Mapping surface roughness and soil moisture using multi-angle radar imagery without ancillary data

The Integral Equation Model (IEM) is the most widely-used, physically based radar backscatter model for sparsely vegetated landscapes. In general, IEM quantifies the magnitude of backscattering as a function of moisture content and surface roughness, which are unknown, and the known radar configurations. Estimating surface roughness or soil moisture by solving the IEM with two unknowns is a classic example of under-determination and is at the core of the problems associated with the use of radar imagery coupled with IEM-like models. This study offers a solution strategy to this problem by the use of multi-angle radar images, and thus provides estimates of roughness and soil moisture without the use of ancillary field data. Results showed that radar images can provide estimates of surface soil moisture at the watershed scale with good accuracy. Results at the field scale were less accurate, likely due to the influence of image speckle. Results also showed that subsurface roughness caused by rock fragments in the study sites caused error in conventional applications of IEM based on field measurements, but was minimized by using the multi-angle approach.     

Evaluation of JERS-1, ERS-1 and Almaz SAR backscatter for rubber and oil palm stands in West Malaysia

While many reports have been published on radar backscatter characteristics of coniferous and deciduous forests, little work appears to have been done on investigating the backscatter properties of palm trees. In this study, Japanese JERS-1 L _HH band, European ERS-1 C _VV band and Russian Almaz-1B S _HH band SAR data have been acquired over parts of Kedah and Penang states in West Malaysia in order to investigate the radar backscatter properties for oil palms and rubber trees for each of these sensors.

Results show that the radar backscatter for the deciduous rubber trees, for both JERS-1 and ERS-1, appear to behave in accordance with what has been reported earlier for coniferous and deciduous trees, that is, scattering on trunks, branches and twigs at L-band and scattering in the canopy at C-band. The JERS-1 backscatter shows limited correlation with the rubber growth while no relation is found in the ERS-1 data.

Oil palms with their characteristic structures affect the radar signal differently compared to the situation for rubber trees. Scattering in the large crown is the dominating backscatter mechanism in both the JERS-1 and ERS-1 data. Leaf area index is correlated closest to the backscatter intensity at both bands.

Results from the investigation of the Almaz S-band data are rather discouraging, contradicting earlier more positive reports on the usefulness of the sensor. In this study, the forest types and their intermediate growing stages were found to be virtually indistinguishable, including the clear felled areas. These results should however not be attributed to S-band or Almaz data in general, but rather to this particular data set. It is obvious that the quality of Almaz data varies significantly.     

Assessment of polarimetric SAR data for discrimination between wet versus dry soil moisture conditions

Radarsat-2 imagery from extreme dry versus wet conditions are compared in an effort to determine the value of using polarimetric synthetic aperture radar (SAR) data for improving estimation of fuel moisture in a chronosequence of Alaskan boreal black spruce ecosystems (recent burns, regenerating forests dominated by shrubs, open canopied forests, moderately dense forest cover). Results show strong distinction between wet and dry conditions for C-HH and C-LR polarized backscatter, and Freeman–Durden and van Zyl surface bounce decomposition parameters (35–65% change for all but the dense spruce site). These four SAR variables have high potential for evaluation of within site surface soil moisture, as well as for relative distinction between wet and dry conditions across sites for lower biomass and sparse canopy forested sites. However, for any given test site except the shrubby regrowth site, van Zyl volume, surface, and double bounce scattering all result in similar percentage increases from dry to wet soil condition. This indicates that for most of these test sites/cases moisture enhances the magnitude of the return for all scattering mechanisms evaluated. Thus, differences in scattering from the interaction of biomass, surface roughness, and moisture condition across sites remains an issue and backscatter due to surface roughness or biomass cannot be uniquely estimated. In contrast, the Cloude–Pottier C-band decomposition variables appear invariant to soil moisture, but may instead account for variations in ecosystem structure and biomass. Further investigation is needed, as results warrant future research focused on evaluation of multiple polarimetric parameters in algorithm development.     

