BSc Thesis-Spatial Resolution Enhancement Using RA-2...LPF: Low Pass Filter MFT: Model Free Tracker...

ISTANBUL TECHNICAL UNIVERSITY

ELECTRICAL – ELECTRONICS ENGINEERING FACULTY

SPATIAL RESOLUTION ENHANCEMENT

USING RADAR ALTIMETER 2

BSc Thesis by

Batuhan OSMANOĞLU

040010250

Department: Electronics and Communication Engineering

Programme: Telecommunication Engineering

Supervisor: Assis. Prof. Dr. Mesut Kartal

May 2005

ii

Batuhan OSMANOĞLU

FOREWORD

I would like to thank Dr. Mesut Kartal for spending his precious time working on this project with me. I would also like to thank Dr. Shimon Wdowinski, and Dr. Tim Dixon at University of Miami, USA for their support, and providing ESA-ENVISAT data. James D. Garlick at De Montford University, UK, is another person that I have to thank for his guidance since the very early stages of this study.

9 May 2005

iii

CONTENTS

FOREWORD ............................................................................................................... ii CONTENTS ................................................................................................................iii ABBREVIATIONS .................................................................................................... iv TABLES ...................................................................................................................... v FIGURES .................................................................................................................... vi SYMBOLS ................................................................................................................. vii ÖZET ........................................................................................................................viii SUMMARY ................................................................................................................ ix 1 INTRODUCTION ............................................................................................. 10

1.1 Introduction ................................................................................................ 10 1.2 General Measurement Principle ................................................................. 11 1.3 Echo Waveform Characteristics................................................................. 12 1.4 Error Sources ............................................................................................. 14

2 ENVISAT RADAR ALTIMETER SYSTEM (RA-2)....................................... 15 2.1 Introduction ................................................................................................ 15 2.2 Technical Details........................................................................................ 16 2.3 Full Deramp Technique ............................................................................. 17 2.4 Model Free Tracker .................................................................................... 19 2.5 Data Format ............................................................................................... 20

3 RESOLUTION ENHANCEMENT ................................................................... 21 3.1 Introduction ................................................................................................ 21 3.2 Simulator .................................................................................................... 21 3.3 Annuluses ................................................................................................... 24 3.4 Crescents .................................................................................................... 26

4 CONCLUSION .................................................................................................. 28 4.1 Overview .................................................................................................... 28 4.2 Results ........................................................................................................ 28

4.2.1 Simulation Result for Annuluses ....................................................... 28 4.2.2 Simulation Result for Crescents ......................................................... 30 4.2.3 RA-2 Example for Crescents ............................................................. 32

REFERENCES .......................................................................................................... 35 APPENDIX A - DATA FORMATS .......................................................................... 36 APPENDIX B – ANNULUS ANNALYSIS RESULTS ........................................... 46 APPENDIX C – SIMULATOR CODES ................................................................... 50 APPENDIX D – PREVIOUS WORK ....................................................................... 55

iv

ABBREVIATIONS

AGC : Automatic Gain Controller CNES : Centre National d’Eutes Spatiales (French Space Agency) CoG : Centre of Gravity DORIS : Doppler Orbitography and Radio-positioning Integrated by Satellite ESA : European Space Agency, Avrupa Uzay Ajansı I : Inverse LADAR : Laser Detection and Ranging LFM : Linear Frequency Modulation LPF : Low Pass Filter MFT : Model Free Tracker MWR : Microwave Radiometer MSS : Mean Sea Surface NASA : National Aeronautics & Space Administration (USA) OCoG : Offset Center of Gravity PRF : Pulse Repetition Frequency Q : Quadrature RA : Radar Altimeter RA-2 : Envisat Radar Altimeter-2 System RWS : Range Window Size, Receive Window Size SWH : Significant Wave Height SSH : Sea Surface Height TEC : Total Electron Content

v

TABLES

Table A.1 RA - 2 MDS .............................................................................................. 36 Table A.2 18 Hz Waveforms MDS ............................................................................ 44 Table B.1 Analysis results on annuluses .................................................................... 46

vi

FIGURES

Fig. 1.1 – Geometric Relations .................................................................................. 11 Fig. 1.2 – Reflected Echo Waveform, Hayne Model. [10] ........................................ 13 Fig. 2.1 – RA-2 Receiver Block Diagram (Ku Band) ................................................ 18 Fig. 2.2 – Illustration of OCoG Algorithm ................................................................ 19 Fig. 3.1 – Block Diagram of the simulator ................................................................ 22 Fig. 3.2 – Graphical Result of Annulus Radiuses ...................................................... 25 Fig. 3.3 – Relationship between Annuluses and Antenna Gain. ................................ 26 Fig. 3.4 – Forming of crescents in consecutive measurements .................................. 27 Fig. 4.1 – Simulator Generated Waveform for a Flat Surface and Its Corrected Form

against Antenna Gain Factor ..................................................................... 29 Fig. 4.2 – Tracking Surface Reflectivity using Annuluses ........................................ 30 Fig. 4.3 – Geometrical Analysis of Crescent Approach ............................................ 30 Fig. 4.4 – Difference of Echo 0 and Echo 1. .............................................................. 31 Fig. 4.5 – Difference of Echo 2 and Echo 1. .............................................................. 32 Fig. 4.6 – Envisat RA-2 Measurements ..................................................................... 33 Fig. 4.7 – Differences between Consecutive Measurements ..................................... 34

vii

SYMBOLS

B : Bandwidth c : Speed of light d : Displacement of the satellite D : Distance E : Elevation ft : Transmit frequency fr : Reference frequency H : Altitude n,N : Number of samples r : Radius of the footprint R : Range α : Incident angle ∆t : Time resolution ∆r : Range resolution µ : Compression ratio φ : Phase of signal ττττ : Pulse length ττττ’ : Uncompressed pulse length ∆ττττ : Two way time delay θ, θ3dB : 3 dB beam width

viii

ÖZET

Radar Altimetre (RA) ilk olarak 1973 yılında SKYLAB olarak adlandırılan bir aktif

uzaktan algılama uydusunda kullanıldı. O günden beri radar altimetre uzaktan

algılama uydularının bir çoğunda kullanılmıştır. Ana tasarım amacı okyanusun

dinamik özelliklerini çıkarmak olsa da, gelişen teknikler radar altimetrenin buz ve

suyun birlikte bulunduğu kutuplara yakın bölgelerde ya da tamamen buzlar ile kaplı

olan kutup bölgelerinde kullanılabileceğini göstermiştir. Öyle ki Avrupa Uzay

Ajansı (European Space Agency, ESA) tarafından hazırlanan ve temmuz ayında

fırlatılacak olan Cryosat kutup inceleme uydusu iki ayrı anten kullanılarak

hazırlanmış bir radar altimetre sistemi kullanmaktadır.

Bu ödevin giriş bölümünde ilk olarak radar altimetrenin kullanım alanları, önceden

kullanılan modellerdeki hatalar ve sorunlar ele alınmıştır. Daha sonra radar altimetre

sistemlerinin çalışma yöntemi genel olarak ele alınmıştır.

Đkinci bölümde çalışmanın temellendirildiği Envisat Radar Altimetre 2 sistemi

incelenmiştir. Sistem parametreleri aktarılmış ve Envisat radar altimetre sisteminin

önceki sistemlerden farkları, yararlı yönleri ortaya konmuştur.

Üçüncü bölüm çalışma çerçevesinde neden bir simulatör’e ihtiyaç duyulduğu ile

başlayıp, kullanılan simulatör ve uygulanan teknikleri tüm detayları ile

kapsamaktadır. Daha sonra çözünürlüğü artırmak için denenen iki yöntemi,

temelleriyle birlikte açıklamaktadır.

Son bölümde ise çalışma sonuçları aktarılmıştır. Kullanılan bu iki yönteme ait

sonuçlar ve bazı özel koşullar için simülatör’de uygulanan metotlar gerçek veri

üzerinde uygulanmış ve sonuçlar karşılaştırılmıştır.

ix

SUMMARY

Radar Altimeter (RA) was first installed on SKYLAB, an active remote sensing

satellite in 1973. Since then, radar altimeters have been installed on most of the

remote sensing satellites. Even though its main objective is to extract dynamic

information of the oceans, it has been shown that radar altimeters can be used over

sea-ice and Polar Regions. Moreover, European Space Agency (ESA) is preparing a

satellite called Cryosat which will inspect polar ice sheets using its “two antenna

radar altimeter system”. Cryosat is planned to be launched in July 2005.

The first part of this work will cover areas where RA’s used, previous systems and

their problematic sides. After that, general principles of a radar altimeter system

have been addressed.

Second part is dedicated to Envisat Radar Altimeter-2 System on which the whole

study is based on. System parameters have been clarified and different aspects of

Envisat Radar Altimeter System from its ancestors have been described.

Third part starts with explaining the need of a simulator for this study and continues

by working out the simulation parameters and clarifying its design. Following these,

techniques that have been implemented to increase efficiency of RA-2 have been

analyzed.

Last part consists of results for both simulator and RA-2 measurements. It contains

simulation and real world examples of how these two techniques can be used.

10

1 INTRODUCTION

1.1 Introduction

Radar Altimeter is an important instrument to obtain vital information about oceans.

It performs by measuring the two way delay of a radar signal to a very high

resolution. Shape and total power of the returned echo reveals significant

information about the surface.

Over the oceans, it observes effects of tides, climate change, hot streams like El

Nino, and ocean topography [1]. Even thought its main purpose is to collect ocean

information there are several other applications that RA are proven to be useful.

Monitoring of sea ice, polar ice sheets and some land surfaces is possible.

Radar Altimeters are in duty since the launch of very first space-borne active

microwave remote sensing satellite, namely Skylab, in 1973. Orbited at 435 km

Skylab’s radar altimetry mission was to inspect ocean state effects on the echo

waveform. With its 0.1 µs pulse length, leading a 15 m range resolution it was able

to show coarse features of ocean geoid such as trenches. After Skylab, radar

altimeters continued to assist scientific community on other satellites. Pulse

compression technique came on to the stage with GEOS-3 launched in 1974 to

compensate for its higher altitude (840 km). It provided better coverage and

resolution than Skylab; however, it was still not good enough to extract useful

science out of it. Four years later, NASA launched SeaSat-1 which employed “Full

Deramp Technique” making compression filters in the receiver pointless. Beyond

SeaSat-1 all radar altimeters use this technique which extensively improves the range

resolution. In 1985, US Navy launched Geosat in order to obtain information on

marine geoid, sea-state and wind conditions which are important for Navy

operations. Geosat provided the first long term high quality altimeter data to

scientific community. Two major families of radar altimeters occurred after Geosat.

