Advances in Meteorology

Volume 2016 (2016), Article ID 4294219, 11 pages

http://dx.doi.org/10.1155/2016/4294219

## Estimating the Surface Air Temperature by Remote Sensing in Northwest China Using an Improved Advection-Energy Balance for Air Temperature Model

^{1}Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China^{2}University of Chinese Academy of Sciences, Beijing 100049, China^{3}Department of Civil, Environmental and Geomatics Engineering, Florida Atlantic University, Florida, FL 33431, USA^{4}State Key Laboratory of Remote Sensing Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing 100101, China^{5}Heihe Remote Sensing Experimental Research Station, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou 730000, China

Received 2 February 2016; Accepted 29 May 2016

Academic Editor: Philippe Ricaud

Copyright © 2016 Suhua Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

To estimate the surface air temperature by remote sensing, the advection-energy balance for the surface air temperature (ADEBAT) model is developed which assumes the surface air temperature is driven by the local driving force and the advective driving force. The local driving force produces a local surface air temperature whereas the advective driving force changes it by adding an exotic air temperature. An advection factor is defined to measure the quantity of the exotic air brought by the advection. Since the is determined by the advection, this paper improves it to a regional scale by using the Inverse Distance Weighting (IDW) method whereas the original ADEBAT model uses a constant of for a block of area. Results retrieved by the improved ADEBAT (IADEBAT) model are evaluated and comparison was made with the in situ measurements, with an (correlation coefficient) of 0.77, an RMSE (Root Mean Square Error) of 0.31 K, and a MAE (Mean Absolute Error) of 0.24 K. The evaluation shows that the IADEBAT model has higher accuracy than the original ADEBAT model. Evaluations together with a -test of the MAD (Mean Absolute Deviation) reveal that the IADEBAT model has a significant improvement.

#### 1. Introduction

Air temperature is a basic variable that is normally measured at the height of 2 or 1.5 m by meteorological stations. It is not only the primary item of weather forecast but also useful for describing the climate change and energy exchange between the earth surface and the atmosphere [1, 2]. Air temperature also plays an essential role in physical processes of evapotranspiration, photosynthesis, and heat transfer [3]. As a result, many land surface process models including those in climatology, hydrology, and ecology require air temperature as an input variable [4].

Up to now, air temperature has traditionally but mainly been obtained by meteorological stations. However, these meteorological stations are deployed in a limited number of places and thus can only provide information representing the specific local area and often lack a broad enough representation for the regional areas [5]. In addition, meteorological stations are with a low spatial density that usually cannot satisfy the needs either in scientific research or in practical applications [6]. In order to extend the air temperature from a point scale to a regional scale, many spatial interpolation methods [7], for example, inverse distance weighting (IDW), spline function method, and the kriging interpolation method, have been used. However, interpolation results usually cannot reflect the detailed spatial variability, and these spatial interpolation methods would produce large errors, especially for the heterogeneous underlying surfaces [8, 9]. Hence, the lack of sufficient spatial density and lack of enough spatial representativeness in the ground-based air temperature would lead to an inaccurate estimation at a regional scale [1]. Benefiting from the fast development of remote sensing techniques, spatially distributed information on the underlying surface can be obtained. Remote sensing techniques provide a straightforward and consistent way to estimate air temperature at a regional scale with more details than meteorological data. Many studies attempted to retrieve near surface air temperature by thermal infrared remote sensing data [10, 11]. Methods for acquiring the surface air temperature include the temperature-vegetation index approaches (TVX), the statistical approaches, the neural network approaches, and the energy balance approaches [3, 10, 12, 13].

The TVX method is a widely used approach based on the correlation between the normalized difference vegetation index (NDVI) and land surface temperature (LST), which form a trapezoid space [14]. This method assumes that the near surface air temperature is approximately equal to the canopy temperature when the vegetation is dense [1, 14]. Actually, vegetation is with an uneven spatial distribution, and then the air temperature under the condition of partial vegetation can be estimated by extrapolating the air temperature of full coverage [15]. A unique advantage of the TVX method is that it only needs the LST and NDVI data rather than ground-based observations. As a result, the special feature makes it possible for researchers to use numerous types of data, such as NOAA/AVHRR [16], EOS/MODIS [17], and Landsat/ETM+ [18]. Although the TVX method is widely used, it has limitations on sparse vegetation regions where great uncertainty is found [19].

