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Contributors: L. Carrea (University Of Reading), C. Merchant (University Of Reading), O. Embury (University Of Reading)

Issued by: L. Carrea, C.J. Merchant

Date: 21/04/2021

Ref: C3S_312b_Lot4_D1.LK.2-v3.0_LSWT_Algorithm_Theoretical_Basis_Document_i1.0

Official reference number service contract: 2018/C3S_312b_Lot4_EODC/SC2

Table of Contents

History of modifications

Issue

Date

Description of modification

Author

(V0.1 312b_Lot4)i0.1

28/01/2021

The present document was modified based on the document with deliverable ID: C3S_312b_Lot4_D1.LK.2-v2.0_202001_Algorithm_Theoretical_Basis_Document_LSWT_v1.0
In the Scope of the Document section modified CDR v2 into CDR v3. Modified the Executive Summary to introduce SLSTR for CDRv3.0. Added a new section (section 1.3) for SLSTR as input data and provided a new section (section 2.3) in the NWP fields to include in-file SLSTR met-fields. Revised LSWT v4.0 to LSWT v4.2 throughout the document when required.

LC

i1.0

21/04/2021

Finalized

RK

List of datasets covered by this document

Deliverable ID

Product title

Product type (CDR, ICDR)

C3S version number

Public version number

Delivery date

D3.LK.3-v3.0

Lake Surface Water Temperature

CDR

V3.0

LSWT-4.2

31/01/2021

Related documents

Acronyms

Acronym

Definition

ATBD

Algorithm Theoretical Basis Document

ATSR

Along Track Scanning Radiometer

AATSR

Advanced Along Track Scanning Radiometer

AVHRR

Advanced Very-High Resolution Radiometer

BT

Brightness Temperature

C3S

Copernicus Climate Change Service

CCI

Climate Change Initiative

CDR

Climate Data Records

CEDA

Centre for Environmental Data Analysis

ECMWF

European Centre for Medium-range Weather Forecasts

EODC

Earth Observation Data Centre

EPS

EUMETSAT Polar System

ERS

European Remote Sensing

ESA

European Space Agency

EUMETSAT

European Organization for the Exploitation of Meteorological Satellites

FRAC

Full Resolution Area Coverage

GAC

Global Area Coverage

GHRSST

Group for High Resolution Sea Surface Temperature

GLWD

Global lakes and Wetland Database

ICDR

Intermediate Climate Data Record

L3C

Level 3 Collated

L3S

Level 3 Super-collated

L3U

Level 3 Un-collated

LECT

Local Equator Crossing Time

LK

Lake

LSWT

Lake Surface Water Temperature

MERIS

Medium Resolution Imaging Spectrometer

MNDWI

Modified Normalised Difference Water Index

NDVI

Normalised Difference Vegetation Index

NERC

Natural Environment Research Council

NOAA

National Oceanic and Atmospheric Administration

NWP

Numerical Weather Prediction

OE

Optimal Estimation

PML

Plymouth Marine Laboratory

RDAC

Regional Data Assembly Centre

RTM

Radiative Transfer Model

SLSTR

Sea and Land Surface Temperature Radiometer

SST

Sea Surface Temperature

UTC

Universal Time Coordinate

General definitions

L2P – Geophysical variables derived from Level 1 source data on the Level 1 grid (typically the satellite swath projection). Ancillary data and metadata added following GHRSST Data Specification.

L3U – Level 3 Un-collated data are L2 data granules remapped to a regular latitude/longitude grid without combining observations from multiple source files. L3U files will typically be "sparse", corresponding to a single satellite orbit.

L3C – Level 3 Collated data are observations from a single instrument combined into a space-time grid. A typical L3C file may contain all the observations from a single instrument in a 24-hour period.

L3S – Level 3 Super-collated data are observations from more than one satellite that have been gridded together into a single grid-cell estimate, for those periods where more than one satellite data stream delivering the geophysical quantity has been available.

Scope of the document

This document is the Algorithm Theoretical Basis Document (ATBD) for the LSWT v4.2 C3S extension product. ("v4.2" is the scientific versioning of the climate data record familiar to users, whereas under C3S numbering this document refers to "CDR v3".) The brokered CDR product was produced within the GloboLakes project from the Along Track Scanning Radiometer (ATSR) and MetOpA Advanced Very-High Resolution Radiometer (AVHRR) instruments, while the extension of the CDR product was produced within C3S from the MetOpA and MetOpB AVHRR instruments. The extension of the CDR v3 product was produced within C3S from Sentinel3A and Sentinel3B SLSTR instruments, which are highly consistent. The ATBD describes the algorithms used to generate the LSWT products, including the (1) identification of water-only pixels for valid retrieval, (2) the LSWT retrieval itself, (3) estimating the daily average LSWT from the instantaneous skin observation, (4) assigning a pixel quality level, (5) remapping the data to a regular global grid, (6) cross-sensor LSWT harmonization.