Investigating the potential for soil moisture and surface roughness monitoring in drylands using ERS SAR data

Multitemporal ERS-1 and ERS-2 SAR data were acquired for northern Jordan between 1995 and 1997 to investigate changes in the backscatter coefficients of a range of typical desert land surfaces. The changes in backscatter found were ascribed to variations in surface soil moisture, and changes in surface roughness caused by a range of natural and anthropogenic factors. Data collected from monitored sites were input into the Integral Equation Model (IEM). The model outputs were strongly correlated with observed backscatter coefficients (r ²=0.84). The results show that the successful monitoring of soil moisture in these environments is strongly dependent on the surface roughness. On surfaces with RMS height 0.5 cm, the sensitivity of the backscatter coefficient to changes in surface microtopography did not allow accurate soil moisture estimation. Microtopographic change on rougher surfaces has less influence on the backscatter coefficient, and the probability of soil moisture estimation from SAR imagery is greater. These results indicate that knowledge of the surface conditions (both in terms of surface roughness and geomorphology) is essential for accurate soil moisture monitoring, whether in a research or operational context. The potential benefits of these findings are discussed in the context of the Jordan Badia Research and Development Project.     

Semi-empirical calibration of the IEM backscattering model using radar images and moisture and roughness field measurements

Estimating surface parameters by radar-image inversion requires the use of well-calibrated backscattering models. None of the existing models is capable of correctly simulating scatterometer or satellite radar data. We propose a semi-empirical calibration of the Integral Equation Model (IEM) backscattering model in order to better reproduce the radar backscattering coefficient over bare agricultural soils. As correlation length is not only the least accurate but also the most difficult to measure of the parameters required in the models, we propose that it be replaced by a calibration parameter that would be estimated empirically from experimental databases of radar images and field measurements. This calibration was carried out using a number of radar configurations with different incidence angles, polarization configurations, and radar frequencies. Using several databases, the relationship between the calibration parameter and the surface roughness was determined for each radar configuration. In addition, the effect of the correlation function shape on IEM performance was studied using the three correlation functions (exponential, fractal, and Gaussian). The calibrated version of the IEM was then validated using another independent set of experimental data. The results show good agreement between the backscattering coefficient provided by the radar systems and that simulated by the calibrated version of the IEM. This calibrated version of the IEM can be used in inversion procedures to retrieve surface roughness and/or moisture values from radar images.     

Radar remote sensing of springtime near-surface soil thaw events at mid-latitudes

Detection of springtime near-surface soil thaw events in mid-latitude areas is important for understanding the near-surface earth surface system. Radar backscatter time series, such as QuikSCAT K_u-band, are valuable for surface thaw detection in permafrost areas, but their usefulness in mid-latitudes remains unverified. In order to validate the application of radar backscatter time series for surface thaw detection in mid-latitude areas, we propose a new multi-step method based on the significant signature of radar backscatter time series when springtime soil thaw events happen. The method mainly focuses on the estimated geographical boundary of thaw events and the detection of the primary thaw date; the duration of the freeze–thaw transition period is a lesser focus. The method is applied to soil freeze–thaw conditions in a mid-latitude area – northern China and Mongolia – including humid land and dryland, and achieves a reliability of R ²?=?0.678 ± 0.021 (P < 0.01) by comparison with ground truth measurements. The results indicate that elevation/temperature and soil moisture conditions are the key drivers of the timing of springtime soil thaw events. The success of our study demonstrates the potential for our method to be applied in mid-latitude areas, and widens the application potential of radar backscatter time series beyond high north and permafrost studies.     

Short contributions

Studies of ERS-1 synthetic aperture radar (SAR) imagery have shown that fire scars in Alaskan forests are significantly brighter (3–6 dB) than surrounding unburned forest. The signature varies seasonally and changes as vegetation re-establishes on the site over longer time periods (>5years). Additionally, it is known that soil water content typically increases following forest fires due to changes in evapotranspiration rates and melting of the permafrost.

