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Soil Moisture estimation using SAR polarimetry Sikdar, Millie 2005

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SOIL MOISTURE ESTIMATION USING SAR POLARIMETRY by MILLIE SIKDAR B.E., Govt. College of Engineering, Aurangabad, India, 2001  A THESIS SUBMITTED IN P A R T I A L F U L F I L L M E N T OF THE REQUIREMENTS FOR THE D E G R E E OF M A S T E R OF APPLIED SCIENCE in THE F A C U L T Y OF G R A D U A T E STUDIES (Electrical and Computer Engineering)  THE UNIVERSITY OF BRITISH C O L U M B I A October 2005  © Millie Sikdar, 2005  Abstract The sensitivity of microwave scattering to both dielectric and geometric characteristics of natural surfaces makes radar remote sensing one of most promising techniques for estimating soil moisture content. The potential of using polarimetric Synthetic Aperture Radar (SAR) for soil moisture estimation is investigated in this thesis. Soil moisture estimation has been an area of significant interest due to its widespread applications in the estimation and modelling of various large-scale ecological processes. Many approaches based on experimental observations or theoretical reasoning have been developed for soil moisture retrieval from SAR systems. Among the major models developed, the empirical model proposed by Dubois et al. in 1995 proves to be a good choice, because of its wide applicability and simplicity of implementation. However, one of the challenges presented by the Dubois Model as well as other originally developed models is their ineffectiveness in accurately estimating the soil moisture content in vegetated regions. In this thesis, this concern is addressed and a methodology for incorporating a suitable vegetation index into the existing Dubois Model is proposed. The Water Cloud Model is used to introduce the vegetation correction into the backscattering coefficients, which are then used in the inversion model to yield better estimation results. The vegetation index used requires the prior knowledge of several ground-measurable vegetation parameters. In order to sustain the true essence of "remote sensing", an approach for minimizing  ii  the need for ground measurements, by remotely estimating the vegetation parameters, is also suggested. The proposed algorithm applied to three different data sets - SIR-C, AIRSAR and CV-580, and its accuracy is evaluated based on the correlation and RMSE between the radar-based estimates and the published ground truth. The results show that soil moisture estimation accuracy can be improved by the addition of the vegetation correction into the model.  iii  Contents Abstract  ii  Contents  iv  List of Figures  viii  List of Tables  xi  List of Abbreviations  xii  Acknowledgements  xiv  1  2  Introduction  1  1.1  State-of-the-Art  3  1.2  Scope and Objectives of the Thesis  5  1.3  Organization of the Thesis  5  Soil Moisture  2.1  2.2  7  Soil moisture content  7  2.1.1  Properties of water  10  2.1.2  Complex dielectric constant  11  Soil Water Measurement  13  2.2.1  Measuring the soil moisture using classical methods . . .  14  2.2.2  Measuring soil moisture with imaging radar  17  iv  3  A Review: Soil M o i s t u r e Retrieval M o d e l s  3.1 Relationship between different parameters  3.2  3.3  19  3.1.1  Dielectric constant and moisture content  19  3.1.2  Dielectric constant and temperature  20  3.1.3  Penetration depth and soil moisture  21  3.1.4  Surface scattering characteristics  23  Models for soil moisture retrieval in bare areas  24  3.2.1  Theoretical surface scattering models  24  3.2.2  Empirical model by Oh et al. (1992)  28  3.2.3  Empirical model by Dubois et al. (1995)  29  3.2.4  Algorithm proposed by Shi et al. (1997)  31  3.2.5  Polarimetric semi empirical model  33  Models for soil moisture retrieval in vegetated areas  35  3.3.1  Estimation model by Jackson et al. (1991)  35  3.3.2  Models developed by regression  37  3.3.3  Models based on introduction of vegetation effects into existing models  4  19  40  D a t a Description  46  4.1 Little Washita Watershed  46  4.2 The Washita'92 Experiment  47  4.2.1  AIRSAR Data  48  4.2.2  Ground measurements during Washita'92  50  4.3 The Washita'94 Experiment  51  4.3.1  SIR-C data  52  4.3.2  Ground Measurements during Washita'94  54  4.4 The Ottawa Greenbelt  57  v  4.5  5  57  4.5.1  CV-580 C / X - S A R data  58  4.5.2  Ground Measurements  61  Proposed Methodology and Implementation  71  5.1  Choice of an existing model  71  5.2  Performance of the Dubois model  73  5.3  Proposed approach  79  5.3.1  Determining soil backscatter by regression  81  5.3.2  Determining soil backscatter using surface roughness  5.3.3  Determining the transmissivity, r  5.3.4  Determining the vegetation water content, W  84  5.3.5  Determining the fractional cover C  84  5.3.6  Determining vegetation sensitivity  85  5.4  6  The 2001 Field Campaign in Ottawa  82  2  c  v  Implementation  86  5.4.1  Modified Empirical Model I  89  5.4.2  Modified Empirical Model II  90  5.4.3  Applicability of the modified empirical models  92  Results and Discussion  6.1  . . 82  97  Illustration and explanation of results  97  6.1.1  Correlation coefficient and R M S error  98  6.1.2  Modified Empirical Model I  99  6.1.3  Modified Empirical Model II  104  6.2  Results from CV-580 data  107  6.3  Algorithm pros and cons  112  6.3.1  112  Pros  vi  6.3.2 7  Cons  113  Conclusions and Future W o r k  115  7.1  Conclusions  115  7.2  Research Contributions  118  7.3  Future work  119  Appendix A  S A R Polarimetry  121  A . l Synthetic aperture radar  121  A.2 Polarimetry in radar remote sensing  123  A.2.1 Polarimetry: basic concepts  123  A.2.2 The polarization state  124  A.2.3 Polarization in radars  126  A.2.4 Polarimetric scattering and target characteristics  . . . . 127  A.2.5 The scattering matrix  127  A.2.6 Polarization signature  130  Appendix B  Intermediate Models  Bibliography  132  137  vii  List of Figures 2.1  The moisture cycle  8  2.2  Schematic diagram of the three phases of soil  9  3.1  Measured dielectric constant for five soils at 1.4GHz  3.2  Measured dielectric constant for a loamy soil at 4 frequencies . . 21  3.3  Temperature dependence of soil dielectric constant for (a) e' (b) e" 22  3.4  Penetration depth as a function of moisture content  3.5  Angular responses for the HH,VV and HV backscatter for a  20  22  smooth surface  23  3.6  Fresnel reflectivity as a function of soil moisture content  ....  24  3.7  Validity regions of SPM, GO and PO models  27  4.1  Little Washita Watershed, OK (Washita'92)  48  4.2  Map of the Little Washita Watershed, OK (Washita 92)  ....  50  4.3  Map of the Little Washita Watershed, OK (Washita 94)  ....  53  4.4  SIR-C polarimetric composite image of region in Washita Watershed  54  4.5  Map of Ottawa Green Belt Farm  58  4.6  CV-580 polarimetric composite image of Ottawa GBF  60  4.7  Field locations for data collection in Ottawa GBF  61  4.8  Overview of corn crop in Field 23  65  4.9  Overview of wheat crop in Field 25  66  viii  4.10 Overview of soybean crop in Field 16  67  4.11 Overview of corn crop in Field ADRI  68  4.12 Site locations for GBF Field 23 (Corn)  69  4.13 Site locations for GBF Field 25 (Wheat)  69  4.14 Site locations for GBF Field 16 (Soybean)  70  4.15 Site locations for GBF Field ADRI (Corn)  70  5.1 Soil moisture maps for the Washita'92 experiment  75  5.2  Soil moisture maps for the Washita'94 experiment  76  5.3  Soil moisture maps for the Ottawa field campaign (2001) . . . . 77  5.4  Scatter plot of measured and estimated volumetric soil moisture for the bare soil sites using the Dubois model  5.5  78  Scatter plot of measured and estimated volumetric soil moisture for the vegetated soil sites using the Dubois model  78  5.6  Backscattering contributions of a canopy over a soil surface . . . 79  5.7  Regression curve describing the L-band  C T £  V  / < 7 °  V  ratio as a func-  tion of NDVI  85  5.8  Regression analysis between  and mf for AIRSAR data . . . 88  5.9  Regression analysis between  and rrif for SIR-C data  88  5.10 Regression analysis between cr^ and rrif for CV-580 data . . . . 89 5.11 Schematic flowchart of Modified Empirical Model I  95  5.12 Schematic flowchart of Modified Empirical Model I  96  6.1 Scatter plots of measured and estimated volumetric soil moisture for the sites in C-band, SIR-C data using Model I 6.2  102  Scatter plots of measured and estimated volumetric soil moisture for the sites in L-band, AIRSAR data using Model I . . . . 103  6.3  Scatter plots of measured and estimated volumetric soil moisture for the sites in L-band, AIRSAR data using Model II . . . 106  ix  6.4  Scatter plots of measured and estimated volumetric soil moisture for the fields in C-band, CV-580 data after vegetation correction  110  6.5 Scatter plots of measured and estimated volumetric soil moisture for the sites in C-band, CV-580 data after vegetation correction  Ill  A . l Flight Geometry for a Synthetic Aperture Radar  122  A.2 Polarization ellipse  124  A.3 Circular and linear polarizations  125  A.4 Scattering Mechanisms  128  A. 5 Co-polarization signatures for ocean surface, urban areas and vegetated region  131  B. l Schematicflowchartof Intermediate Model I  133  B.2 Schematic flowchart of Intermediate Model II  134  B.3 Scatter plot of measured and estimated volumetric soil moisture for AIRSAR data using Intermediate Model I  135  B.4 Scatter plot of measured and estimated volumetric soil moisture for AIRSAR data using Intermediate Model II  x  136  List of Tables 2.1  Coefficients of the polynomial expression used in the Hallikainen Model  16  4.1  N AS A / JPL AIRSAR Parameters  49  4.2  Incidence Angles for AIRSAR during Washita'92  50  4.3  Site Characteristics for the Washita'92 experiment  51  4.4  Average volumetric soil moisture measured at sites during the Washita'92 experiment  51  4.5  SIR-C System Characteristics  55  4.6  Incidence Angles for SIR-C during Washita'94  55  4.7  Site Characteristics for the Washita'94 experiment  56  4.8  Average volumetric soil moisture measured at sites during the  4.9  Washita'94 experiment  56  C/X-SAR System Technical Specifications  59  4.10 Ground measurements for the sites during Ottawa Field Campaign, June 2001  63  4.11 Ground measurements for the sites during Ottawa Field Campaign, July 2001  64  5.1  Vegetation parameters used in the empirical model  92  5.2  Vegetation parameters used in the vegetation corrected model . 93  xi  List of Abbreviations  AAFC  Agriculture and Agri-Food Canada  ADRI  Animal Diseases Research Institute (now CFIA)  AIRSAR  Airborne Synthetic Aperture Radar  ARS  Agricultural Research Service  ASI  Italian Space Agency  CASI  Compact Airborne Spectrographic Imager  CCRS  Canada Centre of Remote Sensing  CFIA  Canadian Food Inspection Agency  dB  Decibel  DLR  German Aerospace Agency  DN  Digital number  GBF  Green Belt Farm  GO  Geometric Optics  GSFC  Goddard Space Flight Center  HH  Horizontal Transmit and Horizontal Receive  HYDROS  Hydrosphere State  IEM  Integral Equation Model  INVIEM  Inverse Integral Equation Model  JPL  Jet Propulsion Laboratory  KA  Kirchhoff Approximation xii  NAD  North American Datum  NASA  National Aeronautics and Space Administration  NDVI  Normalized Difference Vegetation Index  PO  Physical Optics  PolGASP  Polarimetric Generalized Airborne SAR Processor  RASAM  Radiometer Scatterometer  RMSE  Root Mean Square Error  RVI  Radar Vegetation Index  SAR  Synthetic Aperture Radar  SIR-C  Shuttle Imaging Radar-C  SLC  Single Look Complex  SPM  Small Perturbation Model  TDR  Time Domain Reflectometry  TIFF  Tag(ged) Image File Format  USDA  United States Department of Agriculture  UTM  Universal Transverse Mercator  UWSP  University of Wisconsin-Stevens Point  VV  Vertical Transmit and Vertical Receive  xiii  Acknowledgements It is a pleasure to thank the many people who have made this thesis possible. I would like to express my deepest gratitude to my supervisor, Dr. Ian Cumming for his constant support and guidance. He has always provided me with encouragement, sound advice and good ideas during my research at UBC. I am indebted to Dr. Brian Brisco of Noetix Research and Dr. Elizabeth Pattey of Agriculture and Agri-Food, Canada (AAFC), for providing me with CV-580 data as well as technical help during the project. I also acknowledge NSERC for funding this research. I would like to thank Dr. Ron Caves and Bernd Scheuchl of MacDonald Dettwiler &: Assoc. (MDA) for sharing their in-depth knowledge of SAR polarimetry with me. I am also grateful to all my friends and colleagues at UBC, Kaan, Flavio, Yewlam and Shu Li for all their help and advice. All these people at both UBC and MDA have contributed extensively to my learning process. Lastly, and most importantly I would like to thank my parents, my brother and my fiance who have always been there to support and encourage me. I dedicate this thesis to them.  MILLIE SIKDAR  The University of British Columbia OCTOBER 2005  xiv  Chapter 1 Introduction The Earth's surface forms an essential part of the eight different ecosystems which govern life on this planet. From its existence beneath the serene waters of the oceans to the thriving tropical forests, the Earth's surface presents a picture of huge diversity. Thus, a large number of bio & geophysical parameters are required for its detailed description and/or monitoring. The soil beneath our feet is the basic substrate of all terrestrial life and is thus one of the most important elements of the Earth's surface. The intricate and fertile mix composing the soil with its life giving attributes is a most intriguing field of study. Soil, along with water, is one of the fundamental resources of our natural environment. As result, an attempt to understand what constitutes the soil and how it operates is not only a subject of curiosity but also an essential task. Soils are generally parameterized in terms of their dielectric and geometric properties. The dielectric properties of the soil are expressed primarily by the soil moisture content, while the geometric properties are described by the surface roughness. The soil moisture content plays an important role in understanding different ecological processes as well the nature of global change. Recent modelling studies reveal that soil moisture forms a key factor in predicting, estimating and modelling large-scale processes such as evaporation, transpiration, surface run-off and ground water replenishment. Also, the surplus or deficit of soil moisture affects the temporal and spatial dynamics of vegetation systems. 1  Thus, a knowledge of temporal and spatial fluctuations of soil moisture content is relevant to a wide spectrum of applications, such as the prediction of plant growth, determination of the proper time for sowing, the identification of agricultural areas with accelerated soil erosion or water logging and the monitoring of dynamic soil processes acting on the surface (physical, chemical and biological). Furthermore, soil moisture proves to be a key factor in meteorological modelling, weather predictions and flood forecasting. Surface roughness affects the erosion of soil by wind and hence is an important factor in soil erosion monitoring. The rate of erosion decreases with increasing surface roughness because of the diminishing wind velocity that hits the ground. Surface roughness can be produced through tillage operations that form ridges and furrows or that bring clods to the surface. However, over time ridges are filled in and the roughness broken down by abrasion to produce a smoother surface susceptible to the wind, leading to erosion. Even excess tillage can contribute to soil structure breakdown and increased erosion. The classical methods in soil physics were among the earliest techniques used to measure the two surface parameters mentioned above. Methods, such as the gravimetric method, the neutron moisture meter, the gamma ray method and time domain reflectometry, used for measuring the water content in the soil, are based on point measurements. However, the classical methods are time consuming and laborious. Also, they can not provide a reliable estimate of soil moisture over a large area. Through the recent years, the aforementioned drawbacks were overcome to a large extent by the use of remotely sensed information from both airborne and spaceborne sensors. Several remote sensing techniques such as the airborne or spaceborne gamma ray, near to far infrared, thermal infrared spectrometers, passive radiometers and active radar systems, are capable of estimating the soil moisture content as well as the surface roughness with a sufficient degree of accuracy for large areas [2]. Radar remote sensing, with its capability to obtain information independent of weather conditions and an external illumination source as well as its sensitivity to both dielectric and geometric characteristics of the targets, proves to be one of most promising techniques for estimating the soil moisture con-  2  tent. Furthermore, frequent observations of soil moisture, required in certain applications such as weather forecasting, agriculture and water management, can also be made using radar systems. Among the different active radar systems, the synthetic aperture radar (SAR) has attracted significant interest due to the high resolution imagery generated by its unique signal processing techniques. Further, recent advances have enabled SARs to possess the ability to transmit and receive microwave signals in different polarizations. The polarization of a SAR signal essentially refers to the alignment and regularity of the electric field vector in the plane perpendicular to the direction of propagation. This type of SAR data, known as polarimetric SAR imagery, proves to be a richer source of information since the different polarizations tend to react differently to the scatterers on the ground. Consequently, polarimetric SAR data provides useful information regarding the surface roughness, vegetation cover and the soil moisture content at the ground. Since the last decade, research studies have been pursued in order to investigate the potential of polarimetric SAR imagery for soil moisture estimation. Though, there has been substantial progress, further insight is necessary to effectively exploit the vast reserves of information for effective measurement of soil moisture. The work presented in this thesis also derives its motivation from this aspect.  1.1  State-of-the-Art  Remote sensing of soil moisture can be accomplished to some degree by all regions of the electromagnetic spectrum. However, only the microwave region offers the potential for truly quantitative measurement of soil moisture. Over time, many experimental data sets have been accumulated using radars and many approaches have been developed to interpret and predict the scattering behavior which subsequently led to development of algorithms for measuring the soil moisture and surface roughness. In modelling terms, the measurement of soil moisture based on radar observations, is termed as soil moisture retrieval / estimation. The existing retrieval algorithms can be divided into two broad categories.  3  While, one category concentrated on establishing the relationship between the backscattering behavior of the rough surfaces and the surface parameters theoretically, the other direction of research dealt with the development of retrieval algorithms based on simulated and experimental data. The theoretical models included the well known Small Perturbation Model (SPM), the Kirchhoff Approximation (KA) and the more recent model, the Integral Equation Model (IEM), while the algorithms developed from experimental observations were referred to as the regression models, empirical models and semi-empirical models. Empirical or regression models are generally based on the fitting of experimental readings in order to derive the relation between different parameters, rather than on physical theory. All the existing models, however, presented a variety of limitations. For the SPM and KA, the region of validity of the model, defined by the surface roughness and surface correlation length, encloses smooth surfaces only. However, many natural surface conditions fall outside this region [3], thus rendering the SPM and K A ineffective for such surfaces. On the other hand, the IEM lacks theoretical consistency and proves to be confusing due to three different approaches used in its formulation [4]. Though, the empirical and semi-empirical models were much more simplistic in their formulation as compared to the theoretical models and were applicable to a variety of different sites, they also had limited validity in regions with high roughness and with soil moisture content beyond a certain range. This led to an over/under estimation of the soil moisture. In addition, these models were developed based on the data acquired from bare soils and thus did not include the effects due to the backscatter from vegetation. Vegetation forms an integral part of land cover and almost all applications utilizing the soil moisture content require moisture estimation over diverse forms of vegetation such as agricultural crops, pastures and rangelands. Hence, it is essential to take into account the vegetation effects in any retrieval model.  4  1.2  Scope and Objectives of the Thesis  The objective of this thesis is to develop a simple yet effective and accurate model, that incorporates the vegetation effects. Furthermore, the model is to be used for soil moisture retrieval in polarimetric SAR data. Broadly, this work involves two major steps, the first step is to identify the model which proves to be the best choice for soil moisture estimation in terms of simplicity, accuracy and applicability to data from a variety of sensors as well as polarimetric data when compared to all other existing models; and the second step involves the addition of the vegetation correction into the model. This research proves to be another step towards exploring the potential of polarimetric SAR data for effective soil moisture retrieval. Based on this line of thought, the different types of existing models were assessed, and the Dubois model was considered to be the best choice for soil moisture retrieval. However, erroneous results are obtained when the model is applied to vegetated areas. The Water-Cloud model [5] is used in conjunction with the approach in [6] to introduce vegetation effects into the V V backscatter coefficient of the polarimetric data, which is further used in the inversion model. Since the Water-Cloud Model requires a large number of vegetation parameters, two different cases to determine these parameters are considered one in which these parameters are measured directly at the sites and the other where several methods based on [7,8] are used to calculate these parameters. The detailed discussions of the subtasks of this thesis are given in the following chapters which have been summarized in the following section.  1.3  Organization of the Thesis  In Chapter 2, the soil moisture content is introduced along with the different classical methods used to measure the soil moisture. The chapter further delves into the discussion of active and passive radar remote sensing for soil moisture estimation. Chapter 3 presents a critical review of the existing estimation algorithms and the recent advances in developing models for soil moisture retrieval in vegetated regions. These models are chosen in order to provide an  5  overview of the evolution of techniques in soil moisture estimation by radar remote sensing; and to determine which model can prove to be the best choice. As mentioned earlier, the objective of this thesis is to develop a soil moisture estimation algorithm which is applicable to polarimetric SAR data. The model will be tested for its validity on existing airborne and spaceborne polarimetric data from radar sensors such as AIRSAR, SIR-C and CV-580 data. The AIRSAR and SIR-C data were obtained from the Washita experiments conducted in 1992 and 1994, while the CV-580 data is obtained from the Ottawa GBF field campaign in 2001. The geography of the region, details of the sensor used, dates of acquisition, precipitation during the experiment, in-situ ground measurements, and the type of vegetation as well as vegetation parameters at each site are described in further detail in Chapter 4. In Chapter 5, the conception and development of the proposed model to include vegetation effects is presented. The water cloud model, which is used to introduce vegetation correction, is discussed along with the methods for computing the vegetation backscatter; the normalized difference vegetation index (NDVI), sensitivity and fractional cover of the vegetation; and the soil backscatter. Based on a variety of methods used to determine the soil backscatter and vegetation parameters, two different approaches to retrieve the soil moisture are proposed. Chapter 6, discusses the results obtained by implementing the proposed models and applying them to radar measurements. The soil moisture estimates are compared with the ground measurements, and a comparative analysis of the performance of the existing empirical model (Dubois Model) and the proposed algorithms is presented. Furthermore, comparisons between the results obtained from the two suggested approaches are also discussed, followed by a discussion of their pros and cons. In Chapter 7, conclusions are drawn from the results and the comparative analyzes done in the previous chapter. Based on this work, perspectives for further future investigations are also put forth.  