The effect of monomolecular surface films on the microwave brightness temperature of the sea surface

Abstract

Airborne microwave radiometer measurements at 1·43 and 2·65 GHz over a sea surface covered with a monomolecular oleyl alcohol surface film and over adjacent slick sea surfaces are presented. The measurements show that at 2·65 GHz the brightness temperature T _B is not affected by the slick, while at 1·43 GHz it drops from 93 K to a minimum value of almost O K. This implies that at 1·43 GHz the emissivity of the slick-covered sea surface is extremely small, similar to a metallic layer, and that this resonant-type phenomenon is confined to a narrow frequency band of width δ?/ ?<0·6.

The theoretical implications of these experimental findings are discussed in the framework of the Debye relaxation theory of polar liquids. It is conjectured that a thin layer of water molecules polarized by the surface film gives rise to an anomalous dispersion, which causes the large decrease in brightness temperature at 1·43 GHz.

The modulus of the relative dielectric constant ε? is estimated to be ≥ 5·2 × 10^?4 and the thickness of the emitting layer ≤1·9 × 10^?4 m for 1·43 GHz. Furthermore, the film-induced surface activation energy is calculated to be 9·18 × 10^?21 J. These values seem reasonable in the light of the theories on the physicochemical structure of surface layers.     

Model for atmospheric corrections to microwave brightness temperature data

The effects of atmospheric liquid water (cloud) and water vapor on the brightness temperature data acquired by Bhaskara-Satellite Microwave Radiometer at 19.1 and 22.235 GHz near the nadir look angle have been discussed in detail. It has been observed that the net contribution to brightness temperature data due to atmosphere is quite considerable over sea and wet land conditions. Two operational quasistatistical models have been developed for doing atmospheric corrections to brightness temperature data, one applicable under cloud-free conditions and the other under all weather conditions. The physical concepts to arrive at these quasistatistical models have been discussed. The constants of the models are estimated by the method of least squares fit by simulating 200 sets of atmospheric and ground conditions. The root mean square errors in the brightness temperature after applying atmospheric corrections are estimated to be 0.5 and 4 K under cloud-free and all weather conditions respectively. A detailed discussion on the validity and applicability of the models is also presented.     

Hourly simulations of the microwave brightness temperature of seasonal snow in Quebec, Canada, using a coupled snow evolution-emission model

To interpret the snowpack evolution, and in particular to estimate snow water equivalent (SWE), passive microwave remote sensing has proved to be a useful tool given its sensitivity to snow properties. However, the main uncertainties using existing SWE algorithms arise from snow metamorphism which evolves during the winter season, and changes the snow emissivity. To consider the evolution in snow emissivity a coupled snow evolution-emission model can be used to simulate the brightness temperature (T_B) of the snowpack.During a dedicated campaign in the winter season, from November to April, of 2007-2008 two surface-based radiometers operating at 19 GHz and 37 GHz continuously measured the passive microwave radiation emitted through a seasonal snowpack in southern Quebec (Canada). This paper aims at modeling and interpreting this time series of T_B over the whole season, with an hourly step, using a coupled multi-layer snow evolution-emission model. The thermodynamic snow evolution model, referred as to Crocus, was driven by local meteorological measurements. Results from this model provided, in turn, the input variables to run the Microwave Emission Model of Layered Snowpacks (MEMLS) in order to predict T_B at 19 GHz and 37 GHz for both vertical (V) and horizontal (H) polarizations. The accuracy of T_B predicted by the Crocus-MEMLS coupled model was evaluated using continuous measurements from the surface-based radiometers.The weather conditions observed during the winter season were diverse, including several warm periods with melting snow and rain-on-snow events, producing very complex variations in the time series of T_B. To aid our analysis, we identified days with melting snow versus days with dry snow. The Crocus-MEMLS coupled model was able to accurately predict melt events with a success rate of 86%. The residual error was due to an overestimation of the duration of several melt events simulated by Crocus. This problem was explained by 1) a limitation of percolation, and 2) a very long-acting melt of lower layers due to geothermal flux.When the snowpack was completely dry, the global trend of T_B during the season was characterized by a decrease of T_B due to growth in the snow grain size. During most of the season, Crocus-MEMLS correctly predicted the evolution of T_B resulting from temperature gradient metamorphism; the root mean square errors ranged between 2.8 K for the 19 GHz vertical polarization (19V) and 6.9 K for the 37 GHz horizontal polarization (37H). However, during dry periods near the end of the season, the values of T_B were strongly overestimated. This overestimation was mainly due to a limitation of the growth of large snow grains in the wet snowpack simulated by Crocus. This effect was confirmed by estimating snow grain sizes from the observed T_B and the coupled model. The estimated snow grain sizes were larger and more realistic than those initially predicted by the Crocus model.     

