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2.7.1 Level 2 Algorithms

The AATSR Level 2 processing steps are summarised in figure2.12 . The main steps are also outlined below.

Level 2 processing flow diagram (18K)
Figure 2.12 Overview of the Level 2 processing.

2.7.1.1 Prepare Inputs

Before averaged BTs and reflectances can be derived from the input GBTR product, the relevant measurement and annotation data must be extracted from the L1B product as follows.

2.7.1.1.1 Input Annotation Data Sets

The Annotation Data Sets of the GBTR product that are required for Level 2 Processing are read in and converted into appropriate units where necessary.

2.7.1.1.2 Assemble Regridded Brightness Temperature Arrays

Grid co-ordinates and channel brightness temperatures / reflectances for forward and nadir views are read in from the appropriate MDS of the GBTR product and arranged in the required memory configuration.

2.7.1.1.3 Interpolate Solar Angles

The solar azimuth and elevation and satellite azimuth and elevation, all measured at the pixel, are available for a series of uniformly spaced tie point pixels in ADS #5 of the GBTR product for the nadir view and in ADS #6 for the forward view images. This step derives those angles that are required for level 2 processing at every scan, and at the bound edges of the bands, by linear interpolation, between these tie points. Only the solar elevation is required for Level 2 processing as presently defined.

2.7.1.1.4 Interpolate Image Pixel position

The (geodetic) latitudes and longitudes of a series of uniformly space tie point pixels are available in ADS #3 of the GBTR. This module derives the latitude and longitude of each image pixel by linear interpolation, in two dimensions, between these tie points.

2.7.1.2 Derive Gridded Product

This step derives the contents of the GST product at 1 km resolution from the infra-red brightness temperatures. It derives the sea surface temperature (SST) or, over land, the vegetation index (NDVI), at 1 km resolution, using cloud free data.

The derivation of SSTs uses the 11 and 12 µm channels for day time data and for night time data the 11, 12 and 3.7 µm channels. For each 1 km resolution element two results are obtained, one using the combined nadir and forward views and the other using the nadir view alone.

The SSTs are calculated using preset retrieval coefficients. These coefficients are provided for both nadir only and combined view SSTs and are a function of latitude and viewing angle. Smoothing is applied by smoothing the difference between the calculated SST and the 11 µm brightness temperature. The effect is to smooth the atmospheric correction.

Details of the SST retrieval algorithm are contained in the following section:

The NDVIs are calculated using the nadir 0.67 and 0.87 µm channels and the results are returned in the combined image land pixels.

In order to provide completely filled images the 11 µm brightness temperature is returned in the nadir image field when over land. In cloudy conditions the cloud top temperature is returned in the nadir image field and the cloud top height in the combined view image field (see section 2.12.1.5. concerning placeholders).

2.7.1.2.1 SST Retrieval

2.7.1.2.1.1 Physical Justification

2.7.1.2.1.1.1 Introduction

Infrared radiation emitted by the surface is modified by its passage through the atmosphere as a result of absorption by atmospheric gases and absorption and scattering by liquid and solid particles. Accurate measurements of SST from space are only possible when the particle effects are small, when clouds and fog are absent, and when the reflected/scattered solar component of the signal is negligible (i.e., 3.7 µm night). In these conditions the total upwelling infrared radiance L total(ν) observed at a given wavenumber ν by the satellite at an altitude Z is the sum of three components:

  • the radiation emitted by the surface L s (ν);
  • the radiation emitted by the atmosphere L a(ν); and
  • the atmospheric radiation L ar(ν) reflected from the surface back to space.

Thus

eq 2.165

The three terms in Equation (1.1) are as follows;

eq 2.166

eq 2.167

eq 2.168

where εs is the surface emissivity, T s the surface temperature, τ(ν, 0, Z) is the transmission of the atmosphere from the surface to the satellite at height Z, ea is the emissivity of the atmosphere at height z, τ(ν, z, Z) is the transmission of the atmosphere from height z to the satellite, and τ(ν, z, 0) is the transmission of the atmosphere from the height z to the surface. B(ν, T) is the Planck Function, given by the expression

eq 2.169

where C1 and C2 are the first and second radiation constants, respectively.

The observed radiance in the channel of width Dν can be expressed in terms of the brightness temperature of the scene T:

eq 2.170

This equation can be solved to give the brightness temperature T corresponding to the observed radiance.

In the absence of the atmosphere the brightness temperature is a direct measurement of the radiating surface temperature of the Earth. Therefore, in a world without atmosphere, accurate SST could be obtained from a single brightness temperature, provided the surface emissivity were known. However, the presence of the real atmosphere complicates the retrieval of SST, and it is necessary to make measurements at a number of different of wavelengths in parts of the spectrum where the effects of the atmosphere differ; this is known as the multi-channel or multi-spectral approach to atmospheric correction.

The most commonly used multi-channel method is the 'split window' method, in which the 10 - 13 µm atmospheric window is divided into two spectral bands in which the atmospheric effects are markedly different. The two split window channels are at 11 µm and 12 µm respectively; the atmospheric effect in this part of the spectrum is mainly due to water vapour and is much stronger at 12 µmm than at the shorter wavelength. Thus, by using the two split window brightness temperatures it is possible to provide a correction for the effects of the atmospheric water vapour and therefore to retrieve a more accurate SST.

AATSR uses the 11/12 µm split window, and has a further channel at 3.7 µm. This improves the retrieval, as it provides an additional atmospheric measurement and a more accurate determination of temperature because of the stronger temperature dependence of the Planck function at the shorter wavelength. The SST is retrieved using an algorithm that combines the brightness temperatures T i from each channel in the following way:

eq 2.171

In addition to the multi-channel approach, AATSR employs along track scanning to provide a further improvement in the atmospheric correction. The dual angle data are used in the retrieval in the same way as the other brightness temperatures.

eq 2.172

where the subscript i is the spectral channel identifier, and the superscripts n and f are the nadir and forward view brightness temperature data from each channel, respectively. The coefficients in and represent an optimum linear relationship between true sea surface temperature and the measured channel brightness temperatures.