Executive summary

This document summarises the algorithms and auxiliary data used in the production of the Level 2 and Level 3 Lake Surface Water Temperature brokered and extended CDR products. The C3S extensions of the brokered CDR are intended to be used in combination with the corresponding GloboLakes-LSWT-4.0 CDR. All CDR datasets are generated using the same software and algorithms originally developed within the NERC GloboLakes project.
The LSWT version 4.0 NERC GloboLakes CDR provides a baseline record from 1995 through end-2016; and the LSWT version 4.0 C3S CDR provides an ongoing extension in time of the record from Jan-2017 onwards which, unlike GloboLakes, includes AVHRR on Metop-B input data up to Aug 2019. The LSWT version 4.2 (C3S CDR v3) provides a further ongoing extension in time of the record from Sep-2019 onwards and it is derived only from SLSTR on Sentinel3A and Sentinel3B input data. Unlike the GloboLakes CDR which is a reprocessing of historical data, the C3S CDR provides yearly extensions to LSWT data.
Input satellite brightness temperatures (BTs) are screened using the water detection method developed within the GloboLakes project and LSWTs are retrieved using an Optimal Estimation technique (MacCallum and Merchant, 2012). Quality level and retrieval uncertainty estimates are calculated, and the LSWTs are remapped to a regular latitude-longitude grid to produce a global daily product. Since the LSWTs have been generated using different instruments, a cross-sensor adjustment is estimated and applied in order to obtain a harmonized product.

Instruments

AVHRR


The AVHRRs are a series of multipurpose imaging instruments carried onboard the National Oceanic and Atmospheric Administration (NOAA) Polar Operational Environmental Satellites (POES) and EUMETSAT Polar System (EPS) MetOp satellites. The first AVHRR instrument was carried onboard the TIROS-N satellite launched in October 1978, as of 2018 there are four AVHRR instruments still in operation with the final AVHRR launched onboard MetOpC in November 2018. For the C3S CDR extension the data from AVHRR on the MetOpA and MetOpB satellites are processed.
The AVHRR is an across-track scanning radiometer using six spectral channels (early versions of the instrument had four or five channels), with a spatial resolution of approximately 1.1 km at nadir. There are 2048 pixels in each scan for a swath width of about 2800 km. However, due to hardware limitations when the instruments were originally designed it was not possible to record a complete orbit of full resolution data for transmission to the ground station. Therefore, the onboard processor samples the real-time data to produce reduced resolution Global Area Coverage (GAC) data with a nominal resolution of ~4 km. This is achieved by averaging four pixels along the first scanline and then skipping a pixel before averaging the next four pixels. The next two scan lines are discarded before resuming the sampling on the fourth scanline. Each four-pixel average is then considered to be representative of a 15-pixel cell (5 pixels across track by 3 pixels along track). The more recent MetOp satellites do not have this limitation and record full orbit data at native resolution. Note - NOAA distributes the full resolution MetOp data as Full Resolution Area Coverage (FRAC). Table 1 reports the list of platforms carrying an AVHRR instrument where the platforms used for the C3S LSWT v4.0 brokered and extension products have been highlighted, while Table 2 reports the AVHRR channels.

Table 1: List of platforms carrying AVHRR instruments.

Satellite

Type

Overpass Time

Operations start

Operations end

TIROS-N

AVHRR/1


Nov 1978

Jan 1980

NOAA-6

AVHRR/1

AM

Jul 1979

Mar 1982

NOAA-7

AVHRR/2

PM

Sep 1981

Feb 1985

NOAA-8

AVHRR/1

AM

May 1983

Oct 1985

NOAA-9

AVHRR/2

PM

Feb 1985

Nov 1988

NOAA-10

AVHRR/1

AM

Nov 1986

Sep 1991

NOAA-11

AVHRR/2

PM

Nov 1988

Dec 1994

NOAA-12

AVHRR/2

AM

Sep 1991

Dec 1998

NOAA-14

AVHRR/2

PM

Jan 1995

Oct 2002

NOAA-15

AVHRR/3

AM

Oct 1998

Dec 2010

NOAA-16

AVHRR/3

PM

Jan 2001

Dec 2010

NOAA-17

AVHRR/3

AM

Jun 2002

Dec 2010

NOAA-18

AVHRR/3

PM

May 2005

Ongoing

MetOp-A

AVHRR/3

AM

Oct 2006

Ongoing

NOAA-19

AVHRR/3

PM

Feb 2009

Ongoing

MetOp-B

AVHRR/3

AM

Jan 2013

Ongoing

MetOp-C

AVHRR/3

AM

Nov 2018

Ongoing

Table 2: List of AVHRR channels by instrument type. AVHRR can only transmit one of 3A or 3B – typically 3A is used during day and 3B at night; however, some NOAA satellites transmit 3B at all times.