Topex/Poseidon (NASA/CNES) and Jason (CNES) form the first family, which are

designed to perform over the oceans. ERS-1 and ERS-2 together with Envisat form

the second family, which are designed to work on any surface [2].

11

××=2

tan22θ

Hr

1.2 General Measurement Principle

Radars are used to detect a target and reveal its position and speed using the

information extracted from returning pulse. Similarly, radar altimeters measure the

time delay of radar pulse and calculate the range regarding to it. Recent technology

provides better than 2.5 cm of accuracy over the oceans [2]. Sea surface conditions

and surface backscatter coefficient can be estimated looking at the echo waveform.

Radar Altimeter is a nadir looking active microwave instrument. To reduce the size

of the footprint, antennas with narrow beam angles are used. For instance, using an

antenna with 1.2 m diameter, ERS-1 has a 3dB beam width of 1.3 degrees. Using

simple geometric relations, at an altitude of 800 km, these figures lead to 18 km for

the diameter of footprint. Fig. 1.1 and eqn. 1.1 illustrates this relation, where H is

altitude, L is maximum range, θ is 3dB beam angle and r denotes the radius of the

footprint.

Fig. 1.1 – Geometric Relations

(1.1)

There are two limits on the footprint. The first one is due to the antenna 3 dB beam

angle which is described above and depicted in fig. 1.1. The other constraint comes

from the pulse length. As shown in eqn. 1.2, where ∆t is time resolution, ∆r is the

range resolution and c is the speed of light, in order to achieve 5 cm resolution from

800 km a pulse length of 0.3 ns is required. On the other hand, due to the pulse

length-bandwidth relation given in eqn. 1.3 such a pulse requires bandwidth of

around 3 GHz. In eqn. 1.3 τ denotes the pulse length in time domain and B is the

required bandwidth.

12

1=×Bτc

rt

∆=∆

2

( )22 ττ cHcrpulse +=

(1.2)

(1.3)

However, such a huge bandwidth is not always available and would interfere with

the existing links on earth. Even if the bandwidth is available, it is not practicle to

transmit a high peak power in such a short time. 0.3 GHz bandwidth is allocated for

such applications. It turns out that due to roughness of the ocean surface 0.3 GHz of

bandwidth is adequate and it is still possible to reach high accuracy employing the

Brown model.

Another constraint comes from the limited pulse length. As a result of eqn. 1.3, 0.3

GHz bandwidth corresponds to a pulse length of 3 ns. In practice, 20 µs length

pulses are used in order to decrease peak power and distribute it over time. This

technique is called pulse compression. Pulse compression technique and its effect on

range resolution will be described in section 2.2. For a 3 ns pulse, using the relation

illustrated in fig. 1.1 L can be calculated as H+cτ. Keeping this in mind one can

solve the radius of the footprint as shown in eqn 1.4.

(1.4)

For a satellite at 800 km altitude taking the pulse length as 3 ns the maximum radius

of the footprint due to the pulse length can be found around 1.2 km. This radius

corresponds to a very small portion of the 3 dB beam angle therefore the function of

the reflected echo power will be a ramp function. Over the ocean reflected echo

waveform is consistent with the Hayne model (1980) [3]. Hayne model is based on

the model built by Brown in 1977 but “it includes skewness in the Gaussian

assumption of the point target response and in the height distribution of scatterers”

[3].

1.3 Echo Waveform Characteristics

Radar pulse travels towards the earth surface forming a spherical shell as shown in

fig. 1.2. This spherical shell has a thickness related with the pulse length. A surface

with roughness scales in the order of the wavelength is a diffuse scatterer [3]. Energy

reflected from such a surface will be proportional to the instantaneous illuminated

surface.

13

Assuming the earth surface as flat, intersection of spherical radar pulse shell and this

surface will define the illuminated area. Therefore, reflected echo waveform will

consist of three regions. The first region will have an upwards slope as the surface

completely remains inside the shell as shown in fig. 1.2 part a. Part b of the same

figure defines the plateau region where the illuminated area remains almost constant,

due to the expansion of the outer and inner borders. As outer border reaches its

maximum, the power will start to diminish as the inner border continues its

expansion. Reflected echo waveform model is called Hayne model which is depicted

in fig. 1.2.

Fig. 1.2 – Reflected Echo Waveform, Hayne Model. [10]

Echo waveform reveals a lot of information about the surface underneath. It is

known that range information can be calculated using the time delay. Moreover,

slope of the rising edge reveals information about the surface roughness as rough

surfaces result into smaller slopes. Again from the slope of the rising edge it is

possible to measure “Significant Wave Height” (SWH), and mid-point of the rising

edge defines the average “Sea Surface Height” (SSH). Mid-point of the rising edge

is defined as the tracking point as the tracker tries to keep this point at the same bin

for each waveform. Additionally backscatter coefficient can be calculated, which is

estimated through the total area under the echo waveform.

These calculations are under the assumption of a surface with a roughness scale of

the order of wavelength. However, over Polar Regions or land it is possible to have

surfaces with roughness scales much more than the wavelength. In such cases it is

14

not possible to define the tracking point as the mid-point of the rising edge, as there

is no rising edge in the waveform. Early radar altimeters were using trackers that are

conformed to the Brown Model. However, as there are no models for sea-ice, ice or

land, tracking point for such regions is defined as the centroid of the waveform.

1.4 Error Sources

It is well known that ionosphere introduces a group delay to the space borne systems.

Group delay is proportional to the carrier frequency and Total Electron Content

(TEC) which changes with time. Using two different frequencies in a radar altimeter

system it is possible to correct for ionospheric group delays.

Sea state bias is an effect caused by the crests and troughs of the ocean waves. The

crests disperse the radar pulse and the troughs focus them. As a result crests decrease

the power reflected and the troughs increase it. These two effects spoil the leading

edge smoothness and introduce a bias around 5 to 10% of the SWH [1].

Dry and wet tropospheric corrections are connected with the refractive index, which

is a function of air temperature, water vapor content and pressure. Dry tropospheric

error can go up to 2~3 meters while wet tropospheric error is around 0.06~0.3 meters

[1].

Orbit error is associated with the ambiguity of satellite position. Before installation

of GPS satellites around the world, this was one of the main limitations in satellite

ranging systems, however nowadays it is around 0.02 m for the satellites that

implements GPS tracking [1].

15

2 ENVISAT RADAR ALTIMETER SYSTEM (RA-2)

2.1 Introduction

Envisat follows the same ground track as ERS-1 and ERS-2 which will construct a

time series of more than 15 years which will allow inter annual examination of

dynamic ocean circulation patterns, significant wave height climatology and ice-

sheet elevation [4].

Envisat uses two different frequencies to compensate for the ionospheric group

delay. Together with the Microwave Radiometer (MWR) and Doppler Orbitography

and Radio-positioning Integrated by Satellite (DORIS) RA-2 keeps an eye over the

oceans, sea-ice and Polar Regions as well as land surfaces.

Envisat RA-2 is a nadir looking instrument and is in continuous operation that

provides global coverage up to the latitude limit of 81.5 degrees north and south.

Envisat operates with an inclination of 98.5 degrees and it has a complete repeat

cycle of 35 days, consisting of 501 orbits [5]. Such an orbit gives a across track

sampling of 80 km at the equator. This orbit pattern has sub cycles of 3 days and 17

days providing global coverage with coarser sampling. RA provides 18 range

measurements per second which corresponds to a along track sampling interval of

around 400 m. Traveling around the Earth at an altitude of 800 km RA-2 has a

circular footprint of around 18 km in diameter, which may change with the surface

roughness

RA-2 has some advantages when compared with ERS-1 or ERS-2. It provides more

robust tracking due to model free tracker. RA-2 tracker is only responsible for

keeping the echo wave form in the window [4]. Geological calculations are done on

the ground. This simplification results into a more robust tracker. Furthermore, it

provides three different resolutions, allowing increase of the window size to capture

land and ice waveforms. Resolution change is done automatically on board. Another

drastic improvement of RA-2 is the number of samples. RA-2 provides 128 samples

which is double the number of samples for ERS. Moreover a 129th sample is

16

2

τcr =∆

rnSAMPLE ∆×=RWS Size, WindowRange

available and can be positioned anywhere needed to increase precision [5]. Moreover

individual echoes mode makes it possible to obtain 1800Hz waveforms, which are

single waveforms that are not averaged. Envisat is programmed to average 100

consecutive waveforms and obtain range measurements at 18 Hz.

2.2 Technical Details

Main task of RA-2 is to determine the two way delay of the radar echo. It travels at

altitudes between 764 km and 825 km. It is expected for RA-2 to have a range

accuracy of around 5 cm over the ocean. In order to achieve this level of accuracy, a

chirp signal with a bandwidth of 320 MHz is used. Hayne model is applied after the

signal processing to accomplish the accuracy expectations. Due to the relationship

between bandwidth and pulse length given in eqn. 1.3, 320 MHz corresponds to

3.125 ns. Chirp signal is used as a part of pulse compression technique.

In typical radar systems, range resolution is proportional to the pulse length;

however, it is not practical to transmit very high powers for very short durations of

time. In the same manner, RA-2 uses a 20 µs linear frequency modulated signal to

decrease the transmitted peak power and disperse the pulse in time. However, even

with 320 MHz, it is not possible to attain 5 cm accuracy. Range resolution for a

pulse length of 3.125 ns is calculated as 0.46875 meters using the eqn. 2.1.

(2.1)

Range resolution is improved by averaging 100 waveforms and applying Hayne

Model for ocean waveforms. Number of sampling points is defined as 128 for

Envisat RA-2. Together with the range resolution, number of sample points defines

the range window size, 60 meters for high resolution, as shown in the eqn. 2.2.

