New method to estimate surface upwelling long-wave radiation from MODIS cloud-free data

Chunlei Wang; Bo-Hui Tang; Xing Huo; Zhao-Liang Li

doi:10.1364/OE.25.00A574

1. Introduction

As an indispensable component of the earth’s surface radiation budget and symbol of a redistribution of the absorbed radiation from the Sun, Surface Upwelling Long-wave Radiation (SULR), which describes the interaction between land surface and atmosphere, and is an outcome of the land surface energy exchange and mainly represents the capability of thermal radiation from the Earth surface [1]. It is a parameter including latent and sensible heat and is one of the key variables controlling fundamental biospheric and geospheric interactions required for the meteorological, hydrological, and agricultural research [2–4]. High-resolution (down to 1 km) of SULR is more important for short-range and mesoscale of land surface processes researches and numerical weather forecasting studies [5–8]. Although SULR can be accurately measured with in situ sensors, unfortunately a lack of large-scale in situ networks makes the estimation difﬁcult across large regions of space. The availability of satellite-based measurements, however, provides the potential for unprecedented global coverage and horizontal spatial continuity, which can be used to delineate regions from global and temporal observations with good accuracy over ground-based techniques.

However, the retrieval of the SULR from satellite data is a very difficult task. Besides the radiometric calibration and the cloud screening procedures, many types of corrections have to be made, such as temperature and broad band emissivity corrections, atmospheric and topography corrections. With the efforts of researchers, two representative categories of methods are developed. One is the LST-emissivity method, which is by calculating item contribution of the surface emitted radiation and the reflected atmosphere downward radiation [9, 10]. As we know, it is hard to acquire high accuracy of surface skin temperature and the broadband emissivity, moreover, the widely used land surface temperature (LST) retrieval algorithm assumes that the observed pixels are homogeneous and isothermal targets. This assumption is reasonable for pure or quasi pure pixels, but for non-isothermal land cover types, which are mixture in most cases, the spatial heterogeneity of the land surface has a large effect on the LST estimation at the pixel scale [11, 12]. Also, another potential source of issue is the atmosphere downward radiation retrieval. As there are obvious relationships between the Top of the Atmosphere (TOA) thermal radiance and SULR, especially in the dry atmospheric conditions, the hybrid method was introduced to calculate SULR with some of the TOA channel radiances, for which an artificial neural network (ANN) and a linear equation are developed to express the relationships [7]. In the framework of the hybrid method, the spatial heterogeneity of the land surface has been partly considered and the problem of separating LST and emissivity is bypassed. But it does not eliminate the effect of atmospheric scattering and take into account of the impact of atmospheric water vapor contents (WVC), which may cause large errors in the estimation, particularly over moist air and heavy aerosol skies. Also it should be noted that the ANN is a black box that is the knowledge of its internal working is never known and it requires a large amount of training set to be trained properly to build the underlying structure. Comparisons of these two categories of the state-of-the-art retrieval method show that the value estimates based on the LST-emissivity method is more stable and accurate, but they both have underestimate values [7, 13].

Within this context, by investigating and surveying the energy distribution of SULR radiation and its sensitive channels, a simple and relatively straight-forward method was developed to estimate SULR from MODIS cloud-free data. Also, a validation of the proposed method with the Surface Radiation Budget Network Data (SURFRAD) was taken and comparisons of the new method with the LST-emissivity method were made in our research. This paper is organized as follows: Section 2 describes the data used in this study. Section 3 presents the rationale and algorithm development to derive the SULR from the TOA radiances and other satellite derived parameters. Section 4 is preliminary result of the algorithm with simulated data and the sensitivity analysis with respect to all the input parameters. Section 5 describes the validations of the proposed model and the comparisons with the LST-emissivity method with the applications to MODIS data. Finally, Section 6 provides a discussion of the results and the conclusions.

2. Materials and methods

Our research is focused on the passive imaging spectro-radiometer MODIS, which is loaded on NASA’s Earth Observing System (EOS) Terra and Aqua platform, it has 36 arranged spectral bands covering visible and infrared wavelengths from approximately 0.4 to 14.0 µm [14]. But our method is not limited to MODIS, it can also be applied to other sensors which have a number of thermal infrared channels. In order to illustrate the method, it is necessary to present the data used in our study firstly.

