Microsoft Word - D-61923_SRD_Rev B

Surface Water and Ocean Topography Mission

(SWOT§) Project

Science Requirements Document

Rev B

Revisions based on CR114249, CR114632

Document Custodian: Shailen Desai

Revised by Shailen Desai

January 24, 2018

JPL D-61923

©"2018"California"Institute"of"Technology."Government"sponsorship"

acknowledged.

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Signatures

Prepared and Issued by SWOT NASA/JPL Project

Document Custodian:

_______________________

Shailen Desai

SWOT Measurement System Engineer

Approval:

________________________ ________________________

Lee-Lueng Fu Date

SWOT Project Scientist

____________________ ________________________

Selma Cherchali Date

CNES Program Scientist/Manager

__________________ __________________

Parag Vaze Date

SWOT Project Manager

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iii

Concurred by:

________________________ ________________________

Eric Lindstrom Date

NASA-HQ Program Scientist

_______________________ ________________________

Tamlin Pavelsky Date

US Hydrology Science Lead

________________________ ________________________

Rosemary Morrow Date

French Oceanography Science Lead

________________________ ________________________

Jean-François Crétaux Date

French Hydrology Science Lead

________________________ ________________________

Thierry Lafon Date

CNES Project Manager

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CHANGE LOG

DATE

SECTIONS

CHANGED

REASON FOR CHANGE

REVISION

03/19/09

Initial Draft (not

released)

10/10/11

Draft (not

released)

08/28/12

Preliminary

09/04/13

Approved for export –

LRR010661

Initial Release Draft

04/10/14

Approved for export –

LRR013266

Initial Release -

SWOT MDR

Version

03/18/2016

2.5.4.c; 2.6.2.a; 2.6.2.d;

2.6.3a – f; 2.6.4; 2.6.5;

2.7.2.a; 2.8.2-.8.,

2.8.15 (new)

2.8.2b

Clarify requirements (SDT

Recommendation); adjust

references; Revise Fig 1;

revised slope accuracy; add

“non-vegetated.

Remove TBC on TSM river

width

Approved for export -

LRR023412

Revision A

CR 114208

CR 114235

01/24/2018

2.5.4.c; 2.6.2.a; 2.6.3.a;

2.6.3.d; 2.6.3.j; 2.6.7;

2.7.1.a; 2.7.1.b; 2.7.2.a;

2.8.4; 2.8.5

Remove TBC from data

collection requirement;

Change 250 m posting of sea

surface height from goal to

requirement;

Remove sea surface height

slope requirement per 2017

Science Team meeting

recommendation. Per Project

Scientist, the addition of

requirement for 250/500 m

ocean product enables users to

investigate their own algorithms

to generate sea surface height

slope and therefore meets

intent of Level 1 requirement to

include sea surface height

slope in the ocean data

products;

Require validation of science

data products by SWOT

Science Team before release

to general science community;

Clarification that hydrology

Revision B

CR 114249

CR 114632

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performance requirements

apply to non-vegetated water

bodies;

Clarification of pixel cloud and

raster products.

Approved for export -

LRR034387

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Table of Contents

1" SWOT&MISSION&OBJECTIVES&..................................................................................................................&7"

1.1" OCEANOGRAPHY"OBJECTIVES"................................................................................................................................."7"

1.2" HYDROLOGY"OBJECTIVES"........................................................................................................................................."8"

1.3" SYNERGISTIC"SCIENCE"APPLICATIONS"................................................................................................................"10"

2" SWOT&SCIENCE&SPECIFICATIONS&.......................................................................................................&11"

2.1" KEY"TERMS"AND"DEFINITIONS"............................................................................................................................"11"

2.2" BASELINE/THRESHOLD"SCIENCE"MISSIONS"....................................................................................................."11"

2.3" MISSION"PAYLOAD"................................................................................................................................................."12"

2.4" MISSION"LIFETIM E "................................................................................................................................................."12"

2.5" SPACE-TIME"SAMPLING"REQUIREMENTS".........................................................................................................."13"

2.6" SCIENCE"DATA"PRODUCTS"AND"DATA"PRODUCT"DELIVERY".........................................................................."16"

2.7" OCEAN"SCIENCE"PERFORMANCE"SPECIFICATIONS"..........................................................................................."20"

2.8" SURFACE"WATER"SCIENCE"PERFORMANCE"SPECIFICATIONS"........................................................................"25"

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(CR 114249, CR114632) SWOT Science Requirements Document

1 SWOT Mission Objectives

The Surface Water and Ocean Topography (SWOT) mission has been recommended by the

National Research Council decadal survey “Earth Science and Applications from Space:

National Imperatives for the Next Decade and Beyond” for implementation by NASA. The

SWOT mission is a partnership between two communities, physical oceanography and

hydrology, to share high vertical accuracy and high spatial resolution topography data

produced by payload configuration, whose principal instrument is the Ka-band Radar

Interferometer (KaRIN) for making swath measurement of the elevation of land surface water

and ocean surface topography. The SWOT mission will provide a transition from the

conventional profile altimeter to swath altimeter for both oceanographic and hydrologic

applications in the future. The broad scientific objectives specified by the NRC decadal

review have been refined by community involvement in open workshops and the guidance of

an informal science team before the missions’ Phase A, and further improved by the missions’

Science Definition Team during Phase A. A summary of the scientific objectives for each

community is given below:

1.1 Oceanography Objectives

The primary oceanographic objectives of the SWOT mission are to characterize the

ocean mesoscale and submesoscale circulation determined from the ocean surface

topography at spatial resolutions of 15 km (for 68% of the ocean). (Spatial resolution is

defined to be wavelength in the oceanographic context.)

Current altimeter constellations can only resolve the two-dimensional ocean circulation at

resolutions larger than 200 km. Fundamental questions on the dynamics of ocean variability

at scales shorter than 200 km, the mesoscale and submesocale processes, such as the

formation, evolution, and dissipation of eddy variability (including narrow currents, fronts,

and quasi-geostrophic turbulence) and its role in air-sea interaction, are to be addressed by the

new observations.