6  Chapter 2 Soil Moisture T h e soil is a three phase system where the solid phase comprises of solid particles, the liquid phase of soil water and the gaseous phase is made up of the air w i t h i n the soil. A variety of parameters ranging over a l l three phases such as soil texture, soil organic matter, surface roughness, soil moisture content and soil aeration are generally measured i n order to gain a better understanding of the soil dynamics. T h i s chapter as well as the following chapters i n this thesis w i l l focus only on one of these parameters, i.e., the soil moisture content.  2.1  Soil moisture content  T h e moisture i n soils has b o t h atmospheric and subsurface origins. Its principal source is precipitation i n the form of rain and snow. A significant proportion is also supplied by the lateral movement of water above the ground surface and w i t h i n the soil body, to which the ground water storage makes a substantial contribution particularly i n the area of rising groundwater springs. T h e moisture cycle is illustrated i n Fig.2.1. Soil moisture itself influences rainwater infiltration and thus overland flow generation and erosion. T h e rate of drainage of water through the soil is also p a r t l y dependent u p o n its moisture content.  Soil moisture governs natural processes such as plant growth,  transport of nutrients and other materials w i t h i n the soil, survival of the m i croscopic organisms i n the decomposing food chain a n d continued weathering of the parent material from which the soil is derived, thus c o n t r i b u t i n g to the soil structure development. 7  F i g u r e 2.1: T h e moisture cycle Source: R . M i t t e r , U W S P The soil water i n the soil m a t r i x represents the porosity part of the soil. 1  T y p i c a l l y a soil may consist of about 45 to 55 % solid m a t e r i a l a n d 55 to 45% pore space. Usually, the quantity of water i n a soil is less t h a n the total pore volume a n d the soil is said to be unsaturated.  However, i n conditions  of prolonged precipitation the soil may become saturated when a l l pores are water filled [9]. T h e amount of water i n the soil is expressed i n terms of the mass,u;; volume fraction, 9; and the degree of saturation, S, as given below [10]: w  = M IM w  (2.1)  t  9 = V / V w  (2.2)  t  S = V I (V  w  w  where, M  w  lr  + V)  (2.3)  a  is the mass of soil water i n a certain quantity of soil, M  t  is the  The soil matrix constitutes the mineral and organic matter of the soil, and the pore  space.  8  Volume Relations  Figure 2.2: Schematic diagram of the three phases of soil total mass of the quantity of soil including the water content, V is the volume w  of water in the soil, V is the total volume of the quantity of soil (inclusive t  of the soil water) and V is the volume of air in the soil, as illustrated in a  Fig. 2.2. Another useful representation of the soil water content, generally used in most field studies, is obtained by converting from the mass to the volume fraction [11]: 9  = wp j p b  w  (2.4)  In obtaining (2.4), it is assumed that the density of water is unaffected by being adsorbed in the soil so that M / V is equal to the density of pure w  w  free water, p . Here, pb is dry bulk density of the soil. The water content, w  when expressed in terms of the volume fraction, 9, ranges from zero at oven dryness to a value at pore space saturation. The wetter of these is the "field capacity", which is the water content found when a thoroughly wetted soil has drained for about two days. It is determined in the field under conditions that prevent evaporation and allow good drainage. The drier stage is the "permanent wilting point", which is the water content found when the test plants growing on the soil wilt. Field capacity and permanent wilting point are used for marking the upper and lower levels of the water content of a soil at which water is generally available for plants.  9  2.1.1  P r o p e r t i e s of water  Soil water is held within the soil matrix by absorption at surfaces of particles and in capillaries in the the pores. It is not easy to clearly separate the two mechanisms and determine which is responsible for water retention in the soil. However, despite this fact, the nature of each of these mechanisms influence the way soil behaves. For example, water attracted by reactive clay materials will cause swelling of the soil but on the other hand when water is attracted by capillaries into the pores of a sandy soil no swelling occurs. Therefore, in order to understand soil behavior it is necessary to consider the interaction between water and soil, and also the properties of water itself that affects this interaction. Water has unusual properties due to its strongly polarized molecular structure. The single electron of each hydrogen atom is involved in bounding it to the oxygen atom, thus leaving a positive charge on both the hydrogen atoms. Since the two hydrogen atoms are arranged towards one side of the oxygen atom, the water acts as an electric dipole with the positive pole towards the hydrogen atoms and the negative pole towards the oxygen atom.  Further-  more, one molecule of water can further link up with another through hydrogen bonding, thus allowing some degree of association between molecules in liquid water. Since the centers of positive and negative charges are separated, water molecules can be attracted and oriented by the electrostatic field of a charged ion and this results in the hydration of solute ions. In soil, hydration of ions 2  occurs when the polar water molecules interact with the exchangeable cations in the soil particles. This is the principal mechanism in water absorption at the first stage of soil wetting. The other possible mechanisms for absorption are intermolecular attraction between the soil surface and water over a short range due to van der Waals forces, and due to the hydrogen bonding of the water molecules to oxygen atoms on the solid surface [11]. A form of chemical weathering that involves the rigid attachment of H+ and OH- ions to the atoms and molecules of another substance. 2  10  2.1.2  Complex dielectric constant  The phenomenon by which non-conducting materials can also be influenced from an electrical field was first observed by M. Faraday, who named these materials as dielectrica. The key parameter that describes the behavior of a non-conductor in an electrical field is the dielectric constant, which, in simple terms, is a measure of the ability of a material to resist the formation of an electric field within it. Unlike a conductor, when an electrical field is applied to a dielectrica, free charges move till the back force in the solid body equalizes the force affected by the external electrical field. In electromagnetic theory, the complex dielectric constant is considered as a measure of the response of the medium to an electromagnetic (EM) wave; and which is dependent on parameters such as frequency, temperature, salinity and ferromagnetic substances [12]. This response is composed of two parts, the real and imaginary as given below: 6  = e ' - je"  (2.5)  where e' is referred to the permittivity of the medium, and e" is referred to the dielectric loss factor of the material and describes the feasibility of a medium to absorb a wave. Also, the attenuation length of an electrical field in a given medium can be characterized by e". The propagating wave is assumed to have an exponential attenuation with depth and the penetration depth is given 3  as [14]:  = S «"» X  Thus, at longer wavelengths, the penetration depth increases, while at the same time for a fixed wavelength the penetration depth increases with decreasing dielectric constant. At this stage, it is important to note the difference between the and the  penetration  absorption  of a wave. When a wave is absorbed, it is converted into  another form of energy, e.g. heat. However, as discussed above, penetration 3  The depth at which the E M field strength decreases to 1/e of its incident value.  11  of a wave is only indicative of the depth and attenuation of the wave as it travels through the medium. In this case, though the signal is attenuated, it is eventually reflected back. Generally, for most natural surfaces, e"  e'. This implies that for an  incident E M wave, particularly a radar signal in this context, only a small part of wave is absorbed , while a significant portion of the wave is reflected back. Also, the depth to which a radar signal penetrates within the soil surface, before it is scattered back, will depend on its wavelength as given by (2.6). Soil is an insulator . As a result, in case of dry soil, the real part of the 4  dielectric constant varies over a range of two and four; while the imaginary part lies below 0.05 [14]. On the other hand, water possesses a large e' of around 81 towards low frequencies. This can be attributed to the fact that the hydrogen bonding between the molecules causes water to resist any random thermal motions. When water is added to the dry soil for the first time, the water molecules are tightly bounded to the soil particles due to the binding forces in the soil. This causes only a slight increase in the dielectric constant of the soil. As more water is added above the transition value of moisture, the soil's e' rapidly increases. Consequently, for an incident radar signal, the received backscatter from a surface with high moisture content, and hence a large dielectric constant, will be quite large. Many empirical and theoretical models have been developed to relate the dielectric constant of the soil mixture to its constituents. Among the earliest models was the one proposed by Topp et al. in 1980, where the dielectric constant was considered to be dependent only on the volumetric fraction of dry matter and free water in the frequency range of 1 to 10 GHz. Further extensive investigations on the behavior of the dielectric constant in the frequency range of 1.4 to 18 GHz were done by Hallikainen et al. in 1985. They concluded that the dielectric constant is a function of its volumetric soil moisture content and of the soil's textural composition in the mentioned frequency range, and can be expressed in terms of polynomial expressions dependent on the volumetric soil moisture and the percentage of sand and clay contained in the soil. This semiempirical model suggested by Hallikainen et al. produced favorable results with Dry air is an ideal insulator with e' = 1 and e" = 0  4  12  the experimental data used by other investigators, thus proving the accuracy of the model. In order to eliminate the dependence on adjustable parameters required to fit the experimental data and subsequently obtain the polynomial expression, Dobson et al. (1985) proposed an empirical model to relate the dielectric constant to measurable soil characteristics such as the bound water  5  fraction and the free water fraction, according to the pore-size distribution 6  calculated from the particle size distribution [15]. The computation of the parameters used in Dobson's empirical model involves extensive field work and it is difficult to calculate these parameters from the data used for this work. Consequently, the models proposed by Hallikainen et al. and Topp et al. were used in this study, for the conversion from the real part of the dielectric constant to the volumetric soil moisture and vice versa. It is also important to note that these models were implemented interchangeably based on the availability of the soil's textural composition. Also, measurements and evaluation of the imaginary part e" of the complex dielectric constant are not considered because it has a negligible influence on the total amount of e.  2.2  Soil Water Measurement  The need to measure the moisture content in the soil arises frequently in many agronomic, ecological and hydrological investigations. Methods for measuring the mass of soil water have been applied as early as the 15th century. Today the most common method for measuring soil moisture is by taking into account the mass, volume or saturation of the soil. As mentioned in Chapter 1, the classical methods developed in soil physics and the soil moisture retrieval algorithms developed for radar remote sensing, form the two fields encompassing all the existing methods for soil moisture measurement / estimation. 5  Water molecules at the soil surface held by binding forces.  Water molecules present farther from the surface where the binding forces of the soil are low and the molecules move freely. 6  13  2.2.1  Measuring the soil moisture using classical methods  A large number of classical methods are available to measure the soil water content directly or indirectly [11]. A majority of these methods are based on point measurements, which are subsequently extrapolated to a catchment scale (100 m — 10 km). It is claimed in [16] that the full body of hydrology spans over 15 orders of magnitude from the scale of a cluster of water molecules (10 m) to the planetary scale (10 m), and it is the catchment scale -8  7  (10 — 10 m) which is generally preferred in hydrological studies. 4  2  The direct methods include all processes in which the soil water is removed with evaporation, extraction, or chemical reactions, while the indirect methods involve the measurement of parameters such as the soil capacitance and eventually use mathematical models to compute the soil moisture content. In this study, we have used in-situ measurements which were obtained using two methods, the gravimetric method which is a direct method, and time domain reflectometry which is an indirect method. Gravimetric method  The traditional gravimetric method had been introduced by Gradner in 1986 [17] The process involves measuring the soil water content by finding the mass of the water lost upon drying a sample in an oven at 105°C until it reaches a constant mass. The mass difference corresponds to the water loss of the sample during the drying process. The unit of gravimetric soil moisture, M is [g/g] and expresses the weight 9  in percent after multiplying with 100: M (%) = 9  weight of wet soil — weight of dry soil x 100 weight of dry soil  (2.7)  The gravimetric soil moisture can also be expressed as a volumetric percent, m [vol. %], where the bulk density of the soil, pb has to be taken into v  "account: m  v  (%) = M (%) x s  14  P b  (2.8)  This technique of measuring the soil moisture content proves to be sufficiently accurate and reliable. However, the procedure is time consuming and can only cover a small number of discrete samples. Additionally, frequent measurements are difficult, thus making the method unattractive for applications which require the measurement of the variation in the moisture content. Time domain refiectometry The technique of time domain refiectometry (TDR) is based on measuring the electrical capacitance of the soil. The capacitance will depend only on the water content of the soil since the dielectric constant of water (e' « 80) is much higher than that of the dry soil (e' « 5) or dry air (e' w 1) that replaces the water as the soil dries. The procedure involves inserting a parallel, twoelectrode configuration into the soil with a spacing of 50 mm between the two electrodes. The length of the electrodes determines the depth at which the soil moisture is to be measured. Using the expression for the time taken by an electromagnetic pulse to propagate along a transmission line and get reflected back to the origin (electromagnetic transmission theory), the dielectric constant, d can be computed. The detailed mathematical equations are not dealt with in this thesis and can be referred to in [2]. The dielectric constant is then subsequently used in one of the models relating e' to the volumetric soil moisture, as discussed in Section 2.1.2, to compute the soil moisture content. According to the semi-empirical model suggested by Hallikainen et al., the dielectric constant and soil moisture content are related by the following polynomial expression: e' = (ao + aiS + a C) + (b + b S + b C) m + (c + aS + c C) m  2  2  0  2  x  0  v  2  v  (2.9)  where, the constants ao, a\, a , b b\, b , c , C i and c are dependent on the fre2  0l  2  0  2  quency, / of the wave and are given for three different frequencies in Table 2.1, while S and C are the sand and clay components of the soil in percent by weight, respectively [12]. Topp et al. in 1980 empirically established a relation between the real part of the dielectric constant and the volumetric soil moisture, which unlike 15  Table 2.1: Coefficients of the p o l y n o m i a l expression i n (2.9) [12]  /  a  1.4  2.862  -0.012  4  2.927  6  1.993  bo  h  b  Co  Cl  C2  0.001  3.803  0.462  -0.341  119.006  -0.500  0.6333  -0.012  -0.001  5.505  0.371  0.062  114.826  -0.389  -0.547  0.002  0.015  38.086  -0.176  -0.633  10.720  1.256  1.522  a  0  2  2  Hallikainen's model, is independent of the soil composition. T h e empirical model is given as [13]:  e' = 3.03 + + 9 . 3 m „ + 146 m , 2  76.7 m\  (2.10)  A s suggested i n Section 2.1.2, the choice of the model for c o m p u t i n g the volumetric soil moisture from the dielectric constant i n this work w i l l depend on the availability of the soil composition. T h e accuracy of the time domain reflectometry method varies between ± 1 . 3 [vol. % ] . Studies have shown that a slight underestimation of the soil moisture is obtained i n case of clay enriched soil and for soil m i x e d w i t h high organic matter.  These classical methods, however, require a lot of time and labor, which proves to be a major disadvantage. Furthermore, they can not provide a reliable estimate of soil moisture over a large area due to the system of point measurements.  In addition to this, since the measurements are done at the  catchment scale, large errors tend to occur i n the parameterization at the i n terface between the different scales of the hydrological to ecological or climatic models. T h u s , methods for integrating a variety of scientific applications at different scales are required to ensure the credibility and better u t i l i t y of these applications.  16  2.2.2  Measuring soil moisture with imaging radar  The advent of high resolution imaging radars in the 1950s led to the understanding that the terrain-scattered radar wave, which was earlier considered as an interference, is itself the information carrier since the information is derived from the knowledge of how waves scatter from rough surfaces and inhomogeneous media. When operated in a monostatic mode , a radar measures the 7  power backscattered by an illuminated area due to the transmitted incident radiation. The strong sensitivity of the radar's response to the soil moisture content led to a trend of remotely mapping the soil moisture distribution with imaging radars. Both active and passive radar systems have been employed to examine the radar response to soil moisture and eventually estimate the moisture content. The ground-based/truck-mounted radiometers described in [18-20], are among the passive radar systems used for collecting the microwave brightness temperature, T B as well as detecting the electromagnetic radiation from the ground. The techniques for soil moisture retrieval, in these cases, are based on the relationship between the radiation and T B - It is worth mentioning that, currently, the radiometric retrieval algorithms provide more accurate soil moisture estimates for vegetated areas as compared to the active radar algorithms [21]. The capability of active microwave techniques to sense the near surface soil moisture was first explored using truck-mounted scatterometers. Based on the promise shown by the scatterometer results, the experimental efforts were extended to the airborne platform where scatterometers operating at different bands were flown aboard aircrafts. The introduction of the synthetic aperture radar (SAR) brought in a revolution in high resolution radar imaging. Extensive studies of the experimental data revealed that, conceptually, if the radar backscattering coefficient of terrain is sensitive to several scene variables, then it is necessary to use multiple radar channels with different wavelengths/indicence angles/polarization configurations. Another alternative is to use multiple temporal observations. A radar system configuration where the radar receiver and the radar transmitter are at the same location 7  17  Based on this premise, polarimetric airborne SAR systems operating at multiple bands were introduced and used extensively. These systems included the Airborne SAR (AIRSAR) constructed by JPL operating at P, L, and C bands and the Canadian C-band Convair-580 (CV-580). The limitation of airborne sensors of not being able image very large portions of the Earth's surface in a reasonable time time, led to introduction of spaceborne radar systems. Satellites and shuttles were used to carry the SAR systems, such as the SEASAT, SIR-B and the SIR-C/X-SAR. The SIR-C, developed by NASA, was fully polarimetric and operated at two bands-L & C, while the X-SAR developed by DLR was non-polarimetric, X-band system. Empirical efforts to use airborne SAR for investigating soil moisture began in the late 1970s. In comparison to radiometers and scatterometers, the radar measurements have high spatial resolution and provide sub-pixel roughness and vegetation information within the lower resolution radiometer footprint. Over the years, research investigations have attempted to identify a radar configuration (active or passive), by specifying the wavelength, incident angle range and transmit/receive antenna polarization, that would exhibit a radar response which is very sensitive to soil moisture content as well as fairly insensitive to surface roughness and vegetation cover. However, it is necessary to mention at this stage, that even if a radar is operated with the optimum soil moisture configuration, it is not possible to reduce the effects of surface roughness and vegetation completely. An outline of the principle of operation of SAR and the fundamentals of SAR polarimetry are given in Appendix A. The retrieval algorithms, used to estimate the soil moisture from the observed radar backscatter, are discussed in the following chapter.  18  Chapter 3 A Review: Soil Moisture Retrieval Models The ease and convenience involved in measuring the soil moisture with the help of radar systems led to the development of numerous estimation models. One of the most common approaches used to develop the models for soil moisture retrieval, is to model the backscattering coefficients in terms of the soil attributes such as the dielectric constant and the surface roughness, for an area with known characteristics. These direct models are subsequently used in the inverse mode to estimate the surface parameters given the radar measurements. Before these models are discussed in detail, the relationships observed between different parameters, based on which the models were developed, are introduced in the following section.  3.1 3.1.1  Relationship between different parameters Dielectric constant and moisture content  The dependence of the dielectric constant of the soil on the soil moisture content, soil composition and frequency of the radar wave has been demonstrated by several models including the empirical model suggested by Hallikainen et al. given by (2.9) and discussed in Section 2.1.2. 19  Figure 3.1: Measured dielectric constant for five soils at 1.4GHz (Ulaby) et a l , 1986 T h e dielectric constant, e' , for liquid water exhibits a strong dependence w  on microwave frequency and relatively weak sensitivity to physical temperature.  A l s o , the imaginary part, e^, of the dielectric constant is strongly  sensitive to salinity at frequencies below 10 G H z . W h e n compared to dry soil, b o t h e' and e'^, for water are significantly larger. Consequently, the addition w  of liquid water to soil changes the dielectric constant markedly, leading to the radar's strong sensitivity to soil moisture. F i g . 3.1 illustrates the variation of e' and e" w i t h the volumetric soil moisture content, m , v  for five soil types at  1.4 G H z . T h e strong dependence of the dielectric constant on the soil moisture content and a relatively weaker dependence on the soil composition is evident. T h e dielectric constant behaves i n a similar fashion at other frequencies,  as  shown i n F i g . 3.2 [14]  3.1.2  Dielectric constant and temperature  In contrast to the relatively large values for e' and e^,, the dielectric constant w  of ice is comparable to that o f dry soil. Thus, for soils containing a significant fraction of liquid water, the dielectric constant undergoes a large change as the 20  30  25  3-Slit Loam 30.611 Sand 5 5 . « Silt 13.5* Clay  1.4 GHz  IS GHz  0 0.0  0.1  as  o.2  0.4  Volumetric Moisture m.  Figure 3.2: Measured dielectric constant for a loamy soil at four microwave frequencies (Ulaby et al., 1986) soil freezes up, as indicated in Fig. 3.3. However, below the temperature of 0°C, the dielectric constant exhibits a very gentle variation with temperature [22].  3.1.3  Penetration depth and soil moisture  The penetration depth is the depth below the surface at which the wave's power has been reduced to 37% of its value just below the boundary. It is a measure of the penetrability of a radar wave into the soil medium, and therefore the depth at which radar reflections will occur. The penetration depth is given by (2.6), thus being directly proportional to the wavelength and inversely proportional to the dielectric constant. Furthermore, the direct dependence of the dielectric constant on the soil moisture content, implies that the penetration depth is inversely related to the moisture content. In Fig. 3.4, the variation in the penetration depth with the volumetric soil moisture at different frequencies is shown. It is clearly evident that for higher frequencies (smaller wavelengths), the penetration depth decreases. Also, an increasing moisture fraction in the soil leads to a gradual decrease in the pen-  21  Figure 3.4: Penetration depth as a function of moisture content for loamy soil at three microwave frequencies [22]  22  0.  