2.1 Simulated data

To develop a model which is available to estimate SULR under the clear sky, it is crucial to obtain a data set that includes a wide range of coincident measurements of SULR, surface temperature, and emissivities as well as the channel TOA radiance simultaneously with the pixel scales. However, it is not easy to synchronously measure such data in field experiments. Therefore, MODTRAN (Moderate Resolution Atmospheric Transmittance and Radiance Code), which has been extensively validated and severed as a standard atmospheric band model for remote sensing community, can be used to simulate the transmitting procedure of electromagnetic wave between the land surface and satellite level. In MODTRAN, the atmospheric profile data and surface parameter data are the inputs, and different radiative transfer processes are controlled by the cards. Such as card1 is about the main radiation transport driver, card2 is used to set the aerosol and cloud options, etc. For the effects of molecular and particulate absorption/emission and scattering, surface reflections and emission, solar/lunar illumination and spherical refraction are considered, with MODTRAN the radiation flux at ground level under different atmospheric profiles and land surface conditions can be acquired accurately [15].

To make the simulated clear sky TOA radiances generated from worldwide atmospheric situations and land surface types, the Thermodynamic Initial Guess Retrieval (TIGR) database (http://ara.abct.lmd.polytechnique.fr/index.php?page=tigr) which represents a worldwide set of atmospheric conditions from polar to tropical atmosphere was used in our research. Since the objective of this study focuses on retrieving of SULR in cloud-free skies, only the atmospheric profiles suspected as under clear skies were considered. Consequently, the profiles with relative humidity at one of the levels greater than 85% in TIGR were discarded as those seldom happen under clear-sky conditions. About nine hundred and forty-six profiles were selected. For which, the bottom atmosphere temperature (T₀) varies from 231.3K to 314.2K and atmospheric WVC changes from 0.056g/cm² to 6.27 g/cm². Land surface emissivity was obtained from the ASTER spectral library (http://speclib.jpl.nasa.gov/) and UCSB spectral library (http://www.icess.ucsb.edu/modis/EMIS/html/em.html). A total of sixty-nine typical emissivities which can represent the most common land surface types, including forty-six species of soil, fourteen species of vegetation, nine species of water, snow and ice were chosen. Figure 1 is some of the representative emissivities used in the simulations. Since there was no spectral emissivity available beyond the 14μm wavelength and considering the strong absorption of the atmosphere at spectral wavelengths greater than 14μm, the surface emissivity used in MODTRAN simulation beyond this wavelength is assumed to be unity. To increase the representativeness, reasonable variations of LST were set according to the ground level atmospheric temperature. For a definite surface type, taking account of the distribution characteristics of TIGR atmosphere profile database and to make the simulations representatively, reasonable variations of LST are set in the simulation according to the bottom atmospheric temperature $T_{0}$ . LST varies from $T_{0} - 5 K$ to $T_{0} + 15 K$ in steps of 5K when $T_{0} \geq 290 K$ , and from $T_{0} - 5 K$ to $T_{0} + 5 K$ in steps of 5K when $T_{0} < 290 K$ .

Fig. 1 The representative emissivities used in the simulations.

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For the angular dependence of the TOA radiance, six different viewing zenith angles (VZAs) were considered ( $V Z A = 0^{\circ}, 34^{\circ}, 44^{\circ}, 51^{\circ}, 56^{\circ}, 60^{\circ}$ ). After integrating the simulated TOA radiances with the channel response functions of MODIS Thermal Infra-Red (TIR) channels, the MODIS channel radiances were generated. To make it easy to understand, Fig. 2 was used to clarify the simulation process.

Fig. 2 The simulation processes of SULR and TOA brightness temperature.

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2.2 Satellite data

Six MODIS products are also used in our study: 1) MODIS calibrated radiances (MOD021KM/MYD021KM); 2) MODIS geolocation data sets (MOD03/MYD03); 3) MODIS water vapor data sets (MOD05_L2/MYD05_L2); 4) MODIS land surface emissivity product (MOD11_L2/MYD11_L2); 5) MODIS cloud detection product (MOD035_L2/MYD035_L2); and 6) Global land surface satellite broadband emissivity product (GLASS BBE).