The objective of this study was to understand the relation between soil water content and the ERS-1 SAR signature at fire-disturbed sites. To accomplish this objective, we compared soil water in six burned black spruce (Picea mariana (Mill.) B.S.P.) forest sites in interior Alaska to ERS-1 SAR backscalter measurements. The six sites are of various age since burn. Soil water was periodically measured at each site during the summer of 1992 and at one site in 1993 and 1994 when the ERS-1 imaging radar was scheduled to pass overhead. Results indicate that a positive linear relation exists between soil water content and the SAR backscatter coefficient in young burns ( < ～4years). Older burns do not show this relation, a result of vegetation establishment following the burn. This interaction between soil moisture condition and ERS-1 SAR backscatter shows great potential for measuring soil water content and monitoring seasonal variations in soil water content in black spruce sites recently disturbed by wildfire.     

Modeling double‐side printed meander‐line inductors on printed circuit boards

A lumped element model for a double‐side printed meander‐line inductor with closed‐ form expressions for the electrical model parameters L, C, R_l, and R_c is presented. These structures are cheaper than coils and need less area per unit of inductance than single‐side printed meander‐line inductors. The model has been validated with measurements from 30 to 1000 MHz, finding a mean error in the inductance parameter of about 1%. © 2003 Wiley Periodicals, Inc. Int J RF and Microwave CAE 13: 105–112, 2003.     

A new empirical model to retrieve soil moisture and roughness from C-band radar data

A new empirical model for the retrieval, at a field scale, of the bare soil moisture content and the surface roughness characteristics from radar measurements is proposed. The derivation of the algorithm is based on the results of three experimental radar campaigns conducted under natural conditions over agricultural areas. Radar data were acquired by means of several C-band space borne (SIR-C, RADARSAT) or helicopter borne (ERASME) sensors, operating in different configurations of polarization (HH or VV) and incidence angle. Simultaneously to radar acquisitions, a complete ground truth data base was built up with different surface condition measurements of the mean standard deviation (rms) height s, the correlation length l, and the volumetric surface moisture M_v. This algorithm is more specifically developed using the radar cross-section σ⁰ (HH polarization and 39° incidence angle off nadir), namely, σ_0HH,39, and the differential (HH polarization) radar cross-section Δσ₀=σ_0,23°−σ_0,39° in terms of an original roughness parameter, Z_s, namely Z_s=s²/l, and M_v. A good agreement is observed between model outputs and backscattering measurements over different test fields. Eventually, an inversion technique is proposed to retrieve Z_s and M_v from radar measurements.     

Modelling above-ground live trees biomass and carbon stock estimation of tropical lowland Dipterocarp forest: integration of field-based and remotely sensed estimates

Carbon exists as carbon dioxide (CO₂) which is one of the greenhouse gases (GHG) in the atmosphere that has an enormous influence on the impact of climate change. Therefore, the forest plays an undeniably pivotal role as a carbon sink, which absorbs carbon dioxide from the atmosphere. This research aims to develop allometric equation for above-ground live tree biomass (AGB) by combining field-based, combination of field data observation and technology (WV-3 and light detection and ranging (lidar)) and by using only technology derivation. The independent predictor was induced based on the literature review and theories, and an ordinary least square (OLS) estimator will be used to develop multiple linear regression models. During model selection, the best model fit was selected by calculating statistical parameters such as residual of the coefficient of determination (R²) selection methods, adjusted coefficient of determination (R²_adj), root mean square error, graphical analysis of the residuals, standard error (S_yx), and Akaike information criterion. An allometric equation of this research was developed using carbon stocks as dependent variables, and four of the predictor’s variables: diameter at breast height (DBH); total height observed at field (h_F); total height derived from airborne lidar (h_L); and morphometric variables of the crown projection area (CPA). Based on the statistic indicators, the most suitable model is Model 1, ln (S_c) = – β₀ + β₁ ln (h_L) + β₂ ln (DBH) + β₃ ln (CPA) for the combination of remote sensing and field observation; ln (S_c) = – β₀ + β₁ ln (h_F) + β₂ ln (DBH) for field inventory only; and ln (S_c) = – β₀ + β₁ ln (h_L) + β₂ ln (CPA) for remote sensing only. This model is reliable in forest management to estimate the AGB and carbon stock estimation using a selection of variable sources.     