10.  20.  30.  40.  50.  60.  70.  80.  Incident Angle (Degrees)  Figure 3.5: Angular responses of cr{j , cr^L, and a^v f° s = 0.32 cm and m = 0.15 g/cm at 1.5 GHz ( [3])  r a  h  smooth surface with  3  v  etration depth, which would cause a stronger backscatter.  3.1.4  Surface scattering characteristics  The development of both theoretical as well as empirical models requires a complete study of the nature of surface scattering of the E M waves. Measurement of the angular response is one such method of determining the radar backscattering statistics. Fig. 3.5 illustrates the comparison of the angular responses of the backscattering coefficients at different polarizations, a° , , a° and a° . At angles close lh  v  h  to the normal incidence cr{j ~ a^, but at higher angles the two curves diverge h  with cr^, having a higher level than a ° . The cross-polarized coefficient, a® , h  h  however, exhibits a lesser dependence on 6 [3]. Also, for a given surface roughness, the backscattering coefficient is approximately proportional to the Fresnel reflectivity of the soil surface. In physical terms, the Fresnel reflectivity is measure of the efficiency of a surface in reflecting E M waves. Thus, a reflectivity of 1.0 represents total reflection. Furthermore, the Fresnel reflectivity has been demonstrated to exhibit a direct dependence on the radar incidence angle as well as polarization. Fig. 3.6 depicts the variation of the reflectivity with the volumetric soil moisture con23  Figure 3.6: Fresnel reflectivity i n d B at n o r m a l incidence as a function of soil moisture content. F i e l d 1 and 5 are sandy loam and clay loam, respectively [22] tent at n o r m a l incidence for two soil types [22]. In the following sections a critical review of the modelling approaches which have been proposed i n the recent years, is presented.  T h e models have been classified into two groups:  soil moisture retrieval i n bare-soil and i n vegetated areas.  3.2  Models for soil moisture retrieval in bare areas  3.2.1  Theoretical surface scattering models  T o develop a model which exactly describes the scattering behavior of an electromagnetic wave from randomly rough surfaces, has been a research topic for decades. However, no model to date has proved to be satisfactory and exact i n its performance and for most practical applications, approximate methods  24  have been used. Various approximate methods for wave scattering at rough surfaces of a more or less general form have been developed. In the field of radar, the most common methods have been the Kirchhoff Approximation (KA) and the Small Perturbation Model (SPM). In order to understand the formulation of the aforementioned models, it is important, at this stage, to present a statistical description of the surface roughness. Randomly rough surfaces are usually described in terms of their deviation from a smooth 'reference surface'. There are essentially two aspects describing the nature of a randomly rough surface, i.e., the spread of heights about the reference surface and the variation of these heights along the surface. It has been found that the parameter set comprising of the root mean square (RMS) height, s, and the surface correlation length, /, proves to be the best choice for the parametric description of natural surfaces. The RMS height, s, is used to describe the vertical surface roughness and is defined as the standard deviation of the surface height variation. On the other hand, the surface correlation function p(x) and the associated correlation length,  are parameters used for the horizontal description of the surface  roughness. The surface correlation length is defined as the displacement x' for which p(x') between two points is smaller than 1/e.  Thus, the surface  correlation describes the statistical independence of two points on a surface and increases with the correlation between two neighboring points. For a smooth surface I = oo. Both statistical parameters, s and /, are independent from each other such that / can be large or small for a high or low s. The relation of the ground measured RMS height and the surface correlation length to the EM wave are given in terms of the actual wavelength, (k = 2ir/X) with ks and kl. Therefore, ks and kl are decreasing with increasing wavelength. Kirchhoff approximation The KA is valid when the surface roughness dimensions are large compared to the wavelength, and is therefore more suitable for applications with short wavelengths, as for example at X or C-band and for large surface correlation lengths (kl > 6). In this case, the scattering at a point on the surface may be considered as scattering at the plane tangential to this point. Even with this  25  approximation, it is not possible to obtain an analytic solution and additional assumptions are necessary. Therefore, two modifications of the K A have been developed - the Geometric Optics (GO) Model and the Physical Optics (PO) Model. The GO model represents the low frequency solution of the K A where the obtained backscattering coefficients depend mainly on the surface slope, and, is valid for high surface roughness conditions (ks > 2). The PO model, however, represents the high frequency solution of the K A , where the obtained backscattering coefficients depend on the surface roughness and the surface correlation length, and it is valid for surface roughness, ks > 0.25. Small perturbation model In contrast to the KA, SPM assumes that the variation in surface height is small compared to the wavelength and is therefore more appropriate for applications with long wavelengths such as at S-, L- or P- band. Although the validity of the model is only within a limited range of surface parameters, it is one of the most widely used solutions for surface scattering. According to this model, a random surface can be decomposed into its Fourier spectral components. The scattering is mainly due to the spectral component of the surface which matches with the effective wavelength at the angle of incidence. The scattering matrix, S, for a Bragg surface, where the variation of surface height is small relative to the wavelength, is of the form [23]:  S =  R (9,e)  S'HV  0  s  o  _ <SvH  R (e,e)\  (3.1)  v  where m is the backscatter amplitude containing the information about sura  face roughness condition of the surface, and R and R are the Bragg scattering s  p  coefficients perpendicular and parallel to the incident plane, respectively. Both are a function of the complex dielectric constant, e and the local incidence angle, e. sin 0 cos 0 - Ve cos + \/e - sin 0 2  (3.2)  2  (e - 1) (sin fl - 6 (1 + sin fl)) 2  Rp —  2  2  (e cos0 + Ve - sin 0) 2  26  (3.3)  F r o m (3.2) and (3.3), it is important to note that the co-polarization ratio, R /Rp s  depends only on the complex dielectric and the incidence angle, and is  independent of the surface roughness.  Rough Surface  GO  R e g i o n covered by m o s t natural surfaces  PO  SPM Smooth Surface  6  4  S u r f a c e C o r r e h t o i n L e n g t h , fi  Rough Surface  Increasing H  ASmoother Surface  Figure 3.7: V a l i d i t y regions of S P M , G O and P O models [2]  B o t h the S P M and K A , however, had certain limitations and thus are not popular i n their usage for soil moisture estimation. T h e limitations are listed below [3]: • O h et a l . , i n their study [3], demonstrated that most surface roughness conditions exhibited by the radar data fall outside the region of validity for a l l the three models. • None of these models provided a fairly accurate estimate of the soil moisture. • T h e P O model predicts that a'L > a ° , which is contrary to a l l observah  tions.  27  3.2.2  Empirical model by Oh et al. (1992)  The first semi-empirical model to be developed was by Oh et al. in 1992 [3]. The radar measurements used for its development were obtained by a truckmounted scatterometer, (LCX POLARSCAT), operating at three frequencies (1.5, 4.5 and 9.5 GHz) in a fully polarimetric mode with an incidence angle range from 10° to 70°. On the basis of the scatterometer and ground measurements, two empirically determined, multivariate equations for the co- and cross-polarized backscatter ratios were proposed [3]:  a?  q  = -js: = 0.23 vTo (1 -  (3.5)  e~ ) ks  (7° "vv  where p and q indicate the co- and cross-polarized backscatter ratios, respectively; 6 is the local incidence angle, ks is the RMS height normalized to the wavelength, and r is the Fresnel reflectivity coefficient at nadir: 0  To  =  V7>  1 + x/i  (3.6)  7  For a known angle of incidence, (3.4) and (3.5) constitute an inversion model to determine dielectric constant, e', and the surface roughness, ks. Consequently, an estimate of the soil moisture content can be obtained by converting e' to the volumetric soil moisture, m , using the models given in [12,13]. v  Unlike the theoretical models, this model extended the region of validity and was in good agreement with other experimental models. Furthermore, according to [3], p and q are both limited to ks < 3 and p =  < 1, thus  making the model more appropriate for applications at lower frequencies, e.g., S-, L-, and P-band. In spite of the above characteristics, the model has certain disadvantages as summarized below: • The empirical model works well only for certain range of values for ks, kl  and  m , v  i.e., 0.1 <  ks  <  6, 2.5 28  <  kl  <  20, and 9 <  m  v  <  31.  • In regions of high roughness, i.e., ks > 3, the soil moisture is overestimated. • Since, the model constitutes two non-linear equations, an error in determining one parameter will lead to erroneous results for the other. • The model can be used for estimating soil moisture and surface roughness only for regions with bare soil. Vegetation effects were not taken into consideration.  3.2.3  Empirical model by Dubois et al. (1995)  This empirical model is a simplification of the Oh Model addressing only the co-polarized backscatter. The data used in the original study, in order to develop the model, was collected with a truck-mounted radiometer-scatterometer (RASAM) as well as the LCX-POLARSCAT, operating at six different frequencies between 2.5 to 11 GHz. In later investigations, this model was further applied to fully polarimetric airborne and spaceborne SAR data acquired by AIRSAR and SIR-C, respectively. Using the scatterometer data and ground measurements, the empirically determined co-polarized backscatter coefficients cj£ and a° for the horizontal h  v  and vertical polarization, were expressed as a function of system parameters, i.e., the local incidence angle, frequency and soil parameters (the dielectric constant and the surface roughness). As a first step in development of the model, the dependence of the co-polarization ratio on different soil moisture conditions and the local incidence angle was investigated. In the second step, the deviation caused by the surface roughness was accounted for by an empirically derived expression for the roughness term,  sin#). The resulting  log(ks  expressions are given by [1,24]:  a  o  =  1 0  10°028 «' t a „ *  -"5  ( f c s  ^  0)1.4 <).7 A  (3  ?  )  sin 6 a° = IO- ' 2  vv  35  ^ 10 sin 6  0 0 4 6  ^ (ks e  sin0)  11  A  0,7  (3.8)  where 6 is the local incidence angle, ks is the RMS height normalized to the wavelength, and A is the wavelength. 29  The backscatter coefficients in (3.7) and (3.8), decrease with increasing incidence angle and/or with decreasing surface roughness. Also, the backscatter coefficients increase with increasing soil moisture, stronger in a^, than in CT^ .' Furthermore, the co-polarized ratio, cr^h/^vv i roughness dependent and s  h  increases with increasing surface roughness [2]. For a given local incidence angle, the inversion of the Dubois Model is much simpler than that of the Oh Model. This is due to the fact that both the dielectric constant and the surface roughness can be retrieved directly using a two-step inversion algorithm.  e'  =  C  v v  K  - A ) - C « y - Ayy) tan# (Bhh C — Bw Chh) h  (3.9)  h h  h h  v v  \  Bhh K v - A y y ) - Byy K u - A  h —  10  (B  h h  h h  )  Cvv - B w C )  (3.10)  h b  2 7r sin 9 where A  h h  = 1.51og(cos0) - 1.51og(sin0) + 0.71og(A) - 2.75  (3.11)  A  v v  = 31og(cos0) - 31og(sin0) + 0.71og(A) - 2.35  (3.12)  B  h h  = 0.028  B y y = 0.046  (3.13)  C  h h  = 1.4  C  (3.14)  v v  = 1.1  Furthermore, the inversion is sensitive to two types of calibration: absolute calibration and relative calibration of the radar data. An absolute calibration can be modelled as a multiplicative factor affecting both  and a^ . A relative h  calibration error can be modelled as a multiplicative factor to be applied to Results of calibration indicated that the inversion is less sensitive to  hh/ °v  a  a  calibration at larger incidence angles. Also, the inversion is more sensitive to relative than absolute errors. The validity of the model is restricted to the ranges of ks < 2.5,9 > 30° and m < 35%. Also, good soil moisture estimates are obtained for bare soil v  regions and for areas with sparse vegetation. However, the presence of larger amounts of vegetation results in overestimation of the surface roughness and underestimation of the soil moisture. As per the conclusions in [1], the model does not perform well for regions with a^/a^  < —11 dB. As a result, for  effective implementation of the algorithm, the cross-polarized ratio is initially 30  used to determine the extent of vegetation, and subsequently the model is applied for areas with o° /cr° n  v  < —11 dB.  In addition to its several advantages, the model, however, presented the following limitations [1,2]: • The effect of row directions of the crops, in case of agriculturalfieldswas not taken into consideration in the model. When row effects are present, the algorithm overestimates the surface roughness and underestimates the soil moisture. For the inversion, the data was acquired at angles approaching 45° relative to the row direction. • The surface correlation length has not been included explicitly in the model since it is a difficult parameter to measure accurately. • The effects of topography were neglected in the model. • Absolute calibration is more critical for this model, which uses only two backscattering coefficients for the estimation of two parameters. • The model, as mentioned earlier, does not produce good results for regions with considerable amounts of vegetation.  3.2.4  Algorithm proposed by Shi et al. (1997)  An algorithm based on the single scattering Integral Equation Method [25] was developed by Shi et al. in 1997 to provide an estimate of the soil moisture as well as the surface roughness. In the previous models discussed in Sections 3.2.2 and 3.2.3, the surface power spectrum had not been taken into account, which is closely related to the surface roughness and the correlation length. This is based on the fact that backscattering coefficients are not only sensitive to m  v  and s, but also to the surface roughness power spectrum. This model includes the effect of the surface roughness spectrum and is developed by fitting the IEM-based numerical simulations for a wide range of surface roughness and m conditions. v  During the development of the model, firstly, the equations for computing the single backscattering coefficients, <r£ and o^ from the IEM were obtained. h  31  Both the HH and V V backscatter are related to the angle of incidence, Fresnel reflection coefficients, relative permittivity and permeability of the surface, the surface height, the wavenumber, and the surface correlation function. The dependence of the backscattering coefficients on these parameters makes the model complex [26]. Shi et al. simplified the IEM equations to a certain extent using regression analyzes and obtained an approximate linear relation between the normalized co-polarized backscattering coefficients and the surface roughness parameter:  10 log 10  a ppi  = a (8) + b (8) 10 log 10 pp  pp  cr,pp  1 5R  (3.15)  where pp — hh or vv, and (e' - 1)  (3.16)  (cos 8 + V V - sin 6») 2  (e' - 1) (sin  2  - e' (1 + sin 8)) 2  (3.17)  CX-vv  (cos6 + y/e* - sin 6i) 2  2  The two coefficients, a (8) and b (9), from regression, depend only on 8 and pp  pp  polarization pp. The surface roughness parameter, SR, is a combination of the RMS height, correlation length and the surface correlation function. SR can be eliminated when two polarization measurements are available, thus providing a simpler inversion equation: a a;pp  10 log 10  = a (8) + b (8) 10 log 10 pq  pq  a,991 a 0  (3.18)  99  Further, it was found that the pair of the combination of co-polarized measurements, y/a\%  <7h  h  and a° + <rg, proved to be the best among all polarization v  h  measurements with regard to maximum sensitivity to soil moisture changes and least sensitivity to calibration accuracy and vegetation effects. Thus, by replacing the backscatter in (3.18) with the combination of co-polarized measurements and by removing the surface roughness parameter for simplification,  32  the.following expression was obtained: 10 log 10  = a (9) + b {9) 10 log 10 vh  vh  (3.19) All the coefficients used in (3.15) and (3.19) are obtained by regression analyzes and given in [26]. The model was applied to both spaceborne (SIR-C) as well and airborne (AIRSAR) SAR data. Radiometric data was not used for the implementation of this model. A similar inversion model (INVIEM) was also developed by Hoekman et al. in 1999 [27]. It was observed that INVIEM gives a better performance in soil moisture estimation as compared to the Oh-Model. Limitations of the Shi model: • The algorithm and its inversion are complex and difficult to implement. • Large errors occur in estimation in case of large incidence angles. • The algorithm, like the Dubois Model, is sensitive to relative calibration error at small 9. • The algorithm was applied only for regions with bare soil and sparse vegetation.  3.2.5  Polarimetric semi empirical model  The polarimetric semi-empirical model in [28] has been developed based on existing theoretical models and an extensive database obtained by groundbased scatterometers and the JPL airborne SAR system over a wide variety of bare soil surfaces. The input parameters for this model include the incidence angle, the volumetric soil moisture and roughness parameters, ks and kl. It is important to note that the model uses the soil moisture content instead of the dielectric constant for simplicity. As per the suggested model, the overall functional form of the crosspolarized backscatter is as follows: 33  <  h  = 0.11 m°  7 v  (cosfl)™ [ 1 -  E  -0-32M  18  j  ( 3  .  2 0 )  where the constants were determined by applying the minimum mean square technique. Further, the cross-polarized ratio, q, and the co-polarized ratio, p, can be expressed as: q  =  ^Yh  =  Q  1  ( / S  Z  +  s i n l  . ^)i-2  0.35 m " ' 0  -0.9(fe ) 0  3  3  !  S  (3.21)  6 5  Consequently, the V V and HH polarized backscatter can be obtained as: <  v  = ^  (3.23)  <  h  = ~ <h  (3-24)  q  Though the model is based on earlier theoretical models as well as the Oh Model [3], its conception is novel since it also provides explicit expressions for the degree of correlation, a, and co-polarized phase difference, £, in terms of the same input parameters as mentioned above. a = 1 - (0.17 + O.Olkl + 0.5m ) (sinfl) v  £ = (0.44 - 0.95 m  v  11(fcs)  "'  0 4  - ks/kl) 9  (3.25) (3.26)  The other distinguishing feature of this model is that it not only agrees with the experimental observations over a wide range of soil surface conditions, but it also agrees with the IEM and GO model over their individual regions of validity, thus encompassing the full range of surface roughness encountered under natural conditions [29]. Limitations: • Among all the above relations, only the backscattering coefficients in (3.20)(3.22), have been used for the inversion techniques, while the expressions for phase difference and correlation have not been verified yet. This tends to make this model similar to any other empirical model. 34  • For the given data sets the model produced illegal values for 25% of the measurements [30]. • The model was developed for bare soils and vegetation effects were not taken into consideration.  3.3  Models for soil moisture retrieval in vegetated areas  The ineffectiveness of the aforementioned models in soil moisture estimation over areas with significant amounts of vegetation has been a valid concern over the past decade. The extensive application of soil moisture estimation in agriculture and global weather prediction has made it necessary to find a solution to this continuing problem. The presence of vegetation complicates the retrieval of moisture from the underlying soil. The multiple scattering effects, caused by the vegetation, lead to the interaction between the backscatter contributions from both the soil and the vegetation causing the observed backscatter to be highly non-linear. Furthermore, canopies/crops contain moisture of their own, thus, the retrieved surface water content corresponds to the combined signatures of vegetation and soil water. Several models have attempted to address this concern. The following sections provide a brief overview of the significant research contributions.  3.3.1  E s t i m a t i o n m o d e l b y J a c k s o n et a l . (1991)  One of the first approaches, for soil moisture retrieval in vegetated areas, was suggested by Jackson et al. [7] where a quantitative technique for isolating the effect of vegetation was developed using the field normalized brightness temperature. The methodology used was based on the fact that a layer of vegetation over the soil absorbs the emission of the soil and adds to the total radiative flux with its own emission. A model of this process which describes the brightness 35  temperature of a weakly scattering layer above a semi-infinite medium is given by Ulaby et al. [14] T  B  = (1 + R 7) (1 - 7) (1 ~ a) T s  v  + (1 - R ) 7 T s  s  (3.27)  where: TB  = brightness temperature of the vegetation canopy  T  v  = physical temperature of the vegetation (K)  T  s  = physical temperature of the soil (K)  R  s  = microwave reflectivity of the soil surface  7 = transmissivity of the vegetation layer a  — single scattering albedo  1  The physical temperature measurements can be obtained using a radiometer directly, such as the E S T A R radiometer used in [31]. The two vegetation parameters, 7 and a are determined from a vegetation model based on discrete scatter random media techniques. In this model, the vegetation canopy is treated as a collection of discrete scatterers with a certain orientation and position. Using the Born approximation and Peake's formulation permits the model to calculate either the radar scattering coefficients or the radiometric response [31]. A detailed flowchart for the algorithm can be found in [32]. This model was applied to data acquired by both the E S T A R radiometer [32] and A I R S A R [31] during the Washita'92 experiment. Limitations: • The model involves the measurement of the physical temperatures which makes the requirement of a ground-based/airborne radiometer necessary even when a S A R is used for data collection. • This method requires detailed canopy measurements such as size and orientation distributions of major canopy constituents, as an input to the model. Such measurements are generally not available. General term for the ratio of reflected/scattered power to incident power, also called as 'reflection coefficient' 1  36  3.3.2  Models developed by regression  M o d e l p r o p o s e d b y P r e v o t et a l . ( 1 9 9 3 )  The model suggested by Prevot et al. [33], does not formally correct for the vegetation effects in the backscatter, but accounts for the vegetation water content. The method is based on the water-cloud model proposed by Attema & Ulaby in 1978 [5], where the radar cross section of the canopy can be expressed as the incoherent sum of contribution of the vegetation layer, cr° , and the eg  contribution of the underlying soil, a° . Under the assumptions made in [5,33] oil  the model can be represented as given below: o° = < <  s  oil  (3.29)  2  c  r  2  (3.28)  2  = AW cose(l-T )  eg  where r  + ra°  e g  2 _  e  ( - 2 S W  c  s e c 0 )  (  3  _  3  0  )  is the two-way attenuation through the vegetation and W is the c  vegetation water content. For a given radar configuration, the soil contribution is usually expressed as a linear function of it surface moisture content [14]: <  = C + Dm  oil  (3.31)  v  In order to account for the dependence of (3.31) on soil roughness, a simple angular parameterization of the surface roughness was introduced into C along with a parameter F which denotes the radar configuration (frequency and polarization). This parameterization considers the effect of soil moisture and surface roughness as independent: a° s  oil  = C(F,9)  + Dm  (3.32)  - QC {F)  (3.33)  v  with C(F,6)  = d{F)  2  Using the data acquired by AGRISCATT'88 and ERASME scatterometers at different configurations, the model was fitted to obtain the constant D 37  and the parameter  It was found that for each radar configuration, a  C(F,0).  unique value of C is good enough to represent the different fields observed. 