The relationship between brightness temperature and soil moisture Selection of frequency range for microwave remote sensing

Abstract

The analysis of brightness temperature data acquired from field and aircraft experiments demonstrates a linear relationship between soil moisture and brightness temperature. However, the analysis of brightness temperature data acquired by the Skylab radiometer demonstrates a non-linear relationship between soil moisture and brightness temperature. In view of the above and also because of recent theoretical developments for the calculation of the dielectric constant and brightness temperature under varying soil moisture profile conditions, an attempt is made to study the theoretical relationship between brightness temperature and soil moisture as a function of frequency. Through the above analysis, the appropriate microwave frequency range for soil moisture studies is recommended.     

Interpretation of Nimbus-7 37 GHz microwave brightness temperature data in semi-arid southern Africa

Abstract

Monthly 37 GHz microwave polarization difference temperatures (MPDT) derived from the Nimbus-7 scanning multichannel microwave radiometer (SMMR) for southern Africa from 1979 to 1985 are compared with rainfall and Advanced Very High Resolution Radiometer (AVHRR) normalized difference vegetation index (NDVI) data. MPDT rose sharply during a drought episode which occurred within the period included in the data. The rise was seen not only in the growing season, but also in the dry season MPDT when no actively photosynthetic, water-containing leaves are present. The results suggest that scattering of the emitted microwave radiation by dead and living vegetation is a more important factor than has previously been recognized. The sensitivity of MPDT to small quantities of dry vegetation encourages the hope that standing dead vegetation and plant litter may be remotely sensed. In the absence of vegetation, rough terrain reduced the MPDT whereas a damp surface increased it.     

An approximate model for performance evaluation of real-time multimedia communication systems

A Markov Modulated Poisson Process (MMPP) is a doubly stochastic Poisson process which has recently received a lot of attention due to its ability to model a highly correlated arrival stream while retaining analytical tractability. In this paper, the cell arrival process from integrated voice and data sources is approximated by a two-state MMPP with batch arrivals (BMMPP). We propose a new matching technique which leads to more accurate performance prediction than other recent work for both delay estimation and evaluation of tail probabilities. While using BMMPP in the model does not noticeably increase the computational complexity over MMPP, it allows better representation of traffic sources with significantly higher burstiness. Another major contribution of the proposed model is its simplicity which makes the model suitable for real-time traffic control. An extended version of the model for integrated video, voice and data sources is also given with numerical examples again showing that the accuracy is quite satisfactory.     

Using sea surface temperature measurements from microwave and infrared satellite measurements

The Tropical Rainfall Mapping Mission Microwave Imager (TMI) instrument Sea Surface Temperature (SST) product (v1.0) is compared with in situ observations obtained in the Atlantic Ocean. The TMI SST has a mean warm bias of 0.25?K±0.7?K when compared to in situ SST at a depth of 7?m. When TMI SST are compared to in situ skin SST measurements, the bias is 0.6?K±0.5?K. A limited global comparison between TMI SST and co-incident ERS-2 Along-Track Scanning Radiometer (ATSR/2) skin SST demonstrates a bias of 0.6?K±0.6?K consistent with the result obtained using in situ observations. These results are consistent with the predicted accuracy of the TMI SST data products. Based on these results, a simple method to merge the TMI and ATSR data is proposed.     

Simulating the effect of spatial variability of soil hydraulic properties on microwave brightness temperature over a corn field

Spatial variability of L-band (21?cm wavelength) microwave brightness temperature over a corn field, caused by spatial heterogeneity of soil hydraulic properties, is simulated by combining physically based models for microwave emission and for dynamics of soil water. The scaling theory is used for the spatial variability of soil hydraulic parameters, the scaling parameter being represented by a histogram corresponding to a log-normal frequency distribution. The mean and the standard deviation of brightness temperatures over a corn field are calculated as a saturated soil dries progressively under clear-sky conditions. Results are presented for two values for the coefficient of variation (CV)of the scaling parameter, namely 0·45 and 0·65, which encompass the range of a few available field observations. For CV=0·45, the mean brightness temperatures are higher and the standard deviations are lower by about 2 deg K compared with those for CV = 0·65. Results of the present simulation suggest that spatial variability of hydraulic parameters might not be an important consideration for interpreting mean brightness temperatures over reasonably large (a few hectares or larger)vegetated fields, although some information about the frequency distribution of hydraulic parameters would be needed in interpreting the standard deviation of the brightness temperature.     