1) MOD021KM/MYD021KM contains geo-located and calibrated earth view observations, and creates tiled MODIS images at 1 km resolution data. The observed TOA radiances in channels 31 and 32 are used to calculate the corresponding brightness temperatures with the equivalent wavelengths. 2) The geolocation data set MOD03/MYD03 contains geodetic latitude and longitude, surface height above geoid, solar zenith and azimuth angles, VZAs and azimuth angles, and a land/sea mask for each 1 km sample. The latitude and longitude data are used to perform geometric corrections for other products and the VZAs are used to determine the coefficients of the proposed method. 3) The MODIS precipitable water product MOD05_L2/MYD05_L2 consists of column water-vapor amounts, which are generated at the 1 km spatial resolution of the MODIS instrument using the near-infrared algorithm during the day, and at 5x5 1 km pixel resolution both day and night using the infra-red algorithm when at least nine field of views (FOVs) are cloud free. 4) The MOD11_L2/MYD11_L2 products provide per-pixel LST and emissivity values at 1 km resolutions. 5) As clouds play a critical role in the radiative balance of the Earth, MOD035_L2/MYD035_L2 is provided for a determination of the presence of global cloudiness. 6) The GLASS BBE product generated from preprocessed MODIS standard reflectance and albedo product (MOD09A1 and MCD43B3) is used as the reference to calculate the in situ broadband emissivity in this work. These products are available in hierarchical data format (HDF); MODIS products are provided by NASA’s Goddard Space Flight Center (GSFC) and the Atmosphere Archive and Distribution System (LAADS) (http://ladsweb.nascom.nasa.gov/data/), and the GLASS BBE data is available from the Global Land Cover Facility of the University of Maryland (http://glcf.umd.edu/). Each kind of MODIS product is collected at each ground observation site for approximately one year from January 1, 2012 to December 31, 2012 to guarantee the existence of a sufficient number of observations in clear sky conditions.

2.3 Test site and the measurements

Six study sites in the SURFRAD which involves a rigorous regimen of frequent calibration, quality assurance, and data quality control are used to make a validation of our proposed method. SURFRAD is established through the sponsorship of the NOAA's Ofﬁce of Global Programs and to support satellite retrieval validation, modeling, and climate, hydrology, and weather research over the United States. The primary measurements are the downwelling and upwelling broadband solar and thermal infrared radiations, photosynthetically active radiation also some certain meteorological parameters. They are measured under the widely recognized BSRN (Baseline Surface Radiation Network) measurement standard. SURFRAD data are available via the Internet in daily ﬁles of one-minute data (ftp://aftp.cmdl.noaa.gov/data/radiation/surfrad/). The surface outgoing and incoming longwave radiations are measured with the Precision Infrared Pyrgeometers, for which the instrumental errors are within 11 W/m². The upwelling thermal infrared radiations are used to verify the retrievals of the SULR with our proposed model and the downwelling thermal infrared radiations are used to calculate SULR with the LST-emissivity method when the LST and broadband emissivity are acquired from MODIS TIR data. Detailed information of these test sites is given in Table 1. Symbols A-F represent land surface types of cropland, grassland, natural vegetation mosaic, deciduous broadleaf forest, grass and open shrub, respectively. The land cover types are based on the MODIS/Terra Land Cover Types Yearly L3 Global 0.05Deg CMG (MOD12C1), which includes IGBP classification and two additional classification schemes at a ${0.05}^{\circ}$ (~5600m) spatial resolution (http://edcdaac.usgs.gov/modis/mod12c1v4.asp/).

Table 1. Geographic information of the six study sites

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3. Methodology

Theoretically, the fine-resolution SULR is the summation of surface emitted longwave radiation and the reflected downwelling surface longwave radiation (DSLR), when assuming that emissivity is independent of the surface thermal temperature and neglecting the band-pass effect, it can be expressed as [16]:

S U L R = ε \int_{λ_{1}}^{λ_{2}} \int_{0}^{2 π} \int_{0}^{\frac{π}{2}} B_{λ} (T_{s} (θ_{v}, ϕ)) \sin θ_{v} \cos θ_{v} d θ_{v} d ϕ d λ + (1 - ε) D S L R

where $θ_{v}$ is the VZA, and $ϕ$ is the relative azimuth angle between the view azimuth angle and the solar azimuth angle, $ε$ is the surface broadband hemispherical emissivity, $λ$ is the wavelength, $B_{λ} (T_{s} (θ_{v}, ϕ))$ is the surface thermal emission calculated using Planck’s law at the directional surface temperature $T_{s} (θ_{v}, ϕ)$ .