(2.2)

Over non-ocean surfaces it is quite common that height variation is more than 60

meters. Therefore over such surfaces, range resolution is decreased autonomously to

keep the waveform inside the window. RA-2 possesses three different resolutions,

corresponding to three different bandwidths. 320 MHz, 80 MHz, and 20 MHz are the

three bandwidths corresponding to 0.46875 m, 1.875 m, and 7.5 m of range

resolutions respectively [9].

17

RA-2 operates at two different bands, 13.575 GHz (Ku Band) and 3.2 (S Band), to

compensate for the ionospheric delay. For these two frequencies 3 dB beam widths

are 1.35 degrees and 5.5 degrees respectively. For the S Band RA-2 uses only one

chirp signal with a bandwidth of 160 MHz. It was mentioned that RA-2 provides 18

range measurements in Ku Band. Each of these measurements is averaged over 100

samples and this leads to a Pulse Repetition Frequency (PRF) of around 1800 Hz.

PRF of the S-Band is four times less than the Ku Band PRF. Consequently, S Band

measurements are averaged over 25 samples, not 100.

Table 2.1 – Specifications of RA-2 [4, 5]

Parameter Name Description Value Orbit Range km 764 to 825

Operative Frequencies GHz 13.575 and 3.2 Pulse Length µsec 20

Ku chirp bandwidths MHz 320, 80, 20 Ku Range Resolution m 0.46875, 1.875, 7.5 Range Window Width m 60, 240, 960

S chirp bandwidth MHz 160 Transmitter peak power W 60 (Ku) / 60 (S) Number of FFT points 128 (Ku) / 64 (S)

3 dB Beam width Degrees 1.35 (Ku) / 5.5 (S) Pulse Repetition Frequency Hz 1795.33(Ku) / 448.83(S)

Pulse Repetition Interval ms 557 (Ku) / 2228 (S) Antenna Gain dBi 41.6 (Ku) / 29.2 (S)

IF centre frequencies MHz 1223 (Ku)/ 75 (S) RF Losses dB 1.8 (Ku) / 1.7 (S)

Receiver Maximum Gain dB 107 AGC dynamic range dB 60

Receiver Noise Bandwidth MHz 6.4 Receiver Noise Figure dB 3 (Ku) / 2.5 (S)

Spatial Sampling m ~390 Ku Geometric Resolution km ~19

2.3 Full Deramp Technique

The range resolution of RA-2 is around half a meter (3.125 ns) in high resolution

mode. In conventional radar systems to achieve this accuracy a pulse length of 3.125

ns is needed. This approach is commonly used in LADAR (Laser Detection and

Ranging) systems. However in radar altimeters pulse compression techniques are

used. As a result, it is possible to acquire data using lower peak powers using a linear

frequency modulated signal which is called as “chirp signal”. The compressed pulse

resolution is inversely proportional to the chirp bandwidth as shown in eqn. 2.3.

18

B

cr

2 ,Resolution Range =∆ (2.3)

In radar altimeter systems dispersive delay lines are commonly used to generate

linear frequency modulation of the chirp signals. The reflected echo is then passed

through an inverse matched filter to decompress the signal. This whole procedure is

called as “Pulse Compression”. However to obtain 3.125 ns pulse length, 320 MHz

of bandwidth is needed. Dispersive delay lines are the only practical way of

generating chirp signals with such bandwidths. Unfortunately, this fact introduces a

new problem: It is not possible to build an inverse matched filter as the

corresponding frequency division is unattainable [6]. To get around this problem,

“Full Deramp Technique” is used.

When the reflected radar echo is received it is mixed with a replica of the transmitted

chirp. Thus, constant frequency tones appear for different facets at different ranges.

As the process continues, signals from different facets that are at the same range start

to build up. Fig. 2.1 shows the receiver block diagram of RA-2. After multiplication,

the resultant signal is amplified and multiplied with the second local oscillator with a

90 degree phase shift to attain Inverse (I), and Quadrature (Q) channels. I and Q

signals are then sampled and quantized. Hamming window is then utilized to these

signals. FFT is applied to convert time domain samples to frequency domain. At the

end, result of the FFT circuitry is fed to the tracker to close the loop and generate the

chirp signal for the consequent received signal.

Fig. 2.1 – RA-2 Receiver Block Diagram (Ku Band)

19

2.4 Model Free Tracker

RA-2 utilizes a Model Free Tracker (MFT) that does not depend on any waveform

model as the name implies. Rather than a waveform model, MFT uses Offset Center

of Gravity (OCoG) algorithm.

There are several steps to determine the height error using OCoG algorithm. This

algorithm is based on the assumption that the envelope of the echo waveform can be

estimated by a rectangle [7]. First, center of gravity (CoG) of the waveform is

calculated. Double the power level of this CoG defines the height of the rectangle.

Sum of all the power levels give an estimate for the rectangle area, therefore width

of the rectangle can be estimated as the sum of all bins divided by double the CoG

power level. Together with the CoG, rectangle width defines the location of leading

edge. In other words, tracking point is determined by CoG and the width of

rectangle. Envisat uses bins 46, 59.5 and 62.875 as tracking points for high, medium

and low resolutions, respectively [9]. Deviation of tracking point from these

predefined locations indicates height error. Fig. 2.2 illustrates the OCoG algorithm.

Another point worth to mention about the final version of this algorithm is that, as

linear weighting is applied in the computations of CoG location, algorithm is quite

sensitive to noise. To circumvent this problem, samples are squared to increase the

dynamic range artificially [7].

Fig. 2.2 – Illustration of OCoG Algorithm

20

Model Free Tracker, works basically in the same way as the OCoG algorithm,

however, it simplifies it more in order to decrease the computational load. It applies

a threshold to the echo waveform and converts it to binary. Once converted to binary

in most of the cases, mid-point of ones indicate the center of gravity. The offset error

controls the range resolution of the altimeter autonomously. Increase in the offset

error indicates that the echo waveform is moving outside of the receive window.

Therefore the resolution is decreased by changing the chirp bandwidth to keep the

waveform inside the receive window.

2.5 Data Format

Data is distributed on the web and with DVDs delivered courier service. See

Appendix A for the data file format.

21

3 RESOLUTION ENHANCEMENT

3.1 Introduction

In this work a simulator based on Envisat Radar Altimeter-2 has been developed in

order to analyze characteristics of reflected waveforms over different surface types.

Using this simulator new approaches have been developed to enhance the spatial

resolution of RA-2.

Purpose of this project is to add new capabilities to RA-2 and increase its efficiency.

Currently, RA-2 is used to measure ocean parameters such as significant wave

height, mean sea surface, sea state bias, and etc. It is also used to monitor sea-ice and

polar ice sheets. Its large footprint and centimeter scale range resolution makes it

very suitable for ocean monitoring. Thanks to the MFT, RA-2 is capable of keeping

the echo in the range window for most of the cases. As geophysical information is

extracted using on-ground processors, it is possible to run and optimize different re-

tracker algorithms on collected waveforms. Echo waveforms scattered over land are

harder to analyze compared to ocean waveforms as there is no available model. In

this work, spatial resolution of RA-2 is increased using two new concepts, namely

crescents and annuluses.

3.2 Simulator

The aim of this study is to increase spatial sampling resolution. This will be achieved

using coherency analysis of consecutive return echo signals and investigating the

effect of annuluses on the echo waveform. Such analyses not only require the

simulation of envisat radar altimeter processor, but also require having control over

the surface types. First, the simulator is designed to match the characteristics of RA-

2 as described below.

Simulation is carried out using a modified stretch (active correlation) processor

algorithm. Fig.3.1 demonstrates how the stretch processor operates. Linear frequency

modulation (LFM) is used to implement pulse compression. A general name for

22

'0;'2

2exp)( 2 ττ

π ≤≤

−= ttB

tfjts tt

∆−−∆−= 2)('2

)(2exp)( ττ

τπσ tB

tfjts tr

∆−∆+∆−−= 2'2'

)(2exp ττ

ττ

τπBB

tftffjAs trtLPF

LFM signals is “chirp” and equation of the transmitted chirp signal is given in (3.1).

Change of frequency with time for a LFM signal is depicted in fig. 3.1., B stands for

band width, t is time, τ’ is uncompressed pulse length and ft is center frequency in

(3.1).

(3.1)

Fig. 3.1 – Block Diagram of the simulator

From each facet of the surface, transmitted signal will be reflected at a different

time, proportional to range of facets. This round trip delay will take around 5.3

milliseconds. In fig. 3.1 such signals with different round trip delays are drawn.

Additionally, each facet will have a different backscatter coefficient. Keeping these

in mind one can write the equation of a reflected echo as shown in (3.2). Here σ

represent backscatter coefficient and ∆τ symbolize round trip delay.

(3.2)

Reflected signal is mixed with a reference chirp signal, which has the same rate of

frequency change with transmitted signal. Purpose of this operation is to convert

time delays into constant frequency tones, and this is called deramping process. A

low pass filter (LPF) is utilized right after the mixer in order to exclude high

frequency components.

(3.3)

23

2

''22)(2 τ

τπτ

τπτππφ ∆−∆+∆−−=

Bt

Bfff trt

)('

2)(2

'

22

2

1)(

2

1 111 rtrt ff

c

BRff

c

RB

dt

df −−=

−−==τ

πτπ

πφ

π

'

1

2'

2

'

2

τττ==

∆=∆

B

c

c

B

c

RBf

fN∆=Size WindowReceive RWS,

.'

)(2

'

)(2

2minmax

ττ cRRB

c

RWSBfN −=>

∆

Round trip time delays, ∆τ, contain valuable range information of the target and it is

possible to extract it by taking the derivative of the phase of sLPF. Derivative of the

phase term is also named as instantaneous frequency.

(3.4)

(3.5)

Equation (3.5) points out a one to one relationship between instantaneous frequency

and range of targets. Therefore it is important to realize what the minimum

frequency separation should be in order to differentiate two distinct targets located

close to each other in range. Substituting target range in (3.5) with range resolution,

one can get the equation of frequency resolution. Range resolution is defined as c/2B

[8].

(3.6)

Together with number of samples, frequency resolution determine the receive

window size (RWS) in frequency. RWS is an important parameter as it shows the

resolvable maximum difference between closest and furthest target ranges. It is also

known that Fourier transform produces unsymmetrical results for complex inputs.