Channel

Central Wavelength (μm)

AVHRR/1

AVHRR/2

AVHRR/3

1

0.63

X

X

X

2

0.87

X

X

X

3A

1.61



X

3B

3.74

X

X

X

4

10.8

X

X

X

5

12.0


X

X

ATSR

The ATSR instruments are well calibrated, dual-view radiometers intended to produce long-term, consistent LSWT observations. Three ATSR instruments have flown on board ESA's two European Remote Sensing (ERS) satellites and Envisat satellite. All three satellites were in stable sun-synchronous orbits with near-constant Local Equator Crossing Times (LECTs) – the ERS-1 and ERS-2 platforms had a LECT of 10:30 and Envisat had a crossing time of 10:00 all of which were maintained within a few minutes.
The ATSR instruments had four key design features making them better suited to climate applications than the AVHRR instruments:

  • The instrument spectral response functions were accurately measured during pre-flight calibration and characterisation.
  • The ATSRs are exceptionally well calibrated with two accurate on-board calibration targets at temperatures of ~260 K and 300 K which greatly reduces non-linearity errors for ocean observations (for comparison AVHRR instruments have a single on-board target at ~290 K and rely on a space view (2.7 K) to provide the second point.
  • The infrared detectors are actively cooled to ~82 K to reduce instrument noise and avoid temperature dependent effects on calibration. In addition, the instrument fore-optics are cooled below ambient temperature to reduce self-emission issues, and the instrument is enclosed to prevent stray-light affecting the detectors.
  • The dual-view capability using a single telescope with a conical scanning pattern provides both a nadir-view and an inclined forward view (~55°). Having two views of the Earth's surface allows the instrument to gather more information and more effectively separate surface and atmospheric effects, i.e. the SST retrieval can be made more robust to atmospheric conditions, including water vapour and stratospheric aerosol.

The first ATSR carried onboard ERS-1 was a four channel radiometer with channels are 1.6, 3.7, 11, and 12 μm. However, the ATSR-1 instrument would only transmit one of the 1.6 or 3.7 μm channels with the selection based on the 1.6 μm reflectance intended to separate day and night-conditions. There were two major issues affecting the ATSR-1 instrument:

  1. The 3.7 μm channel failed in May 1992, less than a year after the satellite was launched
  2. In order to preserve mission lifetime, the temperature of the actively cooled detectors were allowed to rise, by-end of mission the detectors were operating at over 110 K.

For these reasons, currently data from ATSR1 have not been used to generate LSWT. In Table 3, the instruments used for the C3S LSWT v4.0 brokered product have been highlighted.
The second ATSR carried onboard the ERS-2 added three reflectance channels at 0.55, 0.67, and 0.87 μm mainly for vegetation monitoring. The channels had only limited availability over ocean due to telemetry bandwidth limitations; depending on instrument operating mode the visible channels may be transmitted for a reduced narrow swath, reduced 8-bit digitization, or interlaced (record every-other) pixels. The final, Advanced ATSR, instrument onboard Envisat was functionally the same as ATSR-2 but without the bandwidth limitations so all seven channels are always available in full resolution.

Table 3: List of ATSR channels for each instrument. (1) ATSR1 would only transmit one of 1.6 and 3.7 μm depending on the 1.6 μm intended to separate day and night conditions. However, after the failure of the 3.7 μm channel only 1.6 μm data is transmitted. (2) ATSR2 visible channels have limited availability over ocean resulting in a reduced width swath and/or reduced 8-bit digitisation.

Channel

Central Wavelength (μm)

ATSR1

ATSR2

AATSR

1

0.55


X2

X

2

0.67


X2

X

3

0.87


X2

X

4

1.6

X1

X

X

5

3.7

X1

X

X

6

10.8

X

X

X

7

12.0

X

X

X

SLSTR

The SLSTR instruments are well-calibrated, dual-view radiometers intended to produce long-term, consistent water surface temperature observations. The design of the SLSTR instrument builds on the heritage of the earlier ATSR instruments adding more spectral bands and a wider swath. The swath width is about 1400 km at nadir. The first SLSTR instrument is carried on-board the Sentinel3A satellite launched in February 2016. A second platform, the Sentinel3B was launched in April 2018. The Sentinel3A orbit is near-polar, sun-synchronous orbit with a descending node equatorial crossing at 10:00h Mean Local Solar time. The Sentinel3B orbit is identical to the Sentinel3A's but Sentinel3B flies +/-140° out of phase wit Sentinel3A, after an initial 6 month 'tandem phase' where the two satellites observed the same place on Earth within 30 seconds. The SLSTR channels, together with bandwidth and spatial resolution, are reported in Table 4 where the channels used for the LSWT are highlighted.