Under clear-sky conditions, when neglecting the angular effects, the TOA channel radiance of the sensor onboard the satellite in a TIR channel can be with a good approximation as [17]

B_{i} (T_{i}) = τ_{i} (ε_{i} B_{i} (T_{s}) d λ + (1 - ε_{i}) R_{a t m}^{↓}) + R_{a t m}^{↑}

where

T_{i}

is the channel brightness temperature observed in channel

i

at the TOA,

B_{i} (T_{s})

is the radiance measured as the surface is a black body with temperature

T_{s}

,

ε_{i}

is the channel emissivity in channel

i

,

τ_{i}

is the total atmospheric transmittance along the target to sensor path in channel

i

,

R_{a t m}^{↓}

is the channel downwelling atmospheric radiance from the whole hemisphere in channel

i

, and

R_{a t m}^{↑}

is the thermal path atmospheric upwelling radiance in channel

i

. The first term on the right side of Eq. (2) represents the upwelling irradiance at channel

i

that is attenuated by the atmosphere. The second term represents the upwelling atmospheric emission toward the sensor.

We have made a survey of the energy distribution of SULR and the DSLR at the surface, also the bottom atmosphere irradiance and the land surface irradiance. As is shown in Fig. 3, we just take $L S T = 300 K$ and soil type as an example, the curve of SULR energy density is smooth and is similar to that of the energy radiated by a black body at certain temperature. Therefore, an equivalent black body which has the emitted radiance of $B_{i} (T_{e q})$ is introduced. It can be expressed as,

B_{i} (T_{e q}) = ε_{i} B_{i} (T_{s}) d λ + (1 - ε_{i}) R_{a t m}^{↓}

where

T_{e q}

is the equivalent temperature, when substitute it into Eq. (2), one can get

B_{i} (T_{i}) = τ_{i} B_{i} (T_{e q}) + R_{a t m}^{↑}

Here

T_{e q}

is a temperature has very close relationship with LST. It can be acquired with a split-window (SW) algorithm which is developed on the basis of the differential water vapor absorption in two adjacent infrared channels [18, 21]. According to SW algorithm,

T_{e q}

can be expressed as

T_{e q} = c_{1} + c_{2} T_{31} + c_{3} (T_{31} - T_{32}) + c_{4} (\sec θ_{v} - 1) {(T_{31} - T_{32})}^{2}

S U L R = k \times M (T_{e q}) + b = k \times σ T_{e q}^{4} + b

in which

T_{31}

and

T_{32}

are the brightness temperatures of MODIS TIR channel 31 and channel 32 respectively,

θ_{v}

is the view angle,

M (T_{e q})

is the radiation calculated by the Stefan-Boltzman law. The coefficients c₁-c₄ can be derived from the extensive simulated MODIS data, k and b are the error control coefficients. So far, as there is no available database of in situ SULR measurements in coincidence with the MODIS overpasses, the only possible way to obtain the coefficients in Eq. (5) and Eq. (6) is by statistical regression from the database established with numerical simulation. The initial

T_{e q}

can be deduced by Planck law of the radiance in the wavelength corresponding to MODIS channel 31 or channel 32, without loss of generality, we use MODIS channel 31 in this study.

Fig. 3 Comparisons of the energy distribution of SULR, bottom atmosphere irradiance, land surface irradiance also the downwelling longwave irradiance (LST = 300K, soil type, US standard atmosphere).

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4. Results and sensitivity analysis

4.1 Preliminary results

In order to determine the coefficients c₁-c₄ also k and b, usually, atmospheric WVC and $T_{e q}$ are divided into several tractable sub-ranges to improve the fitting accuracy. As the channel bright temperature and atmosphere transmittance are deeply influenced by WVC, in order to make the regression coefficient fit for different atmosphere conditions, the atmosphere WVC of TIGR here was divided into six overlapping interval groups:[0, 1.5], [1.0, 2.5], [2.0, 3.5], [3.0, 4.5], [4.0, 5.5], [5.0, 6.5]. One other thing to note that, SULR is mostly depended on $T_{e q}$ in reality, to expand the adaptability of the proposed model and to improve the accuracy, here $T_{e q}$ was divided into five sub-ranges with an overlap of 5 K, $T_{e q} \leq 280 K$ , $275 K \leq T_{e q} \leq 295 K$ , $290 K \leq T_{e q} \leq 310 K$ , $305 K \leq T_{e q} \leq 325 K$ , $T_{e q} \geq 320 K$ . The coefficients of Eq. (5) and Eq. (6) can be obtained through statistical regressions method for each VZA and each overlapping sub-range. In view of the fact that there is no equivalent temperature available initially, an approximate $T_{e q}$ is firstly acquired by the coefficients determination from all ranges and then it will be substituted into the corresponding sub-ranges to acquire the equivalent temperature also the SULR.