Hence maximum frequency displayed in frequency window will be all of the RWS.

(3.7)

Limitation for minimum number of samples for a given bandwidth and pulse length

can be calculated combining (3.7) and (3.6).

(3.8)

Above presented is the detailed information about the simulator and how it works. In

general, the processor mentioned above takes two input maps, elevation and

reflectivity. Elevation maps are then converted to range maps as they are easier to

process.

There is a tricky part of the simulation process, which deserves a lot of attention. As

the timings used in the above formulas are all relative, so that ∆t is subtracted from

every t term of received echo, range is also relative! In other words, the receive

window is located around 800 km away from the satellite. Therefore R1 is equal to

24

'τβ

µ =

ββτ

τµ1'

'

1==

∆=∆

frT

R1-Rmin in above equations. Rmin is defined by the tracker and adds constant

frequency shift to the above terms. After preparing 128 time samples for every single

scatterer in the range map, each scatterer’s response is applied to the Fourier

transform and summed up.

3.3 Annuluses

It is described in section 1.3 that the footprint of radar altimeter systems are circular

and usually form annuluses because the pulse width is too short compared with the 3

dB beam width.

Returning back to fig. 1.2, and making a deeper analysis, it is clear that the rising

edge forms during the expansion of external boundary of the footprint, and when

there is no blank circle in the middle. For Envisat, pulse compression ratio µ is

16×1012, and can be calculated as given in eqn 3.9 where β represents “Chirp

Bandwidth (320 MHz)” and τ’ denotes uncompressed pulse length (20 µs).

(3.9)

Together with the frequency resolution (eqn. 3.6), compression ratio can be used to

verify range resolution after pulse compression. In Eqn. 3.10 relationship between

frequency resolution, compression ratio and range resolution in time domain is

given.

(3.10)

This result indicates that even though the actual pulse length of radar signal is 20 µs,

with regard to frequency modulation our range resolution can be increased

drastically. Given that range resolution after pulse compression is 0.46875 m it is

possible to define equi-range areas inside the footprint. These are the areas that are

represented by a single bin in the frequency receive window. Obviously, these areas

will have circular boundaries due to the spherical pulse shape. Using simple

geometrical relations radius for the kth equi-range circle can be calculated as:

(3.11) ( ) .46875.0)( 22 HkHkradius −×+=

25

Computing eqn. 3.11 for every k values from 0 to 127 the exponential curve

illustrated in fig. 3.2 is achieved. Radius values for each k value are given in

appendix B.

Fig. 3.2 – Graphical Result of Annulus Radiuses

Last column of Table B.1 in appendix B draw attention to equal areas of annuluses.

Given that each bin after the leading edge indicates an annulus, analysis of surface

reflectivity can be done for each annulus. In other words, if each bin contains the

power of radar pulse scattered from a single annulus, it is possible to look for back

scatter coefficient (annulus radar cross section) changes among them. However, due

to the effect of incident angle on antenna gain, it is likely that the accuracy of this

analysis will decrease for incident angles close to half of the 3 dB beam width. Fig.

3.3 shows the connection between the antenna gain and annuluses. Antenna gain for

an angle of α less than half of 3 dB beam width can be calculated as shown in eqn.

3.12.

(3.12)

( ) ( ) [dB] /12 23max dBGainGain θαα ×−=

26

Fig. 3.3 – Relationship between Annuluses and Antenna Gain.

3.4 Crescents

Envisat travels around 400 m on its path on Earth between two measurements. Each

measurement is an average of 100 echoes. The diameter of the circular footprint is

around 18 km. In other words, the footprint covers almost the same area for two

consecutive measurements. As a result, difference of two consecutive waveforms

will include information about the area that is covered in the first measurement but

not in the second one, and likewise information about the area that is covered in the

second footprint but not in the first one. Therefore it is possible to analyze along

track coherency by taking differences of consecutive waveforms.

For instance assume Envisat is traveling over the ocean and approaching to a

shoreline a little higher than the mean sea surface (MSS). In such a case at some

point in time one of the two consecutive waveforms will be completely over the

ocean and the next one will have some parts on the land surface. This is going to

introduce a difference in the last bins of the waveform. The radius of annuluses get

closer around 3 dB beam width, therefore a shift of 400 m would change around 6-8

frequency bins at the end of the receive window. Fig. 3.4 illustrates crescents for

consecutive measurements, where:

27

- First footprint consists of areas a, b, and c.

- Second footprint consists of areas b, c, and d.

- Third footprint consists of areas c, d, and e.

Fig. 3.4 – Forming of crescents in consecutive measurements

Additionally, back scatter coefficient differences can also be tracked using the

benefits of crescents, however as mentioned in the previous part due to the antenna

gain decline at incident angles close to 3dB beam width it is not going to be accurate

when two consecutive measurements are compared. On the other hand, such an

analysis might be employed between every 20th samples as the footprint of RA-2

will have changed almost around 50%.

28

4 CONCLUSION

4.1 Overview

In this work several techniques to improve Envisat Radar Altimeter System have

been developed and tested. Two promising new techniques are covered in the

previous section. Next part will illustrate achievements reached by using these

methods.

It worth’s to mention that Envisat also provides individual echoes mode, where this

study may generate more interesting results. Taking the average of 100 echoes cause

them to decoralate which makes it harder to analyze.

4.2 Results

This section contains two simulation and one real data example. One of the

simulation results represents the first technique that employs Annuluses and the

other one demonstrates the second technique that uses Crescents. Only the example

of second method can be illustrated for Envisat data as compensation of gain

controller systems could not be accomplished, which is a necessary step for method

of annuluses. As it is depicted in fig. 4.5, even for consecutive waveforms the power

values change a huge amount. More analysis on Automatic Gain Controller (AGC)

of RA-2 has to be completed before taking further steps.

4.2.1 Simulation Result for Annuluses

As mentioned in section 3 part 3, analysis of annuluses let us differentiate surface

reflectivity changes. Fig. 4.1 shows a sample output of simulator for a zero elevation,

flat surface. Fig. 4.1 also includes its compensated form for the change of antenna

gain regarding the incident angle.

29

Fig. 4.1 – Simulator Generated Waveform for a Flat Surface and Its Corrected Form against Antenna Gain Factor

Fig. 4.1 points out a problematic situation at the last portions of the echo reply. This

fluctuation is a result of simulation map resolution where pixels of 100m on each

side are used. As shown in Table B.1, radius differences for consecutive annuluses

decrease exponentially, and as a result, map resolution does not provide sufficient

number of scatterers for a smooth sum at the edges of footprint.

In order to show how analysis of annuluses is performed, a 0.9km2 (3 by 3) areas

reflectivity coefficients have been increased by ten percent. This area is located on

the eastern side of annulus 3. Fig.4.2 shows both the new simulation result and

difference of results for this elevation map, from the one displayed in fig. 4.1. In

other words, to make the reflectivity change more visible, flat surface response is

subtracted from modified surface response. The curve for relative change has been

given the offset of positive 2000 in order to prevent confusion of two signals.

Moreover, looking at the tiny yellow boxes in fig.4.1 it can be seen that the position

of this reflectivity anomaly lies inside the third annulus (8-5=3rd annulus). As there is

no MFT employed in the simulator, bin 5 corresponds to the end of the leading edge,

which is also the first annulus.

30

Fig. 4.2 – Tracking Surface Reflectivity using Annuluses

4.2.2 Simulation Result for Crescents

Good part of crescents is that they only form in the direction of movement, which

indicates that the satellite is going right on to the target. Along track coherency can

be implemented in the same way, however; it is not possible to pin point the target,

as the footprint is symmetric in across range. Fig. 4.3 illustrates geometric

relationship of crescent analysis. In fig. 4.3, d is the displacement of satellite along

the ground track, elevation is target elevation, “D” is the distance from nadir to new

coming target, H is the altitude and r1, and r2 define different ranges.

Fig. 4.3 – Geometrical Analysis of Crescent Approach

31

Equations for r1 and r2 can be written as:

(4.1)

(4.2a)

(4.2b)

Using these equations it is possible to solve for D and E.

(4.3)

(4.4)

Using the equations above E can be retrieved. Figures 4.4 and 4.5 illustrate how to

implement these equations using the waveforms. Echo 0, represents the waveform of

a complete flat surface and Echo 1 denotes a waveform with a target at 9.1 km east

from the nadir location. Echo 2 is the next waveform of the same scenario, where the

satellite is moving towards east there fore the new location of target is at 8.7 km east

from the nadir point. Fig. 4.5 shows the difference of Echo 2 and Echo 1.

Fig. 4.4 – Difference of Echo 0 and Echo 1.

( ) 2221 DEHr +−=

( ) ( )2222 dDEHr −+−=

d

drrD

2

221

22

−−−

=

( )d

drrrEH

2

221

222

12

−−−

−=−

( ) 22222 2 ddDDEHr +−+−=

32

Fig. 4.5 – Difference of Echo 2 and Echo 1.

In theory, it is possible to use the echo waveform instead of taking difference of two

consequent waveforms. However, as the antenna gain decreases sharply near the

footprint edges, it is not possible to analyze power differences at such locations. The

starting point of the rising edge in fig. 4.4 is at 107 whereas; the same point is on 98

in fig. 4.5. Looking at table B.1, at row 98 and 107 gives us the annulus radius

values as 8.5733 km and 8.9584 km. Difference of these two radiuses, show that the

target appears almost 400 m west according to its previous location. Elevation of the

target can be calculated using the eqn 4.4. Values for r1 and r2 can be calculated

using the equation given below.

(4.5a)

As an example for the given situation in fig. 4.4 r1 is equal to this:

(4.5b)

4.2.3 RA-2 Example for Crescents

Using the Envisat sample data product crescents approach has been tested.

However, it was not possible to apply the method without any modifications. For

instance, the antenna gain is so low at the edge of the footprints that it is usually not

possible to differentiate up coming targets inside the outermost crescent. Fig. 4.5

shows three consequent Envisat RA-2 measurements obtained on 05 July, 2002 at -

68.89° latitude, 156.39° longitude, just before the start of Antarctic ice sheet.