Table 4: List of SLSTR channels

Channel

Central Wavelength (μm)

Spatial resolution (m)

Channel used

S1

0.55

500


S2

0.659

500

X

S3

0.865

500

X

S4

1.375

500


S5

1.61

500

X

S6

2.25

500


S7

3.74

1000


S8

10.85

1000

X

S9

12

1000

X

Input and auxiliary data

AVHRR L1b

AVHRR data is available from NOAA and EUMETSAT; both agencies distribute data in their own "level-1b" formats, but the formats are not equivalent. NOAA L1b contains the instrument counts plus other calibration and telemetry information, the user must apply an appropriate calibration method to obtain instrument radiances or BTs. EUMETSAT L1b (EUMETSAT Polar System) contains the calibrated radiances.
The algorithms described in this document have been applied to the EUMETSAT format data.

AVHRR L1b is available from EUMETSAT: https://navigator.eumetsat.int/

ATSR L1b

ATSR data from the two instruments used with GloboLakes are now available in the Envisat format used for all products from the Envisat satellite. The data are calibrated and geo-located onto a common grid for both nadir and forward views.
ATSR L1b available from ESA: https://earth.esa.int/web/guest/data-access

SLSTR L1b

SLSTR data is available in ESA Standard Archive for Europe (SAFE) format (http://earth.esa.int/SAFE/) which comprises a collection of netCDF4 files and an XML format manifest file. L1b file contains also NWP fields from ECMWF operational data.

SLSTR L1b available is available from the Copernicus Open Access Hub https://scihub.copernicus.eu/

Lake mask

The lake water location input consists of the land water mask (Carrea et al. 2015) derived from maximum water extent observed in ESA CCI Land Cover (v3.0) at 300-m resolution within the GloboLakes project. The land water mask contains water bodies identifiers and distance to land for each water pixel.

The GloboLakes mask is available from CEDA: http://catalogue.ceda.ac.uk/uuid/06cef537c5b14a2e871a333b9bc0b482

NWP data

NWP data are used as input to the radiative transfer model (RTM) needed for LSWT retrieval. The required parameters for the various algorithms are shown in Table 5 below. The NWP LSWT currently are not sufficiently accurate for lake processing, therefore LSWT has been developed within the GloboLakes project to be used as a prior LSWT for optimal estimation retrieval.
The GloboLakes project and C3S LSWT processing used ERA-Interim inputs for scientific version v4.0 products (brokered and extension CDR). Since the ERA-Interim production stops at the end of August 2019, the last use of this auxiliary data stream was for C3S CDR v2.0 which ended in Aug 2019. The CDR v3.0 extends the CDR v2.0 but it is derived only from SLSTR data for which the L1b contains ECMWF operational meteorological fields which are used as auxiliary data for the CDR v3 extension. The lake surface water temperature reported in the table is the prior temperature used for the RTM and the OE algorithms. Since currently no sufficiently accurate lake surface water temperature is available, a climatology has been created and used for the purpose.

Table 5: NWP inputs to algorithms: RTM – Radiative Transfer Model; OE – Optimal Estimation LSWT retrieval. Note: the OE algorithm uses the output from the RTM.

Parameter

Type

Algorithms

Atmospheric temperature

Analysis, profile

RTM

Atmospheric water vapour

Analysis, profile

RTM

Surface pressure

Analysis, surface

RTM

Mean sea level pressure

Analysis, surface

RTM

10m wind U-component

Analysis, surface

RTM

10m wind V-component

Analysis, surface

RTM

2m air temperature

Analysis, surface

RTM

2m dew point temperature

Analysis, surface

RTM

Lake surface water temperature

Created as a climatology

RTM, OE

Skin temperature

Analysis, surface

RTM

Total Column Water Vapour

Analysis, surface

OE

Algorithms

The algorithm to derive LSWT product from imagery of visible and infrared radiometers consists of many components which aim to retrieve the LSWT using the observed reflectance and brightness temperature for water-only pixels. The core of the algorithm is the retrieval part which is based on Optimal Estimation (OE) given simulations and observations. The other components of the algorithm prepare the inputs for the retrieval part, namely simulate the brightness temperatures and classify a pixel as water or non-water. The classification consists of a water detection algorithm applied to pixels defined as GloboLakes lake water in the mask defined in (Carrea et al. 2015). Finally, the observations are gridded into a regular 0.05o resolution grid. Since the observed LSWTs come from different instruments, an adjustment at level 3 has been carried out in order to stabilize the temperatures across the instruments. After the validation with independent in situ measurements of the GloboLakes dataset, the reference for the adjustment has been selected to be the observed lake temperatures from the AVHRR on MetOpA.

The GloboLakes algorithm was based on work carried out within the ESA ARCLake and the ESA CCI SST projects. An important component of the ESA CCI SST algorithm is the Bayesian cloud detection which depends on how accurate the prior surface temperature is. In particular, it has been found that NWP-based lake surface water temperature values are not (at present) sufficiently accurate for this purpose (MacCallum and Merchant, 2012).