As Fig. 4 shows, respectively, the Root Mean Square Errors (RMSEs) between the actual and estimated SULR as functions of the secant VZA for different sub-ranges of WVC and LST, also the RMSEs between the actual SULR (The simulated data acquired from MODTRAN) and the SULR estimated with the coefficients obtained for the whole range of LST. It is important to note that, the lower LST is usually accompanied with much less WVC, also with the lower SULR error in most of the conditions. Therefore, for $T_{e q} \leq 280 K$ and $W V C \leq 1.5 g / c m^{2}$ , the RMSEs of SULR are relatively stable in each VZA, and the minimum value is 4.09 W/m². The RMSEs are less than 13 W/m² for all sub-ranges when $V Z A \leq 30^{\circ}$ ,or for all sub-ranges with the $V Z A \leq 60^{\circ}$ and $W V C \leq 3.5 g / c m^{2}$ . The RMSEs increase dramatically when $W V C > 3.5 g / c m^{2}$ , with the maximum RMSE of 14.2W/m² for the sub-range $W V C \in [4.0, 5.5]$ and $T_{e q} \geq 320 K$ , for $V Z A = 60^{\circ}$ . The RMSEs of SULR are decided by the accuracy of split-window algorithm and the linear regression equation, which increased as the increasing of VZA. High accuracy of the estimated values distributed at low $T_{e q}$ and WVC conditions. It should be pointed out here that, in practice, to keep it simple, the SULR is estimated with two steps. Rough $T_{e q}$ is acquired by using Eq. (5) with the coefficients derived for the whole range of temperature providing that the sub-ranges of WVC are known initially. Then, the precise $T_{e q}$ can be calculated with the coefficients in sub-ranges of rough $T_{e q}$ and WVC, and SULR can be calculated with Eq. (6). But please keeping in mind that the algorithm also requires WVC as model input, it can be acquired with MODIS total precipitable water product MOD05 /MYD05.

Fig. 4 RMSEs between the actual and estimated SULR as function of the secant VZA for different sub-ranges of WVC and T_eq.

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4.2 Sensitivity analysis

As it indicated that the errors are mainly from the uncertainties of the instrument noises and WVC when estimating of SULR with the proposed model, the robustness of which with respect to these two uncertainties is made in the investigation and a series of sensitivity analyses by estimating SULR for the two cohorts are carried out in the following scenarios.

4.2.1 Sensitivity analysis to instrumental noises

In order to see the significance of the instrumental contingency on susceptibility to the retrieval of SULR, the equivalent noise of the instrument detector on calibration of the brightness temperature (NE∆T) which is a Gaussian random distribution error of 0.1 K, 0.3 K and 0.5 K are, respectively added to the TOA brightness temperatures in Eq. (5). Then we estimate the equivalent temperature using split window algorithm with the noised TOA brightness temperatures. As an example, compared the actual value with the estimated value for the whole LST range, in the sub-range of $W V C \in [0, 1.5]$ when $V Z A = 0^{\circ}$ , the RMSE is 4.55 W/m² for NE∆T = 0.1K, 4.70W/m² for NE∆T = 0.3K, and 4.91 W/m² for NE∆T = 0.5K. Compared the RMSE of 4.52 W/m² for no instrumental noise, the accuracy of retrieval LST can be affected by 0.66% for NE∆T = 0.1K, by 3.98% for NE∆T = 0.3K, and by 8.63% for NE∆T = 0.5K. In the sub-range of $W V C \in [3.0, 4.5]$ when $V Z A = 60^{\circ}$ , the RMSE is 11.93W/m² for NE∆T = 0.1K, 12.07W/m² for NE∆T = 0.3K and 12.33W/m² for NE∆T = 0.5K. Compared the RMSE of 11.90W/m² for no instrumental noise, the accuracy of retrieval SULR can be affected by 0.25% for NE∆T = 0.1K, by 1.43% for NE∆T = 0.3K, and by 3.61% for NE∆T = 0.5K.

4.2.2 Sensitivity analysis to the atmospheric WVC

Knowledge of atmospheric WVC is necessary to improve the precision of SULR with our proposed method. However, due to the effect of haze, sub-pixel clouds and uncertainties in the temperature profile, atmospheric WVC is not easily determined from satellite data. In order to ascertain the effect of the uncertainty of the WVC on the retrieval of SULR with our proposed method, the adjacent sub-range of the WVC which can induce a wrong selection is investigated in our work. As described in the previous section, the WVC was divided into six sub-ranges with an overlap of 0.5 g/cm². A certain WVC could be fit for two adjacent sub-ranges and corresponding to two pairs of coefficients. We aim to analyze the effects of the overlap WVC on the retrieval of SULR.