Kinetic energy and tracer transports

Global study of the circulation at scales of 15 -200 km is essential for quantifying the kinetic

energy of ocean circulation and the ocean uptake of heat and carbon that are key factors in

climate change. Exchange of heat and carbon between the ocean and the atmosphere is

regulated by the large-scale mean circulation, as well as by the mesoscale and submesoscale

eddies. Traditional altimeters have revealed the fundamental role of mesoscale eddies in the

horizontal transport of heat and carbon. The uptake of heat and carbon by the ocean is

complete only after the vertical transport process from the surface turbulent boundary layer

into the ocean interior is accomplished. The vertical transport is mostly accomplished by the

submesoscale fronts with horizontal scales 15 - 50 km. The SWOT mission will open a new

window for studying these processes.

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Climate change and ocean circulation

The new knowledge of the kinetic energy of the ocean circulation and the vertical transport of

carbon and heat is crucial for understanding the role of the ocean in regulating climate change

through the interaction of the mesoscale and submesoscale variability with the large-scale

circulation. Accurate knowledge of the large-scale circulation is thus also required to achieve

these objectives, posing a requirement on measurement accuracy from the submesoscale to

the global scale.

Coastal ocean dynamics

Coastal ocean dynamics are important for many societal applications. They have smaller

spatial and temporal scales than the dynamics of the open ocean and require finer-scale

monitoring. SWOT will provide global, high-resolution observations in coastal regions for

observing coastal currents and storm surges. While SWOT is not designed to monitor the fast

temporal changes of the coastal processes, the swath coverage will allow us to characterize

the spatial structure of their dynamics when they occur within the swath.

Coastal tides and internal tides

The new capability of mapping sea surface height down to 15 km scales will improve the

knowledge of coastal tides as well as internal tides that have not been well sampled by

conventional altimetry. This new information is not only crucial for achieving the ocean

circulation objectives by separating tidal signals from circulation signals, but is also important

for applications in both coastal and open oceans (such as navigation in the coastal ocean and

improved understanding of ocean mixing in the open ocean).

1.2 Hydrology Objectives

The SWOT mission will provide measurements of water storage changes in terrestrial surface

water bodies and will provide estimates of discharge in large (wider than 100 m (baseline) or

170 m (threshold) ) rivers, globally. NASA has been developing missions for the global

measurement of the water cycle: the Global Precipitation Mission (GPM) will measure

precipitation globally, the Soil Moisture Active Passive mission (SMAP) will measure near-

surface soil moisture, and the GRACE Follow-On mission will measure the changes in

continental water masses. The SWOT measurements will provide a key complement to these

measurements by directly measuring the surface water (lakes, reservoirs, rivers, and wetlands)

component of the water cycle. The hydrologic science measurement objectives of the SWOT

mission are:

1. To provide a global inventory of all terrestrial surface water bodies whose

surface area exceeds (250m)

(goal: (100m)

, threshold: 1km

) (lakes, reservoirs,

wetlands) and rivers whose width exceeds 100m (goal: 50m, threshold: 170m).

2. To measure the global storage change in terrestrial surface water bodies at sub-

monthly, seasonal, and annual time scales.

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3. To estimate the global change in river discharge at sub-monthly, seasonal, and

annual time scales.

The primary hydrologic objectives of the SWOT mission are to characterize the spatial

and temporal variations in surface waters, globally, and thus address the following

hydrologic science questions:

What are the temporal and spatial scales of the hydrologic processes controlling surface

water storage and transport across the world's continents?

What are the spatially distributed impacts of humans on surface water, for example through

water impoundment behind dams, withdrawals and releases to rivers and lakes, trans-

boundary water sharing agreements, diversions, levees, and other structures?

What are the regional- to global-scale sensitivities of surface water storages and transport to

climate, antecedent floodplain conditions, land cover, extreme droughts, and the cryosphere?

Can regional and global extents of floodable land be quantified through combining remotely

sensed river surface heights, widths, slopes, and inundation edge with coordinated flood

modeling?

What are the hydraulic geometries and three-dimensional spatial structures of rivers

globally, knowledge of which will improve our understanding of water flow?

Terrestrial Water Cycle

In its most basic form, the terrestrial water balance of any basin during a given time period is

expressed as DS = P – ET – Q, where S is total storage, P is precipitation, ET is

evapotranspiration and Q is the net of all surface water discharges and groundwater flows into

and out of the basin. SWOT will provide the first global inventory of the surface water

components in DS and Q. The scientific value of these will provide a quantum improvement

on our current understanding of global fresh water dynamics. For example, some Arctic

basins are experiencing increases in river discharge, yet the magnitude of surface water

storage change remains unknown leaving open questions regarding the underlying physical

processes and their relationship to climate change.

Floodplains and Wetlands

Floodplains and wetlands in large lowland tropical basins such as the Amazon and Congo are

massive in size, yet the amount of water flowing through them remains unknown. This

deficiency results in poor knowledge of the amounts of water exchanged between mainstem

channels, floodplains, wetlands, and uplands. An important role of these floodplains and

wetlands is regulating carbon exchange with the atmosphere via CO

and CH

(carbon dioxide

and methane) evasion directly from the water into the atmosphere. The water surface area

and the changes in depth, both measured directly by SWOT, help govern rates of exchange.

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Transboundary Rivers and Water Resources

Beyond improved characterization of the water cycle, meeting these science objectives will

enable applications of scientific, social, and political importance.

Reservoirs created to store water number in the hundreds of thousands, yet a regular

accounting of the water stored and annually moving through them is not available. The

amount is likely substantial on a global basis, with estimates of over 5000 km

of water stored

in the largest 1000 reservoirs. The amount is unknown for the thousands of remaining

reservoirs.

Rivers crossing international boundaries pose special problems for water management.

Because of a variety of reasons, upstream flows in some countries are not readily shared with

downstream countries. SWOT measurements will permit all countries in a water basin to

equally know the water flows and thus better manage the water volumes.

Floods resulting from either fluvial processes or storm surges cause great losses in terms of

life and economy. While SWOT is not designed to target specific flood events, the swath

coverage will allow the measurement of floodwater elevations for any event within the swath.

Thus, SWOT data can provide useful target of opportunity information for flood events, both

in near-real time and post-event analysis.

1.3 Synergistic Science Applications

In addition to the mission objectives listed above, the SWOT data will be useful for a variety

of other scientific applications. Although these applications will not drive the mission

requirements or cost, they are of synergistic value to the mission’s science return. Therefore

the mission design decisions will not preclude them, assuming that enabling these science

applications will have small or no impact on the mission design or cost.

Although it is impossible to foresee all the applications that could be made of the SWOT data,

a number of applications are natural candidates for consideration:

1. SWOT data can be complementary to the operational oceanographic altimeters in the

TOPEX/Poseidon, Jason series, to improve the understanding of global and regional

sea level change, primarily for scientific and not operational purposes.