2  Subsequently, the inversion of the model was done by neglecting the vegetation term in (3.28) and considering that the effect of vegetation is mainly an attenuation of the signal returned by the underlying soil. The model was thus simplified to the form: o°  =  e  (-2iw sec0) c  (  3  3  4  )  When expressed in dB units, this expression leads to a linear function with variables, W and m : c  v  a°  =  +  B'W sec9 c  C  + Dm  v  (3.35)  As a result, for given measurements of the vegetation water content, the soil moisture content can be estimated. Limitations: • The model is developed by fitting it to the available scatterometer data, thus making the model more specific to the type of sensor, site and vegetation • The assumption that the parameter C is the same for all sites at a partic2  ular radar configuration tends to disregard the effect of each site/vegetation type and its contribution to the backscatter. This may lead to large errors when the model is applied to other data sets. • The model accounts for the vegetation effects by using the vegetation water content only. The vegetation term which represents the backscatter from the vegetation is completely neglected. • As per [33], the measurement of the vegetation water content at the ground is required in order to estimate the soil moisture.  38  M o d e l b y L i n et a l . (1994)  Lin et al., presented an empirical study of the relation between the AIRSAR's signals and land surface parameters [34]. Here the vegetation volume scattering was accounted for by using the vegetation model suggested by Lang et al. in 1983 [35]. Applying the Born approximation, Lang et al. related the total backscatter to a number of land surface parameters: a° = <  d  + o°  + < + r cr °  (3.36)  2  vdr  r  s  oil  a° , o° and a° are the direct, direct-r effect and reflect backscattering cond  d[  T  tributions of the vegetation, respectively; and can be determined from the expression in [35]. The backscatter due to the soil is obtained using the Oh Model [3]. This model was employed in simulating L-band HH and V V responses from grass covered areas for 250 hypothetical conditions. This enhanced data was further used to develop a regression model relating the HH and V V backscatter to the angle of incidence, A, leaf dielectric constant, ei f, canopy thickness, D, ea  soil bulk density, p^, percentage of sand in soil, and the soil moisture content, m  v  [34]. ( ° )- 0  CT  21  h  = 22.28 + 0.000095(fl) - 19.677(ei ) 239  0  01  eaf  - 0.196(D) - 0.2731og(m„)  (3.37)  107  [o° y  = 2.481 + 0.0000016(A) ' - 0.00012(e ) -  on  2 93  v  1  73  ieo/  -  0.32(/9 ) 0  6  39  - 0.232(sand)  107  - 0.888(m„) (3.38) a42  In the above regression models, five statistically important land surface parameters are required. Since these parameters are generally not radar-measurable, Lin et al. combined different sets of AIRSAR data to rearrange the regression relationships to obtain two soil moisture retrieval equations for AIRSAR [34]:  (m„)  = 100 x [0.97 + 0.0000302(A) - 0 . 0 5 « ) - ] ' 227  hh  - 0  3 6  5  5 6  (3.39)  85  (3.40)  h  K ) „ = 100 x [1.311 + 0.000027(A) 212  39  0.26«vr° ] ' 18  3  A combined soil moisture estimate is obtained from the two independent soil moisture estimates using a weighted average algorithm in order to merge the polarization data: m  v  = wi(m ) v  + w {m )  hh  2  v  vv  (3.41)  Limitations: • The algorithm has been developed taking into consideration only one particular sensor, i.e., AIRSAR. As a result the model may not be applicable to data from passive microwave sensors or spaceborne SAR. • Since regression has been used to develop the model, it might not give good results in cases where the soil/vegetation conditions are different from those considered. • Also, the model was developed only for one form of vegetation, i.e., grass. No other forms of vegetation have been taken into consideration, thus causing the model to have limited applicability.  3.3.3  Models based on introduction of vegetation effects into existing models  One of the popular approaches in developing models for soil moisture estimation in vegetated areas has been to incorporate vegetation effects into the existing bare soil models. A few of these models have been discussed in brief in the following sections. Modification of the IEM by Bindlish et al. (2001) The ineffectiveness of the Integral Equation Method (IEM) [25] in estimating the soil moisture content in vegetated regions, proves to be one of its major drawbacks. In 2001, Bindlish et al., proposed to incorporate the vegetation effects into the IEM to address this concern [36]. A simple approach, based on the Water-Cloud model [5] is used to introduce the vegetation effects. The water-cloud model has been described in 40  detail in Section 3.3.2 and is given by (3.28) - (3.30). The parameters A and B depend on the type of vegetation; A represents the vegetation scattering, B is the attenuation parameter. The type and geometrical structure of the canopy as well as the polarization and wavelength of the sensor are accounted for through these parameters. Both A and B are determined by fitting models against experimental data [6,7]. The orientation and geometry of vegetation are key factors in vegetation backscatter. It is possible that when two canopies of different heights are located at the same range, the backscatter from one is affected by the other and vice versa, leading to an over-estimation of the backscatter by the watercloud model. Bindlish et al. [36] propose an exponential vegetation correlation function to model this geometric effect of the vegetation spacing within the water-cloud model, by introducing the concept of vegetation correlation length. The vegetation backscatter computed from (3.29) is corrected as follows: <; where  g  = <  e  g  (l-0  (3.42)  a =  (3.43) •^scale  Here L  v e g  is the vegetation correlation length and L i is the field scale at s c a  e  which representative ground measurements are available. The suggested model was implemented by first running the IEM in the forward mode to estimate the independent contribution of the soil. The vegetation parameters were subsequently derived [6] and finally the full inversion model was run to estimate the soil moisture. An estimation accuracy of 87% was achieved on applying the model to SIR-C data available from the Washita'94 experiment. Limitations: • The proposed model is based on the IEM model and hence requires the knowledge of the surface roughness for estimating the soil moisture • Though the model accounts for the orientation and geometry of the vegetation, it depends on the ground measurements for L  veg  41  and L i . s c a  e  Modification of the Oh Model by Magagi et al. (2001) The approach used by Magagi et al. attempts, not only to introduce vegetation effects into the Oh Model [3], but also to separate the effects of surface roughness and soil moisture from the radar backscatter. For this model, the co-polarized backscattering coefficient, o° , measured p  over a semi-arid area is considered to as the sum of soil and canopy contributions weighted by the vegetation fractional cover, C [37]: v  a°  pp  where  <7 ° c  an  = (1 - C )a° v  = <  + O °  soil  + r <  c  (3-44) (3.45)  2  e g  a n  oil  The vegetation backscatter, cr , is quantified using the single scattering albedo, veg  a, the incidence angle, 6, and a constant e resulting from the assumption that describes the canopy as a Rayleigh scattering medium: <  e g  =  e a  (1 - r ) 2  cos(8)  (3.46)  The two-way vegetation transmissivity, r , can be determined using (3.29) 2  and (3.30), while the soil backscatter, cr° , is obtained from the linear relaoil  tionship given by (3.31). Magagi et al. claim that the parameter C in (3.31) quantifies the surface roughness contribution in the bare soil signal, and the constant D, represents the sensitivity of the signal to the volumetric soil moisture. The basic approach used in this model consists of several steps. First, the contribution of the vegetation is estimated from the B and a data [55], as well as C . Using this estimate and the measured backscatter at any polarization, 2  v  a°, the soil backscatter can be determined. The soil roughness parameter, C, is then estimated based on ground measurements at the end of the dry season (dry soil and no vegetation) and is considered to be constant. Both C and  <7°  O I L  are subsequently used to compute the "first guess" of the volumetric  C can be calculated from the Modified Soil Adjusted Vegetation index (MSAVI) using hyperspectral data. 2  t )  42  soil moisture, m . This estimate of m along with the theoretical ratio of the v  v  two co-polarization ratios,  (pi/p2)^ , 2  is used to classify the pixels into three  categories of moisture content (pi/p2) ^ , 1  2  0, m < 10 and m > 10. The ratio, v  v  is obtained by considering the fore- and mid-beam data, denoted  by subscripts 1 and 2, respectively. (3.47)  When m « 0, ( p i / p 2 ) v  1 / 2  is considered to be independent of the surface  roughness, ks. The second case corresponds to the transition zone where inversion is not possible unless ancillary information is available on either roughness or moisture, and the third category corresponds to the area where (pi/^) ^ 1  2  is completely dependent on roughness. Depending on the category, the surface roughness parameter, ks, is calculated [38]; from which the "second guess" for the soil moisture, m i is obtained, v  using the Oh Model. If the value of m i is unsatisfactory, another iteration v  of all the steps discussed above is performed using m i, in order to obtain a v  second estimate the surface roughness, ks and soil moisture, m . The itera2  v2  tion continues until desirable results are obtained. In this approach the main objective of the coupling between the bare-soil linear relationship and the Oh Model is to separate the effects of surface roughness and soil moisture. Limitations: • At the first step, the algorithm requires the vegetation biomass as an input. Since the proposed model does not mention any particular method to measure the biomass remotely, it will, therefore, need to rely on ground measurements. • The ratio, (pi/p ) ^ , is a key factor in classifying the pixels. In order to 1  2  2  compute (pi/^) ^ two different incidence angles for the same site are 1  2  required. • Since the proposed model depends on the Oh Model for the surface roughness and soil moisture estimates, it tends to have the same limitations as the Oh Model. 43  Model proposed by Kim et al. (2004) In the study, Kim et al. examine a potential inversion algorithm to retrieve soil moisture under vegetation canopies using the L-band polarimetric radar data which will be available through the proposed HYDROS mission. HYDROS will use a combined radar/radiometer L-band instrument to provide the first global view of land soil moisture from space [39]. A vegetation model, which is suitable for L-band and can be further used in the soil moisture retrieval algorithm, is proposed. As per the model, the vegetation scattering is composed of four components: (1) surface backscattering attenuated by the vegetation, (2) branch scattering, (3) trunk-ground double bounce scattering, and (4) branch-ground double bounce scattering. Equations for each of these components at HH, V V and HV polarizations are given in [39]. The first step of the soil moisture estimation algorithm is a segmentation process based on the amount of biomass present in each pixel. The radar vegetation index (RVI) is used for this segmentation: *£k  RVI =  *hh + °vv +  (3.48) 2<C  When the vegetation scattering is dominated by randomly oriented thin cylinders, the radar vegetation index become one (as a maximum). If a pixel indicates the presence of bare surface, an estimation algorithm for bare soils (Section 3.2) is employed. For a pixel with modest vegetation (0.2 < RVI < 0.4) and (?„ >  <7hh,  vegetation attenuation is estimated to apply  the bare surface algorithm. For a pixel with significant vegetation (RVI > 0.4), the attenuated surface scattering component can be ignored. In order to measure the soil moisture directly, the forward ground reflection component must be derived from the double bounce scattering by removing the branch scattering component. The lower resolution soil moisture information, which will be derived from the HYDROS radiometer can be used to enhance the soil moisture retrieval in vegetated areas, while the time variation in the polarimetric radar mea44  surements will be used to improve the soil moisture estimation accuracy even further. Since the H Y D R O S mission is in its early planning stages, the suggested algorithm is still being developed and has not been validated for its performance on an actual data set and no results have been presented [39]. The methodology of the work presented in this thesis is also based on the approach of introducing vegetation effects into an existing model. The bare soil estimation model chosen as well as the proposed algorithm are presented in the following chapters.  45  C h a p t e r  D a t a  4  D e s c r i p t i o n  This chapter describes the test sites and the ground measurements that were used for validating the performance of existing soil moisture retrieval models as well as the proposed models. Two groups of data sets were used in this work. The first group included the data acquired over the the Little Washita Watershed in Oklahoma, USA, during the Washita'92 and Washita'94 experiments. The Washita experiments were conducted as cooperative research programs between NASA, the United States Department of Agriculture (USDA), and several other government agencies and universities in 1992 and 1994. The second group of data sets includes the data acquired over the Ottawa Green Belt Farm (GBF) and Canadian Food Inspection Agency (CFIA) Field Sites, Canada, during the data collection campaign in 2001. This extensive campaign was conducted by Agriculture and Agri-Food Canada (AAFC), Canada Centre of Remote Sensing (CCRS), Noetix Research and McGill University.  4.1  Little Washita Watershed  A tributary of the Washita River in southwest Oklahoma, USA, the Little Washita River Watershed is unique in that it has been the target of extensive research over a period of several years. The Little Washita Watershed, situated in the southern part of the Great Plains of the United States, covers an area of 609 km . The land use can be grouped into 8 categories; range, pasture, 2  46  forest, cropland, oil waste land, quarries, urban/highways, and water. The climate is classified as moist and sub-humid, and the average annual rainfall was 74.74 cm during the period of data collection by the Agricultural Research Service (ARS). Summers are typically long and hot. The average daily high temperature for July is 34°C , and the average accumulative rainfall for July is 5.64 cm. Winters are typically short, and temperate, but are usually very cold for a few weeks. The average daily low temperature for January is —4°C, and the average accumulative precipitation for January is 2.72 cm. Much of the annual precipitation and most of the large floods occur in the spring and fall [40].  4.2  The Washita'92 Experiment  The primary goal of the Washita'92 experiment was to collect a time series of spatially distributed hydrologic data, focusing on soil moisture and evaporative fluxes, using both conventional and remotely sensed methods. The other specific goals during the experiment included the testing and verification of several new remote sensing devices and the collection of data bases for development of algorithms to study scattering mechanisms/behaviour and, thereby, derive other pertinent applications [41]. Data collection was conducted during the period of June 10 through June 18, 1992. The observations followed a period of very heavy rains over several weeks that ended on June 9. Also, saturated soil conditions with standing water were quite common. No rainfall occurred during the experimental period thus allowing the observation of drying conditions. Fig. 4.1 shows a map of the region over which the data was acquired. The two key elements of this experiment were the data acquisition by two aircrafts (supported by NASA), the C-130 and the DC-8 and, the ground measurements conducted by the USDA Water Quality Lab. The C-130 carried the ESTAR L-band microwave radiometer, the 37 GHz microwave radiometer, the laser profiler, the NS001 multispectral scanner, the thermal infrared multispectral scanner, and two cameras. The DC-8 flew the three frequency synthetic aperture radar, AIRSAR. 47  ssoooo  sraco  eooooo  E A S T I N G (m)  Figure 4.1: Little Washita Watershed, OK (Washita'92)  4.2.1  AIRSAR Data  AIRSAR is a side-looking radar instrument that can collect fully polarimetric data at three radar wavelengths: C-, L- and, P- bands. The objectives of the AIRSAR flights with the DC-8 NASA aircraft during the experiment were to provide a spatial and temporal record of soil moisture changes during the study period. The measurement strategy was carried out with the goal of providing additional data over areas where detailed ground data have been taken for development/testing of radar scattering models and soil moisture inversion algorithms. The AIRSAR parameters during the flight are given in Table 4.1. The AIRSAR data set has been made available on the web by the United States Department of Agriculture (USDA) and is easily accessible. Only Land C- band data are included due to uncertainties in the P-band calibration. The original data (compressed in the NASA/JPL format [42]) has been decompressed and processed into single polarization decibel data scaled to one byte (binary). Each file represents a single date, band, and polarization and comprise of digital numbers (DNs) which represent the backscatter scaled in decibels. The scaling varies with band and polarization and the DN at a  48  particular pixel may be interpreted as follows [43]: Actual dB (C HH) = (DN/(255/25)) - 2 5 Actual dB (C VV) = (DN/(255/25)) - 2 5 Actual dB (C HV) = (DN/(255/30)) - 3 5 Actual dB (L HH) - (DN/(255/35)) - 3 5 Actual dB (L VV) = (DN/(255/35)) - 3 5 Actual dB (L HV) = (DN/(255/35)) - 45 The images are in slant range with 1024 samples and 1279 lines. A polarimetric composite image (R:HH, G:HV, B:VV), acquired by the AIRSAR system on June 10, 1994 is shown in Fig. 4.2. The incidence angles used for the data acquisition on each of the days between 10-18 June are given in Table 4.2. Table 4.1: NASA/JPL AIRSAR Parameters [44] Parameter  P-Band  L-Band  C-Band  Frequency (MHz)  438  1249  5298  Wavelength (m)  0.68  0.24  0.06  Resolution (m)  10  10  10  Bandwidth (MHz)  19  19  19  Transmit Pulse Length (us)  11.25  11.25  11.25  Chirp Rate (MHz/s)  1.6  1.6  1.6  Look angle range (deg)  30 to 70  PRF/Polarization (Hz)  250-750  Nominal Altitude (ft)  15,000-40,000  The site maps along with the U T M co-ordinates (NAD 27, Zone 14 S) have been provided for this data set, from which the site locations can be determined on the image. For this work, the ENVI 3.4 software package was used to convert the information conveyed by the U T M co-ordinates to specific pixel locations in the image, and subsequently derive the site locations. The soil moisture retrieval models were applied to these sites, such that the validity and accuracy of the model could be tested based on the respective ground measurements available for each site.  49  Figure 4.2: Polarimetric composite image, A I R S A R , 0 6 / 1 0 / 9 2  4.2.2  Ground measurements during Washita'92  T h e test sites selected for this research work are agricultural (cultivated) fields comprising of corn and alfalfa, bare fields, rangelands, and pastures. Table 4.3 provides the soil texture, i.e., the percentage of sand (S) and clay ( C ) , soil bulk density, p, rms height, s, and correlation length, L, for each site. In the table, the sites are described by a five character code, where the first two characters refer to the l a n d cover category, i.e., A G corresponds to agricultural l a n d and R G refers to rangeland or pasture.  Table 4.2: Incidence Angles for A I R S A R [43] Date  Incidence A n g l e (Near Range)  06/10/92  19.17°  06/13/92  18.39°  06/14/92  18.36°  06/16/92  15.21°  06/18/92  14.87°  50  Table 4.3: Site Characteristics [45] p (g/cm )  (cm)  L (cm)  Site  Land Cover  S(%)  C(%)  AG001  Corn  60.5  11  1.33  1.23  11.25  AG002  Bare  45.5  13.4  1.33  1.82  17.75  AG003  Alfalfa  27.7  21.7  0.5  13.25  AGOll  Corn  60.5  11  1.23  11.25  AG012  Bare  32.5  14.3  1.82  17.75  RG131  Rangeland  27  10.8  1.31  1.23  7.75  RG123  Pasture  45  9.7  1.18  3  b  1.33  5  Table 4.4: Average Volumetric Soil Moisture (m /m ) for each test site from June 10 to 18 [45] 3  3  Site  10  11  12  13  14  16  17  18  AG001  0.29  0.31  0.22  0.25  0.21  0.18  0.14  0.13  AG002  0.29  0.26  0.22  0.21  0.18  0.17  0.15  0.11  AG003  0.25  0.24  0.23  0.21  0.19  0.17  0.12  0.11  AGOll  0.29  0.28  0.26  0.22  0.20  0.16  0.14  0.12  AG012  0.32  0.27  0.22  0.21  0.14  0.14  0.12  0.15  RG131  0.35  0.35  0.32  0.29  0.29  0.19  0.17  0.28  RG123  0.36  0.37  0.35  0.35  0.32  0.31  0.30  0.28  The volumetric soil moisture for each site at each of the dates from June 10 to June 18 were measured using the gravimetric method (Section 2.2) and are given in Table 4.4.  4.3  The Washita'94 Experiment  Washita'94 was a program of large scale hydrologic field experiments conducted over the Little Washita Watershed. The objective of these experiments was to provide combined ground and remotely sensed data sets for modelling and analysis of hydrologic state and flux variables. The principle hydrologic variable analyzed was surface soil moisture. In addition, meteorologic observations 51  were available from an intensive network within the watershed which included evaporative flux stations installed to support the experiments [46]. The Washita'94 program was conducted between 11-18 April and 1-6 October, 1994. During the both missions, the ESTAR passive microwave instrument was flown as part of an aircraft mapping package with one day of overlap with the SIR-C coverage. At the outset of the April experiment, the watershed was very dry. On the day of the first April SIR-C observation there was a significant rainfall event over the entire watershed. Following this event, there was no further rainfall for the duration of the observations which provides an excellent data set for analysis. The meteorologic conditions during the October SIR-C experiment were much more varied with rainfalls occurring over different portions of the study area. A map, providing an overview of the regions imaged, is given in Fig. 4.3.  4.3.1  SIR-C data  The Shuttle Imaging Radar-C and X-Band Synthetic Aperture Radar (SIRC/X-SAR) is a cooperative space shuttle experiment between NASA, DLR, and ASI. The experiment is the next evolutionary step in NASA's Spaceborne Imaging Radar (SIR) program that began with the SEASAT SAR in 1978, and continued with SIR-A in 1981 and SIR-B in 1984. The mission design enables areas to be imaged at multiple aspect and incidence angles, thus providing important parameters for studying many land and ocean processes. The extensive surface measurement campaigns also provide critical data to be used in development of algorithms needed to produce key geophysical products for assessing global change issues. SIR-C can acquire digital images simultaneously at two microwave wavelengths: L- and C- bands; and at four polarization combinations. The SIRC/X-SAR system characteristics are given in Table 4.5. The SIR-C data set for the Washita'94 experiment has been made available on the web by USDA. Both L- and C- band data, in three different polarizations, HH, V V and HV, are included in this data set. The original SIR-C data 52  was processed and calibrated by NASA JPL and assembled by NASA GSFC Hydrological Sciences Branch. Further, the NASA JPL software was modified to output the SAR data as a scaled backscattering coefficient, such that the data files are in the TIFF gray scale format. Each file represents a single date, band and, polarization; and the backscattering coefficient for any pixel can be computed in dB from the corresponding DN in the TIFF files [47]: C band HH and V V dB = (DN/(255/25)) - 25 CbandHVdB  = (DN/(255/25)) - 35  L band HH and V V dB = (DN/(255/35)) - 35 LbandHVdB  = (DN/(255/35)) - 45  The images are in slant range with a resolution of 30m and, consisting of 934 lines and 1467 samples. A polarimetric composite image (R:HH, G:HV, B:VV) for the data acquired on 11 April 1994 is shown in Fig. 4.4 W-15  18-00  m Sotl Moisture S i u *  Figure 4.3: Little Washita Watershed, OK (Washita'94) For the research work presented in this thesis, the data acquired during the April mission was used. A detailed list of the incidence angles used during the data acquisition between 11-18 April are provided in Table 4.6. Similar to the AIRSAR data for the Washita'92 experiment, site maps with U T M co-ordinates (NAD 27, Zone 14 S) have been provided for this data set. As discussed previously, ENVI 3.4 was used to determine the site 53  F i g u r e 4.4: Polarimetric composite image, S I R - C , 0 4 / 1 1 / 9 4 locations on the image by converting the U T M co-ordinates into corresponding pixel locations. T h e soil moisture estimation algorithms were applied to these sites to validate the performance and accuracy of the models based on the respective ground measurements for each site.  4.3.2  Ground Measurements during Washita'94  T h e test sites chosen for the Washita'94 experiment comprised of agricultural lands (winter wheat and alfalfa), rangelands, pastures, a n d bare fields. T h e site number, l a n d cover, soil bulk density, soil texture, vegetation water content, R M S height, and surface correlation length for each site are given i n Table 4.7. The volumetric soil moisture for the sites at each date was measured using the time d o m a i n refiectometry ( T D R ) technique (Section 2.2). T a b l e 4.8 gives a detailed list of these measurements.  