An interpolation procedure for generalizing a look-up table inversion method

The inversion of physically based reflectance models is increasingly efficient for extracting vegetation variables from remote sensing images. It requires a vegetation reflectance model and an inversion method that are accurate and efficient. Usually, the complexity of reflectance models implies to use specific inversion methods (e.g., look-up table and neural network). Unfortunately, these methods are valid only for the view-sun directions for which they are designed. A developed look-up table based inversion method avoids this limitation: it generalizes any look-up table for any view-sun direction, and more generally for any input parameter value. It uses a look-up table made of c_i coefficients of any analytical expression h that fits a set of reflectance values simulated by the Discrete Anisotropic Radiative Transfer (DART) model. Interpolation on coefficients c_i allows h to give reflectance values for any input parameter value. We settled some options of the inversion method with sensitivity studies: tree covers are simulated with 4-tree scenes, expression h has six coefficients c_i and the interpolation is the continuous first derivative interpolation method. Moreover, the robustness of the inversion method was validated. The ability to generalize a look-up table for any view-sun direction was successfully tested with the inversion of SPOT images of Fontainebleau (France) forest. LAI maps proved to be as accurate (i.e., RMSE≈1.3) as those obtained with classical relationships that are calibrated with in situ LAI measurements. Here, the advantage of our inversion method was to avoid this calibration.     

The impact of surface roughness on flow through a rectangular microchannel from the laminar to turbulent regimes

Modifications of fluid flow within microscale flow passages by internal surface roughness is investigated in the laminar, transitional, and turbulent regimes using pressure-drop measurements and instantaneous velocity fields acquired by microscopic particle-image velocimetry (micro-PIV). The microchannel under study is rectangular in cross-section with an aspect ratio of 1:2 (depth: width) and a hydraulic diameter of D_h = 600 \upmu m.D_{\rm h} =600\,\upmu \hbox{m}. Measurements are first performed under smooth-wall conditions to establish the baseline flow characteristics within the microchannel followed by measurements for two different rough-wall cases [with RMS roughness heights of 7.51 \upmu m7.51\,\upmu \hbox{m} (0.0125D _h) and 15.1 \upmu m15.1\,\upmu \hbox{m} (0.025D _h)]. The roughness patterns under consideration are unique in that they are reminiscent of surface irregularities one might encounter in practical microchannels due to imperfect fabrication methods. The pressure-drop results reveal the onset of transition above Re_cr=1,800Re_{\rm cr}=1{,}800 for the smooth-wall case, consistent with the onset of transition at the macroscale, along with deviation from laminar behavior at progressively lower Re with increasing roughness. Mean velocity profiles computed from the micro-PIV ensembles at various Re for each surface condition confirm these trends, meaning Re_crRe_{\rm cr} is a strong function of roughness. The ensembles of velocity fields at each Re and surface condition in the transitional regime are subdivided into fields embodying laminar behavior and fields containing disordered motions. This decomposition reveals a clear hastening of the flow toward a turbulent state due both to the roughness dependence of Re _cr and an enhancement in the growth rate of the non-laminar fraction of the flow when the flow is in the early stages of transition. Nevertheless, the range of Re relative to Re _cr over which the flow transitions from a laminar to a turbulent state is found to be essentially the same for all three surface conditions. From a structural viewpoint, instantaneous velocity fields embodying disordered behavior in the transitional regime are found to contain large-scale motions consistent with hairpin-vortex packets irrespective of surface condition. These observations are in accordance with the characteristics of transitional and turbulent flows at the macroscale and therefore indicate that the overall structural paradigm of the flow is relatively insensitive to roughness. From a quantitative viewpoint, however, the intensity of both the velocity fluctuations and structural activity appear to increase substantially with increasing roughness, particularly in the latter stages of transition. These differences are further supported by the trends of single-point statistics of the non-laminar ensembles and quadrant analysis in which an intensification of the velocity fluctuations by surface roughness is noted in the region close to the wall, particularly for the wall-normal fluctuations.     