2. SWOT data can potentially be used for mapping the thickness of floating sea ice by

measuring sea ice freeboard.

3. SWOT data can potentially be used for measuring the topography of part of the

Greenland and Antarctic ice sheets, and their changes.

4. The SWOT data can be used to estimate the global ocean mean sea surface and

surface slopes. These data can be used to improve estimates the ocean bathymetry at

higher resolution and accuracies than currently possible.

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5. SWOT can collect data over the tidally affected portions of rivers, and estuaries and

wetlands, to help better understand the dynamics of freshwater/marine interaction

dynamics.

6. SWOT data can be used to improve the Earth’s mean land/ice topography, its changes

and potential land-cover classifications.

7. SWOT water surface elevation data over large lakes could allow the determination of

the vertical deflection due to gravity changes by using the computation of mean lake

surface undulations.

8. SWOT could provide valuable information for modeling water circulation in large

lakes such as the Caspian Sea, African lakes, Lake Baikal and Lake Titicaca, and the

Great Lakes of North America.

2 SWOT Science Specifications

2.1 Key Terms and Definitions

2.1.1 Requirement

A "requirement" as used in this document specifies a condition, parameter, or capability with

which the system design must be compliant, verifiable, and have a demonstrated achievement

during the mission. All requirement statements are preceded by the word "Requirement" and

use the verb "shall".

2.1.2 Goal

A "goal" as used in this document specifies a condition, parameter, or capability with which

the system design will strive to be compliant but it is not mandatory that such compliance be

verifiable or have a demonstrated achievement during the mission. Mandatory compliance or

demonstrated achievement are not required because the capabilities in the SWOT systems

limit the performance, because the inherent technical difficulty with the achievement is too

great, or because cost of achievement is too large. Nevertheless, a goal is tracked like a

requirement so if resources or capabilities permit compliance, better system performance will

result. All goal statements are preceded by the word "Goal" and use the verb "will".

2.2 Baseline/Threshold Science Missions

Science requirements for the SWOT mission are categorized into three levels: Science Goals

(SG), Baseline Science Mission (BSM) Requirements and Threshold Science Mission (TSM)

Requirements. The Baseline Science Mission forms the basis for the initial Project

Implementation Plan and the requirements shall be achieved unless the resources of the

Project are insufficient to accomplish them. The Threshold Science Mission Requirements

must be achieved to avoid losing the fundamental science value of the mission and the

threshold justification for the flight of the mission. Descoping to the Threshold Science

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Mission requirements will be exercised only when the resources of the Project are insufficient

to implement the BSM and only after other descope options have been explored. Science

Goals are defined here so that the SWOT engineering team can decide how to make trades

and where to apply resources that might otherwise go unused.

Unless otherwise indicated, requirements are written to reflect the Baseline Science Mission.

Threshold Science Mission Requirements are labeled as [TSM Requirement].

2.3 Mission Payload

2.3.1 [Requirement] The core SWOT payload shall consist of KaRIN, a Ka-band radar

interferometer capable of making the swath topographic measurements with the

coverage, precision and resolution given below.

2.3.2 [Requirement] The payload shall include a precision orbit determination (POD)

system enabling orbit determination to support oceanography and hydrology precision

and accuracy requirements listed below.

2.3.3 [Requirement] In order to meet the long-wavelength oceanography objectives and

the KaRIN cal/val requirement (2.7.7) and goal (2.7.8), profile topography

measurements shall be available with an accuracy equal or better than the Jason series

of altimeters and radiometers, as well as their POD performance, and with a sampling

compatible with the SWOT calibration needs.

The baseline mission requires that these measurements be collected by a Jason-class

altimeter/radiometer combination located on the same platform as KaRIN. In addition, it may

be possible to use profiling ocean topography measurements from other missions flying at the

same time. A baseline payload suite meeting these requirements is assumed to be:

1. A dual-frequency (Ku and C-band) altimeter with capabilities similar to the Poseidon

altimeter on OSTM/Jason-2.

2. A 3-frequency radiometer similar to the Advanced Microwave Radiometer (AMR) on

OSTM/Jason-2, but with the capability of imaging across the swath.

However, other collocated solutions may exist that provide the required calibration

performance.

2.3.4 [Requirement] Capabilities to measure water vapor across the swath over the

ocean shall be implemented.

2.4 Mission Lifetime

2.4.1 [Requirement] The Baseline Science Mission shall operate for at least 42 months,

including three annual cycles (36 months), a 3-month phase of launch/early operation

and payload check out, and a 3-month fast-sampling calibration phase (including orbit

transition).

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A minimum of three years is required to sample seasonal and inter-annual variability for both

the ocean and surface water height changes appropriately. The 36 months include an 8-

month measurement validation phase. It is expected that these phases will produce valid

science data after suitable reprocessing with the calibrated instrument parameters.

2.4.2 [TSM Requirement] The Threshold Science Mission shall operate for at least 18

months, including one annual cycle (12 months), a 3-month phase of launch/early

operation and payload check out, and a 3-month fast-sampling calibration phase

(including orbit transition).

The Threshold Science Mission is required to sample the seasonal variability for one year.

2.5 Space-Time Sampling Requirements

2.5.1 [Requirement] The SWOT sampling for the Baseline Science Mission shall

minimize aliasing of ocean tidal signals.

Tidal signals must be removed from the ocean topography data in order to meet the

mesoscale and submesoscale measurement requirements and associated annual and

interannual variability. This requirement precludes the use of a sun-synchronous orbit, which

aliases solar tides into a very long period signal.

2.5.2 [Requirement] The SWOT orbit inclination for the Baseline Science Mission shall

lie between 74

and 78

A minimum of 74 deg inclination is required to cover all important hydrology land targets.

Extending the inclination to 78 deg is required to cover important polar ocean areas and still

meet the tidal aliasing requirement. This will also cover a large part of the Greenland and

Antarctic ice sheets, particularly in the highly variable coastal regions.

2.5.3.a [Requirement] The SWOT orbit shall be a repeat orbit with a maximum repeat

period of 23 days and a minimum repeat period of 21 days.