54  Table 4.5: SIR-C System Characteristics [48] Parameter  L-Band  C-Band  Wavelength (m)  0.235  0.058  Resolution (m)  20 x 30  20 x 30  Swath Width (km)  15 to 90  15 to 90  Bandwidth (MHz)  10 to 20  10 to 20  Transmit Pulse Length (fjs)  33.8, 16.9 and 8.5  33.8, 16.9 and 8.5  Pulse Repetition Rate (pulses/s)  1395 to 1736  1395 to 1736  Look angle (deg)  17 to 63  17 to 63  Orbital Altitude (km)  225  225  Table 4.6: Incidence Angles for SIR-C [47] Date  Incidence Angle (Near)  04/11/94  28.0°  04/12/94  42.3°  04/13/94  50.1°  04/14/94  56.3°  04/15/94  60.2°  04/16/94  36.2°  04/17/94  30.9°  04/18/94  26.5°  55  Table 4.7: Site Characteristics [49] Site  Land Cover  S(%)  C(%)  p (g/cm )  11  Alfalfa  20.6  27.9  1.36  12  Bare  22.7  21.1  1.05  13  Winter Wheat  37.3  6.0  1.42  14  Range  29.6  13.6  21  Range  92.0  22  Range  23  3  b  W (kg/m ) s (cm) 2  c  L (cm)  0.8  11.3  3.4  13  1.37  0.8  6.0  1.01  0.1  0.7  8.8  0  1.14  0.09  0.9  10.6  92.0  0  1.24  0.12  0.7  11.0  Range  92  0  1.36  0.07  1.3  12.9  53  Winter Wheat  81  5  1.2  0.79  1.2  9.2  54  Pasture  84.9  5  1.15  0.09  0.8  12.8  55  Winter Wheat  81  5  1.39  0.82  0.7  11.5  1.8  Table 4.8: Average Volumetric Soil Moisture (m /m ) [49 17 18 15 16 13 14 Site 11 12 3  3  0.11  0.09  0.1  0.14  0.11  0.12  0.06  0.24  0.21  0.11  0.09  0.13  0.14  0.11  0.13  0.08  0.19  0.13  0.14  0.11  0.13  0.08  0.23  0.19  0.13  0.14  0.11  0.13  0.08  53  0.13  0.11  0.1  0.08  0.06  0.07  54  0.29  0.31  0.33  0.25  0.27  0.25  55  0.31  0.29  0.29  0.2  0.23  0.07  11  0.25  0.24  0.19  0.16  0.13  12  0.28  0.21  0.1  0.06  0.04  13  0.27  0.25  0.22  0.18  14  0.25  0.23  0.24  21  0.15  0.19  22  0.2  23  56  4.4  The Ottawa Greenbelt  The Ottawa Greenbelt covers 200 square kilometers of farms, forests and wetlands that surround Ottawa. There is no land development in the Greenbelt. The region has a temperate climate with a cold and snowy winter and a short, hot, and humid summer. Average temperatures are 11°C in January and 21°C in July. The areas over which data was acquired, i.e., the Ottawa Greenbelt Research Farm and the CFIA farm are located in the greenbelt and also house the Animal Research Facility. Fig 4.5 shows a map of this region.  4.5  The 2001 Field Campaign in Ottawa  The 2001 field campaign was conducted primarily by A A F C in cooperation with other government agencies and comprised of intensive ground data collection over the Green Belt Farm and CFIA field sites in Ottawa, Canada. The extensive field measurements were intended for research studies covering a wide spectrum of applications such as, analyzing crop growth and plant phenology , understanding the interaction between key factors affecting crop yield 1  and, soil and surface roughness estimation using remote sensing techniques. Three field campaigns were conducted during the 2001 growing season, i.e., on June 13 , June 26 , and July 19 to coincide with SAR data acquith  th  sitions. The SAR flights were conducted by the Convair-580 aircraft and were selected to coincide with the phenological growth stages of the crops. The CV580 carried the C/X-SAR system which acquired fully polarimetric SAR data over the specified region. Along with the SAR flights, the Compact Airborne Spectrographic Imager (CASI) was employed to acquire hyperspectral imagery over the same area. The selected fields were mostly homogeneous with a only few sites consisting of standing water and sandy patches. The weather conditions were dry with no rainfall before or during the data acquisition dates. ^ h e relationship between a periodic biological phenomenon and climatic conditions.  57  Figure 4.5: The Ottawa Green Belt Farm, 1:50,000 topographic map, 1998  4.5.1  CV-580 C / X - S A R data  The C/X-SAR system, carried by the Convair-580 aircraft, is an airborne SAR, developed by the Canada Centre for Remote Sensing. Since the commissioning of the C- and X-band SARs, in 1986 and 1988, respectively, the C/X-SAR system has undergone several upgrades, including improvements in real-time processing, more flexible imaging geometries, navigation, motion compensation processing, and a data recording unit. The C/X-SAR system is capable of operating in two different frequency bands, i.e., C- and X-bands. In the C-band, the radar is capable of operating in the polarimetric mode, thus enabling data acquisition for all four polarimetric channels during the campaign. Due to the non-availability of polarimetric data in the X-band, data was not collected at this frequency. The technical specifications for the C/X-SAR system are given in Table 4.9. For this work, the CV-580 data sets acquired over the G B F and CFIA fields were obtained under permission from AAFC. The data comprised of three different sets corresponding to Line-3 Pass-2 (L3P2) for June 26 , L3P2 for th  July 19 and L2P3 for July 19 again. Each data set consists of C-band data th  th  58  Table 4.9: C/X-SAR System Technical Specifications [50] Parameter  C-Band  X-Band  Frequency (MHz)  5300  9250  Wavelength (m)  0.057  0.033  Pulse Repetition Rate (Hz/m/s)  2.32 or 2.57  2.32 or 2.57  Chirp Length (us)  7  15  Estimated NECT° (dB)  -40  -30  in four different polarizations, i.e., HH, HV, V H and VV. The original raw data was processed and calibrated by CCRS and stored as single look complex (SLC) data for each channel separately. The standard format adopted by CCRS for storing the SLC imagery is known as the PolGASP format, where each pixel corresponds to a complex number and is written in big-endian format. The PolGASP files are essentially binary files with the file extension, .img and each file represents the data acquired at a specific date and polarization. The backscatter at a particular pixel can be obtained by computing the magnitude of the complex number and subsequently converting to a dB scale as shown below: If the complex value at a pixel is given as A + j B then, Backscattered Power in dB = 101ogi (.4 + B ) 2  0  2  (4.1)  The images stored in the PolGASP files are in slant range and comprise of 17577 samples and 788 lines. Further, it is interesting to note that these images are considerably stretched with a resolution of 4 m in range and only 0.4 m in azimuth. A polarimetric composite image (R:HH, G:HV, B:VV) of the data acquired on June 26 is shown in Fig. 4.6. The data has been multith  looked by a 10:1 averaging window in order to obtain square pixels for a better display. In order locate the specific test sites, a suitable method would be to use the U T M co-ordinates and convert them into corresponding pixel locations in the image using ENVI, as is done for both the SIR-C and AIRSAR data sets. However, for CV-580 data sets, along with the SLC data, a corresponding 59  Figure 4.6:  Polarimetric composite image of the O t t a w a G B F , C V - 5 8 0 ,  06/26/2001 geocoded image is also available. T h i s image provides a m u c h simpler and convenient way of locating the sites using the U T M co-ordinates.  For this  purpose, differentially corrected U T M coordinates ( N A D 8 3 d a t u m ) for the four corners of each site were provided in the d a t a report [52]. T h e p i x e l co-  (x,y), are located i n the geocoded images using the  ordinates for each corner, reference north, P , N  and reference east, P , E  values along w i t h the resolution  at each pixel (Aw x Al):  P  = pf  + [(x-1) * Aw]  P  = P?  + [ ( y - 1 ) * Ai]  E  N  where P  N  and P  E  (4.2)  are the north and east U T M co-ordinates specified for the  field corner. Site locations i n the S L C images are then m a n u a l l y located using the site locations i n the geocoded images as a guide.  GO  4.5.2  Ground Measurements  T h e test sites selected for this work include a l l the sample sites w i t h i n four different agricultural fields at which the ground measurements were recorded. T h e agricultural fields, as marked i n F i g 4.7, comprise of corn, wheat and soybean crops. T h e photographs of each crop type shown i n Figs 4.8-4.11, provide a general idea as to the height and thickness of the crops, as well as the vegetation water content based on the dryness of the plants. 5018500 — F25 — OF — 5018000  100N 60N  — ON Field 23 (Corn)  — Sandy  \  —Water Feature,  5017500  — Slope — F16 ra  — S o y Site 1  . .  —  |.5017000 \ * \  :o  15016500;  •5016000  0  Field 25 (Wheat): Eastside \  F23 — Corn Site 1  /  \  Soy Site 2  — Soy:Site3  — C o r n Site 2 — Corn Site 3 — Corn Site 4-.  Field IS (Soaay  — ADRI — Site 2 — Site!  5015500 • 439500  440000;  440500  441000  441500  442000  442500  Easting (m)  Figure 4.7: F i e l d locations for the d a t a collection [52] Three fields were located i n the G B F area; F i e l d 23, F i e l d 25 and F i e l d 16, while one field was located at the C F I A ; A D R I F i e l d . For each field a number of test sites were selected. W h i l e most of the fields were homogeneous, the wheat field (Field 25) consisted of a sandy patch and a part w i t h standing water. These regions were also included as test sites. T h e test site locations for each field are shown i n Figs 4.12-4.15. T h e d a t a recorded at each test site included: phenological stage, aboveground phytomass, plant height, plant density, vegetation water content, leaf  61  area index (LAI), fresh and dry biomass, surface RMS height and the TDR measurements for the volumetric soil moisture at depths of 5 cm and 10 cm. For this research, only the plant height, d,.vegetation water content, W , RMS c  height, s, and volumetric soil moisture, m are required and are listed for v  each test site for the two acquisition dates in Tables 4.10 and 4.11. It is important to note that since C-band radar has a wavelength of 5.66 cm, the penetration depth for the radar signal would not be more than its wavelength. Consequently, the volumetric soil moisture measurements taken at 5 cm depth are considered during the model validation. For the given test sites, the soil texture is, however, not provided. This implies that the Topp Model (Section 2.2) will be required for conversion from the dielectric constant to the soil moisture content during the implementation of the proposed models. In addition to the aforementioned ground measurements, the incidence angle, 6, at the centre of each field is required. This is determined using the Polarimetric Workstation (PWS) software package [51] and are also listed in Tables 4.10 and 4.11. For the sake of simplicity during the model implementations, the same incidence angle is used for the all the test sites within a particular field and is considered to be equal to the incidence angle measured at the centre of the field. The application and' performance of the soil moisture retrieval models using the described data sets, is discussed in the following three chapters.  62  Table 4.10: Vegetation parameters, measured volumetric soil moisture, surface roughness and incidence angle for the test sites on June 26, 2001 W (kg/m ) s (cm)  m (m /m )  Field  Site  d (cm)  Field 23  Site 1  50.45  0.4  0.974  0.18  Site 2  93.7  1.77  0.968  0.169  Site 3  113.3  2.48  0.966  1.94  Site 4  43.5  0.5  0.966  0.178  Field 25  2  c  3  v  0  (deg) 55.7  53.79  Sandy-1 97.7  0.594  0.965  0.197  53.7  2.7  0.96  0.167  Site 1  26.6  0.49  0.979  0.173  Site 2  27.6  0.54  0.977  0.142  Site 3  27.9  0.64  0.980  0.153  Site 1  58.17  0.04  0.923  0.179  Site 2  50.5  0.04  0.925  0.153  100%-2  3  Slope-3 Water-4 60%-5 no/ ft U/o-0  OF-7 Field 16  Field ADRI  63  52.27  51.26  Table 4.11: Vegetation parameters, measured volumetric soil moisture, surface roughness and incidence angle for the test sites on July 19, 2001 d (cm)  W (kg/m ) s (cm)  Field  Site  Field 23  Site 1  0.974  Site 2  0.968  Field 25  Field 16  Field ADRI  2  c  m (m /m ) 3  v  0  (deg) 56.05  Site 3  5.80  0.966  0.138  Site 4  3.34  0.966  0.167 0.211  Sandy-1  116.3  1.8  10096-2 Slope-3  107.5  2.9  0.965  95  1.6  0.951  0.206 0.16  Water-4  102.3  1.4  0.957  0.173  60%-5  96.5  1.2  0.96  0.138  0%-6  89.8  1.6  0.962  0.205  OF-7  97.3  2.0  0.965  0.161  Site 1  70.4  1.99  0.979  0.159  Site 2  69.7  2.14  0.977  0.178  Site 3  71.4  2.13  0.980  0.147  Site 1  163.28  3.14  0.923  0.152  Site 2  185.11  3.01  0.925  0.161  64  3  54.05  52.57  51.57  Figure 5.3: Photographs of corn crop in Field 23, Top Left: Overview of field June 26, average plant height is 75 cm; Lower Left: Overview of field on July 19, average plant height is 120 cm; Top & lowerright:Closer view of the crops on corresponding dates  65  Figure 5.3: Photographs of wheat crop in Field 25, Top Left: Overview of field on June 26, average plant height is 76 cm; Lower Left: Overview of field on July 19, average plant height is 101 cm; Top & lower right: Closer view of the crops on corresponding dates  66  Figure 5.3: Photographs of soybean crop in Field 16, Top Left: Overview of field on June 26, average plant height is 27 cm; Lower Left: Overview of field on July 19, average plant height is 70 cm; Top & lowerright:Closer view of the crops on corresponding dates  67  Figure 5.3: Photographs of corn crop in ADRI, Top Left: Overview of field on June 26, average plant height is 54 cm; Lower Left: Overview of field on July 19, average plant height is 174 cm; Top & lower right: Closer view of the crops on corresponding dates  68  Figure 4.12: Site locations for GBF field 23 (Corn)  Figure 4.13: Site locations for GBF field 25 (Wheat)  69  East.-,g (m) :  Figure 4.14: Site locations for GBF field 16 (Soybean)  : (440065.5.5016537.25)  ADRIsSel ~--:ADRTsite2  S.te#2  " Wheel Tracks  ~ A D R ! perimeter y ™ - . w . 5015232.75) - * - G*een FeatureVl  t - ^ o w DirectW' Green Fe sure E \v :.Wheel t r a c k s / : •  Wheel Tricks  •(439778.5016008.25)  433600  439700  439800  433900  440000  440100.  440200  -440300  'Easting  Figure 4.15: Site locations for CFIA field ADRI (Corn)  70  Chapter 5 Proposed Methodology and Implementation In this chapter two modified empirical models for soil moisture retrieval in bare as well as vegetated areas are introduced. As mentioned in Chapter 3, one of the popular approaches for developing models applicable to vegetated areas, is to incorporate vegetation effects into an existing model. The work presented in this thesis is based on the same approach and is discussed in the following sections.  5.1  Choice of an existing model  A critical review of all the suggested approaches for soil moisture estimation in bare soil areas was presented in Chapter 3. Since all the models tend to have their respective pros and cons, the selection of a particular model, for incorporating the vegetation effects, needs to be based on a good compromise between the applicability, simplicity and accuracy of the model. Among all the suggested approaches, the empirical model of Dubois et al. [1] tends to be a better choice. The Dubois Model was originally developed from both radiometer and scatterometer observations, collected at different bare-soil sites, and was subsequently tested for its validity and performance on airborne (AIRSAR) and spaceborne (SIR-C) SAR data. As a result, the model has been applied to data obtained from a variety of sensors (radiometer, 71  scatterometer & SAR) as well as from a number of different sites with varied soil moisture conditions, thus demonstrating its wide applicability. In comparison, the other models were developed/tested on data only from a single sensor or a single site (e.g. regression models), hence rendering their performance on data from other sensors or from sites with different soil moisture conditions, quite questionable. Furthermore, the higher sensitivity of radiometers to the presence of vegetation as compared to other active microwave sensors, and the applicability of the Dubois Model to radiometer data, may prove to be a vital factor influencing the performance of the model in vegetated areas. According to a comparative study, between the performances of the Oh, Dubois, and Shi models, done by Van Zyl et al. [53], the Shi Model shows excellent accuracy in estimation for smooth surfaces. However, when the surfaces become rough, the model significantly underestimates the moisture, giving poor results. Also, the Oh Model tends to underestimate the moisture consistently for wetter surfaces, and overestimates the same for drier surfaces, while, for the extremely rough surfaces, the model fails to produce any results. On an overall basis, the Dubois Model provides reasonable results in different moisture conditions and shows the best accuracy when the surface is rough. Further, the algorithm by Dubois et al. requires fewer measurable parameters, such as surface correlation length, brightness temperature, surface roughness and Fresnel reflectivity for estimating the soil moisture, thus, presenting lesser computational complexity and enabling a simpler implementation as compared to most models. Unlike the IEM Model, this empirical model does not require the knowledge of one surface parameter to determine the other. Though, the Dubois model, presents its own set of limitations (Section  3.2.3),  it provides the necessary balance between performance, accuracy, simplicity and applicability; and is thus chosen for this thesis work.  72  5.2  Performance of the Dubois model  Prior to presenting the methodology for introducing vegetation effects into the Dubois Model, it is desirable to observe the performance of the existing empirical model on the available data sets and its accuracy of estimation in both bare-soil and vegetated areas. The Dubois Model is initially applied to the available data sets, i.e., AIRSAR, SIR-C, and CV-580 data sets to obtain soil moisture maps of the regions over which the images were acquired. Fig. 5.1 shows the moisture maps for Washita'92 experiment between June 10-18. The model was applied to the data pixelwise, thus yielding the moisture at every pixel in the image. As per the color coding given by the moisture scales, the maps indicate wet conditions during the start of the experiment and subsequent drying of the soil over the period of data collection, which was actually the case. The soil moisture maps obtained from SIR-C data for the Washita'94 experiment between April 11-18, are illustrated in Fig. 5.2. Similar to the maps for Washita'92, these maps also indicate high levels of moisture at the beginning of the experiment followed by subsequent dry conditions during the data acquisition period. Furthermore, as mentioned in Chapter 4, the Ottawa Green Belt was quite dry during the CV-580 acquisitions on 26 June and 19 July 2001. This is evident from the dry conditions exhibited by the soil moisture maps shown in Fig. 5.3. In order to test the accuracy of the algorithm, it was applied to specific sites for both AIRSAR and SIR-C data at different dates. The sites chosen were mainly bare-soil areas and areas with a common type for vegetation (alfalfa) for both data sets. The accuracy was measured using the RMS (Root Mean Square) error between the estimated values and the actual ground measurements of the volumetric soil moisture. A large error indicates a lower degree of accuracy in the estimation and vice versa. Fig. 5.4 shows the the Dubois model is fairly accurate in estimating the soil moisture in bare soils by providing a RMS error of 6.6%, as was also observed by Dubois et al. in [1]. However, the performance of the model deteriorates in the presence of vegetation, leading 73  to a RMS error of 35.8%, as indicated in Fig. 5.5. Dubois et al. claim that the model provides good estimation results in areas with bare soil or short vegetation, i.e., regions with a cross-polarization ratio less than - l l d B , while errors increase in areas with more vegetation. Thus the objective of the proposed modelling approach is to incorporate vegetation effects such that the model performs with relatively greater accuracy in areas with  0-£ /cr° v  v  >  —  l l d B and has a result similar to the existing model for other  areas.  74  tOO  200  300  400  60 0  600  700  800  COO 1000  17 June  Figure 5.1: Soil moisture maps for the Washita'92 experiment, June 10-18,1992  75  16 April  17 April  Figure 5.2: Soil moisture maps for the Washita'94 experiment, April 11-18, 1994  76  26 June 2001  19 July, 2001  Figure 5.3: Soil moisture maps for the Ottawa Field Campaign, 2001  77  Measured vs. Estimated Soil Moisture  Figure 5.4: Scatter plot of measured and estimated volumetric soil moisture for the bare soil sites using the Dubois model  Measured vs. Estimated Soil Moisture  Figure 5.5: Scatter plot of measured and estimated volumetric soil moisture for the vegetated (alfalfa) sites using the Dubois model  78  5.3  Proposed approach  The Water-Cloud Model, developed by Attema & Ulaby in 1978, presents a simple approach to include the contribution of the vegetation as well as the soil backscattering coefficient into the existing empirical model. According to the water-cloud model, as already discussed in Section  3.3.2,  the total  power scattered at a co-polarized channel pp, a° , is the incoherent sum of p  the contribution of the vegetation, a° , and that of the underlying soil, of , eg  oil  which is attenuated by the vegetation layer. For a better visualization, each of the three backscattering contributions are illustrated in Fig. 5.6.  (D Direct Backscattering from Plants (2) Direct Backscattering from Soil (Includes Two-Hay Attenuation by Canooy) (D Plant/Soil Multiple Scattering  Figure 5.6: Backscattering contributions of a canopy over a soil surface, Source: [22] The equations representing the water-cloud model are given by (3.30),  (3.28)-  and are again mentioned here for the reader's convenience. For a given  incidence angle, 8, the backscatter coefficient is represented in the water-cloud model by the general form:  a  °  P  P  =  <eg  +  ^veg+soil +  ^ s o i l  t-) 5 1  where r is the two-way vegetation transmissivity. The second term in (5.1) 2  represents the interaction between the vegetation and underlying soil. Since 79  the interaction term is not a dominant term in the co-polarized returns [54] required in the implementation of the Dubois Model (Section 3.2.3), it can be neglected. Therefore, the water cloud model can be represented as: o° = <  + r <  (5.2)  2  e g  o i l  = AW cose(l-r )  o°  (5.3)  2  eg  T  C  2  _  e  (54)  (-2BW sec0) c  where W is the vegetation water content (kg/m ). A and B are parameters 2  c  that depend on the type of vegetation; A represents the vegetation scattering, B is the attenuation parameter. The type and geometrical structure of the canopy as well as the polarization and wavelength of the sensor are accounted for through these parameters. Both A and B are determined by fitting models against experimental data [6,7]. Over the years, several researchers have modified the water-cloud model in order to account for a variety of parameters affecting the backscatter. One such modification was done by Ulaby et al. in 1982 [37] and implemented by Magagi et al. in 1997 [55], where a term for the vegetation fractional cover, C was included in the equations. This term accounted for the spatial v  heterogeneity of natural areas with both vegetation and bare soil within the field of view. The modified equation can be given as: o°  pp  = (1 -  a ) <  o  i  + C>  l  (5-5)  v e g  Another modification was suggested by Bindlish et al. in 2001 [36] to account for the orientation and geometry of the vegetation. An exponential vegetation correlation function is proposed to model the geometric effect of the vegetation spacing within the water-cloud model and has been discussed in detail in Section 3.3.3. The equations are again mentioned here for convenience: <:  g  = <  e  g  ( i - o  (5.6)  Thus, (5.2) is modified to include the corrected vegetation contribution: <  P  =  <:  + ^ <oii 2  g  80  (5.7)  In the proposed algorithms, the water-cloud model, with the above modifications (separately as well as combined), has been implemented and applied on the three different data sets. As can be deduced from (5.2), the backscatter, o° , is now corrected for p  vegetation and can be used in the inversion model to obtain an estimate of the soil moisture. In order to compute o° , the vegetation backscatter, a° , is dep  eg  termined using (5.3), while the backscatter due to the soil, cr° , is determined oil  using two different methods as suggested by Ulaby et al. [14] and Dobson et al. [56].  5.3.1  Determining soil backscatter by regression  Based on the analysis of experimental data sets for bare soil, Ulaby et al. [14, 57] concluded that for a given radar configuration, the backscatter from the underlying soil can usually be expressed as a linear function of the surface soil moisture. <oii =  am  f  + b  (5.8)  where a & b are the linear correlation coefficients determined by a least mean squares (LMS) regression analysis between the backscatter and soil moisture content. Also, in order to account for the dependence of o°  oil  on the soil type,  the soil moisture is expressed in terms of m.f, the percent field capacity, mf  =  100  x  ¥c  =  g  1 0 0  x  F?t  ( 5  -  9 )  Here, m and m are the gravimetric and volumetric moistures of the soil, and g  v  FC and FC are the gravimetric and volumetric moistures of the soil at field g  V  capacity. Here, the field capacity is defined as the moisture content at |-bar soil tension, which is a measure of how tightly bound the water is to the soil particles. Empirical expressions, derived in [58], relate FC and FC to the g  V  soil textural composition: FC  g  = 25.1 - 0 . 