( )Resolution RangePoint) Tracking-BinStart Edge Leading(

Point Trackingat Range

×

+=r

mkmr 46875.0)287(8001 ×−+=

33

As seen from fig. 4.5 tracking points are different for each waveform. The first

tracking point is almost 49, the other one is a little below 48 and the measurement at

the bottom has a tracking point of around 47.5. However, for simplicity, waveforms

are not shifted to match the tracking points. On the other hand, they are fed to

antenna gain compensation algorithm to decrease non-linear effects of it. It is clear

that the compensation algorithm can not work successfully on real Envisat data.

These particular measurements are chosen, because the nadir point is just off the

shore. Therefore, satellite is moving towards the shore line which is consistent with

crescents approach. It is not possible to pin out differences on the waveforms by just

looking at them. Fig. 4.6 shows the differences between consecutive waveforms.

Fig. 4.6 – Envisat RA-2 Measurements

34

Fig. 4.7 – Differences between Consecutive Measurements

As seen from the figure above, there is a difference of one bin between tracking

points and similar waveforms have a difference of 6 bins in between. For the upper

figure there are 43 bins difference between predefined points. For the lower figure

there are 38 bins. Looking up the surface distances for these points from table B.1 it

can be seen that these points have almost ~400 m in between which is equal to the

displacement of satellite on its ground path between two consecutive measurements.

35

REFERENCES

1. Sandwell, D., n.d., “Radar Altimetry”, Retrieved Apr. 14, 2005, from UCSD

Remote Sensing (SIO 236) Web site: http://topex.ucsd.edu/rs/altimetry.pdf.

2. ESA, 2002, “RA-2”, Retrieved Apr. 14, 2005, from Envisat Web site:

http://envisat.esa.int/instruments/ra2/.

3. ESA, 2002, “Concept”, Retrieved Apr. 14, 2005, from Envisat Web site:

http://envisat.esa.int/instruments/ra2/descr/concept.html.

4. Resti. A., Benveniste J., Roca M., Levrini G., and Johannessen J., 1999, The

Envisat Radar Altimeter System (RA-2), ESA Bulletin, (98).

5. ESA, 2002, “ENVISAT RA-2/MWR Handbook, Retrieved Apr. 14, 2005, from

Envisat Web site:

http://envisat.esa.int/pub/ESA_DOC/ENVISAT/RA2/ra2.ProductHandbook.1_2e.pdf.zi

p.

6. ESA, 2002, “Full Deramp”, Retrieved Apr. 14, 2005, from Envisat Web site:

http://envisat.esa.int/instruments/ra2/descr/full-deramp.html.

7. ESA, 2002, “Tracking”, Retrieved Apr. 14, 2005, from Envisat Web site:

http://envisat.esa.int/instruments/ra2/descr/tracking.html.

8. Mahafza, B., 2000. Radar Systems Analysis and Design using Matlab. 1st ed.

Boca Raton, FL: Chapman & Hall/CRC.

9. Garlick, D. James, 2004, Special Conversation.

10. Osmanoglu, B., Kartal, M., 2005, Analysis of Land Topography Using Radar

Altimeter 2, 2nd International Conference on Recent Advances in Space

Technologies, 9-11 June 2005,(not published yet).

36

APPENDIX A - DATA FORMATS

Range information is very important for crescent approach and unfortunately,

receive window does not show the pulse transmit time. Range and other related

information for several retrackers can be obtained from the data set described below.

Table A.1 RA - 2 MDS

RA-2 MDS (from the GDR product) # Description Units Count Type Size

Data Record

0 dsr_time [i] [q]

MDSR Time stamp. Time fields

based on UTC are computed for

each record and referred to the

center of the averaged waveform.

MJD 1 mjd 12 byte(s)

1 quality_flag [i] [q]

Quality Indicator (-1 for blank MDSR, 0 otherwise)

flag 1 BooleanFlag 1 byte(s)

2 spare_1 [i] [q]

Spare

- 1 SpareField 3 byte(s)

3 lat [i] [q]

Geodetic Latitude (positive N, negative S)

(1e-6)

degrees

1 GeoCoordinate 4 byte(s)

4 lon [i] [q]

Longitude (positive E, 0 at

Greenwich, negative W)

(1e-6)

degrees

1 GeoCoordinate 4 byte(s)

5 src_pack_cnt [i] [q]

Source Packet Counter

- 1 ul 4 byte(s)

6 instr_mode_id_flags [i] [q]

Instrument Mode ID

flags 1 ul 4 byte(s)

7 meas_conf_data_flags [i] [q]

Measurement Confidence Data


8 alt_cog_ellip [i] [q]

Altitude of CoG above reference

ellipsoid

mm 1 ul 4 byte(s)

9 hz18_diff_1hz_alt [i] [q]

18 Hz altitude differences from 1 Hz

altitude [20].

mm 20 ss 20*2

byte(s)

37

10 instant_alt_rate [i] [q]

Instantaneous altitude rate

mm/s 1 Ss 2

byte(s)

11 spare_2 [i] [q]

Spare

- 1 SpareField 50

byte(s)

12 hz18_ku_trk_cog [i] [q]

18 Hz Ku tracker range referenced to the

COG (no Doppler correction) [20]

mm 20 ul 20*4

byte(s)

13 hz18_s_trk_cog [i] [q]

18 Hz S tracker range referenced to the

COG (no Doppler correction) [20]

mm 20 ul 20*4

byte(s)

14 map_18hz_ku_trk_flags [i] [q]

Map of valid points for 18 Hz Ku-band

tracker range.

flags 1 ul 4

byte(s)

15 spare_3 [i] [q]

Spare

- 1 SpareField 4

byte(s)

16 ku_band_ocean_range [i] [q]

Ku-band ocean range

mm 1 ul 4

byte(s)

17 s_band_ocean_range [i] [q]

S-band ocean range

mm 1 ul 4

byte(s)

18 hz18_ku_band_ocean [i] [q] 18 Hz Ku-band ocean ranges [20]

mm 20 ul 20*4 byte(s)

19 hz18_s_band_ocean [i] [q] 18 Hz S-band ocean ranges [20]


20 sd_18hz_ku_ocean [i] [q]

Standard deviation of 18 Hz Ku-band ocean range

mm 1 us 2

byte(s)

21 sd_18hz_s_ocean [i] [q]

Standard deviation of 18 Hz S-band ocean

range

mm 1 us 2

byte(s)

22 num_18hz_ku_ocean [i] [q] Number of 18 Hz valid points for Ku-band

ocean range

- 1 us 2 byte(s)

23 num_18hz_s_ocean [i] [q] Number of 18 Hz valid points for S-band

ocean range

- 1 us 2 byte(s)

24 map_18hz_ku_ocean_flags [i] [q]

Map of 18 Hz valid points for Ku-band ocean

range. First 20 least significant bits (bits 0-19) correspond to the 20 values (one per

data bock) containing : 0= valid

measurement, 1= invalid. Unused bits set to

0. Bit 0 applies to the first data block.

flags 1 ul 4

byte(s)

25 map_18hz_s_ocean_flags [i] [q]

Map of 18 Hz valid points for S-band ocean range. First 20 least significant bits (bits 0-

19) correspond to the 20 values(one per

data bock) containing : 0= valid

measurement, 1= invalid. Unused bits set to

0. Bit 0 applies to the first data block.

flags 1 ul 4

byte(s)

26 hz18_ku_ice1 [i] [q] 18 Hz Ku-band ice1 ranges [20]


27 hz18_s_ice1 [i] [q] 18 Hz S-band ice1 ranges [20]


28 hz18_ku_ice2 [i] [q]

18 Hz Ku-band ice2 ranges [20]

mm 20 ul 20*4

byte(s)

38

29 hz18_s_ice2 [i] [q]

18 Hz S-band ice2 ranges [20]

mm 20 ul 20*4

byte(s)

30 hz18_ku_seaice [i] [q]

18 Hz Ku-band sea-ice ranges [20]

mm 20 ul 20*4

byte(s)

31 spare_4 [i] [q]

Spare

- 1 SpareField 80

byte(s)

32 hz18_ku_instr_corr [i] [q]

18 Hz Ku-band range instrumental

correction [20]

mm 20 ss 20*2

byte(s)

33 hz18_s_instr_corr [i] [q] 18 Hz S-band range instrumental correction

[20]

mm 20 ss 20*2 byte(s)

34 hz18_ku_dopp_corr [i] [q]

18 Hz Ku-band Doppler correction [20]

mm 20 ss 20*2

byte(s)

35 hz18_s_dopp_corr [i] [q] 18 Hz S-band Doppler correction [20]


36 hz18_ku_dopp_slp_corr [i] [q] 18 Hz Ku-band Delta Doppler Slope

correction [20]


37 hz18_s_dopp_slp_corr [i] [q] 18 Hz S-band Delta Doppler Slope

correction [20]


38 mod_dry_tropo_corr [i] [q]

Model dry tropospheric correction

mm 1 ss 2

byte(s)

39 inv_barom_corr [i] [q] Inverted barometer correction

mm 1 ss 2 byte(s)

40 mod_wet_tropo_corr [i] [q]

Model wet tropospheric correction

mm 1 ss 2

byte(s)

41 mwr_wet_tropo_corr [i] [q]

MWR derived wet tropospheric correction

mm 1 ss 2

byte(s)

42 ra2_ion_corr_ku [i] [q]

RA2 ionospheric correction on Ku-band

mm 1 ss 2

byte(s)

43 ra2_ion_corr_s [i] [q]

RA2 ionospheric correction on S-band

mm 1 ss 2

byte(s)

44 ion_corr_doris_ku [i] [q] Ionospheric correction from DORIS on Ku-

band

mm 1 ss 2 byte(s)

45 ion_corr_doris_s [i] [q]

Ionospheric correction from DORIS on S-

band

mm 1 ss 2

byte(s)

46 ion_corr_mod_ku [i] [q]

Ionospheric correction from model on Ku-

band

mm 1 ss 2

byte(s)

47 ion_corr_mod_s [i] [q]

Ionospheric correction from model on S-band

mm 1 ss 2

byte(s)

48 sea_bias_ku [i] [q]

Sea state bias on Ku-band

mm 1 ss 2

byte(s)

49 sea_bias_s [i] [q]

Sea state bias on S-band

mm 1 ss 2

byte(s)

50 spare_5 [i] [q]

Spare

- 1 SpareField 20

byte(s)

