Brightness temperature and attenuation diversity statistics at 20.6 and 31.65 GHz for the Colorado Research Network

A limited network of four dual-channel microwave radiometers, with frequencies of 20.6 and 31.65 GHz, was operated in the front range of eastern Colorado from 1985 to 1988. Data, from November 1987 through October 1988 are analyzed to determine both single-station and joint-station brightness temperature and attenuation statistics. Only zenith observations were made. The spatial separations of the stations varied from 50 km to 190 km. Before the statistics were developed, the data were screened by rigorous quality control methods. One such method, that of 20.6 vs. 31.65 GHz scatter plots, is analyzed in detail, and comparisons are made of measured vs calculated data. At 20.6 and 31.65 GHz, vertical attenuations of 5 and 8 dB are exceeded 0.01 percent of the time. For these four stations and at the same 0.01 percent level, diversity gains from 6 to 8 dB are possible with the 50 to 190 km separations

Brightness temperature and attenuation statistics at 20.6 and 31.65 GHz

Attenuation and brightness temperature statistics at 20.6 and 31.65 GHz are analyzed for a year's worth of data. The data were collected in 1988 at Denver and Platteville, Colorado. The locations are separated by 49 km. Single-station statistics are derived for the entire year. Quality control procedures are discussed and examples of their application are given

Atmospheric Phase Correction Using Total Power Radiometry at the Submillimeter Array

Phase noise caused by an inhomogeneous, time-variable water vapor distribution in our atmosphere reduces the angular resolution, visibility amplitude and coherence time of millimeter and submillimeter wavelength interferometers. We present early results from our total power radiometry phase correction experiment carried out with the Submillimeter Array on Mauna Kea. From accurate measurements of the atmospheric emission along the lines of sight of two elements of the array, we estimated the differential atmospheric electrical path between them. In one test, presented here, the phase correction technique reduced the rms phase noise at 230 GHz from 72\degr to 27\degr over a 20 minute period with a 2.5 second integration time. This corresponds to a residual differential electrical path of 98 $\mu$m, or 15 $\mu$m of precipitable water vapor, and raises the coherence in the 20 minute period from 0.45 to 0.9.Comment: Accepted for publication in the SMA Special Volume of the ApJ Letters (9 pages of text, 3 figures

Self-avoiding fractional Brownian motion - The Edwards model

In this work we extend Varadhan's construction of the Edwards polymer model to the case of fractional Brownian motions in $\R^d$, for any dimension $d\geq 2$, with arbitrary Hurst parameters $H\leq 1/d$.Comment: 14 page

Statistical Physics in Meteorology

Various aspects of modern statistical physics and meteorology can be tied together. The historical importance of the University of Wroclaw in the field of meteorology is first pointed out. Next, some basic difference about time and space scales between meteorology and climatology is outlined. The nature and role of clouds both from a geometric and thermal point of view are recalled. Recent studies of scaling laws for atmospheric variables are mentioned, like studies on cirrus ice content, brightness temperature, liquid water path fluctuations, cloud base height fluctuations, .... Technical time series analysis approaches based on modern statistical physics considerations are outlined.Comment: Short version of an invited paper at the XXIth Max Born symposium,Ladek Zdroj, Poland; Sept. 200

Analysis of Radiosonde and Ground-Based Remotely Sensed PWV Data from the 2004 North Slope of Alaska Arctic Winter Radiometric Experiment