With swath coverage, ascending and descending pass swath coverage implies an average

revisit time on the order of approximately 11 days at low latitudes. This temporal sampling is

similar to that obtained by OSTM/Jason-2 and better than the GEOSAT and GFO ocean

altimeter missions. For surface water, an 11-day revisit period allows appropriate sampling

of river dynamics in the tropics. At high latitudes, the swath sampling will produce shorter

revisit periods, compatible with arctic river dynamics. This temporal sampling choice is a

required trade-off for maintaining global coverage including the high-latitude regions and for

minimizing the tidal aliasing.

2.5.3.b [Requirement] The SWOT orbit ground track shall be controlled to within +/- 1

km at least 90% of each year, and not exceed +/- 2.5 km.

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The orbit control requirement is somewhat relaxed compared to the Jason altimeter series,

due to improved knowledge of the mean sea surface, and is required for minimization of geoid

error contribution to the nadir altimeter.

2.5.4.a [Requirement] SWOT shall collect data over a minimum of 90% of all ocean and

land areas covered by the orbit inclination for 90% of the operation time. This

requirement does not apply to the fast sampling calibration/validation phase described

in 2.5.5. This requirement also does not apply when 1) the KaRIN measurement is not

physically feasible, including ice or snow covered surface water; surface water in regions

of extreme topographic layover, or situations where the rain rate is greater than 3

mm/hour and 2) when the KaRIN measurement is not expected to meet performance

requirements during maneuvers, thermal snaps (the solar arrays and/or the KaRIN

mast), and rotations of the solar arrays for sun tracking.

This requirement is similar to that levied for TOPEX/Poseidon and Jason time series. The

requirement ensures that geographic gaps in coverage shall be smaller than 10% of the

Earth’s surface available to the mission. The requirement can only be met by a swath

instrument if one takes into account the temporal sampling requirement.

The coverage requirement cannot be levied when the physical circumstances make the

measurement unfeasible or unreliable. It is impossible to measure water level when the water

is covered by ice or snow, as will be the case for boreal regions in Northern Hemisphere

winter. The coverage of rivers, lakes, and wetlands in areas of extreme topography is also

limited by topographic layover. Although in some situations topographic layover will produce

errors within the surface water requirements, certain rivers and lakes in regions of extreme

topography will be systematically contaminated by topographic layover, independent of

choices in the instrument design. Finally, rain rates above 3mm/hour severely attenuate the

radar signal, making the measurement unfeasible. At any given time, about 7% of the Earth’s

surface will experience these rain rates.

2.5.4.b [Requirement] The total duration that the KaRIn measurements will not meet

performance requirements due to maneuvers, thermal snaps (the solar arrays and/or

the KaRIN mast), and rotations of the solar arrays for sun tracking shall not exceed 5%

of the mission operation time.

2.5.4.c [TSM Requirement] SWOT shall collect data over a minimum of 22% of all areas

covered by the orbit inclination with full swath coverage. This requirement does not apply

to the fast sampling calibration/validation phase described in 2.5.5. This requirement also

does not apply when the KaRIN measurement is not physically feasible, including (1) ice or

snow covered surface water; surface water in regions of extreme topographic layover, or

situations where the rain rate is greater than 3 mm/hour, or (2) when the KaRIN

measurement is not expected to meet performance requirements during maneuvers,

thermal snaps (the solar arrays and/or the KaRIN mast), and rotations of the solar arrays

for sun tracking.

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This threshold requirement is intended to cover anomalous situations (e.g., flight and/or

ground system anomalies, etc.) that impact the ability to meet the baseline coverage and

operability requirements. The minimum 22 % coverage corresponds to the case of the failure

of the onboard processor, causing all data to be acquired in the high-rate mode. The capacity

of the onboard recorder and the ground receiving stations does not allow 100 % download of

the high-rate data. In this eventuality, a contingent sampling plan would be developed by the

mission's science team to trade off available spatial and temporal coverage to achieve a

reduced scope of the mission's science objectives.

Potential failure modes of KaRIn have been identified that result in obtaining only one swath

(left or right) of data. This scenario does not meet this threshold mission requirement of

acquiring 22% of full swath data in HR mode. Science needs full swath coverage (two 50 km

swaths with 20 km nadir gap) to adequately measure the motion of ocean eddies and fronts.

For hydrology, a key science objective is to study water balance. Missing half of the full

swath will make such objectives not achievable.

2.5.5 [Requirement] SWOT shall have a fast-sampling phase after the instrument check

out phase for at most 3 months.

By frequent revisits of calibration sites, the fast-sampling phase will enable the calibration of

radar system parameters in the shortest time, resulting in the fastest transition to the nominal

phase with a fully calibrated system.

In addition, SWOT will demonstrate the first interferometry measurement of ocean water

elevations at 15 km resolution, which has an unknown temporal decorrelation time. We will

need to understand and validate the new measurement at the beginning of the mission to get

ready for subsequent science studies. During this fast-sampling phase, we will need sufficient

amount of data collected in exact repeating coverage for evaluation and comparison to other

independent observations from both in-situ and spaceborne platforms. A 1-day repeat mission

optimizes temporal sampling at the cost of spatial coverage. A 1-day sampling mission also

optimizes the number of cal/val revisits in the fast sampling phase.

One-day repeat sampling is valuable for sampling some submesoscale and mesoscale

phenomena appropriately. The 1-day sampling will give us better temporal coverage of the

evolving submesoscale filament structures and fronts in the ocean. It will also be necessary

for investigating certain dynamical structures in the tropics, including tropical instability

waves, and the filament structures surrounding them. Coastal currents and propagating

waves, and offshore squirts and jets, will also benefit from the higher frequency sampling.

Measuring these phenomena is part of the SWOT ocean science objectives.

2.5.6 [Requirement] The location of the fast sampling phase orbital nodal crossing and

crossovers shall be designed to meet both oceanographic and hydrology science goals.

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2.6 Science Data Products and Data Product Delivery

2.6.1 [Requirement] Level-1B data products shall be produced from the payload data.

2.6.2.a [Requirement] The following Level-2 standard data products shall be produced

for the KaRIn ocean data in a grid covering the entire measurement swath, and for the

nadir altimeter ocean data:

1. KaRIn and nadir altimeter ocean sea surface heights (SSH) (with the KaRIn

spatial posting intervals according to 2.7.1 and nadir altimeter measurements

according to 2.3.3).

2. Estimated KaRIn sea surface height uncertainties (1

) on the same grid as the

SSH measurements.

3. KaRIn and nadir altimeter

measurements on the same grid as the respective

SSH measurements.