51 ku_sig_wv_ht [i] [q] Ku-band Significant wave height

mm 1 ss 2 byte(s)

39

52 s_sig_wv_ht [i] [q]

S-band Significant wave height

mm 1 ss 2

byte(s)

53 sd_18hz_ku_swh [i] [q]

Standard deviation of 18 Hz Ku-band SWH

mm 1 ss 2

byte(s)

54 sd_18hz_s_swh [i] [q]

Standard deviation of 18 Hz S-band SWH

mm 1 ss 2

byte(s)

55 num_18hz_ku_ocean_swh [i] [q]

Number of 18 Hz valid points for Ku-band

ocean SWH

- 1 us 2

byte(s)

56 num_18hz_s_ocean_swh [i] [q] Number of 18 Hz valid points for S-band

ocean SWH

- 1 us 2 byte(s)

57 slp_mod_flags [i] [q]

Slope model present flags [20 bits]: First 20

least significant bits (bits 0-19) correspond to the 20 values (one per data block)

containing: 0= valid measurement, 1=

invalid. Unused bits set to 0. Bit 0 applies to

the first data block

flags 1 ul 4

byte(s)

58 elev_echo_pt [i] [q]

1 Hz Elevation of echoing point

cm 1 sl 4

byte(s)

59 hz18_diff_mean_ech_pt [i] [q]

18 Hz Elevation differences of echoing point

from mean [20]

cm 20 ss 20*2

byte(s)

60 hz18_diff_1hz_lat [i] [q]

18 Hz slope-corrected latitude differences from 1 Hz latitude [20]

10 x m-

degree

20 ss 20*2

byte(s)

61 hz18_diff_1hz_long [i] [q]

18 Hz slope-corrected longitude differences from 1 Hz longitude [20]

10 x m-

degree

20 ss 20*2

byte(s)

62 hz18_ku_ice2_edge_width [i] [q]

18 Hz Ku-band Ice 2 leading edge width

[20]

mm 20 ss 20*2

byte(s)

63 hz18_s_ice2_edge_width [i] [q]

18 Hz S-band Ice 2 leading edge width [20]

mm 20 ss 20*2

byte(s)

64 spare_6 [i] [q] Spare


65 hz18_ku_k_cal_ku [i] [q]

18 Hz Ku-band K_cal_Ku [20]

dB/100 20 ss 20*2

byte(s)

66 hz18_s_k_cal_s [i] [q]

18 Hz S-band K_cal_S [20]

dB/100 20 ss 20*2

byte(s)

67 map_18hz_k_cal_ku_flags [i] [q]

Map of valid points for 18 Hz K-cal_Ku: First

20 least significant bits (bits 0-19) correspond to the 20 values (one per data

block) containing: 0= valid measurement,

1= invalid. Unused bits set to 0. Bit 0

applies to the first data block

flags 1 ul 4

byte(s)

68 spare_7 [i] [q]

Spare

- 1 SpareField 4

byte(s)

69 ku_ocean_bscat_coeff [i] [q]

Ku-band corrected Ocean backscatter coefficient

dB/100 1 ss 2

byte(s)

70 s_ocean_bscat_coeff [i] [q]

S-band corrected Ocean backscatter

dB/100 1 ss 2

byte(s)

40

coefficient

71 sd_18hrz_ku_ocean_bscat [i] [q] Standard deviation of 18 Hz Ku-band ocean

backscatter coefficient

dB/100 1 ss 2 byte(s)

72 sd_18hrz_s_ocean_bscat [i] [q]

Standard deviation of 18 Hz S-band ocean

backscatter coefficient

dB/100 1 ss 2

byte(s)

73 num_18hrz_ku_ocean_bscat [i] [q]

Number of 18 Hz valid points for Ku-band

ocean backscatter coefficient

- 1 us 2

byte(s)

74 num_18hrz_s_ocean_bscat [i] [q]

Number of 18 Hz valid points for S-band

ocean backscatter coefficient

- 1 us 2

byte(s)

75 hz18_ku_ice1_bscat [i] [q]

18 Hz Ku-band Ice1 backscatter coefficient [20]

dB/100 20 ss 20*2

byte(s)

76 hz18_s_ice1_bscat [i] [q]

18 Hz S-band Ice1 backscatter coefficient [20]

dB/100 20 ss 20*2

byte(s)

77 hz18_ku_ice2_edge_bscat [i] [q]

18 Hz Ku-band Ice2 leading edge

backscatter coefficient [20]

dB/100 20 ss 20*2

byte(s)

78 hz18_s_ice2_edge_bscat [i] [q] 18 Hz S-band Ice2 leading edge backscatter

coefficient [20]

dB/100 20 ss 20*2 byte(s)

79 hz18_ku_ice2_bscat [i] [q] 18 Hz Ku-band Ice2 backscatter coefficient

[20]

dB/100 20 ss 20*2 byte(s)

80 hz18_s_ice2_bscat [i] [q]

18 Hz S-band Ice2 backscatter coefficient

[20]

dB/100 20 ss 20*2

byte(s)

81 hz18_ku_seaice_bscat [i] [q]

18 Hz Ku-band sea-ice backscatter

coefficient [20]

dB/100 20 ss 20*2

byte(s)

82 spare_8 [i] [q]

Spare

- 1 SpareField 40

byte(s)

83 ku_net_instr_corr_agc [i] [q]

Ku-band net instrument correction for AGC

dB/100 1 ss 2

byte(s)

84 s_net_instr_corr_agc [i] [q]

S-band net instrument correction for AGC

dB/100 1 ss 2

byte(s)

85 ku_atm_atten_corr [i] [q]

Ku-band atmospheric attenuation

correction.

dB/100 1 ss 2

byte(s)

86 s_atm_atten_corr [i] [q]

S-band atmospheric attenuation correction.

dB/100 1 ss 2

byte(s)

87 k_rai_atten [i] [q] Ku-band rain attenuation

dB/100 1 sl 4 byte(s)

88 off_nad_ang_platf [i] [q]

Off nadir angle of the satellite from platform data

deg^2/10^4 1 ss 2

byte(s)

89 off_nad_ang_wvform [i] [q] Off nadir angle of the satellite from

waveform data

deg^2/10^4 1 ss 2 byte(s)

90 hz18_1st_edge_ice2_ku [i] [q] 18 Hz Ku-band slope of the first part of the

s-1 20 sl 20*4 byte(s)

41

trailing edge from ice-2 retracker [20]

91 hz18_1st_edge_ice2_s [i] [q] 18 Hz S-band slope of the first part of the

trailing edge from ice-2 retracker [20]

s-1 20 sl 20*4 byte(s)

92 hz18_2nd_edge_ice2_ku [i] [q]

18 Hz Ku-band slope of the second part of

the trailing edge from ice-2 retracker [20]

s-1 20 sl 20*4

byte(s)

93 hz18_2nd_edge_ice2_s [i] [q]

18 Hz S-band slope of the second part of

the trailing edge from ice-2 retracker [20]

s-1 20 sl 20*4

byte(s)

94 spare_9 [i] [q]

Spare

- 1 SpareField 40

byte(s)

95 m_sea_surf_ht [i] [q]

Mean sea-surface height

mm 1 sl 4

byte(s)

96 geoid_ht [i] [q] Geoid height

mm 1 sl 4 byte(s)

97 ocean_depland_elev [i] [q] Ocean depth/land elevation

mm 1 sl 4 byte(s)

98 tot_geocen_ocn_tide_ht_sol1 [i] [q]

Total geocentric ocean tide height (solution 1)

mm 1 ss 2

byte(s)

99 tot_geocen_ocn_tide_ht_sol2 [i] [q] Total geocentric ocean tide height(solution

2)

mm 1 ss 2 byte(s)

100 long_period_ocn_tide_ht [i] [q] Long period Tide height

mm 1 ss 2 byte(s)

101 tidal_load_ht [i] [q]

Tidal loading height

mm 1 ss 2

byte(s)

102 solid_earth_tide_ht [i] [q]

Solid earth tide height

mm 1 ss 2

byte(s)

103 geocen_pole_tide_ht [i] [q]

Geocentric pole tide height

mm 1 ss 2

byte(s)

104 mod_surf_atm_pres [i] [q]

Model surface atmospheric pressure

10 Pa 1 ss 2

byte(s)

105 mwr_wvapour_cont [i] [q] MWR water vapour content

10-2 g/cm2 1 ss 2 byte(s)

106 mwr_liq_vapour_cont [i] [q]

MWR liquid water content

10-2 kg/m2 1 ss 2

byte(s)

107 ra2_elec_cont [i] [q]

RA2 Total electron content.

10-1 TECU 1 ss 2

byte(s)

108 ra2_wind_sp [i] [q]

RA2 wind speed

mm/s 1 ss 2

byte(s)

109 mod_wind_sp_u [i] [q]

u component of the model wind vector

mm/s 1 ss 2

byte(s)

110 mod_wind_sp_v [i] [q]

v component of the model wind vector

mm/s 1 ss 2

byte(s)

111 spare_10 [i] [q]

Spare

- 1 SpareField 10

byte(s)

112 interpole_238_temp_mwr [i] [q] Interpolated 23.8 GHz brightness

temperature from MWR

K/100 1 ss 2 byte(s)

113 interpole_365_temp_mwr [i] [q] Interpolated 36.5 GHz brightness


42

temperature from MWR

114 interpole_sd_238_temp_mwr [i] [q] Interpolated standard deviation of MWR

23.8 GHz brightness temperature.


115 interpole_sd_365_temp_mwr [i] [q]

Interpolated standard deviation of MWR

36.5 GHz brightness temperature.

K/100 1 ss 2

byte(s)

116 spare_11 [i] [q]

Spare

- 1 SpareField 2

byte(s)

117 ave_ku_chirp [i] [q] Average Ku chirp band

- 1 us 2 byte(s)

118 ku_chirp_id_flags [i] [q] Ku chirp band id [40 bits] First 40 least

significant bits (bits 0-39) correspond to the

20 values (one per data block). Unused bits set to 0. Bits 0-1 apply to the first data

block.

flags 2 ul 2*4 byte(s)

119 error_flag_chirp_id_flags [i] [q] Error flag for chirp band id [20 bits]First 20

least significant bits (bits 0-19) correspond

to the 20 values (one per data block) containing: 0= valid measurement, 1=

invalid. Unused bits set to 1. Bit 0 applies to

the first data block.