2.7.1.2.1.1.2 Channel selection

The objective of the algorithm is to use the measured infrared brightness temperature values to determine, for each cloud-free pixel over sea, the best estimate of the Sea Surface Temperature (SST) of the pixel, to form an SST image at 1 km resolution.

In practice the derivation of SST makes use of either 2 infra-red channels (11 micron and 12 micron), or of all three infra-red channels (3.7 micron, 11 micron and 12 micron), and may use either one or both views. The selection of the set of channels to be used depends on the availability of the data.

Whenever possible, both the nadir view and forward view pixels are used. Cloud contamination for the forward view pixels is more likely than for the nadir view owing to the larger sampling area in the former, so the possibility of using the brightness temperatures from the nadir view only is also catered for. (It would be possible in theory to derive retrieval coefficients for the case of a forward view image only, but this is not done in practice.)

From eq. 2.171 , the algorithms using the nadir view only are given by

eq 2.173

or

eq 2.174

When both views are used ( eq. 2.172 ), the corresponding equations are

eq 2.175

or

eq 2.176

respectively.

The coefficients a, b, c, d for use in the above equations are pre-determined by means of a radiative transfer modelling calculation. A radiative transfer model (RTM) is used to derive the expected brightness temperatures, essentially by evaluating eq. 2.165 to eq. 2.170 for each of a representative ensemble of atmospheric states and SST values. From the results the coefficients of the linear regression between SST and the measured brightness temperatures are derived. The RTM, and the method of deriving the coefficients, is described in Zavody et al, 1995 1.3. in the context of the ATSR instrument. The derivation of the AATSR coefficients proceeded along similar lines, but with the following differences;

  • The version of the RTM used incorporated certain improvements;
  • Aerosol robust coefficients for the dual view retrieval were derived using the method described by Merchant et al, 1999 1.3. ;
  • A modified across-track banding scheme was used, as described below.

Preset coefficients are specified for each of three geographical regions: tropical, mid-latitude and polar (note that in practice the aerosol-robust dual view coefficients for AATSR are global: that is the same coefficients are defined for each of the three latitude zones). The coefficients also depend on the viewing geometry, and so the across-track distance of the pixel determines the set of coefficients to be used for a given pixel in a given region. In total, 38 different sets of coefficients are given for each geographical region; these represent 38 different across-track distances and correspond to 38 approximately equally spaced air masses across the instrument swath. These issues are discussed in 2.7.1.1.3. and 2.7.1.1.4. following.

2.7.1.2.1.1.3 Latitude zones

The latitude of the pixel governs whether the coefficients for the tropical, temperate, or polar regions are to be used. Three zonal limits are defined, TROPICAL_INDEX, TEMPERATE_INDEX, and POLAR_INDEX. Numerical values are given in .

Table 2.29 Latitude Limits

Index

Value

TROPICAL_INDEX

12.5°

TEMPERATE_INDEX

37.0°

POLAR_INDEX

70.0°

The latitude and across-track band number of the pixel determine the usage of the retrieval coefficients as follows. If the absolute value of the latitude is less than TROPICAL_INDEX, the retrieval coefficients for the tropical zone and for the appropriate across-track distance are used. Similarly if the absolute value of the latitude is greater than or equal to POLAR_INDEX the retrieval coefficients for the polar or high-latitude region and for the appropriate across-track distance are used.

If the pixel lies in the mid-latitude zone, a slightly more complex calculation is undertaken to ensure that the retrieval varies smoothly with latitude. In these cases two retrievals are computed, and the final SST is obtained by linear interpolation between them with respect to latitude. If the absolute value of the latitude is less than TEMPERATE_INDEX but is not less than TROPICAL_INDEX, two retrievals are made using the retrieval coefficients for both the tropical and mid-latitude zones. If these two retrievals are T tropical and T temperate respectively, the final value for the retrieved SST is given by

eq 2.177

where

eq 2.178

and latitude is the latitude of the pixel.

Similarly if the absolute value of the latitude is less than POLAR_INDEX but not less than TEMPERATE_INDEX, two retrievals are made using the retrieval coefficients for the high-latitude and mid-latitude regions. If these two retrievals are T polar and T temperate respectively, the final value for the retrieved SST is given by

eq 2.179

where

eq 2.180

In each of the above cases of course the relevant retrieval coefficients appropriate for the across-track distance of the pixel are used.

This approach ensures that the retrievals do not show discontinuities at latitudes equal to one of the values TROPICAL_INDEX, TEMPERATE_INDEX, or POLAR_INDEX. Note that because the retrieval equations are themselves linear, the method of linear interpolation described above is equivalent to assuming that the individual retrieval coefficients vary linearly with latitude in the ranges TROPICAL_INDEX < latitude < TEMPERATE_INDEX and TEMPERATE_INDEX < latitude < POLAR_INDEX.

2.7.1.2.1.1.4 Across-Track Bands

In the first instance, coefficients are derived off-line for two across-track positions, corresponding to the swath centre and swath edge. To derive retrieval coefficients for intermediate across-track positions, it is assumed that the coefficients should be proportional to the air mass through which the pixel is viewed, and the coefficients for intermediate positions are derived by linear interpolation with respect to nadir air mass between the centre and edge values.

Interpolated coefficients are derived for a set of 38 equally spaced air mass values, which correspond to the centres of 38 bands parallel to the swath on each side of the ground track. The same coefficients are used for all pixels that fall within a band, and the separation between the bands is sufficiently small that perceptible discontinuities are not introduced at the band edges.

The air mass is proportional to secθ, where θis the angle of incidence of the line of sight to the pixel. 2.13 shows the relationship between the normalized air mass secθand the across-track co-ordinate x for the nadir view, and for the nominal scan geometry.