According to many studies, there is a high correlation between the air temperature and LST, and statistical approaches are based upon this relationship [20]. Through linear regression analysis, the method first establishes an experimental equation between air temperatures observed by meteorological stations and LST or brightness temperature of corresponding pixels; then it applies the experimental equation to estimate air temperature in the whole study region. Using data from geostationary satellites, Chen et al. developed a model for simulating surface air temperature at night [21]. Validation results showed a high correlation coefficient of 0.87 and a standard deviation of 1.57 K. Jones et al. used MODIS data to build quantitative relationships between LST and surface air temperature for different geomorphologic types and then applied the quantitative relationships to derive surface air temperature [22]. Results showed that correlation coefficients were from 0.57 to 0.81, and the RMSE were below 0.74 K. Kawashima et al. estimated surface air temperature on the basis of LST derived from Landsat TM, and results showed that the standard error was within 1.85 K [12]. Statistical approaches are simple in principle and convenient to use; however, the modeling highly depends on the time and location of the data caption.

Neural network approaches use plenty of neurons linked to each other to simulate any complicated and nonlinear relationships. Without knowing the physical mechanism among surface air temperature, brightness temperature, and land surface properties, neural network approaches establish relationship between surface air temperature and the input variables by training data alone. Using the AVHRR image, surface elevation and solar zenith angle, together with Julian day as neurons, Jang et al. applied neural network approaches to estimate surface air temperature, and the RMSE of estimates was 1.79°C [10]. Zhao et al. used the albedo, NDVI, DEM, and LST as inputs to the neural network approaches to calculate the daily averaged surface air temperature and the daily maximum and the daily minimum air temperature, and the results indicated that the RMSE was about 0.9°C [23]. Although the method has obvious advantages in expressing the nonlinear relationship between surface air temperature and other variables, it is limited for inputting a large amount of data [11, 24].

Energy and mass exchanging is happening between the land surface and the atmosphere. Without considering the energy transported by horizontal advection and consumed by photosynthesis, the exchange of energy can be described by the energy balance equation:where is the net radiation, is the sensible heat flux, is the latent heat flux, and is the soil heat flux; units of the four items are W/m^{2}. Both the sensible heat flux and the latent heat flux can be regarded as functions of LST and surface air temperature and soil heat flux can be expressed by the net radiation. Through formula derivation, the expression of surface air temperature which contains LST and other land surface variables can be obtained [13]. Using observations at weather stations, surface vegetation, and geomorphology information as inputs to the energy balance equation, Pape and Löffler estimated surface air temperature in the alpine areas [25]. The RMSE of the estimates in their study was between 0.37 and 1.02°C. Zakšek and Schroedter-Homscheidt applied the energy balance equation to estimate surface air temperature [11]. It turned out that 88% of the estimates had absolute deviations within 3°C. The energy balance equation is a physical method with a good portability. However, it needs a large number of variables, and some of the variables, such as aerodynamic resistance and surface roughness, are difficult to acquire by remote sensing. In addition, the presence of advection always characterizes exchanges in near surface layer and contributes to the uncertainty of energy influxes, especially heat storage change; that is to say, the advection would affect the energy balance equation and should be discussed as one of the reasons of energy balance imbalance. That means item () on the left side of (1) is not equal to items () on the right side of (1) [26, 27].

In conclusion, approaches to estimate surface air temperature from remote sensing are usually based on statistical, empirical, and energy balance models. Su et al. proposed an algorithm to expand the surface air temperature to a larger spatial domain, which is based on the fact that the variation of surface air temperature is controlled jointly by the local turbulence of radiant driving force and the horizontal advection of the advective driving force [2]. Zhang et al. developed a model called advection-energy balance for air temperature (ADEBAT) model which is based on the theory put forward by Su et al. [2]. The ADEBAT model assumes that surface air temperature is composed of two parts, the local air temperature and the exotic air temperature [28]. The former is dominated by the radiation effect and mainly indicates the heating effect of longwave radiation on near-surface atmosphere, and this part can be described by the energy balance equation. The latter is caused by the turbulent flow exchange including the turbulent diffusion and exchange of the horizontal advection. Regarding the latter part, an advection factor is defined to measure the quantity of the exotic air. According to the ADEBAT model, Zhang et al. retrieved the surface air temperature in north China, with an higher than 0.77 and an RMSE lower than 0.42 K [28].

The objective of the paper is to improve the ADEBAT model in expanding the advection factor . In the original ADEBAT model, would be shown as blocks with constant values, which is not correct because the advection also has spatial heterogeneity like other geographical elements. The advection factor is affected by the intensity of the advective driving force and will make influence on other places by diffusion. Hence, the spatial distribution of is interpolated by the IDW method in the IADEBAT model.

The outline of this paper is as follows. Section 2 gives a brief description of the ADEBAT model and presents the improvement on of the IADEBAT model. Section 3 describes the study area and the data. Results of the surface air temperature estimation are presented and analyzed in Section 4. The conclusion and discussion are displayed in Sections 5 and 6, respectively.