2 1 5 + 0.22 C percent by weight FC  g  = 0.3 -0.0023 5 + 0.005 C gm/cm 81  3  (5.10)  where S and C are the percentage of sand and clay particles contained in the soil.  5.3.2  Determining soil backscatter using surface roughness  According to Dobson et al. [56], the surface scatter can be obtained as:  <oii  where  k  (kL) cos 9e^ ^  = 4 (k f  6  s  is the wavenumber in free space  4  \T \  kLsind  (2TT/X),  2  0  S  (5.11)  is the rms roughness,  L  is  the surface correlation length, r is the Fresnel reflection coefficient, and 8 is o  the incidence angle. The Fresnel reflectivity, r , can be obtained from the dielectric constant o  using (3.6) in Section 3.2.2. Both the HH and W backscatter are corrected for vegetation effects and further used in the inversion model, thus ensuring that the vegetation effects are incorporated into the model and accurate soil moisture estimates can be obtained. In addition to the concern for better soil moisture estimation in regions with larger amounts of vegetation, it is also desired that a retrieval algorithm should require minimum ground-measurable parameters as inputs and should rely on determining these parameters remotely. For this work, some of the required parameters were computed mathematically within the algorithm as opposed to using their ground measurements with the intention of retaining the essence of "remote-sensing". The parameters, as well as the methods involved in determining them, are discussed in the following sections.  5.3.3  Determining the transmissivity, r  2  The two-way vegetation transmissivity, r , forms one of the essential parame2  ters determining the vegetation backscatter in the water-cloud model as well  82  as its modifications (5.5)-(5.6). However, as shown in (5.4), the vegetation parameter, B, is required to calculate r , causing it to be dependent on several 2  vegetation characteristics measurable at the ground. Ulaby et al. suggested a dielectric model for the vegetation where, the vegetation transmissivity could be calculated as [8]: T = 4TT (d/X) lm[y/e^\  (5.12)  where d is the thickness of the vegetation layer (or, in other words, the plant height), A is the radar wavelength and e is the vegetation dielectric constant v  and can be determined by:  4  9  55  75 _ .18a' J 1 + J//18 7~  +  2.9  _  In the above relation, e is a nondispersive residual r  quency in GHz, a is the ionic conductivity in  +  1 + G//18) ' . (5.13) 0  c o m p o n e n t ,  S i e m e n s  per  5  / is the fre-  m e t e r ,  and both  Vf and Vb are the volume fractions of free water and bulk vegetation-bound w  water, respectively. According to regression curves obtained from a number of experimental data sets, it was concluded that the parameters in (5.13) can be computed by the following equations: m  = m p/[l - m (l - p)\  v  g  (5.14)  g  e = 1.7 - 0.74 m + 6.16 m r  g  Vfw = m (0.55m - 0.076) 5  g  2  (5.15) (5.16)  v = 4.64m /(l + 7.36 m )  (5.17)  o = 1.27  (5.18)  2  2  b  where m and m are the volumetric and gravimetric soil moisture contents, v  g  respectively. As compared to the (5.4), the only ground measurement required in the above dielectric model are the vegetation thickness, d, and the soil bulk density, p. This proves to be a better choice since the parameter B in (5.4), is 83  determined by regression analysis of several ground measurements. Also, it is expected that newer techniques involving optical and SAR data fusion will make the remote estimation of the vegetation thickness possible.  5.3.4  Determining the vegetation water content, W  c  In addition to the vegetation transmissivity, r , the vegetation backscatter also 2  depends on the vegetation water content, W . According to Jackson et al. [32], c  W can be determined from the normalized difference vegetation index (NDVI). c  NDVI is a measure of the vegetative cover and is generally calculated from reflectances measured in the visible and near infrared channels of hyperspectral imagery. The relation between the vegetation water content, W , and the c  NDVI is non-linear and derived by optimizing a polynomial function: If NDVI < 0.5 jy (kg/m ) = 1.91 (NDVI) - 0.31 (NDVI)  (5.19)  VF (kg/m ) = 4.29 (NDVI) - 1.54  (5.20)  3  2  c  If NDVI > 0.5 3  c  In this work, the NDVI is estimated using the cross-polarization ratio, (7^/(7^.  In [1], Dubois et al. provide a regression curve between  a^ /a° , v  v  and the NDVI for L-band data. Consequently, the regression curve, as shown in Fig. 5.7, can be used to determine the NDVI value corresponding to the cross-polarization ratio at a particular pixel in the image.  5.3.5  Determining the fractional cover C  v  The vegetation fractional cover, required in (5.5) in order to incorporate the vegetation effects into the backscatter, can be obtained remotely by the following relation [59]:  r U  _ / NDVI - NDVI \ " VNDVIveg-'NDVI.oJ soil  84  2  -u - " 0  |  ;  ti  o.i  i d,j  i  1  t>i  i  \  of  -it  NDVI  Figure 5.7: Regression curve describing the L-band a^/a^ of NDVI  ratio as a function  where NDVI corresponds to the vegetation index at a particular location at which the vegetation fractional cover, C is required. NDVI ] is the NDVI v  at bare soil, while N D V I  veg  soi  represents the NDVI at regions with maximum  vegetation. As per the definition of the NDVI (Section 5.3.4), it is quite obvious that the minimum value of the NDVI for a data set will approximately correspond to  NDVI ii, so  while the maximum will represent N D V I  veg  [59]. Consequently,  according to the regression curve (Fig. 5.7) used to determine the NDVI in this thesis work, N D V I  m a x  = 0.625 and N D V I  min  = 0.025. Hence,  / N D V I - 0.025 " ~ V 0-625 - 0.025  (5.22)  Once the NDVI is determined from the curve, the fractional cover, C , at v  each pixel can be obtained, thus enabling remote computations without the need for on-site measurements.  5.3.6  Determining vegetation sensitivity  In the Dubois Model, the cross-polarization ratio has been used for estimating the amount of vegetation at a certain pixel or site, i.e., the model was considered to be invalid for regions with  > -11 dB. An alternate approach for 85  indicating the extent of vegetation, suggested by Ulaby et al. in 1979, has also been implemented for this work. In this method, the vegetation-covered soil moisture sensitivity, S and the V  soil moisture sensitivity of bare soil, SB, are used to estimate the amount of vegetation, such that S ~ 0, represents the case where the vegetation completely V  masks the soil, while S ~ SB represents the situation where backscatter is V  dominated by the soil contribution. Consequently, pixels for which S < S V  B  may be considered as vegetated and vegetation correction can be applied only to these pixels. The following equations define SB and S [60]: V  S  B  =  (5.23)  4.34 a  ( 3fc) 1+  where a is the regression coefficient in (5.8), a°  eg  and a°  is determined by (5.8) or (5.11).  5.4  Implementation  oil  (5.24)  can be obtained using (5.3)  Based on the methodology discussed in Section 5.3, the vegetation effects are introduced into the empirical model using the water-cloud model or its modified versions, in conjunction with the approaches discussed for computing the required parameters. Subsequently, the proposed models are applied to the C-band, SIR-C images obtained during the Washita'94 experiment, L-band, AIRSAR images acquired during the Washita'92 experiment and the C-band CV-580 images acquired for the Ottawa Field Campaign in 2001 (Chapter 4). Initially, during the implementation of the proposed algorithm, the vegetation effects were introduced in both the HH and V V backscattering coefficients (as suggested in Section 5.3). However, experimental results indicate that this type of implementation does not provide good results and better results are obtained for vegetation correction being included only in the V V backscatter. Such an observation pertains to the fact that if vegetation in a given area is uniform with a strong vertical orientation, as is the case for the agricultural 86  sites in the given data sets, the vegetation effects will be dominant in the V V backscatter. This effect leads to a greater attenuation in W backscatter as compared to the HH backscatter. Based on the above premise, the vegetation correction is incorporated only in the V V polarized backscatter during the implementation of the proposed models. The first step in the implementation of all the models is a linear regression analysis of the measured V V backscatter, a° , and soil moisture content, m/, v  for each data set. The linear relation between the backscatter and moisture content for the AIRSAR, SIR-C and CV-580 data are given in (5.25) to (5.27), and illustrated by Figs. 5.8 to 5.10: = 2.596m/ - 12.68  (5.25)  S I R - C : < C = 0.0041m/ - 13.39  (5.26)  CV-580:  (5.27)  AIRSAR:  = 18.265 m / - 10.17  87  Backscattering coefficient as a function of soil moisture content  Soil moisture content, m  Figure 5.8: Regression analysis between <r and rrif for AIRSAR data w  These linear relationships are further used in the models, either to determine the backscatter from the underlying soil or to compute the vegetation covered soil moisture sensitivity, S , described in Sections 5.3.1 and 5.3.6. In v  the following sections, two different approaches for incorporating the vegetation correction into the Dubois Model are discussed. At this point it is important to mention that different combinations of the approaches in Section 5.3 were implemented to finally arrive at these models. The detailed discussion of these Backscattering coefficient as a function of soil moisture content Regression: m •o  -6  = 0.0041 m - 13.39 +  +  (  Q  April 94 Oct 94  + +  o at  -10 -12  •• • 1  m > >  "'"o  50  V  100  150  200  250  300  Soil moisture content, m  f  Figure 5.9: Regression analysis between a^, and rrif for SIR-C data 88  Backscattering coefficient as a function of soil moisture content  _,2<  I  0  1  5  10  1  1  15  1  20  1  25  1  1  30  Soil moisture content, m  35  '  1  40  45  50  (  Figure 5.10: Regression analysis between a^, and m/ for CV-580 data intermediate models is beyond the scope of this thesis and are presented in the form of flow charts (Figs. B.1-B.2) in the appendix, Appendix B, for the reader's reference.  5.4.1  Modified Empirical Model I  This model is formulated by incorporating vegetation effects in to the Dubois Model using the modified water-cloud model by Bindlish et al. [36] along with regression analysis for determining the soil backscatter [14]. In this model, the amount of vegetation is estimated by the cross polarization ratio, such that, vegetation correction is applied only for the sites where a° /oZ^ w  > —lldB.  The algorithm is illustrated by a flowchart in Fig. 5.11 and is summarized as follows [62]: 1. The average cr£ , o° , and <r£ are computed for the given site. cr£ and h  v  v  h  a^, are used in the equations of the original inversion model [1] to obtain an initial estimate of the volumetric soil moisture, m . v  2. The cross-polarization ratio, CT£ / cr° , is calculated and if it is greater v  v  than - l l d B then the vegetation correction is applied to the corresponding a^,, as described in the following steps. When cr^ / 0% < —lldB, the 89  estimate of m  obtained in Step 1 is considered to be the final value and  v  no vegetation effects need to be introduced in to the model. 3. The soil moisture content, rrif is computed from the initial volumetric soil moisture estimate, as given by (5.9) and (5.10). 4. The soil moisture content is then used in (5.26), i.e., the linear correlation equation, to determine  a° . oil  5. The vegetation parameters, W , A, B and a for the required site are c  obtained from the ground truth data and subsequently used in (5.3), (5.4) and (5.6) to determine a°* . g  6. The <7°  oil  and cr°* determined in Steps 3 <fe 4, are further employed in g  (5.7) to provide the total V V backscatter,  a^.  7. Finally, the full inversion model is run again using a° computed in Step v  5 and a^h fr°  m  Step 1, to obtain the modified values of m . v  Modified Empirical M o d e l II  5.4.2  In this model, the approach suggested by Ulaby et al. [14], is used for introducing vegetation effects into the Dubois Model. Also the methods discussed in Sections 5.3.2-5.3.6 are used for obtaining the soil backscatter, <r°  oil  and  the vegetation parameters. Furthermore, rather than computing the average values for the H H and V V backscatter, the model is implemented pixel by pixel and volumetric soil moisture is finally averaged to indicate the overall soil moisture for a particular site. Unlike the earlier model, in this model, the amount of vegetation is determined using the vegetation covered soil moisture sensitivity, S . V  A detailed flowchart indicating the steps involved in the implementation of this modified empirical model is shown in Fig. 6.3 and is summarized as follows:  1. The linear relationship between  and rrif given by (5.25) or (5.26) is  used to determine the bare soil moisture sensitivity, SQ and subsequently the vegetation covered soil moisture sensitivity, S  V  90  (Section 5.3.6).  2. If S « SB, the particular pixel is considered to be bare and the original V  inversion model is applied directly using cr£ and a^, to obtain the final h  estimate of the volumetric soil moisture. However, if S < SB, the V  amount of vegetation is large and vegetation correction is included into the model, as discussed in the following steps. 3. The vegetation parameters, W , A, and r are required to compute o° in 2  c  eg  the modified water-cloud model. The vegetation water content W is dec  rived from the NDVI as discussed in Section 5.3.4, while A corresponding each land cover type is obtained from the ground truth. The vegetation transmissivity, r is computed from the method given in Section 5.3.3. 2  4. Once the vegetation backscatter, cr° , is calculated, the next step is to eg  compute the soil backscatter, a° . oil  In this model,  <7°  oil  is determined  using Dobson's model given by (5.11). Here, the Fresnel reflectivity, R and the surface roughness, s are calculated by applying the original Dubois Model to the measured values of a£ and a° , while the surface h  v  correlation length, L, can be determined from the ground measurements available for each data set in Chapter 4. 5. The o°  oil  and  <7°  eg  determined in the Steps 3 &; 4, are further employed  in (5.5) to provide the total, vegetation corrected V V backscatter. The vegetation fractional cover, C , can be calculated from the NDVI as given v  in (5.22). 6. The full inversion model is run again, using the corrected a^, and the measured cr£ , to obtain the modified value of m . h  v  7. Finally, the volumetric soil moisture values corresponding to all the pixels within the given site are averaged to indicate the soil moisture content for the entire site.  91  5.4.3  A p p l i c a b i l i t y of t h e modified e m p i r i c a l models  The implementation and subsequent validation of the aforementioned approaches requires their application to actual SAR data. However, prior to implementing these algorithms on the available data sets, it is necessary to ascertain the applicability of a certain model to a particular data set. This decision is primarily governed by the availability of required parameters within a data set to enable successful implementation of the models. The SIR-C data, collected during the Washita'94 experiment, provided with most of the vegetation parameters such as, W , A, B and a and are listed c  in Table 5.1. Also, sufficient information with regard to the soil composition and the soil bulk density, p, is included in the ground truth report. However, the data lacks the measurements of the vegetation thickness, d, as well as the surface correlation length, L. Furthermore, the data is C-band and is not provided with relevant hyperspectral data. As a result, it is not possible to determine the NDVI and subsequently use it to obtain the vegetation water content W and the vegetation fractional cover, C . These characteristics renc  v  der the data suitable only for validating modified model I and hence modified model II is not applied to this data set. Table 5.1: Vegetation parameters used in the empirical model [6] Land Cover  A  B  a  Alfalfa  0.0012  0.091  2.12  Bare Soil  0  0  0  Winter Wheat  0.0018  0.138  10.6  Rangeland  0.0009  0.032  1.87  0.0014 0.084  1.29  Pasture  On the other hand, the AIRSAR data, unlike the SIR-C data, is L-band and the NDVI can be easily derived in order to determine the vegetation water content as well as the vegetation fractional cover. Additionally, the data set also includes detailed pixelwise information for the NDVI. Among the vegetation parameters listed above, the ground truth report provides measurements of W and d for each crop type. Further, the soil bulk density, surface correlac  92  tion length and the soil composition are well documented for this data set. The only drawback for the AIRSAR data is that other vegetation parameters such as A, B and a are not available, thus making the model partially unsuitable for application of modified model I. By partially, it is meant that if the vegetation parameters are assumed to be the same based on the fact that both the SIR-C and AIRSAR images were acquired for the same region (Little Washita Watershed), model I can be applied to the AIRSAR data. Consequently, this data set is used for assessing the performance of both models. The CV-580 data is also provided with a detailed ground truth report which includes soil moisture and surface roughness measurements (Tables 4.10,4.11) as well as the vegetation water content, W , and vegetation layer thickness (or c  plant height), d. However, the parameters such as the soil bulk density, soil texture/composition, surface correlation length, L, and the vegetation parameters A, B and a are not documented and thus, unavailable for use in the proposed models. Also, the CV-580 data is C-band and appropriate hyperspectral data is also not provided with the data. Table 5.2: Vegetation parameters used in the vegetation corrected model for CV-580 data [6] a L (cm) A B Site Land Cover 25  Wheat  0.0018  0.138  0.96  2.4  23  Corn  0.0012  0.091  2.12  2.55  16  Soybean  0.0014  0.084  0.98  2.6  ADRI  Corn  0.0012  0.091  2.12  2.8  Based on the content of available information, this data set consists of the least amount of pertinent ground truth as compared to both the SIR-C and AIRSAR data sets. Therefore, the data does not prove to be completely suitable for verifying the accuracy of any of the two models. However, by assuming the vegetation parameters, A, B and a to be similar to those for the SIR-C data set, it is possible to apply model I. Also, by estimating the values for correlation length, it would be possible to compute the soil backscatter using Dobson's model in Section 5.3.2. Consequently, the CV-580 data is used to validate a conjunction of approaches used in both models. The vegetation 93  parameters for each crop type as well as the estimated surface correlation length for each field are given i n Table 5.2  94  Measured average a ,*. o*„ and 0  Dubois Mgdelwithno vegetation correction Volumetric soil moisture, m» Calculate Field Capacity, FC + Soil Moisture Content, rnt Regression  " " s o i l = a m, -  b  Calculate o-° / a". hv  (^^CT°hv/a°  vv  No > -I  Apply original Dubois Model  I d B ? ^ ^ .  'Yes; Obtain ground measured parameters from  Vegetation correction for a°»v  Modified Water-Cloud Model (Attoma & Ulaby + Bindlish etal.) a  vv-  a  veo  +  TO  s 0  il  Vegetation corrected o° » + : measured o ° v  hh  Dubois inversion model (with vegetation correction due to  o ) a  w  DielectncGonstant, £ Hallikamen Model to obtain m* from € using soil texture information  Volumetric Soil; Mbisture>,/my  Figure 5.11: Schematic flowchart of Modified Empirical Model I  95  MeasuredCT° and o°„ per pixel hh  Dubois Model with no vegetation correction ^Volumetric soil moisture, m„ Calculate Field Capacity, F C Soil Moisture Content, nit Regression  S = 4.34 a B  Calculate S  v  No.  Apply original Dubois Model  Yes Calculate vegetation parameters, r , W Use ground measured estimate for A 2  c  Vegetation correction for o°v«  Parameters Obtain soil backscatter.a |, using Dobson model  Calculate the fractional cover C  soi  v  Modified Water-Cloud Model (Attema & Ulaby + Ulaby ef al.) ff'iv  =  C»a v 0  + (1 - C )o" ji 0  eB  v  1O  Vegetation corrected a%» + measured 0% Dubois inversion model (with vegetation correction due to a ) w  Dielectric Constant, £ Hallikainen Model to obtain m from £ using soil texture information v  Volumetric Soil Moisture, m  v  Figure 5.12: Schematic flowchart of Modified Empirical Model II  96  C h a p t e r  R e s u l t s  6  a n d  D i s c u s s i o n  In this chapter, the results obtained from the implementation of the two proposed algorithms are presented. These algorithms, as discussed in Chapter 5, are developed with the objective of accurately estimating the soil moisture in vegetated areas. Since both algorithms are essentially the vegetation corrected forms of the empirical model suggested by Dubois et al., their performance and accuracy have been compared to that of the existing Dubois Model.  6.1  Illustration and explanation of results  The data sets used to test the accuracy of the proposed models include C-band, SIR-C data acquired during the Washita'94 experiment; L-band, AIRSAR data acquired during the Washita'92 experiment; and the C-band, CV-580 data acquired during the Ottawa field campaign in 2001 (Chapter 4). Both the modified empirical models I & II were applied to the above data sets. The comparison between the results of the existing Dubois model and the suggested approaches is based on the correlation coefficient and the RMS (Root Mean Square) error between the estimated volumetric soil moisture and the actual ground measurements for each model. A brief discussion of these statistical parameters is given in the following section.  97  6.1.1  Correlation coefficient and R M S error  The correlation coefficient is a measure of how well the predicted values follow the actual values. In other words, it is a measure of how well the predicted values from a forecast model "fit" the ground measurements. The correlation coefficient is a number between 0 and 1. If there is no relationship between the predicted values and the actual values, the correlation coefficient is 0 or very low (the predicted values are no better than random numbers). As the strength of the relationship between the predicted values and actual values increases so does the correlation coefficient. A perfect fit gives a correlation of 1.0. Thus, higher the correlation coefficient, the better. If P and A represent the predicted and actual values, respectively; while P  m  and A  m  are the respective means, then the correlation coefficient, often  denoted as R, can be computed as follows:  5 a a  =  (  5 a p  = X ) (A - Am) (P - P )  A  -  A  -)  2  M  R = J-^Sy 5  a a  (6.3)  (6.4)  Spp  The Root Mean Square (RMS) Error, in essence, is a kind of generalized standard deviation and is obtained as the positive square root of the mean square error. The mean square error is calculated as the mean square of the difference between any quantity and an approximation. As a result, the R M S error can be computed by the following relation: R M S E = l ( b 4 - P|)  2  (6.5)  where A and P denote the actual and predicted values and N is the number of observations (in this case, sites). Ideally, it would be desirable to develop a soil moisture estimation model providing a correlation coefficient of 1 and zero R M S error. However, consider98  ing more practical applications, a retrieval algorithm with R ranging between 0.9 to 0.95 and RMS error below 3% may be considered to provide sufficiently accurate soil moisture estimates. Based on the review of current literature, the vegetation corrected model developed by Bindlish et al. [6] provides the best soil moisture estimation results using SAR data. A considerably high correlation of 0.95 is obtained using this model, provided that the orientation and geometry of the vegetation is taken into account during the implementation. However, if this information is not available, the model is unable to perform as efficiently as the previous case and provides a sufficiently good correlation of 0.87. The performance of the models proposed in this thesis are also compared to the above results obtained by Bindlish et al. It is necessary to keep in mind that the results are compared based on the availability (R = 0.95) or unavailability (R = 0.87) of the orientation and geometry of the vegetation.  