Quantifying spatial and temporal variabilities of microwave brightness temperature over the U.S. Southern Great Plains

Abstract

Abstract. Spatial and temporal variabilities of microwave brightness temperature over the U.S. Southern Great Plains are quantified in terms of vegetation and soil wetness. The brightness temperatures (T_Brpar; are the daytime observations from April to October for 5 years (1979 to 1983) by NIMBUS-7 Scanning Multichannel Microwave Radiometer (SMMR) at 6-6GHz frequency, horizontal polarization. The spatial and temporal variabilities of vegetation are assessed using visible and near-infrared observations by NOAA-7 Advanced Very High Resolution Radiometer (AVHRR), while an Antecedent Precipitation Index (API) model is used for soil wetness. The API model was able to account for more than 50 per cent of the observed variability in T_B although linear correlations between TB and API were generally significant at the I per cent level. The slope of the linear regression between TE and API is found to correlate linearly with an index for vegetation density derived from AVHRR data.     

BEAMR: An exact and approximate model for the p-median problem

The p-median problem is perhaps one of the most well-known location–allocation models in the location science literature. It was originally defined by Hakimi in 1964 and 1965 and involves the location of p facilities on a network in such a manner that the total weighted distance of serving all demand is minimized. This problem has since been the subject of considerable research involving the development of specialized solution approaches as well as the development of many different types of extended model formats. One element of past research that has remained almost constant is the original ReVelle–Swain formulation [ReVelle CS, Swain R. Central facilities location. Geographical Analysis 1970;2:30–42]. With few exceptions as detailed in the paper, virtually no new formulations have been proposed for general use in solving the classic p-median problem. This paper proposes a new model formulation for the p-median problem that contains both exact and approximate features. This new p-median formulation is called Both Exact and Approximate Model Representation (BEAMR). We show that BEAMR can result in a substantially smaller integer-linear formulation for a given application of the p-median problem and can be used to solve for either an exact optimum or a bounded, close to optimal solution. We also present a methodological framework in which the BEAMR model can be used. Computational results for problems found in the OR_library of Beasley [A note on solving large p-median problems. European Journal of Operational Research 1985;21:270–3] indicate that BEAMR not only extends the application frontier for the p-median problem using general-purpose software, but for many problems represents an efficient, competitive solution approach.     

An electrothermal functional model of the microwave FET suitable for nonlinear simulation

This article introduces a CAD-oriented functional model of the microwave FET depending on temperature as an additional state variable in addition to the usual gate and drain voltages. The model is fully conservative and non-quasistatic, and thus considerably more advanced than other currently available empirical models. A novel parameter extraction strategy allows the simultaneous determination of the voltage and temperature dependence of the constitutive relations, making use of a set of DC measurements and bias-dependent scattering matrices obtained at a single ambient temperature. The model can be coupled to a harmonic-balance algorithm for the efficient electrothermal simulation of temperature-dependent nonlinear microwave circuits, which the authors discussed in a previous article.     

An approximate mathematical model for solidification of a flowing liquid in a microchannel

A mathematical model is developed to analyse the combined flow and solidification of a liquid in a small pipe or two-dimensional channel. In either case, the problem reduces to solving a single equation for the position of the solidification front. Results show that for a large range of flow rates the closure time is approximately constant, and the value depends primarily on the wall temperature and channel width. However, the solid shape at closure will be very different for low and high fluxes. As the flow rate increases the closure time starts to depend on the flow rate until the closure time increases dramatically, subsequently the pipe will never close.     

A simple retrieval method for land surface temperature and fraction of water surface determination from satellite microwave brightness temperatures in sub-arctic areas

A strong linear relationship is found between Special Sensor Microwave/Imager (SSM/I) microwave (19 and 37 GHz) surface emissivities at horizontal and vertical polarizations over snow- and ice-free land surfaces. This allows retrieving the land surface emissivity and temperature from satellite microwave brightness temperatures after atmospheric corrections. Over the Canadian sub-arctic continental area, we show that the main factor modifying the emissivity is the fraction of water surface (FWS) within a pixel. Accordingly, a map of the fraction of water surface across the Canadian landmass is derived, given a correspondence within 6% as compared to the 1 km² Canadian National Topographic Database of water-covered areas. The microwave-derived surface temperatures are compared to synchronous in situ air and ground surface temperatures and also with independent satellite IR measurements over areas without snow or ice. Root mean square differences range between 2° and 3.5°, with mean bias error of the order of 1-3°. Better results are always obtained with the 37 GHz channel rather than with the 19 GHz channel. Over dense vegetation, the microwave-derived surface temperature is closer to the air temperature (at surface level) than to the ground temperature. The proposed simple retrieval algorithm, not sensitive to cloud cover, appears very useful for monitoring summer interannual or seasonal trends of the fraction of surface water, as well as the daily land surface temperature variation, which are very important parameters in environmental change analysis.     