Figure 5 and Fig. 6 are used as the examples to make a description. From Fig. 5 one can see that the overlap water vapor content falling into two sub-ranges $W V C \in [0, 1.5]$ and $W V C \in [1.0, 2.5]$ , when we estimate the SULR with the water vapor content $W V C \in [1.0, 2.5]$ using the coefficients corresponding to the sub-range $W V C \in [0, 1.5]$ , the RMSE between the actual and the estimated SULR is 6.98W/m², while using the coefficients corresponding to the sub-range $W V C \in [1.0, 2.5]$ , the RMSE is 6.96W/m². From Fig. 6 one can see that the overlap water vapor content falling into two sub-ranges $W V C \in [2.0, 3.5]$ and $W V C \in [3.0, 4.5]$ , when we estimate the SULR with the water vapor content $W V C \in [3.0, 3.5]$ using the coefficients corresponding to the sub-range $W V C \in [2.0, 3.5]$ , the RMSE between the actual and the estimated SULR is 10.7W/m², while using the coefficients corresponding to the sub-range $W V C \in [3.0, 4.5]$ , the RMSE is 10.6W/m².

Fig. 5 Histogram of the difference between the actual and estimated SULR for the overlap water vapor content WVC ∈ [1.0, 1.5] using the coefficients of different sub-ranges.

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Fig. 6 Histogram of the difference between the actual and estimated SULR for the overlap water vapor content WVC ∈ [3.0, 3.5] using the coefficients of different sub-ranges.

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5. Comparisons and validations

The objective of the present work is to estimate the SULR from MODIS data for cloud-free skies. The model inputs are the TOA brightness temperatures, VZA, and WVC. The TOA brightness temperatures and VZA are directly extracted from the MODIS satellite data. The WVC are obtained from MODIS total precipitable water product MOD05/MYD05. In order to make a comparison, SULR calculated with the LST-emissivity method are also taken in this study. As it is not easy to acquire DSLR with satellite data and to make the comparison for simplicity, DSLR are acquired from site measurement, and the broadband land surface emissivity is calculated by using a nonlinear formula [18]. According to the LST-emissivity method, SULR can be calculated with Eq. (8):

ε_{b r o a d} = 0.273 + 1.778 ε_{31} - 1.807 ε_{31} ε_{32} - 1.037 ε_{32} + 1.774 ε_{32}^{2}

S U L R = ε_{b r o a d} σ T_{s}^{4} + (1 - ε_{b r o a d}) D S L R

where

ε_{b r o a d}

is the broadband emissivity,

ε_{31}

and

ε_{32}

are the emissivities in MODIS channels 31 and 32 provided by MODIS Terra /Aqua LST product MOD11_L2/MYD11_L2,

σ

is the Stefan-Boltman constant and

T_{s}

is the land surface temperature. Due to the extreme difficulty or impossibility to validate broadband emissivity with in situ measurements since there are no corresponding data available, we just validate the final SULR derived from MODIS data.

The sensor viewing zenith angle effect must be considered when using the TOA radiance to estimate SULR. To mitigate the angular effect, only MODIS observations with sensor viewing angles less than 45 were used in the validation. It should be pointed out here the site measured value is single-point data, to make it match concisely and eliminate the abnormal conditions, we integrate the data measured 5 minutes before and after the satellite passing by as the approximate value of the MODIS observation. High/thin clouds have no appreciable effect on the SULR, but it has a cooling effect on the TOA radiance, which will induce errors on SULR retrieval, thus are not considered “clear sky” in our study. The resultant detected clear-sky data are used to estimate flux with our proposed method and make a validation.