Statistical properties of soil moisture images derived from Radarsat-1 SAR data

In this article, we report on the assessment of the spatial variability of soil moisture using synthetic aperture radar (SAR) data. The imagery was acquired during five different periods over the Roseau River watershed in southern Manitoba, Canada. For validation purposes, ground measurements were carried out at 62 locations simultaneous with the satellite data acquisitions. The first step in this analysis was to assess the performance of the Integral Equation Model (IEM) in simulating backscatter coefficients for selected bare soils. In order to reduce the surface roughness effect on radar backscatter, a semi-empirical calibration technique was implemented. This calibrated model was then implemented in a simplex inversion routine in order to estimate and map soil moisture. Derived spatial patterns of near-surface moisture content were then examined using scale analyses. It has been confirmed that the variance of radar-based soil moisture images follows power law decay versus the observation scale. Also, more explicit analysis of the same soil moisture maps shows a ln–ln linear spatial scale with statistical moments. Concave shape dependency of the corresponding slopes with the moment order was observed during all radar acquisition periods. The latter indicates the presence of multifractal effects.     

Timed Modal Logics for Real-Time Systems

In this paper, a timed modal logic L _c is presented for the specification and verification of real-time systems. Several important results for L _c are discussed. First we address the model checking problem and we show that it is an EXPTIME-complete problem. Secondly we consider expressiveness and we explain how to express strong timed bisimilarity and how to build characteristic formulas for timed automata. We also propose a compositional algorithm for L _c model checking. Finally we consider several control problems for which L _c can be used to check controllability.     

Likelihood parameter estimation for calibrating a soil moisture model using radar bakscatter

Land surface model parameter estimation can be performed using soil moisture information provided by synthetic aperture radar imagery. The presence of speckle necessitates aggregating backscatter measurements over large (> 100 m × 100 m) land areas in order to derive reliable soil moisture information from imagery, and a model calibrated to such aggregated information can only provide estimates of soil moisture at spatial resolutions required for reliable speckle accounting. A method utilizing the likelihood formulation of a probabilistic speckle model as the calibration objective function is proposed which will allow for calibrating land surface models directly to radar backscatter intensity measurements in a way which simultaneously accounts for model parameter- and speckle-induced uncertainty. The method is demonstrated using the NOAH land surface model and Advanced Integral Equation Method (AIEM) backscatter model calibrated to SAR imagery of an area in the Southwestern United States, and validated against in situ soil moisture measurements. At spatial resolutions finer than 100 m × 100 m NOAH and AIEM calibrated using the proposed radar intensity likelihood parameter estimation algorithm predict surface level soil moisture to within 4% volumetric water content 95% of the time, which is an improvement over a 95% prediction confidence of 10% volumetric water content by the same models calibrated directly to soil moisture information derived from synthetic aperture radar imagery at the same scales. Results suggest that much of this improvement is due to increased ability to simultaneously estimate NOAH parameters and AIEM surface roughness parameters.     

Further results on the L1 analysis of sampled-data systems via kernel approximation approach

This paper gives two methods for the L₁ analysis of sampled-data systems, by which we mean computing the L_∞-induced norm of sampled-data systems. This is achieved by developing what we call the kernel approximation approach in the setting of sampled-data systems. We first consider the lifting treatment of sampled-data systems and give an operator theoretic representation of their input/output relation. We further apply the fast-lifting technique by which the sampling interval [0, h) is divided into M subintervals with an equal width, and provide methods for computing the L_∞-induced norm. In contrast to a similar approach developed earlier called the input approximation approach, we use an idea of kernel approximation, in which the kernel function of an input operator and the hold function of an output operator are approximated by piecewise constant or piecewise linear functions. Furthermore, it is shown that the approximation errors in the piecewise constant approximation or piecewise linear approximation scheme converge to 0 at the rate of 1/M or 1/M², respectively. In comparison with the existing input approximation approach, in which the input function (rather than the kernel function) of the input operator is approximated by piecewise constant or piecewise linear functions, we show that the kernel approximation approach gives improved computation results. More precisely, even though the convergence rates in the kernel approximation approach remain qualitatively the same as those in the input approximation approach, the newly developed former approach could lead to quantitatively improved approximation errors than the latter approach particularly when the piecewise linear approximation scheme is taken. Finally, a numerical example is given to demonstrate the effectiveness of the kernel approximation approach with this scheme.     