Figure 2.13 Normalized air mass versus across-track position (km)

Suppose the pixels are indexed in an across-track direction by j (0 ≤ j < 512). The across-track co-ordinate x, measured from the centre of the swath, of the mid-point of pixel j is then given by

eq 2.181

Let k (0 ≤ k < 38) be an index to the across-track bands. The bands are defined so that pixel j falls in band k where

eq 2.182

for general k, or

eq 2.183

in the special case k = 0. Here θj is the angle of incidence at pixel j, and Δ is the selected air mass increment (strictly the increment in secθ), which defines the width of the bands. The adopted value of the increment Δ is 0.00207186.

2.14 shows the relationship between band and pixel number. Note that band 0 is centred on the ground track and that the bands are arranged symmetrically about the ground track. The precise mapping between band and pixel numbers is defined in the auxiliary Across-track Band Mapping Look-up Table, which is contained in the SST Retrieval Coefficient Data File (ATS_SST_AX) 6.5.8. .

2.7.1.2.1.1.5 Smoothing

Finally, in the case of the full resolution (gridded) product smoothing is applied to the derived temperature images. This step is required because, although the derived temperatures are valid estimates of the true SST, they are affected by noise to a greater degree than the measured brightness temperatures themselves, because the coefficients multiplying the brightness temperatures in equations ( eq. 2.173 - eq. 2.176 ) may exceed unity, and combine to yield a net increase in variance.

The smoothing technique adopted uses the difference between the derived SST image and the nadir-view 11 micron brightness temperature image. If there were no atmosphere, the 11 micron brightness temperature at near normal incidence would be a very good approximation to the SST (differing only because the emissivity of the sea surface viewed at normal incidence differs slightly from unity). Thus the difference between the retrieved SST and the nadir-view 11 micron brightness temperature is a good measure of the atmospheric attenuation in the 11 micron channel, and might be expected to show only small spatial variations over distances of a few kilometres. Thus if this difference is smoothed, the result may be added to the nadir-view 11 micron brightness temperature to give the smoothed SST.

Figure 2.14 The across-track band number as a function of pixel index

The difference is averaged over square blocks of n by n pixels, the pixels corresponding to valid retrievals being included in the average with equal weight. The size n of the smoothing block is defined by a parameter in the auxiliary file of Processor Configuration Data (ATS_PC2_AX 6.5.7. ). The nominal value of n is 3, so that up to 9 pixels contribute to each average. The smoothed difference is then added to the nadir-view 11 micron brightness temperature to give the final retrieved SST value. If no valid pixels contribute to the average, or if there is no valid nadir view SST, a corrected SST is not calculated and the smoothed SST value is set to - 1. (Note that this over-rides the setting to the 11 micron temperature for invalid SST retrievals noted above.) The smoothing is carried out separately for the nadir and dual view images.

The smoothing takes account of cloud flagging; that is, pixels flagged as cloudy are not included in the average, or an increased variance of the smoothed SST in cloudy areas would result.

The smoothing step is not required in the case of the averaged (AST) product.

2.7.1.2.1.2 Algorithm Description

2.7.1.2.1.2.1 Full resolution (gridded) Surface Temperature Image Product

The AATSR full resolution geophysical product (ATS_NR__2P) contains a single Measurement Data Set (MDS), the contents of which are switchable; that is to say, the content of each pixel field depends on the surface type. Specifically, the content of each data field depends on the setting of the forward and nadir cloud flags and the land flag. Thus the processor must check the flag settings for each pixel before selecting the appropriate procedure for the surface type. These checks are integral to the logical structure of the algorithm, and so are shown in the algorithm description that follows, although the emphasis is on the detailed derivation of SST for clear sea pixels.

In the following, a pixel value is invalid if it does not represent a valid brightness temperature. This is indicated when the numerical value corresponds to an exception value; otherwise the pixel is valid.

The appropriate across-track band index corresponding to an image pixel is obtained by entering the auxiliary Across-track Band Mapping Look-up Table (from the auxiliary file ATS_SST_AX 6.5.8. ) with the across-track index of the pixel. This value is used to index the set of coefficients to extract the set corresponding to the correct air mass value.

The logic of the procedure used for deriving the GSST product at 1 km resolution is as follows. Initially, the GSST confidence word flags nadir_image_valid and combined_image_valid associated with each image pixel are initialised to the value FALSE. The nadir image field is also set to the 11 micron brightness temperature; this is the default if a valid retrieval is not achieved.

Steps 1 to 3 below are executed for each image scan, then Step 4 is executed to smooth the SST image.

1) Calculate the nadir-view image. For each pixel in the scan, the procedure is as follows:

The surface type flags (cloud flag and land/sea flag) associated with each pixel are inspected.

If the pixel is over land, a land surface temperature (LST) retrieval is attempted (see later section). If this is successful, the nadir image valid flag in the confidence word is set to TRUE.

If the pixel is cloudy, the nadir view field is set to the 11 micron brightness temperature, as an estimate of the cloud top temperature, and the nadir image valid flag in the confidence word is set to TRUE.

Otherwise the pixel is a clear sea pixel, and an SST retrieval is attempted.

The nadir-view 11 and 12 micron brightness temperatures are inspected to ensure that both are valid. If either is invalid, an SST cannot be retrieved and processing continues at the next pixel.

If both are valid, an SST retrieval is attempted using either a 2-channel algorithm or a 3 channel algorithm. If the solar elevation is negative (indicating a night-time pixel) and the 3.7 micron brightness temperature is valid, a 3 channel algorithm (Equation) is used, otherwise a two-channel retrieval (Equation) is used. If the 3.7 µm brightness temperature is valid, the corresponding flag of the confidence word is set accordingly. In either case the retrieval is performed using the coefficients for the appropriate across-track band index and taking account of the geographic zone as described below.

1.1) If the pixel lies within the tropical region (latitude < TROPICAL_INDEX) or if the pixel lies within the polar region (pixel latitude = POLAR INDEX), then the SST is calculated using the retrieval coefficients for that region and for the for the appropriate across-track band index. Equation is used if a two-channel retrieval was specified, or Equation is used if a three-channel retrieval was specified.