120 instr_flags [i] [q]

Instrument flag

flags 1 ul 4

byte(s)

121 fault_id_flags [i] [q]

Fault identifier [20 bits] First 20 least

significant bits (bits 0-19) correspond to the 20 values (one per data block) containing:

0= valid measurement, 1= invalid. Unused

bits set to 1. Bit 0 applies to the first data block.

flags 2 ul 2*4

byte(s)

122 spare_12 [i] [q]

Spare

- 1 SpareField 8

byte(s)

123 wvform_fault_id_flags [i] [q]

Waveforms samples fault identifier [40

bits]First 40 least significant bits (bits 0-39) correspond to the 20 values (one per data

block). Unused bits set to 0. Bits 0-1 apply

to the first data block.

flags 2 ul 2*4

byte(s)

124 instr_id_data_level_flags [i] [q]

Instrument mode ID at data block level [80 bits]First 80 least significant bits (0-79)

correspond to the 20 values (one per data

block). Unused bits set to 0. Bits 0 to 3

apply to the first data block.

flags 3 ul 3*4

byte(s)

125 num_meas_ku_calibr [i] [q]

No. of measures for Ku flight calibration factor evaluation.

- 1 us 2

byte(s)

126 num_meas_s_calibr [i] [q]

No. of measures for Ku flight calibration factor evaluation.

- 1 us 2

byte(s)

127 mwr_instr_flags [i] [q] MWR instrument flag

flags 1 us 2 byte(s)

128 spare_13 [i] [q]

Spare

- 1 SpareField 6

byte(s)

43

129 spare_14 [i] [q]

Spare

- 1 SpareField 8

byte(s)

130 spare_15 [i] [q]

Spare

- 1 SpareField 8

byte(s)

131 ku_ocean_retrk_qua_flags [i] [q]

Ku-band ocean retracking quality [20 bits].

First 20 least significant bits (bits 0-19)

correspond to the 20 values (one per data block) containing: 0=valid, 1=invalid.

Unused bits set to 0. Bit 0 applies to the

first data block.

flags 1 ul 4

byte(s)

132 s_ocean_retrk_qua_flags [i] [q]

S-band ocean retracking quality [20 bits]. First 20 least significant bits (bits 0-19)


block) containing: 0=valid, 1=invalid. Unused bits set to 0. Bit 0 applies to the

first data block.

flags 1 ul 4

byte(s)

133 ku_ice1_retrk_qua_flags [i] [q] Ku-band ice1 retracking quality [20 bits].

First 20 least significant bits (bits 0-19)

correspond to the 20 values (one per data block) containing: 0=valid, 1=invalid.


first data block.


134 s_ice1_retrk_qua_flags [i] [q]

S-band ice1 retracking quality [20 bits].

First 20 least significant bits (bits 0-19) correspond to the 20 values (one per data

block) containing: 0=valid, 1=invalid.

Unused bits set to 0. Bit 0 applies to the first data block.

flags 1 ul 4

byte(s)

135 ku_ice2_retrk_qua_flags [i] [q]

Ku-band ice2 retracking quality [20 bits]. First 20 least significant bits (bits 0-19)




first data block.

flags 1 ul 4

byte(s)

136 s_ice2_retrk_qua_flags [i] [q]

S-band ice2 retracking quality [20 bits].

First 20 least significant bits (bits 0-19) correspond to the 20 values (one per data



first data block.

flags 1 ul 4

byte(s)

137 ku_seaice_retrk_qua_flags [i] [q]

Ku-band sea-ice retracking quality [20 bits]. First 20 least significant bits (bits 0-19)




first data block.

flags 1 ul 4

byte(s)

138 ku_peak [i] [q]

1 Hz Ku-band peakiness

0.001 1 us 2

byte(s)

139 s_peak [i] [q]

1 Hz S-band peakiness

0.001 1 us 2

byte(s)

140 altim_landocean_flag [i] [q] flag 1 us 2

44

Altimeter surface type flag byte(s)

141 radio_landocean_flag [i] [q] Radiometer land/ocean flag

flag 1 us 2 byte(s)

142 mwr_qua_interp_flag [i] [q]

MWR Quality interpolation flag

flag 1 us 2

byte(s)

143 rain_flag [i] [q]

Altimeter rain flag

flag 1 us 2

byte(s)

144 interpole_flag [i] [q]

Interpolation flag

flag 1 us 2

byte(s)

145 spare_16 [i] [q]

Spare

- 1 SpareField 6

byte(s)

Record Length : 2492

18 Hz averaged waveform data is used through out the studies and below is given the dataset for it.

Table A.2 18 Hz Waveforms

MDS

18 Hz Waveforms MDS

# Description Units Count Type Size

Data Record

0 dsr_time [i] [q]

Time stamp

MJD 1 mjd 12 byte(s)

1 quality_flag [i] [q]

Quality Indicator (-1 for blank

MDSR, 0 otherwise)

flag 1 BooleanFlag 1 byte(s)

2 spare_1 [i] [q]

Spare


3 src_pack_cnt [i] [q]

Source Packet Counter

- 1 ul 4 byte(s)

4 spare_2 [i] [q]

Spare


5 data_blk_info [i] [q]

Data Block information. The structure is repeated 20 times, once

for each data block.

- 20 data_blk_infoStruct 20*428.0

byte(s)

a ave_ku_wvforms_if [i] [q]

Average Ku band waveforms corrected

for IF transfer function (128 samples)

FFT

power

units

128 us 128*2

byte(s)

b cen_ku_dft_if [i] [q] Central Ku band filters from DFT

corrected for IF transfer function (2

samples)

FFT power

units

2 us 2*2 byte(s)

c ave_s_wvforms_if [i] [q]

Average S band waveforms corrected

for IF transfer function (64 samples)

FFT

power

units

64 us 64*2

byte(s)

d ind_2_dft_samp [i] [q] - 2 ss 2*2

45

# Description Units Count Type Size

Indexes of 2 DFT samples byte(s)

e offset_fft_filt [i] [q] Delta offset in FFT filters units

1/256 1 ss 2 byte(s)

f spare_1 [i] [q]

Spare

- 1 SpareField 18

byte(s)

g noise_pow_meas [i] [q]

Noise power measurement

dB/100 1 ss 2 byte(s)

h agc_noise_pow_meas [i] [q]

AGC of noise power measurement

dB/100 1 us 2 byte(s)

i ref_pow_val [i] [q]

reference power value

dB/100 1 us 2 byte(s)

j spare_2 [i] [q] Spare


Record Length : 8588

46

APPENDIX B – ANNULUS ANNALYSIS RESULTS

Table B.1 holds every important parameter in analysis of annuluses. “k” denotes the index of the annulus, where 0 indicates the most inner circle. “∆r” indicates the range difference between kth annuluses and 0th annulus. “Radius” is the radius of the kth annulus and “alfa” is the incident angle. Alfa is calculated by:

(B.1)

As described in part “1.2 General Measurement Principles” alfa is limited by half of the 3 dB beam width, which is 0.675 degrees. According to this, number of annuluses is 118 not 127. Additionally, as Envisat uses bin 46 as the tracking point the actual number of annuluses represented in a single waveform is even less than 118.

Another important information is given in last column, which holds the area for each annulus. It is clear that each annulus has almost the same area or same number of scatterers. Using this result and taking back the effects of antenna gain loss due to incident angle, it is possible to analyze differences in back scatter coefficients for each annulus.

Table B.1 Analysis results on annuluses

ANALYSIS RESULTS ON ANNULUSES K ∆r [m] Radius

[km] Alfa

[degree] Area [km2]

0 0 0 0 0 1 0.46875 0.866 0.062024486 2.356056 2 0.9375 1.2247 0.087715195 2.355987 3 1.40625 1.5 0.107432629 2.35654 4 1.875 1.7321 0.12405599 2.35673 5 2.34375 1.9365 0.138695416 2.35576 6 2.8125 2.1213 0.151931046 2.355822 7 3.28125 2.2913 0.164106666 2.356641 8 3.75 2.4495 0.175437141 2.356177 9 4.21875 2.5981 0.18608004 2.356425

10 4.6875 2.7386 0.196142796 2.355586 11 5.15625 2.8723 0.205718518 2.356752 12 5.625 3 0.214864503 2.355857 13 6.09375 3.1225 0.223638049 2.356214 14 6.5625 3.2404 0.23208213 2.356779 15 7.03125 3.3541 0.240225395 2.355549 16 7.5 3.4641 0.248103654 2.356201

.tan 1

= −Altitude

radiusalfa

47

17 7.96875 3.5707 0.255738394 2.355911 18 8.4375 3.6742 0.263151102 2.355714 19 8.90625 3.7749 0.270363265 2.356585 20 9.375 3.873 0.277389206 2.357008 21 9.84375 3.9686 0.28423609 2.355117 22 10.3125 4.062 0.290925401 2.356377 23 10.78125 4.1533 0.297464302 2.356373 24 11.25 4.2427 0.303867118 2.358087 25 11.71875 4.3301 0.310126687 2.353878 26 12.1875 4.4159 0.316271657 2.357472 27 12.65625 4.5 0.322294866 2.355652 28 13.125 4.5826 0.328210639 2.356894 29 13.59375 4.6637 0.334018976 2.355802 30 14.0625 4.7434 0.339727039 2.355396 31 14.53125 4.8218 0.34534199 2.355917 32 15 4.899 0.350870992 2.357595 33 15.46875 4.975 0.356314044 2.357527 34 15.9375 5.0498 0.361671147 2.355739 35 16.40625 5.1235 0.366949463 2.355479 36 16.875 5.1962 0.372156154 2.356955 37 17.34375 5.2679 0.37729122 2.357061 38 17.8125 5.3386 0.382354662 2.355816 39 18.28125 5.4084 0.38735364 2.356636 40 18.75 5.4773 0.392288157 2.356272 41 19.21875 5.5453 0.39715821 2.354739 42 19.6875 5.6125 0.401970964 2.355579 43 20.15625 5.6789 0.406726417 2.355406 44 20.625 5.7446 0.411431732 2.357841 45 21.09375 5.8095 0.416079746 2.355758 46 21.5625 5.8737 0.420677623 2.356388 47 22.03125 5.9372 0.425225362 2.35617 48 22.5 6 0.429722963 2.355114 49 22.96875 6.0622 0.434177588 2.357039 50 23.4375 6.1238 0.438589237 2.35826 51 23.90625 6.1847 0.442950749 2.354899 52 24.375 6.245 0.447269285 2.354658 53 24.84375 6.3048 0.451552008 2.357696 54 25.3125 6.364 0.455791754 2.356172 55 25.78125 6.4227 0.459995688 2.358014 56 26.25 6.4808 0.464156646 2.355231 57 26.71875 6.5384 0.468281791 2.355899 58 27.1875 6.5955 0.472371122 2.356024 59 27.65625 6.6521 0.47642464 2.355611 60 28.125 6.7083 0.480449507 2.358879 61 28.59375 6.7639 0.484431398 2.353224 62 29.0625 6.8192 0.4883918 2.359793 63 29.53125 6.8739 0.492309228 2.353092 64 30 6.9283 0.496205166 2.358832