Switching linear parameter‐varying control with improved local performance and optimized switching surfaces

This paper presents a novel approach to designing switching linear parameter‐varying (SLPV) controllers with improved local performance and an algorithm for optimizing switching surfaces to further improve the performance of the SLPV controllers. The design approach utilizes the weighted average of the local L₂‐gain bounds (representing the local performance) as the cost function to be minimized, whereas the maximum of the local L₂‐gain bounds (representing the worst‐case performance over all subsets) is bounded with a tuning parameter. The tuning parameter is useful for taking the trade‐off between the local performance and the worst‐case performance. An algorithm based on the particle swarm optimization is introduced to optimize the switching surfaces of an SLPV controller. The efficacy of the proposed SLPV controller design approach and switching surface optimization algorithm is demonstrated on both a numerical example and a physical example of air‐fuel ratio control of an automotive engine.     

Noncertainty equivalent adaptive control of robot manipulators without velocity measurements

This paper presents a noncertainty equivalent adaptive motion control scheme for robot manipulators in the absence of link velocity measurements. A new output feedback adaptation algorithm, based on the attractive manifold design approach, is developed. A proportional-integral adaptation is selected for the adaptive parameter estimator to strengthen the passivity of the system. In order to relieve velocity measurements, an observer is designed to estimate the velocities. The controller guarantees semiglobal asymptotic motion tracking and velocity estimation, as well as L_∞ and L₂ bounded parameter estimation error. The effectiveness of the proposed controller is verified by simulations for a two-link robot manipulator and a four-bar linkage. The results are further compared with the earlier certainty-equivalent adaptive partial and full state feedback controller to highlight potential closed-loop performance improvements.     

A ground-based radar backscatter investigation in the percolation zone of the Greenland ice sheet

Satellite radar altimeters and scatterometers deployed over ice sheets experience backscatter from the surface and from within the snowpack, termed surface and volume backscatter respectively. In order to assess the errors in satellite altimeter measurements it is vital to know where the return is originating from in the snowpack. This return can vary spatially and temporally. Seasonal variations in the volume backscatter can be a major complicating factor in the radar return from the percolation zone. Ground-based step-frequency radar was deployed in the percolation zone of the Greenland Ice Sheet at ∼ 1945 m elevation (69 51N, 47 15W). Previous measurements in this area made by scientists from the Byrd Polar Research Centre and the University of Kansas, undertaken prior to summer melt events, have shown the strongest backscatter from ice features at around 1 m depth buried beneath the previous end-of-summer surface. In autumn 2004, radar measurements in the Ku band with bandwidths of 1 and 8 GHz were made alongside detailed stratigraphic observations within a 1 km² site. The radar results revealed no continuous reflecting horizons in the upper 3.5 m of the firn. Shallow cores and snowpits also indicated that there were no spatially continuous stratigraphic horizons across the study site. An average electromagnetic wave velocity of 2.11 ± 0.05 × 10⁸ m s^− 1 was determined for the upper metre of the firn. Surface and volume backscatter at vertical incidence were calculated using a standard model. The contribution of the surface backscatter to the total backscatter was on average 6 dB higher than that of the volume backscatter. However, at the higher 8 GHz bandwidth the strongest return frequently originated not from the surface but from within the upper 30 cm of the snowpack, most probably from thin ice layers. At 1 GHz bandwidth these ice layers were not always resolved; their return merged with the surface return, causing it to broaden, with the peak and leading edge moving down. Modelling using density and thickness measurements from shallow cores and snowpits showed that the backscatter from these shallow, thin ice layers could be stronger than the surface return owing to constructive interference from the top and base of the layers.     

On the Power of Multiple Reads in a Chip

A chip algorithm is called r-multilective if it reads its input bits r times. In this paper we relate the r-bound communication complexity of a language L and the area requirement for an r-multilective chip algorithm of a related language . More specifically Improving known lower bounds on the r-bound communication complexity of certain languages, we obtain several hierarchies of r-multilective languages depending on the parameter r. For example, if 0 < r < s, then there are constants 0 < c, c′ such that for infinitely many n there is a language L_n {0, 1}ⁿ such that there is an s-multilective algorithm recognizing L_n using area at most c log n and any r-multilective algoerithm recognizing L_n requires area at least c′n/log n. Similar results have been known only for s = 2 and r = 1 and have been open in other cases.