1.2) If the pixel lies within the temperate region, then the SST value is calculated using the coefficients for the temperate region, and a second SST value is calculated using the coefficients for the polar or tropical region. The coefficients for the tropical region are used if the pixel latitude is less than TEMPERATE_INDEX, otherwise the coefficients for the polar region are used. In either case the retrieval coefficients for the appropriate across-track band index are used, with Equation if a two-channel retrieval was specified, or Equation if a three-channel retrieval was specified. A linear interpolation with latitude is used to obtain the SST value from those calculated for the two regions, using Equation or Equation as appropriate.

1.3) In either case the 'nadir-only SST is valid flag' of the confidence word is set.

2) Calculate the dual-view image. For each pixel in the scan the dual-view SST is calculated as follows:

The surface type flags (cloud flag and land/sea flag) associated with the pixel in each view are inspected.

If the pixel is over land, and the 0.87 and 0.67 micron channel reflectances are valid, the NDVI is computed and assigned to the combined image field, and the combined image valid flag in the confidence word is set to TRUE.

If the pixel is cloudy, the combined image field is set to zero, and the combined image valid flag in the confidence word is set to FALSE. (The combined image field is reserved for the cloud top height value in a future revision of the processor.)

Otherwise the pixel is a clear sea pixel, and an SST retrieval is attempted.

If the 11 or 12 micron brightness temperature values of the pixel for either view are invalid, an SST cannot be retrieved and processing continues at the next pixel.

If all are valid, an SST retrieval is attempted using either a 4-channel algorithm or a 6-channel algorithm. If the solar elevation is negative (indicating a night-time pixel) and the 3.7 micron brightness temperature is valid in both views, a 6-channel algorithm (Equation) is used, otherwise a four-channel retrieval (Equation) is used. If the 3.7 µm data is valid, the corresponding flag of the confidence word is set accordingly. In either case the retrieval is performed using the coefficients for the appropriate across-track band index and taking account of the geographic zone as described below.

2.1) If the pixel lies within the tropical region (latitude < TROPICAL_INDEX) or if the pixel lies within the polar region (latitude = POLAR_INDEX), then the SST is calculated using the retrieval coefficients for that region and for the appropriate across-track band index. Equation is used if a four-channel retrieval was specified, or Equation if a six-channel retrieval was specified.

2.2) If the pixel lies within the temperate region, then the SST value is calculated using the coefficients for the temperate region, and a second SST value is calculated using the coefficients for the polar or tropical region. The coefficients for the tropical region are used if the pixel latitude is less than TEMPERATE_INDEX, otherwise the coefficients for the polar region are used. In each case the retrieval coefficients for the appropriate across-track band index are to be used, with Equation if a four-channel retrieval was specified, or Equation if a six-channel retrieval was specified. A linear interpolation with latitude is used to obtain the SST value from those calculated for the two regions, using Equation or Equation as appropriate.

2.3) In each case the combined image valid flag of the confidence word is set.

3) The confidence word flags that relate to cloud, blanking pulses, and cosmetic fill are set appropriately.

4) Finally, the SST image is smoothed as described in section 2.7.1.2.1.1.5. above

2.7.1.2.2 Land Surface Temperature Retrieval

2.7.1.2.2.1 Physical Justification

The definition [3] of the LST algorithm selected for AATSR is based on work by Prata [1, 2] to develop algorithms to retrieve land surface temperature (LST) from ATSR and AVHRR data. These algorithms are based on radiative transfer theory applied to the exchange of radiation between the surface and atmosphere, and have been subjected to extensive validation using a network of ground-truth sites across Australia.

The algorithm for LST retrieval is based on a split-window algorithm similar to that used for two-channel nadir-only SST retrieval:

eq 2.184

where a0 , b0 and c0 are coefficients that depend on the land surface characteristics, viewing angle, and atmospheric water vapour, and T11 and T12 represent the brightness temperatures in the 11 and 12 micron channels respectively. In order to permit an additional tuning of the algorithm, a weak non-linearity is introduced by replacing Equation eq. 2.184 by

eq 2.185

where the index n depends on the incidence angle θ as follows:

eq 2.186

Here m is an empirical constant. Currently, the value m = 5 is adopted. Equation eq. 2.185 reduces to Equation eq. 2.184 when n = 1. If T 11 - T12 is negative, then the term (T11 - T12 ) n in Equation eq. 2.185 is in general complex. This case can certainly arise in practice, and the solution adopted is to set n = 1 if T11 < T12 ; in other words, to revert to Equation eq. 2.184 in this case. The value n = 1 is also adopted in the case of inland lakes.

2.7.1.2.2.1.1 Retrieval Coefficients

The essence of the algorithm is to apply Equation eq. 2.184 above to the 11 and 12 micron brightness temperatures in the nadir view. The retrieval coefficients a 0, b 0, c 0, depend on surface characteristics and atmospheric water vapour. Their values must reflect the complex variability of the surface, and this is achieved by means of look-up tables read from the auxiliary files. These define the local characteristics of the surface, and the local climatology, at a resolution of 0.5° in latitude by 0.5° in longitude.

Let the latitude and longitude of the pixel indexed by [i, j] be represented by φ(i, j), λ(i, j) respectively, with the conventions that

eq 2.187
, and

eq 2.188

It is convenient to redefine the origin of latitude and longitude so that both are positive. We thus define the shifted co-ordinates

eq 2.189

The auxiliary files define the surface class and vegetation fraction in cells of dimension 0.5° in latitude by 0.5° in longitude. Suppose that each cell is identified by the co-ordinates of its origin, defined to be its lower left-hand (i.e. south-west) corner. The cells form a two dimensional array indexed by latitude and longitude indices lat_index and lon_index, such that the origin of the cell indexed by lat_index and lon_index is

eq 2.190

where Δj, Δl are the cell dimensions in latitude and longitude respectively. In the present case

$\Delta\phi=\Delta\lambda=0.5\,degrees$ eq 2.191
,

and so the indices of the cell containing the point (φ, λ) are

eq 2.192

For each cell, entries in a look-up table [LUT] define the following quantities:

  • The surface type classification within the cell. The cell is assigned to one of 14 surface types represented by an integer in the range 1 to 14. The surface types adopted comprise 13 land cover classes or biomes together with an additional class representing inland lakes, and are listed in Table 1. In the following the surface type classification will be represented by the symbol class.
  • The vegetation fraction f (0 < f < 1) representative of the cell. This quantity has a seasonal variation that is represented in the tables by defining 12 values of f, one for each calendar month. The basis of the definition of this variation is defined in [3].
  • The monthly mean precipitable water at the centre of the cell. Again 12 values are given, one for each month, to represent the seasonal variation.