6.1.2  Modified Empirical Model I  The methodology used in the development of this model as well as the steps of implementation are described in Chapter 5. This model was applied to the Cband, SIR-C data as well as the AIRSAR data. As mentioned in Section 5.4.3, the availability of necessary parameters renders the SIR-C data appropriate for the validation of Model I. However for the AIRSAR data, the vegetation parameters are assumed to be same as those specified for the SIR-C data set. Also, the proposed model is applied only to the specific sites for which the land cover description and the actual, ground measured, soil moisture values are available. The detailed list of these sites is given in Tables 4.3 to 4.8 (Chapter 4). Figs. 6.1 and 6.2 illustrate the overall results obtained by applying Model I to the SIR-C and AIRSAR data sets, respectively. These results present a comparison between the original Dubois Model and the modified model based on the measured and estimated values for volumetric soil moisture. Each symbol, in the figures, represents the soil moisture estimates for the all the sites listed for a particular data set, at a certain date. Additionally, the two different colors used for the symbols are indicative of a site being vegetated 99  (green) or bare(brown). The 45° black line represents the ideal case (R = 1, RMSE = 0) where the estimated and measured values are equal and lie on the line. As can be observed from Fig. 6.1(a), the Dubois Model is far from being ideal. However, for certain sites, the estimates, denoted with brown colored symbols, appear to be quite close to R = 1. This is indicative of the fact that the Dubois Model provides good estimation results for bare-soil regions and maintains this trend for all the five days. Apart from these measurements, the remaining estimates are completely scattered, thus proving the poor performance of the Dubois Model in vegetated regions. A total correlation of R = 0.58 and RMS error = 7.8%, can be computed for the Dubois Model, with all the 10 different sites taken together. On the other hand, for the AIRSAR data, as shown in Fig. 6.1(a), the Dubois Model provides a correlation of 0.77 and an RMS error of 2.5%. A higher correlation coefficient and a significantly lower RMS error for the AIRSAR data may be attributed to the fact that out of the four sites used for the validation, two are bare-soil sites. As a result, the ability of the Dubois model to perform well in bare-soil regions tends to dominate 50% of the AIRSAR results. During the implementation of the modified model vegetation correction was applied only for vegetated regions, while the soil moisture estimates for bare-soils are same as those obtained by applying the existing Dubois Model. In comparison to the original model, the estimation results for the modified empirical model I, as shown in Fig. 6.1(b), provide a total correlation of R = 0.81 and RMS error = 5.6%. Further, the measurements in the scatter plot are significantly closer to the ideal case. It is evident that, for the SIR-C data set, the incorporation of the vegetation effects into the Dubois Model has led to increased accuracy in soil moisture estimation. However, in accordance to the results in Fig. 6.2(b), no significant improvement can be observed on applying Model I to the AIRSAR data. The correlation remains the same as that obtained for the Dubois model, while the RMS error decreases only by 0.02%. One of the major reasons for the poor performance of Model I when applied to AIRSAR data maybe be due to the fact that accurate measurements for the vegetation parameters are not available for this data set and these values are assumed to be similar to those for the SIR-C data. Consequently, vegetation 100  correction seems to be ineffective on the AIRSAR data and the results are almost similar to those obtained for the original empirical model. When compared to the results obtained by the model proposed by Bindlish et al., the modified model I does not perform well. Since, the information regarding the orientation and geometry are also available for the SIR-C data, a correlation of R = 0.81 falls short in comparison to a correlation of R = 0.95 provided by the Bindlish model. Furthermore, it is important to note that the measurements obtained for the proposed model have a negative bias (Fig. 6.1). According to studies done by other researchers, this under estimation of soil moisture can be attributed to the use of the water-cloud model. Since the modified water-cloud model suggested by Bindlish et al., used here, does not essentially change the original water-cloud model and only adds an extra equation to it, it may be concluded that the negative bias is due to the implementation of the water-cloud model for vegetation correction. The implementation and validation of Model I was followed by further development of intermediate models, which were developed by combining new approaches with the first model. These models proved to be the stepping stones in finally arriving at modified model II. The results obtained for these models are given in Appendix B (Figs. B.3 to Figs. B.4).  101  (a)  Measured vs. Estimated Soil Moisture Correlation = 0.58  :0.3  I ;  RMS Error = 7.8%  \ i  £ £  0.25  2  Q:  :f  :  :  •  0 x  o  1-1 Apill 11 April 12 April 13 April 10 April 17;  ,0o  0,2  'O:  Soil  •2-  0.15  o 13 £  1 0.1  Ul  0  4*  Measured Soil Moisture (cm /cm ) 3  3  Measured vs. Estimated'Soil Moisture  (b)  Correlation = 0.81 :  RMS Error = 5.6%  O  0 X  o A  • -1 April 11 April 12 April 13 April 10 April 17  ..  o 2 O 0.15 CO •b  ra  a-  S.  E  Tr IU  o.i  0  o  Measured Soil Moisture (cm .'cm ) 3  3  Figure 6.1: Scatter plot of measured and estimated volumetric soil moisture for the sites in C-band, SIR-C data (Table 4.7) using: (a) the original Dubois Model (b) the modified empirical model I. Green represents vegetated sites and, brown represents bare-soil sites.  102  (a)  Measured vs; Estimated Soil Moisture . . . . -1-1  Correlation = 0.77  o  Jim'ft 10 >'Jurie<1_3 June 14 jillie 16 Jlllie;18  *+*: • O X. O  June 10 June 13 June 14 .June. 16 June 18  •  o  RMS Error = 2.53%  X  x  0.5  &  x>  Mb  o  +  0  O *  .  • •  B  ™ 0.3 !•  Oy  +  • 0.1  0.2  0.3  0.4  :0.5  0.7.  0.6  0.8  0.9  Measured Soil Moisture (cm ,'cm ) 3  3  Measu red; vs? Estimated SoilMoisture  (b)  Correlation = 0.77 RMS Error = 2.51%  o O  0  o  +  x  0  T3  0.1  .0.2  0.3  0.4  :0.5  0.6.:  0.7:  0.8  0.9  :  Measured Soil Moisture (cm .'cm ) 3  3  Figure 6.2: Scatter plot of measured and estimated volumetric soil moisture for the sites in L-band, AIRSAR data (Table 4.3) using: (a) the original Dubois Model (b) the modified empirical model I. Green represents vegetated sites and, brown represents bare-soil sites.  103  6.1.3  M o d i f i e d E m p i r i c a l M o d e l II  As mentioned earlier in Section 5.3.2, in addition to the accurate estimation of soil moisture in vegetated regions, the objective of this work is ensure the minimum requirement of parameters determined from ground based measurements. Since the modified empirical model I provided promising results for vegetated areas, further modifications were introduced within this algorithm, thus leading to the development of modified model II. The modifications included the estimation of vegetation sensitivity to determine the extent of vegetation at each pixel; and the remote computation of vegetation transmissivity, r and 2  the vegetation water content, W . c  Furthermore, in addition to the use of inaccurate vegetation parameters, another explanation for the inefficient performance of modified model I for the AIRSAR data, may also be due to the fact that regression analysis is used to determine the soil backscatter,cr° . This analysis, in actual terms, is based oil  on the soil moisture values derived from the initial application of the Dubois Model (Section 5.4) and hence may lead to the inclusion of errors. The use of this linear regression equation is eliminated by using the approach suggested by Dobson et al. [56], where the surface roughness, Fresnel reflectivity and surface correlation length are employed in order to determine the soil backscatter. Also, in order to rectify further problems due to the negative bias introduced by the water-cloud model, the modified water-cloud model suggested by Ulaby et al. [14] is used for the purpose of implementing the vegetation correction. A detailed flowchart has been shown in Fig. 6.3. The model was applied pixel wise to the specific sites in the L-band, AIRSAR data and, the soil moisture estimate for each site was subsequently determined by averaging the estimates obtained for each pixel. The choice of this data set is governed by the fact that the computation of the NDVI, as per the method described in Section 5.3.4, is possible only for L-band data. The NDVI is further required to obtain W . A list of the sites used, their land c  cover type and the corresponding ground measurements for soil moisture, is given in Tables 4.3 k, 4.4. Figs. 6.3(a) & (b) show the results obtained when the existing Dubois Model and the modified empirical model II are applied to the AIRSAR data set. 104  The performance of the Dubois Model is the same as shown in Sections 6.1.2. However, as can be observed in Fig. 6.3(b), there is a considerable increase in the accuracy of estimation for the modified empirical model II, as compared to Model I and the intermediate models (see Appendix B). The measurements, though not representing the ideal case, have moved much closer to the black line, resulting in a correlation coefficient of R = 0.89 as opposed to R = 0.77 obtained for the original model as well as modified model I. Further, there is a sufficient drop in the RMS error from 2.5% for the Dubois Model to 1.4% for the proposed model II. The results, thus, signify that the introduction of alternate techniques for incorporating the vegetation correction, i.e., obtaining the soil backscatter using Dobson's model, and determining the extent of vegetation through the vegetation covered soil moisture sensitivity provides a good estimation accuracy and does not deteriorate the performance of the model. Also, remote computation of the vegetation parameters, as opposed to assuming these values to be same as that for the SIR-C data, leads to the effective inclusion of the vegetation correction into the model. Furthermore, another striking fact about this model is that it does not produce an under estimation in the soil moisture measurements, as was in the case of the modified empirical model I. This is mainly due to the fact that this model uses the modified water-cloud model suggested by Ulaby et al. which completely modifies the original water-cloud model by introducing the vegetation fractional cover C as the weighting factor. v  In comparison to the Bindlish model, the modified model II fairs quite well. For similar conditions, i.e., unavailability of the vegetation orientation and geometry, Model II performs slightly better with R = 0.89, as opposed to R = 0.87 for the Bindlish model.  105  (a)  Measured vs; Estimated Soil Moisture -1-1  Correlation = 0J7 RMS Error = 2.53% 0.7 -  x 0  E  H-0 . 6 & .3  0.5 -  O  «  0.4 •  ro.  0.3 •  s  o  +  •  Juna;lO °Jnne-13 . Junft'14  o  ..Jtin&:18  oX  1G  .  o  O  X  0  a  ';§'  w  02 -  .0.2  0.3  :0:s  0.4  0.6  0.7  0.8  0.9  Measured Soil Moisture (cm /cm ) 3  3  Measured vs. Estimated Soil Moisture ----- r - 1  Correlation = 0.89  4^ •  RMS Error = 1.4%  :  ' *  . *  L:,,.:0^  1  r  3;  0.1  - x  v  0.2  •  ......i  •:  y  0.3  0.4  June 10 Juno 13  0  June II  X O  June 16 Jime.18  •  *  0.5  0.6:  0.7  Measured Soil Moisture (cm /cm ) • + 3  Q.Q  0.9  3  Figure 6.3: Scatter plot of measured and estimated volumetric soil moisture for the sites i n L - b a n d , A I R S A R data (Table 4.3) using: (a) the original Dubois M o d e l (b) the modified empirical model II. Green represents vegetated sites and, brown represents bare-soil sites.  106  6.2  Results from CV-580 data  In accordance to the discussion in Section 5.4.3, due to the unavailability of required ground measurements, neither of the proposed models can be completely applied to the C-band, CV-580 data set. Consequently, a combination of approaches used in the above models, was applied to this data set. These approaches include: • using the modified water-cloud model suggested by Bindlish et al. from Model I • determining the extent of vegetation at a particular pixel by computing the vegetation sensitivity, S  v  • using Dobson's model, rather than the regression equations, to obtain the soil backscatter, a°  oil  For the CV-580 data set, the vegetation parameters required in the watercloud model cannot be determined remotely, since the soil bulk density, pb, for the given sites is not documented in the ground truth report. As a result, the vegetation parameters are assumed to be the same as that for SIR-C data. Also, as mentioned earlier, the surface correlation length was estimated and the values are given in Table 5.2 for each site. The vegetation corrected model obtained by the combination of the aforementioned approaches was applied pixelwise to each field as a whole (Case I) as well as to each test site within the fields (Case II). On an average, each field comprises of 200,000 pixels, while each test site consists of 350 pixels. The soil moisture estimate shown in the results is an average of the moisture values obtained at individual pixels. The results for both cases are illustrated in Figs. 6.4 and 6.5. At this stage it is important to note that the results obtained for the CV-580 data are only for two different dates, as opposed to four to five different dates for AIRSAR and SIR-C data. As a result, the number of sample points for computing the correlation are not sufficient and consequently, the correlation coefficient can not be considered as an useful parameter to gauge the performance of the model. The accuracy of the model  107  is, therefore, discussed based on the RMS error between the measured and estimated volumetric soil moisture. As can be observed in Fig. 6.4(a), for Case I, i.e., when the Dubois model is applied to the entire fields, the model performs reasonably well by providing a RMS error of 7.3%. In comparison, the scatter plot obtained by applying the vegetation corrected model, as shown in Fig. 6.4(b), indicates a significant improvement with a RMS error of 2%. On the other hand, for Case II, the estimation results for the original Dubois model, as illustrated in Fig. 6.5(a), leads to an error of 8.4%, while the estimation accuracy for the vegetation corrected model does not seem to improve and the RMS error increases to a value of 10.3%(Fig. 6.5(b)). However, it is worthwhile to note that on applying the modified model to the each test site, the distinct positive bias in the moisture estimates obtained with the bare-soil model, is removed. This positive bias (or overestimation of moisture values) observed for the original Dubois model, is in fact contrary to the model's expected performance. As discussed in Section 3.2.3, for vegetated regions the model tends to underestimate the soil moisture and a negative bias is expected in the scatter plots between the measured and estimated values. Consequently, these results may be attributed to the fact that the data may not be well calibrated, since CV-580 is a difficult platform to calibrate. Also, averaging the soil moisture over 350 to 200,000 pixels may lead to a bias due to soil variability effects. The above results tend to raise several questions regarding the relative performance of the same model in the two cases. The first issue to be addressed is the wide difference between the results for Cases I Sz II. This may be attributed to the fact that each test site within a single field is different from the other, leading to statistical variability within each field. The variability between the test sites, within a certain field, is particularly due to significant variations in the measured soil moisture and plant height within a single field. Such variations are observed especially in the wheat and corn field. Also, the vegetation water content differs by a large extent between the test sites, which in turn would affect the vegetation correction applied. Consequently, by averaging for the entire field, the statistical variability is reduced and the model tends to be more accurate. This observation is in concurrence with the observation by other researchers that the Dubois and Shi models perform better on 108  multi-looked data, as compared to single look data. The next concern is the significant increase in the RMS error for the estimation results when the vegetation corrected model is applied to each test site. One of the reasons for a lower degree of accuracy is that for certain sites, the HH backscatter, <r£ , is larger than the V V backscatter, rj^. According to the h  limitations of the Dubois model specified in [1], for effective implementation of the model, the co-polarized ratio, a^/a^,  should be less than 1. Since, the  vegetation corrected model is based on the Dubois model, for good estimation results  fj^  must be greater than  crjj . h  However, this effect is more pronounced  in Case II rather than in Case I, which may, yet again, be due to the fact that, in Case I, singular characteristics of one site are eclipsed by another. In an interesting observation for the results for the vegetation corrected model, it is found that when  cr£  h  <  for a particular test site, the model  performs really well and the estimation accuracy is better than that of the bare soil model. For example, for Site 2 in Field 17 (ADRI: Corn) with a^ = h  —14.05 dB and a^, = —13.55 dB, the volumetric soil moisture, m„, estimated by the vegetation corrected model is 0.14 and the m estimated by the Dubois v  model is 0.26. The soil moisture measured at the ground for this test site is 0.15, thus indicating that the modified model performs considerably well when  ^ h h  < c  Finally, it is important to discuss how the accuracy of the vegetation corrected model depends on different parameters. Since, the water-cloud model used, was same as that used in Model I, this model is also sensitive to accurate measurements of the vegetation parameters. The availability of accurate measurements would ensure a better performance for the model. Furthermore, Dobson's model used for computing cr° , is extremely sensitive to the surface oil  correlation length. For small variations in the surface correlation length, significant variations in the estimation accuracy was observed. This observation indicates that C-band data, due to its shorter wavelength, is considerably more sensitive to roughness variations as compared to soil moisture changes. Also, measuring correlation length accurately at the ground is a delicate task due to its high variability throughout the growing season. For this data set, due to unavailability of ground measurements, values of surface correlation length providing the best vegetation correction to the data, are used. 109  Measured vs. Estimated Soil Moisture r»1 June 26  :0  July 19  Measured Soil Moisture (cm /cm ) 3  3  Measured vs. Estimated Soil Moisture  ---- r - 1 +  b  o.os  0.1 C.15 02 Measured Soil Moisture (cm /cm ) 3  0.25  June 26: July 19  OJ  3  Figure 6.4: Scatter plot of measured and estimated volumetric soil moisture for the entire fields i n C-band, C V - 5 8 0 data (Table 4.10 & 4.11) using: (a) the original Dubois M o d e l (b) the vegetation corrected model  110  t-i — + June 26 6 July 19  Measured Soil Moisture (cm /cm ) 3  3  Measured vs: Estirhated'Sdil Moisture: — . . .  +  o  T-1  June 26 July 19  Measured Soil Moislure (cm-/cm j 3  Figure 6.5: Scatter plot of measured and estimated volumetric soil moisture for different test sites in C-band, CV-580 data (Table 4.10 &: 4.11) using: (a) the original Dubois Model (b) the vegetation corrected model  111  A l g o r i t h m pros a n d cons  6.3  The promising results obtained by the implementation of both the modified empirical models I & II using AIRSAR and SIR-C data, would lead to an obvious question — which model is better and why? An attempt to answer this question is made through a critical review of the proposed models, as given below.  6.3.1  Pros  1. Both the models incorporate vegetation correction into the V V backscatter, thus improving the overall soil moisture estimation accuracy. 2. Model I involves lesser mathematical complexity and is thus simple in its implementation. 3. Soil backscatter is determined using regression in Model I, thus eliminating the need for surface correlation length for obtaining the soil backscatter as was suggested by Dobson et al. [56]. 4. Since Model I uses the modified water-cloud model proposed by Bindlish et al. [36], it accounts for the orientation and geometry of the vegetation. 5. Model II introduces the remote computation of several ground measurable vegetation parameters, thus requiring minimum on-site measurements for implementing the model. 6. Unlike Model I, Model II is not based on regression to compute the soil backscatter.  It employs the method suggested by Dobson et al.;  regression is only used to estimate S . v  7. Model II proves to be more adaptive since it estimates the amount of vegetation at every pixel and applies the vegetation correction accordingly. 8. The use of fully polarimetric data in both models, provides the linear cross polarization, HV, as an additional channel of information.  112  9. Since the water-cloud model modified by Ulaby et al. [14] is used in Model II, under estimation is not observed in the soil moisture measurements and the nature of the distribution remains quite similar to that of the original Dubois Model.  6.3.2  Cons  1. Model II is a combination of several approaches and leads to tedious mathematical computations in its implementation. 2. Since Dobson's approach for computing the soil backscatter is employed in Model II, it requires the prior knowledge of surface correlation length. 3. The orientation and geometry of the vegetation are not accounted for in Model II since the modified water-cloud model suggested by Bindlish et al. is not used. 4. A look-up table is used in Model I for determining the required vegetation parameters. The model does not employ approaches for the remote calculation of these parameters, as is the case for Model II. 5. The computation of soil backscatter is based on regression in Model I. 6. Model I utilizes the information available through the HV channel to determine the cross polarization ratio, which is subsequently used to determine the extent of vegetation at a particular site. Unlike, Model II, this model does not use the HV polarization for any other purpose, rendering less utilization of information available in multi-polarized data. 7. As discussed in Section 6.1.2, Model I produces a significant under estimation in the soil moisture measurements. 8. Model II could be tested for its validity only on L-band data due to the method used to compute the NDVI (Section 5.3.4)  From the above discussion, it is apparent that settling on a single, best model is not a trivial task. Remote determination of vegetation parameters and the simplicity of implementation have been two major concerns in the 113  development of the models. From the above review, it is evident that both concerns do not go hand and hand and it is necessary to compromise one for the other. However, as compared to the advantage offered by the remote computation of required parameters in order to minimize the dependence on laborious ground measurements, the mathematical complexity of a model does not pose to be a serious concern with the increasing availability of faster processors. A detailed discussion of the conclusions and future work is presented in the next chapter.  