Within the GloboLakes project, PML has derived an indicator of cloudiness using MERIS data. Since the MERIS instrument was on the same platform as AATSR and offering higher resolution, the cloudiness indicator was used to decide if a pixel was cloudy or cloud-free. However, more data from different instruments needed to be processed. Therefore, a classification of water-only pixels which does not rely on the Bayesian cloud detection and therefore on an accurate prior was attempted. To this aim, the probability of clouds generated by PML using MERIS data for the GloboLakes lakes has been used to derive a climatology to be used as prior temperature from the AATSR data, and to tune the water detection algorithm introduced within ARCLake to detect water in presence of clouds.

The prior information is still needed since it is an input for the OE retrieval algorithm. However, the OE algorithm is more robust with respect to the prior and together with the retrieved temperature the OE outputs the sensitivity to the prior and the χ2 of the retrieval.
The same algorithms are used for both the brokered GloboLakes CDR and C3S CDR extension products and across all instruments. Figure 1 shows how the algorithms are used to generate the different product levels: L2P though L3S.
In this ATBD, the following aspects of the GloboLakes algorithm are described:

  • LSWT retrieval: the Optimal Estimation algorithm
  • Pixel classification: water detection
  • Prior temperature: derivation of the temperature prior to be used in the OE algorithm
  • Definition of the quality levels
  • Remapping (L3U)
  • Daily collation (L3C)
  • Sensor adjustments (L3S)

Figure 1: Overview of algorithm steps as applied to different processing levels.

LSWT retrieval

Optimal Estimation retrieval has been used for LSWT for all the sensors since it is based on physics and can be applied where no in situ data for retrieval tuning are available. This gives good reasons to expect stable performance across domains in time and space.
For single-view instruments, the LSWT was retrieved using an optimal estimation (OE) scheme (MacCallum and Merchant, 2012):

\[ \bf \hat x=x_a+G(y-F(x_a)) \] \[ \bf G=(K^TS_ε^{-1}K+S_a^{-1})^{-1}K^TS_ε^{-1} \]

The retrieved state  \( \hat x \) is the prior state plus an increment of \( \bf G(y-F(x_a)) \) . F is the forward model The matrix K expresses how the observations change for departures from the prior state x_a, i.e., it is a matrix where a given row contains the partial derivatives of the BT in a particular channel with respect to each element of the state vector in turn. The partial derivatives are the tangent linear outputs from the forward model F. Sε is the error covariance of the differences between the model and observed BTs. This error covariance matrix is the sum of the radiometric error covariance in the observations (So) and estimated error covariance of the forward model (Sm). Sa is the error covariance matrix for the prior state variables.

It has been shown that a reduced state vector, \( \bf z(x) = \begin{bmatrix} x \\ w \end{bmatrix} \) where x is the LSWT and w the total column water vapour can be used in the retrieval instead of the full prior state vector xa. However, the full prior state vector xa is used in the forward model (see (MacCallum and Merchant, 2012).)

Retrieval uncertainties

The uncertainty due to radiometric noise (assumed uncorrelated between pixels) and due to uncertainty in the retrieval (assumed correlated on synoptic scales) is given by:

\[ \sqrt{GS_oG^T} \]

and:

\[ \sqrt{GS_mG^T} \]

Retrieval χ2

In addition to the uncertainty information a further diagnostic on the retrieval is provided in the form of the 2 statistics. It measures the consistency of the retrieval with the satellite observations.
The expression used to quantify χ2 is given in (Rodgers, 2000) as:

\[ Kz'-y'TSεK SaKT+Sε-1-1Kz'-y' \]

where  \( \bf y' = y- F(x_a) \)

and \( \ \hat z= \hat z- z_a \)

Sensitivity

In addition to the uncertainty and the χ2, the sensitivity k of retrieved LSWT to true changes in LSWT is computed as the element corresponding to LSWT of the matrix.

GK

Water Detection

Overview

Water detection is a fundamental pre-processing step for LSWT retrieval. It was introduced during the ARCLake project to enable inclusion of targets with variable surface area. Within the GloboLakes project, the water detection is applied to a fixed mask defined in (Carrea et al. 2015) for day-time observations. Moreover, the thresholds set within ARCLake have been tuned using the probability of clouds derived by PML on MERIS observations to attempt to detect water in presence of clouds not relying on the Bayesian cloud detection. The ARCLake thresholds are reported in Table 6.

Table 6: ARCLake thresholds test for water detection

Channel/Normalised difference

Threshold

R550

<0.15

R670

<0.1

R870

<0.1

R1600

<0.1

BT10850

>260

MNDWI

>0.1

NDVI

<0

MNDWI-NDVI

>0.4


A score s has been introduced to be able to evaluate the performance of the test for X especially close to the thresholds:

\[ s=\begin{cases} 0 & \quad if \quad X \leq t_0 \\ \frac{X-t_0}{t_1-t_0} & \quad if \quad t_0 < X < t_1 \\ 1 & \quad if \quad X \geq t_1 \end{cases} \]

where t0 is the threshold is Table 2 and t1> t0 enough to lower the risk of mis-detection. The value t1 has been selected after a visual inspection of a number of images. The score has been initially computed only for four parameters, R1600, NDVI, MNDWI and D=MNDWI-NDVI:

\[ s=s_{1600}+s_{NDVI}+s_{MNDWI}+s_D \]