A further table defines four sets of regression coefficients a, b and c for each surface type, corresponding to vegetation and bare soil, and to day and night conditions.

Table 2.30 The land type classification used by the AATSR LST algorithm.

Type

Description

Type

Description

1

Broadleaf evergreen trees

8

Broadleaf shrubs with groundcover

2

Broadleaf deciduous trees

9

Broadleaf shrubs with bare soil

3

Broadleaf and needleleaf trees

10

Dwarf trees, shrubs with groundcover

4

Needleleaf evergreen trees

11

Bare soil

5

Needleleaf deciduous trees

12

Broadleaf deciduous trees with winter wheat

6

Broadleaf trees with groundcover

13

Perennial land ice

7

Groundcover

14

Permanent inland lakes

Thus for a given pixel, its latitude and longitude define the 0.5° ´ 0.5° cell within which the pixel falls according to the equations eq. 2.192 . The surface type for this cell, and the vegetation fraction for the current month and for the same cell, are extracted from the look-up tables.

The vegetation fraction is used to take account of the seasonal variation of vegetation cover, and the consequent effect on the retrieved surface temperature. For each surface type, and for day and night conditions separately, two sets of regression coefficients are provided, representing bare soil and vegetated surfaces. The coefficients used for the retrieval are derived as a linear combination of these with the relative weights determined by the vegetation fraction.

Thus given the surface type, the table of coefficients is entered to extract the two sets of regression coefficients a, b and c for this surface class for both vegetation and bare soil. The day or night-time coefficients, as appropriate, are extracted, and the following linear combinations are derived from the mean of the vegetation and bare soil values, weighted by f, (1 - f) respectively. Thus we have

$a_f(class)=f\,*\,a(class,\nu)\,+\,(1.0\,-\,f)\,*\,a(class,s)$ eq 2.193

$b_o(class)=f\,*\,b(class,\nu)\,+\,(1.0\,-\,f)\,*\,b(class,s)$ eq 2.194

$c_o(class)=f\,*\,c(class,\nu)\,+\,(1.0\,-\,f)\,*\,c(class,s)$ eq 2.195

In these equations the indices v, s designate vegetation and bare soil respectively, so that for example a(class, v) represents the coefficient a applicable to a vegetated surface of surface type class, and so on. Finally, before eq. 2.184 is evaluated, a correction is applied to the coefficient a 0 that depends on the precipitable water.

$a_o = a_f + d * (cosec(\pi * satelev / 180.0) - 1.0) * pw$ eq 2.196

In this equation sat_elev represents the satellite elevation as seem from the pixel, in degrees,, and pw represents the total precipitable water (in units of cm) at the position of the pixel. This is derived from the tabulated values using a bilinear interpolation. The look-up table of precipitable water values is valid everywhere; that is, it includes a value for each cell, including sea and coastal cells as well as land cells; there are no invalid values. The coefficients a 0, b 0 and c 0 given by equations , and are the required retrieval coefficients.

In the case of the inland lake surface type, class = 14, the two sets of coefficients for vegetation and bare soil are identical, so the coefficients are independent of vegetation fraction, and the precipitable water correction of equation is not applied, equivalent to setting d = 0.

In the above we have not specified the units in which temperature is expressed, but the retrieval coefficients have been developed with all temperatures expressed in degrees Celsius. If temperatures are expressed in Kelvin, then in place of Equation eq. 2.184 we have the following equation for the LST in K:

eq 2.197

This is the equation actually used for the LST retrieval. In it, T 0 is the temperature in Kelvin at 0°C.

The LST is stored in the product as a 16-bit short integer in units of 0.01K, and it is possible that the retrieval will give a result that exceeds the maximum value that can be represented in this way. In this case, if the retrieved LST (in units of 0.01K) exceeds 32767.5, then the output LST is set to 32767 and the nadir image valid flag is set to false, to indicate an out-of-range value. Otherwise the LST is rounded to the nearest integer and the nadir image valid flag is set to true.

As well as the quantities described above, a topographic variance flag field is defined for each cell in a further LUT. This is a two-bit field that is not used by the processing, but is passed to the product confidence word as a guide to the quality of the retrieved LST. The topographic variance field indicates the surface height range within the cell; a low topographic variance is likely to be associated with greater homogeneity of the surface type within the cell, and so a better quality LST. Reference [3] defines the meaning of the topographic variance field values as follows.

Value

Meaning

0

Extremely flat ground (very high confidence)

1

Some topographic variation (good confidence)

2

Significant topographic variation (low confidence)

3

Extreme topographic variation (no confidence)

The topographic variance flag values have been derived from a digital elevation model.

2.7.1.2.2.1.2 Interpolation of precipitable water

The water vapour sample indexed by lat_index, lon_index and corresponding to the cell whose origin is at is taken to refer to the point at the centre of the half-degree cell, whose (shifted) co-ordinates are , and so the water vapour samples form a grid whose origin is at the point Δ φ/2, Δ λ/2.

For example, the cell at 58N, 7E extends over the latitude range 58.0 to 58.5 and the longitude range 7.0 to 7.5, and is indexed by lat_index = 296, lon_index = 374, and the surface class and vegetation fraction associated with this cell are taken to apply to all pixels within the specified range. However, the precipitable water value is taken to refer to the centre of the cell. Thus the precipitable water value associated with the cell [296][374] refers to the point at latitude 58.25 N, longitude 7.25 E. This must be taken into account in the interpolation of precipitable water. The centre points of the cells are the grid points for the interpolation of the precipitable water pw.