48

65 30.46875 6.9822 0.500065291 2.355491 66 30.9375 7.0357 0.503896765 2.356061 67 31.40625 7.0888 0.507699589 2.356229 68 31.875 7.1415 0.511473761 2.355996 69 32.34375 7.1938 0.515219282 2.355366 70 32.8125 7.2458 0.518943314 2.358894 71 33.28125 7.2973 0.522631534 2.352958 72 33.75 7.3485 0.526298265 2.35577 73 34.21875 7.3994 0.529943507 2.358293 74 34.6875 7.4499 0.533560098 2.355848 75 35.15625 7.5001 0.5371552 2.357734 76 35.625 7.5499 0.540721652 2.354592 77 36.09375 7.5994 0.544266615 2.35585 78 36.5625 7.6486 0.54779009 2.356828 79 37.03125 7.6975 0.551292075 2.357527 80 37.5 7.7461 0.554772572 2.357951 81 37.96875 7.7943 0.558224419 2.353201 82 38.4375 7.8423 0.561661939 2.357944 83 38.90625 7.89 0.565077971 2.357548 84 39.375 7.9374 0.568472513 2.356882 85 39.84375 7.9845 0.571845568 2.355948 86 40.3125 8.0313 0.575197134 2.354748 87 40.78125 8.0779 0.578534373 2.358358 88 41.25 8.1241 0.581842963 2.351584 89 41.71875 8.1702 0.585144387 2.359861 90 42.1875 8.2159 0.588417162 2.352565 91 42.65625 8.2615 0.591682771 2.360497 92 43.125 8.3067 0.594919731 2.352684 93 43.59375 8.3518 0.598149526 2.360273 94 44.0625 8.3965 0.601350671 2.35195 95 44.53125 8.4411 0.604544651 2.359201 96 45 8.4854 0.607717144 2.355704 97 45.46875 8.5295 0.61087531 2.357316 98 45.9375 8.5733 0.614011988 2.353375 99 46.40625 8.617 0.617141501 2.360015

100 46.875 8.6604 0.620249526 2.355689 101 47.34375 8.7036 0.623343225 2.356587 102 47.8125 8.7466 0.626422598 2.357321 103 48.28125 8.7893 0.629480483 2.352371 104 48.75 8.8319 0.632531203 2.358278 105 49.21875 8.8743 0.635567597 2.358528 106 49.6875 8.9164 0.638582504 2.353017 107 50.15625 8.9584 0.641590245 2.358524 108 50.625 9.0001 0.6445765 2.352643 109 51.09375 9.0417 0.647555589 2.357887 110 51.5625 9.0831 0.650520353 2.357347 111 52.03125 9.1243 0.653470791 2.35665 112 52.5 9.1653 0.656406902 2.355797

49

113 52.96875 9.2061 0.659328688 2.354791 114 53.4375 9.2468 0.662243309 2.35944 115 53.90625 9.2872 0.665136443 2.352342 116 54.375 9.3275 0.668022412 2.356736 117 54.84375 9.3677 0.670901217 2.361055 118 55.3125 9.4076 0.673758535 2.353475 119 55.78125 9.4474 0.676608688 2.357542 120 56.25 9.487 0.679444516 2.355573 121 56.71875 9.5264 0.682266018 2.353455 122 57.1875 9.5657 0.685080355 2.357198 123 57.65625 9.6049 0.687887528 2.360868 124 58.125 9.6438 0.690673215 2.352344 125 58.59375 9.6826 0.693451736 2.355768 126 59.0625 9.7213 0.696223094 2.359119 127 59.53125 9.7598 0.698980126 2.356265

50

APPENDIX C – SIMULATOR CODES

MatLab codes of the simulator are given below. RunSimulator.m, is responsible for preparing the surface map and calling simstrecth.m processor function accordingly.

RunSimulator.m

function [out]=RunSimulator %Define Map Size(As each pixel is 100 m & footprint diameter is around 19 km) mapw=199; %Map Width; maph=mapw; %Map Height; %Nadir Point Coordinates mpw=(mapw+1)/2; %Mid Point of Width mph=mpw; %Mid Point of Height %Pixel Size: How many meters is a side of each pixel symbolize? pixelwidth=1e2; %[m] %Define Simulation Constants H=8e5; %Altitude [m] nscat=mapw*maph; %Number of Scatterers pulselen=20e-6; %Uncompressed Pulse Length [s] centerfreq=13575e6; %Carrier Frequency [Hz] BandWidth=320e6; %Chirp Bandwidth [Hz] windowsize=60; %Frequency Window Size winid=1; %Smoothing Window ID, [1=Hamming] w=1:1:mapw; %Horizontal Axis Vector h=1:1:maph; %Vertical Axis Vector nmaps=1; %number of maps mwh=0; %maximum wave height out=zeros(1,128); %Output Variable for n=1:nmaps %Cycle Through each map %Prepare Elevation Map %Map 1: Single Elevation, Smooth Surface elev=mwh.*ones(mapw,maph); %Map 2: Wavy Surface %fi=0.1*n; %Phase term, to get different maps.(if nmaps>1) %elev=5*(sin(2*pi*2/mapw.*w+fi)'*cos(2*pi*2/maph.*h+fi)); reflectivity=0.1*ones(mapw,maph); %Defines Reflectivity Map for each pixel mapdata=[mapw maph mpw mph pixelwidth]; %Put All Map Data in an Array... %Prepare Range Map for hh=1:1:maph for ww=1:1:mapw

51

%Calculate Range... range(ww, hh)=sqrt(((ww-mpw)^2+(hh-mph)^2)*pixelwidth^2+(H - elev(ww,hh))^2); %Calculate Look Angle teta(ww, hh)=atan(sqrt((ww-mpw)^2+(hh-mph)^2)*pixelwidth/(H - elev(ww,hh))); end end %Output the Map Number to show progress... display(['Range Map ',num2str(n),' of ',num2str(nmaps),' Complete. Starting Simulation']); %Run Simulator1(works with exp function) out_prime=simstretch(H, pulselen,centerfreq,BandWidth,windowsize,range,reflectivity,teta,winid,mapdata); %Run Simulator2(works with cos function) %out_prime=simstretchos(H, pulselen,centerfreq,BandWidth,windowsize,range,reflectivity,teta,winid,mapdata); out=out+abs(out_prime); %Sum Up all the outputs... save('backup.mat', 'out', 'n'); end figure(1);plot(out) %Plot Output... end

52

simstretch.m function [out] = simstretch(H,pulselen,centerfreq,BandWidth,windowsize,scat_range,reflectivity,teta,winid, mapdata) %pulselen: Uncompressed Pulse Length [s] %centerfreq: Carrier Frequency [Hz] %BandWidth: Chirp Bandwidth [Hz] %windowsize: Size of Frequency Window %scat_range: Array of Scatterer Ranges %Reflectivity: Array of Scatterer Reflectivities %teta: Array of Scatterer incident angles %winid: Smoothing window ID %mapdata: Consists of Map dimensions, nadir point location and pixelwidth c = 3.e8; %Define speed of Light [m/s] %Extract Map Dimensions mapw = mapdata(1); %map width maph = mapdata(2); %map height mpw = mapdata(3); %nadir point location/antenna boresight mph = mapdata(4); %nadir point location/antenna boresight pixelwidth=mapdata(5); %Pixel Width beamwidth=(1.35/180)*pi; %3 dB Beamwidth [radian] nscat=mapw*maph; %Number of Scatterers delta_t = 2. * windowsize / c; %Maximum two way time delay n = fix(delta_t * BandWidth); %number of samples, 128 m = power_integer_2(n); %m is a dummy variable, 7 nfft = 2.^m; %nfft, number of fft samples is 128, so m=7 xsingle(1:n) = 0.; %initialize reflected echo variable for single scatterer(Receiver Input) ysingle(1:n) = 0.; %initialize fft result variable for single scatterer(System Output) y(1:n) = 0.; %initialize fft result variable (System Output) %Set Smoothing Window if( winid == 0.) win(1:n) = 1.; win =win'; else if(winid == 1.) win = hamming(n); else if( winid == 2.) win = kaiser(n,pi); else if(winid == 3.) win = chebwin(n,60); end end

53

end end %end of set Smoothing Window... delta_r = c / (2.* BandWidth); %Range Resolution. max_ws = delta_r * nfft; %maximum window size minr= min(min(scat_range)); %minimum scatterer range trout=45*0.46875; %Tracker Output (Previous) fr=12352e6; %Reference Chirp Carrier Frequency. (13575-12352=1.223GHz, IF Freq=1.223GHz) frr=1223e6;%1223e6; %2nd Local Oscillator Freq. to produce base band signal... for w = 1:1:mapw for h=1:1:maph if teta(w,h)G(teta)=41.6-12(teta/beamwidth)^2 gain=33.02/2 - 12*(teta(w,h)/beamwidth)^2; %[dB] gain=10^(gain/10); xsingle(k) = reflectivity(w,h) * gain .* exp(i * phase1 + i * phase2); %calculate instantaneous output %Add Noise %snr=10; %Define Signal to No

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BSc Thesis-Spatial Resolution Enhancement Using RA-2...LPF: Low Pass Filter MFT: Model Free Tracker...

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