Table 2. Summary of validation results about the two methods using MODIS data (unit: W/m²)

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Figure 7 and Fig. 8 are the comparison between the SULR estimated using the proposed (solid circles) and LST-emissivity methods (hollow circles) and those measured in situ at SURFRAD test sites for clear sky conditions at the moment of MODIS Terra and Aqua overpass respectively. As we can see, for Terra data, with the LST-emissivity method, the RMSEs of the SULR between site measurements and the retrieved value with the proposed method are from 17.8 to 29.5 W/m², with the biases ranging from −6.3 to −25.2 W/m² for the six sites respectively. With our proposed method, the RMSEs of the SULR between site measurements and the retrieved value with the proposed method are from 14.0 to 28.9 W/m², with the biases ranging from −23.8 to 5.9 W/m² for the six sites respectively. Similar results can be seen in Aqua data, which has relatively higher accuracy compared with it in Terra data. More details of the validation results about the two methods using MODIS data can be seen in Table 2. Compared with LST-emissivity method, the proposed model has relatively high accuracy, especially in the high WVC conditions, and it is faster and better to apply to images with no DSLR available.

Fig. 7 Comparison between the SULR estimated using the proposed (solid circles) and LST-emissivity methods (hollow circles) and those measured in situ at SURFRAD test sites for clear sky conditions at the moment of MODIS Terra overpass. The scattering diagrams of the WVC (plus sign) as function of the actual SULR are also shown.

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Fig. 8 Comparison between the SULR estimated using the proposed (solid circles) and LST-emissivity methods (hollow circles) and those measured in situ at SURFRAD test sites for clear sky conditions at the moment of MODIS Aqua overpass. The scattering diagrams of the WVC (plus sign) as function of the actual SULR are also shown.

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It is important to note that the two models do not work as good as in the simulated data, which may be caused by several reasons. The spatial mismatch issue must be considered when satellite-derived SULR is compared with SURFRAD ground measurements. Unlike DSLR, SULR is sensitive to many surface factors that vary over time, such as vegetation cover, snow cover, and soil moisture. The spatial resolution of MODIS-derived SULR is 1 km at nadir and the footprint of SURFRAD PIRs that measure SULR is about 200m². Ground data used in this study may be less representative of MODIS footprint than that measured using multiple ground sensors within the MODIS footprint simultaneously [19]. However, SURFRAD station locations are chosen such that the landform around the station is uniform, the surface type may change in one year of long-term continuous monitoring sites which may not be suitable to assess errors in individual observations. The earth’s surface behaves almost as an isothermal and homogeneous surface at night. The spatial mismatch problem between the MODIS footprint and ground measurements is more severe at daytime, which may be the reason that less scattering was observed for nighttime observations for the two methods.

The Desert Rock site has the largest bias and RMSE for the two methods. As a high elevation desert site, it is partially vegetated. The errors caused by the Lambertion assumption and spatial mismatch are bigger at this site than at others [20]. Also, cloud contamination is a significant source of error at this site. Cloud contamination is an important factor that leads to negative biases in SULR. MODIS cloud product cannot mask all cloud cover, especially cirrus clouds. Some pixels used in the study may be cloud-contaminated even after manual screening. On the whole, our results are similar with [13], whether the LST-emissivity method or the proposed method, which has underestimate SULR in most of the clear-sky conditions. We also notice that, at least for our cases, the two methods give the similar predicted trends and comparable SULR, and the accuracies are confined to the split-window algorithm. It should be pointed out here that all the SURFRAD sites used are limited to a range of 34°N - 44°N and 117°W - 77° W, thus only one climate region. Also, as there are no other ground measurements available for us, no validation is done over snow/ice/urban/sea surface. A further validation to take all these issues into account will be worked on in the future.

6. Conclusions

Using infrared radiative transfer modeling through the atmosphere, with properties determined by TIGR profiles which are the accurate representations of the atmospheric state, the energy distribution of SULR radiation has been investigated and an equivalent temperature is introduced through which a “split-window” atmospheric correction algorithm is developed for MODIS data to estimate SULR in the clear sky. The presence of the method has potentially severe consequences on the use of satellite data in retrieving SULR with unknown broadband emissivity and DSLR. It is a simple and feasible method which is particularly applicable to MODIS data to acquire relatively high precision SULR under clear sky for which qualified WVC and thermal channel brightness temperatures are available. Compared with the conventional models, it does not need any ground meteorology data as model input in the estimation of SULR.

Preliminary researches with the simulated data show that the model is VZA dependent. The RMSEs are less than 13 W/m² for all sub-ranges with the VZA less than 30°, or for all sub-ranges with the VZA less than 60° and the WVC less than 3.5 g/cm². The RMSEs of SULR are decided by the accuracy of split-window algorithm and the linear regression equation, which increased as the increasing of VZA. High accuracy of the estimated values distributed at low LST and WVC conditions.