The precipitable water is interpolated to the position of the pixel using a bilinear interpolation between the four points of this grid that surround the pixel. These are the corner points of a quadrilateral enclosing the pixel.

The origin of this quadrilateral is not necessarily the sample point corresponding to the cell in which the pixel falls. The grid defined by the water vapour sample points divides the cell at (φ 0, λ 0) into four quadrants, each of which falls in a different interpolation quadrilateral. The quadrant into which the pixel (φ, λ) falls defines the interpolation quadrilateral, and its origin is calculated as follows.

The pixel (φ, λ) falls within the cell (φ0, λ0), as given by the equations and above. The nearest water vapour sample to the pixel is that which falls within the same cell, at co-ordinates (Δ φ/2, Δ λ/2) relative to the origin of the cell, and this sample is one of the corner points of the interpolation quadrilateral. The co-ordinates of the pixel relative to the cell origin are

$d\phi=\phi-\phi_o$ eq 2.198

$d\lambda=\lambda-\lambda_o$ eq 2.199

and relative to the centre point (the precipitable water sample) its position is

$d\phi-\Delta\phi/2=\eta\Delta\phi$ eq 2.200

$d\lambda-\Delta\lambda/2=\epsilon\Delta\lambda$ eq 2.201

with -0.5 ≤ ε, η < 0.5.

The relative indices of the origin of the interpolation quadrilateral are given by the fractional parts, algebraically defined, of the displacements e, h.

Thus

eq 2.202

eq 2.203

The indices of the cell containing the origin of the interpolation quadrilateral are lat_index + iy, lon_index + ix. If the array of precipitable water samples for the current month is pw_table(lat_index, lon_index), we then have

$pw00=pw_table(lat_index + iy,lon_index +jx)$ eq 2.204

$pw01=pw_table(lat_index + iy + 1,lon_index +jx)$ eq 2.205

$pw10=pw_table(lat_index + iy,lon_index + jx + 1)$ eq 2.206

$pw11=pw_table(lat_index + iy + 1,lon_index + jx +1 )$ eq 2.207

Note the table must wrap round when the longitude index exceeds 719, so that lon index = 720 is interpreted as lon index = 0 (i.e. the longitude index is interpreted modulo 720).

The fractional displacements of the pixel relative to the origin of the interpolation quadrilateral are

$q=\eta-iy$

$p=\epsilon-ix$

The interpolated precipitable water value at the pixel is then given by

$pw=0.001*((1-p)(1-q)pw00 + (1-p)q*pw01+p(1-q)pw10+pq*pw11)$ eq 2.208

2.7.1.2.2.2 Algorithm Description

The following steps are carried out for each pixel for which the 11 and 12 micron nadir view brightness temperatures (T 11 and T 12) are both valid. If either of these brightness temperatures in the nadir view is invalid, no retrieval is attempted for that pixel, and the nadir image valid flag remains FALSE. Otherwise the calculation proceeds as follows.

  1. Latitude and longitude indices are derived from the pixel latitude and longitude according to the equations ( eq. 2.192 ).
  2. The solar elevation at the centre of the across-track band in which the pixel falls is inspected. If it is positive, a day/night flag is set to indicate day-time observations, otherwise the flag is set to indicate night.
  3. A linear interpolation is used to determine the satellite elevation at the pixel from the band edge satellite elevation values. If T 11 > T 12 the non-linear exponent n is calculated using equation ( eq. 2.186 ), otherwise n is set to 1.
  4. The retrieval coefficients to be used for this pixel are determined, using the latitude and longitude indices determined at Step 1 to extract the vegetation fraction f and surface classification class appropriate for this cell from the look-up tables. The precipitable water pw is calculated by linear interpolation as in ( 2.7.1.2.2.1.2. ). If class < 1 or class > NCLASS (the number of valid surface types) then the class index is out of range; the calculation for this pixel is abandoned and the nadir_image_valid flag remains false. Otherwise the retrieval coefficients are calculated using equations ( eq. 2.193 , eq. 2.194 , eq. 2.195 , eq. 2.196 ). If class = 14, n = 1.
  5. The land surface temperature is calculated using Equation (), trapping the condition that the resulting LST is out of range.
  6. The topographic variance flag for the pixel is set to the value appropriate to the half-degree cell, taken from the table. Note that this is a two-bit flag.

2.7.1.3 Derive Averaged Product (Half-Degree cells)

Averaged BTs and reflectances, and then averaged SST and NDVI are derived for the half-degree cells via the following steps.

2.7.1.3.1 Spatial Averaging

For the averaged products in half-degree cells, the globe is imagined as divided into cells 0.5° in latitude by 0.5° in longitude, and these cells are further subdivided into 9 sub-cells extending 10 arcmin in latitude by 10 arcmin in longitude. For each channel, the average brightness temperature (for the infra-red channels) or reflectance (for the visible channels) is averaged over all pixels of each type that fall within each sub-cell, to give distributions of a brightness temperature and radiance at 10 arc minute resolution. Averages are performed for the forward and nadir views separately, and a separate average is performed for each surface type (land and sea) and cloud state (clear or cloudy). There are thus 4 averages per channel per view. The mean across-track pixel number in each cell is also derived, for use by the averaged SST algorithm.

2.7.1.3.2 Averaged SST Retrieval

The Averaged Surface Temperature (AST) Product ATS_AR_2P contains averaged geophysical quantities at two different resolutions, and with respect to two different averaging schemes.

Measurement Data Sets at resolutions of 0.5° by 0.5° and 10 by 10 arc minutes with respect to a latitude / longitude grid provide continuity with existing ATSR-2 products. Other data sets contain data averaged over equal area cells of 50 by 50 km and 17 by 17 km aligned with the satellite ground track.

