of which falls during the summer monsoon between July and September.The groundwater table varies from 1.5 m to 3.5 m with an average of 2.5 m.
In the study, field measurements at 40 standard meteorological stations were used, shown in Figure 1.The measurements include air temperature, vapor pressure, wind speed, wind direction and solar radiation at about a 2-m height above the surface at 2:00, 8:00, 14:00, 20:00.Ta, ea and solar radiation at the satellite overpass time are obtained by a linear interpolation.The measurements from about 20 stations were used to calculate f and Tawl/eawl.The measurements at the other stations were used to validate the estimates of Ta and ea.The triangle symbol in Figure 1 is Dongping Lake.The circle on the upper right corner is a water area close to Bohai Gulf.
Considering that the effect of the local driving force on near-surface atmosphere is only obvious within a small area, Landsat TM data with a high spatial resolution of 120 m in the infrared wave band were used in the study to estimate regional Ta and ea.The overpass time of Landsat TM in the study area is at about 10:40 local time.The single-window method presented by Qin et al. [41] was used to retrieve LST in the daytime.Surface albedo was retrieved by Liang's method [42].August).The imaging radiometer consists of one visible channel and four infrared channels.A surface temperature inversion method corresponding to FY-2C [43] was used to retrieve FY-2C LST at the time before sunrise.A bilinear interpolation method was used to downscale the FY-2C LST from 5 km to 120 m to match the spatial resolution of Landsat TM.Table 1 lists the variables and the sources used in the study.In the study, three clear-sky days on 8 April, 30 August and 17 October in 2009 were selected to perform the calculations.The sunrise times for the 3 days are at 6:49, 5:42 and 6:23 local time, respectively, so FY-2C data with the acquisition time closest to the sunrise for the 3 days were used to obtain the daily minimum surface temperatures.
For evaluating the methods, the IDW method was also used to estimate Ta and ea.The same stations used in the methods of ADEBAT and ADEBAV were used to perform the IDW interpolation and the validations.The two sets of estimates of Ta/ea obtained from the IDW method, the ADEBAT method and the ADEBAV method, respectively, were compared.

Air Temperature Retrievals by the ADEBAT Method and Its Validation
The comparisons between Ta estimated from the ADEBAT method and the IDW method and the measurements for the three days are given in Figure 2, respectively.It shows that the correlation coefficient (R 2 ) for the ADEBAT method, with R 2 of 0.77, 0.82 and 0.80, respectively, for the three days, is obviously higher than that for the IDW method, with R 2 of 0.3, 0.50 and 0.25.The root mean square error (RMSE) for the ADEBAT method, with RMSE of 0.42K, 0.35K and 0.20K, respectively, for the three days, is smaller than that for the IDW method, with RMSE of 0.82K, 0.39K and 0.65K.Figure 2 also shows that Ta estimates from the ADEBAT method are closer to the 1:1 line than those from the IDW method.This illustrates that the accuracy of the Ta estimation based on the ADEBAT method is obviously higher than that based on the IDW method.Compared with the geostatistical interpolation methods, like the IDW method, the ADEBAT method takes into account the effects of not only horizontal advection, but also the local driving force on near-surface atmosphere, while the IDW method only considers some effects of horizontal advection by calculating the distance of the pixel to be interpolated to the weather station.In other words, it does not consider any information about the effects of the local driving force on Ta.When there is a relatively uniform surface within the study area, which means the effects of the local surface condition on near-surface atmosphere are similar over the area, or there is strong horizontal advection when the local condition has few effects, like in windy weather, the geostatistical interpolation method may be proper.However, when the local surface condition dominates Ta, the geostatistical interpolation method would produce large errors.In this case, the ADEBAT method would have a great advantage over the IDW method.
Taking Ta estimates at Dongping Lake as an example, the advantage of the ADEBAT method over the geostatistical method was illustrated further.Dongping Lake is located in Doping county of Shandong province (see Figure 1), which covers an area of 124.3 km 2 .The average water depth is 2.5 m.This large water body could have a great effect on the near-surface atmosphere over it, so Ta over the lake and over the land should have a large difference.Table 2 lists the comparisons between the estimated Ta by the IDW method and the ADEBAT method and the Ta measurements at Dongping Lake.It can be seen that the absolute bias (AB) between the estimates and the observations for the ADEBAT method is much smaller than that for the IDW method.AB for the ADEBAT method is less than 0.5K, while AB for the IDW method is more than 2K.Table 2 also gives the Ta measurements at the two selected stations (Station 1 and Station 2) used to calculate f and Tawl at Dongping Lake in the ADEBAT method.There are large differences in Ta between the two stations, with a grassland underlying surface, and Dongping Lake, due to the large difference of land surface type.Because the ADEBAT method takes into account the effect of the local driving force on Ta, the estimated Ta at Dongping Lake is still very close to the observations.Therefore, the ADEBAT method is better than the IDW method, especially for an area with a large heterogeneous surface, in which case the effect of the local driving force on near-surface atmosphere may have a large difference.
Table 2. Comparisons between the estimated air temperatures by the IDW method and the ADEBAT method and the Ta measurements at Dongping Lake (K).