Tuning the water detection with MERIS probability of clouds

Within the GloboLakes project a probability of cloud has been generated by PML using MERIS data. Since both instruments were on the same platform, Envisat, it was possible to verify and adjust the water detection performance on the AATSR data. The algorithm for the detection and classification of clouds over water was proposed by Schiller (Schiller et al. 2008) and it produces a graduated scale, as an indicator of the extent to which a signal is influenced by the presence of clouds. The indicator was evaluated for the 1000 GloboLakes lakes for the whole set of MERIS data and a cloud indicator quality has been introduced which is related to the number of cloud-free MERIS pixels (300m resolution) within one AATSR pixel (1km resolution).


Figure 2: False colour composite image of reflectance at 1600 nm (R), 870 nm (G) and 670 nm (B), quality of the MERIS cloud indicator and water detection score for lake Michigan in USA on the 15-Feb-2011.

Figure 2 shows an example (lake Michigan in the USA) where the water detection mis-classify cloudy pixels as water pixels. In order to be able to use the water detection algorithm in presence of clouds we considered to tune the thresholds of the water detection algorithm applied to the AATSR data according to the quality of the cloud indicator computed on the MERIS data. In order to statistically investigate the relationship between the MERIS cloud indicator and the water detection thresholds, histograms of clear and cloudy pixels according to quality of the MERIS cloud indicator have been inspected for the different parameters involved in the water detection threshold test described in Sec. 3.2.1. Figure 3 shows an example of the MNDWI histogram of cloudy and clear pixels (according to the MERIS cloud indicator) for lake Michigan in USA.


Figure 3: Histogram for MNDWI for AATSR pixels classified as cloudy with the MERIS data (grey) and as cloud-free pixels with different quality levels for lake Michigan. The legend shows for each colour the quality level of the MERIS data according to the size of the window (example 5: 7x 7). The legend shows also for each colour the fraction of pixels having the correspondent quality level. The solid red line in the plot represents the threshold defined in Table 6 and the red dotted line represents the level where the score reaches the value of 1 (see Sec. 3.2.1).

In order to tune the thresholds according to the cloud indicator from the MERIS data, the threshold was found in the overlapping area of the two histograms defined as the location of the maximum entropy of the posterior probability that a certain pixel is cloudy or cloud-free. An example of the plot of the entropy together with the posterior probability is shown for MNDWI for lake Michigan in Figure 4.

Figure 4: The upper plot shows the pdf for cloud (grey) for cloud-free (light-blue) and for all pixels (red) for lake Michigan in USA. The lower plot shows the posterior probability (grey for clouds and light blue for cloud-free) and the entropy (red) for MNDWI.

This has been done per–lake and then a common threshold for all the lakes has been chosen for each of the water detection parameters, although all the lakes with less than 500 pixels (less than 1% of the lakes) have been discarded from the evaluation. The new thresholds are reported in Table 7.

Table 7: GloboLakes thresholds test for water detection

Channel/Normalised difference

Score

Thresholds

R670

\[ s=\begin{cases} 0 & \quad if \quad X \leq t_0 \\ \frac{X-t_0}{t_1-t_0} & \quad if \quad t_0 < X < t_1 \\ 1 & \quad if \quad X \geq t_1 \end{cases} \]

t0 = 0.132
t1 = 0.032

R870

\[ s=\begin{cases} 0 & \quad if \quad X \leq t_0 \\ \frac{X-t_0}{t_1-t_0} & \quad if \quad t_0 < X < t_1 \\ 1 & \quad if \quad X \geq t_1 \end{cases} \]

t0 = 0.097
t1 = 0.022

R1600

\[ s=\begin{cases} 0 & \quad if \quad X \leq t_0 \\ \frac{X-t_0}{t_1-t_0} & \quad if \quad t_0 < X < t_1 \\ 1 & \quad if \quad X \geq t_1 \end{cases} \]

t0 = 0.048
t1 = 0.012

MNDWI

\[ s=\begin{cases} 0 & \quad if \quad X \leq t_0 \\ \frac{X-t_0}{t_1-t_0} & \quad if \quad t_0 < X < t_1 \\ 1 & \quad if \quad X \geq t_1 \end{cases} \]

t0 = 0.295
t1 = 0.515

NDVI

\[ s=\begin{cases} 0 & \quad if \quad X \leq t_0 \\ \frac{X-t_0}{t_1-t_0} & \quad if \quad t_0 < X < t_1 \\ 1 & \quad if \quad X \geq t_1 \end{cases} \]

t0 = -0.085
t1 = -0.245

MNDWI-NDVI

\[ s=\begin{cases} 0 & \quad if \quad X \leq t_0 \\ \frac{X-t_0}{t_1-t_0} & \quad if \quad t_0 < X < t_1 \\ 1 & \quad if \quad X \geq t_1 \end{cases} \]

t0 = 0.375
t1 = 0.685

A total score which is the sum of the scores for each parameter

\[ s=s_{870}+s_{1600}+s_{NDVI}+s_{MNDWI}+s_D \]

is introduced to quantify the performance of the water detection algorithm, where the reflectance at 670 nm has been removed since lakes can have different spectral properties especially in the visible range. The new water detection thresholds improve the water detection for lake Michigan as shown in Figure 5.