4. KaRIn and nadir altimeter wind speed (but not direction) estimates derived from

the radar

on the same grid as the respective SSH measurements.

5. Nadir altimeter data products consistent with the Jason-series Geophysical Data

Records (GDR’s).

2.6.2.b [Goal] Estimates of ocean significant wave height on the same grid as the SSH

measurements.

2.6.2.c [Goal] Lower accuracy data with the same sampling characteristics as the level 2

ocean data for swath and nadir altimetry, but with degraded accuracy, will be produced

in near real time (1 day-lag from data downlink) in support of operational applications.

2.6.2.d [Requirement] A Level 2 product shall also be provided on a geographically

fixed grid, containing selected data products from those specified in 2.6.2.a. The

selection will be done by the Science Team in the course of mission development.

The measurement geographic grid needs to remain constant over the mission to minimize

geoid errors and enable the construction of a mean sea surface and variability studies.

2.6.3.a [Requirement] A Level-2 pixel cloud data product shall be produced for the

surface water data. The pixel cloud data product includes:

• For each pass, a geolocated water mask of all water bodies identified in the data

downlinked by SWOT, regardless of surface area. The mask resolution will be

reported at the finest resolution consistent with meeting appropriate geolocation

accuracy. The mask will be reported as a geolocated point cloud (including data

described below), which will have irregular spatial sampling and varying average

point separation from near to far range.

• As noted below, SWOT required performance will be evaluated using non-

vegetated water bodies meeting the minimum size criteria set in the science

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requirements, i.e., water bodies with area greater than (250 m)

and rivers of

width greater than 100 m. However, the SWOT performance will be

characterized for non-vegetated water bodies meeting the minimum size criteria

in the science goals; i.e., water bodies with area greater than (100 m)

and rivers

of width greater than 50 m. Only non-vegetated water bodies in regions of

moderate topographic relief (i.e., where layover contamination is negligible) are

to be used to assess SWOT performance.

• Estimated surface water elevations with the same sampling as the water mask.

• Estimated surface water elevation uncertainties (1

) with the same sampling as

the water mask.

• Estimated surface area represented by each point in the pixel cloud with the

same sampling as the water mask.

• Additional data and meta-data (e.g., collection time, water brightness) that might

be required for deriving additional data products.

“Pixel cloud” is a point cloud where the points are pixels. The Level-2 data product is

reported at the finest resolution consistent with accurate geolocation, which implies that some

range and azimuth averaging (“multi-looking”) will be done at the interferogram level to

achieve geolocation errors that will scale approximately as the square root of the number of

samples upon further spatial averaging for derived data products. All other hydrology data

products listed below will be derived from this Level-2 data product. The elevation, mask, and

error products for water bodies and rivers smaller than those over which the performance

can be guaranteed will provide useful information that can be supplemented with in situ or

other data to improve the science return from SWOT. Thus, these data products should be

produced for all water bodies where surface water is detected by SWOT.

2.6.3.b-1 [Requirement] For each pass a global set of vectors denoting rivers shall be

produced meeting the performance requirements in Section 2.8. The detected water

bodies will be linked to an a priori database of water bodies, but provision will be made

for collecting additional bodies.

2.6.3.b-2 [Requirement] The pass-based river vector product shall include at least

location, inundated area/extent, height, slope, width, and discharge with the associated

uncertainties and other relevant data. The reported discharge will be an estimate of the

reach-averaged discharge, and the extent of reach averaging will be selected to optimize

global estimates of river discharge. Discharge calculations require ancillary

information, such as river bathymetry and roughness coefficient. Discharge calculations

will utilize the best available ancillary information, which may be updated during the

mission.

Reach boundaries and the ancillary parameters required for river discharge calculation will

be provided by the Science Team.

2.6.3.c-1 [Requirement] For each pass a global set of vectors denoting lakes, reservoirs,

and similar water bodies with well-defined, enclosed boundaries shall be produced

meeting the performance requirements in Section 2.8. The detected water bodies will be

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linked to an a priori database of water bodies, but provision will be made for collecting

additional bodies.

2.6.3.c-2 [Requirement] The pass-based enclosed vector product shall include at least

location, water area/extent, height and storage change with the associated uncertainties

and other relevant data.

The a priori database will contain lake boundaries derived from visible-band imagery, and

will be supplied by the Science Team.

2.6.3.d [Requirement] A raster product including at least location, classification, height,

brightness, and uncertainties for these quantities shall be generated.

The raster products enable a highly usable data product for surface water hydrologic

environments that are not well represented by the river and lake vector products described in

the sections above, such as wetlands and estuaries, as well as for detection of variations

within large water bodies such as major lakes. The raster product has no requirements on

resolution or height accuracy. Appropriate limits on spatial area and/or resolution may be

negotiated by the data distribution agent with users.

2.6.3.e-1 [Requirement] A global set of vectors denoting rivers shall be produced by

averaging data over a period of at least one orbit repeat cycle (~21 days) but no more

than one month.

2.6.3.e-2 [Requirement] The averaged river product shall include at least location,

height, slope, inundated area/extent, width, and discharge with uncertainties and

appropriate auxiliary data.

For some of the global science to be done with SWOT measurements, it is essential to provide

the community with averages of data products at the temporal scale utilized in global

hydrologic models and large scale hydroclimatology studies. A product developed for

individual SWOT cycles will have a common set of observations from cycle to cycle, while a

monthly product would match many existing products used in hydrologic studies.

2.6.3.f-1 [Requirement] A global set of vectors denoting lakes and other enclosed bodies

shall be produced by averaging data over a period of at least one orbit repeat cycle (~21

days) but no more than one month.

2.6.3.f-2 [Requirement] The averaged enclosed vector product shall include a

representative polygon, with attributes to include at least location, height, storage

change, and area with uncertainties and appropriate auxiliary data.

These cycle-based products are required to address variations in global lake storage change

and their impacts on water cycle science using SWOT.

2.6.3.g [Requirement] The discharge product shall be available to the science

community starting six months after the SWOT validation meeting.

The global estimation and validation of these additional parameters implies that operational

production of discharge can only start after one seasonal cycle and subsequent validation,

hence the production timeline. This product will be updated at least one time during the

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mission to reflect improvements in knowledge of bathymetry and roughness together with in

situ calibration.

2.6.3.h [Requirement] A final discharge data product shall be available at the end of the

mission incorporating the best bathymetry and roughness information estimated during

the mission.