Abstract During 9 March–9 April 2004, the North Slope of Alaska Arctic Winter Radiometric Experiment was conducted at the Atmospheric Radiation Measurement Program's (ARM) "Great White" field site near Barrow, Alaska. The major goals of the experiment were to compare microwave and millimeter wavelength radiometers and to develop forward models in radiative transfer, all with a focus on cold (temperature from 0° to −40°C) and dry [precipitable water vapor (PWV) < 0.5 cm] conditions. To supplement the remote sensors, several radiosonde packages were deployed: Vaisala RS90 launched at the ARM Duplex and at the Great White and Sippican VIZ-B2 operated by the NWS. In addition, eight dual-radiosonde launches were conducted at the Duplex with Vaisala RS90 and Sippican GPS Mark II, the latter one modified to include a chilled mirror humidity sensor. Temperature comparisons showed a nighttime bias between VIZ-B2 and RS90, which reached 3.5°C at 30 hPa. Relative humidity comparisons indicated better than 5% average agreement between the RS90 and the chilled mirror. A bias of about 20% for the upper troposphere was found in the VIZ-B2 and the Mark II measurements relative to both RS90 and the chilled mirror. Comparisons in PWV were made between a microwave radiometer, a microwave profiler, a global positioning system receiver, and the radiosonde types. An RMS agreement of 0.033 cm was found between the radiometer and the profiler and better than 0.058 cm between the radiometers and GPS. RS90 showed a daytime dry bias on PWV of about 0.02 cm

Tropospheric Phase Calibration in Millimeter Interferometry

We review millimeter interferometric phase variations caused by variations in the precipitable water vapor content of the troposphere, and we discuss techniques proposed to correct for these variations. We present observations with the Very Large Array at 22 GHz and 43 GHz designed to test these techniques. We find that both the Fast Switching and Paired Array calibration techniques are effective at reducing tropospheric phase noise for radio interferometers. In both cases, the residual rms phase fluctuations after correction are independent of baseline length for b > b_{eff}. These techniques allow for diffraction limited imaging of faint sources on arbitrarily long baselines at mm wavelengths. We consider the technique of tropospheric phase correction using a measurement of the precipitable water vapor content of the troposphere via a radiometric measurement of the brightness temperature of the atmosphere. Required sensitivities range from 20 mK at 90 GHz to 1 K at 185 GHz for the MMA, and 120 mK for the VLA at 22 GHz. The minimum gain stability requirement is 200 at 185 GHz at the MMA assuming that the astronomical receivers are used for radiometry. This increases to 2000 for an uncooled system. The stability requirement is 450 for the cooled system at the VLA at 22 GHz. To perform absolute radiometric phase corrections also requires knowledge of the tropospheric parameters and models to an accuracy of a few percent. It may be possible to perform an `empirically calibrated' radiometric phase correction, in which the relationship between fluctuations in brightness temperature differences with fluctuations in interferometric phases is calibrated by observing a celestial calibrator at regular intervals.Comment: AAS LATEX preprint format. to appear in Radio Science 199

PROGRESS REPORT OF FY 2004 ACTIVITIES: IMPROVED WATER VAPOR AND CLOUD RETRIEVALS AT THE NSA/AAO

The basic goals of the research are to develop and test algorithms and deploy instruments that improve measurements of water vapor, cloud liquid, and cloud coverage, with a focus on the Arctic conditions of cold temperatures and low concentrations of water vapor. The importance of accurate measurements of column amounts of water vapor and cloud liquid has been well documented by scientists within the Atmospheric Radiation Measurement Program. Although several technologies have been investigated to measure these column amounts, microwave radiometers (MWR) have been used operationally by the ARM program for passive retrievals of these quantities: precipitable water vapor (PWV) and integrated water liquid (IWL). The technology of PWV and IWL retrievals has advanced steadily since the basic 2-channel MWR was first deployed at ARM CART sites Important advances are the development and refinement of the tipcal calibration method [1,2], and improvement of forward model radiative transfer algorithms [3,4]. However, the concern still remains that current instruments deployed by ARM may be inadequate to measure low amounts of PWV and IWL. In the case of water vapor, this is especially important because of the possibility of scaling and/or quality control of radiosondes by the water amount. Extremely dry conditions, with PWV less than 3 mm, commonly occur in Polar Regions during the winter months. Accurate measurements of the PWV during such dry conditions are needed to improve our understanding of the regional radiation energy budgets. The results of a 1999 experiment conducted at the ARM North Slope of Alaska/Adjacent Arctic Ocean (NSA/AAO) site during March of 1999 [5] have shown that the strength associated with the 183 GHz water vapor absorption line makes radiometry in this frequency regime suitable for measuring low amounts of PWV. As a portion of our research, we conducted another millimeter wave radiometric experiment at the NSA/AAO in March-April 2004. This experiment relied heavily on our experiences of the 1999 experiment. Particular attention was paid to issues of radiometric calibration and radiosonde intercomparisons. Our theoretical and experimental work also supplements efforts by industry (F. Solheim, Private Communication) to develop sub-millimeter radiometers for ARM deployment. In addition to quantitative improvement of water vapor measurements at cold temperature, the impact of adding millimeter-wave window channels to improve the sensitivity to arctic clouds was studied. We also deployed an Infrared Cloud Imager (ICI) during this experiment, both for measuring continuous day-night statistics of the study of cloud coverage and identifying conditions suitable for tipcal analysis. This system provided the first capability of determining spatial cloud statistics continuously in both day and night at the NSA site and has been used to demonstrate that biases exist in inferring cloud statistics from either zenith-pointing active sensors (lidars or radars) or sky imagers that rely on scattered sunlight in daytime and star maps at night [6]