114  Chapter 7 Conclusions and Future W o r k 7.1  Conclusions  The primary objective of this work was to develop a simple and accurate empirical model for effective soil moisture estimation in regions with considerable amounts of vegetation using polarimetric SAR data. In addition, it was also desired to remotely compute the vegetation parameters, required to incorporate the vegetation correction, thus enabling the estimation of soil moisture without the need for any on-site measurements. Models developed through the years, based on both theoretical studies and experimental observation, for soil moisture retrieval in bare as well as vegetated areas were discussed. Based on this review, the popular technique of incorporating vegetation effects into already existing bare soil models, such that they produce accurate results even for vegetated regions, was adopted for this work. Through a critical analysis of the models, it was concluded that the Dubois Model would be the best choice due to its simplicity of implementation, least requirement of ground measured parameters to estimate the soil moisture, better performance for rough surfaces and its applicability to data acquired by a variety of sensors as well as from different sites. The major focus of this thesis is on the applicability of the model on polarimetric SAR data, both airborne and spaceborne, and since the Dubois Model had been tested for its validity on both types of data, it proved most suitable. The data sets used for this work mainly comprised of fully polarimetric,  115  C-band, SIR-C data acquired during the Washita'94 experiment in April 1994, fully polarimetric L-band AIRSAR data acquired during the Washita'92 experiment in June 1992 and C-band Convair-580 data acquired during the Ottawa Field Campaign in 2001. All three data sets were provided with detailed insitu ground measurements for a number of sites consisting of different forms of vegetation. Two modified empirical models were developed by introducing the vegetation effects into the backscattering coefficients, which were further used in the Dubois inversion model, thus accounting for the vegetation effects. While the modified empirical model I primarily focussed on incorporating the vegetation effects using the water-cloud model, the modified empirical model II concentrated on introducing the remote computation of the vegetation parameters required in the water-cloud model, in addition to the vegetation correction. From the preliminary results, it was concluded that when both the HH and V V backscatter were corrected for vegetation effects, the results did not show any improvement when compared to the results for the existing Dubois Model. However, including the vegetation effects only in the V V backscatter produces a substantial increase in the estimation accuracy. This conclusion was based on the fact that the presence of vegetation with strong vertical orientation, which was the case for most of the given sites, leads to considerable attenuation of the V V backscatter. During the implementation, the modified empirical model I was applied to the C-band SIR-C data set and the modified empirical model II was applied to L-band AIRSAR data. A combination of both approaches was applied to the C-band CV-580 data set based on the availability of required ground measurements. An overall analysis of the results, concludes that the introduction of the vegetation correction into the Dubois Model has considerably improved the accuracy in soil moisture retrieval for vegetated areas. Both the models were designed to initially assess the extent of vegetation in a site or at a particular pixel, thus applying the vegetation correction whenever necessary. A further inspection of the results, reveals that the modified empirical model I produced a negative bias in the soil moisture estimates, which was subsequently eliminated in the modified empirical model II. The difference  116  in the behavior is attributed to the use of a modified water-cloud model in the second algorithm. Another important conclusion which can be drawn by comparing the two models is that the remote computation of the vegetation parameters as well as the use of vegetation sensitivity to make the model more adaptive does not lead to a decrease in the estimation accuracy. This proves to be one of the most encouraging results since it preserves the fundamental goal of remote sensing technology. Also, the estimation results for the modified empirical model II proved to be better which may be due to the use of Dobson's model for estimating the surface backscatter as opposed to the use of regression analysis in the first model. The results obtained by applying the models on the CV-580 data indicates that, in addition to all above observations, the vegetation correction proved to be effective only if the statistical variability within a field is reduced by averaging for the entire field. Statistical variations between the test sites in a field are possibly due to variations in the surface roughness, soil moisture, plant height and vegetation water content. Consequently, the vegetation corrected model was found to perform well for the C-band CV-580 data only if the fields are at least 30,000 m in size. On a slightly different note, the CV-580 data also 2  exhibited an overestimation in the moisture values obtained from the original Dubois model. This brings in to picture the possibility of calibration errors being present in the data. Based on the study of the mathematical complexity of both models, it was deduced that the modified empirical model II proved to be much more complex as compared to the modified empirical model I. This is mainly due to the fact that the modified model II is extremely sensitive to the accurate computation of the the vegetation transmissivity, r , as well as to any errors introduced 2  during the ground measurements. The latter effect was observed particularly in the case of CV-580 data where small variations in the surface correlation length led to significant variations in estimation accuracy of the vegetation corrected model. This is indicative of the fact that the surface roughness dominates over water content changes at C-band due to its shorter wavelength. Consequently, a better approach would be to either obtain accurate ground measurements of the surface correlation length or use sensors with longer wavelengths such as L/P-band to ensure lesser sensitivity to surface roughness and greater soil 117  penetration. Furthermore, Model II involves a combination of several different approaches used in computing the parameters required in the model, leading to a larger number of computations. This, however, does not pose a major concern due to the availability of fast processors. Based on the above, it can be concluded that a good model requires a suitable balance between remote computations and its overall simplicity. Both models, developed in this work, prove to provide a good degree of accuracy in soil moisture estimation in vegetated areas and can be chosen for implementation based on the availability of necessary parameters. This work, though a small contribution to the on going global research in soil moisture estimation, is an effort to develop models with the potential to utilize the vast resources of data which will be available through future missions such as RADARSAT-II and the HYDROS mission.  7.2  Research Contributions  The research work presented in this thesis is a step towards the larger goal of remotely estimating the soil moisture and thus aid a variety of applications. The contribution this work offers to the scientific community may be enumerated as follows: 1. A detailed analysis of the different algorithms developed for soil moisture retrieval using SAR data, in both bare soil as well as vegetated areas. 2. A complete step-wise methodology outlining the incorporation of a vegetation index into the existing Dubois Model. 3. An attempt to emphasize the true meaning of "remote sensing" and its advantages in the field of active soil moisture estimation. A thorough investigation of existing literature is done to determine suitable methods for the remote estimation of vegetation and soil parameters, generally measured at the ground. 4. Validation of the theoretical basis for the proposed algorithms by applying them to three different data sets comprising of both airborne and 118  spaceborne SAR data, i.e., AIRSAR, SIR-C and CV-580. 5. Recommendations for data sets (C/L/P-band) suitable for soil moisture estimation, using the proposed models, as well as on a more general basis. 6. A foundation for future research using data available from future missions - RADARSAT-II, ALOS PALSAR and HYDROS. 7. Recommendations for further future work in order to improve performance and ensure accurate results. 8. Two publications, [62] and [63] in the proceedings of the IEEE Geoscience and Remote Sensing Symposium, 2004 and 2005.  7.3  Future work  Based on this study, the following are some of the issues which may be considered for future work: 1. Due to time constraints of this project as well as unavailability of necessary in-situ ground measurements for validating the models, it was not possible to apply the models to data sets from other SAR systems such as ENVISAT (dual pol capability) and ESAR (fully polarimetric). It would be worthwhile to test the performance of the model on a variety, of data sets, thus ensuring the accuracy as well as robustness of the models. 2. It would be of considerable interest to further reduce the need for on-site ground measurements by computing the vegetation thickness, d, and soil bulk density, pb, remotely. The vegetation thickness can be estimated from optical data (hence multi-sensor data fusion is important) and bulk density may be determined from soils maps or other field measurement programs since it proves to be considerably stable [64]. 3. Due to the unavailability of hyperspectral imagery for the AIRSAR data set, NDVI was computed through a regression curve. Hyperspectral data would provide a better estimate of the NDVI, thus removing the inconsistencies which may have been caused by the regression. 119  4. In future missions fully polarimetric data along with the corresponding phase information will be available. Incorporating the co-polarized phase difference and the co-polarized correlation coefficient into the model would lead to the complete utilization of the accessible information. This approach has been discussed on a theoretical basis in [30]. 5. In this work, the backscatter due to the interaction between the soil surface and the vegetation was neglected. Accounting for this term, which is very prevalent in lightly to moderately vegetated targets, would most definitely improve the accuracy in soil moisture retrieval from active SAR systems. 6. The results obtained in this work, yet again, emphasize the sensitivity of the soil moisture estimation models to the surface roughness. Eliminating the need for surface correlation length and, using polarization ratios and/or polarimetric approaches is expected to minimize the roughness effects. 7. A multi-frequency radar approach using polarimetric interferometry such that both roughness and vegetation affects can be dealt with, might prove to be a better way of approaching the problem of soil moisture estimation under vegetated regions [65].  120  A p p e n d i x  S A R  A.l  A  P o l a r i m e t r y  Synthetic aperture radar  Synthetic Aperture Radar or SAR is a side-looking electromagnetic imaging sensor often used in remote sensing applications. The SAR sensor is mounted on an aircraft or a satellite, and is used to make a high-resolution image of the earth's surface. Digital signal processing is used to focus the image and obtain a resolution higher than that achieved by conventional radar systems. The length of the radar antenna determines the resolution in the azimuth (alongtrack) direction of the image: the longer the antenna, the finer the resolution in this dimension. Synthetic Aperture Radar (SAR) refers to a technique used to synthesize a very long antenna by combining signals (echoes) received by the radar as it moves along its flight track. Aperture means the opening used to collect the reflected energy that is used to form an image and in a radar it is the antenna. A synthetic aperture is constructed by moving a real aperture or antenna through a series of positions along the flight track. Fig. 2.1 shows a simple geometric model of the radar location and the beam footprint on the Earths surface. As the radar moves, a pulse is transmitted at each position and reflected back. The return echoes pass through the receiver and are recorded. Because the radar is moving relative to the ground, the returned echoes are Doppler-shifted (negatively as the radar approaches a target; positively as it moves away). Comparing the Doppler-shifted frequencies to a reference fre-  121  quency allows many returned signals to be focused on a single point, effectively increasing the length of the antenna that is imaging that particular point. T h i s focusing operation is commonly k n o w n as S A R processing [67].  Figure A . l : F l i g h t Geometry for a Synthetic A p e r t u r e R a d a r , Source  [66]  Synthetic aperture radar is now a mature technique used to generate radar images i n which fine detail can be resolved. S A R s provide unique capabilities as an imaging t o o l . Since they provide their own i l l u m i n a t i o n (the radar pulses), they can image at any time of day or night, regardless of the sun i l l u m i n a t i o n . In addition, since the radar wavelengths are much longer than those of visible or infrared light, S A R s can also see through cloudy and dusty conditions that visible and infrared instruments cannot. R a d a r systems can be monostatic, bistatic or multi-static, depending upon the location of the receiver i n relation to the transmitter.  122  A.2 A.2.1  Polarimetry in radar remote sensing Polarimetry: basic concepts  A n electromagnetic wave has time-varying electric and magnetic field components in a plane perpendicular to the direction of travel. The two fields are orthogonal to each other and travel at the speed of light. Polarization of an electromagnetic wave refers to the alignment and regularity of the electric and magnetic field components, in the plane perpendicular to the direction of propagation. Since the two fields are always orthogonal to one another, the thesis follows the convention of characterizing the behavior of the electromagnetic wave using the electric field vector only. The electric field vector can itself be considered to be a sum of two orthogonal components.  The two .components-horizontal and vertical, can be  characterized in terms of their amplitude and relative phase. The tip of the electric field vector traces out a regular pattern, generally an ellipse, along the direction of propagation, as shown the Fig. A.2. The shape of this ellipse, called as the polarization ellipse, is governed by the orientation and the relative phase between the horizontal and vertical components of the electric field vector; and defines the polarization state of the wave. Furthermore, the ellipse has a semi-major axis and a semi-minor axis. The angle of the semi-major axis measured counter-clockwise from the positive horizontal axis is known as the  orientation, tp; and the degree to which the ellipse of oval is described by its ellipticity, %• When the components are in phase, the polarization is linear with ip = 45° .and X — 0, while when the phase is 90° with the orientation as ±45° and ellipticity as ±45°, the wave is said to be circularly polarized. Fig. A.3 illustrates these two different states of polarization [68].  123  Figure A.2: Polarization ellipse showing orientation angle and ellipticity  A.2.2  The polarization state  The British Physicist, Gabriel Stokes, described the polarization state of an electromagnetic wave by a 4-element vector, known as the Stokes vector, and given as:  ' S '  " \E \ + \E \ ' 2  0  Q u  v  \K?  =  _V_ where Eh and E  2  v  h  -  \E \  2  h  (A.l)  2R{E E } v  ,  23  h  .  are the horizontal and vertical components of the electric  field vector, respectively, while | . | represents the absolute value and * is used to express the complex conjugate. Depending on the polarization state, a wave can be completely polarized, partially polarized or completely unpolarized. For the case when the wave is  124  X= 135" T = 45  4  (d)  Figure A.3: The shape of the polarization ellipse at: (a),(b) Linear Polarization (c),(d) Circular Polarization completely polarized, the degree of polarization is 1 [68] and the power relation is given by:  5  2 0  = Q + U + V 2  2  2  (A.2)  If the electromagnetic wave is partially polarized, it can be expressed as the sum of a completely polarized wave and a completely unpolarized wave. In this case, the total power is greater than the polarized power as shown in (A.3), while the degree of polarization is less than 1 and is given by (A.4).  S  2  > Q + U + V 2  2  (A.3)  2  y/Q* + m + V  2  Dpoi —  125  (A.4)  A.2.3  Polarization in radars  Polarization diversity has long been recognized as a technique providing a more complete inference of natural surface or other target parameters. A radar system can create polarized waves using an antenna which is designed to transmit and receive waves with specific polarizations. The two most common polarizations are the horizontal linear (H) or the vertical linear (V). The orientation and phase angle of the components of the electric field vector at these polarizations are shown in Fig. A.2. Circular polarizations are also used and the basis components are denoted by R for the right-hand circular and L for the left-hand circular polarizations. In simple radar systems the same antenna is often configured to transmit and receive only one type of polarization. However, nowadays more complex radar systems have been designed which have the ability to transmit and receive more than one polarization. By representing the transmit and receive wave by a pair of symbols, a radar system using H and V polarization can have the following channels: • HH-for horizontal transmit and horizontal receive • VV-for vertical transmit and vertical receive • HV-for horizontal transmit and vertical receive • VH-for vertical transmit and horizontal receive The first two are referred to as are referred to as  cross  polarized.  like  polarized  while, the last two combinations  A radar system may also have different levels  of polarization complexity: • single polarized-HH / V V / HV / V H • dual polarized-HH & HV / W & V H / VH & HH / HH & V V • four polarizations-HH, W , HV & V H A quadrature polarized radar, or in other words, a fully polarimetric radar, uses these four polarizations and measures the phase difference and magnitude between the channels.  126  A.2.4  Polarimetric scattering and target characteristics  Many radar targets are inherently polarimetric. Thus, a knowledge of the transmitted wave and complete polarimetric reception of the scattered wave are essential to determine the target characteristics. As mentioned in the previous section, a quadrature polarization radar transmits with two orthogonal polarizations, often the linear horizontal (H) and the linear vertical (V), and receives the backscattered wave on the same two polarizations. HH, VV, HV and VH represent the backscatter recorded for the four different combinations of the transmit and receive signals. These channels convey all the information required to determine the polarimetric scattering properties of the target. The ocean surface, bare and/or tilled land, urban areas, regions with sparse vegetation and forests are a few of the targets which can be identified through polarimetric analysis. The ocean surface and bare land represent rough surfaces where the scatter is generally single bounce resulting in a co-polarized return. Thus, in such a case, the HH or V V polarization is more dominant as compared to HV or VH. In contrast, the polarimetric microwave scattering for urban areas is characteristic of double reflections from the ground to buildings and back to the radar. More than one bounce of backscattering tends to depolarize the pulse, causing the cross polarized return in this case to be larger than that with the single bounce reflection. In a forest, multiple bounces, as illustrated in Fig. A.4, lead to a diffuse scattering and the radar backscatter consists of both co-polarized and cross-polarized returns [42,69].  A.2.5  The scattering matrix  The backscattering properties of a target can be expressed mathematically by a scattering matrix, S, which describes the transformation of the electric field of the incident wave to that of the scattered wave.  .EZ .  Shh Shv Syh q vv u  ' E\'  (A.5)  .Et.  The superscripts, S and i, represent the scattered and incident waves, respectively. The four elements in the scattering matrix are complex and can be 127  (a)  (c) Figure A.4: Scattering Mechanisms (a) Slightly rough surface (b) Dihedral corner reflector (c) Forested area [l:direct canopy backscatter; 2:double bounce backscatter; 3:direct ground backscatter; 4:direct tree trunk backscatter]  128  obtained from the magnitudes and phases measured by the four polarimetric channels. For monostatic radars, the reciprocity property is applicable for most targets, in which  C3.SG  Sfiv  —  ^vhi  i'G.j  the scattering matrix is symmetrical  and has only three independent elements. Using the elements of the scattering matrix, a number of polarimetric parameters can be computed that have useful physical interpretation. The following parameters are frequently used [68]: Total power: This represents the total power received by all the four channels of the radar system. In terms of the scattering matrix it is given as, Ptot  =  \S  \  + \S  2  hh  \  +  2  VV  \S \  2  hv  +  \S \  2  vh  (A.6)  For the monostatic radar, the total power will be, Ptot  =  \S  \  2  hh  + \S  + 2  \  2  VV  (A.7)  \S \  2  hv  Co-polarization correlation coefficient: The co-pol correlation coefficient expresses the correlation between the two co-polarized channels, HH and VV. It is generally complex as shown in Eq. A.8  52 ™  (A.8)  ShhS  \J\Shh\  2  S^h and S  vv  \s \  2  vv  are the complex amplitudes of the HH and W channels, respec-  tively. Co-polarization phase difference:  This is the phase difference between  the two co-polarized channels and can be obtained as the phase angle of the complex co-pol correlation coefficient. Degree of polarization:  The degree of polarization is given by the ratio  of the power in the polarized part of the wave to the total power of the wave and is expressed in (A.4) in terms of the Stokes parameters.  129  A.2.6  Polarization signature  In order to gain a better understanding of the scattering from different kinds of targets, it is helpful to have a graphical method of visualizing the variation of the scattering with the incident and backscattered polarizations. One such visualization is the polarimetric signature which expresses the scattering coefficient as a function of the transmit and receive antenna polarization. The polarimetric signature is a three dimensional plot, where the the ellipticity % ranging between ^45° and the orientation between 0 and 180°, are mapped along the x- and y-axes, respectively. For an incident wave of unit amplitude, the power of the co-polarized (or cross-polarized) component of the scatter wave is presented along the z-axis. These polarization plots have peaks at polarizations that give maximum power and valleys where the received power is low. The pedestal height is also an important parameter and is indicative of the presence of an unpolarized scattering component in the received signal. Higher the degree of polarization, lesser is the pedestal height and vice versa. [68] The co-polarization signatures for the different forms of scattering discussed in Section A.2.4 are illustrated in Fig. A.5. As can be observed, the backscatter from the ocean surface is dominated by the co-polarized response, while in case of urban areas co-polarized response has lower strength. The high pedestal observed for the regions with vegetation, points to a high degree of variation in scattering properties from one pixel to the next [42].  130  OCEAN  URBAN  PARK  Figure A.5: Co-polarization signatures for ocean surface, urban areas and vegetated region, Source: [42]  131  A p p e n d i x  B  I n t e r m e d i a t e  M o d e l s  During the process of formulating the modified empirical models I and II, several combinations of the different methods discussed in Section 5.3 were used. The flowcharts indicating the steps involved in the implementation of these intermediate models are illustrated in Figs. B . l and B.2. The results obtained by applying intermediate models I and II to the available L-band AIRSAR data are shown in Figs. B.3 and B.4, respectively. The intermediate model I provides a correlation of 0.77 and a RMS error of 2.52% between the measured and estimated values, thus indicating no significant improvement as compared to the bare-soil model. On the other hand, model II leads to a slight decrease in the error, while the correlation coefficient increases to 0.78.  132  Measured a°M> and a ° per pixel m  Dubois Model with no vegetation correction Volumetric soil moisture, m«  Calculate Field Capacity. FC Soil Moisture Content, nv Regression •:  S = B  a  4.34  Calculate S  C  soil  c  v  Apply original Dubois Model  S„< S ? B  Yes  Calculate-vegetation parameters, r?;; W Use ground measured estimate for A,a :  c  Vegetation correction: for  a°vv  &  veg  Modified Water-Cloud Model (A ttema & Ulaby + Bindlish ef al.) o « - cr  v,s j  T a°,oii J  +  Vegetation corrected a •„ + measured a ° i , h  Dubois inversion model (with vegetation correction due to o ° w ) Dielectric Constant, t Hoilikainen Model to, obtain m from z using soil texture infornlation v  Volumetric Soil Moisture, m  v  Figure B . l : Schematic flowchart of Intermediate Model I (Regression + Bindlish et al. model)  133  Measured a° and o° per pixel hh  vv  Dubois Model withno vegetation correction ^Volumetric soil moisture, ,m»  Calculate Field Capacity, FC + Soil Moisture Content, nv Regression  c^ii'arrv-b  S = 4.34 a 8  Calculate S  v  Apply original Dubois Model  C^^~Sv< S ~ ~ ~ ^ > ~ 7  B  Yes  Calculate vegetation parameters, r . W Use ground measured estimate for A,a 2  c  Vegetation correction for a w 0  Parameters. R.L.s  Obtain soil backscatter.o using Dobson model  Modified Water-Cloud Model (Attema & Ulaby + Bindlish ef al.)  Vegetation corrected a „ + measured O^M, Dubois inversion model (with vegetation correction due to o w) Dielectric Constant, E Hallikainen Model to obtain m from £ using soil texture information v  t Volumetric Soil Moisture. m»  Figure B.2: Schematic flowchart of Intermediate Model II (Dobson model + Bindlish et al. model)  134  (a)  Measured vs. Estimated Soil Moisture  1  Correlation = 0.77  r—  +  •  RMS Error = 2.53%  oX  6.8  o  in* 0.7  1-1 Juna to June 13 June 14 Jllllfr 16 Jima:1B  E \r  I.  oi  i  05  Soil  ..a_trt:  :E to Ul  o  0.4  •  .  i-"®  ••••  ...M  0.3  oi  . 0  0.2  0.1  0.3  0.4  0:5  6.8  0.7  06  0.9  Measured Soil Moisture (cm /cm ) 3  (b)  3  Measured vs. Estimated Soil Moisture -—-1-1 + June 10 • Juno 13 O June U X June- Iii O Juiitt 18  Correlation = 0.75 «*• : . :+ • • '  ! RMS Error = 2.52%  |  •• • •  0.7  t  \  *  »  ••:**•• -••  5  6.5  $  0.4  ; .. O O  •  ••'  •  : 0 +  3in.  I  r  •  ., ... :>.•:  :  D  >:  ....  ....  -  .p......?*:.-.  0.3  :  (  *• V -  I iO.I  J 0:2  i  0.3  L 6;4  0.5  OUJ:  :  0.7  :;0.8  0.9.  Measured Soil Moisture (cm /cm ) 3  3  Figure B . 3 : Scatter plot of measured and estimated volumetric soil moisture for the sites i n L - b a n d , A I R S A R data (Table 4.3) using: (a) the original Dubois M o d e l (b) the intermediate model I. Green represents vegetated sites and, brown represents bare-soil sites.  135  (a)  Measured vs. Estimated Soil Moisture + • O X O  RMS Error = 2.53%  x  -1 June 10 June 13 June 14 June IC June. 18 1  Correlation = 0.77  +  0 . o a o* 0  (0:0.6  3  : tn  •:*5  0*' +  W 0.4  E:  '•a  0.1  -0.2  0.3  0:4  0.5  0.8  0.7.  0.8  0.9:  Measured Soil Moisture (cm /cm ) 3  3  Measured vs. Estimated Soil Moisture :  1  — T  rr  1  Correlation = 0.78  1  '  .-' v .  RMS Error = 2.4% 0.7  I f)  :•'  0.6  L o o O  . § 0-5  'o:  W  >  • • y.- •  ...Kr.  0  ox  X  0  +  ..  ; •;.  +  ---- i - i + June 10 • June 13 Q JuiieU X June 16 O June 18  <»*  !  y  . y'>:• >•  :  V D+  : X : *  t  ;  -  •.  —i— 0.1 ;— 0.2 -i  :— 0.3t-—:  0.4 1  0.5  0.8  0.7:  0.8  0.9  Measured Soil Moisture (cm /cm ) 1  3  3  Figure B.4: Scatter plot of measured and estimated volumetric soil moisture for the sites in L-band, A I R S A R data (Table 4.3) using: (a) the original Dubois Model (b) the intermediate model II. Green represents vegetated sites and, brown represents bare-soil sites.  136  B i b l i o g r a p h y  [1] P. C. Dubois, J. van Zyl, and E. T. Engman, Measuring Soil Moisture with Imaging Radars, IEEE Trans. Geosci. Rem. Sensing, 1995, Vol. 33, No. 4, pp. 915-927 [2] I. Hajnsek, Inversion of Surface Parameters using Polarimetric SAR, Ph.D Dissertation, 2001, Institut fr Hochfrequenztechnik und Radarsysteme Abteilung SAR Technologie [3] Y . Oh, K . 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