2.6.3.i [Goal] A Level-2 standard data product will be a topographic map of all land

elevations. This global digital elevation model (DEM) will be constructed from many

SWOT orbits. Given the present SWOT configuration, it is not clear if sufficient signal-

to-noise will be available to ensure any land elevations. Thus the height and geolocation

accuracies of the DEM cannot yet be specified. Ideally, the height accuracies will be

better than 1m and geolocation accuracies will be the same as those noted for the water

bodies in requirement 2.6.3.a. Prior to launch, should studies demonstrate that a land

DEM is not possible from SWOT, then the Project will engage with other DEM oriented

satellite missions (e.g., the TanDEM-X mission) to determine the possibilities of using

their global topographic data products within the overall SWOT science.

2.6.3.j [Requirement] The Level-1 single-look radar data products shall be available to

selected investigators on a regional basis.

It is expected that, subsequent to launch, algorithm improvements at the finest possible

resolution may be possible. Making the single-look data available on a regional basis to

selected investigators will enable refinement of SWOT algorithms, while limiting the need to

distribute at large the prohibitively large global data set.

Single-look data products will only be generated from available KaRIn high-rate data.

2.6.4.a [Requirement] A DEM of land elevations near the boundary of water bodies shall

be derived from water elevations and extent.

2.6.4.b [Requirement] This DEM shall be produced annually starting with the first year

of data after the conclusion of the fast-sampling phase.

The estimation of storage change for both rivers and lakes requires known bathymetry (i.e.,

topography) for the case when flooding is initiated across previously dry land (e.g., the first

pulse of floodwaters across a floodplain or that of a rising lake level across a low slope

shore). In addition, floodplain Digital Elevation Models (DEMs) are a key data set for

understanding flood dynamics. Floodplain DEMs may be produced by using the varying river

or lake stage and extent to contour the floodplain topography. The topography maps cannot

be produced for each pass since they require the observation of the river stage history over

the mission lifetime.

2.6.5 [Requirement] After the calibration phase, the Level-2 data production rate shall

keep up with the data acquisition rate during the rest of the mission to avoid data

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backlogs and to ensure the availability of the data products to the science team within 60

days of data collection.

Pass-based products will be produced day-by-day when all inputs are available.

The availability time for data products will be counted from the end of the data collection

period, particularly for averaged products.

2.6.6 [Goal] Routine access in near real time (<30 days) to vector elevation data for a

limited (<1000) number of large water bodies (e.g., reservoirs selected by the SDT) will

be allowed.

Over 90% of water stored in reservoirs is contained in the largest 1000 reservoirs and access

to these data will greatly benefit SWOT goals such as trans-boundary water management and

monitoring. The large size of these reservoirs guarantees that one month is sufficient

temporal sampling for their monitoring, and a one-month delay guarantees timely data access

for monitoring. The data product will be identical to the one described in 2.6.3.c restricted to

the largest reservoirs and with a faster access time.

2.6.7 [Requirement] All Level-2 data products shall be made available for distribution to

the general scientific community after validation by the SWOT Science Team.

Post-launch checkout of science data products includes validation by the Science Team.

2.6.8 [Requirement] For distribution to the general scientific community, Level 2

products shall be accompanied by an assessment of the quality of the product relative to

the measurement requirements. The quality assessment is provided by the Science

Team.

2.6.9 [Goal] Reprocessing will be conducted on the SWOT Standard data products to

correct for known errors and/or improved algorithms, in parallel with normal

processing of incoming data.

2.6.10 [Requirement] All Level 0, 1 and 2 Standard data products shall be delivered to

NASA and CNES to be placed in a permanent archive at the end of the mission.

2.7 Ocean Science Performance Specifications

In order to achieve the ocean science objectives, the following measurement science

requirements and goals for the SWOT mission are imposed:

2.7.1.a [Requirement] The spatial posting of KaRIn sea surface height measurements

shall be no coarser than 2 km.

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2.7.1.b [Requirement] KaRIn sea surface height measurements at scales finer than 2 km

shall be provided with the same average spatial posting interval that is available from

downloaded instrument data.

A measurement posting is defined as the location of the geographical center of a set of higher

spatial resolution instrument height measurements which are merged to form an estimate of

the sea surface height.

In order to achieve a resolution of 15 km, as set in the science objectives, a sampling of 7.5

km is required by the Nyquist sampling criterion. In order to calculate geostrophic velocities

and relative vorticity, derivatives of the height field must be computed. To reduce errors in

estimating these derivatives, it is required to oversample the height field relative to

instrument resolution. A 2km over-sampling will achieve this requirement.

For sea surface height slope, coastal, estuarine, and ice applications, it is desirable to have

the higher spatial sampling available from the KaRIn instrument (nominally 250 m posting

and 500 m resolution). Due to expected variations in the orbital altitude as well as pointing,

etc., variations in the pixel size and spacing in the order of +/- 10% are expected as well.

2.7.2.a [Requirement] The sea surface height error spectrum (cross-track average of the

along-track spectra computed at different cross-track locations over the swath) in the

wavelength range smaller than 1,000 km shall not exceed the spectrum envelope given in

Figure 1 and the formulas below. This requirement holds for significant waveheights

(SWH) less than 2 meters.

Mapping of mesoscale and submesoscale phenomena at 15-25 km resolution requires that the

measurement noise be smaller than or equal to the signal for the resolved wavelengths. It is

desirable to have the signal strength be at least one order of magnitude greater than the

measurement noise..

Achieving basin scale (~1,000 km to 10,000 km) SSH consistency is not required in order to

meet the threshold science objectives, but will enable basin scale oceanography, as a

complement to the TOPEX/Jason altimeter series.

Define the SSH error spectrum, E(f), as a function of the spatial frequency f (i.e.,

f=1/wavelength=1/

) (the same as the term of "wavenumber" used in some oceanographic

literature) such that the expected SSH error variance in the wavelength interval

min

max

] is

given by the integral of E(f):

(1)

Then the SSH spectrum in the ranges defined above is given by



(h)





1/

min

1/

max

E(f) df

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E(f) = 2 + 0.00125f

-2

[cm

/cycle/km] 15 km <

< 1,000 km (2)

which consists of a constant white noise contribution, which dominates at small wavelengths,

and a correlated noise contribution, which dominates at longer wavelengths, representing

residual geophysical errors, orbit and attitude restitution errors.

In the SSH validation process, the “truth” profiles used for validation of the SSH

measurements is defined as profiles of the true ocean surface filtered to remove all

wavelength components with wavelengths smaller than 15 km.