Vapor Pressure Retrievals by the ADEBAV Method and Its Validation
Figure 3 displays the scatter plots of ea estimates and ea measurements for the three days for the IDW method and the ADEBAV method, respectively.Compared with the ea estimates based on the IDW method, the results estimated by the ADEBAV method are much better.Clearly, the ADEBAV method obtained better values of R 2 and RMSE.For the ADEBAV method, the values of R 2 are 0.85, 0.88 and 0.88 and the RMSE values are 0.24hpa, 0.35hpa and 0.16hpa, respectively, for the three days; while for the IDW method, the R 2 values are only 0.22, 0.33 and 0.03 and the RMSE values are 1.45hpa, 0.96hpa and 0.45hpa.Figure 3 also shows that the ea estimates from the ADEBAT method are closer to the 1:1 line than those from the IDW method.3 gives the ea estimates by the IDW method and the ADEBAV method and the measurements at Dongping Lake.Smaller AB for ea of 0.5, 0.7 and 0.6hpa for the three days for the ADEBAV method were obtained.Comparatively, AB for the IDW method is five-to 10-times as much as that for the ADEBAV method, reaching 4.87, 3.78 and 5.13hpa for the three days.Lack of consideration for the local driving force on ea in the IDW method is the main reason for this.Table 3. Comparisons between the estimated vapor pressure by the IDW method and the ADEBAT method and the ea measurements at Dongping Lake (hpa).ADEBAV, advection-energy balance for air water vapor pressure.

Comparisons of the Spatial Distributions of Ta and ea
Figures 4 and 5 show the spatial distributions of Ta estimates and ea estimates by the IDW method and the ADEBAT/ADEBAV method.It can be seen that the distributions of Ta estimates and ea estimates exhibit an obvious circular spatial pattern for the IDW method.It centers on several areas and radiates out from these centers with a gradient trend form.This kind of spatial pattern actually does not exist in nature.
Limited by the algorithm of the IDW method, the maximum and the minimum Ta or ea in the study area are completely determined by the maximum and the minimum Ta or ea observations at weather stations.Because the IDW method totally depends on the number and the spatial distributions of the weather stations and the Ta/ea measurements at the weather stations, these unreasonable phenomena were produced.
Comparatively, the results based on the ADEBAT/ADEBAV method provide more details about the spatial patterns of Ta and ea.At Dongping Lake, no differences in the estimates of Ta and ea between the lake and the land were obtained for the IDW method.In addition, Ta/ea estimates from the ADEBAT/ADEBAV method display large differences between the lake and the land.Ta over the lake is obviously lower than that over the land, and ea over the lake is obviously higher than that over the land.Lower Ta estimates and higher ea estimates were also obtained over the water area close to Bohai Gulf.The performance of Ta and ea estimates at the water surface suggests that the result obtained from the ADEBAT/ADEBAV method is more reasonable than that from the IDW method.

Sensitivity Analysis
Sensitivity analysis plays a fundamental role in understanding the contributions of variables and parameters to model output.In this study, the sensitivity of Ta to the inputs of T0, Rn-G, ra and β for the ADEBAT method and the sensitivity of ea to the inputs of T0, Ta (used to calculate es), Rn-G, ra, rs and β for the ADEBAV method were analyzed, respectively.Perturbations of T0 and Ta were specified as [−2K, 2K], with a variation step of 1K.Perturbations of Rn−G, β, ra and rs were specified as [−20%, 20%], with a variation step of 10%.
Results (Table 4) show that for the ADEBAT method, ra, Rn−G and β are negatively correlated with Ta, but T0 is positively correlated with Ta.Comparing the sensitivity of Ta to the four inputs, Ta is most sensitive to T0.A 1K increase of T0 could result in a 0.6K increase in Ta estimates.A similar sensitivity of Ta to ra and Rn−G was observed.A 10% increase of ra or Rn−G could result in a 0.35K decrease in Ta estimates.The sensitivity of Ta to β is the least.A 10% variation of β only produces about a 0.24K variation of Ta.
For the ADEBAV method (Table 5), ra, rs and Rn−G are all negatively correlated with ea estimates.Ta and β are positively correlated with ea estimates.The order of the sensitivities of ea to the five inputs from the most to the least is Rn−G, rs, ra, β and Ta, respectively.A 10% increase of Rn−G could result in a 0.37-hpa decrease of ea estimates.A 10% increase of ra or rs could produce about a 0.23-hpa decrease in ea estimates.A 10% variation of β produces about a 0.2-hpa variation of Ta.A 1K increase of Ta only produces a 0.1-hpa increase in ea estimates.
In application, the calculation of β has more uncertainty.However, the good thing is that the ADEBAT method and the ADEBAV method are not very sensitive to β according to the sensitivity analysis.There is still some uncertainty about the determinations of ra and rs, which are difficult to estimate precisely.Fortunately, the ADEBAT method and the ADEBAV method are not very sensitive to them.