An efficient approximate analysis method based on an exact univariate model for the element loads

Approximate analysis modules for structural design are usually based on a linear Taylor expansion of the nodal displacements in terms of the reciprocals of the design variables. Direct approximations of the member forces have received lesser attention. This paper describes an approach for the direct calculation of the member forces in a truss as a function of the design variables. It is based on the exact expression of the member forces if only one design variable is allowed to vary at a time. In the case of an arbitrary move in the design space the method gives approximate results of a very good quality. This is obtained by enforcing zero order homogeneity of the element loads and by refining the results via a virtual work equation. The method is illustrated with numerical results on previously published test cases for elastic trusses. Preliminary results for an elastic frame are also presented. This new approximate force model is shown to yield excellent results.     

Land cover-based optimal deconvolution of PALS L-band microwave brightness temperatures

An optimal deconvolution (ODC) technique has been developed to estimate microwave brightness temperatures of agricultural fields using microwave radiometer observations. The technique is applied to airborne measurements taken by the Passive and Active L and S band (PALS) sensor in Iowa during Soil Moisture Experiments in 2002 (SMEX02). Agricultural fields in the study area were predominantly soybeans and corn. The brightness temperatures of corn and soybeans were observed to be significantly different because of large differences in vegetation biomass. PALS observations have significant over-sampling; observations were made about 100 m apart and the sensor footprint extends to about 400 m. Conventionally, observations of this type are averaged to produce smooth spatial data fields of brightness temperatures. However, the conventional approach is in contrast to reality in which the brightness temperatures are in fact strongly dependent on land cover, which is characterized by sharp boundaries. In this study, we mathematically deconvolve the observations into brightness temperature at the field scale (500-800 m) using the sensor antenna response function. The result is more accurate spatial representation of field-scale brightness temperatures, which may in turn lead to more accurate soil moisture retrieval.     

An information retrieval approach for approximate queries

With the growing availability of online information systems, a need for user interfaces that are flexible and easy to use has arisen. For such type of systems, an interface that allows the formulation of approximate queries can be of great utility since these allow the user to quickly explore the database contents even when he is unaware of the exact values of the database instances. Our work focuses on this problem, presenting a new model for ranking approximate answers and a new algorithm to compute the semantic similarity between attribute values, based on information retrieval techniques. To demonstrate the utility and usefulness of the approach, we perform a series of usability tests. The results suggest that our approach allows the retrieval of more relevant answers with less effort by the user.     

An approximate microaggregation approach for microdata protection

Microdata protection is a hot topic in the field of Statistical Disclosure Control, which has gained special interest after the disclosure of 658,000 queries by the America Online (AOL) search engine in August 2006. Many algorithms, methods and properties have been proposed to deal with microdata disclosure. One of the emerging concepts in microdata protection is k-anonymity, introduced by Samarati and Sweeney. k-Anonymity provides a simple and efficient approach to protect private individual information and is gaining increasing popularity. k-Anonymity requires that every record in the microdata table released be indistinguishably related to no fewer than k respondents.In this paper, we apply the concept of entropy to propose a distance metric to evaluate the amount of mutual information among records in microdata, and propose a method of constructing dependency tree to find the key attributes, which we then use to process approximate microaggregation. Further, we adopt this new microaggregation technique to study k-anonymity problem, and an efficient algorithm is developed. Experimental results show that the proposed microaggregation technique is efficient and effective in the terms of running time and information loss.     

An approximate nonmyopic computation for value of information

It is argued that decision analysts and expert-system designers have avoided the intractability of exact computation of the value of information by relying on a myopic assumption that only one additional test will be performed, even when there is an opportunity to make large number of observations. An alternative to the myopic analysis is presented. In particular, an approximate method for computing the value of information of a set of tests, which exploits the statistical properties of large samples, is given. The approximation is linear in the number of tests, in contrast with the exact computation, which is exponential in the number of tests. The approach is not as general as in a complete nonmyopic analysis, in which all possible sequences of observations are considered. In addition, the approximation is limited to specific classes of dependencies among evidence and to binary hypothesis and decision variables. Nonetheless, as demonstrated with a simple application, the approach can offer an improvement over the myopic analysis