Because KaRIN will make 2 dimensional measurement, the noise can be reduced by 2-d

smoothing to a level lower than by 1-d smoothing. To resolve 15 km wavelength, the Nyquist

is 7.5 km. Therefore the noise is to be smoothed over a domain of 7.5 km x 7.5 km. Along-

track wavenumber spectrum is then performed on the 2-d smoothed SSH at various locations

across the swath. The average of such spectra is then evaluated against the requirement.

The requirement should only be imposed to wavelengths of 15 km and longer. However, the

data should be posted without the 2-d smoothing, which is only to be applied for evaluating

the spectral performance.

Due to the inherent noise in estimating the spectrum of a noisy process, validation of this

requirement is understood in an ensemble sense, to insure that the estimation errors

associated with the error spectral power for any given frequency are suitable to insure that

the requirement has been met with a probability greater than 68%.

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Figure 1: SSH baseline requirement spectrum (red curve) as a function of wavenumber.

Blue curve is the threshold requirement. Shown, for reference is the global mean SSH

spectrum estimated from the Jason-1 and Jason-2 observations (thick black line), the

lower boundary of 68% of the spectral values (the upper gray dotted line), and the lower

boundary of 95% of the spectral values (the lower gray dotted line). The intersections of

the two dotted lines with the baseline spectrum at ~ 15 km (68%) and ~ 30 km (95%)

determine the resolving capabilities of the SWOT measurement. The respective

resolution for the threshold requirement is ~ 25 km (68%) and ~ 35 km (95%).

The SWH requirement is consistent with the Jason requirement of operations for SWH < 2m.

2.7.2.b [Goal] The white noise component of the error spectrum will not exceed 1

/cycle/km.

This noise level, consistent with a spatial resolution of 12 km for the SSH spectrum shown

above (compared to the 15 km spatial resolution requirement for the Baseline Science

Mission) will yield improved understanding of ocean submesoscale circulation, internal tides,

and non-geostrophic contributions to SSH at scales consistent with small submesoscale

phenomena.

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2.7.2.c [TSM Requirement] The Threshold Science Mission white noise component of

the error spectrum shall not exceed 4 cm

/cycle/km.

This noise level, consistent with a spatial resolution of 25 km for the SSH spectrum shown

above (compared to the 15 km spatial resolution for the Baseline Science Mission) will still

yield significant science results for high-frequency ocean mesoscale and surface water

studies. The key contribution of the SWOT mission to oceanography is in the study of

mesoscale and submesoscale phenomena. Measuring longer scales is not critical to the

threshold mission success, although it would demonstrate the consistency with the previous

altimeter data record and provide a complement to the altimeter constellation flying at the

same time as SWOT.

2.7.3 [Requirement] The height postings shall be geographically fixed, and independent

of spacecraft position and attitude.

The measurement geographic grid needs to remain constant over the mission to minimize

geoid errors and enable the construction of mean sea surface and variability studies.

2.7.4 [Requirement] SWOT shall provide flagging of height postings affected by rain

with 68 % accuracy of the rain (More than 68% of rain-contaminated data must be

correctly flagged).

Rain cells significantly distort Ka-band radar measurements due to signal attenuation. An

estimated 5%-10% of all data (depending on latitude) will be affected by rain events. This

specification is inherited from the OSTM mission requirements for rain flagging.

2.7.5 [Requirement] SWOT shall provide flagging of sea ice over the ocean with 68 %

accuracy of the sea ice flag. (More than 68% of sea-ice-contaminated data must be

correctly flagged.)

2.7.6 [Requirement] The SWOT ocean performance shall be verified by payload

independent measurements or analysis during a post-launch calibration/validation

period.

2.7.7 [Requirement] The cross-track averaged SSH from KaRIN shall be cross-

calibrated against the nadir altimeter at wavelengths shorter than 1000 km and longer

than 200 km with an aim for consistency to the extent of the accuracy of the nadir

altimeter.

The nadir altimeter measurement is affected by instrument noise at wavelengths shorter than

200 km. At 200-1000 km, the performance of KaRIN is to be evaluated by comparison to the

nadir altimeter measurement.

2.7.8 [Goal] The cross-track averaged SSH from KaRIN will be cross-calibrated against

the nadir altimeter at wavelengths longer than 1000 km with an aim for consistency to

the extent of the accuracy of the nadir altimeter.

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Although there is no requirement levied on the performance of KaRIN at wavelengths longer

than 1000 km, its performance is to be assessed by comparison to the nadir altimeter

measurement. It is a goal of the mission for assessing the performance of KaRIN for

observing ocean variability at all scales.

2.8 Surface Water Science Performance Specifications

In order to achieve the surface water science objectives, the following measurement science

requirements and goals for the SWOT mission are imposed:

2.8.1 [Requirement] The post separation for surface water Level-2 data shall be

consistent with (1) the finest spatial separation commensurate with geolocation

accuracy; (2) minimization of the estimation errors for irregular water bodies; (3) cross-

swath variation with maximum less than the 70m range resolution in the near swath.

2.8.2.a [Requirement] The surface water areas estimated using the Level-2 water mask

(requirement 2.6.3a) shall have a relative error smaller than 15% (1

) of the total water

body area for water bodies whose non-vegetated surface area exceeds (250m)

or river

reaches whose width exceeds 100 m on average and length exceeds 10 km.

2.8.2.b [TSM Requirement] The surface water areas estimated using the Level-2 water

mask (requirement 2.6.3a) shall have a relative error smaller than 15% (1

) of the total

water body area for water bodies whose non-vegetated surface area exceeds 1km

river reaches whose width exceeds 170 m on average and length exceeds 10 km.

2.8.2.c [Goal] The surface water areas estimated using the Level-2 water mask

(requirement 2.6.3a) will have a relative error smaller than 25% (1

) of the total water

body area for water bodies whose non-vegetated surface area is between (100m)

and

(250m)

or river reaches whose width is between 50 m and 100m on average and length

exceeds 10 km.

2.8.3 [Requirement] The lake and reservoir, height accuracy of the Level-2 data

(requirement 2.6.3.c) shall be (1) 10 cm (1

) or better, for water bodies whose non-

vegetated surface area exceeds 1 km

and (2) 25 cm or better for water bodies whose

non-vegetated surface area is between (250m)

and 1 km

To measure storage change, only relative changes in water level are required. The (250m)

size requirement is consistent with the river precision requirement, 2.8.4, and is expected to

capture up to 65% of lake storage changes, which will be a significant advance compared

with the current capability, which is estimated to capture only 15% of the storage variability.