Conclusions
Radiation conditions, local meteorological conditions and land surface properties are the primary local factors determining near-surface air temperature and vapor pressure.Horizontal advection is the exotic factor determining them.In the study, by considering the effects of the local driving force and horizontal advection on Ta and ea, methods for estimating Ta and ea on a regional scale were proposed on the basis of the linear mixing theory.The energy balance equation was used to deduce the air temperature and the air vapor pressure in the condition of no horizontal advection.The measurements of wind speed, wind direction, Ta and ea at weather stations were used to determine Ta and ea affected by horizontal advection.One important assumption for the method proposed in the paper is that there is a similar horizontal advection in the pixel to be interpolated and the searched nearest two weather stations.Because horizontal advection usually has a similar effect at a regional scale, this assumption is reasonable.For example, similar wind speed can be observed within even several dozen kilometers in windy weather Twenty weather stations were used in the study to perform the calculations of the ADEBAT/ADEBAV method, and another 20 weather stations were used to validate the method.The IDW method was also used to estimate the distributions of Ta and ea and was compared with the methods presented in the paper.The results show that the accuracy of Ta and ea estimates from the ADEBAT/ADEBAV method is much greater than that from the IDW method.R 2 between Ta estimates from the ADEBAT method and Ta measurements at weather stations are 0.77, 0.82 and 0.80 for the three days, while R 2 for the IDW method are only 0.3, 0.50 and 0.25.RMSE for the ADEBAT method are 0.42K, 0.35K and 0.2K, while for the IDW method 0.82K, 0.39K and 0.65K.Similar results were also observed for the ADEBAV method and for the IDW method.The ADEBAV method obtained better values of R 2 and RMSE.The values of R 2 are 0.85, 0.88, 0.88, and the RMSE values are 0.24hpa, 0.35hpa and 0.16hpa, respectively, for the three days; while for the IDW method, R 2 values are only 0.22, 0.33 and 0.03 and RMSE values 1.45hpa, 0.96hpa and 0.45hpa.
The advantage of the ADEBAT/ADEBAV method is that it takes into account the effects of not only horizontal advection, but also the local driving force on the near-surface atmosphere.While the IDW method only considers some effects of horizontal advection by calculating the distance of the pixel to be interpolated to the weather stations.The comparisons between the estimates of Ta and ea from the ADEBAT/ADEBAV method and from the IDW method at Doping Lake proved this.The absolute biases between Ta/ea estimates from the ADEBAT method and Ta/ea measurements at the weather station of Doping Lake are 0.19K, 0.42K and 0.35K (0.5hpa, 0.7hpa and 0.6hpa), respectively, for the three days.Comparatively, the absolute biases between Ta/ea estimates from the IDW method and Ta/ea measurements are 4.33K, 2.36K and 3.33K (4.87hpa, 3.78hpa and 5.13hpa).
The results of the sensitivity analysis show that the ADEBAT method is sensitive most to surface temperature.A 1K increase of surface temperature could result in a 0.6K increase in Ta estimates.The ADEBAV method is most sensitive to Rn−G.A 10% increase of Rn−G could result in a 0.37-hpa decrease of ea estimates.As is known, the Bowen ration is difficult to estimate at a regional scale.However, the two methods are not very sensitive to it.

Figure 1 .
Figure 1.Study area and the distribution of the weather stations.

Figure 2 .
Figure 2. Comparisons between Ta measurements and Ta estimates from the inverse distance weighted (IDW) method (left) and the advection-energy balance for air temperature (ADEBAT) method (right) on 8 April, 30 August and 17 October in 2009.

Figure 3 .
Figure 3. Comparisons between ea measurements and ea estimates from the IDW method (left) and the ADEBAT method (right) on 8 April, 30 August and 17 October in 2009

Figure 4 .
Figure 4. Spatial distributions of Ta estimates from the IDW method (left) and the ADEBAT method (right) on 8 April, 30 August and 17 October in 2009.

Figure 5 .
Figure 5. Spatial distributions of ea estimates from the IDW method (left) and the ADEBAV method (right) on 8April, 30 August and 17 October in 2009.

Table 1 .
Variables and the sources used in the study.FY-2C, Fengyun Meteorological satellite.
Solar radiation, wind speed, air temperature, water vapor pressure Meteorological stations

Table 4 .
The sensitivity of Ta estimates from the ADEBAT method to each input variable.Variations of T0 are in K, and variations of other variables are a percentage (%).

Table 5 .
The sensitivity of ea estimates from the ADEBAV method to each input variable.Variations of Ta are in K, and variations of other variables are a percentage (%).