In the first averaging scheme, the globe is imagined to be divided into cells 0.5° in latitude by 0.5° in longitude, and each of these cells is further subdivided into 9 sub-cells extending 10 arcmin in latitude by 10 arcmin in longitude. Averaged brightness temperatures and reflectances are derived, for cloud-free and cloudy pixels separately, by averaging the data over these cells and sub-cells. For those sub-cells containing clear sea pixels, an averaged sea surface temperature is derived from the averaged brightness temperature as described below. Finally the averaged SST for each 0.5° cell is derived by averaging the valid SST values for the component sub-cells.

The sub-cells within each cell are identified by an index in the 0 to 8 as follows:

6

7

8

3

4

5

0

1

2

Further notes on AST product structure are given in Section 2.7.2.2. below.

The derivation of averaged SST is in principle the same as that described above for gridded SST, but with the following practical differences:

  • The retrieval is based on the average brightness temperature for clear sea pixels within a sub-cell;
  • Appropriate new criteria for the validity of brighness temperatures are introduced;
  • Different retrieval coefficients are used.

In the following, the notation M( ch , v) is used to denote the number of valid clear sea pixels for channel ch and view v (v = nadir ¦ forward) that fall within the 10 arc minute sub-cell under consideration.

The appropriate across-track band index corresponding to a sub-cell is obtained by entering the auxiliary Across-track Band Mapping Look-up Table 6.5.8. with the mean across-track pixel number for the sub-cell. This value is used to index the table of coefficients to extract those corresponding to the correct air mass value.

The logic of the procedure used for deriving the averaged SST for the AST product is as follows. Steps 1 and 2 below are executed for each sub-cell in a half-degree cell, then Step 3 is executed to determine averaged quantities for the whole cell.

1) Calculate the nadir-view retrieval.

The minimum number of pixels required for the cell in the nadir view is determined;

minpn= 340 * NADIR_PIXELS_THRESH * cos ((π/180)x latitude) + 1,

where latitude is the latitude of the sub-cell, in degrees. The value NADIR_PIXELS_THRESH is taken from the auxiliary file of Level 2 Processor Configuration Data(ATS_PC2_AX) 6.5.7. .

The number of pixels that have contributed to the average clear sea nadir brightness temperature in each of the 11 and 12 micron channels is inspected. If this is less that minpn for either channel, an SST cannot be retrieved, and the AST field is set to an exception value of –1.

Otherwise, if M( ir12, n)minpn and M(ir11, n)minpn, an SST retrieval is attempted, using either a 2- channel algorithm or a 3 channel algorithm. If the solar elevation associated with the parent cell (not the sub-cell) is negative (indicating a night-time measurement) and a valid 3.7 micron brightness temperature average is available, a 3 channel algorithm (Equation) is used, otherwise a two-channel retrieval (Equation) is used.

For night-time data the 3.7 micron brightness temperature average is considered to be valid if the ratio of the number of contributing pixels at 3.7 microns to the number at 11 microns,

float{M(ir37, n)} / float{M(ir11, n)} ≥ IR37_THRESH.

If the ratio is less than IR37_THRESH the two-channel algorithm is used. The two-channel algorithm is always used for day-time data. The parameter IR37_THRESH is taken from the auxiliary file of Level 2 Processor Configuration Data 6.5.7. .

If a three-channel retrieval is possible, the corresponding flag of the confidence word is set accordingly. In either case the retrieval is performed using the coefficients for the appropriate across-track band index and taking account of the geographic zone as described below.

1.1) If the sub-cell falls in the tropical region (latitude < TROPICAL_INDEX) or if it falls in the polar region (latitude = POLAR INDEX), then the SST is calculated using the retrieval coefficients for that region and for the appropriate across-track band index. Equation is used if a two-channel retrieval is required, or Equation is used for a three-channel retrieval.

1.2) Otherwise the sub-cell lies within the temperate region. Two SST values are calculated, one using the coefficients for the temperate region, and the second using the coefficients for the polar or tropical region. The coefficients for the tropical region are used if the subcell latitude is less than TEMPERATE_INDEX, otherwise the coefficients for the polar region are used. In each case the retrieval coefficients for the appropriate across-track band index are used, with Equation if a two-channel retrieval is required, or Equation if a three-channel retrieval is required. A linear interpolation with respect to latitude is then used to obtain the final SST value from the two regional values, using Equation or Equation as appropriate.

2) Calculate the dual-view retrieval.

The minimum number of pixels required for the cell in the forward view is determined;

minpf= 340 * FRWRD_PIXELS_THRESH * cos ((π/180) x latitude) + 1,

where latitude is the latitude of the sub-cell, in degrees. The value FRWRD_PIXELS_THRESH is taken from the auxiliary file of Level 2 Processor Configuration Data (ATS_PC2_AX) 6.5.7. .

For each view, and for each of the 11 and 12 micron channels, the number of pixels that have contributed to the corresponding average clear sea brightness temperature in the sub-cell is inspected. If this is less than minpn or minpf, as appropriate, for either channel in either view, an SST cannot be retrieved, and the AST field is set to an exception value of –1.

Otherwise, if

M( ir12, n)minpnand M(ir11, n)minpn

and

M( ir12, f)minpfand M(ir11, f)minpf

an SST retrieval is attempted, using either a 4-channel algorithm or a 6-channel algorithm. If the solar elevation associated with the parent cell (again not the sub-cell) is negative (indicating a night-time measurement) in each view, and if valid 3.7 micron brightness temperature averages are available for both the nadir and the forward views, a 6-channel algorithm (Equation) is used, otherwise a 4-channel retrieval (Equation) is used.

For night-time data the 3.7 micron brightness temperature average is considered to be valid if the ratio of the total number of contributing pixels in the two views at 3.7 microns to that at 11 microns,

float{M(ir37, n) + M(ir37, f)} / float{M(ir11, n) + M(ir11, f)} ≥ IR37_THRESH.

If the ratio is less than IR37_THRESH the two-channel algorithm is used. The two-channel algorithm is always used for day-time data.