Figure 5: ARCLake water detection, GloboLakes water detection and MERIS probability of cloud quality for lake Michigan.

Prior temperature

The prior temperature is a necessary input for the OE algorithm. For the GloboLakes lakes it has been generated in form of a spatially filled climatology by an iterative method. The method starts by processing AATSR data and uses the MERIS cloud indicator together with the ARCLake water detection, using as a prior the 2m Tair with high uncertainty.

Determining Quality Level

Quality level is treated as a concept that is distinct from uncertainty: a highly uncertain LSWT can have the highest quality level if all the conditions for giving a valid LSWT and valid LSWT uncertainty are met: the quality level reflects the degree of confidence in the validity of the uncertainty estimate, not the magnitude of data uncertainty.

The quality level assigned to a pixel will be the lowest level (row of table) which matches any of the conditions shown in the table below. The assignments are compatible with GHRSST conventions [D1]: i.e., a particular level is given if none of the conditions higher up any column of the table are met. In Table 8, d is the distance to land in km.

Table 8: Quality Level definitions

Level

Meaning

Water detection score (0.5<d<=1.5)

Water detection score (d>=1.5)

Sensitivity

χ2

Other

0

No data

<0

<0



No data; non-GloboLakes lakes pixel

1

Bad data

<0.5

<0

<0.1

>3

LSWT < 273.15

2

Worst quality

<2

<0.5

<0.5

>2

Limb (θsat > 55)

3

Low quality

<3.5

<2

<0.9

>1


4

Acceptable quality

<4.5

<3.5


>0.35


5

Best quality


<4.5





For instance, any pixel where s is unavailable (value is less than zero), required input BTs are unavailable, or which is over land will be assigned quality level of 0. Next, any pixels close to land which have s < 0.5, calculated LSWT sensitivity < 0.1 etc. will be assigned quality level of 1 and so on.

  • Quality level 0 pixels should contain no other data
  • Quality level 2-5 pixels should always contain valid data
  • Quality level 1 pixels contain data, but the data is not suitable for use (bad_data). For instance, the LSWT retrieval may have been attempted, but rejected as bad_data due to low sensitivity etc
  • We recommend using quality level 4 and 5, and consideration of use of quality level 3 with caution, depending on the user's application.

Remapping (L3U)

The remapping from the L2 data in swath projection to the fixed L3 grid proceeds as follows:

  • Identify L2 pixels contributing to a L3 cell
  • Select highest quality level pixel(s) in the L3 cell
  • Calculate average LSWT from the pixels that share the highest quality level and propagate uncertainties to the uncertainty in this average (Bulgin et al. 2016a)

When averaging from the pixel scale to L3 grid scale, the component or uncertainty from uncorrelated errors reduces (uncertainty in the mean is scaled by the familiar "1n"). Uncertainty in the from correlated error components are not reduced by averaging, since over these small scales the degree of correlation will be very high and is taken to be perfect ("r = 1"). The total uncertainty in the average is found by combining the propagated component uncertainties.

If the grid cell contains pixels which were not included in the averaging (e.g. due to the presence of cloud etc.), then there is an additional uncertainty due to incomplete sampling. This is calculated following Bulgin et al. (2016b) (derived for application to sea surface temperature uncertainty estimation) and is added to the uncorrelated component.

Daily Collation (L3C)

The polar orbiting satellite carrying the AVHRR/ATSR sensors typically complete 14-15 orbits each day resulting in the same number of L2P or L3U products. While L3U files are on a global grid, they are very sparse as the sensor will only observe a small fraction of the Earth’s surface in each orbit. For ease of use the LSWT outputs are collated to produce one file for each 24-hour period, corresponding to day-time observations.

Following the GHRSST conventions [D1], when collating observations from overlapping orbits in the same day the L3C will contain the highest quality observation available in the 24-hour period. The selection of best observation is done as follows:

  • Choose input cells with the highest quality level
  • If multiple observations have the same quality level, then average.

Inter-sensor adjustment (L3S)

The adjustment due to different sensors has been carried out using as reference the AVHRR on MetOpA since the validation in GloboLakes indicated a better agreement throughout the lakes with the in situ data. The inter-sensor adjustment has been calculated per lake averaging per month and per lake and it has been applied only if:

  • Enough observations where available to estimate the adjustment for the lake (more than 3 months of data).
  • The uncertainty of the adjustment was < 0.049 – which was valid for 80% of the lakes.