The 1km

lake area threshold requirement will capture an estimated 50% of storage

variability and still represents a significant improvement over current knowledge. The

baseline 100 m river width requirement is for resolving river basins larger than 50,000 km^2

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at 70% globally, which will be a significant advance beyond the current capability. The 170

m threshold river width requirement is for resolving river basins larger than 150,000 km^2 at

70 % globally. Observations at this level of performance would still improve on the historical

gauge network, especially in areas like the Congo basin that are currently poorly observed.

Figure 2: Estimated non-vegetated water body total height accuracy for water-only pixels as

a function of averaging area used to form the estimate (solid curve). Shown, for reference, is

the KaRIN random error only contribution to the height accuracy (dashed curve). The total

height accuracy is 10 cm for an equivalent water area of 1 km

, 21 cm for (250 m)

, and 50

cm for (100 m)

. Due to changes in spatial resolution and signal-to-noise-ratio, the

performance will vary across the swath. The shaded area shows the expected variability in

performance as a function of the averaging area.

2.8.4 [Requirement] Using the pass-by-pass data of requirement 2.6.3.b, after processing

elevations, river height accuracy shall be (1) 10 cm (1

) or better over an area of 1 km

inside the non-vegetated river mask, and (2) 25 cm or better for water bodies whose

non-vegetated surface area is between (250m)

and 1 km

All river requirements assume that the elevations are processed to average height and slope

by fitting a polynomial of suitable order to the irregularly sampled elevation data. The

requirement applies for any given location along the river reach where the minimum width

requirements are met.

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2.8.5 [Requirement] Using the Level-2 data of requirement 2.6.3.b, after processing

elevations over a maximum 10 km of flow distance, river water slope accuracy shall be

1.7 cm/1km (17

rad) (1

) or better for river widths greater than 100 m.

The requirement is formulated for a spatially continuous non-vegetated river surface area

with width greater than 100 m and a minimum reach length of 10 km. It does not include the

influence of water/land classification errors along the river margin. The accuracy of the

estimated slope depends on both the length of the averaging reach and the width of the river,

and the location of the measurement within the SWOT swath. For rivers whose reach-

averaged width is greater than 100 m, the length of the flow distance required to meet the

rad requirement will be smaller, while it will be greater for rivers whose reach-averaged

width is smaller than 100 m. The dependence on the averaging reach and the river width is

presented in Figure 3 for rivers in the middle of the SWOT Swath. Rivers that are imaged in

the far swath will have greater slope accuracy. Slope accuracy for rivers only imaged in the

near swath (within 20 km of nadir) have lower accuracy and will not be used to evaluate this

requirement.

Figure 3: River slope error (in

rad) as a function of river averaging length (in km) for

reach-averaged river widths from 100 m to 500 m based on a height performance consistent

with Figure 2.

2.8.6 [TSM Requirement] Using the pass-by-pass data of requirement 2.6.3.c, the lake

and reservoir height accuracy shall be 11 cm (1

) or better, for water bodies whose non-

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vegetated surface area exceeds 1 km

. For TSM, no requirement is levied against

smaller water bodies.

2.8.7 [TSM Requirement] Using the pass-by-pass data of requirement 2.6.3.b, after

processing elevations over an area of 1 km

inside the river mask, river height accuracy

shall be 11 cm (1

) or better. For TSM, no requirement is levied against smaller rivers.

2.8.8 [TSM Requirement] Using the Level-2 data of requirement 2.6.3.b, after

processing elevations over a maximum 10 km of flow distance, river water slope

accuracy shall be 3cm/1km (30

rad) (1

) or better for river widths greater than 100 m.

These threshold science requirements will still enable significant advances on our current

knowledge of global water balance.

2.8.9 [Requirement] SWOT shall provide flagging of height postings affected by rain in

both the pass-by-pass and global data, with 68% accuracy of the rain flag.

Rain cells significantly distort Ka-band radar measurements due to signal attenuation. An

estimated 5%-10% of all data (depending on latitude) will be affected by rain events.

2.8.10 [Requirement] SWOT shall provide flagging of height postings affected by

topographic layover in both the pass-by-pass and global data, with 68% accuracy of the

layover flag.

Topographic layover (radar energy from surrounding topography or vegetation and arriving

at the same time as the water signal) can significantly affect the height error, if the layover

radar energy is sufficiently great compared to the water return.

2.8.11 [Requirement] SWOT shall provide flagging of frozen surface water in both the

pass-by-pass and global data, with 68% accuracy of the frozen water flag.

2.8.12 [Requirement] The SWOT surface water elevation shall be verified by a payload

independent measurement or analysis during a post-launch validation period as well as

during the mission lifetime.

2.8.13 [Requirement] The SWOT surface water discharge equations shall be calibrated

for unknown bathymetry and roughness coefficient by observation of river dynamics

and the use of in situ and a priori data collected on selected water bodies pre and post-

launch.

2.8.14 [Requirement] The SWOT discharge performance shall be quantified by a

payload independent measurement or analysis during a post-launch validation period as

well as during the mission lifetime.

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2.8.15 [Requirement] SWOT elevation and inundation extent performance in vegetated

wetlands shall be quantified by a payload independent measurement or analysis during

a post-launch validation period as well as during the mission lifetime.

Because vegetation impacts SWOT elevation and inundation extent measurements in complex

and poorly understood ways that depend on vegetation characteristics that vary in both space

and time, it is not possible to set specific performance targets for wetlands. However, it is

important that SWOT wetland capabilities be assessed for a range of different wetland types.

In order to define an area as a wetland, it must be identifiably different from a lake or a

river. Here, we define a vegetated wetland as meeting two conditions: (1) it does not appear

in either the lake or river a priori databases used during processing and (2) it comprises an

area of open, non-vegetated water smaller than (250 m)2 in area and has a mean width of

open, non-vegetated water <100 m. Margins of rivers and lakes that contain dense, flooded

vegetation can be considered wetlands, though in such circumstances the river itself cannot

be. Besides, mixed pixels not connected to any lake or river, for which a height can be

retrieve should be included in this product with a specific flag.

Acknowledgment

The research was carried out at the Jet Propulsion Laboratory, California Institute of

Technology, under a contract with the National Aeronautics and Space Administration.