If a 3 channel retrieval is possible, the corresponding flag of the confidence word is set accordingly. In either case the retrieval is performed using the coefficients for the appropriate across-track band index and taking account of the geographic zone as described below.

2.1 If the sub-cell falls in the tropical region (latitude < TROPICAL_INDEX) or if it falls in the polar region (pixel latitude = POLAR INDEX), then the SST is calculated using the retrieval coefficients for that region and for the for the appropriate across-track band index. Equation is used if a 4-channel retrieval was specified, or Equation if a 6-channel retrieval was specified.

2.2) Otherwise the sub-cell lies within the temperate region. Two SST values are calculated, one using the coefficients for the temperate region, and the second using the coefficients for the polar or tropical region. The coefficients for the tropical region are used if the sub-cell latitude is less than TEMPERATE_INDEX, otherwise the coefficients for the polar region are used. In each case the retrieval coefficients for the appropriate across-track band index are used, with Equation if a 4-channel retrieval is required, or Equation if a 6-channel retrieval is required. A linear interpolation with latitude is then used to obtain the final SST value from the two regional values, using Equation or Equation as appropriate.

3) Calculate cell averages.

When the nadir and dual view SST values have been calculated for each of the sub-cells that contribute to a cell, average nadir and dual view SST values are calculated for the cell.

For up to nine 10-arcmin cells within the half-degree cell, the mean nadir view SST for the half-degree cell is derived.

This is repeated for the dual-view retrieval.

where k∈{0 ≤ k ≤ 8} is an index to the sub-cells and in each case the sum is over all values of k for which the respective sub-cell temperature is valid (i.e. has a positive value), and where μ1 and μ2 are the numbers of such valid temperatures in the nadir and forward views, respectively. If either of the values μ1 or μ2 is zero, the corresponding temperature is set to -1.

The standard deviations of the 10-arcmin SST values are also calculated, as is the mean across-track pixel number to be associated with the 30 arc minute SST:

sst_mean_pixel ( cell) = if μ1 > 0

sst_mean_pixel ( cell) = -1 if μ1 = 0

where the sum is over all k ∈ {0 ≤ k ≤ 8} for which corresponding SST T nadir(k, cell) is valid (≠-1.)

2.7.1.3.3 Averaged NDVI and LST Retrieval

The NDVI is calculated for each sub-cell for which average reflectances over land have been calculated. The averaged NDVI over all the subcells, and its standard deviation, are also computed.

The algorithm for Averaged LST retrieval is essentially the same as that described in Section 2.7.1.2.2. above, but applied to the averaged brightness temperature values for clear pixels within the cell in place of the pixel brightness temperatures.

2.7.1.3.4 Spatially Averaged Cloud Parameters

This step provides physical information on the cloud state additional to the results of the cloud flagging provided by the cloud clearing algorithms. The product is based on the same half-degree cells defined above. The frequency distribution of brightness temperature for the cloudy pixels within the cell is given together with representative parameters and an estimate of the cloud-top temperature. The latter is interpreted as the mean brightness temperature of the coldest 25% of the cloudy pixels in the cell.

For each half-degree cell, information is given for the nadir and forward views separately. The information consists of the number of cloudy and cloud-free pixels falling within the cell, a histogram of the 11 µm brightness temperatures of the cloudy pixels, and various statistical parameters derived from the histogram. The 11 µm channel is used as the basis of the product following the practice of ATSR and ATSR-2.

The product is generated as follows. Two histograms are generated of the frequency distribution of 11 µm brightness temperature, for cloudy pixels over sea and land respectively. The histograms represent the brightness temperature at 0.1 K resolution between 190 K and 290 K. Thus each contains 1000 bins where the first bin contains the number of pixels with temperatures in the range 190.0 to 190.1 K, and the last bin contains the number of pixels with temperatures in the range 289.9 to 290.0 K. The cloud state of each filled pixel falling within the cell is inspected. If it is clear, a count of the number of clear pixels is incremented; if it is cloudy, the 11 µm channel BT is inspected and the count in the appropriate histogram bin is incremented. Note that cosmetic fill pixels are included in the processing.

As each pixel is inspected, a test is made to determine whether its 11 µm BT is lower than the lowest value previously encountered, and if so to store the location of the pixel. Then when the histogram is complete the identity of the minimum pixel will be known, and can be used to extract its channel values.

Once the histogram is complete for a given cell, that is once all the pixels falling within the cell have been inspected, the cloud temperature and coverage results are derived from it. Firstly the total number of cloudy pixels detected is computed by summing the histogram samples. If this total is less than 20 no further derivations are performed. If 20 or more cloudy pixels have been identified and included in the histogram, the mean 11 µm brightness temperature and its standard deviation are calculated from the histogram.

The histogram is searched for the lowest temperature represented by the histogram. This is the temperature corresponding to the first non-zero bin of the histogram. Next, the cloud-top temperature is estimated. The histogram bin containing the 25th percentile is identified; this is the first bin (as the histogram is searched in the direction of ascending temperature) for which the cumulative total of the bins up to and including itself exceeds 25% of the total number of cloudy pixels. The mean temperature represented by the bins up to and including this bin is calculated.

[Note that the cloud top temperature so derived may represent the mean of slightly more than 25% of the cloudy pixels, since the cumulative total including the 25th percentile bin may exceed 25%.]

Finally the percentage cloud cover is calculated from the ratio of cloudy pixels to total pixels.

2.7.1.4 Derive Averaged Product (50 km cells)

For this part of the product, averaged BTs, reflectances, SST and NDVI are derived using the same method as in section 2.7.1.3.1. to section 2.7.1.3.4. , but averaged over cells and sub-cells of nominal dimensions 50 km x 50 km and 17 x 17 km respectively.

The SST retrieval algorithm used for 50 / 17 km resolution is essentially the same as that for the half-degree cells described in Section 2.7.1.3. except that the latitude dependence is omitted from the calculation of the validity thresholds minpn etc., because the cell and sub-cell areas are independent of latitude in this case.


Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry