*2.1. GOES Satellite Data*

The GOES system is operated by the National Oceanic and Atmospheric Administration, National Environmental Satellite, Data and Information Service (NESDIS). The GOES system is based on the use of satellites designed to operate at an orbit of 35,790 km above the earth, remaining stationary to a given point on the ground. The GOES provides data at high temporal frequency (15 min) with continental-scale coverage (N. and S. America). In this study observations from GOES-12 (4/1/2003–4/14/2010) will be utilized (Table 1). Typically, the GOES imager includes five spectral channels (one visible, four infrared). For GOES 8-10 the channels are located at 3.9, 6.75, 10.7, and 12.2 µm whereas for GOES 11–15, the 6.75 µm channel was moved to 6.5 µm and the 12 µm channel was moved to 13.3 µm. The visible, mid-infrared and 11 µm band are typically used for cloud screening while the two thermal infra-red (TIR) bands (10.2–11.2 µm and 11.5–12.5 µm) are used in what is known as a "split-window" approach to retrieve LST.



Note: GOES-8 information is provided since cloud algorithm was originally developed for GOES-8. Channel 2 is separated into the reflected solar radiation component (R2) and the emitted infrared radiation component (T2) [52]; Channel 3 is not used in any of the cloud screening tests.

Aspects of GOES satellite systems that need to be addressed before deriving LST include the spectral characteristics of the GOES sensors and their filter functions, calibration of visible and IR channels, cloud screening methodology (that requires snow analysis information) and the selection of cloud screening tests as appropriate for each satellite configuration, with special distinction between night-time and day-time conditions. Over the period of this study, two separate operational GOES Imagers, one located at a longitude of −75◦ (referred to as GOES-East) and one located at a longitude of −135◦ (referred to as GOES-West) continuously provided imagery over North and South America. In this study, observation from GOES-East only will be utilized for years 2004–2009. The temporal sampling of the GOES Imager is every 30-min over North America and every 3-h over the full disk. Spectral distribution of the GOES 8–15 series are provided in NOAA NESDIS STAR GOES Imager LST ATBD (Version 3.0).

#### *2.2. Visible and Thermal Channel Calibration*

Visible channels are used in the cloud screening part of data processing. Their calibration is done in two stages. First, applied are the pre-launch calibration coefficients to get the first step "nominal reflectance" (A*pre*), and then, the post-lunch calibration coefficients are applied to obtain the final calibrated nominal reflectance (A*post*).

The nominal reflectance is defined as the ratio of reflected radiance to nominal solar irradiance given as:

$$\mathbf{A}p\mathbf{r}e = \mathbf{p}\mathbf{i}^\ast \mathbf{R}\mathbf{/}\mathbf{F}\_0 \tag{1}$$

where pi = 3.141593, R is satellite observed upwelling radiance, and F<sup>0</sup> is the solar irradiance at local zenith and mean Sun-Earth distance.

The pre-launch nominal reflectance is:

$$\mathbf{A}pre = \mathbf{k} \ (\mathbf{\mathcal{X}} - \mathbf{\mathcal{X}}space) \tag{2}$$

where k is the pre-launch calibration constant to convert satellite observed digital counts to nominal reflectance. X is the instrument raw digital count, X*space* is the raw count of the space scene (has been adjusted to 29 for all GOES imagers at NOAA). The Post-lunch calibration is applied by multiplying the A*pre* by a coefficient:

$$\mathbf{A}p\mathbf{ost} = \mathbf{A}p\mathbf{re}^{\mathbf{\*}}\mathbf{C} \tag{3}$$

The pre-launch coefficient for GOES-12 for radiance calibration was 0.5771 and for nominal reflectance it was 0.001141.

NOAA/STAR monitors the GOES imager and updates the post-launch coefficients every month. Coefficients are considered optimal for the days on or after the second Tuesday of the month following the coefficient generation month. For more details, see: http://www.star.nesdis.noaa.gov/smcd/spb/ fwu/homepage/GOES\_Imager\_Vis\_OpCal.php.

Inter-calibration of the infrared channels on the GOES series of satellites has been performed using under-passes of the well calibrated NASA Atmospheric Infrared Sounder (AIRS) sensor on the Aqua platform [36]. Infrared imager data from GOES are stored in GOES Variable Format (GVAR) counts and radiances can be derived from GVAR counts by applying the calibration and scaling coefficients using a procedure described in [37].

Calibration of IR channels of GOES imager data is also done in two stages: (1) converting the imager GVAR raw count to scene radiance; (2) converting the radiance to temperature. To convert a 10-bit GVAR count to scene radiance we use:

$$\mathbf{R} = (\mathbf{\mathcal{X}} - \mathbf{b})/\mathbf{m} \tag{4}$$

where X is the GVAR raw count (10-bit, range from 0 to 1023), m and b are calibration coefficients. The values for m and b depend on channel selected, but are constant for a given channel. The obtained radiance can be convert to effective temperature (K) by inverse of the Planck function:

$$\mathbf{T\_{eff}} = \mathbf{C\_2} \mathbf{^\*n/ln} \left( \mathbf{1} + \mathbf{C\_1} \mathbf{^\*n^3/R} \right) \tag{5}$$

C<sup>1</sup> = 1.191066 × 10e−<sup>5</sup> [m·W/(m<sup>2</sup> ·sr·cm−<sup>4</sup> )], C<sup>2</sup> = 1.438833 (K/cm−<sup>1</sup> ), "n" is the central wave-number of the channel and varies from instrument to instrument.

The effective temperature Teff is further converted to actual temperature by:

$$\mathbf{T} = \mathbf{a} + \mathbf{b} \, \mathbf{\*} \mathbf{T}\_{\mathrm{eff}} + \mathbf{g} \, \mathbf{\*} \, \mathbf{T}\_{\mathrm{eff}} \mathbf{^2} \tag{6}$$

where "a", "b" and "g" are coefficients and their values and central wave-numbers can be found at: https://www.ospo.noaa.gov/Operations/GOES/calibration/gvar-conversion.html#radiance.

Evaluation of calibration was done by comparison of radiances in each channel with NOAA values.