In order to show the applicability of the proposed method, field measurements at six sites of SURFRAD under clear sky conditions at the moment of MODIS overpass have been used to make a validation. For Terra data, with our proposed method, the RMSE of the SULR between site measurements and the retrieved value with the proposed method are from 14.0 to 28.9 W/m², with the biases ranging from −23.8 to 5.9 W/m² for the six sites respectively. Similar results can be seen in Aqua data, which has relatively higher accuracy compared with it in Terra data. Compared with LST-emissivity method, the proposed model has relatively high accuracy, especially in the high WVC conditions.

Such an approach has been shown to be feasible when applied to SULR measurements of MODIS, especially when there is no broadband emissivity and DSLR available. Adaption of such an approach to ASTER and other well-calibrated infrared imagers is a topic worthy of further research. Although this study has been directed towards the infrared SULR retrievals of MODIS, the results and conclusions are applicable to SULR retrievals from other scanning infrared radiometers on polar-orbiting satellites and radiometers on geostationary satellites. The regression coefficients presented here will of course change in value because each sensor has its own specific spectral response functions, but the designing concepts are expected to hold across a wide range of sensors.

Funding

National Key Research and Development Program of China (NO.2016YFA0600103); National Natural Science Foundation of China (61572167,61502136,41571353 and 41231170); Innovation Project of LREIS (O88RA801YA), International Cooperation Project of Ministry of Science and Technology Of China (NO.2015DFA11450).

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Site	Name	Location		Altitude(m)	Surface type
A	Bondville, IL	40.05°N,	88.37°W	213	Cropland
B	Boulder, CO	40.13°N,	105.24W	1689	Grassland
C	Goodwin Creek, MS	34.25°N,	89.87°W	98	Nature vegetation Mosaic
D	Penn State, PA	40.72°N,	77.93°W	376	Deciduous Broadleaf Frost
E	Sioux Falls, SD	43.73°N,	96.62°W	473	Grass
F	Desert Rock	36.63°N,	116.02°W	1007	Open Shrubland

Site
	Bias	RMSE	Bias	RMSE	Bias	RMSE	Bias	RMSE
A	−6.3	18.6	−1.4	17.4	−5.2	15.9	−3.3	15.2
B	−7.7	18.5	−4.1	15.7	−8.9	17.9	−4.0	14.1
C	−14.9	19.3	−8.4	16.2	−15.6	19.2	−13.7	18.7
D	−14.3	23.3	−9.9	21.2	−18.6	22.7	−12.2	19.3
E	−7.8	17.8	5.9	14.0	−9.7	17.0	−1.2	16.3
F	−25.2	29.5	−23.8	28.9	−23.2	28.7	−21.3	28.2

Site	Name	Location		Altitude(m)	Surface type
A	Bondville, IL	40.05°N,	88.37°W	213	Cropland
B	Boulder, CO	40.13°N,	105.24W	1689	Grassland
C	Goodwin Creek, MS	34.25°N,	89.87°W	98	Nature vegetation Mosaic
D	Penn State, PA	40.72°N,	77.93°W	376	Deciduous Broadleaf Frost
E	Sioux Falls, SD	43.73°N,	96.62°W	473	Grass
F	Desert Rock	36.63°N,	116.02°W	1007	Open Shrubland

Site
	Bias	RMSE	Bias	RMSE	Bias	RMSE	Bias	RMSE
A	−6.3	18.6	−1.4	17.4	−5.2	15.9	−3.3	15.2
B	−7.7	18.5	−4.1	15.7	−8.9	17.9	−4.0	14.1
C	−14.9	19.3	−8.4	16.2	−15.6	19.2	−13.7	18.7
D	−14.3	23.3	−9.9	21.2	−18.6	22.7	−12.2	19.3
E	−7.8	17.8	5.9	14.0	−9.7	17.0	−1.2	16.3
F	−25.2	29.5	−23.8	28.9	−23.2	28.7	−21.3	28.2

New method to estimate surface upwelling long-wave radiation from MODIS cloud-free data

Abstract

1. Introduction

2. Materials and methods

2.1 Simulated data

2.2 Satellite data

2.3 Test site and the measurements

3. Methodology

4. Results and sensitivity analysis

4.1 Preliminary results

4.2 Sensitivity analysis

4.2.1 Sensitivity analysis to instrumental noises

4.2.2 Sensitivity analysis to the atmospheric WVC

5. Comparisons and validations

6. Conclusions

Funding

References and links

Cited By

Figures (8)

Tables (2)

Equations (8)

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