#### 2. Methodology

##### 2.1. The ADEBAT Model

In this section, the advection-energy balance for air temperature (ADEBAT) model is briefly introduced. The basic idea of the ADEBAT model [28] is as follows. The surface air temperature is determined by two physical processes, the heating effect produced by the longwave radiation from land surface and the advective effect resulting from the turbulent flow exchange. The two effects are also called the local driving force and the advective driving force, respectively. For the former, surface air temperature increases with the accumulation of absorbing surface longwave radiation. For the latter, the advection disturbs the surface air temperature by the turbulent diffusion exchange which develops between land surface and near-surface atmosphere.

Assuming there is one cubic meter of air, the temperature of it is dominated only by the heating effect from land surface, which corresponds to a namely surface energy balance closure. In this case, the surface air temperature is equal to the local air temperature . However, the energy is imbalanced for the advective effect in most situations [29]. The exotic air comes into the one cubic meter and mixes up with the local air in it. If the air temperature driven by the advective effect due to the exotic energy is defined as , then the actual air temperature is a mixture of and . In order to retrieve the surface air temperature, variables related to the two physical processes need to be determined.

###### 2.1.1. Obtaining the Surface Air Temperature

Two situations are treated differently when calculating : energy balance closure and energy balance misclosure.

In the case of energy balance closure, namely, the surface air temperature is controlled by local driving force only. The exchange of energy is described by the energy balance equation (1). The sensible heat flux (see (2)) and the definition of the Bowen ratio (see (3)) are as follows:where is the volumetric heat capacity of air, is the air aerodynamic resistance under the condition of no wind and no advection, and is aerodynamic temperature which is usually substituted by LST in applications [30, 31].

By combining (1), (2), and (3), the surface air temperature can be derived as

Because is equal to the local air temperature under the condition of energy balance closure, hence, can be replaced by in (4), and we attain as follows:

In most cases, the surface energy balance of the near surface air is not closed due to the advective driving force. Like windy days, the effect of local driving force on the air temperature becomes less dominant; at the same time the advective driving force would be more dominant. Both the local driving force and the advective driving force have an impact on the , and is mixed up by and . Provided that the mixing satisfies the linear mixed theory, can be calculated aswhere is the real air temperature and is the volume ratio that is also known as the advection factor. is the air volume that equals the sum of and ; and are the volumes of the exotic air and the local air after the mixing, respectively. Because is the proportion of mixture, it ranges from 0 to 1. When , it means there is no exotic air that corresponds to the situation of energy balance closure, and equals . If , it indicates that the exotic air entirely replaces the local air. In practice, the vast majority of cases is .

###### 2.1.2. Obtaining the Proportion of Mixture

In order to calculate , two other variables, and , need to be acquired (as in (6)) with the aid of air temperature, wind speed, and wind direction observed at meteorological stations. Assuming the subscript represents any pixel in the study area, for and to be calculated, we firstly identify two nearest meteorological stations which have the similar wind speed and wind direction, because it is supposed that similar wind speed and wind direction supply similar advection. The two pixels covering the two meteorological stations are expressed as Pixel 1 and Pixel 2; then we obtain the relationship below: , [28]. Based on (6), two new relationships can be derived:where and are air temperatures of the two weather stations, respectively. and are local air temperatures driven by the local driving force, respectively, and can be calculated by (4) and (5); then and of Pixel can be obtained by solving (9):

After solving and by (10) at every pixel, at every pixel can be obtained by (6).

##### 2.2. Improvement on the ADEBAT Model

According to formula derivation in Section 2.1.2, we know that every inputted meteorological station would get an advection factor by solving (10). For two nearest weather stations with similar wind speed and similar wind direction, that is, with similar advection, pixels around them would use the same advection factor, so the result of the advection factor would be shown as blocks with constant value which are stations-centered. This is how to get in the ADEBAT model. However, the result of acquired by the ADEBAT model is unreasonable for spatial heterogeneity. Hence, it is necessary to make improvement on obtaining the spatial distribution of . The IADEBAT model uses the IDW method to expand the ground-based from a point scale to a regional scale to obtain the spatial distribution of . The reason for applying the IDW method can be described as follows.

The advection factor is affected by the intensity of the advective driving force which goes to other places by diffusion. As a result, to the advective driving force of a certain station, with increasing the distance from the station, the advection factor is becoming less affected by it. Since the IDW method interpolates according to the distance between two inputted objectives, it is appropriate to obtain the spatial distribution of the advection factor by the IDW method. Formulas can be written aswhere is the advection factor of any pixel to be calculated, is the number of the inputted meteorological station, is the advection factor of the station number , is the weight, is the distance between Pixel and the station number , and is the specified power exponent. Different from the ADEBAT model, the IADEBAT model would get gradual distribution results of . Figure 1 gives the sketch on difference between models of the ADEBAT and the IADEBAT.