A flag indicating whether the adjustment has been applied is present in the files and the uncertainty of the bias correction is included in the total uncertainty. For lakes where the flag is not set, the impact of changes in sensor on the long-term trends in LSWT is less well constrained, and trends should be treated with caution.
The final L3S product has been created using the available observations and in case of more than one observation per pixel, the best quality has been chosen as of L3C:

  • Choose input cells with the highest quality level
  • If multiple observations have the same quality level, then average.

Output data

The following sections present a brief overview of the data file format, naming convention and structure. Further information can be found in the Product User Guide and Specification for these products [D2].

File format and naming scheme

The output data are in netCDF4-classic format and are guided by the GHRSST data specifications [D1]. The file names have the format:

<Date><Time>-<RDAC>-<Level>-LSWT-<Dataset>-fv01.0.nc

Note:

  • fv01.0 refers to the file version.


Table 9: Filenaming convention components

Component

Definition

Description

<Date>

YYYYMMDD

The identifying date for this file in ISO8601 basic format

<Time>

HHMMSS

The identifying time for this file in ISO8601 basic format

<RDAC>

GloboLakes or C3S

The RDAC where the file was created

<Level>

L3S

The data processing level

<Dataset>

v4.0/v4.2

Indicates the scientific version number

Date

The identifying date for this file, using the ISO8601 basic format: YYYYMMDD.

Time

The identifying time for this file in UTC, using the ISO8601 basic format: HHMMSS. The time used depends on the processing level of the dataset:

L3S:centre time of collation window (120000 for daily files)

RDAC

GHRSST Regional Data Assembly Centre (RDAC) where the dataset was generated. Two codes are used for C3S products:

C3S : Copernicus Climate Change Service
GloboLakes: NERC GloboLakes

Level

The GHRSST processing level for this product will be L3S.

Dataset

Indicates the scientific version number of the product. Current strings in use is:
v4.0/v4.2

File contents

L3S files are supplied on a regular latitude/longitude grid and variables have dimensions:

time:1 (defined as unlimited)
lat: Number of latitude points (3600)
lon: Number of longitude points (7200)

Table 10: Output fields

Variable name

Description

lake_surface_water_temperature

Best estimate of LSWTskin as observed by the satellite

lswt_uncertainty

Total uncertainty in LSWTskin

quality_level

Quality level of the LSWT: 0 for no data; 1 for bad data; 2 for worst usable data; 3 for low quality; 4 for good quality; 5 for best quality

obs_instr

The instruments used for the correspondent observation

flag_bias_correction

It indicates if the inter-sensor adjustment has been applied

lakeid

Lake identifiers: GLWD identifiers for the GloboLakes lakes

References

Bulgin, C. E., Embury, O., Corlett, G. and Merchant, C. J. (2016a) Independent uncertainty estimates for coefficient based sea surface temperature retrieval from the Along-Track Scanning Radiometer instruments. Remote Sensing of Environment, 178. pp. 213-222. ISSN 0034-4257 doi:10.1016/j.rse.2016.02.022

Bulgin, C. E., Embury, O. and Merchant, C. J. (2016b) Sampling uncertainty in gridded sea surface temperature products and Advanced Very High Resolution Radiometer (AVHRR) Global Area Coverage (GAC) data. Remote Sensing of Environment, 117. pp. 287-294. ISSN 0034-4257 doi:10.1016/j.rse.2016.02.021

Carrea, L., Embury, O. and Merchant, C. J. (2015) Datasets related to in-land water for limnology and remote sensing applications: distance-to-land, distance-to-water, water-body identifiers and lake-centre co-ordinates. Geoscience Data Journal, 2(2). pp. 83-97. ISSN 2049-6060 doi:10.1002/gdj3.32

MacCallum, S.N. and Merchant, C. J. (2012) Surface water temperature observations for large lakes by optimal estimation. Canadian Journal of Remote Sensing, 38(1). pp. 25-45. ISSN 1712-7971 doi:10.5589/m12-010

Rodgers, C.D. (2000) Inverse methods for atmospheric sounding. World Scientific

Schiller H., Brockmann C., Krasemann H. and Schoenfeld W. (2008) A method for detection and classification of clouds over water. In Proc. of the 2nd MERIS (A)ATSR User Workshop.


This document has been produced in the context of the Copernicus Climate Change Service (C3S).

The activities leading to these results have been contracted by the European Centre for Medium-Range Weather Forecasts, operator of C3S on behalf of the European Union (Delegation Agreement signed on 11/11/2014 and Contribution Agreement signed on 22/07/2021). All information in this document is provided "as is" and no guarantee or warranty is given that the information is fit for any particular purpose.

The users thereof use the information at their sole risk and liability. For the avoidance of all doubt , the European Commission and the European Centre for Medium - Range Weather Forecasts have no liability in respect of this document, which is merely representing the author's view.

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