Cloud optical depth retrievals from the Aerosol Robotic Network (AERONET) cloud mode observations

Cloud optical depth is one of the most poorly observed climate variables. The new “cloud mode” capability in the Aerosol Robotic Network (AERONET) will inexpensively yet dramatically increase cloud optical depth observations in both number and accuracy. Cloud mode optical depth retrievals from AERONET were evaluated at the Atmospheric Radiation Measurement program’s Oklahoma site in sky conditions ranging from broken clouds to overcast. For overcast cases, the 1.5 min average AERONET cloud mode optical depths agreed to within 15% of those from a standard ground‐based flux method. For broken cloud cases, AERONET retrievals also captured rapid variations detected by the microwave radiometer. For 3 year climatology derived from all nonprecipitating clouds, AERONET monthly mean cloud optical depths are generally larger than cloud radar retrievals because of the current cloud mode observation strategy that is biased toward measurements of optically thick clouds. This study has demonstrated a new way to enhance the existing AERONET infrastructure to observe cloud optical properties on a global scale

Critical Exponents, Hyperscaling and Universal Amplitude Ratios for Two- and Three-Dimensional Self-Avoiding Walks

We make a high-precision Monte Carlo study of two- and three-dimensional self-avoiding walks (SAWs) of length up to 80000 steps, using the pivot algorithm and the Karp-Luby algorithm. We study the critical exponents $\nu$ and $2\Delta_4 -\gamma$ as well as several universal amplitude ratios; in particular, we make an extremely sensitive test of the hyperscaling relation $d\nu = 2\Delta_4 -\gamma$. In two dimensions, we confirm the predicted exponent $\nu = 3/4$ and the hyperscaling relation; we estimate the universal ratios $\ / \ = 0.14026 \pm 0.00007$, $\ / \ = 0.43961 \pm 0.00034$ and $\Psi^* = 0.66296 \pm 0.00043$ (68\% confidence limits). In three dimensions, we estimate $\nu = 0.5877 \pm 0.0006$ with a correction-to-scaling exponent $\Delta_1 = 0.56 \pm 0.03$ (subjective 68\% confidence limits). This value for $\nu$ agrees excellently with the field-theoretic renormalization-group prediction, but there is some discrepancy for $\Delta_1$. Earlier Monte Carlo estimates of $\nu$, which were $\approx\! 0.592$, are now seen to be biased by corrections to scaling. We estimate the universal ratios $\ / \ = 0.1599 \pm 0.0002$ and $\Psi^* = 0.2471 \pm 0.0003$; since $\Psi^* > 0$, hyperscaling holds. The approach to $\Psi^*$ is from above, contrary to the prediction of the two-parameter renormalization-group theory. We critically reexamine this theory, and explain where the error lies.Comment: 87 pages including 12 figures, 1029558 bytes Postscript (NYU-TH-94/09/01